ALBERT

Description: Recently, non-standard Lagrangians have gained a growing importance in theoretical physics and in the theory of non-linear differential equations. However, their formulations and implications in general relativity are still in their infancies despite some advances in contemporary cosmology. The main aim of this paper is to fill the gap. Though non-standard Lagrangians may be defined by a multitude form, in this paper, we considered the exponential type. One basic feature of exponential non-standard Lagrangians concerns the modified Euler-Lagrange equation obtained from the standard variational analysis. Accordingly, when applied to spacetime geometries, one unsurprisingly expects modified geodesic equations. However, when taking into account the time-like paths parameterization constraint, remarkably, it was observed that mutually discrete gravity and discrete spacetime emerge in the theory. Two different independent cases were obtained: A geometrical manifold with new spacetime coordinates augmented by a metric signature change and a geometrical manifold characterized by a discretized spacetime metric. Both cases give raise to Einstein’s field equations yet the gravity is discretized and originated from “spacetime discreteness”. A number of mathematical and physical implications of these results were discussed though this paper and perspectives are given accordingly.

Description: By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map equivalence classes of functions into other classes in a one-to-one fashion. This suggests that Tsallis’ q-statistics may revolve around equivalence classes of distributions and not individual ones, as orthodox statistics does. We solve here the qFT’s non-invertibility issue, but discover a problem that remains open.

Description: We develop isometry and inversion formulas for the Segal–Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.

Description: Using torus gauge fixing, Hahn in 2008 wrote down an expression for a Chern-Simons path integral to compute the Wilson Loop observable, using the Chern-Simons action \(S_{CS}^\kappa\), \(\kappa\) is some parameter. Instead of making sense of the path integral over the space of \(\mathfrak{g}\)-valued smooth 1-forms on \(S^2 \times S^1\), we use the Segal Bargmann transform to define the path integral over \(B_i\), the space of \(\mathfrak{g}\)-valued holomorphic functions over \(\mathbb{C}^2 \times \mathbb{C}^{i-1}\). This approach was first used by us in 2011. The main tool used is Abstract Wiener measure and applying analytic continuation to the Wiener integral. Using the above approach, we will show that the Chern-Simons path integral can be written as a linear functional defined on \(C(B_1^{\times^4} \times B_2^{\times^2}, \mathbb{C})\) and this linear functional is similar to the Chern-Simons linear functional defined by us in 2011, for the Chern-Simons path integral in the case of \(\mathbb{R}^3\). We will define the Wilson Loop observable using this linear functional and explicitly compute it, and the expression is dependent on the parameter \(\kappa\). The second half of the article concentrates on taking \(\kappa\) goes to infinity for the Wilson Loop observable, to obtain link invariants. As an application, we will compute the Wilson Loop observable in the case of \(SU(N)\) and \(SO(N)\). In these cases, the Wilson Loop observable reduces to a state model. We will show that the state models satisfy a Jones type skein relation in the case of \(SU(N)\) and a Conway type skein relation in the case of \(SO(N)\). By imposing quantization condition on the charge of the link \(L\), we will show that the state models are invariant under the Reidemeister Moves and hence the Wilson Loop observables indeed define a framed link invariant. This approach follows that used in an article written by us in 2012, for the case of \(\mathbb{R}^3\).

Description: We discuss a new approach to represent fractional operators by Sinc approximation using convolution integrals. A spin off of the convolution representation is an effective inverse Laplace transform. Several examples demonstrate the application of the method to different practical problems.

Description: Given a hyperbolic quadric of PG(5, 2), there are 28 points off this quadric and 56 lines skew to it. It is shown that the (286; 563)-configuration formed by these points and lines is isomorphic to the combinatorial Grassmannian of type G2(8). It is also pointed out that a set of seven points of G2(8) whose labels share a mark corresponds to a Conwell heptad of PG(5, 2). Gradual removal of Conwell heptads from the (286; 563)-configuration yields a nested sequence of binomial configurations identical with part of that found to be associated with Cayley-Dickson algebras (arXiv:1405.6888).

Description: Applications of fractional time derivatives in physics and engineering require the existence of nontranslational time automorphisms on the appropriate algebra of observables. The existence of time automorphisms on commutative and noncommutative C*-algebras for interacting many-body systems is investigated in this article. A mathematical framework is given to discuss local stationarity in time and the global existence of fractional and nonfractional time automorphisms. The results challenge the concept of time flow as a translation along the orbits and support a more general concept of time flow as a convolution along orbits. Implications for the distinction of reversible and irreversible dynamics are discussed. The generalized concept of time as a convolution reduces to the traditional concept of time translation in a special limit.

Description: We find a Selberg zeta function expression of certain one-loop spin partition functions on three-dimensional thermal anti-de Sitter space. Of particular interest is the partition function of higher spin fermionic particles. We also set up, in the presence of spin, a Patterson-type formula involving the logarithmic derivative of zeta.

Description: This article is devoted to the study of the ASARCO demolition seismic data. Two different classes of modeling techniques are explored: First, mathematical interpolation methods and second statistical smoothing approaches for curve fitting. We estimate the characteristic parameters of the propagation medium for seismic waves with multiple mathematical and statistical techniques, and provide the relative advantages of each approach to address fitting of such data. We conclude that mathematical interpolation techniques and statistical curve fitting techniques complement each other and can add value to the study of one dimensional time series seismographic data: they can be use to add more data to the system in case the data set is not large enough to perform standard statistical tests.

Description: Root-operator factorization à la Dirac provides an effective tool to deal with equations, which are not of evolution type, or are ruled by fractional differential operators, thus eventually yielding evolution-like equations although for a multicomponent vector. We will review the method along with its extension to root operators of degree higher than two. Also, we will show the results obtained by the Dirac-method as well as results from other methods, specifically in connection with evolution-like equations ruled by square-root operators, that we will address to as relativistic evolution equations.

Description: Phys and Math are two colleagues at the University of Saçenbon (Crefan Kingdom), dialoguing about the remarkable efficiency of mathematics for physics. They talk about the notches on the Ishango bone and the various uses of psi in maths and physics; they arrive at dessins d’enfants, moonshine concepts, Rademacher sums and their significance in the quantum world. You should not miss their eccentric proposal of relating Bell’s theorem to the Baby Monster group. Their hyperbolic polygons show a considerable singularity/cusp structure that our modern age of computers is able to capture. Henri Poincaré would have been happy to see it.

Description: The isomorphism of Karoubi-Villamayor K-groups with smooth K-groups for monoid algebras over quasi stable locally convex algebras is established. We prove that the Quillen K-groups are isomorphic to smooth K-groups for monoid algebras over quasi-stable Frechet algebras having a properly uniformly bounded approximate unit and not necessarily m-convex. Based on these results the K-regularity property for quasi-stable Frechet algebras having a properly uniformly bounded approximate unit is established.

Description: We investigate various scenarios for ending the San Francisco MSM (men having sex with men) HIV/AIDS epidemic (1978–1984). We use our previously developed model and explore changes due to prevention strategies such as testing, treatment and reduction of the number of contacts. Here we consider a “what-if” scenario, by comparing different treatment strategies, to determine which factor has the greatest impact on reducing the HIV/AIDS epidemic. The factor determining the future of the epidemic is the reproduction number R0; if R0 〈 1, the epidemic is stopped. We show that treatment significantly reduces the total number of infected people. We also investigate the effect a reduction in the number of contacts after seven years, when the HIV/AIDS threat became known, would have had in the population. Both reduction of contacts and treatment alone, however, would not have been enough to bring R0 below one; but when combined, we show that the effective R0 becomes less than one, and therefore the epidemic would have been eradicated.

Description: This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N2) for storing the dense or even full matrices that arise from application of numerical methods and how to manage the significant computational work count of O(N3) per time step, where N is the number of spatial grid points. In this paper, a fast iterative finite difference method is developed, which has a memory requirement of O(N) and a computational cost of O(N logN) per iteration. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

Description: Extending Eilenberg–Mac Lane’s cohomology of abelian groups, a cohomology theory is introduced for commutative monoids. The cohomology groups in this theory agree with the pre-existing ones by Grillet in low dimensions, but they differ beyond dimension two. A natural interpretation is given for the three-cohomology classes in terms of braided monoidal groupoids.

