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The ancient Vedic mathematics is well known for quicker handy multiplications but its recognition as an integrated circuit core against existing hardware multipliers is not established. As optimized hardware implementation of binary multiplier is one of the prominent unsolved problems in computer architecture, this paper proposes efficient Urdhava Tiryakbhyam Vedic multiplier architecture and compares it with the set of hierarchical multiplication algorithms which generate multiplication result in a single clock cycle. Two innovative algorithms are proposed here, one with a compact structure and another for faster execution. Also, its optimized transistor level layout is designed and implemented. To maintain homogeneity for comparison, all the algorithms are programmed on a common HDL language platform and analyzed with the same tool and technology. Final results indicate that the proposed architecture delivers 15.5% less power delay product (PDP) compared to closest competitor algorithm. [ABSTRACT FROM AUTHOR]

This study investigates the axisymmetric postbuckling of functionally graded graphene platelets reinforced composite (FG-GPLRC) annular plates resting on nonlinear elastic medium in thermal environment. Five kinds of graphene platelets (GPLs) distribution patterns including U -pattern, X -pattern, O -pattern, A -pattern, and V -pattern have been considered. The nonlinear equilibrium equations and associated boundary conditions are obtained based upon the Mindlin plate theory. The governing equations are solved via the generalized differential quadrature method (GDQM). Afterwards, the direct iterative method is implemented to accomplish postbuckling loads using the buckling mode deflection. In order to confirm the accuracy of the present model, comparisons between our data with those published in the available literature are put forth. Eventually, this paper emphasizes the impact of diverse parameters such as geometrical parameters of the structure, GPLs patterns and their geometric, GPLs weight fraction, boundary conditions, elastic medium's parameters and temperature change on the buckling and postbuckling response of nanocomposite annular plates. It can be found that elastic medium overshadows the applicability of distribution patterns and weight fraction of GPLs. [ABSTRACT FROM AUTHOR]

In this paper, we study the maximum number of limit cycles for the unfolding of codimension-3 planar singularities with nilpotent linear parts. In [J. Math. Anal. Appl.499 (2017)], the authors proved that when parameter a ∈ (− 1 , 1) \ { 0 , − 2 / 3 } is rational, the corresponding problem could be transformed to solving semi-algebraic systems. At the same time, it is pointed out that when a = − 2 / 3 , the logarithmic function will appear according to the method, which makes it impossible to solve the problem. In this paper, we use some techniques to avoid the occurrence of logarithmic function, and get the corresponding system to produce at most two limit cycles. [ABSTRACT FROM AUTHOR]

For a graph G = (V , E) and a set S ⊆ V (G) of size at least 2 , a path in G is said to be an S -path if it connects all vertices of S. Two S -paths P 1 and P 2 are said to be internally disjoint if E (P 1) ∩ E (P 2) = ∅ and V (P 1) ∩ V (P 2) = S. Let π G (S) denote the maximum number of internally disjoint S -paths in G. The k -path-connectivity π k (G) of G is then defined as the minimum π G (S) , where S ranges over all k -subsets of V (G). In [M. Hager, Path-connectivity in graphs, Discrete Math. 59 (1986) 53–59], the k -path-connectivity of the complete bipartite graph K a , b was calculated, where k ≥ 2. But, from his proof, only the case that 2 ≤ k ≤ min { a , b } was considered. In this paper, we calculate the situation that min { a , b } + 1 ≤ k ≤ a + b and complete the result. [ABSTRACT FROM AUTHOR]

The g -extra edge-connectivity is an important measure for the reliability of interconnection networks. Recently, Yang et al. [Appl. Math. Comput. 320 (2018) 464–473] determined the 3 -extra edge-connectivity of balanced hypercubes B H n and conjectured that the g -extra edge-connectivity of B H n is λ g ( B H n) = 2 (g + 1) n − 4 g + 4 for 2 ≤ g ≤ 2 n − 1. In this paper, we confirm their conjecture for n ≥ 6 − 1 2 g + 1 and 2 ≤ g ≤ 8 , and disprove their conjecture for n ≥ 3 e g ( B H n) g + 1 and 9 ≤ g ≤ 2 n − 1 , where e g ( B H n) = max { | E ( B H n [ U ]) | | U ⊆ V (B H n) , | U | = g + 1 }. [ABSTRACT FROM AUTHOR]

