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  • Articles  (56,303)
  • Oxford University Press  (56,303)
  • National Academy of Sciences
  • Mathematics  (56,303)
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  • 1
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    Spectral flow, crossing forms and homoclinics of Hamiltonian systems (2015)
    Oxford University Press
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    Publication Date: 2015-08-05
    Description: We prove a spectral flow formula for one-parameter families of Hamiltonian systems under homoclinic boundary conditions, which relates the spectral flow to the relative Maslov index of a pair of curves of Lagrangians induced by the stable and unstable subspaces, respectively. Finally, we deduce sufficient conditions for bifurcation of homoclinic trajectories of one-parameter families of non-autonomous Hamiltonian vector fields.
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  • 2
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    The Schur-Horn problem for normal operators (2015)
    Oxford University Press
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    Publication Date: 2015-08-05
    Description: We consider the Schur–Horn problem for normal operators in von Neumann algebras, which is the problem of characterizing the possible diagonal values of a given normal operator based on its spectral data. For normal matrices, this problem is well known to be extremely difficult, and in fact, it remains open for matrices of size greater than $3$ . We show that the infinite-dimensional version of this problem is more tractable, and establish approximate solutions for normal operators in von Neumann factors of type I $_\infty$ , II, and III. A key result is an approximation theorem that can be seen as an approximate multivariate analogue of Kadison's Carpenter Theorem.
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  • 3
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    Asymptotic h-expansiveness rate of C{infty} maps (2015)
    Oxford University Press
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    Publication Date: 2015-08-05
    Description: We study the rate of convergence to zero of the tail entropy of $C^\infty$ maps. We give an upper bound of this rate in terms of the growth in $k$ of the derivative of order $k$ and give examples showing the optimality of the established rate of convergence. We also consider the case of multimodal maps of the interval. Finally, we prove that homoclinic tangencies give rise to $C^r$ $(r\geqslant 2)$ robustly non- $h$ -expansive dynamical systems.
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  • 4
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    Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras III (2015)
    Oxford University Press
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    Publication Date: 2015-08-05
    Description: Let ${{\mathscr {C}}}^0_{{{\mathfrak {g}}}}$ be the category of finite-dimensional integrable modules over the quantum affine algebra $U_{q}'({{\mathfrak {g}}})$ and let $R^{A_\infty }{\mbox {-}\mathrm {gmod}}$ denote the category of finite-dimensional graded modules over the quiver Hecke algebra of type $A_{\infty }$ . In this paper, we investigate the relationship between the categories ${{\mathscr {C}}}^0_{A_{N-1}^{(1)}}$ and ${{\mathscr {C}}}^0_{A_{N-1}^{(2)}}$ by constructing the generalized quantum affine Schur–Weyl duality functors ${\mathcal {F}}^{(t)}$ from $R^{A_\infty }{\mbox {-}\mathrm {gmod}}$ to ${{\mathscr {C}}}^0_{A_{N-1}^{(t)}}\ (t=1,2)$ .
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  • 5
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    Darmon points on elliptic curves over number fields of arbitrary signature (2015)
    Oxford University Press
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    Publication Date: 2015-08-05
    Description: We present new constructions of complex and $p$ -adic Darmon points on elliptic curves over base fields of arbitrary signature. We conjecture that these points are global and present numerical evidence to support our conjecture.
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  • 6
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    Tree-based methods for individualized treatment regimes (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: Individualized treatment rules recommend treatments on the basis of individual patient characteristics. A high-quality treatment rule can produce better patient outcomes, lower costs and less treatment burden. If a treatment rule learned from data is to be used to inform clinical practice or provide scientific insight, it is crucial that it be interpretable; clinicians may be unwilling to implement models they do not understand, and black-box models may not be useful for guiding future research. The canonical example of an interpretable prediction model is a decision tree. We propose a method for estimating an optimal individualized treatment rule within the class of rules that are representable as decision trees. The class of rules we consider is interpretable but expressive. A novel feature of this problem is that the learning task is unsupervised, as the optimal treatment for each patient is unknown and must be estimated. The proposed method applies to both categorical and continuous treatments and produces favourable marginal mean outcomes in simulation experiments. We illustrate it using data from a study of major depressive disorder.
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  • 7
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    Diagnostic studies in sufficient dimension reduction (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: Sufficient dimension reduction in regression aims to reduce the predictor dimension by replacing the original predictors with some set of linear combinations of them without loss of information. Numerous dimension reduction methods have been developed based on this paradigm. However, little effort has been devoted to diagnostic studies within the context of dimension reduction. In this paper we introduce methods to check goodness-of-fit for a given dimension reduction subspace. The key idea is to extend the so-called distance correlation to measure the conditional dependence relationship between the covariates and the response given a reduction subspace. Our methods require minimal assumptions, which are usually much less restrictive than the conditions needed to justify the original methods. Asymptotic properties of the test statistic are studied. Numerical examples demonstrate the effectiveness of the proposed approach.
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  • 8
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    Bayesian sensitivity analysis with the Fisher-Rao metric (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: We propose a geometric framework to assess sensitivity of Bayesian procedures to modelling assumptions based on the nonparametric Fisher–Rao metric. While the framework is general, the focus of this article is on assessing local and global robustness in Bayesian procedures with respect to perturbations of the likelihood and prior, and on the identification of influential observations. The approach is based on a square-root representation of densities, which enables analytical computation of geodesic paths and distances, facilitating the definition of naturally calibrated local and global discrepancy measures. An important feature of our approach is the definition of a geometric $\epsilon$ -contamination class of sampling distributions and priors via intrinsic analysis on the space of probability density functions. We demonstrate the applicability of our framework to generalized mixed-effects models and to directional and shape data.
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  • 9
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    Efficient estimation of nonparametric genetic risk function with censored data (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: With the discovery of an increasing number of causal genes for complex human disorders, it is crucial to assess the genetic risk of disease onset for individuals who are carriers of these causal mutations and to compare the distribution of the age-at-onset for such individuals with the distribution for noncarriers. In many genetic epidemiological studies that aim to estimate causal gene effect on disease, the age-at-onset of disease is subject to censoring. In addition, the mutation carrier or noncarrier status of some individuals may be unknown, due to the high cost of in-person ascertainment by collecting DNA samples or because of the death of older individuals. Instead, the probability of such individuals’ mutation status can be obtained from various other sources. When mutation status is missing, the available data take the form of censored mixture data. Recently, various methods have been proposed for risk estimation using such data, but none is efficient for estimating a nonparametric distribution. We propose a fully efficient sieve maximum likelihood estimation method, in which we estimate the logarithm of the hazard ratio between genetic mutation groups using B-splines, while applying nonparametric maximum likelihood estimation to the reference baseline hazard function. Our estimator can be calculated via an expectation-maximization algorithm which is much faster than existing methods. We show that our estimator is consistent and semiparametrically efficient and establish its asymptotic distribution. Simulation studies demonstrate the superior performance of the proposed method, which is used to estimate the distribution of the age-at-onset of Parkinson's disease for carriers of mutations in the leucine-rich repeat kinase 2, LRRK2, gene.
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  • 10
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    Efficient computation of smoothing splines via adaptive basis sampling (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: Smoothing splines provide flexible nonparametric regression estimators. However, the high computational cost of smoothing splines for large datasets has hindered their wide application. In this article, we develop a new method, named adaptive basis sampling, for efficient computation of smoothing splines in super-large samples. Except for the univariate case where the Reinsch algorithm is applicable, a smoothing spline for a regression problem with sample size n can be expressed as a linear combination of n basis functions and its computational complexity is generally O ( n 3 ). We achieve a more scalable computation in the multivariate case by evaluating the smoothing spline using a smaller set of basis functions, obtained by an adaptive sampling scheme that uses values of the response variable. Our asymptotic analysis shows that smoothing splines computed via adaptive basis sampling converge to the true function at the same rate as full basis smoothing splines. Using simulation studies and a large-scale deep earth core-mantle boundary imaging study, we show that the proposed method outperforms a sampling method that does not use the values of response variables.
