Search

This editorial paper presents the papers published in a special issue devoted to the modeling and simulation of mutating virus pandemics in a globally connected world. The presentation is proposed in three parts. First, motivations and objectives are presented according to the idea that mathematical models should go beyond deterministic population dynamics by considering the multiscale, heterogeneous features of the complex system under consideration. Subsequently, the contents of the papers in this issue are presented referring to the aforementioned complexity features. Finally, a critical analysis of the overall contents of the issue is proposed, with the aim of providing a forward look to research perspectives. [ABSTRACT FROM AUTHOR]

Liu's inference is a process of deriving consequences from uncertain knowledge or evidence via the tool of conditional uncertainty. Using membership functions, this paper derives some expressions of Liu's inference rule for uncertain systems. This paper also discusses Liu's inference rule with multiple antecedents and with multiple if-then rules. [ABSTRACT FROM AUTHOR]

This is a reply to Ramon Ferrer-I-Cancho's paper in this issue "Some Word Order Biases from Limited Brain Resources: A Mathematical Approach." In this reply, I challenge the Euclidean distance model proposed in that paper by proposing a simple alternative model based on linear ordering. [ABSTRACT FROM AUTHOR]

This paper deals with the mathematical analysis of a model of urban dynamics, which was proposed by Miyata and Yamaguchi in the context of a region of Japan. The model is a complex system of first-order nonlinear ordinary differential equations. The study undertaken by Miyata and Yamaguchi is essentially computational, while an extensive study of the asymptotic behavior of the solutions is performed in this paper related to a detailed analysis of the qualitative properties of the system. [ABSTRACT FROM AUTHOR]

In this paper we present a simulation of an acyclic n×n DR-Mesh on an n×n LR-Mesh. The simulation is efficient in regards to size since both models use the same number of processors. The worst execution time for this simulation is O(n2) time, but we demonstrate that its average execution time is O(logn). The fastest existing simulation takes O(logn) time, but it uses an extremely large number of processors. On the other hand, the most efficient simulation in terms of size takes O(log2n) time with O(n4/log2n) processors. Both of the existing simulations are for the unrestricted DR-Mesh. This paper provides an important step towards efficiently simulating the unrestricted DR-Mesh on weaker models such as the R-Mesh and the LR-Mesh. [ABSTRACT FROM AUTHOR]

This paper proposes a procedure to design fault tolerant algorithms for the R-Mesh and some of its restrictive variations. This procedure first identifies a healthy sub-mesh from a faulty model using the bypass and removal fault model. Then it uses scalable algorithms to simulate the larger faulty model on the resulting healthy sub-mesh. The algorithms for the bypass model tolerates n faults in an n×n R-Mesh (LR-Mesh) and runs in O(T log n) (O(T)) time, where T is the execution time on the original mesh without faults. For the removal model, we design fault tolerant algorithms for some interesting variations of the R-Mesh, specifically, the NXR-Mesh and the NXLR-Mesh. We propose the first scaling simulations for these models and present a simulation of the R-Mesh on the NXR-Mesh. The results of this paper enable us to consider certain reconfigurable models in a more practical environment than previously allowed. [ABSTRACT FROM AUTHOR]

For any C¹ differential system S on a compact Riemannian manifold M of dimension d with d ≥= 2, this paper studies the Liao style numbers, κ(S) (or respectively, κ*(S)) of S from the view-point of ergodic theory. Here κ(S) (κ* (S)) is the largest number of moving vectors (or respectively, conjugate-) of the differential system S that are mean linearly independent. For any ergodic measure v of S, two positive integers κ* (v) and κ(v), called the reduced and non-reduced style number of v respectively, are introduced. The connection between the style numbers of the system (M, S) and ones of the ergodic system (M, S; v) are discovered by the variational principle of style number proved in the paper. Several characterization theorems with respect to the style numbers κ* (S), κ*(v), κ(S) and κ(v) are presented respectively. [ABSTRACT FROM AUTHOR]