This paper reports that synergetics are used to analyze the crazing evolution. On this basis, chaotic effect is explored. The chaos equation is established and verified. The theoretical derivation are consistent with the experimental results. We design a special specimen with a special loading mode, the transient monitoring function of acoustic emission (AE) technology is used to track and detect the crazing inside the PMMA in real time, and the experiments show that synergetics can explain the crazing properties of polymer. Importantly, the mathematical explanation is also given. The AE analysis, synergetics, and craze photo reached a conclusion that the crazing has chaotic behavior. After analyzing the AE events and crazing at different stress levels, the accuracy of synergetic approach for crazing is verified. By studying the course of AE events and crazing, the self-organization effect is proposed. The research results will provide data support for the application of PMMA in ship, aircraft, and precision instruments. [ABSTRACT FROM AUTHOR]

Passive synthesis of fractional driving-point immittance function is one of the most important research topics in fractional circuits. The synthesis method for a class of fractional driving-point immittance function is proposed in this paper. Firstly, the immittance function of passive fractional circuit is transformed to multivariable positive-real function by proper variable substitution. Secondly, to synthesize the function, except one variable, other high-order variables are transformed to the combination of products of different one-order variables by introducing new variables. Thirdly, synthesize the new function by traditional method. At last, substitute elements inversely twice and the final circuit for fractional driving-point immittance function can be achieved. The method is verified by giving synthesis demonstration. [ABSTRACT FROM AUTHOR]

Sparse representation classification (SRC) has been successfully applied into hyperspectral image (HSI). A test sample (pixel) can be linearly represented by a few training samples of the training set. The class label of the test sample is then decided by the reconstruction residuals. To incorporate the spatial information to improve the classification performance, a patch matrix, which includes a spatial neighborhood set, is used to replace the original pixel. Generally, the objective function of the reconstruction residuals is represented as Frobenius-norm, which actually treats the elements in the reconstruction residuals in the same way. However, when a patch locates in the image edge, the samples in the patch may belong to different classes. Frobenius-norm is not suitable to compute the reconstruction residuals. In this paper, we propose a robust patch-based sparse representation classification (RPSRC) based on -norm. An iteration algorithm is given to compute RPSRC efficiently. Extensive experimental results on two real-life HSI datasets demonstrate the effectiveness of RPSRC. [ABSTRACT FROM AUTHOR]

Perpetual points represent a new interesting topic in the literature of nonlinear dynamics. This paper introduces some chaotic flows with four different structural features from the viewpoint of fixed points and perpetual points. [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]

In this paper we discuss two modifications of the surrogate data method based on phase randomization, see [Theiler et al., 1992]. By construction, phase randomized surrogates are circular stationary. In this respect they differ from the original time series. This can cause level inaccuracies of surrogate data tests. We will illustrate this. These inaccuracies are caused by end to end mismatches of the original time series. In this paper we will discuss two approaches to remedy this problem: resampling from subsequences without end to end mismatches and data tapering. Both methods can be understood as attempts to make non-circular data approximately circular. We will show that the first method works quite well for a large range of applications whereas data tapering leads only to improvements in some examples but can be very unstable otherwise. [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]

