On a New Approach for Finding All the Modified Cut-Sets in an Incompatibility Graph

Assessing the stability of a clustering method involves the measurement of the extent to which the generated clusters are affected by perturbations in the input data. A measure which specifies the disturbance in a set of clusters as the minimum number of operations required to restore the set of modified clusters to the original ones is adopted. A number of well-known graph theoretic clustering methods are compared in terms of their stability as determined by this measure. Specifically, it is shown that among the clustering methods in any of several families of graph theoretic methods, clusters defined as the connected components are the most stable and the clusters specified as the maximal complete subgraphs are the least stable. Furthermore, as one proceeds from the method producing the most narrow clusters (maximal complete subgraphs) to those producing relatively broader clusters, the clustering process is shown to remain at least as stable as any method in the previous stages. Finally, the lower and the upper bounds for the measure of stability, when clusters are defined as the connected components, are derived.

Compatibility relations in effect algebras and their connections with refinements of the orthogonal partitions of unity are studied. Properties of blocks as maximal sets of compatible elements are discussed. Some special kinds of effect algebras are characterized using properties of compatibility. Using refinements, an additional structure on the effect test spaces is introduced and used to a characterization of different types of effect algebras.

CENTERS OF TRIANGULATED GRAPHS V. D. Chepoi Let G = (X, U) be an ordinary graph with arbitrarily (not necessarily finitely) many vertexes, any two of which are joined by some finite chain. We endow G with a standard metric d(x, y) equal to the number of edges in the chain of shortest length joining vertexes x, y. The eccentricity e(z) of a vertex z is defined as {d(z, v): v e X}. The radius r(G) is the least eccentricity of the vertexes, and the diameter d(G) is the largest eccentricity. The center C(G) of G is the subgraph generated by the set of vertexes with minimal eccentricity. It is well known [I, 2] that any graph G, even if it is not connected, is the center of some graph G', i.e., G = C(G'). At the same time, if one confines attention to special classes of graphs, their centers may have rather specific features. Thus, a well-known re- sult of Jordan [3] states that the center of any finite tree consists of one vertex or two adjacent vertexes; that is to say, the only two possibilities are the graphs K l and K 2 (where K n denotes the complete subgraph on n vertexes). The centers of maximal outerplanar graphs and 2-trees were described in [4, 5]. In this paper we characterize the centers of triangu- lated graphs. In this connection, we note that metric properties, including in particular properties of the centers, of triangulated graphs have been studied by various authors [6-9]. Our Theorems 1 and 2 were proved in [8], but they are established here in a more general form and the proofs are simpler. Recall [i0] that a graph G is said to be triangulated if, in any simple cycle F of length more than 3, there are two vertexes not adjacent in r but joined by an edge in G. Recall moreover that a clique of a graph G is any maximal complete subgraph (with re- spect to inclusion). The density of a graph G is the cardinality of the largest clique in G (if such a clique exists). Throughout this paper, the term triangulated graph will mean a triangulated graph of finite diameter without infinite complete subgraphs. Let CT denote the family of graphs which are centers of triangulated graphs. We shall need a number of additional concepts and definitions. Given sets M c X in a graph G and any number r ~ 0, we put where

Covering all cliques of a graph

Analysis of the structural properties of social networks has gained much interest nowadays due to its diverse range of applications. When communications between entities (i.e., edges) of a social network (graph) are stamped with time, we want to analyze all subgraphs within an arbitrary query time slice so that the number of a specific subgraph can be counted and reported quickly. We present data structures to answer such queries for triangles, quadrangles, complete subgraphs, and maximal complete subgraphs.

Network biology integrates different kinds of data, including physical or functional networks and disease gene sets, to interpret human disease. A clique (maximal complete subgraph) in a protein-protein interaction network is a topological module and possesses inherently biological significance. A disease-related clique possibly associates with complex diseases. Fully identifying disease components in a clique is conductive to uncovering disease mechanisms. This paper proposes an approach of predicting disease proteins based on cliques in a protein-protein interaction network. To tolerate false positive and negative interactions in protein networks, extending cliques and scoring predicted disease proteins with gene ontology terms are introduced to the clique-based method. Precisions of predicted disease proteins are verified by disease phenotypes and steadily keep to more than 95%. The predicted disease proteins associated with cliques can partly complement mapping between genotype and phenotype, and provide clues for understanding the pathogenesis of serious diseases.