This paper reports some novel approach on linguistic logic with our intention to realize CWW, Computing With Words, via a simple example which consists of only five words. As a by product, this simple example of the linguistic logical system may serve as a mathematical model, modeling the degree of truthfulness in daily usage. The five words set of a linguistic variable modeling the degree of truthfulness are; true, nearly true, undecided, nearly false and false. We subjectively choose trapezoidal fuzzy numbers as our linguistic truth values in order to model our linguistic logic system. Firstly, some natural operations and linguistic logic operators are defined to suit our objective of developing a closed linguistic variable set. Then the computation of linguistic truth values for this linguistic logical system is developed in order to facilitate us to perform the linguistic inferences. Properties of these natural operations can be derived accordingly. It is perhaps quite rewarding to see numerous linguistic truth relations defined on a single linguistic truth set and linguistic implications ended up with numerous linguistic truth tables. In addition, the linguistic inferences of generalized modus ponens and generalized tollens determined by linguistic compositional rules based on the linguistic truth relation and some natural operations are introduced. The simple examples of the linguistic inferences of the various generalized tautologies are illustrated. Finally, we have proved via a simple dictionary that a closed and self consistent linguistic logical system indeed can be constructed and it is possible to move a chunk of information as modeled by a fuzzy set to a higher level according to the theory of semiotics. These results have shown some promise in realizing the appealing theory of CWW. [ABSTRACT FROM AUTHOR]

One of the most important issues in the field of fuzzy preference modelling is the construction of a fuzzy strict preference relation and a fuzzy indifference relation from a fuzzy weak preference relation. Here, we focus on a particular class of fuzzy weak preference relations, the so-called fuzzy orderings. The definition of a fuzzy ordering involves a fuzzy equivalence relation and, in this paper, the latter will be considered as the corresponding fuzzy indifference relation. We search for fuzzy strict preference relations compatible with a given fuzzy ordering and its fuzzy indifference relation. In many situations, depending on the t-norm and t-conorm used, this quest results in a unique fuzzy strict preference relation. Our aim is to characterize these fuzzy strict preference relations and to study their transitivity. [ABSTRACT FROM AUTHOR]

A group G is said to be a B(n,k) group if for any n-element subset {a1,..., an} of G, |{aiaj | 1≤i, j≤n}|≤ k. In this paper, characterizations of B(4,11) groups, B(4,12) groups, and B(4,13) non-2-groups are given. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear mathematical model is proposed and analyzed to study the effect of environmental toxicant on the immune response of the body. Criteria for local stability, instability and global stability are obtained. It is shown that the immune response of the body decreases as the concentration of environmental toxicant increases, and certain criteria are obtained under which it settles down at its equilibrium level. In the absence of toxicant, an oscillatory behavior of immune system and pathogenic growth is observed. However, in the presence of toxicant, oscillatory behavior is not observed. These studies show that the toxicant may have a grave effect on our body's defense mechanism. [ABSTRACT FROM AUTHOR]

The aim of this paper is first to review the derivation of a model describing the propagation of an optical wave in a photorefractive medium and to present various mathematical results on this model: Cauchy problem, solitary waves. [ABSTRACT FROM AUTHOR]

A new evolving network based on the scale-free network of Barabási and Albert (BA) is studied, and the accelerated attachment of new edges is considered in its evolving process. The accelerated attachment is different from the previous accelerated growth of edges and has two particular meanings in this paper. One is that a new vertex with the edges is inserted into the network with acceleration at each time step; the other is that, with a given probability, some additional edges are linked with the vertices in proportion to the number of their obtained edges in the latest evolving periods. The new model describes the cases of those complex networks with a few exceptional vertices. The attachment mechanism of the new adding edges for these vertices does not follow the preferential attachment rule. Comparing with the linear edge growth model, the characteristics of the accelerated growth model are studied theoretically and numerically. We show that the degree distributions of these models have a power law decay and the exponents are larger than that of the BA model. We point out that the characteristics of the exceptional vertices and the aging vertices in an aging network are not identical. The reasons for neglecting this attachment in most of evolving networks are also summarized. [ABSTRACT FROM AUTHOR]