The longest common subsequence is a well known and popular method for measuring similarity between sequences. It advocates the use of information contained in the longest common subsequence as an indication of similarity. In this paper we consider the count of all common subsequences as a measure of sequence similarity with the view that all common information is captured. This measure is inspired and derived from a generic similarity measure, neighborhood counting metric. The close connection of the neighborhood counting metric with probability and the Bayes classifier helps gain an insight from the probabilistic perspective into the all-common subsequences measure. We design algorithms to calculate this measure and we also carry out an experiment in the framework of k-nearest neighbors on a gene sequence classification task. The experiment shows that the all-common subsequences measure and the longest common subsequence measure have little difference for small k values, but differ significantly for large k values. The performance of the all-common subsequences measure remains steady as k gets larger, but the performance of the longest common subsequence measure drops sharply as k gets larger. Such a property may be useful for those tasks where we are interested not only in the nearest neighbor, but also in the first k nearest neighbors. The main contribution of this paper is a suite of algorithms for finding all common subsequences. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamical behavior of nonautonomous, almost-periodic discrete FitzHugh–Nagumo system defined on infinite lattices. We prove that the nonautonomous infinite-dimensional system has a uniform attractor which attracts all solutions uniformly with respect to the translations of external terms. We also establish the upper semicontinuity of uniform attractors when the infinite-dimensional system is approached by a family of finite-dimensional systems. This paper is based on a uniform tail method, which shows that, for large time, the tails of solutions are uniformly small with respect to bounded initial data as well as the translations of external terms. The uniform tail estimates play a crucial role for proving the uniform asymptotic compactness of the system and the upper semicontinuity of attractors. [ABSTRACT FROM AUTHOR]

When a CDMA signal is passed through an RF transmitter, nonlinear elements cause spectral regrowth which result in reduction of spectral efficiency. CDMA signal has a pseudo noise nature; hence its mathematical treatment is too complex to analysis. In this paper, first it will be shown how to simplify the complex mathematics of CDMA signal. Then, a deterministic signal replaces the CDMA signal and the system response to both of them is calculated. In this paper, for the first time, ACPR is explicitly calculated for both the CDMA and deterministic signals. ACPR is calculated in terms of the nonlinear system coefficients and input power, and therefore, can be used in design objectives. In addition, it will be shown that if input power of the deterministic signal is multiplied by $\sqrt{20}$ (i.e., correction factor), ACPR error of these kinds of signals in -55 dBc is less than 2.2% for the system nonlinearity orders up to 13. This correction factor is obtained by both theoretical and simulation methods. [ABSTRACT FROM AUTHOR]

In this paper, attribute reduction in variable precision rough set model is discussed. Several kinds of reducts preserving some of lower approximations, upper approximations, boundary regions and the unpredictable region are discussed. Relations among those kinds of reducts are investigated. As a basis for reduct computation, Boolean function representations of the preservation of lower approximations, upper approximations, boundary regions and the unpredictable region are discussed. Throughout this paper, the great difference between the analysis using variable precision rough sets and the classical rough set analysis is emphasized. [ABSTRACT FROM AUTHOR]

Many of the tools of dynamical systems and control theory have gone largely unused for fluids, because the governing equations are so dynamically complex, both high-dimensional and nonlinear. Model reduction involves finding low-dimensional models that approximate the full high-dimensional dynamics. This paper compares three different methods of model reduction: proper orthogonal decomposition (POD), balanced truncation, and a method called balanced POD. Balanced truncation produces better reduced-order models than POD, but is not computationally tractable for very large systems. Balanced POD is a tractable method for computing approximate balanced truncations, that has computational cost similar to that of POD. The method presented here is a variation of existing methods using empirical Gramians, and the main contributions of the present paper are a version of the method of snapshots that allows one to compute balancing transformations directly, without separate reduction of the Gramians; and an output projection method, which allows tractable computation even when the number of outputs is large. The output projection method requires minimal additional computation, and has a priori error bounds that can guide the choice of rank of the projection. Connections between POD and balanced truncation are also illuminated: in particular, balanced truncation may be viewed as POD of a particular dataset, using the observability Gramian as an inner product. The three methods are illustrated on a numerical example, the linearized flow in a plane channel. [ABSTRACT FROM AUTHOR]