Description: The Aharonov-Vaidman gauge additively transforms the mean energy of a quantum mechanical system into a weak valued system energy. In this paper, the equation of motion of this weak valued energy is used to provide a mathematical statement of an extended 1st Law of Thermodynamics that is applicable to the mean energy of a closed quantum system when the mean energy is expressed in the Aharonov-Vaidman gauge, i.e., when the system’s energy is weak valued. This is achieved by identifying the generalized heat and work exchange terms that appear in the equation of motion for weak valued energy. The complex valued contributions of the additive gauge term to these generalized exchange terms are discussed and this extended 1st Law is shown to subsume the usual 1st Law that is applicable for the mean energy of a closed quantum system. It is found that the gauge transformation introduces an additional energy uncertainty exchange term that—while it is neither a heat nor a work exchange term—is necessary for the conservation of weak valued energy. A spin-1/2 particle in a uniform magnetic field is used to illustrate aspects of the theory. It is demonstrated for this case that the extended 1st Law implies the existence of a gauge potential ω and that it generates a non-vanishing gauge field F. It is also shown for this case that the energy uncertainty exchange accumulated during the evolution of the system along a closed evolutionary cycle C in an associated parameter space is a geometric phase. This phase is equal to both the path integral of ω along C and the integral of the flux of F through the area enclosed by C.

Description: The fractional order differential equation \(u'(t)=Au(t)+\gamma D_t^{\alpha} Au(t)+f(t), \ t>0\), \(u(0)=a\in X\) is studied, where \(A\) is an operator generating a strongly continuous one-parameter semigroup on a Banach space \(X\), \(D_t^{\alpha}\) is the Riemann–Liouville fractional derivative of order \(\alpha \in (0,1)\), \(\gamma>0\) and \(f\) is an \(X\)-valued function. Equations of this type appear in the modeling of unidirectional viscoelastic flows. Well-posedness is proven, and a subordination identity is obtained relating the solution operator of the considered problem and the \(C_{0}\)-semigroup, generated by the operator \(A\). As an example, the Rayleigh–Stokes problem for a generalized second-grade fluid is considered.

Description: This paper is a follow-up of a previous paper of the author published in Mathematics journal in 2015, which treats the so-called continuous fractional orthogonal derivative. In this paper, we treat the discrete case using the fractional orthogonal difference. The theory is illustrated with an application of a fractional differentiating filter. In particular, graphs are presented of the absolutel value of the modulus of the frequency response. These make clear that for a good insight into the behavior of a fractional differentiating filter, one has to look for the modulus of its frequency response in a log-log plot, rather than for plots in the time domain.

Description: We address the recently posed question as to whether the nonlocality of a single member of an entangled pair of spin 1 / 2 particles can be shared among multiple observers on the other wing who act sequentially and independently of each other. We first show that the optimality condition for the trade-off between information gain and disturbance in the context of weak or non-ideal measurements emerges naturally when one employs a one-parameter class of positive operator valued measures (POVMs). Using this formalism we then prove analytically that it is impossible to obtain violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality by more than two Bobs in one of the two wings using unbiased input settings with an Alice in the other wing.

Description: A smooth function of the second moments of N continuous variables gives rise to an uncertainty relation if it is bounded from below. We present a method to systematically derive such bounds by generalizing an approach applied previously to a single continuous variable. New uncertainty relations are obtained for multi-partite systems that allow one to distinguish entangled from separable states. We also investigate the geometry of the “uncertainty region” in the N ( 2 N + 1 ) -dimensional space of moments. It is shown to be a convex set, and the points on its boundary are found to be in one-to-one correspondence with pure Gaussian states of minimal uncertainty. For a single degree of freedom, the boundary can be visualized as one sheet of a “Lorentz-invariant” hyperboloid in the three-dimensional space of second moments.

Description: This study deals with the control of chaotic dynamics of tumor cells, healthy host cells, and effector immune cells in a chaotic Three Dimensional Cancer Model (TDCM) by State Space Exact Linearization (SSEL) technique based on Lie algebra. A non-linear feedback control law is designed which induces a coordinate transformation thereby changing the original chaotic TDCM system into a controlled one linear system. Numerical simulation has been carried using Mathematica that witness the robustness of the technique implemented on the chosen chaotic system.

Description: In this paper, we consider the time-dependent Schrödinger equation: i ∂ ψ ( x , t ) ∂ t = 1 2 ( − Δ ) α 2 ψ ( x , t ) + V ( x ) ψ ( x , t ) , x ∈ R , t > 0 with the Riesz space-fractional derivative of order 0 〈 α ≤ 2 in the presence of the linear potential V ( x ) = β x . The wave function to the one-dimensional Schrödinger equation in momentum space is given in closed form allowing the determination of other measurable quantities such as the mean square displacement. Analytical solutions are derived for the relevant case of α = 1 , which are useable for studying the propagation of wave packets that undergo spreading and splitting. We furthermore address the two-dimensional space-fractional Schrödinger equation under consideration of the potential V ( ρ ) = F · ρ including the free particle case. The derived equations are illustrated in different ways and verified by comparisons with a recently proposed numerical approach.

Description: The rate of change of any function versus its independent variables was defined as a derivative. The fundamentals of the derivative concept were constructed by Newton and l’Hôpital. The followers of Newton and l’Hôpital defined fractional order derivative concepts. We express the derivative defined by Newton and l’Hôpital as an ordinary derivative, and there are also fractional order derivatives. So, the derivative concept was handled in this paper, and a new definition for derivative based on indefinite limit and l’Hôpital’s rule was expressed. This new approach illustrated that a derivative operator may be non-linear. Based on this idea, the asymptotic behaviors of functions were analyzed and it was observed that the rates of changes of any function attain maximum value at inflection points in the positive direction and minimum value (negative) at inflection points in the negative direction. This case brought out the fact that the derivative operator does not have to be linear; it may be non-linear. Another important result of this paper is the relationships between complex numbers and derivative concepts, since both concepts have directions and magnitudes.

Description: In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternative proofs of two identities of the Catalan numbers. The three identities of the Catalan-Qi numbers generalize three identities of the Catalan numbers.

Description: We focus on inverse preconditioners based on minimizing F ( X ) = 1 − cos ( X A , I ) , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X ) on a suitable compact set. For this, we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of F ( X ) on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included.

Description: Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can there be some trade-off relation between the coherence measures in different reference bases? We show that the quantum coherence of a state as quantified by the relative entropy of coherence in two or more noncommuting reference bases respects uncertainty like relations for a given state of single and bipartite quantum systems. In the case of bipartite systems, we find that the presence of entanglement may tighten the above relation. Further, we find an upper bound on the sum of the relative entropies of coherence of bipartite quantum states in two noncommuting reference bases. Moreover, we provide an upper bound on the absolute value of the difference of the relative entropies of coherence calculated with respect to two incompatible bases.

Description: Although versions of Poisson’s Summation Formula (PSF) have already been studied extensively, there seems to be no theorem that relates discretization to periodization and periodization to discretization in a simple manner. In this study, we show that two complementary formulas, both closely related to the classical Poisson Summation Formula, are needed to form a reciprocal Discretization-Periodization Theorem on generalized functions. We define discretization and periodization on generalized functions and show that the Fourier transform of periodic functions are discrete functions and, vice versa, the Fourier transform of discrete functions are periodic functions.

Description: In this communication we take up the age-old problem of the possibility to incorporate quantum jumps. Unusually, we investigate quantum jumps in an extended quantum setting, but one of rigorous mathematical significance. The general background for this formulation originates in the Balslev-Combes theorem for dilatation analytic Hamiltonians and associated complex symmetric representations. The actual jump is mapped into a Jordan block of order two and a detailed derivation is discussed for the case of the emission of a photon by an atom. The result can be easily reassigned to analogous cases as well as generalized to Segrè characteristics of arbitrary order.

Description: The purpose of this paper is to present a consistent mathematical framework that shows how the EPR (Einstein. Podolsky, Rosen) phenomenon fits into our view of space time. To resolve the differences between the Hilbert space structure of quantum theory and the manifold structure of classical physics, the manifold is taken as a partial representation of the Hilbert space. It is the partial nature of the representation that allows for action at a distance and the failure of the manifold picture.

Description: For many scientific calculations, particularly those involving empirical data, IEEE 32-bit floating-point arithmetic produces results of sufficient accuracy, while for other applications IEEE 64-bit floating-point is more appropriate. But for some very demanding applications, even higher levels of precision are often required. This article discusses the challenge of high-precision computation, in the context of mathematical physics, and highlights what facilities are required to support future computation, in light of emerging developments in computer architecture.

