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  • 1
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    Localized pointwise error estimates for direct flux approximation (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: Pointwise error estimates for the first-order div least-squares (LS) finite element method for second-order elliptic partial differential equations are presented. Direct flux approximation is considered as an important advantage of the LS method. However, there are no known pointwise error estimates for the direct flux approximation. In this paper, we provide optimal pointwise estimates which show local dependence of the error at a point and weak dependence of the global norm. As an elementary consequence of these estimates, we provide an asymptotic error expansion inequality. The inequality has applications to superconvergence and a posteriori estimates.
    Print ISSN: 0272-4979
    Electronic ISSN: 1464-3642
    Topics: Mathematics
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  • 2
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    Fast multiscale regularization methods for high-order numerical differentiation (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: The first-order and higher-order derivatives of a function can be viewed as the solutions of Volterra integral equations of the first kind. In this paper we propose a fast multiscale solver for the numerical solution of the Tikhonov regularization of the Volterra equations. In association with the special form of the kernels, the matrices resulting from the discretization by multiscale bases are sparse. Moreover, they can be truncated using proper strategies with only a minor loss of accuracy. In the best case, the number of nonzero entries of the truncated matrices is linear with respect to the dimensions of the matrices. The accuracy of the solution from the solver is analysed theoretically and verified by numerical experiments.
    Print ISSN: 0272-4979
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    Topics: Mathematics
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  • 3
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    Convergence and supercloseness of a finite element method for a singularly perturbed convection-diffusion problem on an L-shaped domain (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: The finite element method with $\mathscr {Q}_p$ elements is applied to a singularly perturbed convection–diffusion problem on an L-shaped domain. As an effect of corner singularities the exact solution is not $H^2$ -regular. Therefore, we combine a layer-adapted Shishkin mesh with a special grading adapted to the corner singularity. On such meshes we prove error estimates and estimates for the closeness error which explicitly show the influence of the grading parameter $\mu$ . Hence, $\mu$ can be chosen such that optimal error bounds are obtained. Thereby, it turns out that in the problem studied the influence of the corner singularity becomes small if the perturbation parameter $\varepsilon$ decreases. Moreover, we conduct numerical experiments that verify the theoretical results.
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    Topics: Mathematics
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  • 4
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    Ptak's nondiscrete induction and its application to matrix iterations (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: Pták's method of nondiscrete induction is based on the idea that in the analysis of iterative processes one should aim at rates of convergence as functions rather than just numbers, because functions may give convergence estimates that are tight throughout the iteration rather than just asymptotically. In this paper we motivate and prove a theorem on nondiscrete induction, originally due to Potra and Pták, and we apply it to the Newton iterations for computing the matrix polar decomposition and the matrix square root. Our goal is to illustrate the application of the method of nondiscrete induction in the finite-dimensional numerical linear algebra context. We show the sharpness of the resulting convergence estimate analytically for the polar decomposition iteration and on some examples for the square root iteration. We also discuss some of the method's limitations and possible extensions.
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  • 5
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    A first-order system Petrov-Galerkin discretization for a reaction-diffusion problem on a fitted mesh (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: We consider the numerical solution, by a Petrov–Galerkin finite-element method, of a singularly perturbed reaction–diffusion differential equation posed on the unit square. In Lin & Stynes (2012, A balanced finite element method for singularly perturbed reaction-diffusion problems. SIAM J. Numer. Anal. , 50 , 2729–2743), it is argued that the natural energy norm, associated with a standard Galerkin approach, is not an appropriate setting for analysing such problems, and there they propose a method for which the natural norm is ‘balanced’. In the style of a first-order system least squares method, we extend the approach of Lin & Stynes (2012, A balanced finite element method for singularly perturbed reaction-diffusion problems. SIAM J. Numer. Anal. , 50 , 2729–2743) by introducing a constraint which simplifies the associated finite-element space and the method's analysis. We prove robust convergence in a balanced norm on a piecewise-uniform (Shishkin) mesh, and present supporting numerical results. Finally, we demonstrate how the resulting linear systems are solved optimally using multigrid methods.
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  • 6
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    Tensor-product surface patches with Pythagorean-hodograph isoparametric curves (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: The construction of tensor-product surface patches with a family of Pythagorean-hodograph (PH) isoparametric curves is investigated. The simplest nontrivial instances, interpolating four prescribed patch boundary curves, involve degree $(5,4)$ tensor-product surface patches $\bf{x}(u,v)$ whose $v=\hbox {constant}$ isoparametric curves are all spatial PH quintics. It is shown that the construction can be reduced to solving a novel type of quadratic quaternion equation, in which the quaternion unknown and its conjugate exhibit left and right coefficients, while the quadratic term has a coefficient interposed between them. A closed-form solution for this type of equation is derived, and conditions for the existence of solutions are identified. The surfaces incorporate three residual scalar freedoms which can be exploited to improve the interior shape of the patch. The implementation of the method is illustrated through a selection of computed examples.
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  • 7
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    Computing interior eigenvalues of domains from far fields (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: Interior eigenvalues of bounded scattering objects can be rigorously characterized from multi-static and multi-frequency far field data, that is, from the behaviour of scattered waves far away from the object. This characterization, the so-called inside–outside duality, holds for various types of penetrable and impenetrable scatterers and is based on the behaviour of a particular eigenvalue of the far field operator. It naturally leads to a numerical algorithm for computing interior eigenvalues of a scatterer that does not require shape or physical properties of the scatterer as input. Since the nonlinear inverse problem to compute such interior eigenvalues from far field data is ill-posed, we propose a regularizing algorithm that is shown to converge as the noise level of the far field data tends to zero. We illustrate feasibility and accuracy of our algorithm by numerical experiments where we compute interior transmission eigenvalues and Robin eigenvalues of the Laplacian in three-dimensional domains from scattering data of these domains due to plane incident waves.
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    Topics: Mathematics
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  • 8
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    Does changing the subject from A to B really provide an enlarged understanding of A? (2016)
    Oxford University Press
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    Publication Date: 2016-07-15
    Description: There are various ways of achieving an enlarged understanding of a concept of interest. One way is by giving its proper definition. Another is by giving something else a proper definition and then using it to model or formally represent the original concept. Between the two we find varying shades of grey. We might open up a concept by a direct lexical definition of the predicate that expresses it, or by a theory whose theorems define it implicitly. At the other end of the spectrum, the modelling-this-as-that option also admits of like variation, ranging from models rooted in formal representability theorems to models conceived of as having only heuristic value. There exist on both sides of this divide further differences still. In one of them, both the definiendum and definiens of a definition are words or phrases of some common natural language. In others, the item of interest is a natural language expression and its representation is furnished by the artificial linguistic system that models it. The modern history of these approaches is both very large and growing. Much of this evolution has given too short a shrift to the history of the demotion of ‘intuitive’ concepts in favour of the artificially contrived ones intended to model them. A working assumption of this article is that in the absence of a good understanding of what motivated the modelling-turn in the foundations of mathematics and the intuitive theory of truth, the whole notion of formal representability will have been inadequately understood. In the interests of space, I will concentrate on seminal issues in set theory as dealt with by Russell and Frege, and in the theory of truth in natural languages as dealt with by Tarski. The nub of the present focus is the representational role of model theory in the logics of formalized languages.
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
    Topics: Mathematics
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  • 9
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    Common cause abduction: The formation of theoretical concepts and models in science (2016)
    Oxford University Press
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    Publication Date: 2016-07-15
    Description: An important distinction is that between selective abductions , which select an optimal candidate from given multitude of possible explanations, and creative abductions , which introduce new theoretical concepts and models. The article focuses on creative abductions, which are essential for scientific progress, although they are rarely discussed in the literature. Scientifically, fruitful creative abductions are demarcated from purely speculative abductions by means of three virtues which are possessed by the former but not by the latter: (i) providing unification , (ii) detecting common causes and (iii) generating novel predictions by means of which they can be independently tested . Based on historical examples it is demonstrated that common cause abduction from correlated dispositions is the fundamental abductive operation by which new theoretical concepts and models are scientifically generated. Statistical factor analysis can be regarded as a statistical generalization of common cause abduction.
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    Logic programming for modeling morality (2016)
    Oxford University Press
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    Publication Date: 2016-07-15
    Description: This article investigates the appropriateness of LP-based reasoning to machine ethics, an interdisciplinary field of inquiry that emerges from the need of imbuing autonomous agents with the capacity for moral decision making. The first contribution of the article is that of identifying morality viewpoints, as studied in moral philosophy and psychology, which are amenable to computational modelling, and then mapping them to appropriate LP-based reasoning features. The identified viewpoints are covered by two morality themes: moral permissibility and the dual-process model. In the second contribution, various LP-based reasoning features are applied to model these identified morality viewpoints, via classic moral examples taken offthe-shelf from the literature. For this purpose, our Q UALM system, which features a combination of LP abduction, updating and counterfactuals, supported by LP tabling mechanisms, are mainly employed. The applications are also supported by other existing LP-based systems, featuring preference handling and probabilistic reasoning, which complement Q UALM in addressing the morality viewpoints in question.
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    Automorphism group of split Cartan modular curves (2016)
    Oxford University Press
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    Publication Date: 2016-07-21
    Description: We determine the automorphism group of the split Cartan modular curves $X_{{\rm split}}(p)$ for all primes $p$ .
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
    Topics: Mathematics
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  • 12
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    Hyperbolic Coxeter groups with Sierpinski carpet boundary (2016)
    Oxford University Press
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    Publication Date: 2016-07-21
    Description: We give a necessary and sufficient condition for a hyperbolic Coxeter group with planar nerve to have Sierpiłski curve as its Gromov boundary.
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  • 13
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    Dilemmas and paradoxes: cycles in argumentation frameworks (2016)
    Oxford University Press
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    Publication Date: 2016-07-27
    Description: In this article, I offer an interpretation of cycles in Dung-style argumentation frameworks in which even length cycles are treated as dilemmas and odd length cycles as paradoxes. The different properties of cycles with different parities arising from the use of preferred semantics are argued to be coherent with this interpretation.
    Print ISSN: 0955-792X
    Electronic ISSN: 1465-363X
    Topics: Computer Science , Mathematics
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  • 14
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    Preferred semantics as socratic discussion (2016)
    Oxford University Press
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    Publication Date: 2016-07-27
    Description: In abstract argumentation theory, preferred semantics has become one of the most popular approaches for determining the sets of arguments that can collectively be accepted. However, the description of preferred semantics, as it was originally stated by Dung, has a mainly technical and mathematical nature, making it difficult for lay persons to understand what the concept of preferred semantics is essentially about. In the current article, we aim to bridge the gap between mathematics and philosophy by providing a reformulation of (credulous) preferred semantics in terms of Socratic discussion. In order to do so, we first provide a (semi-)formal treatment of some of the concepts in Socratic dialogue.
