On the global avalanche characteristics between two Boolean functions and the higher order nonlinearity

The criterion for the global avalanche characteristics (GAC) of cryptographic functions is an important property. To measure the correlation between two arbitrary Boolean functions, we propose two new criteria called the sum-of-squares indicator and the absolute indicator of the cross-correlation between two Boolean functions. The two indicators generalize the GAC criterion. Based on the properties of the cross-correlation function, we deduce the rough lower and the rough upper bounds on the two indicators by hamming weights of two Boolean functions, and generalize some properties between the Walsh spectrum and the cross-correlation function. Furthermore, we give the tight upper and the tight lower bounds on the two indicators. Finally, we show some relationships between the upper bounds on the two indicators and the higher order nonlinearity.     

The global avalanche characteristics of two Boolean functions and algebraic immunity

The global avalanche characteristics criterion of two Boolean functions was introduced by Zhou et al. [On the global avalanche characteristics criterion of two Boolean functions and the higher order nonlinearity, Inform. Sci. 180(2) (2010), pp. 256–265] to measure the cryptographic behaviour in a global characteristic. The two indicators σ _{f, g} and Δ _{f, g} of Boolean functions f and g were presented. In this paper, a new upper bound on σ _{f, g} is derived, and a technique on constructing Boolean functions to attain the lower bound on the sum-of-squares indicator is described by using the disjoint spectra method. Some new upper bounds on Δ _{f, g} and σ _{f, g} are deduced for two special Boolean functions. Two relationships between σ _{f, g} and algebraic immunity of the two Boolean functions are obtained. Finally, some links among different cryptographic indicators are shown.     

Partial Partitions,Partial Connections and Connective Segmentation

In connective segmentation (Serra in J. Math. Imaging Vis. 24(1):83–130, [2006]), each image determines subsets of the space on which it is “homogeneous”, in such a way that this family of subsets always constitutes a connection (connectivity class); then the segmentation of the image is the partition of space into its connected components according to that connection. Several concrete examples of connective segmentations or of connections on sets, indicate that the space covering requirement of the partition should be relaxed. Furthermore, morphological operations on partitions require the consideration of wider framework. We study thus partial partitions (families of mutually disjoint non-void subsets of the space) and partial connections (where connected components of a set are mutually disjoint but do not necessarily cover the set). We describe some methods for generating partial connections. We investigate the links between the two lattices of partial connections and of partial partitions. We generalize Serra’s characterization of connective segmentation and discuss its relevance. Finally we give some ideas on how the theory of partial connections could lead to improved segmentation algorithms.

Bridges 2002: Mathematical Connections in Art,Music, and Science

Nexus Network Journal - .     

Bridges 2006: Mathematical Connections in Art,Music, and Science

B. Lynn Bodner reports on the Bridges 2006 conference.     

Euclidean condition and block relative gain: Connections, conjectures, and clarifications

Given an arbitrary nonsingular complex matrix, certain quantitative relationships between its Euclidean condition number and its associated block relative gains are established. In addition, an as yet unproven relation of this type is conjectured. The control theoretic implications of the established relations are briefly discussed, clarifying the role of the block relative gain concept in control theory.     

Vector Median Filters, Inf-Sup Operations, and Coupled PDE's: Theoretical Connections

In this paper, we formally connect between vector median filters, inf-sup morphological operations, and geometric partial differential equations. Considering a lexicographic order, which permits to define an order between vectors in R^N, we first show that the vector median filter of a vector-valued image is equivalent to a collection of infimum-supremum morphological operations. We then proceed and study the asymptotic behavior of this filter. We also provide an interpretation of the infinitesimal iteration of this vectorial median filter in terms of systems of coupled geometric partial differential equations. The main component of the vector evolves according to curvature motion, while, intuitively, the others regularly deform their level-sets toward those of this main component. These results extend to the vector case classical connections between scalar median filters, mathematical morphology, and mean curvature motion.     

Selectivity and stability via dendritic nonlinearity

Inspired by recent studies regarding dendritic computation, we constructed a recurrent neural network model incorporating dendritic lateral inhibition. Our model consists of an input layer and a neuron layer that includes excitatory cells and an inhibitory cell; this inhibitory cell is activated by the pooled activities of all the excitatory cells, and it in turn inhibits each dendritic branch of the excitatory cells that receive excitations from the input layer. Dendritic nonlinear operation consisting of branch-specifically rectified inhibition and saturation is described by imposing nonlinear transfer functions before summation over the branches. In this model with sufficiently strong recurrent excitation, on transiently presenting a stimulus that has a high correlation with feed- forward connections of one of the excitatory cells, the corresponding cell becomes highly active, and the activity is sustained after the stimulus is turned off, whereas all the other excitatory cells continue to have low activities. But on transiently presenting a stimulus that does not have high correlations with feedforward connections of any of the excitatory cells, all the excitatory cells continue to have low activities. Interestingly, such stimulus-selective sustained response is preserved for a wide range of stimulus intensity. We derive an analytical formulation of the model in the limit where individual excitatory cells have an infinite number of dendritic branches and prove the existence of an equilibrium point corresponding to such a balanced low-level activity state as observed in the simulations, whose stability depends solely on the signal-to-noise ratio of the stimulus. We propose this model as a model of stimulus selectivity equipped with self-sustainability and intensity-invariance simultaneously, which was difficult in the conventional competitive neural networks with a similar degree of complexity in their network architecture. We discuss the biological relevance of the model in a general framework of computational neuroscience.     