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  • 11
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    Entropy testing for nonlinear serial dependence in time series (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: We propose tests for nonlinear serial dependence in time series under the null hypothesis of general linear dependence, in contrast to the more widely studied null hypothesis of independence. The approach is based on combining an entropy dependence metric, which possesses many desirable properties and is used as a test statistic, with a suitable extension of surrogate data methods, a class of Monte Carlo distribution-free tests for nonlinearity, and a smoothed sieve bootstrap scheme. We show how, in the same way as the autocorrelation function is used for linear models, our tests can in principle be employed to detect the lags at which a significant nonlinear relationship is present. We prove the asymptotic validity of the proposed procedures and the corresponding inferences. The small-sample performance of the tests in terms of power and size is assessed through a simulation study. Applications to real datasets of different kinds are also presented.
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  • 12
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    Robust estimation under heavy contamination using unnormalized models (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: Contamination caused by outliers is inevitable in data analysis, and robust statistical methods are often needed. In this paper we develop a new approach for robust data analysis on the basis of scoring rules. A scoring rule is a discrepancy measure to assess the quality of probabilistic forecasts. We propose a simple method of estimating not only parameters in the statistical model but also the contamination ratio, i.e., the ratio of outliers. The outliers are detected based on the estimated contamination ratio. For this purpose, we use scoring rules with extended statistical models called unnormalized models. Regression problems are also considered. We study complex heterogeneous contamination wherein the contamination ratio in a response variable may depend on covariate variables, and propose a simple method to estimate a robust regression function and expected contamination ratio. Simulation studies demonstrate the effectiveness of our method.
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  • 13
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    A cautionary note on robust covariance plug-in methods (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: The sample covariance matrix, which is well known to be highly nonrobust, plays a central role in many classical multivariate statistical methods. A popular way of making such multivariate methods more robust is to replace the sample covariance matrix with some robust scatter matrix. The aim of this paper is to point out that multivariate methods often require that certain properties of the covariance matrix hold also for the robust scatter matrix in order for the corresponding robust plug-in method to be a valid approach, but that not all scatter matrices possess the desired properties. Plug-in methods for independent components analysis, observational regression and graphical modelling are considered in more detail. For each case, it is shown that replacing the sample covariance matrix with a symmetrized robust scatter matrix yields a valid robust multivariate procedure.
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  • 14
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    Big data and precision (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: So-called big data are likely to have complex structure, in particular implying that estimates of precision obtained by applying standard statistical procedures are likely to be misleading, even if the point estimates of parameters themselves may be reasonably satisfactory. While this possibility is best explored in the context of each special case, here we outline a fairly general representation of the accretion of error in large systems and explore the possible implications for the estimation of regression coefficients. The discussion raises issues broadly parallel to the distinction between short-range and long-range dependence in time series theory.
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  • 15
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    Hysteretic autoregressive time series models (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: This paper extends the classical two-regime threshold autoregressive model by introducing hysteresis to its regime-switching structure, which leads to a new model: the hysteretic autoregressive model. The proposed model enjoys the piecewise linear structure of a threshold model but has a more flexible regime switching mechanism. A sufficient condition is given for geometric ergodicity. Conditional least squares estimation is discussed, and the asymptotic distributions of its estimators and information criteria for model selection are derived. Simulation results and an example support the model.
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  • 16
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    A note on convergence of an iterative algorithm for semiparametric odds ratio models (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: This paper points out an error in Davidov and Iliopoulos's ( Biometrika 100 , 778–80) proof of convergence of an iterative algorithm for the proportional likelihood ratio model. It is shown that the iterative algorithm increases the likelihood in each iteration and converges under mild additional conditions when the odds ratio function is bounded.
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  • 17
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    Order selection in finite mixture models: complete or observed likelihood information criteria? (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: Choosing the number of components in a finite mixture model is a challenging task. In this article, we study the behaviour of information criteria for selecting the mixture order, based on either the observed likelihood or the complete likelihood including component labels. We propose a new observed likelihood criterion called aic mix , which is shown to be order consistent. We further show that when there is a nontrivial level of classification uncertainty in the true model, complete likelihood criteria asymptotically underestimate the true number of components. A simulation study illustrates the potentially poor finite-sample performance of complete likelihood criteria, while aic mix and the Bayesian information criterion perform strongly regardless of the level of classification uncertainty.
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  • 18
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    Outlier detection for high-dimensional data (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: Outlier detection is an integral component of statistical modelling and estimation. For high-dimensional data, classical methods based on the Mahalanobis distance are usually not applicable. We propose an outlier detection procedure that replaces the classical minimum covariance determinant estimator with a high-breakdown minimum diagonal product estimator. The cut-off value is obtained from the asymptotic distribution of the distance, which enables us to control the Type I error and deliver robust outlier detection. Simulation studies show that the proposed method behaves well for high-dimensional data.
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  • 19
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    Nonparametric Bayesian testing for monotonicity (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: This paper adopts a nonparametric Bayesian approach to testing whether a function is monotone. Two new families of tests are constructed. The first uses constrained smoothing splines with a hierarchical stochastic-process prior that explicitly controls the prior probability of monotonicity. The second uses regression splines together with two proposals for the prior over the regression coefficients. Via simulation, the finite-sample performance of the tests is shown to improve upon existing frequentist and Bayesian methods. The asymptotic properties of the Bayes factor for comparing monotone versus nonmonotone regression functions in a Gaussian model are also studied. Our results significantly extend those currently available, which chiefly focus on determining the dimension of a parametric linear model.
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  • 20
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    Benchmarked empirical Bayes methods in multiplicative area-level models with risk evaluation (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: The paper develops hierarchical empirical Bayes and benchmarked hierarchical empirical Bayes estimators of positive small area means under multiplicative models. The usual benchmarking requirement is that the small area estimates, when aggregated, should equal the direct estimates for the larger geographical areas. However, while estimating positive small area parameters, the conventional squared error or weighted squared error loss subject to the usual benchmark constraint may not produce positive estimators, so it is necessary to seek other loss functions. We consider a multiplicative model for the original data for estimating positive small area means, and suggest a variant of the Kullback–Leibler divergence as a loss function. The prediction errors of the suggested hierarchical empirical Bayes estimators are investigated asymptotically, and their second-order unbiased estimators are provided. Bootstrapped estimators of these prediction errors for both hierarchical empirical Bayes and benchmarked hierarchical empirical Bayes estimators are also given. The performance of the suggested procedures is investigated through simulation as well as with an example.
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  • 21
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    Semiparametric causal inference in matched cohort studies (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: Odds ratios can be estimated in case-control studies using standard logistic regression, ignoring the outcome-dependent sampling. In this paper we discuss an analogous result for treatment effects on the treated in matched cohort studies. Specifically, in studies where a sample of treated subjects is observed along with a separate sample of possibly matched controls, we show that efficient and doubly robust estimators of effects on the treated are computationally equivalent to standard estimators, which ignore the matching and exposure-based sampling. This is not the case for general average effects. We also show that matched cohort studies are often more efficient than random sampling for estimating effects on the treated, and derive the optimal number of matches for a given set of matching variables. We illustrate our results via simulation and in a matched cohort study of the effect of hysterectomy on the risk of cardiovascular disease.
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  • 22
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    Sieve maximum likelihood regression analysis of dependent current status data (2015)
    Oxford University Press
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    Publication Date: 2015-08-21
    Description: Current status data occur in contexts including demographic studies and tumorigenicity experiments. In such cases, each subject is observed only once and the failure time of interest is either left- or right-censored (Kalbfleisch & Prentice, 2002). Many methods have been developed for the analysis of such data (Huang, 1996; Sun, 2006), most of which assume that the failure time and the observation time are independent completely or given covariates. In this paper, we present a sieve maximum likelihood approach for current status data when independence does not hold. A copula model and monotone I-splines are used and the asymptotic properties of the resulting estimators are established. In particular, the estimated regression parameters are shown to be semiparametrically efficient. An illustrative example is provided.
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  • 23
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    Asymptotic stability of the black soliton for the Gross-Pitaevskii equation (2015)
    Oxford University Press
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    Publication Date: 2015-08-05
    Description: We introduce a new framework for the analysis of the stability of solitons for the one-dimensional Gross–Pitaevskii equation. In particular, we establish the asymptotic stability of the black soliton with zero speed.
