Existence and Exponential Stability of Multiple Periodic Solutions for a Multidirectional Associative Memory Neural Network

The paper proposes several mathematical models of the multidirectional associative memory (MAM) neural network by analyzing its structure. A model of MAM with distributed delays is studied. Under some new assumptions on activation functions, 2^n₀[m/2]{2^{n_0[m/2]}} invariant subsets of MAM are constructed. Then the existence and the exponential stability of 2^n₀[m/2]{2^{n_0[m/2]}} periodic solutions located on invariant subsets are obtained by constructing a suitable Liapunov function and a Poincaré mapping. An estimating method of the exponential convergence rate is given. The obtained results are new to MAM neural networks. An example is given to illustrate the effectiveness of the results.     

New receipt-free voting scheme using double-trapdoor commitment

It is considered to be the most suitable solution for large scale elections to design an electronic voting scheme using blind signatures and anonymous channels. Based on this framework, Okamoto first proposed a receipt-free voting scheme [30] for large scale elections. However, in the following paper, Okamoto [31] proved that the scheme [30] was not receipt-free and presented two improved schemes. One scheme requires the help of the parameter registration committee and the other needs a stronger physical assumption of the voting booth. In this paper, we utilize the double-trapdoor commitment to propose a new receipt-free voting scheme based on blind signatures for large scale elections. Neither the parameter registration committee nor the voting booth is required in our scheme. We also present a more efficient zero-knowledge proof for secret permutation. Therefore, our scheme is much more efficient than Okamoto’s schemes [30] and [31] with the weaker physical assumptions. Moreover, we prove that our scheme can achieve the desired security properties.     

Convergence properties of the softassign quadratic assignment algorithm.

The softassign quadratic assignment algorithm is a discrete-time, continuous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its convergence properties have not been studied. Here, we construct discrete-time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.     

Responses of the reflectance indices PRI and NDVI to experimental warming and drought in European shrublands along a north-south climatic gradient

The aim of this study was to evaluate the use of ground-based canopy reflectance measurements to detect changes in physiology and structure of vegetation in response to experimental warming and drought treatment at six European shrublands located along a North-South climatic gradient. We measured canopy reflectance, effective green leaf area index (green LAIe) and chlorophyll fluorescence of dominant species. The treatment effects on green LAIe varied among sites. We calculated three reflectance indices: photochemical reflectance index PRI [531 nm; 570 nm], normalized difference vegetation index NDVI₆₈₀ [780 nm; 680 nm] using red spectral region, and NDVI₅₇₀ [780 nm; 570 nm] using the same green spectral region as PRI. All three reflectance indices were significantly related to green LAIe and were able to detect changes in shrubland vegetation among treatments. In general warming treatment increased PRI and drought treatment reduced NDVI values. The significant treatment effect on photochemical efficiency of plants detected with PRI could not be detected by fluorescence measurements. However, we found canopy level measured PRI to be very sensitive to soil reflectance properties especially in vegetation areas with low green LAIe. As both soil reflectance and LAI varied between northern and southern sites it is problematic to draw universal conclusions of climate-derived changes in all vegetation types based merely on PRI measurements. We propose that canopy level PRI measurements can be more useful in areas of dense vegetation and dark soils.     

The new extended Jacobian elliptic function expansion algorithm and its applications in nonlinear mathematical physics equations

More recently we have presented the extended Jacobian elliptic function expansion method and its algorithm to seek more types of doubly periodic solutions. Based on the idea of the method, by studying more relations among all twelve kinds of Jacobian elliptic functions. we further extend the method to be a more general method, which is still called the extended Jacobian elliptic function expansion method for convenience. The new method is more powerful to construct more new exact doubly periodic solutions of nonlinear equations. We choose the (2+1)-dimensional dispersive long-wave system to illustrate our algorithm. As a result, twenty-four families of new doubly periodic solutions are obtained. When the modulus m→1 or 0, these doubly periodic solutions degenerate as soliton solutions and trigonometric function solutions. This algorithm can be also applied to other nonlinear equations.     