A general and a comprehensive theory of fuzzy topological spaces on the basis of a fixed quadruple M = (L, ≤, ⊗, *), where (L, ≤), ⊗ and *, respectively, denote a complete lattice and binary operations on L satisfying some further axioms, was introduced by Höhle and Šostak. L-topological spaces, convergence structure of L-topological spaces and L-continuous functions form an important part of their work. The present paper continues the study in this area, and provides new results on the convergence structure of L-topological spaces and the continuity in L-topological spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of fuzzy prime and fuzzy semiprime S-subacts, where S is a monoid with a zero and S-acts are representations of S. We establish their basic properties and prove some fundamental results in a fuzzy context, analogous to the results in ordinary semigroups and S-acts. It is shown, among other results, that if a fuzzy right S-subact is fuzzy irreducible, then the difference between fuzzy prime and fuzzy semiprime disappears. [ABSTRACT FROM AUTHOR]

A new multi-class classifier, decision tree SVM (DTSVM) which is a binary decision tree with a very simple structure is presented in this paper. In DTSVM, a problem of multi-class classification is decomposed into a series of ones of binary classification. Here, the binary decision tree is generated by using kernel clustering algorithm, and each non-leaf node represents one binary classification problem. By compared with the other multi-class classification methods based on the binary classification SVMs, the scale and the complexity of DTSVM are less, smaller number of support vectors are needed, and has faster test speed. The final simulation results confirm the feasibility and the validity of DTSVM. [ABSTRACT FROM AUTHOR]

This paper addresses a novel sentence reduction algorithm based on a decision tree model in which semantic information is used to enhance the accuracy of sentence reduction. The proposed algorithm is able to deal with the changeable order problem in sentence reduction. Furthermore, the use of decision list to solve the fragment problem in sentence reduction based decision tree model is also discussed. Our experimental results show an improvement when compared with earlier methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotic behavior of global solutions to a parabolic–hyperbolic coupled system which describes the evolution of the relative temperature θ and the order parameter χ in a material subject to phase transitions. For the system with homogeneous Neumann boundary conditions for both ¸ and χ, under the assumption that the nonlinearities λ and ϕ are real analytic functions, we prove the convergence of a global solution to an equilibrium as time goes to infinity by means of a suitable Łojasiewicz–Simon type inequality. [ABSTRACT FROM AUTHOR]

This paper treats the opinion dynamics of an unequal, initial opinion distribution. We simulate the Deffuant model on a directed Barabási–Albert network with discrete opinions and several subjects. We notice a focusing of the the resulting opinion distribution during the simulation towards the average value of the initial opinion distribution. A small change of the focusing is seen. A dependency of this change on the number of subjects and opinions is detected and indicates the change as a consequence of discretization of the opinions. Hereby the average value of the initial opinion distribution can be identified as the guide of opinion forming. [ABSTRACT FROM AUTHOR]

This paper presents the results of a modification of well known simple model of social phenomena called Sznajd Model. Although this model has been extensively studied and applied to different topologies I am going to show the influence of slight randomization introduced into the most basic one-dimensional approach. The modification leads to a drastic increase of time needed to reach one of the steady states and to the stabilization of lifetime of governments. [ABSTRACT FROM AUTHOR]

Let (X, L) be a polarized manifold of dimension 3. In this paper, we consider a lower bound for h0(KX + 2L). We prove that h0(KX + 2L) > 0 if KX + 2L is nef, which is a conjecture of Beltrametti–Sommese for polarized 3-folds. Moreover we classify polarized 3-folds (X, L) with h0(KX + 2L) = 1 under the assumption that KX + 2L is nef. [ABSTRACT FROM AUTHOR]