Illuminative deformation patterns of a honeycomb structure are presented. A representative volume element of a honeycomb structure consisting of 2 × 2 hexagonal cells is modeled to be a ${\rm D}_6\dot{+}({\rm C}_2\times\tilde{\rm C}_2)$-equivariant system. The bifurcation mechanism and an exhaustive list of possible bifurcated patterns are obtained by group-theoretic bifurcation theory. A flower mode of the honeycomb is shown to have the same symmetry as the so-called anti-hexagon in the Rayleigh–Bénard convection. A numerical bifurcation analysis is conducted on an elastic in-plane honeycomb structure consisting of 2×2 cells to produce beautiful wallpapers of bifurcating deformation patterns and, in turn, to highlight the achievement of the paper. New deformation patterns of a honeycomb structure have been found and classified in a systematic manner. Knowledge of the symmetries of the bifurcating solutions has turned out to be vital in the successful numerical tracing of the bifurcated paths. This paper paves the way for the introduction of the results hitherto obtained for flow patterns in fluid dynamics into the study of patterns on materials. [ABSTRACT FROM AUTHOR]

The subject of this paper is a generalized approach to relative scalar cardinalities of fuzzy sets. In the main part of the paper, we discuss basic properties of triangular norm-based relative cardinality such as valuation property, the cartesian product rule and complementary rule. Examples of cardinalities satisfying those properties are also given. [ABSTRACT FROM AUTHOR]

A system that consists of a damped oscillator impacting two immovable fenders has been considered in this paper. In the first part a method of analytical determination of the existence of periodic solutions to the equations of motion and a method of analysis of the stability of these solutions have been presented. The results of the computations carried out by means of these methods have been illustrated by a few examples. In the second part of the paper, the results of some numerical investigations have been presented. The goal of these studies was to determine, in which regions of parameters characterizing the system, the motion of the oscillator is periodic and stable. [ABSTRACT FROM AUTHOR]

By applying the undetermined coefficient method, this paper finds homoclinic and heteroclinic orbits in the Chen system. It analytically demonstrates that the Chen system has one heteroclinic orbit of Ši'lnikov type that connects two nontrivial singular points. The Ši'lnikov criterion guarantees that the Chen system has Smale horseshoes and the horseshoe chaos. In addition, there also exists one homoclinic orbit joined to the origin. The uniform convergence of the series expansions of these two types of orbits are proved in this paper. It is shown that the heteroclinic and homoclinic orbits together determine the geometric structure of Chen's attractor. [ABSTRACT FROM AUTHOR]

In this paper we study phase space relations in a certain class of discrete dynamical systems over graphs. The systems we investigate are called Sequential Dynamical Systems (SDSs), which are a class of dynamical systems that provide a framework for analyzing computer simulations. Specifically, an SDS consists of (i) a finite undirected graph Y with vertex set {1,2,…,n} where each vertex has associated a binary state, (ii) a collection of Y-local functions (Fi,Y)i∈v[Y] with $F_{i,Y}: \mathbb{F}_2^n\to \mathbb{F}_2^n$ and (iii) a permutation π of the vertices of Y. The SDS induced by (i)–(iii) is the map \[ [F_Y,\pi] = F_{\pi(n),Y} \circ \cdots \circ F_{\pi(1),Y}\,. \] The paper is motivated by a general reduction theorem for SDSs which guarantees the existence of a phase space embedding induced by a covering map between the base graphs of two SDSs. We use this theorem to obtain information about phase spaces of certain SDSs over binary hypercubes from the dynamics of SDSs over complete graphs. We also investigate covering maps over binary hypercubes, $Q_2^n$, and circular graphs, Circn. In particular we show that there exists a covering map $\phi: Q_2^n\to K_{n+1}$ if and only if 2n≡0 mod n+1. Furthermore, we provide an interpretation of a class of invertible SDSs over circle graphs as right-shifts of length n-2 over {0,1}2n-2. The paper concludes with a brief discussion of how we can extend a given covering map to a covering map over certain extended graphs. [ABSTRACT FROM AUTHOR]

An emulated digital CNN-UM (CASTLE) architecture was published few years ago.1 Different emulated digital CNN-UM architectures are analyzed in the paper. These new modified architectures are optimized according to the silicon area, operating speed or dissipated power. A reconfigurable arithmetic core will also be shown in the paper, by which solution of the neighborhood size can be changed. An advanced CASTLE with pipe-lining is presented. The operation frequency is increased by using this solution in approximately 10 times. [ABSTRACT FROM AUTHOR]