Existence criteria of periodic oscillations in cyclic gene regulatory networks

In this paper, we consider the existence conditions of periodic oscillations in large-scale cyclic gene regulatory networks. Using the Poincaré–Bendixson theorem for cyclic systems, we first show that the local instability of an equilibrium point implies the existence of periodic oscillations. We then derive the graphical and its equivalent analytic criteria for the existence of periodic oscillations based on local instability analysis. These criteria have a remarkable feature that they can be applied systematically to a large-scale cyclic gene regulatory network consisting of any number of genes. The latter part of this paper is devoted to analyze the relation between an equilibrium point and the biochemical parameters. This leads to an analytic existence criterion that explicitly takes the dependence of the equilibrium state on biochemical parameters into account, which is often overlooked in nonlinear system analyses. In particular, the novel physical quantities that are essential for determining the existence of periodic oscillations are obtained based on the rigorous analytic criterion.     

A note on maximizing the spread of influence in social networks

We consider the spread maximization problem that was defined by Domingos and Richardson (2001, 2002) [7] and [22]. In this problem, we are given a social network represented as a graph and are required to find the set of the most “influential” individuals that by introducing them with a new technology, we maximize the expected number of individuals in the network, later in time, that adopt the new technology. This problem has applications in viral marketing, where a company may wish to spread the rumor of a new product via the most influential individuals in popular social networks such as Myspace and Blogsphere.The spread maximization problem was recently studied in several models of social networks (Kempe et al. (2003, 2005) [14] and [15], Mossel and Roch (2007) [20]). In this short paper we study this problem in the context of the well studied probabilistic voter model. We provide very simple and efficient algorithms for solving this problem. An interesting special case of our result is that the most natural heuristic solution, which picks the nodes in the network with the highest degree, is indeed the optimal solution.     

GNet: A generalized network model and its applications in qualitative spatial reasoning

A data model, named generalized network (GNet), is proposed to perform various network-tracing tasks, especially tracing conceptual proposition networks in qualitative spatial reasoning (QSR). The GNet model can be defined as a 6-tuple: (V, A, q, ⊕, ∼, L). By specifying each element in the 6-tuple, a GNet can function as a conventional network, or an activity on edge (AOE) network, etc. The algorithm for searching for the generalized optimum path weight (GOPW) between two vertices in a GNet is developed by extending the Bellman-Ford algorithm (EBFA). Based on the GNet model, this paper focuses on representing spatial knowledge, which consists of a set of binary relations. We present two applications of GNets, namely the RCC8 network and the hybrid RCC8 network involving cardinal direction relations. Both can be traced to infer new spatial knowledge using EBFA. The applications demonstrate that the GNet model provides a promising approach to dealing with proposition-based geospatial knowledge based on weak composition. We also point out that EBFA can check whether a network is algebraically closed, or path-consistent when the corresponding composition table is extensional.     

On Euclidean norm approximations

Euclidean norm calculations arise frequently in scientific and engineering applications. Several approximations for this norm with differing complexity and accuracy have been proposed in the literature. Earlier approaches [1], [2] and [3] were based on minimizing the maximum error. Recently, Seol and Cheun [4] proposed an approximation based on minimizing the average error. In this paper, we first examine these approximations in detail, show that they fit into a single mathematical formulation, and compare their average and maximum errors. We then show that the maximum errors given by Seol and Cheun are significantly optimistic.     

Artifact analysis on triangular box-splines and subdivision surfaces defined by triangular polyhedra

Surface artifacts are features in a surface which cannot be avoided by movement of control points. They are present in B-splines, box splines and subdivision surfaces. We showed how the subdivision process can be used as a tool to analyse artifacts in surfaces defined by quadrilateral polyhedra ( [Sabin et al., 2005] and [Augsd?rfer et al., 2011]).In this paper we are utilising the subdivision process to develop a generic expression which can be employed to determine the magnitude of artifacts in surfaces defined by any regular triangular polyhedra. We demonstrate the method by analysing box-splines and regular regions of subdivision surfaces based on triangular meshes: Loop subdivision, Butterfly subdivision and a novel interpolating scheme with two smoothing stages. We compare our results for surfaces defined by triangular polyhedra to those for surfaces defined by quadrilateral polyhedra.     

ANFIS-based approach for predicting sediment transport in clean sewer

The necessity of sewers to carry sediment has been recognized for many years. Typically, old sewage systems were designated based on self-cleansing concept where there is no deposition in sewer. These codes were applicable to non-cohesive sediments (typically storm sewers). This study presents adaptive neuro-fuzzy inference system (ANFIS), which is a combination of neural network and fuzzy logic, as an alternative approach to predict the functional relationships of sediment transport in sewer pipe systems. The proposed relationship can be applied to different boundaries with partially full flow. The present ANFIS approach gives satisfactory results (r² = 0.98 and RMSE = 0.002431) compared to the existing predictor.     

