On the V-stability of complex dynamical networks

This paper introduces the concept of Lyapunov V-stability for complex dynamical networks. Under the new framework, each dynamical node is associated with a passivity degree, which indicates to what extent an effort is required for stabilizing the node. From this approach, the network stability problem is converted to measuring the negative definiteness of one simple matrix that characterizes the topology of the network. Pinning control is then suggested and investigated based on the new V-stability formulation. As an illustrative example, a network with different node dynamics and non-uniform coupling strengths is simulated to verify the analytic results. Moreover, a comparison study for three different kinds of networks is provided to further illustrate the novelty and efficacy of the proposed V-stability criterion and stabilization scheme.     

Exponential p-stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays

In this paper, we study the impulsive stochastic Cohen–Grossberg neural networks with mixed delays. By establishing an L-operator differential inequality with mixed delays and using the properties of M-cone and stochastic analysis technique, we obtain some sufficient conditions ensuring the exponential p-stability of the impulsive stochastic Cohen–Grossberg neural networks with mixed delays. These results generalize a few previous known results and remove some restrictions on the neural networks. Two examples are also discussed to illustrate the efficiency of the obtained results.     

Real structured singular value conditions for the strong D-stability

Recently, Chen et al. (Systems Control Lett. 24 (1995) 19) proposed conditions for D-stability and strong D-stability in terms of structured singular values. In this paper, simpler conditions for the strong D-stability are derived.     

A nonlinear explicit two-step fourth algebraic order method of order infinity for linear periodic initial value problems

We examine a nonlinear explicit two-step method of fourth algebraic order and infinite phase-lag order for solving one-dimensional second-order linear periodic initial value problems (IVPs) of ordinary differential equations. Applying special vector arithmetic with respect to an analytic function, the method can be extended to be vector-applicable for multidimensional problems. Numerical results to illustrate the efficiency of the method are presented and sensitivity analysis indicates the validity of the method in the frequency regime.     

Absolute stability criteria with prescribed decay rate for finite-dimensional and delay systems

We provide here an extension of Popov criterion, permitting to check exponential stability with prescribed decay rate (otherwise called α-stability) of nonlinear delay systems with sector-bounded nonlinearities. As for the celebrated result, the main hypothesis is expressed under a frequency form. For the delay-free case, the latter is equivalent to a linear matrix inequality, whose solution may be found by widespread algorithms.     

Computing Bessel functions of the second kind in extreme parameter regimes

A useful method of computing the integral order Bessel functions of the second kind Y_n(x+iy) when either, the absolute value of the real part, or the imaginary part of the argument z=x+iy is small, is described. This method is based on computing the Bessel functions for extreme parameter regimes when x∼0 (or y∼0) and is useful because a number existing algorithms and methods fail to give correct results for small x or small y. The approximating equations are derived by expanding the Bessel function in Taylor series, are tested and discussed. The present work is a continuation of the previous one conducted in regard to the Bessel function of the first kind. The results of our formalism are compared to the available existing numerical methods used in Mathematica, IMSL, MATLAB, and the Amos library. Our numerical method is easy to implement, efficient, and produces reliable results. In addition, this method reduces the computation of the Bessel functions of the second complex argument to that of real argument which simplify the computation considerably.     

Intuitionistic fuzzy Hv-submodules

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to H_v-modules. The notion of an intuitionistic fuzzy H_v-submodule of an H_v-module is introduced, and some related properties are investigated. Characterizations of intuitionistic fuzzy H_v-submodules are given.     

Efficient parallel algorithm for the two-dimensional diffusion equation subject to specification of mass

An efficient L ₀-stable parallel algorithm is developed for the two-dimensional diffusion equation with non-local time-dependent boundary conditions. The algorithm is based on subdiagonal Padé approximation to the matrix exponentials arising from the use of the method of lines and may be implemented on a parallel architecture using two processors running concurrently with each processor employing the use of tridiagonal solvers at every time-step. The algorithm is tested on two model problems from the literature for which discontinuities between initial and boundary conditions exist. The CPU times together with the associated error estimates are compared.     

