12965386
A Note on the Relationships Between the Generalized Bernoulli and Euler Polynomials
1. IntroductionIn many contexts, matrix representation of a particular counting se-quence is considered, and such a representation provides a powerful com-putational tool for deriving identities and explicit formulas related to thesequence, see, for example [3, 7].Recently, Cheon [2] rederived several known properties and relationshipsinvolving the classical Bernoulli polynomials
22669776
Identities via Bell matrix and Fibonacci matrix
In this paper, we study the relations between the Bell matrix and the Fibonacci matrix, which provide a unified approach to some lower triangular matrices, such as the Stirling matrices of both kinds, the Lah matrix, and the generalized Pascal matrix. To make the results more general, the discussion is also extended to the generalized Fibonacci numbers and the corresponding matrix. Moreover, based on the matrix representations, various identities are derived.
17247210
Identities on Bell polynomials and Sheffer sequences
In this paper, we study exponential partial Bell polynomials and Sheffer sequences. Two new characterizations of Sheffer sequences are presented, which indicate the relations between Sheffer sequences and Riordan arrays. Several general identities involving Bell polynomials and Sheffer sequences are established, which reduce to some elegant identities for associated sequences and cross sequences.
6659460
Generalized Riordan arrays
In this paper, we generalize the concept of Riordan array. A generalized Riordan array with respect to c"n is an infinite, lower triangular array determined by the pair (g(t),f(t)) and has the generic element d"n","k=[t^n/c"n]g(t)(f(t))^k/c"k, where c"n is a fixed sequence of non-zero constants with c"0=1. We demonstrate that the generalized Riordan arrays have similar properties to those of the classical Riordan arrays. Based on the definition, the iteration matrices related to the Bell polynomials are special cases of the generalized Riordan arrays and the set of iteration matrices is a subgroup of the Riordan group. We also study the relationships between the generalized Riordan arrays and the Sheffer sequences and show that the Riordan group and the group of Sheffer sequences are isomorphic. From the Sheffer sequences, many special Riordan arrays are obtained. Additionally, we investigate the recurrence relations satisfied by the elements of the Riordan arrays. Based on one of the recurrences, some matrix factorizations satisfied by the Riordan arrays are presented. Finally, we give two applications of the Riordan arrays, including the inverse relations problem and the connection constants problem.
11841640
Accelerating Profile Queries in Elevation Maps
Elevation maps are a widely used spatial data representation in geographical information systems (GIS). Paths on elevation maps can be characterized by profiles, which describe relative elevation as a function of distance. In this research, we address the inverse of this mapping - given a profile, how to efficiently find paths that could have generated it. This is called the profile query problem. Profiles have a wide variety of uses that include registering tracking information, or even other maps, to a given map. We describe a probabilistic model to characterize the maximal likelihood that a point lying on a path matches the query profile. Propagation of such probabilities to neighboring points can effectively prune the search space. This model enables us to efficiently answer queries of arbitrary profiles with user-specified error tolerances. When compared to existing spatial index methods, our approach supports more flexible queries with orders of magnitude speedup.
13324501
Local Structure Comparison of Proteins
Abstract Protein local structure comparison aims to recognize structural similarities between parts of proteins. It is an active topic in bioinformatics research, integrating computer science concepts in computational geometry and graph theory with empirical observations and physical principles from biochemistry. It has important biological applications, including protein function prediction. In this chapter, we provide an introduction to the protein local structure comparison problem including challenges and applications. Current approaches to the problem are reviewed. Particular consideration is given to the discovery of local structure common to a group of related proteins. We present a new algorithm for this problem that uses a graph-based representation of protein structure and finds recurring subgraphs among a group of protein graphs.
7156676
The design and implementation of scalable information services in a grid environment
This paper proposes an Extensible Monitoring and Discovery Service for grid environment MASSIVE (MEMDS). The MASSIVE project focuses on developing a multidisciplinary applications-oriented simulation and visualization environment. In the MEMDS, appropriate mechanisms make custom information services established and deployed easily, and the developed APIs simplify the access to the MDS and provide a uniform interface for programmers. Corresponding practices show that the MEMDS improves the extensibility and flexibility of the grid information service.
3122822
Clustering pair-wise dissimilarity data into partially ordered sets
Ontologies represent data relationships as hierarchies of possibly overlapping classes. Ontologies are closely related to clustering hierarchies, and in this article we explore this relationship in depth. In particular, we examine the space of ontologies that can be generated by pairwise dissimilarity matrices. We demonstrate that classical clustering algorithms, which take dissimilarity matrices as inputs, do not incorporate all available information. In fact, only special types of dissimilarity matrices can be exactly preserved by previous clustering methods. We model ontologies as a partially ordered set (poset) over the subset relation. In this paper, we propose a new clustering algorithm, that generates a partially ordered set of clusters from a dissimilarity matrix.
46086053
Similarity Join Algorithms: An Introduction
A multi-function type sheet counting machine capable of counting sheets under a desired operational mode selected from a plurality of operational modes. As the sheets to be counted are deflected one after another away from a stack of sheets, electrical count pulses corresponding to the number of deflected sheets are generated, and a count corresponding to the number of generated pulses is stored in a counter. A reset circuit is provided so that, at the time of changing over to the add mode from any other operational mode, the counter is automatically reset to clear the count previously stored in the counter.