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  • 15
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    Stage semantics and the SCC-recursive schema for argumentation semantics (2016)
    Oxford University Press
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    Publication Date: 2016-07-27
    Description: Recently, stage and cf 2 semantics for abstract argumentation attracted specific attention. By distancing from the notion of defence, they are capable to select arguments out of odd-length cycles. In case of cf 2 semantics, the SCC-recursive schema guarantees that important evaluation criteria for argumentation semantics, like directionality, weak- and $$\mathcal{C}$$ $$\mathcal{F}$$ -reinstatement, are fulfilled. Beside several desirable properties, both stage and cf 2 semantics still have some drawbacks. The stage semantics does not satisfy the above mentioned evaluation criteria, whereas cf 2 semantics produces some questionable results on frameworks with cycles of length ≥ 6. Therefore, we suggest to combine stage semantics with the SCC-recursive schema of cf 2 semantics. The resulting stage 2 semantics overcomes the problems regarding cf 2 and stage semantics. We study properties of stage 2 semantics and its relations to existing semantics, show that it fulfills the mentioned evaluation criteria, study strong equivalence for stage 2 semantics and provide a comprehensive complexity analysis of the associated reasoning problems. Besides the analysis of stage 2 semantics, we also complement existing complexity results for cf 2 by an analysis of tractable fragments and fixed parameter tractability. Furthermore, we provide answer-set programming (ASP) encodings for stage 2 semantics and labelling-based algorithms for cf 2 and stage 2 semantics.
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  • 16
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    RP-DeLP: a weighted defeasible argumentation framework based on a recursive semantics (2016)
    Oxford University Press
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    Publication Date: 2016-07-27
    Description: In this article, we propose a recursive semantics for warranted formulas in a general defeasible logic argumentation framework by formalizing a notion of collective (non-binary) conflict among arguments. The recursive semantics for warranted formulas is based on the intuitive grounds that if an argument is rejected, then further arguments built on top of it should also be rejected. The main characteristic of our recursive semantics is that an output (or extension) of a knowledge base is a pair consisting of a set of warranted and a set of blocked formulas. Arguments for both warranted and blocked formulas are recursively based on warranted formulas but, while warranted formulas do not generate any collective conflict, blocked conclusions do. Formulas that are neither warranted nor blocked correspond to rejected formulas. Then we extend the framework by attaching levels of preference to defeasible knowledge items and by providing a level-wise definition of warranted and blocked formulas. After we consider the warrant recursive semantics for the particular framework of Possibilistic Defeasible Logic Programming (RP-DeLP for short). Since RP-DeLP programmes may have multiple outputs, we define the maximal ideal output of an RP-DeLP programme as the set of conclusions which are ultimately warranted, and we present an algorithm for computing it in polynomial space and with an upper bound on complexity equal to P NP . Finally, we propose an efficient and scalable implementation of this algorithm using SAT encodings, and we provide an experimental evaluation when solving test sets of instances with single and multiple preference levels for defeasible knowledge.
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  • 17
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    Beyond admissibility: accepting cycles in argumentation with game protocols for cogency criteria (2016)
    Oxford University Press
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    Publication Date: 2016-07-27
    Description: In this article, we extend Dung's formal approach from admissibility to less demanding extension semantics allowing arguments in cycles of attacks. We present an acceptance criterion leading to the characterization of three semantics called pairwise cogency , weak cogency and cyclic cogency . Particular game-theoretic protocols allow us to identify winning strategies with extensions in different semantics. Furthermore, an algorithmic characterization of those games exhibits clearly how self-attacking or in odd-length cycles of attack can be rationally managed beyond the limits of admissibility.
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  • 18
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    Universal sequences for the order-automorphisms of the rationals (2016)
    Oxford University Press
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    Publication Date: 2016-07-29
    Description: In this paper, we consider the group $ \hbox {Aut}( \mathbb {Q}, \leq )$ of order-automorphisms of the rational numbers, proving a result analogous to a theorem of Galvin's for the symmetric group. In an announcement, Khélif states that every countable subset of $ \hbox {Aut}( \mathbb {Q}, \leq )$ is contained in an $N$ -generated subgroup of $ \hbox {Aut}( \mathbb {Q}, \leq )$ for some fixed $N\in \mathbb {N}$ . We show that the least such $N$ is 2. Moreover, for every countable subset of $ \hbox {Aut}( \mathbb {Q}, \leq )$ , we show that every element can be given as a prescribed product of two generators without using their inverses. More precisely, suppose that $a$ and $b$ freely generate the free semigroup $\{a,b\}^+$ consisting of the non-empty words over $a$ and $b$ . Then we show that there exists a sequence of words $w_1, w_2,\ldots $ over $\{a,b\}$ such that for every sequence $f_1, f_2, \ldots \in \hbox {Aut}( \mathbb {Q}, \leq )$ there is a homomorphism $\phi :\{a,b\}^{+}\to \hbox {Aut}( \mathbb {Q}, \leq )$ where $(w_i)\phi =f_i$ for every $i$ . As a corollary to the main theorem in this paper, we obtain a result of Droste and Holland showing that the strong cofinality of $ \hbox {Aut}( \mathbb {Q}, \leq )$ is uncountable, or equivalently that $ \hbox {Aut}( \mathbb {Q}, \leq )$ has uncountable cofinality and Bergman's property.
    Print ISSN: 0024-6107
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    Effective Ratner theorem for Formula and gaps in Formula modulo 1 (2016)
    Oxford University Press
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    Publication Date: 2016-07-29
    Description: Let $G= {{\rm SL}}(2, { \mathbb R})\ltimes { \mathbb R}^2$ and $\Gamma = {{\rm SL}}(2, { \mathbb Z})\ltimes { \mathbb Z}^2$ . Building on recent work of Strömbergsson, we prove a rate of equidistribution for the orbits of a certain one-dimensional unipotent flow of $\Gamma {\backslash } G$ , which projects to a closed horocycle in the unit tangent bundle to the modular surface. We use this to answer a question of Elkies and McMullen by making effective the convergence of the gap distribution of $\sqrt n \ {\rm mod}\,1$ .
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    On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class (2016)
    Oxford University Press
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    Publication Date: 2016-07-29
    Description: We establish the equivalence of conjectures concerning the pair correlation of zeros of $L$ -functions in the Selberg class and the variances of sums of a related class of arithmetic functions over primes in short intervals. This extends the results of Goldston and Montgomery [‘Pair correlation of zeros and primes in short intervals’, Analytic number theory and Diophantine problems (Stillwater, 1984) , Progress in Mathematics 70 (1987) 183–203] and Montgomery and Soundararajan [‘Primes in short intervals’, Comm. Math. Phys. 252 (2004) 589–617] for the Riemann zeta-function to other $L$ -functions in the Selberg class. Our approach is based on the statistics of the zeros because the analogue of the Hardy–Littlewood conjecture for the auto-correlation of the arithmetic functions we consider is not available in general. One of our main findings is that the variances of sums of these arithmetic functions over primes in short intervals have a different form when the degree of the associated $L$ -functions is 2 or higher to that which holds when the degree is 1 (for example, the Riemann zeta-function). Specifically, when the degree is 2 or higher, there are two regimes in which the variances take qualitatively different forms, whilst in the degree-1 case there is a single regime.
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    Coxeter groups, quiver mutations and geometric manifolds (2016)
    Oxford University Press
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    Publication Date: 2016-07-29
    Description: We construct finite volume hyperbolic manifolds with large symmetry groups. The construction makes use of the presentations of finite Coxeter groups provided by Barot and Marsh, and involves mutations of quivers and diagrams defined in the theory of cluster algebras. We generalize our construction by assigning to every quiver or diagram of finite or affine type a CW-complex with a proper action of a finite (or affine) Coxeter group. These CW-complexes undergo mutations agreeing with mutations of quivers and diagrams. We also generalize the construction to quivers and diagrams originating from unpunctured surfaces and orbifolds.
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    An analytic model for left-invertible weighted shifts on directed trees (2016)
    Oxford University Press
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    Publication Date: 2016-07-29
    Description: Let $\mathscr {T}$ be a rooted directed tree with finite branching index $k_{\mathscr {T}}$ , and let $S_{\lambda } \in B(l^2(V))$ be a left-invertible weighted shift on ${\mathscr {T}}$ . We show that $S_{\lambda }$ can be modelled as a multiplication operator $\mathscr {M}_z$ on a reproducing kernel Hilbert space $\mathscr H$ of $E$ -valued holomorphic functions on a disc centred at the origin, where $E:=\ker S^*_{\lambda }$ . The reproducing kernel associated with $\mathscr H$ is multi-diagonal and of bandwidth $k_{\mathscr {T}}.$ Moreover, $\mathscr H$ admits an orthonormal basis consisting of polynomials in $z$ with at most $k_{\mathscr {T}}+1$ non-zero coefficients. As one of the applications of this model, we give a spectral picture of $S_{\lambda }.$ Unlike the case $\dim E=1$ , the approximate point spectrum of $S_{\lambda }$ could be disconnected. We also obtain an analytic model for left-invertible weighted shifts on rootless directed tree with finite branching index.
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    Non-commutativity of the central sequence algebra for separable non-type I C*-algebras (2016)
    Oxford University Press
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    Publication Date: 2016-07-29
    Description: We show that if $A$ is a (not necessarily unital) separable, simple and non-type I C $^{\ast }$ -algebra, then for every properly infinite hyperfinite von Neumann algebra $M$ with separable predual, its Ocneanu central sequence algebra $M'\cap M^{\omega }$ arises as a sub-quotient of the central sequence algebra $F(A)$ defined by the second-named author. In particular, this answers affirmatively the question of Kirchberg [‘Central sequences in C $^{\ast }$ -algebras and strongly purely infinite algebras’, Operator algebras: the Abel Symposium 2004 , Proceedings of the First Abel Symposium, Oslo, 3–5 September 2004 (eds O. Bratteli, S. Neshveyev and C. Skau; Springer, Berlin, Heidelberg, 2006), X, 279, 175–231]: the central sequence C $^{\ast }$ -algebra of the reduced free group C $^{\ast }$ -algebra $C_{\rm {red}}^{\ast }(\mathbb {F}_2)$ is non-commutative.
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    Solutions of the fractional Allen-Cahn equation which are invariant under screw motion (2016)
    Oxford University Press
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    Publication Date: 2016-07-29
    Description: We establish existence and non-existence results for entire solutions to the fractional Allen–Cahn equation in $\mathbb {R}^3$ , which vanish on helicoids and are invariant under screw motion. In addition, we prove that helicoids are surfaces with vanishing non-local mean curvature.