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  • 24
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    Ikeda's conjecture on the period of the Duke-Imamoglu-Ikeda lift (2015)
    Oxford University Press
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    Publication Date: 2015-08-05
    Description: Let $k$ and $n$ be positive even integers. For a cuspidal Hecke eigenform $h$ in the Kohnen plus space of weight $k-n/2+1/2$ for $\varGamma _0(4),$ let $I_n(h)$ be the Duke–Imamo $\bar {{\text {g}}}$ lu–Ikeda lift of $h$ in the space of cusp forms of weight $k$ for ${\rm Sp}_n({{\bf{Z}}}),$ and $f$ be the primitive form of weight $2k-n$ for ${\rm SL}_2({{\bf{Z}}})$ corresponding to $h$ under the Shimura correspondence. We then express the ratio $\displaystyle {\langle I_n(h), I_n(h) \rangle / \langle h, h \rangle }$ of the period of $I_n(h)$ to that of $h$ in terms of special values of certain $L$ -functions of $f$ . This proves the conjecture proposed by Ikeda concerning the period of the Duke–Imamo $\bar {{\text {g}}}$ lu–Ikeda lift.
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  • 25
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    HOMOLOGICAL FINITENESS PROPERTIES OF WREATH PRODUCTS (2015)
    Oxford University Press
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    Publication Date: 2015-06-05
    Description: We study the homological finiteness properties ${\rm FP}_m$ of wreath products $\Gamma = H \wr _X G$ . We show that, when $H$ has infinite abelianization, $\Gamma$ is of type ${\rm FP}_m$ if and only if both $G$ and $H$ have type ${\rm FP}_m$ and $G$ acts (diagonally) on $X^i$ with stabilizers of type ${\rm FP}_{m-i}$ and with finitely many orbits for all $1 \leq i \leq m$ . If furthermore $H$ is torsion-free, we give a criterion for $\Gamma$ to be Bredon- ${\rm FP}_m$ with respect to the class of finite subgroups of $\Gamma$ . Finally, when $H$ has infinite abelianization and $\chi : \Gamma \to \mathbb {R}$ is a non-zero homomorphism with $\chi (H) = 0$ , we classify when $[\chi ]$ belongs to the Bieri–Neumann–Strebel–Renz invariant $\Sigma ^m(\Gamma , \mathbb {Z})$ .
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
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    A TORELLI-TYPE PROBLEM FOR LOGARITHMIC BUNDLES OVER PROJECTIVE VARIETIES (2015)
    Oxford University Press
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    Publication Date: 2015-06-05
    Description: We investigate the logarithmic bundles associated to arrangements of hypersurfaces with a fixed degree in a smooth projective variety. We then specialize to the case when the variety is a quadric hypersurface and a multiprojective space to prove a Torelli-type theorem in some cases.
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  • 27
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    HIGHER DIFFERENTIABILITY FOR SOLUTIONS OF A CLASS OF PARABOLIC SYSTEMS WITH L1, {theta}- DATA (2015)
    Oxford University Press
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    Publication Date: 2015-06-05
    Description: We study the higher differentiability of the very weak solution of the Cauchy–Dirichlet problem associated to the linear parabolic system with Hölder continuous coefficients and L 1 right-hand side of the form $$\begin{align*} \dfrac{\partial u}{\partial t} -{\rm div}(A(x,t)Du) & = \mu \quad \mbox{in } \Omega \,{\times}\,]0, T[,\\ u & = 0 \quad \mbox{on } \partial \Omega \,{\times}\,]0, T[,\\ u & = 0 \quad \mbox{on } \Omega \times \{ 0\}. \end{align*}$$
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  • 28
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    A review of the use of multicriteria and multi-objective models in maintenance and reliability (2015)
    Oxford University Press
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    Publication Date: 2015-06-09
    Description: This article evaluates 186 papers, published between 1978 and 2013 in 16 representative scientific journals, related to maintenance and reliability problems that were tackled from a multi-criteria (MC) perspective. An overview and insights are presented. This study may be useful to researchers and others concerned with maintenance and reliability who seek not only to understand the potential of MC and multi-objective models but also to develop and apply an MC decision model to help solve a real problem in these areas. There are some discussions on some principles for the application of MC in maintenance and reliability and some guidance on how to choose a suitable MC method is given, based on previous applications.
    Print ISSN: 1471-678X
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    Topics: Mathematics
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  • 29
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    Explicit formulas for pricing credit-linked notes with counterparty risk under reduced-form framework (2015)
    Oxford University Press
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    Publication Date: 2015-06-09
    Description: A credit-linked note (CLN) is a type of credit derivative, constructed with a bond and an embedded credit default swap, which allows the issuer to transfer a specific credit risk to credit investors. In this paper, we model CLNs with and without counterparty risk in the reduced-form framework. For CLNs with counterparty risk, we consider two different scenarios, i.e. the issuer of CLNs and reference assets have either positive correlation or negative correlation. Assuming the interest rate follows the Cox–Ingersoll–Ross (CIR) model (Cox et al ., 1985) and the default events mainly depend on the interest rate, we model the two different correlations. Explicit formulas for value functions are obtained through a partial differential equation approach. In addition, counterparty valuation adjustment and the dependence on related parameters are also investigated.
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    'KL'-gain adaptation for attractive ellipsoid method (2015)
    Oxford University Press
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    Publication Date: 2015-09-15
    Description: This paper presents the development of an adaptive state estimator and an output controller based on the attractive ellipsoid method (AEM) for a class of uncertain non-linear systems (quasi-Lipschitz with external perturbations). The proposed method guarantees that, under a specific persistent excitation condition, the controlled system trajectories converge to an ellipsoid having a smaller trace of the corresponding inverse ellipsoidal matrix comparing to classical AEM without adaptation. An underactuated vertical double pendulum is considered as an experimental illustrative example of the suggested approach.
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    Sub-optimal stabilizing controller design for non-linear slowly varying systems: application in a benchmark system (2015)
    Oxford University Press
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    Publication Date: 2015-09-15
    Description: In this paper, non-linear time-varying systems with slowly varying parameters are considered. Using slowly varying control Lyapunov function and considering a cost function, a controller (with closed-form structure) is presented which guarantees asymptotic stability of the closed-loop non-linear slowly varying system. Moreover, the Hamilton–Jacobi–Bellman equation is analysed to show that the proposed controller is a sub-optimal controller and the response of the closed-loop system may be very close to its optimal solution. Additionally, in order to show the applicability of the proposed method, it is applied to the time-varying inertia pendulum, which is one of the famous benchmarks among the non-linear time-varying systems. Then, the efficiency of the designed controller is compared with that of a numerical optimal controller, which is called, ‘receding horizon generalization of point-wise min-norm controller’. Simulation results demonstrate the applicability and efficiency of the proposed method.
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    Static output feedback sliding mode controller design for minimum phase uncertain systems (2015)
    Oxford University Press
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    Publication Date: 2015-09-15
    Description: This paper addresses the problem of designing a static output feedback sliding mode control algorithm for linear MIMO systems with mismatched parameter uncertainties and matched perturbations. Once the system is in the sliding mode, the proposed output-dependent sliding variable can guarantee robust stability of the closed-loop system. The existence condition of the sliding variable is determined by solving the coupled algebraic Riccati equations which are involved with the original system parameters. The developed control law having the min–max property can guarantee that the system states are globally driven to and are finally maintained on the sliding variable in finite time. The high-gain control problem can be effectively avoided. The feasibility of the proposed method is demonstrated by simulation results.
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    Regional boundary observability of semilinear hyperbolic systems: sectorial approach (2015)
    Oxford University Press
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    Publication Date: 2015-09-15
    Description: The objective of this paper is to study the notion of regional observability of a distributed parameter system governed by semilinear hyperbolic equations. This original concept is interested in the reconstruction of the state only on a subregion of the boundary of the system evolution domain . We give definition and some properties of this notion and we show that under some hypothesis, the regional boundary observability is guarantied. We use the analytical case by sectorial property of the considered dynamic operator and converted to a fixed point problem, and we show that it is possible to reconstruct such a state on a desired subregion . This approach leads to interesting results which are performed through numerical example and simulations.