This paper considers a renewal process in which the interarrival times and rewards are characterized as fuzzy variables. A fuzzy elementary renewal theorem shows that the expected number of renewals per unit time is just the expected reciprocal of the interarrival time. Furthermore, the expected reward per unit time is provided by a fuzzy renewal reward theorem. Finally, a numerical example is presented for illustrating the theorems introduced in the paper. [ABSTRACT FROM AUTHOR]

Uncertain differential system is a type of differential system involving uncertain processes. Stability analysis has been widely studied but no work has been dedicated to attractivity analysis of uncertain differential systems. In this paper, some concepts of attractivity for uncertain differential systems are presented. Then the corresponding sufficient and necessary conditions are given. Furthermore, the stability of the solutions and α-path of uncertain differential systems are studied. [ABSTRACT FROM AUTHOR]

By using the method of dynamical systems, this paper studies the exact traveling wave solutions and their bifurcations in the Gardner equation. Exact parametric representations of all wave solutions as well as the explicit analytic solutions are given. Moreover, several series of exact traveling wave solutions of the Gardner-KP equation are obtained via an auxiliary function method. [ABSTRACT FROM AUTHOR]

Under an interpretation of the principles of non-contradiction and excluded-middle based on the concept of self-contradiction, this paper mainly deals with the principles' verification in the case of the unit interval of the real line. Such verification is done in the three following cases: (1) The unit interval is totally ordered by the restriction to it of the usual order of the real line, (2) the unit interval is partially ordered by the sharpened order, and (3) the unit interval is under a new particular preorder. The first case is immediately extended to characterize the case of fuzzy sets. [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]

Many papers have addressed the task of proposing a set of convenient axioms that a good rule interestingness measure should fulfil. We provide a new study of the principles proposed until now by means of the logic model proposed by Hájek et al.14 In this model association rules can be viewed as general relations of two itemsets quantified by means of a convenient quantifier.28 Moreover, we propose and justify the addition of two new principles to the three proposed by Piatetsky-Shapiro.27 We also use the logic approach for studying the relation between the different classes of quantifiers and these axioms. We define new classes of quantifiers according to the notions of strong and very strong rules, and we present a quantifier based on the certainty factor measure,317 studying its most salient features. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotic behavior of the solutions u(x,t) of the Swift–Hohenberg equation with quintic nonlinearity on a one-dimensional domain (0, L). With α and the length L of the domain regarded as bifurcation parameters, branches of nontrivial solutions bifurcating from the trivial solution at certain points are shown. Local behavior of these branches are also studied. Global bounds for the solutions u(x,t) are established and then the global attractor is investigated. Finally, with the help of a center manifold analysis, two types of structures in the bifurcation diagrams are presented when the bifurcation points are closer, and their stabilities are analyzed. [ABSTRACT FROM AUTHOR]

Watermarking is now considered as an efficient means for assuring copyright protection and data owner identification. Watermark embedding techniques depend on the representation domain of the image (spatial, frequency, and multiresolution). Every domain has its specific advantages and limitations. Moreover, each technique in a chosen domain is found to be robust to specific sets of attack types. So we need to propose more robust domains to defeat these limitations and respect all the watermarking criterions (capacity, invisibility and robustness). In this paper, a new watermarking method is presented using a new domain for the image representation and the watermark embedding: the mathematical Hessenberg transformation. This domain is found to be robust against a wide range of STIRMARK attacks such as JPEG compression, convolution filtering and noise adding. The robustness of the new technique in preserving and extracting the embedded watermark is proved after various attacks types. It is also improved when compared with other methods in use. In addition, the proposed method is blind and the use of the host image is not needed in the watermark detection process. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy set, was introduced by Atanassov, has been applied to many different fields, such as logic programming, pattern recognition, and decision making, etc. However, so far there has been few investigation on how to transform attribute tested values of alternative into a intuitionistic fuzzy number, and then complete decision making by intuitionistic fuzzy information. In this paper, the original attribute value (objective information) are characterized by crisp number which are given by decision maker. We define the concepts of supporting, opposing and neutral set of alternative respectively, develop an approach for transform attribute values into intuitionistic fuzzy number, and determine the order of alternatives based on the score and the degree of accuracy of the intuitionistic fuzzy number. Finally, a practical example is provided to illustrate the developed method. [ABSTRACT FROM AUTHOR]