Testing cost is becoming increasingly important as system-on-chip circuits continue to become more complex. In this paper, we address the issue of reducing test cost by shortening test application time and reducing the volume of data needs to be stored on a tester. The number of scan channels on a tester and/or the number of pins on an SOC are limited. We propose a method to enhance the Illinois scan architecture for use with a small number of scan-in pins. Pin reduction is achieved by connecting a single pin to several scan chains together depending on their compatibility relations. With the use of an incompatibility graph and graph colouring algorithm, the number of pins needed is minimized.

We consider the problem of minimizing the makespan on a batch processing machine, in which jobs are not all compatible. Only compatible jobs can be included into the same batch. This relation of compatibility is represented by a split graph. Jobs have release dates. The capacity of the batch processing machine is finite or infinite. The processing time of a batch is given by the processing time of the longest job in the batch. We establish the NP-hardness of the general problem and present polynomial algorithms for several special cases. Relating scheduling theory and graph theory appears to be an interesting and important concept.

This chapter contains sections titled: Introduction Current Challenges in Catalysis What is a Nanostructured Catalyst? Benefits of Nanostructuring Catalysts Current Approaches to Nanostructured Catalysts Building Block Approaches to Nanostructured Materials and Catalysis Nanostructured Catalysts via a Non-Aqueous Building Block Methodology A Model for the Growth of Building Block Matrices and a Nanostructuring Strategy A General Procedure for Preparing Nanostructured Catalysts in Silicate Matrices Atomically Dispersed Titanium and Vanadium, Single Site Catalysts Bridge between Nanostructuring and Catalysis Summary Acknowledgments References

A generalization of Naundorf's fixpoint theorem

Foreign language learning anxiety continues to influence college students' acquisition of foreign languages, and the factors that trigger this anxiety have received increasing attention. This study aims to explore the differences in foreign language learning anxiety and emotional regulation strategies among college students in different disciplinary contexts. Using the most widely accepted classification method, data were collected from 140 students in science and engineering disciplines and humanities and social sciences disciplines via the Foreign Language Classroom Anxiety Scale (FLCAS short form) and the Emotional Regulation Questionnaire (ERQ short form). The results showed that students in science and engineering disciplines generally had higher overall foreign language anxiety levels than did those in humanities and social sciences disciplines, with significant differences, particularly in dimensions such as “classroom speaking anxiety” and “self-comparison anxiety”. Humanities students exhibited significantly higher frequencies of cognitive reappraisal strategies than science and engineering students did, whereas science and engineering students tended to rely more on emotion suppression and avoidance strategies. This study elucidates the mechanisms underlying disciplinary differences in the formation and regulation of foreign language learning anxiety, providing empirical evidence for universities to implement differentiated foreign language instruction and optimize classroom emotional atmospheres.

Scheduling hybrid flowshop with parallel batching machines and compatibilities

Ionomic exploration of the geographical and geological origins of mountain pasture cow milks in the French Massif central

In this note a method is presented for finding in a quick way the set of all maximal compatibles of an incompletely specified sequential machine. The basic tool is the modified merger diagram. The closed set of compatibles corresponds to the set of state of the new reduced machine.

We are considering a 6 d.o.f. Gough platform that has to move within a given workspace or on a trajectory. The legs of the robot are assumed to be constituted of a set of finite cylindrical elements and we address the problem of determining if any pair of such element would intersect during the robot motion. Collision conditions may be written mathematically according to various equivalent formulations. We show however that these formulations are not numerically equivalent and exhibit an efficient interference checking algorithm based on interval analysis that allows to check 6D workspace or arbitrary time-function trajectories for interference