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    Distributed robust consensus control for nonlinear multi-agent systems by using output regulation approach (2015)
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    Publication Date: 2015-09-15
    Description: This paper deals with the distributed robust output regulation problem for the multi-agent systems with general nonlinear dynamics and uncertainty parameters. Assume that the information of active leaders or environmental disturbances cannot be completely measurable for all other agents. By employing the centre manifold theory and characteristics of the agents’ communication, the nonlinear distributed dynamic feedback controllers are designed to make the agents asymptotically track the references or reject the disturbance signals, which are generated by the exosystem. Two numerical examples are provided to show the effectiveness of the main results.
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    Event-triggered consensus of multi-agent systems under jointly connected topology (2015)
    Oxford University Press
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    Publication Date: 2015-09-15
    Description: This paper investigates event-triggered leaderless and leader-following consensus problems of multi-agent systems under jointly connected topology. A state-dependent event condition is proposed for each agent, which only relies on its own state and the last sampled data of itself and its neighbours. Based on the Lyapunov technique and algebraic graph theory, the designed event-triggered control strategies are proved to solve the leaderless and leader-following consensus problems when the topology is jointly connected. Moreover, such strategies can exclude Zeno-behaviour. Simulations illustrate the effectiveness of the theoretical results.
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    Stabilization of one-dimensional wave equations coupled with an ODE system on general tree-shaped networks (2015)
    Oxford University Press
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    Publication Date: 2015-09-15
    Description: By the theory of Sturm–Liouville eigenvalue problems, it is shown that the stability of one-dimensional wave equations with variable coefficients coupled with an ordinary differential equation (ODE) system on general tree-shaped networks is equivalent to that of its subsystem (called the base system). Thus, it is proved that the coupled system can arrive at asymptotical stability, if, for every interior vertex of the subsystem, the spectra of any two edges joined one common interior vertex of the subsystem are disjoint. Especially, the coupled system with one fixed root is exponentially stable. In the end, a star with three edges and a tree-shaped networks with 10 edges are given to verify the theoretical results.
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    On the synthesis of H{infty} consensus for multi-agent systems (2015)
    Oxford University Press
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    Publication Date: 2015-09-15
    Description: This paper studies the H consensus problem of multi-agent systems by means of a simultaneous stabilization approach. It is shown that the H consensus design problem for n coupled agents can be equivalently characterized as a problem of the simultaneous H stabilization of n – 1 independent subsystems. A new consensus analysis condition is obtained by investigating the corresponding simultaneous H stabilization problem. Based upon the analysis condition, a necessary and sufficient condition is derived to guarantee the consensus of multi-agent systems with a prescribed H performance, where the controller gain matrix is not coupled with the Lyapunov matrices, but parametrized by a positive-definite matrix. Iterative convex optimization approaches are further developed to solve the synthesis condition and to choose the initial values. Finally, a numerical example is given to show the applicability of the results.
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    On controllability of second-order impulsive neutral integrodifferential systems with infinite delay (2015)
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    Publication Date: 2015-09-15
    Description: This article is concerned with the controllability of damped second-order impulsive neutral integrodifferential systems with infinite delay in Banach spaces. A set of sufficient conditions for the controllability of such systems are formulated by using a fixed point analysis approach. In particular, the compactness condition on the cosine family of operators appearing in various literatures is not required here. At last, an example is given to illustrate the obtained result.
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    Numerical solution of the time-delayed optimal control problems with hybrid functions (2015)
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    Publication Date: 2015-09-15
    Description: We consider an approximation scheme using hybrid functions for solving time-delayed optimal control problems with terminal inequality constraints. Using a Páde approximation, the problem is first transformed into one without a time-delayed argument. A computational method based on hybrid functions in time-domain is then proposed for solving the obtained non-delay optimal control problem. Hybrid functions integral operational matrix and direct collocation method are utilized to find the approximated optimal trajectory and the optimal control law of the original problem. Numerical results are also given to demonstrate the efficiency of the method.
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    D-stability performance analysis and stabilization of Sun-Earth L2 formation flying system (2015)
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    Publication Date: 2015-09-15
    Description: This paper investigates the problem of D-stability performance of an L 2 point formation control system with parametric uncertainties. A Quasi linear parameter varying (QLPV) model is introduced for the L 2 point formation flying, based on which a nonlinear control strategy is developed via the polynomial eigenstructure assignment (PEA) approach. The designed controller can guarantee the closed-loop system with invariant performance over a wide range of conditions due to its special structure with varying parameters. The robust D-stability of the multiple input and multiple output (MIMO) system is also addressed. It is shown that the D-stability performance of the L 2 point formation control system with parametric uncertainties can be ensured by using PEA controller. Finally, a simulation of formation flying is performed to illustrate the effectiveness of the proposed control approach.
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    Optimal timing control of switched stochastic systems (2015)
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    Publication Date: 2015-09-15
    Description: This paper considers an optimal control problem for switched stochastic systems. The controlled parameter consists of the switching times, and the cost criterion has the form of the mixed integral and endpoint cost terms of performance functions defined on the system's state trajectory. An approach to finding the optimal switching times is proposed. First, we derive the derivative of the cost with respect to the switching time for one switching time case. Then, for the problem with multi-switching times, we present the corresponding gradient formula. The obtained formulas have an especially simple form and can be directly used in gradient descent algorithms to locate the optimal switching instants. Finally, the validity of the proposed method is demonstrated by two numerical examples.
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    On the K-theory of truncated polynomial rings in non-commuting variables (2015)
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    Publication Date: 2015-09-19
    Description: We compute the algebraic $K$ -theory of the non-commutative ring $k\langle x_1,\ldots ,x_n \rangle /(m^a)$ when $k$ is a perfect field of positive characteristic and $m=(x_1,\ldots ,x_n)$ . We express the answer in terms of the truncation poset Witt vectors developed in Angeltveit [‘Witt vectors and truncation posets’, Preprint, 2014, arXiv:1409.4156].
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    Grassmannian BGG complexes and Hodge numbers of irregular varieties (2015)
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    Publication Date: 2015-09-19
    Description: In this paper, we investigate the exactness of the Grassmannian Bernstein-Gel’fand-Gel’fand complexes introduced in a previous work of the author, and obtain some inequalities between some Hodge numbers of some irregular varieties. In particular, we obtain sharp lower bounds for the Hodge numbers of smooth subvarieties of Abelian varieties, as well as some improvements of results of Lazarsfeld-Popa and Lombardi concerning threefolds and fourfolds.
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    On acylindrical hyperbolicity of groups with positive first {ell}2-Betti number (2015)
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    Publication Date: 2015-09-19
    Description: We prove that every finitely presented group with positive first $\ell ^2$ -Betti number that virtually surjects onto $\mathbb Z$ is acylindrically hyperbolic. In particular, this implies acylindrical hyperbolicity of finitely presented residually finite groups with positive first $\ell ^2$ -Betti number as well as groups of deficiency at least $2$ .
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    Yet again on two examples by Iyama and Yoshino (2015)
    Oxford University Press
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    Publication Date: 2015-09-19
    Description: We give an elementary proof of Iyama–Yoshino's classification of rigid maximal Cohen-Macaulay modules on Veronese embeddings in $\mathbb P ^9$ .
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    Dimension of monopoles on asymptotically conic 3-manifolds (2015)
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    Publication Date: 2015-09-19
    Description: The virtual dimensions of both framed and unframed SU(2) magnetic monopoles on asymptotically conic 3-manifolds are obtained by computing the index of a Fredholm extension of the associated deformation complex. The unframed dimension coincides with the one obtained by Braam for conformally compact 3-manifolds. The computation follows from the application of a Callias-type index theorem.