In this paper we investigate, via numerical simulations, the parameter space of the set of autonomous differential equations of a Chua oscillator, where the piecewise-linear function usually taken to describe the nonlinearity of the Chua diode was replaced by a cubic polynomial. As far as we know, we are the first to report that this parameter-space presents islands of periodicity embedded in a sea of chaos, scenario typically observed only in discrete-time models until recently. We show that these islands are self-similar, and organize themselves in period-adding bifurcation cascades. [ABSTRACT FROM AUTHOR]

Chua's circuit is very suitable as a programmable chaos generator because of its robust nonlinearity. In addition to exhibiting a rich variety of bifurcation and chaos phenomenon, this circuit can be modeled and realized with a fixed main system block and many different nonlinear function blocks such as piecewise-linear function, cubic-like function, piecewise-quadratic function and other trigonometric functions. This paper presents a FPAA (Field Programmable Analog Array) based programmable implementation of Chua's circuit. Nonlinear function blocks used in Chua's circuit are modeled with an FPAA and hence a model can be rapidly changed for realization of other nonlinear functions. In this study, four FPAA-based reconfigurable implementations of Chua's circuit have been realized. Experimental results agree with numerical simulation and results obtained from discrete electronic implementations of Chua's circuit. [ABSTRACT FROM AUTHOR]

This paper proposes a new technique for generating random-looking binary digits based on an irregularly decimated chaotic map. We present a class of irregularly decimated chaos-based keystream generators, related to the shrinking generator, for the generation of binary sequences. Each generator consists of two subsystems: a control subsystem and a generating subsystem, where each subsystem is based on a single chaotic map. This chaotic map is presented as a 1-D piecewise chaotic map related to the chaotic logistic map. We conduct an analysis of the dynamical behavior of the proposed map to integrate it as a component in the proposed generators subsystems. The output bits of these keystream generators are produced by applying a threshold function to convert the floating-point iterates of the irregularly decimated map into a binary form. The generated keystream bits are demonstrated to exhibit high level of security, long period length, high linear complexity measure and random-like properties at given certain parameter values. Standard statistical tests on the proposed generators, as well as other keystream generators, are performed and compared. [ABSTRACT FROM AUTHOR]

In this paper, we consider a planar dynamical system with a piecewise linear function containing two dropping sections and approximating some continuous nonlinear function. Studying all possible local and global bifurcations of its limit cycles, we prove that such a piecewise linear dynamical system, with five singular points, can have at most four limit cycles, three of which surround the foci one by one and the fourth limit cycle surrounds all of the singular points of this system. [ABSTRACT FROM AUTHOR]

Equilibrium manifold is a manifold that consists of equilibrium points. Planar systems with one-dimensional equilibrium manifolds are considered in this paper. First, for such planar systems, a unified equation with the horizontal axis as the equilibrium curve is formulated. Then, according to the corresponding linearized systems, different cases are discussed: For the nondegenerate case, the simplest normal form of a system with simplified Bogdanov–Takens singularities is obtained; for the general first-order degenerative case, the simplest normal forms are completely characterized; finally, for the general higher-order degenerative case, deduction of the simplest normal form is illustrated. [ABSTRACT FROM AUTHOR]

