Super restricted edge connected Cartesian product graphs

An edge-cut F of a connected graph G is called a restricted edge-cut if G−F contains no isolated vertices. The minimum cardinality of all restricted edge-cuts is called the restricted edge-connectivity λ^′(G) of G. A graph G is said to be λ^′-optimal if λ^′(G)=ξ(G), where ξ(G) is the minimum edge-degree of G. A graph is said to be super-λ^′ if every minimum restricted edge-cut isolates an edge. This article gives a sufficient condition for Cartesian product graphs to be super-λ^′. Using this result, certain classes of networks which are recursively defined by the Cartesian product can be simply shown to be super-λ^′.     

On the complexity of sandpile critical avalanches

In this work, we study The Abelian Sandpile Model from the point of view of computational complexity. We begin by studying the length distribution of sandpile avalanches triggered by the addition of two critical configurations: we prove that those avalanches are long on average, their length is bounded below by a constant fraction of the length of the longest critical avalanche which is, in most of the cases, superlinear. At the end of the paper we take the point of view of computational complexity, we analyze the algorithmic hardness of the problem consisting in computing the addition of two critical configurations, we prove that this problem is P complete, and we prove that most algorithmic problems related to The Abelian Sandpile Model are NC reducible to it.     

Super connectivity of line graphs

The super connectivity κ^′ and the super edge-connectivity λ^′ are more refined network reliability indices than connectivity κ and edge-connectivity λ. This paper shows that for a connected graph G with order at least four rather than a star and its line graph L(G), κ^′(L(G))=λ^′(G) if and only if G is not super-λ^′. As a consequence, we obtain the result of Hellwig et al. [Note on the connectivity of line graphs, Inform. Process. Lett. 91 (2004) 7] that κ(L(G))=λ^′(G). Furthermore, the authors show that the line graph of a super-λ^′ graph is super-λ if the minimum degree is at least three.     

Stability properties of reset systems

Stability properties for a class of reset systems, such as systems containing a Clegg integrator, are investigated. We present Lyapunov based results for verifying L₂ and exponential stability of reset systems. Our results generalize the available results in the literature and can be easily modified to cover L_p stability for arbitrary p∈[1,∞]. Several examples illustrate that introducing resets in a linear system may reduce the L₂ gain if the reset controller parameters are carefully tuned.     

The solitary solution of the Liouville equation produced by the Exp-function method does not hold for all initial conditions

In this paper we argue that the solitary solution of the Liouville equation produced by the Exp-function method does not satisfy the original differential equation for all initial conditions. Moreover, the region where the solution is correct is located entirely on a curve in the parameter plane of initial conditions. We derive the explicit equation for this curve and argue that classical Exp-function type methods cannot identify such constraints related to initial conditions.     

Equivalence of rational representations of behaviors

This article deals with the equivalence of representations of behaviors of linear differential systems. In general, the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel and image representations. Two kernel representations are called equivalent if they represent one and the same behavior. For kernel representations defined by polynomial matrices, necessary and sufficient conditions for equivalence are well known. In this paper, we deal with the equivalence of rational representations, i. e. kernel and image representations that are defined in terms of rational matrices. As the first main result of this paper, we will derive a new condition for the equivalence of rational kernel representations of possibly noncontrollable behaviors. Secondly we will derive conditions for the equivalence of rational representations of a given behavior in terms of the polynomial modules generated by the rows of the rational matrices. We will also establish conditions for the equivalence of rational image representations. Finally, we will derive conditions under which a given rational kernel representation is equivalent to a given rational image representation.     

A simple and efficient method for variable ranking according to their usefulness for learning

The selection of a subset of input variables is often based on the previous construction of a ranking to order the variables according to a given criterion of relevancy. The objective is then to linearize the search, estimating the quality of subsets containing the topmost ranked variables. An algorithm devised to rank input variables according to their usefulness in the context of a learning task is presented. This algorithm is the result of a combination of simple and classical techniques, like correlation and orthogonalization, which allow the construction of a fast algorithm that also deals explicitly with redundancy. Additionally, the proposed ranker is endowed with a simple polynomial expansion of the input variables to cope with nonlinear problems. The comparison with some state-of-the-art rankers showed that this combination of simple components is able to yield high-quality rankings of input variables. The experimental validation is made on a wide range of artificial data sets and the quality of the rankings is assessed using a ROC-inspired setting, to avoid biased estimations due to any particular learning algorithm.     

Penalized cluster analysis with applications to family data

The goal of cluster analysis is to assign observations into clusters so that observations in the same cluster are similar in some sense. Many clustering methods have been developed in the statistical literature, but these methods are inappropriate for clustering family data, which possess intrinsic familial structure. To incorporate the familial structure, we propose a form of penalized cluster analysis with a tuning parameter controlling the tradeoff between the observation dissimilarity and the familial structure. The tuning parameter is selected based on the concept of clustering stability. The effectiveness of the method is illustrated via simulations and an application to a family study of asthma.     

Fitting finite mixtures of generalized linear regressions in R

R package flexmix provides flexible modelling of finite mixtures of regression models using the EM algorithm. Several new features of the software such as fixed and nested varying effects for mixtures of generalized linear models and multinomial regression for a priori probabilities given concomitant variables are introduced. The use of the software in addition to model selection is demonstrated on a logistic regression example.     

Bootstrap approach to the multi-sample test of means with imprecise data

A bootstrap approach to the multi-sample test of means for imprecisely valued sample data is introduced. For this purpose imprecise data are modelled in terms of fuzzy values. Populations are identified with fuzzy-valued random elements, often referred to in the literature as fuzzy random variables. An example illustrates the use of the suggested method. Finally, the adequacy of the bootstrap approach to test the multi-sample hypothesis of means is discussed through a simulation comparative study.     