In recent years, the spectral properties of the translation invariant Nelson model has been studied. Some of the results obtained did not extend to the related polaron model for technical reasons related to the typical assumption of boundedness of the phonon dispersion relation in the polaron model. In this paper, we work with a large class of linearly coupled translation invariant models which includes both the Nelson model and H. Fröhlich's polaron model. The problems considered are chosen based on relevance for the polaron model. A key input is an analysis of the behavior of the bottom of the spectrum of the fiber Hamiltonians at large total momentum. [ABSTRACT FROM AUTHOR]

Let A be an algebra over an operad in a cocomplete closed symmetric monoidal category. We study the category of A-modules. We define certain symmetric product functors of such modules generalizing the tensor product of modules over commutative algebras, which we use to define the notion of a jet module. This in turn generalizes the notion of a jet module over a module over a classical commutative algebra. We are able to define Atiyah classes (i.e., obstructions to the existence of connections) in this generalized context. We use certain model structures on the category of A-modules to study the properties of these Atiyah classes. The purpose of the paper is not to present any really deep theorem. It is more about the right concepts when dealing with modules over an algebra that is defined over an arbitrary operad, i.e., the aim is to show how to generalize various classical constructions, including modules of jets, the Atiyah class and the curvature, to the operadic context. For convenience of the reader and for the purpose of defining the notations, the basic definitions of the theory of operads and model categories are included. [ABSTRACT FROM AUTHOR]

This paper deals with the scattering of time-harmonic acoustic waves by inhomogeneous medium. We study the problem to recover the near and the far field using a priori information about the refractive index and the support of inhomogeneity. The incident spherical wave is modified in such a way as to recover the plane wave incidence when the source point approaches infinity. Applying the low-frequency expansions, the scattering medium problem is reduced to a sequence of potential problems for the approximation coefficients in the presence of a monopole singularity located at the source of incidence. Complete expansions for the integral representation formula in the near field as well as for the scattering amplitude in the far field are provided. The method is applied to the case of a spherical region of inhomogeneity and a radial dependent refractive index. As the point singularity tends to infinity, the relative results recover the scattering medium problem for plane wave incidence. [ABSTRACT FROM AUTHOR]

In the present paper the small quantum cohomology ring of some Fano threefolds which are obtained as one- or two-curve blow-ups from ℙ3 or the quadric Q3 is explicitely computed. Because of systematic usage of the associativity property of quantum product only a very small and enumerative subset of Gromov–Witten invariants is needed. Then, for these threefolds the Dubrovin conjecture on the semisimplicity of quantum cohomology is proven by checking the computed quantum cohomology rings and by showing that a smooth Fano threefold X with b3(X) = 0 admits a complete exceptional set of the appropriate length. [ABSTRACT FROM AUTHOR]

In this paper, we extend a Howards–Luecke's theorem on strongly n-trivial knots to link case. We show that a link is strongly n-trivial for all n if and only if it is a trivial link. [ABSTRACT FROM AUTHOR]

Akbulut generalized Fintushel–Stern knot surgery in a certain way. He showed that an operation C(K#(-K)) → {diffeo type of X} is not injective, where C(K#(-K)) is self-concordance set of K#(-K) and K is trefoil knot. In the present paper we prove that the same phenomenon occurs for any knot K and for some other knots L instead of K#(-K). [ABSTRACT FROM AUTHOR]

The Multi-Tier (M-Tier) algorithm proposed in [1], has enabled an enhanced correlation between dynamic resource utilization and QoS guarantees. The algorithm favored the delay sensitive applications. Indirectly, this infers that the assignment of priorities practiced in the algorithm is static. In redesigning the algorithm, priority assignments should be able to be implemented dynamically. Thus, enabling an embedded element to provide implementation mobility. This would depend upon the current status of the classified buffers and the tolerance level of the delay sensitive traffic. Integrating control parameters to enable alternation in scheduling priorities is an option to resolve the element of partiality present in the M-Tier algorithm. Thereafter, the proposed algorithm will be denoted as the M-Tier(T) algorithm [2]. The paper proposes a detailed mathematical model for the analysis of dynamic resource reservation algorithms implemented in IP switches. The semi-markov process (SMP) approach utilized provides an accurate performance prediction and representation of resource reservation mechanisms. The algorithm correlates the average packet delay and packet loss ratio parameters to activate the dynamic resource reservation mechanism in a hierarchical manner. The developed models are validated through discrete-event simulation. The performance of the algorithm is studied in terms of average packet delay and network throughput. [ABSTRACT FROM AUTHOR]