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    The Łojasiewicz exponent of semiquasihomogeneous singularities (2015)
    Oxford University Press
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    Publication Date: 2015-09-19
    Description: Let $f : (\mathbb {C}^n, 0) \rightarrow (\mathbb {C}, 0)$ be a semiquasihomogeneous function. We give a formula for the local Łojasiewicz exponent ${\mathcal L}_0 (f)$ of $f$ , in terms of weights of $f$ . In particular, in the case of a quasihomogeneous (QH) isolated singularity $f$ , we generalize a formula for ${\mathcal L}_0 (f)$ of Krasiłski, Oleksik and Płoski from 3 to $n$ dimensions. This was previously announced in the paper [ 19 ] of Tan, Yau and Zuo [Łojasiewicz inequality for weighted homogeneous polynomial with isolated singularity, Proc. Amer. Math. Soc. 138 (2010) 3975–3984], but as a matter of fact it was not proved correctly there, as noted by the AMS reviewer Tadeusz Krasiłski. As a consequence of our result, we obtain that the Łojasiewicz exponent is invariant in topologically trivial families of singularities coming from a QH germ. This is an affirmative partial answer to Teissier's conjecture.
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    Higher convexity of coamoeba complements (2015)
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    Publication Date: 2015-09-19
    Description: We show that the complement of the closure of the coamoeba of a variety of codimension $k + 1$ is $k$ -convex, in the sense of Gromov and Henriques. This generalizes a result of Nisse for hypersurface coamoebas. We use this to show that the complement of the nonarchimedean coamoeba of a variety of codimension $k + 1$ is $k$ -convex.
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    Lagrange's theorem for continued fractions on the Heisenberg group (2015)
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    Publication Date: 2015-09-19
    Description: We prove an analog of Lagrange's theorem for continued fractions on the Heisenberg group: points with an eventually periodic continued fraction expansion are those that satisfy a particular type of quadratic form, and vice-versa.
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    Lower bound of Ricci flow's existence time (2015)
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    Publication Date: 2015-09-19
    Description: Let $(M^n, g)$ be a compact $n$ -dimensional ( $n\geq 2$ ) manifold with nonnegative Ricci curvature, and if $n\geq 3,$ then we assume that $(M^n, g)\times \mathbb {R}$ has nonnegative isotropic curvature. The lower bound of the Ricci flow's existence time on $(M^n, g)$ is proved. This provides an alternative proof for the uniform lower bound of a family of closed Ricci flows' maximal existence times, which was first proved by E. Cabezas-Rivas and B. Wilking. We also get an interior curvature estimate for $n= 3$ under ${\rm Rc}\geq 0$ assumption among others. Combining these results, we proved the short-time existence of the Ricci flow on a large class of three-dimensional open manifolds, which admit some suitable exhaustion covering and have nonnegative Ricci curvature.
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    Uniformly bounded orthonormal polynomials on the sphere (2015)
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    Description: Given any $\varepsilon 〉 0$ , we construct an orthonormal system of $n_k$ uniformly bounded polynomials of degree at most $k$ on the unit sphere in $\mathbb {R}^{m+1}$ where $n_k$ is bigger than $1-\varepsilon $ times the dimension of the space of polynomials of degree at most $k$ . Similarly, we construct an orthonormal system of sections of powers $A^k$ of a positive holomorphic line bundle on a compact Kähler manifold with cardinality bigger than $1-\varepsilon $ times the dimension of the space of global holomorphic sections to $A^k$ .
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    Fermat's last theorem: basic tools (Translations of Mathematical Monographs 243) By Takeshi Saito * Fermat's last theorem: the proof (Translations of Mathematical Monographs 245) By Takeshi Saito (2015)
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    Publication Date: 2015-09-19
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    Marstrand's density theorem in the Heisenberg group (2015)
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    Publication Date: 2015-09-19
    Description: We prove that if $\mu $ is a Radon measure on the Heisenberg group $\mathbb {H}^n$ such that the density $\Theta ^s(\mu ,\cdot )$ , computed with respect to the Korányi metric $d_H$ , exists and is positive and finite on a set of positive $\mu $ measure, then $s$ is an integer. The proof relies on an analysis of uniformly distributed measures on $(\mathbb {H}^n,d_H)$ . We provide a number of examples of such measures, illustrating both the similarities and the striking differences of this sub-Riemannian setting from its Euclidean counterpart.
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    New irreducible weight modules over Witt algebras with infinite-dimensional weight spaces (2015)
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    Publication Date: 2015-09-19
    Description: Let $d 〉 1$ be an integer. In 1986, Shen defined a class of weight modules $F^\alpha _b(V)$ over the Witt algebra $\mathcal {W}_d$ for $\alpha \in {\mathbb C} ^d$ , $b\in {{\mathbb C}}$ , and an irreducible module $V$ over the general linear Lie algebra $\mathfrak {gl} _d$ on which the identity matrix acts as multiplication by $b$ . In 1996, Eswara Rao determined necessary and sufficient conditions for these modules to be irreducible when $V$ is finite-dimensional. In this note, we will determine necessary and sufficient conditions for all these modules $F^\alpha _b(V)$ to be irreducible where $V$ is not necessarily finite-dimensional. In this way, we obtain a large new family of irreducible $\mathcal {W}_d$ -modules with infinite-dimensional weight spaces.
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    The ER(n)-cohomology of BO(q) and real Johnson-Wilson orientations for vector bundles (2015)
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    Publication Date: 2015-09-19
    Description: Using the Bockstein spectral sequence developed previously by the authors, we compute the ring $ER(n)^\ast (BO(q))$ explicitly. We then use this calculation to show that the ring spectrum $MO[2^{n+1}]$ is $ER(n)$ -orientable (but not $ER(n+1)$ -orientable), where $MO[2^{n+1}]$ is defined as the Thom spectrum for the self-map of $BO$ given by multiplication by $2^{n+1}$ .
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    Commuting probabilities of finite groups (2015)
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    Description: The commuting probability of a finite group is defined to be the probability that two randomly chosen group elements commute. Let ${{\mathcal P}}\subset (0,1]$ be the set of commuting probabilities of all finite groups. We prove that every point of ${{\mathcal P}}$ is nearly an Egyptian fraction of bounded complexity. As a corollary, we deduce two conjectures of Keith Joseph from 1977: all limit points of ${{\mathcal P}}$ are rational, and ${{\mathcal P}}$ is well ordered by $ 〉 $ . We also prove analogous theorems for bilinear maps of abelian groups.
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    A note on some new classes of constitutive relations for elastic bodies (2015)
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    Publication Date: 2015-09-19
    Description: The class of elastic bodies, that is bodies incapable of dissipation in whatever motion that they undergo, has been significantly enlarged recently (see Rajagopal 2003, On implicit constitutive theories. Appl. Math. , 48 , 279–319; Rajagopal 2007, The elasticity of elasticity. Z. Angew. Math. Phys. 58 , 309–317; Rajagopal, K. R. & Srinivasa, A. R. 2007, On the response of non-dissipative solids. Proc. R. Soc. Lond. A , 463 , 357–367). The new classes include fully implicit constitutive relations for the stress and the deformation gradient, and the interesting sub-class wherein the Cauchy–Green tensor or the linearized strain tensor bears a non-linear relationship to the stress. While a fully thermodynamic treatment of such elastic bodies, when defined through implicit constitutive relations between the Piola stress and the Green–St. Venant strain, within a 3D framework has been carried out (see Rajagopal, K. R. & Srinivasa, A. R. 2007, On the response of non-dissipative solids, Proc. R. Soc. Lond. A , 463 , 357–367), other possible implicit relationships between other stress and kinematic measures have not been investigated. This paper is devoted to the determination of the consequences of thermodynamics on the new class of elastic bodies, when they are expressed through implicit relations for different stress and stretch/strain measures.
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    Travelling wave solutions for Kolmogorov-type delayed lattice reaction-diffusion systems (2015)
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    Publication Date: 2015-09-19
    Description: This work investigates the existence and non-existence of travelling wave solutions for Kolmogorov-type delayed lattice reaction–diffusion systems. Employing the cross iterative technique coupled with the explicit construction of upper and lower solutions in the theory of quasimonotone dynamical systems, we can find two threshold speeds $c^* $ and $c_* $ with $c^* \geq c_* 〉 0.$ If the wave speed is greater than $c^* ,$ then we establish the existence of travelling wave solutions connecting two different equilibria. On the other hand, if the wave speed is smaller than $c_* ,$ we further prove the non-existence result of travelling wave solutions. Finally, several ecological examples including one-species, two-species and three-species models with various functional responses and time delays are presented to illustrate the analytical results.