For the purpose of estimating the mixing matrix under the nonstrictly sparse condition, this paper presents the algorithms to approximate the mixing matrix in two different situations in which the source vectors are 1-sparse and (m - 1)-sparse. When the source signals are 1-sparse, we use the generalized spherical coordinate transformation to convert the matrix of observation signals into the new one, which makes the process of estimating column A become the process of finding the center point of these new data. For the situation that source signals are (m - 1)-sparse, we propose a new algorithm for the underdetermined mixtures blind source separation based on hyperplane clustering. The algorithm firstly finds out the linearly independent vectors from the observations, and secondly determines all the normal vectors of hyperplanes by analyzing the number of observations that are in the same hyperplane. Finally, we identify the column vectors of the mixing matrix A by calculating the vectors which are orthogonal to the clustered normal vectors. These two new algorithms for estimating the mixing matrix are more suitable for the general cases as they have lower requirement for the sparsity of the observations. [ABSTRACT FROM AUTHOR]

This paper concerns the nondegenerate center problem in certain families of differential systems in ℝ2. We study the existence of uniformly isochronous centers and the form of their commutators. We also classify all centers of the family of the BiLiénard systems of degree five and the maximum number of limit cycles which can bifurcate from a fine focus. [ABSTRACT FROM AUTHOR]

As we know, Hopf bifurcation is an important part of bifurcation theory of dynamical systems. Almost all known works are concerned with the bifurcation and number of limit cycles near a nondegenerate focus or center. In the present paper, we study a general near-Hamiltonian system on the plane whose unperturbed system has a nilpotent center. We obtain an expansion for the first order Melnikov function near the center together with a computing method for the first coefficients. Using these coefficients, we obtain a new bifurcation theorem concerning the limit cycle bifurcation near the nilpotent center. An interesting application example & a cubic system having five limit cycles & is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we propose a mathematical framework for studying word order optimization. The framework relies on the well-known positive correlation between cognitive cost and the Euclidean distance between the elements (e.g. words) involved in a syntactic link. We study the conditions under which a certain word order is more economical than an alternative word order by proposing a mathematical approach. We apply our methodology to two different cases: (a) the ordering of subject (S), verb (V) and object (O), and (b) the covering of a root word by a syntactic link. For the former, we find that SVO and its symmetric, OVS, are more economical than OVS, SOV, VOS and VSO at least 2/3 of the time. For the latter, we find that uncovering the root word is more economical than covering it at least 1/2 of the time. With the help of our framework, one can explain some Greenbergian universals. Our findings provide further theoretical support for the hypothesis that the limited resources of the brain introduce biases toward certain word orders. Our theoretical findings could inspire or illuminate future psycholinguistics or corpus linguistics studies. [ABSTRACT FROM AUTHOR]

There are well established methods for fuzzy clustering especially for the cases where the feature values are numerical of ratio or interval scale. Not so well established are methods to be applied when the feature values are ordinal or nominal. In that case there is no one best method it seems. This paper discusses a method where unknown numeric variables are assigned to the ordinal values. Part of minimizing an objective function for the clustering is to find numeric values for these variables. Thus real numbers of interval scale and even ratio scale for that matter are assigned to the original ordinal values. The method uses the same objective function as used in fuzzy c-means clustering but both the membership function and the ordinal to real mapping are determined by gradient descent. Since the ordinal to real mapping is not known it cannot be verified for its legitimacy. However the ordinal to real mapping that is found is best in terms of the clustering produced. Simulations show the method to be quite effective. [ABSTRACT FROM AUTHOR]

During the last years nature inspired intelligent techniques have become attractive for analyzing large data sets and solving complex optimization problems. In this paper, one of the most interesting of them, the Ant Colony Optimization (ACO), is used for the construction of a hybrid algorithmic scheme which effectively handles the Pap Smear Cell classification problem. This algorithmic approach is properly combined with a number of nearest neighbor based approaches for performing the requested classification task, through the solution of the so-called optimal feature subset selection problem. The proposed complete algorithmic scheme is tested in two sets of data. The first one consists of 917 images of pap smear cells and the second set consists of 500 images, classified carefully by expert cyto-technicians and doctors. Each cell is described by 20 numerical features, and the cells fall into seven (7) classes, four (4) representing normal cells and three (3) abnormal cases. Nevertheless, from the medical diagnosis viewpoint, a minimum requirement corresponds to the general two-class problem of correct separation between normal from abnormal cells. [ABSTRACT FROM AUTHOR]