In this paper, we present a historical overview of the development of fuzzy mathematics. We mainly concentrate on the evolution of the mathematical representation of fuzziness by means of fuzzy set theory. From the many remaining recently introduced models to represent imprecise and uncertain information, we briefly treat rough set theory. [ABSTRACT FROM AUTHOR]

The brain has evolved to enable organisms to survive in a complicated and dynamic world. Its operation is based upon a priori models of the environment which are adapted, during learning, in response to new and changing stimuli. The same qualities that make biological learning mechanisms ideal for organisms make their underlying mathematical algorithms ideal for certain technological applications, especially those concerned with understanding the physical processes giving rise to complicated data sets. In this paper, we offer a mathematical model for the underlying mechanisms of biological learning, and we show how this mathematical approach to learning can yield a solution to the problem of imaging time-varying objects from X-ray computed tomographic (CT) data. This problem relates to several practical aspects of CT imaging including the correction of motion artifacts caused by patient movement or breathing. [ABSTRACT FROM AUTHOR]

In this paper, we consider a set of mobile nodes, each of which moves with constant velocity. We present algorithms to determine which of these mobile nodes can be captured the soonest by a set of one or more pursuers. We use a time parameterized R-tree (TPR-tree) to index these moving points. We then develop algorithms that operate on the TPR-tree to answer three query variations: (1) a single pursuer that is faster than all of the mobile nodes, (2) a single pursuer that is slower than some of the mobile nodes and (3) multiple pursuers. Experimental results show that our algorithms are simpler and faster than other approaches to solve the problem. [ABSTRACT FROM AUTHOR]

In this paper, the authors establish the inhomogeneous Plancherel­Pôlya inequalities on spaces of homogeneous type by use of the inhomogeneous discrete Calderón reproducing formulas. As an application, the authors prove that the Lebesgue norms of the inhomogeneous Littlewood­Paley γ-function and S-function on spaces of homogeneous type are equivalent. All results are new even for Rn. [ABSTRACT FROM AUTHOR]

The paper reviews single-neuron learning rules for minor component analysis and suggests a novel minor component learning rule. In this rule, the weight vector length is self-stabilizing, i.e., moving towards unit length in each learning step. In simulations with low- and medium-dimensional data, the performance of the novel learning rule is compared with previously suggested rules. [ABSTRACT FROM AUTHOR]

This paper introduces an automatic robust nonlinear identification algorithm using the leave-one-out test score also known as the PRESS (Predicted REsidual Sums of Squares) statistic and regularised orthogonal least squares. The proposed algorithm aims to achieve maximised model robustness via two effective and complementary approaches, parameter regularisation via ridge regression and model optimal generalisation structure selection. The major contributions are to derive the PRESS error in a regularised orthogonal weight model, develop an efficient recursive computation formula for PRESS errors in the regularised orthogonal least squares forward regression framework and hence construct a model with a good generalisation property. Based on the properties of the PRESS statistic the proposed algorithm can achieve a fully automated model construction procedure without resort to any other validation data set for model evaluation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the possibility of using closed timelike curves (CTCs) in relativistic hypercomputation. We introduce a wormhole based hypercomputation scenario which is free of the common worries, such as the blueshift problem. We also discuss the physical reasonability of our scenario, and why we cannot simply ignore the possibility of the existence of spacetimes containing CTCs. [ABSTRACT FROM AUTHOR]