New Mathematics and Natural Computation

Black's Median Voter Theorem is among the more useful mathematical tools available to political scientists for predicting choices of political actors based on their preferences over a finite set of alternatives within an institutional or constitutional setting. If the alternatives can be placed on a single-dimensional continuum such that the preferences of all players descend monotonically from their ideal point, then the outcome will be the alternative at the median position. We demonstrate that the Median Voter Theorem holds for fuzzy preferences. Our approach considers the degree to which players prefer options in binary relations.

Predictions concerning voting outcomes in crisp spatial models rely heavily on the existence of a core, in the absence of which political players choosing among a set of alternatives by majority rule will not be able to arrive at a stable choice. No matter which option they might initially choose, most voting rules will permit another option to defeat the previously chosen one. Such problems particularly plague majority rule spatial models at dimensionalities greater than one. In a series of recent papers, we have argued that fuzzy spatial models offer a partial solution to this problem. In this paper, we explore the existence of a fuzzy core. Our major conclusion is that a fuzzy core is more likely in two or more dimensions as the number of players increases.

In this paper, we initiate the study of intuitionistic fuzzy subacts of an S-act, where S is a monoid with zero and S-acts are representations of S. We introduce the notions of pure intuitionistic fuzzy, purely intuitionistic maximal and purely intuitionistic fuzzy prime ideals of a monoid. It is shown that the set of purely intuitionistic fuzzy prime ideals of S admits the structure of a topological space, called the pure intuitionistic fuzzy spectrum of S. We also define a pure intuitionistic fuzzy subact of an S-act and call an S-act intuitionistic fuzzy normal if each of its intuitionistic fuzzy subact is pure. Monoids, of which all S-acts are intuitionistic fuzzy normal, are characterized. It is shown among other results that such monoids are right weakly regular.

Binding MOAD (Mother of All Databases) is the largest collection of high-quality, protein-ligand complexes available from the Protein Data Bank. It has grown to 9837 hand-curated entries. Here, we describe our semi-annual updating procedures and BUDA (Binding Unstructured Data Analysis), a custom workflow tool that incorporates natural language processing technologies to facilitate the annotation process.

The intensity gradient-based methods are commonly used in edge detection of images. However, these methods are not very suitable for color images and they change the shapes of object contours in large scales. In this paper, a novel density gradient-based method is proposed to solve these problems. The proposed method locates the edges using the density gradients of image pixels instead of the color/intensity gradients. Comparing with the traditional methods, the proposed approach can be applied more effectively to all types of images: gray level, color and multispectral images; and the detection results are invariant to the detection scales as well. It may find wide applications in computer vision and image processing.

Protein structure alignment facilitates the analysis of protein functionality. Through superimposed structures and the comparison of variant components, common or specific features of proteins can be identified. Several known protein families exhibit analogous tertiary structures but divergent primary sequences. These proteins in the same structural class are unable to be aligned by sequence-based methods. The main objective of the present study was to develop an efficient and effective algorithm for multiple structure alignment based on geometrical correlation of secondary structures, which are conserved in evolutionary heritage. The method utilizes mutual correlation analysis of secondary structure elements (SSEs) and selects representative segments as the key anchors for structural alignment. The system exploits a fast vector transformation technique to represent SSEs in vector format, and the mutual geometrical relationship among vectors is projected onto an angle-distance map. Through a scoring function and filtering mechanisms, the best candidates of vectors are selected, and an effective constrained multiple structural alignment module is performed. The correctness of the algorithm was verified by the multiple structure alignment of proteins in the SCOP database. Several protein sets with low sequence identities were aligned, and the results were compared with those obtained by three well-known structural alignment approaches. The results show that the proposed method is able to perform multiple structural alignments effectively and to obtain satisfactory results, especially for proteins possessing low sequence identity.

Biological systems are complex, consisting of many elements of different nature. As a whole, they are robust, and a general system description can be done in a semi-quantitative way when it comes to phenotype behaviors. We used these properties earlier¹ to develop a new systems biology method, causal mapping (CMAP). In this paper, we pinpoint some problems with the earlier version of CMAP, and develop it further. CMAP used linguistic variables (LV) to describe the behaviour of biological systems, and here we use the procedure of fuzzyfications to improve CMAP. The numerical methods to calculate the ranges of LV are agreeable to reality in a very intuitive manner. The new version of CMAP reproduced the physical data on cortical oscillations² in spreading cells with depolymerized microtubules. Further, predictions were made on the dependency of the myosin activity on the period of oscillations.

The presented development lies on the way to a more general approach that should be able to address questions of biological robustness, modularity and hierarchy.

This paper aims at supplying a decision support system tool to investors having options written on an underlying asset driven by a fractional Brownian motion (fBm). The results presented here rely on the theory of nonlinear transformations of fBm and provide the calculus of the probability estimate that the underlying asset crosses nonlinear barriers. Recent results stating a Black and Scholes-like pricing formula for fBm monitor the expected behaviour of options on the basis of the dynamics of the underlying asset. We rely on the results drawn for plain vanilla options, leaving their extension to barrier options for future work. The theory of speculative bubbles due to endogenous causes provides a useful suggestion for the detection of periods in which these results should be used. The application of the above results is shown through the NASDAQ case study.