Feature selection is an important task in pattern recognition. Support Vector Machine (SVM) and Minimax Probability Machine (MPM) have been successfully used as the classification framework for feature selection. However, these paradigms cannot automatically control the balance between prediction accuracy and the number of selected features. In addition, the selected feature subsets are also not stable in different data partitions. Minimum Error Minimax Probability Machine (MEMPM) has been proposed for classification recently. In this paper, we outline MEMPM to select the optimal feature subset with good stability and automatic balance between prediction accuracy and the size of feature subset. The experiments against feature selection with SVM and MPM show the advantages of the proposed MEMPM formulation in stability and automatic balance between the feature subset size and the prediction accuracy. [ABSTRACT FROM AUTHOR]

Media theory is a new branch of discrete applied mathematics originally developed in mid-nineties to deal with stochastic evolution of preference relations in political science and mathematical psychology. The theory focuses on a particular semigroup of ‘messages’ acting as transformations of a set of ‘states’, called a ‘medium’, whose axioms are both strong and natural. The term ‘medium’ stems from a particular application in which the transformations formalize the effects, on an individual, of ‘tokens’ of information delivered by the environment—that is, the ‘medium’. However, many different types of examples can be found, ranging from learning spaces to hypercube computers, suggesting that this concept is ubiquitous. The paper presents very basic concepts and results of media theory and is aimed at a wide body of researchers in discrete applied mathematics. [ABSTRACT FROM AUTHOR]

In this paper we present a precise description of the connectedness locus of the family of polynomials (z2 + x)2 + y, where x, y are real numbers. [ABSTRACT FROM AUTHOR]

In the past years, research in eye tracking development and applications has attracted much attention and the possibility of interacting with a computer employing just gaze information is becoming more and more feasible. Efforts in eye tracking cover a broad spectrum of fields, system mathematical modeling being an important aspect in this research. Expressions relating to several elements and variables of the gaze tracker would lead to establish geometric relations and to find out symmetrical behaviors of the human eye when looking at a screen. To this end a deep knowledge of projective geometry as well as eye physiology and kinematics are basic. This paper presents a model for a bright-pupil technique tracker fully based on realistic parameters describing the system elements. The system so modeled is superior to that obtained with generic expressions based on linear or quadratic expressions. Moreover, model symmetry knowledge leads to more effective and simpler calibration strategies, resulting in just two calibration points needed to fit the optical axis and only three points to adjust the visual axis. Reducing considerably the time spent by other systems employing more calibration points renders a more attractive model. [ABSTRACT FROM AUTHOR]

This paper presents a weighted support vector machine (WSVM) to improve the outlier sensitivity problem of standard support vector machine (SVM) for two-class data classification. The basic idea is to assign different weights to different data points such that the WSVM training algorithm learns the decision surface according to the relative importance of data points in the training data set. The weights used in WSVM are generated by a robust fuzzy clustering algorithm, kernel-based possibilistic c-means (KPCM) algorithm, whose partition generates relative high values for important data points but low values for outliers. Experimental results indicate that the proposed method reduces the effect of outliers and yields higher classification rate than standard SVM does when outliers exist in the training data set. [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 complex model for evolving the update strategy of a Particle Swarm Optimisation (PSO) algorithm is described in this paper. The model is a hybrid technique that combines a Genetic Algorithm (GA) and a PSO algorithm. Each GA chromosome is an array encoding a meaning for updating the particles of the PSO algorithm. The Evolved PSO algorithm is compared to several human-designed PSO algorithms by using ten artificially constructed functions and one real-world problem. Numerical experiments show that the Evolved PSO algorithm performs similarly and sometimes even better than the Standard approaches for the considered problems. The Evolved PSO is highly scalable (regarding the size of the problem's input), being able to solve problems having different dimensions. [ABSTRACT FROM AUTHOR]