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    Global asymptotic stability of stochastic Lotka-Volterra systems with infinite delays (2015)
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    Description: In this paper, sufficient criteria for global asymptotic stability of a general stochastic non-autonomous Lotka–Volterra system with infinite delays are established. Then these criteria are applied to a competitive system, a predator–prey system and a cooperative system to demonstrate their applicability and effectiveness. Some recent results are extended and improved.
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    Second method of Lyapunov and almost periodic solutions for impulsive differential systems of fractional order (2015)
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    Publication Date: 2015-09-19
    Description: In the paper, the problem of existence of almost periodic solutions to non-linear impulsive systems of Caputo fractional order is addressed. Sufficient conditions for stability of almost periodic solutions are also established. The investigations are carried out by using of a fractional comparison principle and the Lyapunov's function method. We apply our results to an impulsive cellular neural network model of fractional order.
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    Subgaussian 1-cocycles on discrete groups (2015)
    Oxford University Press
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    Publication Date: 2015-09-20
    Description: We prove the $L_p$ Poincaré inequalities with constant $C\sqrt {p}$ for $1$ -cocycles on countable discrete groups under Bakry–Émery's $\Gamma _2$ -criterion. These inequalities determine an analog of subgaussian behavior for 1-cocycles. Our theorem improves some of our previous results in this direction, and in particular implies Efraim and Lust-Piquard's Poincaré-type inequalities for the Walsh system. The key new ingredient in our proof is a decoupling argument. As complementary results, we also show that the spectral gap inequality implies the $L_p$ Poincaré inequalities with constant $C{p}$ under some conditions in the noncommutative setting. New examples which satisfy the $\Gamma _2$ -criterion are provided as well.
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    Degenerations of real irrational toric varieties (2015)
    Oxford University Press
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    Publication Date: 2015-09-20
    Description: A real irrational toric variety $X$ is an analytic subset of the simplex associated to a finite configuration of real vectors. The positive torus acts on $X$ by translation, and we consider limits of sequences of these translations. Our main result identifies all possible Hausdorff limits of translations of $X$ as toric degenerations using elementary methods and the geometry of the secondary fan of the vector configuration. This generalizes work of García-Puente et al. , who used algebraic geometry and work of Kapranov, Sturmfels and Zelevinsky, when the vectors were integral.
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    Closed manifolds with transcendental L2-Betti numbers (2015)
    Oxford University Press
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    Publication Date: 2015-09-20
    Description: In this paper, we show how to construct examples of closed manifolds with explicitly computed irrational, even transcendental $L^2$ Betti numbers, defined via the universal covering. We show that every non-negative real number shows up as an $L^2$ -Betti number of some covering of a compact manifold, and that many computable real numbers appear as an $L^2$ -Betti number of a universal covering of a compact manifold (with a precise meaning of computable given below). In algebraic terms, for many given computable real numbers (in particular for many transcendental numbers) we show how to construct a finitely presented group and an element in the integral group ring such that the $L^2$ -dimension of the kernel is the given number. We follow the method pioneered by Austin [‘Rational group ring elements with kernels having irrational dimension’, Proc. London Math. Soc. (3) 107 (2013) 1424–1448], but refine it to get explicit calculations which make the above statements possible.
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    On class groups of imaginary quadratic fields (2015)
    Oxford University Press
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    Publication Date: 2015-09-20
    Description: In this paper, it is proved that one can find imaginary quadratic fields with class number not divisible by a specified prime $l$ and with certain specified splitting conditions at a finite number of primes. Such existence theorems are useful in the arithmetic of elliptic curves and, potentially, also in certain lifting problems for reducible two-dimensional Galois representations. The methods used are a blend of geometry and the theory of modular forms, especially the trace formula.
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    Convergence properties of the Gronwall area formula for quadratic Julia sets (2015)
    Oxford University Press
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    Publication Date: 2015-09-20
    Description: Gronwall area formula can be used to express the area of the filled Julia set of connected quadratic Julia sets. Using parabolic enrichment, it is shown that there is no approximation of this formula by partial sums which is uniform along the boundary of the main cardioid of the Mandelbrot set.
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    Ballistic dynamics of Dirac particles in electro-magnetic fields (2015)
    Oxford University Press
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    Publication Date: 2015-09-20
    Description: Investigating properties of two-dimensional Dirac operators coupled to an electric and a magnetic field (perpendicular to the plane) requires in general unbounded (vector-) potentials. If the system has a certain symmetry, then the fields can be described by one-dimensional potentials $V$ and $A$ . Assuming that $|A| 〈 |V|$ outside some arbitrary large ball, we show that absolutely continuous states of the effective Dirac operators spread ballistically. These results are based on well-known methods in spectral dynamics together with certain new Hilbert–Schmidt bounds. We use Lorentz boosts to derive these new estimates.
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    p-parts of character degrees (2015)
    Oxford University Press
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    Publication Date: 2015-09-20
    Description: We show that if $p$ is an odd prime and $G$ is a finite group satisfying the condition that $p^2$ divides the degree of no irreducible character of $G$ , then $|G:\mathbf {O}_p (G)|_p \le p^4,$ where $\mathbf {O}_p (G)$ is the largest normal $p$ -subgroup of $G$ , and if $P$ is a Sylow $p$ -subgroup of $G$ , then $P''$ is subnormal in $G$ . Our investigations suggest that if $p^a$ is the largest power of $p$ dividing the degrees of irreducible characters of $G$ , then $|G:\mathbf {O}_p(G)|_p$ is bounded by $p^{f(a)},$ where $f (a)$ is a function in $a$ and $P^{(a+1)}$ is subnormal in $G$ .
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    One-connectivity and finiteness of Hamiltonian S1-manifolds with minimal fixed sets (2015)
    Oxford University Press
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    Publication Date: 2015-09-20
    Description: Let the circle act effectively in a Hamiltonian fashion on a compact symplectic manifold $(M, \omega )$ . Assume that the fixed point set $M^{S^1}$ has exactly two components, $X$ and $Y$ , and that $\dim (X) + \dim (Y) +2 = \dim (M)$ . We first show that $X$ , $Y$ and $M$ are simply connected. Then we show that, up to $S^1$ -equivariant diffeomorphism, there are finitely many such manifolds in each dimension. Moreover, we show that in low dimensions, the manifold is unique in a certain category. We use techniques from both areas of symplectic geometry and geometric topology.
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    Optimal design problems with fractional diffusions (2015)
    Oxford University Press
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    Publication Date: 2015-09-20
    Description: In this article, we study optimization problems ruled by fractional diffusion operators with volume constraints. By means of penalization techniques, we prove existence of solutions. We also show that every solution is locally of class $C^{0,\alpha }$ (optimal regularity), and that the free boundary is a $C^{1,\gamma }$ surface, up to an $\mathcal {H}^{n-1}$ -negligible set.
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    Forms representing forms: the definite case (2015)
    Oxford University Press
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    Publication Date: 2015-09-20
    Description: Let $\psi$ and $F$ be positive-definite forms with integral coefficients of equal degree. Using the circle method, we establish an asymptotic formula for the number of identical representations of $\psi$ by $F$ , provided that $\psi$ is everywhere locally representable and the number of variables of $F$ is large enough. In the quadratic case, this supersedes a recent result due to Dietmann and Harvey. Another application addresses the number of primitive linear spaces contained in a hypersurface.
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    Theta lifts of Bianchi modular forms and applications to paramodularity (2015)
    Oxford University Press
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    Publication Date: 2015-09-20
    Description: We explain how the work of Johnson-Leung and Roberts on lifting Hilbert modular forms for real quadratic fields to Siegel modular forms can be adapted to imaginary quadratic fields. For this, we use archimedean results from Harris, Soudry and Taylor and replace the global arguments of Roberts by the non-vanishing result of Takeda. As an application of our lifting result, we exhibit an abelian surface $B$ defined over $\mathbb {Q}$ , which is not a restriction of scalars of an elliptic curve and satisfies the paramodularity Conjecture of Brumer and Kramer.