Contourlet相关性和PCA的图像融合算法

Contourlet变换克服了小波变换在处理高维信号时的不足,它比小波变换具有更好的方向性和更好的稀疏表达性能。将Contourlet变换应用于图像融合领域,能更好地提取图像边缘特征,为融合提取更多的特征信息。基于Contourlet变换系数相关性的图像融合算法是将图像进行Contourlet变换分解后,针对高频分解系数尺度内以及尺度间像素点具有的相关性设计图像融合规则,低频信息选择PCA的方法进行融合,最后通过重构得到融合图像。实验结果表明Contourlet能够为融合图像保留更全面的原始图像信息,基于相关性的图像融合算法能够更加有效、准确地提取图像中的特征,是一种有效可行的图像融合算法。     

Connections between score matching, contrastive divergence, and pseudolikelihood for continuous-valued variables.

Score matching (SM) and contrastive divergence (CD) are two recently proposed methods for estimation of nonnormalized statistical methods without computation of the normalization constant (partition function). Although they are based on very different approaches, we show in this letter that they are equivalent in a special case: in the limit of infinitesimal noise in a specific Monte Carlo method. Further, we show how these methods can be interpreted as approximations of pseudolikelihood.     

Connections between finite-gain and asymptotic stability

The relationship between input-output and Lyapunov stability properties for nonlinear systems is studied. Well-known definitions for the input-output properties of finite-gain and passivity, even with quite reasonable minimality assumptions on a state-space representation, do not necessarily imply any form of stability for the state. Attention is given to the precise versions of input-output and observability properties which guarantee asymptotic stability. Particular emphasis is given to the possibility of multiple equilibria for the dynamical system.     

基于特征词关联性的同义词集挖掘算法*

一词多义和多词同义是语言中广泛存在的现象,它给自然语言处理带来了很多困难,解决这个难题的有效办法是建立包含上下文信息的同义词集。深入分析了概念、词汇和特征词三者的内在关系,并在此基础上提出了一种基于同义词汇的特征词的关联性,从文本中挖掘同义词集的算法。根据特征词之间存在关联性的特点,算法以成熟的关联规则挖掘算法作为基础,获得了明显优于同类算法的实验效果。算法获得的同义词集附带上下文信息,可有效解决文本中词汇的多义性和同义性问题。     

Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching

The problem of delay-dependent stability in the mean square sense for stochastic systems with time-varying delays, Markovian switching and nonlinearities is investigated. Both the slowly time-varying delays and fast time-varying delays are considered. Based on a linear matrix inequality approach, delay-dependent stability criteria are derived by introducing some relaxation matrices which can be chosen properly to lead to a less conservative result. Numerical examples are given to illustrate the effectiveness of the method and significant improvement of the estimate of stability limit over some existing results in the literature.     

Control-relevant nonlinearity measure and integrated multi-model control

A control-relevant nonlinearity measure (CRNM) method is proposed based on the gap metric and the gap metric stability margin to measure the nonlinear degree of a system once a linear control strategy is selected. Supported by the CRNM method, an integrated multi-model control framework is developed, in which the multi-model decomposition and local controller design are closely integrated, model redundancy is avoided, computational load is reduced, and dependency on a prior knowledge is reduced. Besides, a 1/δ gap-based weighting method is put forward to combine the local controllers. On one hand, the 1/δ gap-based weighting method has merely one tuning parameter and can be computed off-line; on the other hand, it is sensitive to the tuning parameter, flexible and easy to tune. Two continuous stirred tank reactor (CSTR) systems are investigated. Closed-loop simulations validate the effectiveness and benefits of the proposed integrated multi-model control approach based on CRNM.     

Connections between stochastic control and dynamic games

We consider duality relations between risk-sensitive stochastic control problems and dynamic games. They are derived from two basic duality results, the first involving free energy and relative entropy and resulting from a Legendre-type transformation, the second involving power functions. Our approach allows us to treat, in essentially the same way, continuous- and discrete-time problems, with complete and partial state observation, and leads to a very natural formal justification of the structure of the cost functional of the dual. It also allows us to obtain the solution of a stochastic game problem by solving a risk-sensitive control problem.     

Connections between subwords and certain matrix mappings

Parikh matrices recently introduced have turned out to be a powerful tool in the arithmetizing of the theory of words. In particular, many inequalities between (scattered) subword occurrences have been obtained as consequences of the properties of the matrices. This paper continues the investigation of Parikh matrices and subword occurrences. In particular, we study certain inequalities, as well as information about subword occurrences sufficient to determine the whole word uniquely. Some algebraic considerations, facts about forbidden subwords, as well as some open problems are also included.