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    On two constructions of an effective field theory (2016)
    Oxford University Press
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    Publication Date: 2016-07-29
    Description: In this paper, we discuss two constructions of an effective field theory starting from a local interaction functional. One relies on the well-established graphical combinatorics of the Bogoliubov-Parasiuk-Hepp-Zimmermann algorithm to renormalize divergent Feynman amplitudes. The other, more recent and due to Costello, relies on an inductive construction of local counterterms that uses no graphical combinatorics whatsoever. We show that these two constructions produce the same effective field theory.
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    KPZ formula derived from Liouville heat kernel (2016)
    Oxford University Press
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    Publication Date: 2016-07-29
    Description: In this paper, we establish the Knizhnik–Polyakov–Zamolodchikov (KPZ) formula of Liouville quantum gravity (LQG), using the heat kernel of Liouville Brownian motion. This derivation of the KPZ formula was first suggested by F. David and M. Bauer in order to get a geometrically more intrinsic way of measuring the dimension of sets in LQG. We also provide a careful study of the (no)-doubling behaviour of the Liouville measures in the appendix, which is of independent interest.
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    Topics: Mathematics
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    Double eta polynomials and equivariant Giambelli formulas (2016)
    Oxford University Press
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    Publication Date: 2016-07-29
    Description: We use Young's raising operators to introduce and study double eta polynomials , which are an even orthogonal analogue of Wilson's double theta polynomials. Our double eta polynomials give Giambelli formulas which represent the equivariant Schubert classes in the torus-equivariant cohomology ring of even orthogonal Grassmannians, and specialize to the single eta polynomials of Buch, Kresch, and the author.
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    Limits of topological minimal sets with finitely generated coefficient groups (2016)
    Oxford University Press
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    Publication Date: 2016-07-29
    Description: We prove that the (local) Hausdorff limit of topological minimal sets (with finitely generated coefficient group) is topologically minimal. The key idea is to reduce the homology group on the space to the homology group on the sphere, and then reduce the homology group on the sphere to a finitely representable one, by ‘glueing’ grids with small measure to block local elements in the homology group.
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    Some highlights from 50 years of the IMA Journal of Applied Mathematics (2016)
    Oxford University Press
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    Publication Date: 2016-08-02
    Description: Written to coincide with the anniversary of the launch of our journal, this survey reviews some of the highlights from the first fifty years of the IMA Journal of Applied Mathematics and its predecessor the Journal of the IMA. Rather than an exhaustive survey, we have chosen some of our personal favourite articles from the last fifty years. For each, we have given only the briefest of summaries—readers can download each of these papers for themselves, as they have each been put on open access to coincide with this Issue. We also attempt to put the work in context. More importantly, these papers were chosen as they have had, and continue to have, a considerable influence. For each, we try to spell out the impact of the work, and by implication, the impact of our journal.
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    Topic time series analysis of microblogs (2016)
    Oxford University Press
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    Publication Date: 2016-08-02
    Description: Social media data tend to cluster around events and themes. Local newsworthy events, sports team victories or defeats, abnormal weather patterns and globally trending topics all influence the content of online discussion. The automated discovery of these underlying themes from corpora of text is of interest to numerous academic fields as well as to law enforcement organizations and commercial users. One useful class of tools to deal with such problems are topic models, which attempt to recover latent groups of word associations from the text. However, it is clear that these topics may also exhibit patterns in both time and space. The recovery of such patterns complements the analysis of the text itself and in many cases provides additional context. In this work we describe two methods for mining interesting spatio-temporal dynamics and relations among topics, one that compares the topic distributions as histograms in space and time and another that models topics over time as temporal or spatio-temporal Hawkes process with exponential trigger functions. Both methods may be used to discover topics with abnormal distributions in space and time. The second method also allows for self-exciting topics and can recover intertopic relationships (excitation or inhibition) in both time and space. We apply these methods to a geo-tagged Twitter dataset and provide analysis and discussion of the results.
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    Spherical squirmers: models for swimming micro-organisms (2016)
    Oxford University Press
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    Publication Date: 2016-08-02
    Description: In 1952, Lighthill introduced the simplest possible model of a swimming micro-organism of finite size, intended as a model of a single-celled protozoan covered in beating cilia. The model consisted of a sphere, on the surface of which material points undergo small-amplitude oscillations. In 1971, Lighthill’s student, John Blake, completed the calculations and applied the theory to various species of ciliate. Subsequently we, and many others, have used the even simpler (though less realistic) model of a steady squirmer, a sphere whose surface moves tangentially with time-independent velocity. In this article we survey: -low-Reynolds-number locomotion, nutrient uptake and optimisation of individual squirmers; -hydrodynamic interactions between pairs of steady squirmers and their influence on clustering, self-diffusion and rheology in suspensions of squirmers, including the effect of being bottom-heavy; -measurements and modelling of metachronal waves in Volvox , the only truly sphericalmulti-celled organism, culminating in predictions of the mean swimming speed and angular velocity of free-swimming Volvox . The predictions are compared with experiment.
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    Will big data yield new mathematics? An evolving synergy with neuroscience (2016)
    Oxford University Press
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    Publication Date: 2016-08-02
    Description: New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin–Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics.
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    Localized structures and front propagation in systems with a conservation law (2016)
    Oxford University Press
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    Publication Date: 2016-08-02
    Description: The properties of spatially localized structures in systems with a conservation law are reviewed and related to the properties of fronts in such systems. The theory is illustrated using the conserved Swift–Hohenberg equation, and the insights gained used to shed light on the process of crystallization from a melt and on two problems arising in hydrodynamics: convection in a rotating layer and convection in an imposed magnetic field. Spatially localized structures in systems with time-periodic forcing are also considered. Several open problems are highlighted.
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    Growth, biomass allocation and photosynthetic responses are related to intensity of root severance and soil moisture conditions in the plantation tree Cunninghamia lanceolata (2016)
    Oxford University Press
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    Publication Date: 2016-08-03
    Description: We employed the warm temperate conifer Cunninghamia lanceolata (Lamb.) Hook. as a model of plantation forest species to investigate ecophysiological responses to root treatments (control (0%), and ~25, 50 or 75% of the initial root mass) under well-watered and water-limited conditions. Our results indicated that total root dry mass accumulation was negatively associated with the severity of root pruning, but there was evidence of multiple compensatory responses. The plants exhibited higher instantaneous and long-term (assessed by carbon isotope composition, 13 C) water-use efficiency in pruning treatments, especially under low water availability. Root pruning also increased the fine root/total root mass ratio, specific root length and fine root vitality in both water availability treatments. As a result of the compensatory responses, under well-watered conditions, height, stem dry mass accumulation, leaf/fine root biomass ratio (L/FR), transpiration rate, photosynthetic capacity and photosynthetic nitrogen-use efficiency ( E N ) were the highest under 25% pruning. Yet, all these traits except L/FR and foliage nitrogen content were severely reduced under 75% pruning. Drought negatively affected growth and leaf gas exchange rates, and there was a greater negative effect on growth, water potential, gas exchange and E N when 〉25% of total root biomass was removed. The stem/aboveground mass ratio was the highest under 25% pruning in both watering conditions. These results indicate that the responses to root severance are related to the excision intensity and soil moisture content. A moderate root pruning proved to be an effective means to improve stem dry mass accumulation.
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    Environmental drivers of cambial phenology in Great Basin bristlecone pine (2016)
    Oxford University Press
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    Publication Date: 2016-08-03
    Description: The timing of wood formation is crucial to determine how environmental factors affect tree growth. The long-lived bristlecone pine ( Pinus longaeva D. K. Bailey) is a foundation treeline species in the Great Basin of North America reaching stem ages of about 5000 years. We investigated stem cambial phenology and radial size variability to quantify the relative influence of environmental variables on bristlecone pine growth. Repeated cellular measurements and half-hourly dendrometer records were obtained during 2013 and 2014 for two high-elevation stands included in the Nevada Climate-ecohydrological Assessment Network. Daily time series of stem radial variations showed rehydration and expansion starting in late April–early May, prior to the onset of wood formation at breast height. Formation of new xylem started in June and lasted until mid-September. There were no differences in phenological timing between the two stands, or in the air and soil temperature thresholds for the onset of xylogenesis. A multiple logistic regression model highlighted a separate effect of air and soil temperature on xylogenesis, the relevance of which was modulated by the interaction with vapor pressure and soil water content. While air temperature plays a key role in cambial resumption after winter dormancy, soil thermal conditions coupled with snowpack dynamics also influence the onset of wood formation by regulating plant–soil water exchanges. Our results help build a physiological understanding of climate–growth relationships in P. longaeva , the importance of which for dendroclimatic reconstructions can hardly be overstated. In addition, environmental drivers of xylogenesis at the treeline ecotone, by controlling the growth of dominant species, ultimately determine ecosystem responses to climatic change.
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    Monitoring intra-annual dynamics of wood formation with microcores and dendrometers in Picea abies at two different altitudes (2016)
    Oxford University Press
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    Publication Date: 2016-08-03
    Description: Seasonal analyses of cambial cell production and day-by-day stem radial increment can help to elucidate how climate modulates wood formation in conifers. Intra-annual dynamics of wood formation were determined with microcores and dendrometers and related to climatic signals in Norway spruce ( Picea abies (L.) Karst.). The seasonal dynamics of these processes were observed at two sites of different altitude, Savignano (650 m a.s.l.) and Lavazè (1800 m a.s.l.) in the Italian Alps. Seasonal dynamics of cambial activity were found to be site specific, indicating that the phenology of cambial cell production is highly variable and plastic with altitude. There was a site-specific trend in the number of cells in the wall thickening phase, with the maximum cell production in early July (DOY 186) at Savignano and in mid-July (DOY 200) at Lavazè. The formation of mature cells showed similar trends at the two sites, although different numbers of cells and timing of cell differentiation were visible in the model shapes; at the end of ring formation in 2010, the number of cells was four times higher at Savignano (106.5 cells) than at Lavazè (26.5 cells). At low altitudes, microcores and dendrometers described the radial growth patterns comparably, though the dendrometer function underlined the higher upper asymptote of maximum growth in comparison with the cell production function. In contrast, at high altitude, these functions exhibited different trends. The best model was obtained by fitting functions of the Gompertz model to the experimental data. By combining radial growth and cambial activity indices we defined a model system able to synchronize these processes. Processes of adaptation of the pattern of xylogenesis occurred, enabling P. abies to occupy sites with contrasting climatic conditions. The use of daily climatic variables in combination with plant functional traits obtained by sensors and/or destructive sampling could provide a suitable tool to better investigate the effect of disturbances on response strategies in trees and, consequently, contribute to improving our prediction of tree growth and species resilience based on climate scenarios.