Some new sequence spaces derived by the domain of the triple band matrix

Let λ denote any of the classical spaces ?_∞,c,c₀, and ?_p of bounded, convergent, null, and absolutely p-summable sequences, respectively, and let λ(B) also be the domain of the triple band matrix B(r,s,t) in the sequence space λ, where 1<p<∞. The present paper is devoted to studying the sequence space λ(B). Furthermore, the β- and γ-duals of the space λ(B) are determined, the Schauder bases for the spaces c(B), c₀(B), and ?_p(B) are given, and some topological properties of the spaces c₀(B), ?₁(B), and ?_p(B) are examined. Finally, the classes (λ₁(B):λ₂) and (λ₁(B):λ₂(B)) of infinite matrices are characterized, where λ₁∈{?_∞,c,c₀,?_p,?₁} and λ₂∈{?_∞,c,c₀,?₁}.     

Vague soft hemirings

Xu et al. introduced the concept of vague soft sets, which is an extension to the soft set and the vague set. In this paper, we apply the concept of vague soft sets to hemiring theory. The notion of (∈,∈∨q)-vague (soft) left h-ideals of a hemiring is introduced and some related properties are investigated.     

Three-dimensional beta shapes

The Voronoi diagram of a point set has been extensively used in various disciplines ever since it was first proposed. Its application realms have been even further extended to estimate the shape of point clouds when Edelsbrunner and Mücke introduced the concept of α-shape based on the Delaunay triangulation of a point set.In this paper, we present the theory of β-shape for a set of three-dimensional spheres as the generalization of the well-known α-shape for a set of points. The proposed β-shape fully accounts for the size differences among spheres and therefore it is more appropriate for the efficient and correct solution for applications in biological systems such as proteins.Once the Voronoi diagram of spheres is given, the corresponding β-shape can be efficiently constructed and various geometric computations on the sphere complex can be efficiently and correctly performed. It turns out that many important problems in biological systems such as proteins can be easily solved via the Voronoi diagram of atoms in proteins and β-shapes transformed from the Voronoi diagram.     

On the hardness of finding near-optimal multicuts in directed acyclic graphs

Given an edge-weighted (di)graph and a list of source-sink pairs of vertices of this graph, the minimum multicut problem consists in selecting a minimum-weight set of edges (or arcs), whose removal leaves no path from each source to the corresponding sink. This is a well-known NP-hard problem, and improving several previous results, we show that it remains APX-hard in unweighted directed acyclic graphs (DAG), even with only two source-sink pairs. This is also true if we remove vertices instead of arcs.     

On the strong stabilization of slowly time-varying linear systems

This paper considers the strong stabilization problem: Given a linear time-varying system which is stabilizable by dynamic feedback, when can the stabilizer be chosen to be itself stable? We consider here the case of the algebra of discrete-time time-varying systems which are slowly time varying.     

Extended rate, more GFUN

We present a software package that guesses formulae for sequences of, for example, rational numbers or rational functions, given the first few terms. We implement an algorithm due to Bernhard Beckermann and George Labahn, together with some enhancements to render our package efficient. Thus we extend and complement Christian Krattenthaler’s program Rate.m, the parts concerned with guessing of Bruno Salvy and Paul Zimmermann’s GFUN, the univariate case of Manuel Kauers’ Guess.m and Manuel Kauers’ and Christoph Koutschan’s qGeneratingFunctions.m.     

Linguistic truth-valued lattice-valued propositional logic system ?P(X) based on linguistic truth-valued lattice implication algebra

In the semantics of natural language, quantification may have received more attention than any other subject, and syllogistic reasoning is one of the main topics in many-valued logic studies on inference. Particularly, lattice-valued logic, a kind of important non-classical logic, can be applied to describe and treat incomparability by the incomparable elements in its truth-valued set. In this paper, we first focus on some properties of linguistic truth-valued lattice implication algebra. Secondly, we introduce some concepts of linguistic truth-valued lattice-valued propositional logic system ?P(X), whose truth-valued domain is a linguistic truth-valued lattice implication algebra. Then we investigate the semantic problem of ?P(X). Finally, we further probe into the syntax of linguistic truth-valued lattice-valued propositional logic system ?P(X), and prove the soundness theorem, deduction theorem and consistency theorem.     

On using prototype reduction schemes to enhance the computation of volume-based inter-class overlap measures

In most pattern recognition (PR) applications, it is advantageous if the accuracy (or error rate) of the classifier can be evaluated or bounded prior to testing it in a real-life setting. It is also well known that if the two class-conditional distributions have a large overlapping volume (almost all the available work on “overlapping of classes” deals with the case when there are only two classes), the classification accuracy is poor. This is because if we intend to use the classification accuracy as a criterion for evaluating a PR system, the points within the overlapping volume tend to lead to maximal misclassification. Unfortunately, the computation of the indices which quantify the overlapping volume is expensive. In this vein, we propose a strategy of using a prototype reduction scheme (PRS) to approximately, but quickly, compute the latter. In this paper, we demonstrate, first of all, that this is an extremely expedient proposition. Indeed, we show that by completely discarding (we are not aware of any reported scheme which discards “irrelevant” sample (training) points, and which simultaneously attains to an almost-comparable accuracy) the points not included by the PRS, we can obtain a reduced set of sample points, using which, in turn, the measures for the overlapping volume can be computed. The value of the corresponding figures is comparable to those obtained with the original training set (i.e., the one which considers all the data points) even though the computations required to obtain the prototypes and the corresponding measures are significantly less. The proposed method has been rigorously tested on artificial and real-life datasets, and the results obtained are, in our opinion, quite impressive—sometimes faster by two orders of magnitude.