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    Tropical geometry of moduli spaces of weighted stable curves (2015)
    Oxford University Press
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    Publication Date: 2015-09-20
    Description: Hassett's moduli spaces of weighted stable curves form an important class of alternate modular compactifications of the moduli space of smooth curves with marked points. In this article, we define a tropical analog of these moduli spaces, and show that the naive set-theoretic tropicalization map can be identified with a natural deformation retraction onto the non-Archimedean skeleton. This result generalizes work of Abramovich, Caporaso, and Payne treating the Deligne–Knudsen–Mumford compactification of the moduli space of smooth curves with marked points. We also study tropical analogs of the tautological maps, investigate the dependence of the tropical moduli spaces on the weight data, and consider the example of Losev–Manin spaces.
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    Nested sequents for provability logic GLP (2015)
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    Publication Date: 2015-09-22
    Description: We present a proof system for the provability logic GLP in the formalism of nested sequents and prove the cut elimination theorem for it. As an application, we obtain the reduction of GLP to its important fragment called J syntactically.
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    Base-extension semantics for intuitionistic sentential logic (2015)
    Oxford University Press
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    Publication Date: 2015-09-22
    Description: Intuitionistic sentential logic is shown to be sound and complete with respect to a semantics centered around extensions of atomic bases (i.e. sets of inference rules for atomic sentences). The result is made possible through a non-standard interpretation of disjunction, whereby, roughly speaking, a disjunction is taken to hold just in case every atomic sentence that follows from each of the disjuncts separately holds; it is argued that this interpretation makes good sense provided that rules in atomic bases are conceived of as being accepted hypothetically rather than categorically.
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    Relative expressive power of navigational querying on graphs using transitive closure (2015)
    Oxford University Press
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    Publication Date: 2015-09-22
    Description: Motivated by both established and new applications, we study navigational query languages for graphs (binary relations). The simplest language has only the two operators union and composition, together with the identity relation. We make more powerful languages by adding any of the following operators: intersection; set difference; projection; coprojection; converse; transitive closure; and the diversity relation. All these operators map binary relations to binary relations. We compare the expressive power of all resulting languages, both for binary-relation queries as well as for boolean queries. In the absence of transitive closure, a complete Hasse diagram of relative expressiveness has already been established [ 8 ]. Moreover, it has already been shown that for boolean queries over a single edge label, transitive closure does not add any expressive power when only projection and diversity may be present [ 11 ]. In the present article, we now complete the Hasse diagram in the presence of transitive closure, both for the case of a single edge label, as well as for the case of at least two edge labels. The main technical results are the following: (1) In contrast to the above-stated result [ 11 ] transitive closure does add expressive power when coprojection is present. (2) Transitive closure also adds expressive power as soon as converse is present. (3) Conversely, converse adds expressive power in the presence of transitive closure. In particular, the converse elimination result from [ 8 ] no longer works in the presence of transitive closure. (4) As a corollary, we show that the converse elimination result from [ 8 ] necessitates an exponential blow-up in the degree of the expressions.
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    21st Workshop on Logic, Language, Information and Computation (WoLLIC 2014) (2015)
    Oxford University Press
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    Publication Date: 2015-09-22
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    Logical consistency in simultaneous statistical test procedures (2015)
    Oxford University Press
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    Publication Date: 2015-09-22
    Description: Many authors have argued that, when performing simultaneous statistical test procedures, one should seek for solutions that lead to decisions that are consistent and, consequently, easier to communicate to practitioners of statistical methods. In this way, the set of hypotheses that are rejected and the set of hypotheses that are not rejected by a testing procedure should be consistent from a logic standpoint. For instance, if hypothesis A implies hypothesis B , a procedure that rejects B should also reject A , a property not always met by multiple test procedures. We contribute to this discussion by exploring how far one can go in constructing coherent procedures while still preserving statistical optimality. This is done by studying four types of logical consistency relations. We show that although the only procedures that satisfy more than (any) two of these properties are simple tests based on point estimation, it is possible to construct various interesting methods that fulfil one or two of them while preserving different statistical optimality criteria. This is illustrated with several Bayesian and frequentist examples. We also characterize some of these properties under a decision-theoretic framework.
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    A Problem with the Dependence of Informal Proofs on Formal Proofs (2015)
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    Publication Date: 2015-09-22
    Description: Derivationists, those wishing to explain the correctness and rigour of informal proofs in terms of associated formal proofs, are generally held to be supported by the success of the project of translating informal proofs into computer-checkable formal counterparts. I argue, however, that this project is a false friend for the derivationists because there are too many different associated formal proofs for each informal proof, leading to a serious worry of overgeneration. I press this worry primarily against Azzouni's derivation-indicator account, but conclude that overgeneration is a major obstacle to a successful account of informal proofs in this direction.
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    The Representational Foundations of Computation (2015)
    Oxford University Press
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    Description: Turing computation over a non-linguistic domain presupposes a notation for the domain. Accordingly, computability theory studies notations for various non-linguistic domains. It illuminates how different ways of representing a domain support different finite mechanical procedures over that domain. Formal definitions and theorems yield a principled classification of notations based upon their computational properties. To understand computability theory, we must recognize that representation is a key target of mathematical inquiry. We must also recognize that computability theory is an intensional enterprise: it studies entities as represented in certain ways, rather than entities detached from any means of representing them.
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    Mathematical Structuralism, Modal Nominalism, and the Coherence Principle (2015)
    Oxford University Press
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    Publication Date: 2015-09-22
    Description: According to Stewart Shapiro's coherence principle, structures exist whenever they can be coherently described. I argue that Shapiro's attempts to justify this principle (along with his position, ante rem structuralism) are circular, as he relies on criticisms of modal nominalism which presuppose the coherence principle. I argue further that when the coherence principle is not presupposed, his reasoning more strongly supports modal nominalism than ante rem structuralism.
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    Identity in Homotopy Type Theory, Part I: The Justification of Path Induction (2015)
    Oxford University Press
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    Publication Date: 2015-09-22
    Description: Homotopy Type Theory (HoTT) is a proposed new language and foundation for mathematics, combining algebraic topology with logic. An important rule for the treatment of identity in HoTT is path induction , which is commonly explained by appeal to the homotopy interpretation of the theory's types, tokens, and identities as (respectively) spaces, points, and paths. However, if HoTT is to be an autonomous foundation then such an interpretation cannot play a fundamental role. In this paper we give a derivation of path induction, motivated from pre-mathematical considerations, without recourse to homotopy theory.
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    Logic, Essence, and Modality Bob Hale. Necessary Beings: An Essay on Ontology, Modality, & the Relations Between Them. Oxford University Press, 2013. ISBN: 978-0-19-966262-3 (hbk); 978-0-19-874803-8 (pbk); 978-0-19-164834-2 (e-book). Pp. ix + 298 (2015)
    Oxford University Press
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    Bernard Bolzano. Theory of Science. Volumes I-IV. Paul Rusnock and Rolf George, trans. Oxford: Oxford University Press, 2014. ISBN: 978-0-19-968438-0. Pp. 2044. (2015)
    Oxford University Press
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    Pavel Pudlak. Logical Foundations of Mathematics and Computational Complexity: A Gentle Introduction. Springer Monographs in Mathematics. Springer, 2013. ISBN: 978-3-319-00118-0 (hbk); 978-3-319-00119-7 (ebook). Pp. xiv + 695 (2015)
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    Mark van Atten. Essays on Godel's Reception of Leibniz, Husserl, and Brouwer. Logic, Epistemology, and the Unity of Science; 35. Dordrecht: Springer, 2015. ISBN 978-3-319-10030-2 (hbk); 978-3-319-10031-9 (e-book). Pp. xiv + 328 (2015)
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    Gabriele Lolli, Marco Panza, and Giorgio Venturi, eds. From Logic to Practice: Italian Studies in the Philosophy of Mathematics. Boston Studies in the Philosophy and History of Science; 308. Springer, 2015. ISBN 978-3-319-10433-1 (hbk); 978-3-319-10434-8 (2015)
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    When Do Some Things Form a Set? (2015)
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    Description: This paper raises the question under what circumstances a plurality forms a set, parallel to the Special Composition Question for mereology. The range of answers that have been proposed in the literature are surveyed and criticised. I argue that there is good reason to reject both the view that pluralities never form sets and the view that pluralities always form sets. Instead, we need to affirm restricted set formation. Casting doubt on the availability of any informative principle which will settle which pluralities form sets, the paper concludes by affirming a naturalistic approach to the philosophy of set theory.