Description: This is a survey paper illuminating the distinguished role of the Mittag-Leffler function and its generalizations in fractional analysis and fractional modeling. The content of the paper is connected to the recently published monograph by Rudolf Gorenflo, Anatoly Kilbas, Francesco Mainardi and Sergei Rogosin.

Description: The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials. Expansions in terms of orthogonal polynomials are very common in many applications. While the connection problem may be solved by directly computing the change–of–basis matrix, this approach is computationally expensive. A recent approach to solving the connection problem involves the use of the spectral connection matrix, which is a matrix whose eigenvector matrix is the desired change–of–basis matrix. In Bella and Reis (2014), it is shown that for the connection problem between any two different classical real orthogonal polynomials of the Hermite, Laguerre, and Gegenbauer families, the related spectral connection matrix has quasiseparable structure. This result is limited to the case where both the source and target families are one of the Hermite, Laguerre, or Gegenbauer families, which are each defined by at most a single parameter. In particular, this excludes the large and common class of Jacobi polynomials, defined by two parameters, both as a source and as a target family. In this paper, we continue the study of the spectral connection matrix for connections between real orthogonal polynomial families. In particular, for the connection problem between any two families of the Hermite, Laguerre, or Jacobi type (including Chebyshev, Legendre, and Gegenbauer), we prove that the spectral connection matrix has quasiseparable structure. In addition, our results also show the quasiseparable structure of the spectral connection matrix from the Bessel polynomials, which are orthogonal on the unit circle, to any of the Hermite, Laguerre, and Jacobi types. Additionally, the generators of the spectral connection matrix are provided explicitly for each of these cases, allowing a fast algorithm to be implemented following that in Bella and Reis (2014).

Description: In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are compared with those presented in this paper. By using the Bernstein characterization theorem we find the conditions under which the even moments are non-negative.

Description: In this paper, we have presented a family of fourth order iterative methods, which uses weight functions. This new family requires three function evaluations to get fourth order accuracy. By the Kung–Traub hypothesis this family of methods is optimal and has an efficiency index of 1.587. Furthermore, we have extended one of the methods to sixth and twelfth order methods whose efficiency indices are 1.565 and 1.644, respectively. Some numerical examples are tested to demonstrate the performance of the proposed methods, which verifies the theoretical results. Further, we discuss the extraneous fixed points and basins of attraction for a few existing methods, such as Newton’s method and the proposed family of fourth order methods. An application problem arising from Planck’s radiation law has been verified using our methods.

Description: In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for first order semi linear impulsive neutral functional differential evolution inclusions with infinite delay using a recently developed nonlinear alternative for contractive multivalued maps in Frechet spaces due to Frigon combined with semigroup theory. The existence result has been proved without assumption of compactness of the semigroup. We introduced a new phase space for impulsive system with infinite delay and claim that the phase space considered by different authors are not correct.

Description: We consider two principal bundles of embeddings with total space E m b ( M , N ) , with structure groups D i f f ( M ) and D i f f + ( M ) , where D i f f + ( M ) is the groups of orientation preserving diffeomorphisms. The aim of this paper is to describe the structure group of the tangent bundle of the two base manifolds: B ( M , N ) = E m b ( M , N ) / D i f f ( M ) and B + ( M , N ) = E m b ( M , N ) / D i f f + ( M ) from the various properties described, an adequate group seems to be a group of Fourier integral operators, which is carefully studied. It is the main goal of this paper to analyze this group, which is a central extension of a group of diffeomorphisms by a group of pseudo-differential operators which is slightly different from the one developped in the mathematical litterature e.g. by H. Omori and by T. Ratiu. We show that these groups are regular, and develop the necessary properties for applications to the geometry of B ( M , N ) . A case of particular interest is M = S 1 , where connected components of B + ( S 1 , N ) are deeply linked with homotopy classes of oriented knots. In this example, the structure group of the tangent space T B + ( S 1 , N ) is a subgroup of some group G L r e s , following the classical notations of (Pressley, A., 1988). These constructions suggest some approaches in the spirit of one of our previous works on Chern-Weil theory that could lead to knot invariants through a theory of Chern-Weil forms.

Description: We propose a stochastic model to develop a partial integro-differential equation (PIDE) for pricing and pricing expression for fixed type single Barrier options based on the Itô-Lévy calculus with the help of Mellin transform. The stock price is driven by a class of infinite activity Lévy processes leading to the market inherently incomplete, and dynamic hedging is no longer risk free. We first develop a PIDE for fixed type Barrier options, and apply the Mellin transform to derive a pricing expression. Our main contribution is to develop a PIDE with its closed form pricing expression for the contract. The procedure is easy to implement for all class of Lévy processes numerically. Finally, the algorithm for computing numerically is presented with results for a set of Lévy processes.

Description: The representation of the cost of a therapy is a key element in the formulation of the optimal control problem for the treatment of infectious diseases. The cost of the treatment is usually modeled by a function of the price and quantity of drugs administered; this function should be the cost as subjectively perceived by the decision-maker. Nevertheless, in literature, the choice of the cost function is often simply done to make the problem more tractable. A specific problem is also given by very expensive therapies in the presence of a very high number of patients to be treated. Firstly, we investigate the optimal treatment of infectious diseases in the simplest case of a two-class population (susceptible and infectious people) and compare the results coming from five different shapes of cost functions. Finally, a model for the treatment of the HCV virus using the blowing-up cost function is investigated. Some numerical simulations are also given.

Description: We propose a derivative-free iterative method with fifth order of convergence for solving systems of nonlinear equations. The scheme is composed of three steps, of which the first two steps are that of third order Traub-Steffensen-type method and the last is derivative-free modification of Chebyshev’s method. Computational efficiency is examined and comparison between the efficiencies of presented technique with existing techniques is performed. It is proved that, in general, the new method is more efficient. Numerical problems, including those resulting from practical problems viz. integral equations and boundary value problems, are considered to compare the performance of the proposed method with existing methods. Calculation of computational order of convergence shows that the order of convergence of the new method is preserved in all the numerical examples, which is not so in the case of some of the existing higher order methods. Moreover, the numerical results, including the CPU-time consumed in the execution of program, confirm the accurate and efficient behavior of the new technique.

Description: The elementary symmetric functions play a crucial role in the study of zeros of non-zero polynomials in C [ x ] , and the problem of finding zeros in Q [ x ] leads to the definition of algebraic and transcendental numbers. Recently, Marques studied the set of algebraic numbers in the form P ( T ) Q ( T ) . In this paper, we generalize this result by showing the existence of algebraic numbers which can be written in the form P 1 ( T ) Q 1 ( T ) ⋯ P n ( T ) Q n ( T ) for some transcendental number T, where P 1 , … , P n , Q 1 , … , Q n are prescribed, non-constant polynomials in Q [ x ] (under weak conditions). More generally, our result generalizes results on the arithmetic nature of z w when z and w are transcendental.

Description: Machine learning algorithms have been widely used in the field of client credit assessment. However, few of the algorithms have focused on and solved the problems of concept drift and class imbalance. Due to changes in the macroeconomic environment and markets, the relationship between client characteristics and credit assessment results may change over time, causing concept drift in client credit assessments. Moreover, client credit assessment data are naturally asymmetric and class imbalanced because of the screening of clients. Aiming at solving the joint research issue of concept drift and class imbalance in client credit assessments, in this paper, a novel sample-based online learning ensemble (SOLE) for client credit assessment is proposed. A novel multiple time scale ensemble classifier and a novel sample-based online class imbalance learning procedure are proposed to handle the potential concept drift and class imbalance in the client credit assessment data streams. The experiments are carried out on two real-world client credit assessment cases, which present a comprehensive comparison between the proposed SOLE and other state-of-the-art online learning algorithms. In addition, the base classifier preference and the computing resource consumption of all the comparative algorithms are tested. In general, SOLE achieves a better performance than other methods using fewer computing resources. In addition, the results of the credit scoring model and the Kolmogorov–Smirnov (KS) test also prove that SOLE has good practicality in actual client credit assessment applications.

Description: This paper adapts the multivariate optimal control theory to a Riemannian setting. In this sense, a coherent correspondence between the key elements of a standard optimal control problem and several basic geometric ingredients is created, with the purpose of generating a geometric version of Pontryagin’s maximum principle. More precisely, the local coordinates on a Riemannian manifold play the role of evolution variables (“multitime”), the Riemannian structure, and the corresponding Levi–Civita linear connection become state variables, while the control variables are represented by some objects with the properties of the Riemann curvature tensor field. Moreover, the constraints are provided by the second order partial differential equations describing the dynamics of the Riemannian structure. The shift from formal analysis to optimal Riemannian control takes deeply into account the symmetries (or anti-symmetries) these geometric elements or equations rely on. In addition, various submanifold integral cost functionals are considered as controlled payoffs.