A discrete geometry approach for dominant point detection

We propose two fast methods for dominant point detection and polygonal representation of noisy and possibly disconnected curves based on a study of the decomposition of the curve into the sequence of maximal blurred segments [2]. Starting from results of discrete geometry [3] and [4], the notion of maximal blurred segment of width ν[2] has been proposed, well adapted to possibly noisy curves. The first method uses a fixed parameter that is the width of considered maximal blurred segments. The second method is deduced from the first one based on a multi-width approach to obtain a non-parametric method that uses no threshold for working with noisy curves. Comparisons with other methods in the literature prove the efficiency of our approach. Thanks to a recent result [5] concerning the construction of the sequence of maximal blurred segments, the complexity of the proposed methods is O(n log n). An application of vectorization is also given in this paper.     

基于人工代谢算法的TSP问题求解分析

通过分析生物体新陈代谢的生理机能,建立人工代谢算法模型.通过分析底物和生成物之间的浓度差建立多步催化反应动力学模型.通过对城市网络和代谢网络进行类比,建立基于浓度差的TSP问题寻优模型.实例推导表明,人工代谢算法能有效地实现TSP问题的寻优规划.     

Electrocatalytic determination of hydrazine by a glassy carbon electrode modified with PEDOP/MWCNTs-Pd nanoparticles

The electrocatalysis of hydrazine oxidation by poly-ethylenedioxy pyrrole (PEDOP)-coated MWCNTs-palladium nanoparticles [PEDOP/MWCNTs-Pd] was investigated as an electrochemical sensor on the surface of glassy carbon electrode (GCE) in aqueous medium. Electrochemical oxidation of hydrazine in phosphate buffer (pH 7.4) was performed using cyclic voltammetry (CV) and chronoamperometry (CA) methods. Using the proposed electrode, the catalytic oxidation peak current of hydrazine was high and the overpotential of its oxidation decreased. Based on the obtained results, a mechanism for electrooxidation of hydrazine at [PEDOP/MWCNTs-Pd/GCE] demonstrated an irreversible diffusion-controlled electrode process and a four-electron transfer involved in the overall reaction. The experimental results showed that the mediated oxidation peak currents of the hydrazine were linearly dependent on the concentration of hydrazine in the range of 1.0 × 10⁻⁷ to 5.0 × 10⁻³ M. The detection limit (S/N = 3) was found to be 4 × 10⁻⁸ M with a fast response time of 10 s.     

The concept of duality for automata over a changing alphabet and generation of a free group by such automata

In the paper, we deal with the notion of an automaton over a changing alphabet, which generalizes the concept of a Mealy-type automaton. We modify the methods based on the idea of a dual automaton and its action used by B. Steinberg et al. (2011) and M. Vorobets and Ya. Vorobets (2007, 2010) [16], [17] and [18] and adapt them to automata over a changing alphabet. We show that this modification provides some naturally defined automaton representations of a free nonabelian group by a 2-state automaton over a changing alphabet.     

Albedo and LAI estimates from FORMOSAT-2 data for crop monitoring

This paper aimed at estimating albedo and Leaf Area Index (LAI) from FORMOSAT-2 satellite that offers a unique source of high spatial resolution (eight meters) images with a high revisit frequency (one to three days). It mainly consisted of assessing the FORMOSAT-2 spectral and directional configurations that are unusual, with a single off nadir viewing angle over four visible-near infra red wavebands. Images were collected over an agricultural region located in South Eastern France, with a three day frequency from the growing season to post-harvest. Simultaneously, numerous ground based measurements were performed over various crops such as wheat, meadow, rice and maize. Albedo and LAI were estimated using empirical approaches that have been widely used for usual directional and spectral configurations (i.e. multidirectional or single nadir viewing angle over visible-near infrared wavebands). Two methods devoted to albedo estimation were assessed, based on stepwise multiple regression and neural network (NNT). Although both methods gave satisfactory results, the NNT performed better (relative RMSE = 3.5% versus 7.3%), especially for low vegetation covers over dark or wet soils that corresponded to albedo values lower than 0.20. Four approaches for LAI estimation were assessed. The first approach based on a stepwise multiple regression over reflectances had the worst performance (relative RMSE = 65%), when compared to the equally performing NDVI based heuristic relationship and reflectance based NNT approach (relative RMSE ≈ 34%). The NDVI based neural network approach had the best performance (relative RMSE = 27.5%), due to the combination of NDVI efficient normalization properties and NNT flexibility. The high FORMOSAT-2 revisit frequency allowed next replicating the dynamics of albedo and LAI, and detecting to some extents cultural practices like vegetation cuts. It also allowed investigating possible relationships between albedo and LAI. The latter depicted specific trends according to vegetation types, and were very similar when derived from ground based data, remotely sensed observations or radiative transfer simulations. These relationships also depicted large albedo variabilities for low LAI values, which confirmed that estimating one variable from the other would yield poor performances for low vegetation cover with varying soil backgrounds. Finally, this empirical study demonstrated, in the context of exhaustively describing the spatiotemporal variability of surface properties, the potential synergy between 1) ground based web-sensors that continuously monitor specific biophysical variables over few locations, and 2) high spatial resolution satellite with high revisit frequencies.     