Multi-scale,multi-resolution brain cancer modeling

In advancing discrete-based computational cancer models towards clinical applications, one faces the dilemma of how to deal with an ever growing amount of biomedical data that ought to be incorporated eventually in one form or another. Model scalability becomes of paramount interest. In an effort to start addressing this critical issue, here, we present a novel multi-scale and multi-resolution agent-based in silico glioma model. While ‘multi-scale’ refers to employing an epidermal growth factor receptor (EGFR)-driven molecular network to process cellular phenotypic decisions within the micro-macroscopic environment, ‘multi-resolution’ is achieved through algorithms that classify cells to either active or inactive spatial clusters, which determine the resolution they are simulated at. The aim is to assign computational resources where and when they matter most for maintaining or improving the predictive power of the algorithm, onto specific tumor areas and at particular times. Using a previously described 2D brain tumor model, we have developed four different computational methods for achieving the multi-resolution scheme, three of which are designed to dynamically train on the high-resolution simulation that serves as control. To quantify the algorithms’ performance, we rank them by weighing the distinct computational time savings of the simulation runs vs. the methods’ ability to accurately reproduce the high-resolution results of the control. Finally, to demonstrate the flexibility of the underlying concept, we show the added value of combining the two highest-ranked methods. The main finding of this work is that by pursuing a multi-resolution approach, one can reduce the computation time of a discrete-based model substantially while still maintaining a comparably high predictive power. This hints at even more computational savings in the more realistic 3D setting over time, and thus appears to outline a possible path to achieve scalability for the all-important clinical translation.     

Automatic moment segmentation and peak detection analysis of heart sound pattern via short-time modified Hilbert transform

This paper proposes a novel automatic method for the moment segmentation and peak detection analysis of heart sound (HS) pattern, with special attention to the characteristics of the envelopes of HS and considering the properties of the Hilbert transform (HT). The moment segmentation and peak location are accomplished in two steps. First, by applying the Viola integral waveform method in the time domain, the envelope (E_T) of the HS signal is obtained with an emphasis on the first heart sound (S1) and the second heart sound (S2). Then, based on the characteristics of the E_T and the properties of the HT of the convex and concave functions, a novel method, the short-time modified Hilbert transform (STMHT), is proposed to automatically locate the moment segmentation and peak points for the HS by the zero crossing points of the STMHT. A fast algorithm for calculating the STMHT of E_T can be expressed by multiplying the E_T by an equivalent window (W_E). According to the range of heart beats and based on the numerical experiments and the important parameters of the STMHT, a moving window width of N = 1 s is validated for locating the moment segmentation and peak points for HS. The proposed moment segmentation and peak location procedure method is validated by sounds from Michigan HS database and sounds from clinical heart diseases, such as a ventricular septal defect (VSD), an aortic septal defect (ASD), Tetralogy of Fallot (TOF), rheumatic heart disease (RHD), and so on. As a result, for the sounds where S2 can be separated from S1, the average accuracies achieved for the peak of S1 (AP₁), the peak of S2 (AP₂), the moment segmentation points from S1 to S2 (AT₁₂) and the cardiac cycle (ACC) are 98.53%, 98.31% and 98.36% and 97.37%, respectively. For the sounds where S1 cannot be separated from S2, the average accuracies achieved for the peak of S1 and S2 (AP₁₂) and the cardiac cycle ACC are 100% and 96.69%.     

(?, T)-fuzzy rough approximation operators and the TL-fuzzy rough ideals on a ring

In this paper, we consider a ring as a universal set and study (?, T)-fuzzy rough approximation operators with respect to a TL-fuzzy ideal of a ring. First, some new properties of generalized (?, T)-fuzzy rough approximation operators are obtained. Then, a new fuzzy algebraic structure - TL-fuzzy rough ideal is defined and its properties investigated. And finally, the homomorphism of (?, T)-fuzzy rough approximation operators is studied.     

Fusion of color, local spatial and global frequency information for face recognition

This paper presents a novel face recognition method by means of fusing color, local spatial and global frequency information. Specifically, the proposed method fuses the multiple features derived from a hybrid color space, the Gabor image representation, the local binary patterns (LBP), and the discrete cosine transform (DCT) of the input image. The novelty of this paper is threefold. First, a hybrid color space, the RC_rQ color space, is constructed by combining the R component image of the RGB color space and the chromatic component images, C_r and Q, of the YC_bC_r and YIQ color spaces, respectively. The RC_rQ hybrid color space, whose component images possess complementary characteristics, enhances the discriminating power for face recognition. Second, three effective image encoding methods are proposed for the component images in the RC_rQ hybrid color space to extract features: (i) a patch-based Gabor image representation for the R component image, (ii) a multi-resolution LBP feature fusion scheme for the C_r component image, and (iii) a component-based DCT multiple face encoding for the Q component image. Finally, at the decision level, the similarity matrices generated using the three component images in the RC_rQ hybrid color space are fused using a weighted sum rule. Experiments on the Face Recognition Grand Challenge (FRGC) version 2 Experiment 4 show that the proposed method improves face recognition performance significantly. In particular, the proposed method achieves the face verification rate (ROC III curve) of 92.43%, at the false accept rate of 0.1%, compared to the FRGC baseline performance of 11.86% face verification rate at the same false accept rate.     