Description: Positioning devices allow users’ movement to be recorded. The GPS (Global Positioning System) trajectory data typically consists of spatiotemporal points, which make up the major part of the big data concerning urban life. Existing knowledge extraction methods about the trajectory share a general limitation—they only investigate data from a spatiotemporal aspect, but fail to take the semantic information of trajectories into consideration. Therefore, extracting the semantic information of trajectories with the context of big data is challenging pattern recognition task that has practical application prospects. In this paper, a system is proposed to extract the semantic trajectory patterns of positioning device users. Firstly, a spatiotemporal threshold and clustering based pre-processing model is proposed to process the raw data. Then, we design a probabilistic generative model to annotate the semantic information of each trajectory after the pre-processing procedure. Finally, we apply the PrefixSpan algorithm to mine the semantic trajectory patterns. We verify our system on a large dataset of users’ real trajectories over a period of 5 years in Beijing, China. The results of the experiment indicate that our system produces meaningful patterns.

Description: Three-way decisions, as a decision-making mode which is consistent with human cognition, have been widely used in various fields. In this paper, we fuse the theory of reliability into the three-way decisions method, replace the conditional probability in the three-way decisions method with reliability, and then propose a novel three-way decisions method. We also describe the loss functions with single-valued triangular neutrosophic numbers (SVTNNs) and propose an operator to calculate the score function of triangular neutrosophic numbers. Then, the result of decision is attained according to the principle of minimizing loss. Finally, we apply this method to the overhaul of machines in a factory, which proves the practicability and effectiveness of the proposed methods.

Description: The solutions for many real life problems may be obtained by interpreting the given problem mathematically in the form f ( x ) = x . One such example is that of the famous Borsuk–Ulam theorem in which, using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this article, some new results concerning coincidence and a common fixed point for an A φ -contraction and a generalized ϕ -type weak contraction are established. We prove our results for set valued maps without using continuity of the corresponding maps and completeness of the relevant space. Our results generalize and extend several existing results. Some new examples are given to demonstrate the generality and non-triviality of our results.

Description: Studies related to pattern recognition and visualization using computer technology have been introduced. In particular, deep neural networks (DNNs) provide good performance for image, speech, and pattern recognition. However, a poisoning attack is a serious threat to a DNN’s security. A poisoning attack reduces the accuracy of a DNN by adding malicious training data during the training process. In some situations, it may be necessary to drop a specifically chosen class of accuracy from the model. For example, if an attacker specifically disallows nuclear facilities to be selectively recognized, it may be necessary to intentionally prevent unmanned aerial vehicles from correctly recognizing nuclear-related facilities. In this paper, we propose a selective poisoning attack that reduces the accuracy of only the chosen class in the model. The proposed method achieves this by training malicious data corresponding to only the chosen class while maintaining the accuracy of the remaining classes. For the experiment, we used tensorflow as the machine-learning library as well as MNIST, Fashion-MNIST, and CIFAR10 as the datasets. Experimental results show that the proposed method can reduce the accuracy of the chosen class by 43.2%, 41.7%, and 55.3% in MNIST, Fashion-MNIST, and CIFAR10, respectively, while maintaining the accuracy of the remaining classes.

Description: In this manuscript, we define generalized Kincses-Totik type contractions within the context of metric space and consider the existence of a fixed point for such operators. Kincses-Totik type contractions extends the renowned Banach contraction mapping principle in different aspects. First, the continuity condition for the considered mapping is not required. Second, the contraction inequality contains all possible geometrical distances. Third, the contraction inequality is formulated for some iteration of the considered operator, instead of the dealing with the given operator. Fourth and last, the iteration number may vary for each point in the domain of the operator for which we look for a fixed point. Consequently, the proved results generalize the acknowledged results in the field, including the well-known theorems of Seghal, Kincses-Totik, and Banach-Caccioppoli. We present two illustrative examples to support our results. As an application, we consider an Ulam-stability of one of our results.

Description: We propose a derivative free one-point method with memory of order 1.84 for solving nonlinear equations. The formula requires only one function evaluation and, therefore, the efficiency index is also 1.84. The methodology is carried out by approximating the derivative in Newton’s iteration using a rational linear function. Unlike the existing methods of a similar nature, the scheme of the new method is easy to remember and can also be implemented for systems of nonlinear equations. The applicability of the method is demonstrated on some practical as well as academic problems of a scalar and multi-dimensional nature. In addition, to check the efficacy of the new technique, a comparison of its performance with the existing techniques of the same order is also provided.

Description: In this short note we give an elementary description of the linear part of the minimal free resolution of a Stanley-Reisner ring of a simplicial complex Δ . Indeed, the differentials in the linear part are simply a compilation of restriction maps in the simplicial cohomology of induced subcomplexes of Δ . Along the way, we also show that if a monomial ideal has at least one generator of degree 2, then the linear strand of its minimal free resolution can be written using only ± 1 coefficients.

Description: In this paper, we propose a branch-and-bound algorithm to solve exactly the minimum vertex cover (MVC) problem. Since a tight lower bound for MVC has a significant influence on the efficiency of a branch-and-bound algorithm, we define two novel lower bounds to help prune the search space. One is based on the degree of vertices, and the other is based on MaxSAT reasoning. The experiment confirms that our algorithm is faster than previous exact algorithms and can find better results than heuristic algorithms.

Description: We present fixed points results of multivalued Prešić type k-step iterative mappings satisfying generalized weakly contraction conditions in metric spaces. An example is presented to support the main result proved herein. The stability of fixed point sets of multivalued Prešić type weakly contractive mappings are also established. Global attractivity result for the class of matrix difference equations is derived as application of the result presented herein. These results generalize and extend various comparable results in the existing literature.

Description: We define a family of observables for abelian Yang-Mills fields associated to compact regions U ⊆ M with smooth boundary in Riemannian manifolds. Each observable is parametrized by a first variation of solutions and arises as the integration of gauge invariant conserved current along admissible hypersurfaces contained in the region. The Poisson bracket uses the integration of a canonical multisymplectic current.

Description: Video analysis is currently the main non-intrusive method for the study of collective behavior. However, 3D-to-2D projection leads to overlapping of observed objects. The situation is further complicated by the absence of stall shapes for the majority of living objects. Fortunately, living objects often possess a certain symmetry which was used as a basis for morphological fingerprinting. This technique allowed us to record forms of symmetrical objects in a pose-invariant way. When combined with image skeletonization, this gives a robust, nonlinear, optimization-free, and fast method for detection of overlapping objects, even without any rigid pattern. This novel method was verified on fish (European bass, Dicentrarchus labrax, and tiger barbs, Puntius tetrazona) swimming in a reasonably small tank, which forced them to exhibit a large variety of shapes. Compared with manual detection, the correct number of objects was determined for up to almost 90 % of overlaps, and the mean Dice-Sørensen coefficient was around 0.83 . This implies that this method is feasible in real-life applications such as toxicity testing.

Description: In the year 2004, Chang and Teng investigated an inventory model for deteriorating items in which the supplier not only provides a cash discount, but also allows a permissible delay in payments. The main purpose of the present investigation is three-fold, as follows. First, it is found herein that Theorem 1 of Chang and Teng (2004) has notable shortcomings in terms of their determination of the optimal solution of the annual total relevant cost Z ( T ) by adopting the Taylor-series approximation method. Theorem 1 in this paper does not make use of the Taylor-series approximation method in order to overcome the shortcomings in Chang and Teng (2004) and alternatively derives all the optimal solutions of the annual total relevant cost Z ( T ) . Secondly, this paper systematically revisits the annual total relevant cost Z ( T ) in Chang and Teng (2004) and presents in detail the mathematically correct ways for the derivations of Z ( T ) . Thirdly, this paper not only shows that Theorem 1 of Chang and Teng (2004) is not necessarily true for finding the optimal solution of the annual total relevant cost Z ( T ) , but it also demonstrates how Theorem 1 in this paper can locate all of the optimal solutions of Z ( T ) . The mathematical analytic investigation presented in this paper is believed to be useful for correct managerial considerations and managerial decisions.