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    Coordination between growth, phenology and carbon storage in three coexisting deciduous tree species in a temperate forest (2016)
    Oxford University Press
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    Publication Date: 2016-08-03
    Description: In deciduous trees growing in temperate forests, bud break and growth in spring must rely on intrinsic carbon (C) reserves. Yet it is unclear whether growth and C storage occur simultaneously, and whether starch C in branches is sufficient for refoliation. To test in situ the relationships between growth, phenology and C utilization, we monitored stem growth, leaf phenology and stem and branch nonstructural carbohydrate (NSC) dynamics in three deciduous species: Carpinus betulus L., Fagus sylvatica L. and Quercus petraea (Matt.) Liebl. To quantify the role of NSC in C investment into growth, a C balance approach was applied. Across the three species, 〉95% of branchlet starch was consumed during bud break, confirming the importance of C reserves for refoliation in spring. The C balance calculation showed that 90% of the C investment in foliage (7.0–10.5 kg tree –1 and 5–17 times the C needed for annual stem growth) was explained by simultaneous branchlet starch degradation. Carbon reserves were recovered sooner than expected, after leaf expansion, in parallel with stem growth. Carpinus had earlier leaf phenology (by ~25 days) but delayed cambial growth (by ~15 days) than Fagus and Quercus , the result of a competitive strategy to flush early, while having lower NSC levels.
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    Scaling of photosynthesis and constitutive and induced volatile emissions with severity of leaf infection by rust fungus (Melampsora larici-populina) in Populus balsamifera var. suaveolens (2016)
    Oxford University Press
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    Publication Date: 2016-08-03
    Description: Fungal infections result in decreases in photosynthesis, induction of stress and signaling volatile emissions and reductions in constitutive volatile emissions, but the way different physiological processes scale with the severity of infection is poorly known. We studied the effects of infection by the obligate biotrophic fungal pathogen Melampsora larici-populina Kleb., the causal agent of poplar leaf rust disease, on photosynthetic characteristics, and constitutive isoprene and induced volatile emissions in leaves of Populus balsamifera var. suaveolens (Fisch.) Loudon. exhibiting different degrees of damage. The degree of fungal damage, quantified by the total area of chlorotic and necrotic leaf areas, varied between 0 (noninfected control) and ~60%. The rates of all physiological processes scaled quantitatively with the degree of visual damage, but the scaling with damage severity was weaker for photosynthetic characteristics than for constitutive and induced volatile release. Over the whole range of damage severity, the net assimilation rate per area ( A A ) decreased 1.5-fold, dry mass per unit area 2.4-fold and constitutive isoprene emissions 5-fold, while stomatal conductance increased 1.9-fold and dark respiration rate 1.6-fold. The emissions of key stress and signaling volatiles (methanol, green leaf volatiles, monoterpenes, sesquiterpenes and methyl salicylate) were in most cases nondetectable in noninfested leaves, and increased strongly with increasing the spread of infection. The moderate reduction in A A resulted from the loss of photosynthetically active biomass, but the reduction in constitutive isoprene emissions and the increase in induced volatile emissions primarily reflected changes in the activities of corresponding biochemical pathways. Although all physiological alterations in fungal-infected leaves occurred in a stress severity-dependent manner, modifications in primary and secondary metabolic pathways scaled differently due to contrasting operational mechanisms.
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    Genetic variability and heritability of chlorophyll a fluorescence parameters in Scots pine (Pinus sylvestris L.) (2016)
    Oxford University Press
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    Publication Date: 2016-08-03
    Description: Current knowledge of the genetic mechanisms underlying the inheritance of photosynthetic activity in forest trees is generally limited, yet it is essential both for various practical forestry purposes and for better understanding of broader evolutionary mechanisms. In this study, we investigated genetic variation underlying selected chlorophyll a fluorescence (ChlF) parameters in structured populations of Scots pine ( Pinus sylvestris L.) grown on two sites under non-stress conditions. These parameters were derived from the OJIP part of the ChlF kinetics curve and characterize individual parts of primary photosynthetic processes associated, for example, with the exciton trapping by light-harvesting antennae, energy utilization in photosystem II (PSII) reaction centers (RCs) and its transfer further down the photosynthetic electron-transport chain. An additive relationship matrix was estimated based on pedigree reconstruction, utilizing a set of highly polymorphic single sequence repeat markers. Variance decomposition was conducted using the animal genetic evaluation mixed-linear model. The majority of ChlF parameters in the analyzed pine populations showed significant additive genetic variation. Statistically significant heritability estimates were obtained for most ChlF indices, with the exception of DI 0 /RC, D0 and P0 ( F v / F m ) parameters. Estimated heritabilities varied around the value of 0.15 with the maximal value of 0.23 in the ET 0 /RC parameter, which indicates electron-transport flux from Q A to Q B per PSII RC. No significant correlation was found between these indices and selected growth traits. Moreover, no genotype  x  environment interaction (G  x  E) was detected, i.e., no differences in genotypes’ performance between sites. The absence of significant G  x  E in our study is interesting, given the relatively low heritability found for the majority of parameters analyzed. Therefore, we infer that polygenic variability of these indices is selectively neutral.
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    Transgenic poplar overexpressing the endogenous transcription factor ERF76 gene improves salinity tolerance (2016)
    Oxford University Press
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    Publication Date: 2016-08-03
    Description: The ethylene response factor (ERF) family is one of the largest plant-specific transcription factor families, playing an important role in plant development and response to stresses. The ERF76 gene is a member of the poplar ERF transcription factor gene family. First, we validated that the ERF76 gene expressed in leaf and root tissues is responsive to salinity stress. We then successfully cloned the ERF76 cDNA fragment containing an open reading frame from di-haploid Populus simonii   x   Populus nigra and proved that ERF76 protein is targeted to the nucleus. Finally, we transferred the gene into the same poplar clone by the Agrobacterium -mediated leaf disc method. Using both RNA-Seq and reverse transcription-quantitative polymerase chain reaction, we validated that expression level of ERF76 is significantly higher in transgenic plants than that in the nontransgenic control. Using RNA-Seq data, we have identified 375 genes that are differentially expressed between the transgenic plants and the control under salt treatment. Among the differentially expressed genes, 16 are transcription factor genes and 45 are stress-related genes, both of which are upregulated significantly in transgenic plants, compared with the control. Under salt stress, the transgenic plants showed significant increases in plant height, root length, fresh weight, and abscisic acid (ABA) and gibberellin (GA) concentration compared with the control, suggesting that overexpression of ERF76 in transgenic poplar upregulated the expression of stress-related genes and increased the ability of ABA and GA biosynthesis, which resulted in stronger tolerance to salt stress.
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    Adaptive mechanisms and genomic plasticity for drought tolerance identified in European black poplar (Populus nigra L.) (2016)
    Oxford University Press
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    Publication Date: 2016-08-03
    Description: Summer droughts are likely to increase in frequency and intensity across Europe, yet long-lived trees may have a limited ability to tolerate drought. It is therefore critical that we improve our understanding of phenotypic plasticity to drought in natural populations for ecologically and economically important trees such as Populus nigra L. A common garden experiment was conducted using ~500 wild P. nigra trees, collected from 11 river populations across Europe. Phenotypic variation was found across the collection, with southern genotypes from Spain and France characterized by small leaves and limited biomass production. To examine the relationship between phenotypic variation and drought tolerance, six genotypes with contrasting leaf morphologies were subjected to a water deficit experiment. ‘North eastern’ genotypes were collected at wet sites and responded to water deficit with reduced biomass growth, slow stomatal closure and reduced water use efficiency (WUE) assessed by 13 C. In contrast, ‘southern’ genotypes originating from arid sites showed rapid stomatal closure, improved WUE and limited leaf loss. Transcriptome analyses of a genotype from Spain (Sp2, originating from an arid site) and another from northern Italy (Ita, originating from a wet site) revealed dramatic differences in gene expression response to water deficit. Transcripts controlling leaf development and stomatal patterning, including SPCH , ANT , ER , AS1 , AS2 , PHB , CLV1 , ERL1–3 and TMM , were down-regulated in Ita but not in Sp2 in response to drought.
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    Gene expression analysis of disabled and re-induced isoprene emission by the tropical tree Ficus septica before and after cold ambient temperature exposure (2016)
    Oxford University Press
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    Publication Date: 2016-08-03
    Description: Isoprene is the most abundant type of nonmethane, biogenic volatile organic compound in the atmosphere, and it is produced mainly by terrestrial plants. The tropical tree species Ficus septica Burm. F. (Rosales: Moraceae) has been shown to cease isoprene emissions when exposed to temperatures of 12 °C or lower and to re-induce isoprene synthesis upon subsequent exposure to temperatures of 30 °C or higher for 24 h. To elucidate the regulation of genes underlying the disabling and then induction of isoprene emission during acclimatization to ambient temperature, we conducted gene expression analyses of F. septica plants under changing temperature using quantitative real-time polymerase chain reaction and western blotting. Transcription levels were analyzed for 17 genes that are involved in metabolic pathways potentially associated with isoprene biosynthesis, including isoprene synthase ( ispS ). The protein levels of ispS were also measured. Changes in transcription and protein levels of the ispS gene, but not in the other assessed genes, showed identical temporal patterns to isoprene emission capacity under the changing temperature regime. The ispS protein levels strongly and positively correlated with isoprene emission capacity ( R 2  = 0.92). These results suggest that transcriptional regulation of ispS gave rise to the temporal variation in isoprene emission capacity in response to changing temperature.
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    Physiological integration of connected balsam poplar ramets (2016)
    Oxford University Press
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    Publication Date: 2016-08-03
    Description: Clonal integration between ramets can be an ecological advantage of clonal plant species in environments where resources are patchily distributed. We investigated physiological integration among Populus balsamifera L. ramets under drought stress in order to demonstrate water sharing between connected ramets. Pairs of connected ramets were grown in separate pots in the greenhouse where half of ramets had the parental root connection severed and half were left intact. Drought stress was applied to one ramet, and growth, specific leaf area (SLA), net photosynthesis, stomatal conductance, leaf water potential and carbon isotopic composition ( 13 C) were measured after an 8-week growing period. Droughted ramets connected to watered ramets were able to maintain high gas exchange activity and water potential, similar to watered ramets. Leaf water potential and SLA results showed that the root connection was more beneficial for proximal compared with distal ramets. The parental root connection also allowed droughted ramets to discriminate more against 13 C compared with severed ramets. In conclusion, this study shows compelling evidence of physiological integration of connected P. balsamifera ramets through water sharing.