Innovative model to simulate exhalation phase in human respiratory system

In this paper, we present a mathematical model, which mimics the bronchial resistances of human's lung in an expiratory act. The model is implemented in Matlab. The inputs that are used in this model derive from spirometry test. This model is able to study a physiologic condition, a pathologic one and the patient's follow up after drug treatment. We split our study into two parts. The first one focuses the analysis on the gas fluido dynamic inside of the respiratory pathways. The second part takes care of the pressure equilibrium in the exchange zone. We use the outputs that derive from the second subsystem to solve the Bernoulli's equation of the first part. The model was validated with data provided from “Clinical Physiology Institute” of CNR and G. Monasterio Foundation of Pisa.     

Computing the λ-covers of a string

Given a string x of length n and an integer constant λ, the λ-Cover Problem is defined to be the identification of all the sets of λ substrings each of equal length that cover x. This problem can be solved by a general algorithm in O(n²) time for constant alphabet size. We also generalize the λ-Cover Problem, whereby a set of λ substrings of different lengths are considered, which can be computed using the general algorithm in O(n²) time.     

Applications of interval valued t-norms (t-conorms) to fuzzy n-ary sub-hypergroups

In this paper, we study a generalization of group, hypergroup and n-ary group. Firstly, we define interval-valued fuzzy (anti fuzzy) n-ary sub-hypergroup with respect to a t-norm T (t-conorm S). We give a necessary and sufficient condition for, an interval-valued fuzzy subset to be an interval-valued fuzzy (anti fuzzy) n-ary sub-hypergroup with respect to a t-norm T (t-conorm S). Secondly, using the notion of image (anti image) and inverse image of a homomorphism, some new properties of interval-valued fuzzy (anti fuzzy) n-ary sub-hypergroup are obtained with respect to infinitely ∨-distributive t-norms T (∧-distributive t-conorms S). Also, we obtain some results of T-product (S-product) of the interval-valued fuzzy subsets for infinitely ∨-distributive t-norms T (∧-distributive t-conorms S). Lastly, we investigate some properties of interval-valued fuzzy subsets of the fundamental n-ary group with infinitely ∨-distributive t-norms T (∧-distributive t-conorms S).     

On probabilistic n-ary hypergroups

The T-fuzzy n-ary subhypergroups of an n-ary hypergroup are defined by using triangular norms and some related properties are hence obtained. In particular, we consider the probabilistic version of n-ary hypergroups by using random sets and show that the fuzzy n-ary hypergroups defined by triangular norms are consequences of some probabilistic n-ary hypergroups under certain conditions. Some results on n-ary hypergroups recently given by Davvaz and Corsini are extended.     

A (4n − 9)/3 diagnosis algorithm on n-dimensional cube network

As a generalization of the precise and pessimistic diagnosis strategies of system-level diagnosis of multicomputers, the t/k diagnosis strategy can significantly improve the self-diagnosing capability of a system at the expense of no more than k fault-free processors (nodes) being mistakenly diagnosed as faulty. In the case k ? 2, to our knowledge, there is no known t/k diagnosis algorithm for general diagnosable system or for any specific system. Hypercube is a popular topology for interconnecting processors of multicomputers. It is known that an n-dimensional cube is (4n − 9)/3-diagnosable. This paper addresses the (4n − 9)/3 diagnosis of n-dimensional cube. By exploring the relationship between a largest connected component of the 0-test subgraph of a faulty hypercube and the distribution of the faulty nodes over the network, the fault diagnosis of an n-dimensional cube can be reduced to those of two constituent (n − 1)-dimensional cubes. On this basis, a diagnosis algorithm is presented. Given that there are no more than 4n − 9 faulty nodes, this algorithm can isolate all faulty nodes to within a set in which at most three nodes are fault-free. The proposed algorithm can operate in O(N log₂ N) time, where N = 2ⁿ is the total number of nodes of the hypercube. The work of this paper provides insight into developing efficient t/k diagnosis algorithms for larger k value and for other types of interconnection networks.     

TL-filters of integral residuated l-monoids

In this paper, we introduce and discuss the concept of TL-filters of integral residuated l-monoids. First we study some basic properties of TL-filters and give the formula for calculating the TL-filters generated by L-subsets. Then we discuss some properties of TL-filters under homomorphisms and study the relationship between TL-filters and T-congruence L-relations on integral commutative residuated l-monoids.     

Lattice structure of e-implications on L

In this paper, we consider the set of all e-implications on L^∗ and define two operations on the set of all representable e-implications on L^∗, thus endowing it with monoid structure which is also a distributive complete lattice.