Description: This paper characterizes the retailer’s loss aversion by introducing a loss aversion coefficient and proposes a new loss aversion utility function for the retailer. To hedge against the risk arising from the uncertain market demand, we use the Conditional Value-at-Risk (CVaR) measure to quantify the potential risks and obtain the optimal order quantity for the retailer to maximize the CVaR objective of loss aversion utility. It is shown that that the optimal order quantity for a retailer to maximize the expected loss aversion utility is smaller than expected profit maximizing (EPM) order quantity in the classical newsvendor model, which can help to explain decision bias in the newsvendor model. This study shows that the optimal order quantity with the CVaR objective can decrease in retail price under certain conditions, which has never occurred in the newsvendor literature. With the optimal order quantity under the CVaR objective, it is proved that the retailer’s expected loss aversion utility is decreasing in the confidence level. This confirms the fact that high return means high risk, while low risk comes with low return. Based on the results, several management insights are suggested for the loss-averse newsvendor model.

Description: As an extension of the fuzzy set, the hesitant fuzzy set is used to effectively solve the hesitation of decision-makers in group decision-making and to rigorously express the decision information. In this paper, we first introduce some new hesitant fuzzy Hamacher power-aggregation operators for hesitant fuzzy information based on Hamacher t-norm and t-conorm. Some desirable properties of these operators is shown, and the interrelationships between them are given. Furthermore, the relationships between the proposed aggregation operators and the existing hesitant fuzzy power-aggregation operators are discussed. Based on the proposed aggregation operators, we develop a new approach for multiple-attribute decision-making problems. Finally, a practical example is provided to illustrate the effectiveness of the developed approach, and the advantages of our approach are analyzed by comparison with other existing approaches.

Description: In this paper, we are concerned with a nonlinear system containing some essential symmetrical structures (e.g., cross-diffusion) in the two-dimensional setting, which is proposed to model the biological transport networks. We first provide an a priori blow-up criterion of strong solution of the corresponding Cauchy problem. Based on this, we also establish a priori upper bounds to strong solution for all positive times.

Description: We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely, four integral identities. The second main result is regarding the temporal behavior of our thermoelastic body with a dipolar structure. This behavior is studied by means of some relations on a partition of various parts of the energy associated to the solution of the problem.

Description: Feature interaction is a newly proposed feature relevance relationship, but the unintentional removal of interactive features can result in poor classification performance for this relationship. However, traditional feature selection algorithms mainly focus on detecting relevant and redundant features while interactive features are usually ignored. To deal with this problem, feature relevance, feature redundancy and feature interaction are redefined based on information theory. Then a new feature selection algorithm named CMIFSI (Conditional Mutual Information based Feature Selection considering Interaction) is proposed in this paper, which makes use of conditional mutual information to estimate feature redundancy and interaction, respectively. To verify the effectiveness of our algorithm, empirical experiments are conducted to compare it with other several representative feature selection algorithms. The results on both synthetic and benchmark datasets indicate that our algorithm achieves better results than other methods in most cases. Further, it highlights the necessity of dealing with feature interaction.

Description: A chaotic system and two Nonlinear Feadback Shift Registers (NFSRs) are used to generate a new stream cipher in this paper. This design can be used for efficient encryption in resource-constrained devices or environments. The chaotic system is quantified and integrated with two NFSRs based on the technology of Field Programmable Gate Array (FPGA). Many analyses are made from the angle of entropy in order to verify the cryptographic characteristics of the stream cipher, and National Institute of Standards and Technology (NIST) statistical test is completed to analyze the cipher. The test results show that the stream cipher here has good cryptographic characteristics.

Description: In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of B-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principles. We convert the integral equation to a system of linear equations. We provide an example of the construction of quasi-affine tight framelet systems. We also give some numerical evidence to illustrate our method. The numerical results confirm that the method is efficient, very effective and accurate.

Description: The security issue on the physical layer is of significant challenge yet of paramount importance for 5G communications. In some previous works, transmit power allocation has already been studied for orthogonal frequency division multiplexing (OFDM) secure communication with Gaussian channel inputs for both a single user and multiple users. Faced with peak transmission power constraints, we adopt discrete channel inputs (e.g., equiprobable Quadrature Phase Shift Keying (QPSK) with symmetry) in a practical communication system, instead of Gaussian channel inputs. Finite-alphabet inputs impose a more significant challenge as compared with conventional Gaussian random inputs for the multiuser wiretap OFDM systems. This paper considers the joint resource allocation in frequency-domain artificial noise (AN) assisted multiuser wiretap OFDM channels with discrete channel inputs. This security problem is formulated as nonconvex sum secrecy rate optimization by jointly optimizing the subcarrier allocation, information-bearing power, and AN-bearing power. To this end, with a suboptimal subcarrier allocation scheme, we propose an efficient iterative algorithm to allocate the power between the information and the AN via the Lagrange duality method. Finally, we carry out some numerical simulations to demonstrate the performance of the proposed algorithm.

Description: A Friedmann–Robertson–Walker Universe was studied with a dark energy component represented by a quintessence field. The Lagrangian for this system, hereafter called the Friedmann–Robertson–Walker–quintessence (FRWq) system, was presented. It was shown that the classical Lagrangian reproduces the usual two (second order) dynamical equations for the radius of the Universe and for the quintessence scalar field, as well as a (first order) constraint equation. Our approach naturally unified gravity and dark energy, as it was obtained that the Lagrangian and the equations of motion are those of a relativistic particle moving on a two-dimensional, conformally flat spacetime. The conformal metric factor was related to the dark energy scalar field potential. We proceeded to quantize the system in three different schemes. First, we assumed the Universe was a spinless particle (as it is common in literature), obtaining a quantum theory for a Universe described by the Klein–Gordon equation. Second, we pushed the quantization scheme further, assuming the Universe as a Dirac particle, and therefore constructing its corresponding Dirac and Majorana theories. With the different theories, we calculated the expected values for the scale factor of the Universe. They depend on the type of quantization scheme used. The differences between the Dirac and Majorana schemes are highlighted here. The implications of the different quantization procedures are discussed. Finally, the possible consequences for a multiverse theory of the Dirac and Majorana quantized Universe are briefly considered.

Description: In this work, we consider the general class of difference equations (covered many equations that have been studied by other authors or that have never been studied before), as a means of establishing general theorems, for the asymptotic behavior of its solutions. Namely, we state new necessary and sufficient conditions for local asymptotic stability of these equations. In addition, we study the periodic solution with period two and three. Our results essentially extend and improve the earlier ones.

Description: This study considers an asset-liability optimization model based on constraint robustness with the chance constraint of capital to risk assets ratio in a safety-first framework under the condition that only moment information is known. This paper aims to extend the proposed single-objective capital to risk assets ratio chance constrained optimization model in the literature by considering the multi-objective constraint robustness approach in a modified safety-first framework. To solve the optimization model, we develop a deterministic convex counterpart of the capital to risk assets ratio robust probability constraint. In a consolidated risk measure of variance and safety-first framework, the proposed distributionally-robust capital to risk asset ratio chance-constrained optimization model guarantees banks will meet the capital requirements of Basel III with a likelihood of 95% irrespective of changes in the future market value of assets. Even under the worst-case scenario, i.e., when loans default, our proposed capital to risk asset ratio chance-constrained optimization model meets the minimum total requirements of Basel III. The practical implications of the findings of this study are that the model, when applied, will provide safety against extreme losses while maximizing returns and minimizing risk, which is prudent in this post-financial crisis regime.

Description: In this paper, a mathematical model based on the one-parameter Mittag-Leffler function is proposed to be used for the first time to describe the relation between the unemployment rate and the inflation rate, also known as the Phillips curve. The Phillips curve is in the literature often represented by an exponential-like shape. On the other hand, Phillips in his fundamental paper used a power function in the model definition. Considering that the ordinary as well as generalised Mittag-Leffler function behave between a purely exponential function and a power function it is natural to implement it in the definition of the model used to describe the relation between the data representing the Phillips curve. For the modelling purposes the data of two different European economies, France and Switzerland, were used and an “out-of-sample” forecast was done to compare the performance of the Mittag-Leffler model to the performance of the power-type and exponential-type model. The results demonstrate that the ability of the Mittag-Leffler function to fit data that manifest signs of stretched exponentials, oscillations or even damped oscillations can be of use when describing economic relations and phenomenons, such as the Phillips curve.