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    A posteriori error estimates for fully discrete fractional-step {vartheta}-approximations for parabolic equations (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: We derive optimal-order a posteriori error estimates for fully discrete approximations of initial and boundary value problems for linear parabolic equations. For the discretization in time we apply the fractional-step $\vartheta $ -scheme, and for the discretization in space the finite element method with finite element spaces that are allowed to change with time. The first optimal-order a posteriori error estimates for the norms of $L^\infty (0,T;L^2(\varOmega ))$ and $L^2(0,T;H^1(\varOmega ))$ are derived by applying the reconstruction technique.
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    A fast and accurate numerical method for symmetric Levy processes based on the Fourier transform and sinc-Gauss sampling formula (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: In this paper, we propose a fast and accurate numerical method based on Fourier transforms to solve Kolmogorov forward equations of symmetric scalar Lévy processes. The method is based on the accurate numerical formulas for Fourier transforms proposed by Ooura. These formulas are combined with nonuniform fast Fourier transforms (FFT) and fractional FFT to speed up the numerical computations. Moreover, we propose a formula for numerical indefinite integration on equispaced grids as a component of the method. The proposed integration formula is based on the sinc-Gauss sampling formula, which is a function approximation formula. This integration formula is also combined with the FFT. Therefore, all steps of the proposed method are executed using the FFT and its variants. The proposed method allows us to be free from some special treatments for a nonsmooth initial condition and numerical time integration. The numerical solutions obtained by the proposed method appear to be exponentially convergent on the interval if the corresponding exact solutions do not have sharp cusps. Furthermore, the real computational times are approximately consistent with the theoretical estimates.
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    Spectral discretization of Darcy's equations coupled with the heat equation (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: In this paper, we consider the heat equation coupled with Darcy's law with a nonlinear source term describing heat production due to an exothermic chemical reaction. The existence and uniqueness of a solution are established. Next, a spectral discretization of the problem is presented and thoroughly analysed. Finally, we present some numerical experiments which confirm the interest of the discretization.
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    On the convergence of the quadratic method (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: The convergence of the so-called quadratic method for computing eigenvalue enclosures of general self-adjoint operators is examined. Explicit asymptotic bounds for convergence to isolated eigenvalues are found. These bounds turn out to improve significantly upon those determined in previous investigations. The theory is illustrated by means of several numerical experiments performed on particularly simple benchmark models of one-dimensional Schrödinger operators.
    Print ISSN: 0272-4979
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    Carnapian truthlikeness (2016)
    Oxford University Press
    Details
    Publication Date: 2016-07-15
    Description: Theories of truthlikeness (or verisimilitude) are currently being classified according to two independent distinctions: that between ‘content’ and ‘likeness’ accounts, and that between ‘conjunctive’ and ‘disjunctive’ ones. In this article, I present and discuss a new definition of truthlikeness, which employs Carnap's notion of the content elements entailed by a theory or proposition, and is then labelled ‘Carnapian’. After studying in detail the properties and shortcomings of this definition, I argue that it occupies a unique position in the landscape of different approaches to truthlikeness. More precisely, I show that it provides the only explication of truthlikeness which is both ‘conjunctive’ and ‘content-based’ in a suitably defined sense.
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
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    For a dynamical approach to human computation (2016)
    Oxford University Press
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    Publication Date: 2016-07-15
    Description: In this article, we show that, in agreement with Alan Turing's original view, but contrary to many of his interpreters, high-level cognitive activities like algorithm execution are better described as dynamical activities, which involve the coordinate work of both internal (mental) resources and external ones, like paper and pencil or similar external tools. We, then, propose to exploit the basic dynamical features of a Turing machine in order to develop a dynamical approach to the cognitive explanation of human computational activities.
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    Cycles of modules and finite representation type (2016)
    Oxford University Press
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    Publication Date: 2016-07-21
    Description: We prove that an artin algebra $A$ is of finite representation type if and only if almost all finitely generated indecomposable $A$ -modules are cycle-finite. Moreover, we prove that every cycle-finite module category of an artin algebra $A$ of infinite representation type contains infinitely many left stable and infinitely many right stable directing modules. In particular, the main results of the paper provide solution of the open problem concerning infinity of directing modules over cycle-finite artin algebras of infinite representation type.
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
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    Toeplitz flows and model sets (2016)
    Oxford University Press
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    Publication Date: 2016-07-21
    Description: We show that binary Toeplitz flows can be interpreted as Delone dynamical systems induced by model sets and analyse the quantitative relations between the respective system parameters. This has a number of immediate consequences for the theory of model sets. In particular, we use our results in combination with special examples of irregular Toeplitz flows from the literature to demonstrate that irregular proper model sets may be uniquely ergodic and do not need to have positive entropy. This answers questions by Schlottmann and Moody.
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    Hölder inequality for symmetric operator spaces and trace property of K-cycles (2016)
    Oxford University Press
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    Publication Date: 2016-07-21
    Description: We prove a general version of the Hölder inequality for symmetric operator spaces and symmetric functionals (traces) on such spaces, answering some open questions in the literature. We also prove a general version of the result establishing the trace property of the non-commutative integral defined via an arbitrary positive symmetric functional on a symmetric operator space. Our main tool is the so-called uniform Hardy–Littlewood majorization.
    Print ISSN: 0024-6093
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    Motivic homological stability for configuration spaces of the line (2016)
    Oxford University Press
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    Publication Date: 2016-07-21
    Description: We lift the classical theorem of Arnol'd on homological stability for configuration spaces of the plane to the motivic world. More precisely, we prove that the schemes of unordered configurations of points in the affine line satisfy stability with respect to the motivic $t$ -structure on mixed Tate motives.
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    Quasicircles as equipotential lines, homotopy classes and geodesics (2016)
    Oxford University Press
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    Publication Date: 2016-07-21
    Description: We give an application of our earlier results concerning the quasiconformal extension of a germ of a conformal map to establish that in two dimensions, the equipotential level lines of a capacitor are quasicircles whose distortion depends only on the capacity and the level. As an application, we find that given disjoint, nonseparating and nontrivial continua $E$ and $F$ in $\hat {\mathbb {C}}=\mathbb {C}\cup \{\infty \}$ , the closed hyperbolic geodesic generating the fundamental group $\pi _1(\hat {\mathbb {C}}\setminus (E\cup F) ) \cong \mathbb {Z}$ is a $K$ -quasicircle separating $E$ and $F$ with explicit distortion bound depending only on the capacity of $\hat {\mathbb {C}}^{\vphantom {A^A}}\setminus (E\cup F)$ . This result is then extended to obtain distortion bounds on a quasicircle representing a given homotopy class of a simple closed curve in a planar domain. Finally, we are able to use these results to show that a simple closed hyperbolic geodesic in a planar domain is a quasicircle with a distortion bound depending explicitly, and only, on its length.
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    An existence time estimate for Kähler-Ricci flow (2016)
    Oxford University Press
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    Publication Date: 2016-07-21
    Description: Fix a complete non-compact Kähler manifold $(M^n,h_0)$ with bounded curvature. Let $g(t)$ be a bounded curvature solution to the Kähler–Ricci flow starting from some $g_0$ that is uniformly equivalent to $h_0$ . We estimate the existence time of $g(t)$ together with $C^0$ bounds and curvature bounds, where the estimates depend only on $h_0$ and the $C^0$ distance between $g_0$ and $h_0$ . We also generalize these results to cases when $g_0$ may have unbounded curvature.
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    The bi-Hamiltonian cohomology of a scalar Poisson pencil (2016)
    Oxford University Press
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    Publication Date: 2016-07-21
    Description: We compute the bi-Hamiltonian cohomology of an arbitrary dispersionless Poisson pencil in a single dependent variable using a spectral sequence method. As in the Korteweg-de Vries case, we obtain that $BH^p_d( \hat { \mathcal {F}}, d_1,d_2)$ is isomorphic to $ {\mathbb {R}}$ for $(p,d)=(0,0)$ , to $C^\infty ( {\mathbb {R}})$ for $(p,d)=(1,1)$ , $(2,1)$ , $(2,3)$ , $(3,3)$ , and vanishes otherwise.
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    On K-stability of finite covers (2016)
    Oxford University Press
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    Publication Date: 2016-07-21
    Description: We show that certain Galois covers of K-semistable Fano varieties are K-stable. We use this to give some new examples of Fano manifolds admitting Kähler–Einstein metrics, including hypersurfaces, double solids and threefolds.
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    Introduction to the special issue on Loops in Argumentation (2016)
    Oxford University Press
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    Publication Date: 2016-07-27
    Print ISSN: 0955-792X
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    Topics: Computer Science , Mathematics
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    The handling of loops in argumentation networks (2016)
    Oxford University Press
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    Publication Date: 2016-07-27
    Description: This article is about busting loops in abstract argumentation networks. We propose several approaches to how to deal with networks which have loops (such as even or odd cycles) and get new extensions which are ‘in’, ‘out’ extensions, with no undecided elements.
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    On the acceptance of loops in argumentation frameworks (2016)
    Oxford University Press
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    Publication Date: 2016-07-27
    Description: Current approaches for giving semantics to abstract argumentation frameworks dismiss altogether any possibility of having conflicts among accepted arguments by requiring that the latter should be ‘conflict free’. In reality, however, contradictory phenomena coexist, or it may happen that one cannot make a choice between conflicting indications but still would like to keep track to all of them. For this purpose we introduce in this article a new kind of argumentation semantics, called ‘conflict-tolerant’, in which all the accepted arguments must be justified (in the sense that each one of them can be defended), but some of them may still attack each other. In terms of graphical representation of argumentation systems, where attacks are represented by directed edges, this means that the possibility of accepting ‘loops’ of arguments is not automatically ruled out without any further considerations. To provide conflict-tolerant semantics, we enhance the two standard approaches for defining coherent (conflict-free) semantics for argumentation frameworks. The extension-based approach is generalized by relaxing the ‘conflict-freeness’ requirement of the chosen sets of arguments, and the three-valued labelling approach is replaced by a four-valued labelling system that allows to capture mutual attacks among accepted arguments. We show that our setting is not a substitute of standard (conflict-free) semantics, but rather a generalized framework that accommodates both conflict-free and conflict-tolerant semantics. Moreover, the one-to-one relationship between extensions and labellings of conflict-free semantics is carried on to a similar correspondence between the extended approaches for providing conflict-tolerant semantics. Thus, in our setting as well, these are essentially two points of views for the same thing.
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    The role of self-attacking arguments in characterizations of equivalence notions (2016)
    Oxford University Press
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    Publication Date: 2016-07-27
    Description: A special case of loops in argumentation are self-attacking arguments. While their role with respect to the ontological nature of argumentation is controversially discussed, their presence (or absence) in the abstract setting of Dung-style argumentation frameworks seems to be less crucial for semantics or fundamental properties. There are, however, a few exceptions where self-attacking arguments have essential influence. One such exception concerns characterizations of (strong) equivalence notions between argumentation frameworks. Different notions of equivalence have recently been proposed in the literature and several characterization results for different semantics have been obtained. In this article, we will survey the current state of this research direction with a particular emphasis on the effect of (dis)allowing self-conflicting arguments. We also provide some novel results for stage, eager and naive semantics in order to present a full classification of ten prominent semantics and four equivalence notions.