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    Polynomially parsable unification grammars (2015)
    Oxford University Press
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    Publication Date: 2015-09-29
    Description: Unification grammars (UGs) are a grammatical formalism that underlies several contemporary linguistic theories, including lexical-functional grammar and head-driven phrase-structure grammar. UG is an especially attractive formalism because of its expressivity, which facilitates the expression of complex linguistic structures and relations. Formally, UG is Turing-complete, generating the entire class of recursively enumerable languages. This expressivity, however, comes at a price: the universal recognition problem is undecidable for arbitrary unification grammars. We define a constrained version of UG that is equivalent to range concatenation grammar, a formalism that generates exactly the class of languages recognizable in deterministic polynomial time. We thus obtain a constrained unification grammar formalism that guarantees efficient processing.
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    The syntactic concept lattice: Another algebraic theory of the context-free languages? (2015)
    Oxford University Press
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    Publication Date: 2015-09-29
    Description: The syntactic concept lattice is a residuated lattice associated with a given formal language; it arises naturally as a generalization of the syntactic monoid in the analysis of the distributional structure of the language. In this article we define the syntactic concept lattice and present its basic properties, and its relationship to the universal automaton and the syntactic congruence; we consider several different equivalent definitions, as Galois connections, as maximal factorizations and finally using universal algebra to define it as an object that has a certain universal (terminal) property in the category of complete idempotent semirings that recognize a given language, applying techniques from automata theory to the theory of context-free grammars (CFGs). We conclude that grammars that are minimal, in a certain weak sense, will always have non-terminals that correspond to elements of this lattice, and claim that the syntactic concept lattice provides a natural system of categories for representing the denotations of CFGs.
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    A formalization of argumentation schemes for legal case-based reasoning in ASPIC+ (2015)
    Oxford University Press
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    Publication Date: 2015-09-29
    Description: In this article we offer a formal account of reasoning with legal cases in terms of argumentation schemes. These schemes, and undercutting attacks associated with them, are formalized as defeasible rules of inference within the ASPIC+ framework. We begin by modelling the style of reasoning with cases developed by Aleven and Ashley in the CATO project, which describes cases using factors, and then extend the account to accommodate the dimensions used in Rissland and Ashley's earlier HYPO project. Some additional scope for argumentation is then identified and formalized.
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    On deontic action logics based on Boolean algebra (2015)
    Oxford University Press
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    Publication Date: 2015-09-29
    Description: The aim of this article is to provide a metalogical systematization in the area of deontic action logic based on Boolean algebra. Differences among the systems involve two aspects: the level of closedness of a deontic action logic and the possibility of performing no action at all . It is also shown that the existing definitions of obligation in these systems are unacceptable due to their non-intuitive interpretation or paradoxical consequences. As a solution we propose a minimal axiomatic characterization of obligation with an adequate class of models. This article also describes how deontic action logic can be used to answer the questions from the Polish driving license test.
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    Blending margins: the modal logic K has nullary unification type (2015)
    Oxford University Press
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    Publication Date: 2015-09-29
    Description: We investigate properties of the formula p -〉 p in the basic modal logic K . We show that K satisfies an infinitary weaker variant of the rule of margins -〉 / , ¬ , and as a consequence, we obtain various negative results about admissibility and unification in K . We describe a complete set of unifiers (i.e. substitutions making the formula provable) of p -〉 p , and use it to establish that K has the worst possible unification type: nullary. In well-behaved transitive modal logics, admissibility and unification can be analysed in terms of projective formulas, introduced by Ghilardi; in particular, projective formulas coincide for these logics with formulas that are admissibly saturated (i.e. derive all their multiple-conclusion admissible consequences) or exact (i.e. axiomatize a theory of a substitution). In contrast, we show that in K , the formula p -〉 p is admissibly saturated, but neither projective nor exact. All our results for K also apply to the basic description logic $$\mathcal{ALC}$$ .
    Print ISSN: 0955-792X
    Electronic ISSN: 1465-363X
    Topics: Computer Science , Mathematics
    Published by Oxford University Press
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    Random algebraic construction of extremal graphs (2015)
    Oxford University Press
    Details
    Publication Date: 2015-11-21
    Description: We present a motivated construction of large graphs not containing a given complete bipartite subgraph. The key insight is that the algebraic constructions yield very non-smooth probability distributions.
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
    Topics: Mathematics
    Published by Oxford University Press
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    Connected Polish groups with ample generics (2015)
    Oxford University Press
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    Publication Date: 2015-11-21
    Description: In this paper, we give the first examples of connected Polish groups that have ample generics, answering a question of Kechris and Rosendal. We show that any Polish group with ample generics embeds into a connected Polish group with ample generics and that full groups of type III hyperfinite ergodic equivalence relations have ample generics. We also sketch a proof of the following result: the full group of any type III ergodic equivalence relation has topological rank 2.
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
    Topics: Mathematics
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    Mean value estimates for odd cubic Weyl sums (2015)
    Oxford University Press
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    Publication Date: 2015-11-21
    Description: We establish an essentially optimal estimate for the ninth moment of the exponential sum having argument $\alpha x^3+\beta x$ . The first substantial advance in this topic for over 60 years, this leads to improvements in Heath-Brown's variant of Weyl's inequality, and other applications of Diophantine type.
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
    Topics: Mathematics
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    Classical and multilinear harmonic analysis: volumes I and II (Cambridge Studies in Advanced Mathematics 137 and 138) By Camil Muscalu and Wilhelm Schlag (2015)
    Oxford University Press
    Details
    Publication Date: 2015-11-21
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
    Topics: Mathematics
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    Foundations of free noncommutative function theory (Mathematical Surveys and Monographs 199) By Dmitry S. Kaliuzhnyi-Verbovetskyi and Victor Vinnikov (2015)
    Oxford University Press
    Details
    Publication Date: 2015-11-21
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
    Topics: Mathematics
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    On the Farrell and Jones warping deformation (2015)
    Oxford University Press
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    Publication Date: 2015-11-24
    Description: The Farrell–Jones warping deformation is a powerful geometric construction that has been crucial in the proofs of many important contributions to the theory of manifolds of negative curvature. In this paper, we study this construction in depth, in a more general setting, and obtain explicit quantitative results. The results in this paper are key ingredients in the problem of smoothing Charney–Davis strict hyperbolizations.
    Print ISSN: 0024-6107
    Electronic ISSN: 1469-7750
    Topics: Mathematics
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    Groupes de Galois et nombres automatiques (2015)
    Oxford University Press
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    Publication Date: 2015-11-24
    Description: Galois groups and automatic numbers : In the frame of Mahler's method for algebraic independence, we show that the algebraic relations over $\overline {\mathbf {Q}}$ linking the values of functions solutions of a system of functional equations come from the algebraic relations between the functions themselves, by specialization. We deduce some new results on the linear independence of values of $q$ -regular functions. Résumé Nous montrons dans le cadre de la théorie de Mahler, que les relations de dépendance algébrique sur $\overline {\mathbf {Q}}$ entre les valeurs de fonctions solutions d'un système d'équations fonctionnelles proviennent, par spécialisation, des relations entre les fonctions elle-mêmes. Nous en déduisons quelques résultats nouveaux sur l'indépendance linéaire des valeurs de fonctions $q$ -réguliéres.
    Print ISSN: 0024-6107
    Electronic ISSN: 1469-7750
    Topics: Mathematics
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    Heegaard Floer groups of Dehn surgeries (2015)
    Oxford University Press
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    Publication Date: 2015-11-24
    Description: We use an algorithm by Ozsváth and Szabó to find closed formulae for the ranks of the hat version of the Heegaard Floer homology groups for nonzero Dehn surgeries on knots in $S^3$ . As applications, we provide new bounds on the number of distinct ranks of the Heegaard Floer groups a Dehn surgery can have. These in turn give a new lower bound on the rational Dehn surgery genus of a rational homology 3-sphere. We also provide novel obstructions for a knot to be a potential counterexample to the Cabling Conjecture.
    Print ISSN: 0024-6107
    Electronic ISSN: 1469-7750
    Topics: Mathematics
    Published by Oxford University Press
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