Description: The main contribution in this paper is to construct an implicit fixed coefficient Block Backward Differentiation Formulas denoted as A ( α ) -BBDF with equal intervals for solving stiff ordinary differential equations (ODEs). To avoid calculating the differentiation coefficients at each step of the integration, the coefficients of the formulas will be stored, with the intention of optimizing the performance in terms of precision and computational time. The plots of their A ( α ) stability region are provided, and the order of the method is also verified. The necessary conditions for convergence, such as the consistency and zero stability of the method, are also discussed. The numerical results clearly showed the efficiency of the method in terms of accuracy and execution time as compared to other existing methods in the scientific literature.

Description: Each loop in a multi-loop rail network consists of two segments, both of which have roughly the same conditions and mileage and are approximately symmetrical. This paper is devoted to optimizing the paths of trains formed at the loading area in a multi-loop rail network. To attain this goal, three different situations are analyzed, and two models are proposed for networks with adequate and inadequate capabilities. Computational experiments are also carried out using the commercial software Lingo, with the branch and bound algorithm. The results show that the models can achieve the same solution with different solution times. To solve the problem of path selection for large-scale train flows, a genetic algorithm is also designed and proves to perform well in a set of computational experiments.

Description: This paper is concerned with the design of an improved El-Gamal cryptosystem based on chaos synchronization. The El-Gamal cryptosystem is an asymmetric encryption algorithm that must use the public and private keys, respectively, in the encryption and decryption processes. However, in our design, the public key does not have to appear in the public channel. Therefore, this proposed improved El-Gamal cryptosystem becomes a symmetric-like encryption algorithm. First, a discrete sliding mode controller is proposed to ensure the synchronization of master and slave chaotic systems; next, a novel improved El-Gamal cryptosystem is presented. In the traditional El-Gamal cryptosystem, the public key is static and needs to be open which provides an opportunity to attack. However, in this improved design, due to the chaos synchronization, the public key becomes dynamic and does not appear in public channels. As a result, drawbacks of long cipher text and time-consuming calculation in the traditional El-Gamal cryptosystem are all removed. Finally, several performance tests and comparisons have shown the efficiency and security of the proposed algorithm.

Description: By using the Kolmogorov-Arnold-Moser (KAM) theory, we investigate the stability of two elliptic equilibrium points (zero equilibrium and negative equilibrium) of the difference equation t n + 1 = α t n + β t n 2 − t n − 1 , n = 0 , 1 , 2 , … , where are t − 1 , t 0 , α ∈ R , α ≠ 0 , β 〉 0 . By using the symmetries we find the periodic solutions with some periods. Finally, some numerical examples are given to verify our theoretical results.

Description: In this paper, we focus on methods to prevent shoulder-surfing attacks. We initially adopted digraph substitution rules from PlayFair cipher as our proposed method. PlayFair cipher is a modern cryptography method, which exists at the intersection of the disciplines of mathematics and computer science. However, according to our preliminary study it was insufficient to prevent shoulder-surfing attacks. Thus, a new method had to be proposed. In this new proposed method, we improvised the digraph substitution rules and used these rules together with an output feedback method to determine a pass-image. Our proposed method was evaluated with a user study. The results showed our proposed method was robust against both direct observation and video-recorded shoulder-surfing attacks.

Description: In this paper, by applying the decision theorem of the Schur-power convex function, the Schur-power convexity of a class of complete symmetric functions are studied. As applications, some new inequalities are established.

Description: A competing risks model under progressively type II censored data following the Rayleigh distribution is considered. We establish the maximum likelihood estimation for unknown parameters and compute the observed information matrix and the expected Fisher information matrix to construct the asymptotic confidence intervals. Moreover, we obtain the Bayes estimation based on symmetric and non-symmetric loss functions, that is, the squared error loss function and the general entropy loss function, and the highest posterior density intervals are also derived. In addition, a simulation study is presented to assess the performances of different methods discussed in this paper. A real-life data set analysis is provided for illustration purposes.

Description: A Couette-Poiseuille flow between parallel plates saturated with porous medium is studied with emphasis on viscous dissipation effect on the temperature field; assuming a fully developed flow, with both plates subjected to unequal and uniform heat flux. Temperature field and Nusselt number are derived as a function of Brinkman number and porous medium shape factor. By specifying the ratio of wall to mean velocity as one, the resulting velocity and temperature fields attribute to a significant increase in Nusselt number for the moving wall as the permeability of porous medium increases. Increased permeability signifies competing effect between enhanced convection in the proximity of the moving wall and higher local viscous dissipation. When the former effect dominates, heat transfer coefficient increases. Effects of Reynolds number on the temperature field is elucidated, including a comparison between a microchannel and conventional duct to evaluate the characteristic length scale effect. As Reynolds number goes up in a microchannel, heat generation in the form of viscous dissipation intensifies and overrides the convection effect, causing an increase in the highest temperature along the duct on the contrary to the findings in conventional duct.

Description: In this study, we present an analytical study on blood flow analysis through with a tapered porous channel. The blood flow was driven by the peristaltic pumping. Thermal radiation effects were also taken into account. The convective and slip boundary conditions were also applied in this formulation. These conditions are very helpful to carry out the behavior of particle movement which may be utilized for cardiac surgery. The tapered porous channel had an unvarying wave speed with dissimilar amplitudes and phase. The non-dimensional analysis was utilized for some approximations such as the proposed mathematical modelling equations were modified by using a lubrication approach and the analytical solutions for stream function, nanoparticle temperature and volumetric concentration profiles were obtained. The impacts of various emerging parameters on the thermal characteristics and nanoparticles concentration were analyzed with the help of computational results. The trapping phenomenon was also examined for relevant parameters. It was also observed that the geometric parameters, like amplitudes, non-uniform parameters and phase difference, play an important role in controlling the nanofluids transport phenomena. The outcomes of the present model may be applicable in the smart nanofluid peristaltic pump which may be utilized in hemodialysis.

Description: The mean-shift method is a convenient mode-seeking method. Using a principle of the sample mean over an analysis window, or kernel, in a data space where samples are distributed with bias toward the densest direction of sample from the kernel center, the mean-shift method is an attempt to seek the densest point of samples, or the sample mode, iteratively. A smaller kernel leads to convergence to a local mode that appears because of statistical fluctuation. A larger kernel leads to estimation of a biased mode affected by other clusters, abnormal values, or outliers if they exist other than in the major cluster. Therefore, optimal selection of the kernel size, which is designated as the bandwidth in many reports of the literature, represents an important problem. As described herein, assuming that the major cluster follows a Gaussian probability density distribution, and, assuming that the outliers do not affect the sample mode of the major cluster, and, by adopting a Gaussian kernel, we propose a new mean-shift by which both the mean vector and covariance matrix of the major cluster are estimated in each iteration. Subsequently, the kernel size and shape are updated adaptively. Numerical experiments indicate that the mean vector, covariance matrix, and the number of samples of the major cluster can be estimated stably. Because the kernel shape can be adjusted not only to an isotropic shape but also to an anisotropic shape according to the sample distribution, the proposed method has higher estimation precision than the general mean-shift.

Description: In this paper, we establish generalized Suzuki-simulation-type contractive mapping and prove fixed point theorems on non-Archimedean quasi modular metric spaces. As an application, we acquire graphic-type results.

Description: In this study we introduce several new Ostrowski-type inequalities for both left and right sided fractional integrals of a function g with respect to another function ψ . Our results generalized the ones presented previously by Farid. Furthermore, two illustrative examples are presented to support our results.

Description: The purpose of this article is to define almost ( α , F σ ) -contractions and establish some generalized fixed-point results for a new class of contractive conditions in the setting of complete metric spaces. In application, we apply our fixed-point theorem to prove the existence theorem for Fredholm integral inclusions ϖ ( t ) ∈ f ( t ) + ∫ 0 1 K ( t , s , x ( s ) ) ϑ s , t ∈ [ 0 , 1 ] where f ∈ C [ 0 , 1 ] is a given real-valued function and K : [ 0 , 1 ] × [ 0 , 1 ] × R → K c v ( R ) is a given multivalued operator, where K c v represents the family of nonempty compact and convex subsets of R and ϖ ∈ C [ 0 , 1 ] is the unknown function. We also provide a non-trivial example to show the significance of our main result.

Description: Composite quantile regression (CQR) estimation and inference are studied for varying coefficient models with response data missing at random. Three estimators including the weighted local linear CQR (WLLCQR) estimator, the nonparametric WLLCQR (NWLLCQR) estimator, and the imputed WLLCQR (IWLLCQR) estimator are proposed for unknown coefficient functions. Under some mild conditions, the proposed estimators are asymptotic normal. Simulation studies demonstrate that the unknown coefficient estimators with IWLLCQR are superior to the other two with WLLCQR and NWLLCQR. Moreover, bootstrap test procedures based on the IWLLCQR fittings is developed to test whether the coefficient functions are actually varying. Finally, a type of investigated real-life data is analyzed to illustrated the applications of the proposed method.