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    Higher differentiability of solutions of parabolic systems with discontinuous coefficients (2016)
    Oxford University Press
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    Publication Date: 2016-07-29
    Description: We consider weak solutions $u:\Omega _T\to \mathbb {R}^N$ to parabolic systems of the type \[ u_t-{\rm div}\,a(x,t,Du)=0 \quad\mbox{in }\Omega_T=\Omega\times(0,T), \] where the function $a(x,t,\xi )$ satisfies standard $p$ -growth and ellipticity conditions for $p\ge 2$ with respect to the gradient variable $\xi $ . We study the regularity of the solutions in the case of possibly discontinuous coefficients. More precisely, the partial maps $x\mapsto a(x,t,\xi )$ under consideration may not be continuous, but may only possess a Sobolev-type regularity. In a certain sense, our assumption means that the weak derivatives $D_xa(\cdot ,\cdot ,\xi )$ are contained in the class $L^\alpha (0,T;L^\beta (\Omega ))$ , where the integrability exponents $\alpha ,\beta $ are coupled by \[ \frac{p(n+2)-2n}{2\alpha}+\frac n\beta=1. \] In the particular case $\alpha =\beta =p(n + 2)/2$ , our assumption reduces to $D_xa\in L_{{\rm loc}}^{p(n + 2)/2}(\Omega _T)$ . The aim of this paper is to prove a higher differentiability result of the solutions in the spatial directions as well as the existence of a weak time derivative $u_t\in L^{p/{(p-1)}}_{{\rm loc}}(\Omega _T)$ .
    Print ISSN: 0024-6107
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    Thixotropy in yield stress fluids as a limit of viscoelasticity (2016)
    Oxford University Press
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    Publication Date: 2016-08-02
    Description: Thixotropic yield stress fluids have a yield stress and viscosity which change slowly over time as the fluid undergoes structural changes. This article reviews recent work which shows how such behaviour can arise as a limit of viscoelastic flow when a relaxation time becomes large. The large relaxation time introduces a small parameter which can be used as a basis for singular perturbation studies. A simple prototype for a viscoelastic model will be used to illustrate the analysis. We review the behaviour in startup of shear flow, oscillatory shear flow and elongational flow and identify potential directions for future research.
    Print ISSN: 0272-4960
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    The Painleve paradox in contact mechanics (2016)
    Oxford University Press
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    Publication Date: 2016-08-02
    Description: The 120-year-old so-called Painlevé paradox involves the loss of determinism in models of planar rigid bodies in point contact with a rigid surface, subject to Coulomb-like dry friction. The phenomenon occurs due to coupling between normal and rotational degrees-of-freedom such that the effective normal force becomes attractive rather than repulsive. Despite a rich literature, the forward evolution problem remains unsolved other than in certain restricted cases in 2D with a single contact point. Various practical consequences of the theory are revisited, including models for robotic manipulators and the strange behaviour of chalk when pushed rather than dragged across a blackboard. Reviewing recent theory, a general formulation is proposed, including Poisson or energetic impact laws. The general problem in 2D with a single point of contact is discussed and cases of inconsistency or indeterminacy enumerated. Strategies to resolve the paradox via contact regularization are discussed from a dynamical systems point of view. By passing to the infinite stiffness limit and allowing impact without collision, inconsistent and indeterminate cases are shown to be resolvable for all open sets of conditions. However, two unavoidable ambiguities that can be reached in finite time are discussed in detail, so called dynamic jam and reverse chatter. A partial review is given of 2D cases with two points of contact showing how a greater complexity of inconsistency and indeterminacy can arise. Extension to fully 3D analysis is briefly considered and shown to lead to further possible singularities. In conclusion, the ubiquity of the Painlevé paradox is highlighted and open problems are discussed.
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    The Schottky-Klein prime function: a theoretical and computational tool for applications (2016)
    Oxford University Press
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    Publication Date: 2016-08-02
    Description: This article surveys the important role, in a variety of applied mathematical contexts, played by the so-called Schottky–Klein (S–K) prime function. While it is a classical special function, introduced by 19th century investigators, its theoretical significance for applications has only been realized in the last decade or so, especially with respect to solving problems defined in multiply connected, or ‘holey’, domains. It is shown here that, in terms of it, many well-known results pertaining only to the simply connected case (no holes) can be generalized, in a natural way, to the multiply connected case, thereby contextualizing those well-known results within a more general framework of much broader applicability. Given the wide-ranging usefulness of the S–K prime function it is important to be able to compute it efficiently. Here we introduce both a new theoretical formulation for its computation, as well as two distinct numerical methods to implement the construction. The combination of these theoretical and computational developments renders the S–K prime function a powerful new tool in applied mathematics.
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    Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae (2016)
    Oxford University Press
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    Publication Date: 2016-08-06
    Description: A formula for the norm of a bilinear Schur multiplier acting from the Cartesian product $\mathcal S^2\times \mathcal S^2$ of two copies of the Hilbert–Schmidt classes into the trace class $\mathcal S^1$ is established in terms of linear Schur multipliers acting on the space $\mathcal S^\infty $ of all compact operators. Using this formula, we resolve Peller's problem on Koplienko–Neidhardt trace formulae. Namely, we prove that there exist a twice continuously differentiable function $f$ with a bounded second derivative, a self-adjoint (unbounded) operator $A$ and a self-adjoint operator $B\in \mathcal S^2$ such that \[ f(A+B)-f(A)-\left.\frac{d}{dt}(f(A+tB))\right\vert_{t=0}\notin \mathcal S^1. \]
    Print ISSN: 0024-6115
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    Bounding marginal densities via affine isoperimetry (2016)
    Oxford University Press
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    Publication Date: 2016-08-06
    Description: Let $\mu $ be a probability measure on $ \mathbb R^n$ with a bounded density $f$ . We prove that the marginals of $f$ on most subspaces are well-bounded. For product measures, studied recently by Rudelson and Vershynin, our results show there is a trade-off between the strength of such bounds and the probability with which they hold. Our proof rests on new affinely invariant extremal inequalities for certain averages of $f$ on the Grassmannian and affine Grassmannian. These are motivated by Lutwak's dual affine quermassintegrals for convex sets. We show that key invariance properties of the latter, due to Grinberg, extend to families of functions. The inequalities we obtain can be viewed as functional analogues of results due to Busemann–Straus, Grinberg and Schneider. As an application, we show that without any additional assumptions on $\mu $ , any marginal $\pi _E(\mu )$ , or a small perturbation thereof, satisfies a nearly optimal small-ball probability.
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    Serre's problem on the density of isotropic fibres in conic bundles (2016)
    Oxford University Press
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    Publication Date: 2016-08-06
    Description: Let $\pi :X\to \mathbb {P}^1_{\mathbb {Q}}$ be a non-singular conic bundle over $\mathbb {Q}$ having $n$ non-split fibres and denote by $N(\pi ,B)$ the cardinality of the fibres of Weil height at most $B$ that possess a rational point. Serre showed in 1990 that a direct application of the large sieve yields \[ N(\pi,B)\ll B^2(\log B)^{-n/2} \] and raised the problem of proving that this is the true order of magnitude of $N(\pi ,B)$ under the necessary assumption that there exists at least one smooth fibre with a rational point. We solve this problem for all non-singular conic bundles of rank at most 3. Our method comprises the use of Hooley neutralisers, estimating divisor sums over values of binary forms, and an application of the Rosser–Iwaniec sieve.
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    Dimer models and cluster categories of Grassmannians (2016)
    Oxford University Press
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    Publication Date: 2016-08-06
    Description: We associate a dimer algebra $A$ to a Postnikov diagram $D$ (in a disc) corresponding to a cluster of minors in the cluster structure of the Grassmannian ${\rm Gr}(k,n)$ . We show that $A$ is isomorphic to the endomorphism algebra of a corresponding Cohen–Macaulay module $T$ over the algebra $B$ used to categorify the cluster structure of ${\rm Gr}(k,n)$ by Jensen–King–Su. It follows that $B$ can be realised as the boundary algebra of $A$ , that is, the subalgebra $eAe$ for an idempotent $e$ corresponding to the boundary of the disc. The construction and proof uses an interpretation of the diagram $D$ , with its associated plabic graph and dual quiver (with faces), as a dimer model with boundary. We also discuss the general surface case, in particular computing boundary algebras associated to the annulus.
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    A categorification of Grassmannian cluster algebras (2016)
    Oxford University Press
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    Publication Date: 2016-08-06
    Description: We describe a ring whose category of Cohen–Macaulay modules provides an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of $k$ -planes in $n$ -space. More precisely, there is a cluster character defined on the category which maps the rigid indecomposable objects to the cluster variables and the maximal rigid objects to clusters. This is proved by showing that the quotient of this category by a single projective–injective object is Geiss–Leclerc–Schröer's category Sub $Q_k$ , which categorifies the coordinate ring of the big cell in this Grassmannian.
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    Hyperbolic 4-manifolds, colourings and mutations (2016)
    Oxford University Press
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    Publication Date: 2016-08-06
    Description: We develop a way of seeing a complete orientable hyperbolic 4-manifold $ {\mathcal {M}}$ as an orbifold cover of a Coxeter polytope $ {\mathcal {P}} \subset \mathbb {H}^4$ that has a facet colouring. We also develop a way of finding a totally geodesic sub-manifold $ {\mathcal {N}}$ in $ {\mathcal {M}}$ , and describing the result of mutations along $ {\mathcal {N}}$ . As an application of our method, we construct an example of a complete orientable hyperbolic 4-manifold $ {\mathcal {X}}$ with a single non-toric cusp and a complete orientable hyperbolic 4-manifold ${\mathcal {Y}}$ with a single toric cusp. Both $ {\mathcal {X}}$ and $ {\mathcal {Y}}$ have twice the minimal volume among all complete orientable hyperbolic 4-manifolds.
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    What Can We Learn about the Effects of Food Stamps on Obesity in the Presence of Misreporting? (2016)
    Oxford University Press
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    Publication Date: 2016-07-09
    Description: There is an increasing perception among policy makers that food stamp benefits contribute positively to adult obesity rates. We show that these results are heavily dependent on one’s assumptions regarding the accuracy of reported food stamp participation. When allowing for misreporting, we find no evidence that Supplemental Nutrition Assistance Program participation significantly increases the probability of being obese or overweight among adults. Our results also highlight the inherent bias and inconsistency of common point estimates when ignoring misreporting, with treatment effects from instrumental variable methods exceeding the nonparametric upper bounds by over 200% in some cases.