Investigating data preprocessing methods for circuit complexity models

Preprocessing the data is an important step while creating neural network (NN) applications because this step usually has a significant effect on the prediction performance of the model. This paper compares different data processing strategies for NNs for prediction of Boolean function complexity (BFC). We compare NNs’ predictive capabilities with (1) no preprocessing (2) scaling the values in different curves based on every curve’s own peak and then normalizing to [0, 1] range (3) applying z-score to values in all curves and then normalizing to [0, 1] range, and (4) logarithmically scaling all curves and then normalizing to [0, 1] range. The efficiency of these methods was measured by comparing RMS errors in NN-made BFC predictions for numerous ISCAS benchmark circuits. Logarithmic preprocessing method resulted in the best prediction statistics as compared to other techniques.     

A soft computing method of performance evaluation with MCDM based on interval-valued fuzzy numbers

This study presented a new performance evaluation method for tackling fuzzy multicriteria decision-making (MCDM) problems based on combining VIKOR and interval-valued fuzzy sets. The performance evaluation problem often exists in complex administrative processes in which multiple evaluation criteria, subjective/objective assessments and fuzzy conditions have to be taken into consideration simultaneously in management. Here, the subjective, imprecise, inexact and uncertain evaluation processes are modeled as fuzzy numbers by means of linguistic terms, as fuzzy theory can provide an appropriate tool to deal with such uncertainties. However, the presentation of linguistic expressions in the form of ordinary fuzzy sets is not clear enough [15] and [21]. Interval-valued fuzzy sets can provide more flexibility [4] and [14] to represent the imprecise/vague information that results, and it can also provide a more accurate modeling. This paper presents the interval-valued fuzzy VIKOR, which aims to solve MCDM problems in which the weights and performances of criteria are unequal by using the concepts of interval-valued fuzzy sets. A case study for evaluating the performances of three major intercity bus companies from an intercity public transport system is conducted to illustrate the effectiveness of the method.     

Traveling bumps and their collisions in a two-dimensional neural field

A neural field is a continuous version of a neural network model accounting for dynamical pattern forming from populational firing activities in neural tissues. These patterns include standing bumps, moving bumps, traveling waves, target waves, breathers, and spiral waves, many of them observed in various brain areas. They can be categorized into two types: a wave-like activity spreading over the field and a particle-like localized activity. We show through numerical experiments that localized traveling excitation patterns (traveling bumps), which behave like particles, exist in a two-dimensional neural field with excitation and inhibition mechanisms. The traveling bumps do not require any geometric restriction (boundary) to prevent them from propagating away, a fact that might shed light on how neurons in the brain are functionally organized. Collisions of traveling bumps exhibit rich phenomena; they might reveal the manner of information processing in the cortex and be useful in various applications. The trajectories of traveling bumps can be controlled by external inputs.     

Interval type-2 fuzzy membership function generation methods for pattern recognition

Type-2 fuzzy sets (T2 FSs) have been shown to manage uncertainty more effectively than T1 fuzzy sets (T1 FSs) in several areas of engineering [4], [6], [7], [8], [9], [10], [11], [12], [15], [16], [17], [18], [21], [22], [23], [24], [25], [26], [27] and [30]. However, computing with T2 FSs can require undesirably large amount of computations since it involves numerous embedded T2 FSs. To reduce the complexity, interval type-2 fuzzy sets (IT2 FSs) can be used, since the secondary memberships are all equal to one [21]. In this paper, three novel interval type-2 fuzzy membership function (IT2 FMF) generation methods are proposed. The methods are based on heuristics, histograms, and interval type-2 fuzzy C-means. The performance of the methods is evaluated by applying them to back-propagation neural networks (BPNNs). Experimental results for several data sets are given to show the effectiveness of the proposed membership assignments.