Description: This paper reports on the Walnut Digital Signature Algorithm (WalnutDSA), which is an asymmetric signature scheme recently presented for standardization at the NIST call for post-quantum cryptographic constructions. WalnutDSA is a group theoretical construction, the security of which relies on the hardness of certain problems related to an action of a braid group on a finite set. In spite of originally resisting the typical attacks succeeding against this kind of construction, soon different loopholes were identified rendering the proposal insecure (and finally, resulting in it being excluded from Round 2 of the NIST competition). Some of these attacks are related to the well-structured and symmetric masking of certain secret elements during the signing process. We explain the design principles behind this proposal and survey the main attack strategies that have succeeded, contradicting its claimed security properties, as well as the recently-proposed ideas aimed at overcoming these issues.

Description: Analysis of motion symmetry constitutes an important area with many applications in engineering, robotics, neurology and biomedicine. This paper presents the use of microelectromechanical sensors (MEMS), including accelerometers and gyrometers, to acquire data via mobile devices so as to monitor physical activities and their irregularities. Special attention is devoted to the analysis of the symmetry of the motion of the body when the same exercises are performed by the right and the left limb. The analyzed data include the motion of the legs on a home exercise bike under different levels of load. The method is based on signal analysis using the discrete wavelet transform and the evaluation of signal segment features such as the relative energy at selected decomposition levels. The subsequent classification of the evaluated features is performed by k-nearest neighbours, a Bayesian approach, a support vector machine, and neural networks. The highest average classification accuracy attained is 91.0% and the lowest mean cross-validation error is 0.091, resulting from the use of a neural network. This paper presents the advantages of the use of simple sensors, their combination and intelligent data processing for the numerical evaluation of motion features in the rehabilitation and monitoring of physical activities.

Description: Multipath diversity significantly impacts multipath transmission quality. Enough multipath diversity would minimize the negative influence brought by an individual path, thus improving tolerance capability of network congestion and failure. However, multipath diversity is hard to guarantee on overlay networks because of inaccurate awareness of underlay network and multipath generating methods considering little about underlay diversity. In this paper, we design a multi-dimension spatial method for topology awareness and multipath generating. Analyzing that the complicated underlay networks with multiple autonomous systems reduce the accuracy of network positioning for topology awareness, we decompose the underlay networks into multiple dimensions, namely intra and inter autonomous system dimensions. We generate independent views for each autonomous system and merge views by embedding exchange points. Then, we design some spatial mechanisms to evaluate link diversity and to constrain multipath generating. Based on the multi-dimensional view, multipath generating is conducted in inter and intra autonomous system phases. Experiments demonstrate that the proposed method improves topology awareness accuracy and guarantees multipath diversity better and the transmission quality is improved.

Description: Brazil is an important player when it comes to biofuel and agricultural production. The knowledge of the price relationship between these markets has increasing importance. This paper adopts several tools, namely the Bai–Perron test of breakpoints, the Johansen cointegration test and the vector error correction model exploited by the orthogonal impulse response and the forecast error variance decomposition, for investigating the price transmission among the ethanol and the main Brazil’s agricultural commodities (sugar, cotton, arabica coffee, robusta coffee, live cattle, corn and soybean). The data series cover the period from January 2011 up to December 2018. The results suggest a stronger price transmission from the ethanol commodity to the agricultural commodities, rather than the opposite situation.

Description: We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional differences with discrete Mittag–Leffler kernels. The iteration process depends on the binomial theorem. We note in particular the fact that the iterated fractional sums have a certain semigroup property, and hence, the new introduced iterated fractional difference-sum operators have this semigroup property as well.

Description: In this article, we make a detailed study of some mathematical aspects associated with a generalized Lévy process using fractional diffusion equation with Mittag–Leffler kernel in the context of Atangana–Baleanu operator. The Lévy process has several applications in science, with a particular emphasis on statistical physics and biological systems. Using the continuous time random walk, we constructed a fractional diffusion equation that includes two fractional operators, the Riesz operator to Laplacian term and the Atangana–Baleanu in time derivative, i.e., a A B D t α ρ ( x , t ) = K α , μ ∂ x μ ρ ( x , t ) . We present the exact solution to model and discuss how the Mittag–Leffler kernel brings a new point of view to Lévy process. Moreover, we discuss a series of scenarios where the present model can be useful in the description of real systems.

Description: This research paper proposes a derivative-free method for solving systems of nonlinear equations with closed and convex constraints, where the functions under consideration are continuous and monotone. Given an initial iterate, the process first generates a specific direction and then employs a line search strategy along the direction to calculate a new iterate. If the new iterate solves the problem, the process will stop. Otherwise, the projection of the new iterate onto the closed convex set (constraint set) determines the next iterate. In addition, the direction satisfies the sufficient descent condition and the global convergence of the method is established under suitable assumptions. Finally, some numerical experiments were presented to show the performance of the proposed method in solving nonlinear equations and its application in image recovery problems.

Description: In this paper, a kernel recursive maximum Versoria-like criterion (KRMVLC) algorithm has been constructed, derived, and analyzed within the framework of nonlinear adaptive filtering (AF), which considers the benefits of logarithmic second-order errors and the symmetry maximum-Versoria criterion (MVC) lying in reproducing the kernel Hilbert space (RKHS). In the devised KRMVLC, the Versoria approach aims to resist the impulse noise. The proposed KRMVLC algorithm was carefully derived for taking the nonlinear channel equalization (NCE) under different non-Gaussian interferences. The achieved results verify that the KRMVLC is robust against non-Gaussian interferences and performs better than those of the popular kernel AF algorithms, like the kernel least-mean-square (KLMS), kernel least-mixed-mean-square (KLMMN), and Kernel maximum Versoria criterion (KMVC).

Description: GOX (3QVR), glucose oxidase, is an oxidoreductase enzyme, which has found many applications in biotechnology and modern diagnostics with typical assays including biosensors useful in the determination of free glucose in body fluids. PEI (polyethylenimines) are polymer molecules made up of amine groups and two aliphatic carbons, which are cyclically repeated. PEI are transfection reagents which, using positively charged units, bind well to anionic DNA residues. During the studies on GOX, PEI were used both in their linear and branched structures. Rhombellanes, RBL, are structures decorated with rhombs/squares. The aim of the paper is to study the interactions of two kinds of linear ligands: PEIs (Polyethylenimines) and CHRs (ethers of Hexahydroxy-cyclohexane) with the glucose oxidase enzyme, GOX (3QVR). To understand the structure-activity relationship between the GOX enzyme and the linear ligands PEI and CHR, two steps of docking simulation were performed; mapping the whole area of the 3QVR enzyme and docking on the first and second surface of the enzyme, separately. The studied ligands interacted with amino acids of GOX inside the protein and on its surface, with stronger and shorter bonds inside of the protein. However, long chain ligands can only interact with amino acids on the external protein surface. After the study, two domains of the enzyme were clearly evidenced; the external surface domain more easily creates interactions with ligands, particularly with CHR ligands.

Description: In this article, we study an extension of the sinh Cauchy model in order to obtain asymmetric bimodality. The behavior of the distribution may be either unimodal or bimodal. We calculate its cumulative distribution function and use it to carry out quantile regression. We calculate the maximum likelihood estimators and carry out a simulation study. Two applications are analyzed based on real data to illustrate the flexibility of the distribution for modeling unimodal and bimodal data.

Description: Cisplatin (cisPt) is one of the strongest anticancer agents with proven clinical activity against a wide range of solid tumors. Its mode of action has been linked to its ability to crosslink with the canonical purine bases, primarily with guanine. Theoretical studies performed at the molecular level suggest that such nonspecific interactions can also take place with many competitive compounds, such as vitamins of the B group, containing aromatic rings with lone-pair orbitals. This might be an indicator of reduction of the anticancer therapeutic effects of the Cisplatin drug in the presence of vitamins of the B group inside the cell nucleus. That is why it seems to be important to connect CisPt with nanostructures and in this way prevent the drug from combining with the B vitamins. As a proposal for a new nanodrug, an attempt was made to implement Cispaltin (CisPt) ligand on functionalized C60 fullerenes and on a cube rhombellane homeomorphic surface. The symmetry of the analyzed nanostructures is an important factor determining the mutual affinity of the tested ligand and nanocarriers. The behavior of Cisplatin with respect to rhombellane homeomorphs and functionalized fullerenes C60, in terms of their (interacting) energy, geometry and topology was studied and a detailed analysis of structural properties after docking showed many interesting features.