    Keywords: C11 - Bayesian Analysis, I10 - General, I38 - Government Policy ; Provision and Effects of Welfare Programs
    Print ISSN: 0002-9092
    Electronic ISSN: 1467-8276
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Economics
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    Temperature Changes, Household Consumption, and Internal Migration: Evidence from Tanzania (2016)
    Oxford University Press
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    Publication Date: 2016-07-09
    Description: Large rural-urban wage gaps observed in many developing countries are suggestive of barriers to migration that keep potential migrants in rural areas. Using long panel data spanning nearly two decades, I study the extent to which migration rates are constrained by liquidity constraints in rural Tanzania. The analysis begins by quantifying the impact of weather variation on household welfare. The results show how household consumption co-moves with temperature, rendering households vulnerable to local weather events. These temperature-induced income shocks are then found to inhibit long-term migration among men, thus preventing them from tapping into the opportunities brought about by geographical mobility.
    Keywords: O12 - Microeconomic Analyses of Economic Development, O15 - Human Resources ; Human Development ; Income Distribution ; Migration, Q54 - Climate ; Natural Disasters ; Global Warming, R23 - Regional Migration ; Regional Labor Markets ; Population
    Print ISSN: 0002-9092
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Economics
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    A Declining Farm Workforce: Analysis of Panel Data from Rural Mexico (2016)
    Oxford University Press
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    Publication Date: 2016-07-09
    Description: Analysis of nationally representative individual-level panel data from 1980 to 2010 reveals a significant negative trend in the agricultural labor supply from rural Mexico, which is the primary source of hired workers for U.S. farms. These findings offer an explanation for the rise over time in U.S. farm wages. Concomitants of the agricultural transformation, including growth in the non-farm economy, falling birth rates, and an increase in rural education, accelerate the transition of rural Mexicans out of farm work. Higher U.S. farm wages and increased border enforcement slow the transition, but the combined impact of these offsetting variables is relatively small. A diminishing farm labor supply has far-reaching implications for farmers, farm labor organizers, rural communities, and agricultural workers.
    Keywords: J21 - Labor Force and Employment, Size, and Structure, J43 - Agricultural Labor Markets, O15 - Human Resources ; Human Development ; Income Distribution ; Migration, Q12 - Micro Analysis of Farm Firms, Farm Households, and Farm Input Markets
    Print ISSN: 0002-9092
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Economics
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    Sugar Coated, a documentary film directed by Michele Hozer. (2016)
    Oxford University Press
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    Publication Date: 2016-07-09
    Print ISSN: 0002-9092
    Electronic ISSN: 1467-8276
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Economics
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    The covariogram and Fourier-Laplace transform in Cn (2016)
    Oxford University Press
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    Publication Date: 2016-07-09
    Description: The covariogram $g_{K}$ of a convex body $K$ in $ \mathbb {R}^n$ is the function that associates to each $x\in \mathbb {R}^n$ the volume of the intersection of $K$ with $K+x$ . Determining $K$ from the knowledge of $g_K$ is known as the Covariogram Problem. It is equivalent to determining the characteristic function $1_K$ of $K$ from the modulus of its Fourier transform $\widehat {{1_K}}$ in $ \mathbb {R}^n$ , a particular instance of the Phase Retrieval Problem. We connect the Covariogram Problem to two aspects of the Fourier transform $\widehat {{1_K}}$ seen as a function in $\mathbb {C}^n$ . The first connection is with the problem of determining $K$ from the knowledge of the zero set of $\widehat {{1_K}}$ in $\mathbb {C}^n$ . To attack this problem T. Kobayashi studied the asymptotic behavior at infinity of this zero set. We obtain this asymptotic behavior assuming less regularity on $K$ and we use this result as an essential ingredient for proving that when $K$ is sufficiently smooth and in any dimension $n$ , $K$ is determined by $g_K$ in the class of sufficiently smooth bodies. The second connection is with the irreducibility of the entire function $\widehat {{1_K}}$ . This connection also shows a link between the Covariogram Problem and the Pompeiu Problem in integral geometry.
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    Topics: Mathematics
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    Aristotelian Continua (2016)
    Oxford University Press
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    Publication Date: 2016-06-21
    Description: In previous work, Hellman and Shapiro present a regions-based account of a one-dimensional continuum. This paper produces a more Aristotelian theory, eschewing the existence of points and the use of infinite sets or pluralities. We first show how to modify the original theory. There are a number of theorems (such as the existence of bisections) that have to be added as axioms. Building on some work by Linnebo, we then show how to take the ‘potential’ nature of the usual operations seriously, by using a modal language, and we show that the two approaches are equivalent.
    Print ISSN: 0031-8019
    Electronic ISSN: 1744-6406
    Topics: Mathematics , Philosophy
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    Using Mathematics to Explain a Scientific Theory (2016)
    Oxford University Press
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    Publication Date: 2016-06-21
    Description: We answer three questions: 1. Can we give a wholly mathematical explanation of a physical phenomenon? 2. Can we give a wholly mathematical explanation for a whole physical theory ? 3. What is gained or lost in giving a wholly, or partially, mathematical explanation of a phenomenon or a scientific theory? To answer these questions we look at a project developed by Hajnal Andréka, Judit Madarász, István Németi and Gergely Székely. They, together with collaborators, present special relativity theory in a three-sorted first-order formal language.
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    Topics: Mathematics , Philosophy
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    Stephen Pollard. A Mathematical Prelude to the Philosophy of Mathematics (2016)
    Oxford University Press
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    Publication Date: 2016-06-21
    Print ISSN: 0031-8019
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    Topics: Mathematics , Philosophy
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    Nick Haverkamp. Intuitionism vs. Classicism: A Mathematical Attack on Classical Logic. Studies in Theoretical Philosophy, Vol. 2. Frankfurt: Klostermann, 2015. ISBN 978-3-465-03906-8 (pbk). Pp. xvi + 270 (2016)
    Oxford University Press
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    Publication Date: 2016-06-21
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    Topics: Mathematics , Philosophy
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    Sorin Costreie, ed. Early Analytic Philosophy: New Perpectives on the Tradition (2016)
    Oxford University Press
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    Publication Date: 2016-06-21
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    Topics: Mathematics , Philosophy
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    Ernest Davis and Philip J. Davis eds. Mathematics, Substance and Surmise: Views on the Meaning and Ontology of Mathematics (2016)
    Oxford University Press
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    Publication Date: 2016-06-21
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    Topics: Mathematics , Philosophy
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    Rota's Philosophy in its Mathematical Context (2016)
    Oxford University Press
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    Publication Date: 2016-06-21
    Description: The goal of this paper is to connect Rota's discussion of the Husserlian notion of Fundierung with Rota's project of giving combinatorics a foundation in his 1964 paper ‘On the foundations of combinatorial theory I’. Section 2 gives the basic tenets of this seminal paper. Sections 3 and 4 spell out the connections made there between Rota's philosophical writings and his mathematical achievements. Section 5 shows how these two developments fit into Rota's analysis of the place of combinatorics in mathematics.
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    Topics: Mathematics , Philosophy
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    Claire Ortiz Hill and Jairo Jose da Silva. The Road Not Taken: On Husserl's Philosophy of Logic and Mathematics (2016)
    Oxford University Press
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    Publication Date: 2016-06-21
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    Feng Ye. Strict Finitism and the Logic of Mathematical Applications (2016)
    Oxford University Press
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    Publication Date: 2016-06-21
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    Reinhard Kahle and Michael Rathjen, eds. Gentzen's Centenary: The Quest for Consistency (2016)
    Oxford University Press
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    Publication Date: 2016-06-21
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    John W. Dawson, Jr. Why Prove it Again: Alternative Proofs in Mathematical Practice (2016)
    Oxford University Press
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    Publication Date: 2016-06-21
    Print ISSN: 0031-8019
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    Forest health in a changing world: effects of globalization and climate change on forest insect and pathogen impacts (2016)
    Oxford University Press
    In: Forestry
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    Publication Date: 2016-05-06
    Description: Forests and trees throughout the world are increasingly affected by factors related to global change. Expanding international trade has facilitated invasions of numerous insects and pathogens into new regions. Many of these invasions have caused substantial forest damage, economic impacts and losses of ecosystem goods and services provided by trees. Climate change is already affecting the geographic distribution of host trees and their associated insects and pathogens, with anticipated increases in pest impacts by both native and invasive pests. Although climate change will benefit many forest insects, changes in thermal conditions may disrupt evolved life history traits and cause phenological mismatches. Individually, the threats posed to forest ecosystems by invasive pests and climate change are serious. Although interactions between these two drivers and their outcomes are poorly understood and hence difficult to predict, it is clear that the cumulative impacts on forest ecosystems will be exacerbated. Here we introduce and synthesize the information in this special issue of Forestry with articles that illustrate the impacts of invasions of insects and pathogens, climate change, forest management and their interactions, as well as methods to predict, assess and mitigate these impacts. Most of these contributions were presented at the XXIV IUFRO World Congress in 2014.
    Print ISSN: 0015-752X
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    Preparing for the invasion: efficacy of DNA barcoding to discern the host range of myrtle rust (Puccinia psidii) among species of Myrtaceae (2016)
    Oxford University Press
    In: Forestry
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    Publication Date: 2016-05-06
    Description: Puccinia psidii is a major threat to members of the Myrtaceae worldwide. New Zealand is still free of P. psidii but possesses significant Eucalyptus plantations as well as valuable native tree species such as Metrosideros excelsa and Leptospermum scoparium that could be at risk in the event of an incursion. As part of preparing for a potential incursion, we generated a barcode reference library for 〉100 diverse species of Myrtaceae occurring in New Zealand by sequencing internal transcribed spacer (ITS), external transcribed spacer (ETS) and maturase K ( matK ), or by obtaining relevant sequences from GenBank. The Myrtaceae DNA barcoding database will enable rapid identification of large numbers of host species in the event of a myrtle rust incursion. We undertook a comparative analysis of the ability for the three mentioned loci to discriminate species. Interspecific divergence was assessed by mean interspecific distance, prime and minimum interspecific distance; intraspecific variation was evaluated by mean intraspecific difference, and coalescent depth. Overall identification efficiency of the three loci sequenced was determined using BLAST1 and Near Distance methods. Barcoding gaps between inter- and intraspecific divergences were also analysed. ITS and ETS share similar mean interspecific distance, prime and minimum interspecific distance values – both higher than obtained for matK . In contrast, in terms of intraspecific variation, matK had higher values than ITS and ETS in all three metrics analysed. ITS had the highest identification success rate for species followed by matK and ETS, respectively, as measured by BLAST1 and Near Distance methods. Overall identification success rate increases when a combination of ITS and matK in particular is used. The sequence data are not only a valuable reference collection for a myrtle rust response but also a national botanical resource.
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    Elevational shifts in thermal suitability for mountain pine beetle population growth in a changing climate (2016)
    Oxford University Press
    In: Forestry
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    Publication Date: 2016-05-06
    Description: Future forests are being shaped by changing climate and disturbances. Climate change is causing large-scale forest declines globally, in addition to distributional shifts of many tree species. Because environmental cues dictate insect seasonality and population success, climate change is also influencing tree-killing bark beetles. The mountain pine beetle, Dendroctonus ponderosae , is a major disturbance in Pinus forests of the western US. Using a mechanistic, phenology-based demographic model driven by downscaled daily temperature data, we describe recent and future spatial and temporal thermal suitability for mountain pine beetle population growth in a topographically complex region. Trends in model-predicted growth rates among Global Climate Models were similar and suggest that, relative to future trends, mountain pine beetle population growth within the past 60 years was most optimal at middle elevations and least optimal at the lowest and highest elevations. This trend aligns with observed mountain pine beetle-caused tree mortality that was greatest at middle elevations between 1997 and 2013, as estimated from Aerial Detection Surveys. However, thermal suitability for optimal phenological synchrony was predicted to shift in recent years, and by the end of the century, the best thermal habitats for mountain pine beetle will be at the lowest and highest elevations. Mechanistic demographic models are valuable tools for modelling future thermal regimes that may be both beneficial and maladaptive for mountain pine beetle population growth and subsequent tree mortality.
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    Determining forest degradation, ecosystem state and resilience using a standard stand stocking measurement diagram: theory into practice (2016)
    Oxford University Press
    In: Forestry
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    Publication Date: 2016-05-06
    Description: Forest degradation is a major issue for policy-makers that is exacerbated by no clear and globally accepted definition of the term. For forest managers, a loss of forest productive capacity is one form of forest degradation. We present a quantitative method to assess forest degradation from a productivity perspective. Our method uses a standard stocking chart and calculation methods based on standard forest inventory data, to derive a clear threshold value for stocking, below which a forest should be considered degraded. The method is illustrated using the example of a self-regenerating Nothofagus production forest type from Chile. For that forest type, we determined that harvesting trees to below a specific basal area relative to site type, resulted in a loss of resilience, an unpredictable shift in ecosystem state, and a degraded condition. Our method illustrates how over-harvesting can degrade the long-term productivity of a stand and forest resilience. Nevertheless, it is important to consider that forests can also be degraded from other perspectives, such as loss of biodiversity, carbon, or protective functions as a result of excessive disturbances. Ecosystem management requires that managers consider degradation from a range of perspectives. We see the quantified approach used here as a way to provide practitioners with, in part, a transition from sustained yield to ecosystem management with an ultimate objective of providing a pathway towards adaptive management of complex systems and avoiding degradation.
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    Analysis of costs and benefits of Asian longhorned beetle eradication in Italy (2016)
    Oxford University Press
    In: Forestry
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    Publication Date: 2016-05-06
    Description: The Asian longhorned beetle (ALB), Anoplophora glabripennis (Coleoptera: Cerambycidae), is one of the most harmful invasive species in Europe and North America, causing enormous economic damage to broadleaved trees growing in urban parks and gardens. As a quarantine species, everywhere it has been introduced ALB has led to the application of expensive eradication programmes often associated with additional indirect costs due to the loss of ornamental value connected with the presence of trees in urban areas. The aims of this article are to quantify the impact of ALB in terms of tree mortality and their ornamental value during the first year eradication of an infestation in Northern Italy, and to perform an economic assessment of the eradication programme vs inaction. During the first year of eradication 367 ALB infested trees were removed from the infestation area at a total cost of about 48 000, comprising scientific advice (21 per cent), tree survey (38 per cent) and plant removal (41 per cent). The ornamental value of the infested trees was assessed at about 850 per tree. The ALB eradication programme allowed a reduction of 52 per cent of the damage expected in the following year, corresponding to an ornamental value of about 300 000. The ornamental value of the saved trees was ~6 times higher than the costs for their protection.
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    Lifting free divisors (2016)
    Oxford University Press
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    Publication Date: 2016-05-07
    Description: Let $\varphi :X\to S$ be a morphism between smooth complex analytic spaces and let $f=0$ define a free divisor on $S$ . We prove that if the deformation space $T^1_{X/S}$ of $\varphi $ is a Cohen–Macaulay $\mathcal {O}_X$ -module of codimension 2, and all of the logarithmic vector fields for $f=0$ lift via $\varphi $ , then $f\circ \varphi =0$ defines a free divisor on $X$ ; this is generalized in several directions. Among applications we recover a result of Mond–van Straten, generalize a construction of Buchweitz–Conca, and show that a map $\varphi :\mathbb {C}^{n+1}\to \mathbb {C}^n$ with critical set of codimension 2 has a $T^1_{X/S}$ with the desired properties. Finally, if $X$ is a representation of a reductive complex algebraic group $G$ and $\varphi $ is the algebraic quotient $X\to S=X\!{/\!/} G$ with $X\!{/\!/} G$ smooth, then we describe sufficient conditions for $T^1_{X/S}$ to be Cohen–Macaulay of codimension 2. In one such case, a free divisor on $\mathbb {C}^{n+1}$ lifts under the operation of ‘castling’ to a free divisor on $\mathbb {C}^{n(n+1)}$ , partially generalizing work of Granger–Mond–Schulze on linear free divisors. We give several other examples of such representations.
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    Petites valeurs propres des fibres principaux en tores (2016)
    Oxford University Press
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    Publication Date: 2016-05-07
    Description: Let $M^n$ be a compact manifold of dimension $n$ with free $T^k$ -action. We consider collapsings of $M$ on $N=M/T^k$ such that the sectional curvature and diameter of $M$ satisfy $|K(M)|\leq a$ and $ {\rm diam}(M) 〈 d$ , and give examples of collapsings for all $k$ such that the first non-zero eigenvalue of Laplacian acting on 1-forms and 2-forms of $M$ are bounded above by $c(M)\cdot \hbox {inj}(M)^{2k}$ . Moreover, we prove that the first non-zero eigenvalue of Laplacian acting on 1-forms of all principal $T^k$ -bundle $M$ over $N$ is bounded below by $c(n,a,d,N)\cdot {\rm Vol}(M)^2$ and $c\cdot \hbox {inj}(M)^{2k}$ when $M$ collapses on $N$ .
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    Optimal control of elliptic PDEs at points (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these points, which means that our problem is related to ones with state constraints at points. The analysis and numerical analysis differs from when the fidelity is in the $L^2$ -norm because we need the state space to embed into the space of continuous functions. In this paper, we discretize the problem using two different piecewise linear finite element methods. For each discretization we use two different approaches to prove a priori $L^2$ -error estimates for the control. We discuss the differences between these methods and approaches, and present numerical results that agree with our analytical results.
    Print ISSN: 0272-4979
    Electronic ISSN: 1464-3642
    Topics: Mathematics
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    A simple scheme for the approximation of elastic vibrations of inextensible curves (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: A numerical scheme for the approximation of large vibration deformations of inextensible elastic curves is devised. Its unconditional stability and convergence under a regularity assumption on the velocities are demonstrated and numerical experiments are provided.
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    Hybrid expansion-contraction: a robust scaleable method for approximating the H{infty} norm (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: We present a new scaleable algorithm for approximating the $H_{\infty }$ norm, an important robust stability measure for linear dynamical systems with input and output. Our spectral-value-set-based method uses a novel hybrid expansion–contraction scheme that, under reasonable assumptions, is guaranteed to converge to a stationary point of the optimization problem defining the $H_{\infty }$ norm, and, in practice, typically returns local or global maximizers. We prove that the hybrid expansion–contraction method has a quadratic rate of convergence that is also confirmed in practice. In comprehensive numerical experiments, we show that our new method is not only robust but exceptionally fast, successfully completing a large-scale test set 25 times faster than an earlier method by Guglielmi, Gürbüzbalaban & Overton (2013, SIAM J. Matrix Anal. Appl. , 34 , 709–737), which occasionally breaks down far from a stationary point of the underlying optimization problem.
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    L2 best approximation of the elastic stress in the Arnold-Winther FEM (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: The first part of this paper enfolds a medius analysis for mixed finite element methods (FEMs) and proves a best-approximation result in $L^2$ for the stress variable independent of the error of the Lagrange multiplier under stability, compatibility and efficiency conditions. The second part applies the general result to the FEM of Arnold and Winther for linear elasticity: the stress error in $L^2$ is controlled by the $L^2$ best-approximation error of the true stress by any discrete function plus data oscillations. The analysis is valid without any extra regularity assumptions on the exact solution and also covers coarse meshes and Neumann boundary conditions. Further applications include Raviart–Thomas finite elements for the Poisson and the Stokes problems. The result has consequences for nonlinear approximation classes related to adaptive mixed FEMs.
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    Nonlocal diffusions on fractals: qualitative properties and numerical approximations (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: We propose a numerical method to approximate the solution of a nonlocal diffusion problem on a general setting of metric measure spaces. These spaces include, but are not limited to, fractals, manifolds and Euclidean domains. We obtain error estimates in $L^\infty (L^p)$ for $p=1,\infty $ under the sole assumption of the initial datum being in $L^p$ . An improved bound for the error in $L^\infty (L^1)$ is obtained when the initial datum is in $L^2$ . We also derive some qualitative properties of the solutions like stability, comparison principles and study the asymptotic behaviour as $t\to \infty $ . We finally present two examples on fractals: the Sierpinski gasket and the Sierpinski carpet, which illustrate on the effect of nonlocal diffusion for piece-wise constant initial datum.
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    Nonsmooth trust region algorithms for locally Lipschitz functions on Riemannian manifolds (2016)
    Oxford University Press
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    Publication Date: 2016-07-13
    Description: This paper presents a Riemannian trust region algorithm for unconstrained optimization problems with locally Lipschitz objective functions defined on complete Riemannian manifolds. To this end we define a function $\Phi :TM\rightarrow \mathbb {R}$ on the tangent bundle $TM$ , and at the $k$ th iteration, using the restricted function $\Phi |_{T_{x_k}M}$ , where $T_{x_k}M$ is the tangent space at $x_k$ , a local model function $Q_k$ that carries both first- and second-order information for the locally Lipschitz objective function $f:M\rightarrow \mathbb {R}$ on a Riemannian manifold $M$ , is defined and minimized over a trust region. We establish the global convergence of the proposed algorithm. Moreover, using the Riemannian $\varepsilon $ -subdifferential, a suitable model function is defined. Numerical experiments illustrate our results.
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