Description: It is known that every element in the alternating group A n , with n ≥ 5 , can be written as a product of at most two Engel words of arbitrary length. However, it is still unknown if every element in an alternating group is an Engel word of Arbitrary length. In this paper, a different approach to this problem is presented, getting new results for small alternating groups.

Description: As a global-optimized and naturally inspired algorithm, particle swarm optimization (PSO) is characterized by its high quality and easy application in practical optimization problems. However, PSO has some obvious drawbacks, such as early convergence and slow convergence speed. Therefore, we introduced some appropriate improvements to PSO and proposed a novel chaotic PSO variant with arctangent acceleration coefficient (CPSO-AT). A total of 10 numerical optimization functions were employed to test the performance of the proposed CPSO-AT algorithm. Extensive contrast experiments were conducted to verify the effectiveness of the proposed methodology. The experimental results showed that the proposed CPSO-AT algorithm converges quickly and has better stability in numerical optimization problems compared with other PSO variants and other kinds of well-known optimal algorithms.

Description: Race walking has been theoretically described as a walking gait in which no flight time is allowed and high travelling speed, comparable to running (3.6–4.2 m s−1), is achieved. The aim of this study was to mechanically understand such a “hybrid gait” by analysing the ground reaction forces (GRFs) generated in a wide range of race walking speeds, while comparing them to running and walking. Fifteen athletes race-walked on an instrumented walkway (4 m) and three-dimensional GRFs were recorded at 1000 Hz. Subjects were asked to performed three self-selected speeds corresponding to a low, medium and high speed. Peak forces increased with speeds and medio-lateral and braking peaks were higher than in walking and running, whereas the vertical peaks were higher than walking but lower than running. Vertical GRF traces showed two characteristic patterns: one resembling the “M-shape” of walking and the second characterised by a first peak and a subsequent plateau. These different patterns were not related to the athletes’ performance level. The analysis of the body centre of mass trajectory, which reaches its vertical minimum at mid-stance, showed that race walking should be considered a bouncing gait regardless of the presence or absence of a flight phase.

Description: This paper deals with separable and entangled qudits | ψ d 〉 (quantum states in dimension d) constructed from Dicke states made of N = d − 1 qubits. Such qudits present the property to be totally symmetric under the interchange of the N qubits. We discuss the notion of perma-concurrence P d for the qudit | ψ d 〉 , introduced by the authors (Entropy 2018, 20, 292), as a parameter for characterizing the entanglement degree of | ψ d 〉 . For d = 3 , the perma-concurrence P 3 constitutes an alternative to the concurrence C for symmetric two-qubit states. We give several expressions of P d (in terms of matrix permanent and in terms of unit vectors of R 3 pointing on the Bloch sphere) and precise the range of variation of P d (going from separable to maximally entangled states). Numerous examples are presented for P d . Special attention is devoted to states of W type and to maximally entangled states of Bell and Greenberger–Horne–Zeilinger type.

Description: In social and health sciences, many statistical procedures and estimation techniques rely on the underlying distributional assumption of normality of the data. Non-normality may lead to incorrect statistical inferences. This study evaluates the performance of selected normality tests within the stringency framework for skewed alternative space. The stringency concept allows us to rank the tests uniquely. The Bonett and Seier test (Tw) turns out to represent the best statistics for slightly skewed alternatives and the Anderson–Darling (AD); Chen–Shapiro (CS); Shapiro–Wilk (W); and Bispo, Marques, and Pestana (BCMR) statistics are the best choices for moderately skewed alternative distributions. The maximum loss of Jarque–Bera (JB) and its robust form (RJB), in terms of deviations from the power envelope, is greater than 50%, even for large sample sizes, which makes them less attractive in testing the hypothesis of normality against the moderately skewed alternatives. On balance, all selected normality tests except Tw and Daniele Coin’s COIN-test performed exceptionally well against the highly skewed alternative space.

Description: With the improvement of human living standards, users’ requirements have changed from function to emotion. Helping users pick out the most suitable product based on their subjective requirements is of great importance for enterprises. This paper proposes a Kansei engineering-based grey relational analysis and techniques for order preference by similarity to ideal solution (KE-GAR-TOPSIS) method to make a subjective user personalized ranking of alternative products. The KE-GRA-TOPSIS method integrates five methods, including Kansei Engineering (KE), analytic hierarchy process (AHP), entropy, game theory, and grey relational analysis-TOPSIS (GRA-TOPSIS). First, an evaluation system is established by KE and AHP. Second, we define a matrix variate—Kansei decision matrix (KDM)—to describe the satisfaction of user requirements. Third, the AHP is used to obtain subjective weight. Next, the entropy method is employed to obtain objective weights by taking the KDM as input. Then the two types of weights are optimized using game theory to obtain the comprehensive weights. Finally, the GRA-TOPSIS method takes the comprehensive weights and the KMD as inputs to rank alternatives. A comparison of the KE-GRA-TOPSIS, KE-TOPSIS, KE-GRA, GRA-TOPSIS, and TOPSIS is conducted to illustrate the unique merits of the KE-GRA-TOPSIS method in Kansei evaluation. Finally, taking the electric drill as an example, we describe the process of the proposed method in detail, which achieves a symmetry between the objectivity of products and subjectivity of users.

Description: The operation of many real-world systems, e.g., servers of data centers, is accompanied by the heating of a server. Correspondingly, certain cooling mechanisms are used. If the server becomes overheated, it interrupts processing of customers and needs to be cooled. A customer is lost when its service is interrupted. To prevent overheating and reduce the customer loss probability, we suggest temporal termination of service of new customers when the temperature of the server reaches the predefined threshold value. Service is resumed after the temperature drops below another threshold value. The problem of optimal choice of the thresholds (with respect to the chosen economical criterion) is numerically solved under quite general assumptions about the parameters of the system (Markovian arrival process, phase-type distribution of service time, and accounting for customers impatience). Numerical examples are presented.

Description: Metric learning aims to measure the similarity among samples while using an optimal distance metric for learning tasks. Metric learning methods, which generally use a linear projection, are limited in solving real-world problems demonstrating non-linear characteristics. Kernel approaches are utilized in metric learning to address this problem. In recent years, deep metric learning, which provides a better solution for nonlinear data through activation functions, has attracted researchers' attention in many different areas. This article aims to reveal the importance of deep metric learning and the problems dealt with in this field in the light of recent studies. As far as the research conducted in this field are concerned, most existing studies that are inspired by Siamese and Triplet networks are commonly used to correlate among samples while using shared weights in deep metric learning. The success of these networks is based on their capacity to understand the similarity relationship among samples. Moreover, sampling strategy, appropriate distance metric, and the structure of the network are the challenging factors for researchers to improve the performance of the network model. This article is considered to be important, as it is the first comprehensive study in which these factors are systematically analyzed and evaluated as a whole and supported by comparing the quantitative results of the methods.

Description: Aviation bearing assembled detection is the final barrier to quality and safety. Therefore, an accurate detection method of aviation bearing that is based on local characteristics is designed to solve the detection problem of mis-assembly and miss-assembly of balls in aviation bearing assembled. When considering the spatial limitation of aviation bearing assembled image acquisition, the dynamic distribution of balls and the interference of lubricating grease on the surface, a dynamic local ball segmentation model that is based on U-Net network with symmetrical structure is designed to achieve the accurate segmentation of the local ball region of aviation bearing. Subsequently, an incomplete circle fitting algorithm is designed based on the segmented local ball image and Hough transform principle. These two algorithms make the measurement error of aviation bearing ball size less than 100 μm. Using bearings validates the algorithm. The results show that the accuracy of dynamic local ball segmentation model that is based on U-Net network with symmetrical structure is over 99%. At the same time, on the basis of accurate segmentation in aviation bearing local ball, the designed Hough circle algorithm is used for circle detection. The experimental results show that the false detection rate of mis-assembly and miss-assembly of balls is less than 3%. Further, the goal of zero-missed detection of mis-assembly and miss-assembly of balls in aviation bearing is achieved. The accurate segmentation of aviation bearing local ball and the effective identification of mis-assembly and miss-assembly of balls are realized. This method can provide a theory for the improvement of mis-assembly and miss-assembly of balls detection in aviation bearing. Furthermore, it has high application value.