Combinatorial structures

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  • This chapter and the next are devoted to enumeration, where the problem is to determine the number of combinatorial configurations described by finite rules, and do so for all possible sizes. This chapter presents the following content: Symbolic method, trees and strings, powersets and multisets, compositions and partitions, substitution.

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  • Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài:On the combinatorial structure of arrangements of oriented pseudocircles...

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  • This chapter introduces analytic combinatorics, a modern approach to the study of combinatorial structures of the sort that we encounter frequently in the analysis of algorithms. The approach is predicated on the idea that combinatorial structures are typically defined by simple formal rules that are the key to learning their properties.

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  • Many scientific endeavours demand precise quantitative information on probabilistic properties of parameters of combinatorial objects. This chapter introduce to combinatorial parameters and MGFs. This chapter presents the following content: Basics, moment calculations, OBGF examples, labelled classes.

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  • In this paper, an attempt is made to carry out the comparative study on some mathematical tools for analyze the properties of interleaved sequences used in modern communications, cryptography, watermarking. The comparison begins with the review of the well-known algebraic and combinatorial structure methods for generation and analysis of such sequences.

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  • Why do proteins adopt the conformations that they do, and what determines their stabilities? While we have come to some understandingof the forces that underlie protein architecture, a precise, predictive, physicochemical explanation is still elusive. Two obstacles to addressing these questions are the unfathomable vastness of protein sequence space, and the difficulty in makingdirect phy-sical measurements on large numbers of protein variants. Here, we review combinatorial methods that have been applied to problems in protein biophysics over the last 15 years.

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  • This paper describes a wide-coverage statistical parser that uses Combinatory Categorial Grammar (CCG) to derive dependency structures. The parser differs from most existing wide-coverage treebank parsers in capturing the long-range dependencies inherent in constructions such as coordination, extraction, raising and control, as well as the standard local predicate-argument dependencies. A set of dependency structures used for training and testing the parser is obtained from a treebank of CCG normal-form derivations, which have been derived (semi-) automatically from the Penn Treebank. ...

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  • The structure imposed upon spoken sentences by intonation seems frequently to be orthogohal to their traditional surface-syntactic structure. However, the notion of "intonational structure" as formulated by Pierrehumbert, Selkirk, and others, can be subsumed under a rather different notion of syntactic surface structure that emerges from a theory of grammar based on a "Combinatory" extension to Categorial Gram, mar.

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  • Chapter 6: Trees investigates properties of many different types of trees, fundamental structures that arise implicitly and explicitly in many practical algorithms. Our goal is to provide access to results from an extensive literature on the combinatorial analysis of trees, while at the same time providing the groundwork for a host of algorithmic applications.

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  • Chapter 7: Permutations surveys combinatorial properties of permutations (orderings of the numbers 1 through N) and shows how they relate in a natural way to fundamental and widely-used sorting algorithms.

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  • Chapter 8: String and Tries studies basic combinatorial properties of strings, sequences of characters or letters drawn from a fixed alphabet, and introduces algorithms that process strings ranging from fundamental methods at the heart of the theory of computation to practical text-processing methods with a host of important applications.

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  • In this chapter, we examine some of the most important classes of labelled objects, including surjections, set partitions, permutations, as well as labelled graphs, trees, and mappings from a finite set into itself. Certain aspects of words can also be treated by this theory, a fact which has important consequences not only in combinatorics itself but also in probability and statistics.

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  • The primary goal of this chapter is to provide combinatorial illustrations of the power of complex analytic methods, and specifically of the rational–meromorphic framework developed in the previous chapter. At the same time, we shift gears and envisage counting problems at a new level of generality.

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  • In Chapter 3 we have shown that the topological structures of kinematic chains can be represented by graphs. Several useful structural characteristics of graphs of kinematic chains were derived. In this chapter we show that graphs of kinematic chains can be enumerated systematically by using graph theory and combinatorial analysis. There are enormous graphs.

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  • Enumeration of Graphs of Kinematic Chains In Chapter 3 we have shown that the topological structures of kinematic chains can be represented by graphs. Several useful structural characteristics of graphs of kinematic chains were derived. In this chapter we show that graphs of kinematic chains can be enumerated systematically by using graph theory and combinatorial analysis. There are enormous graphs. Obviously, not all of them are suitable for construction of kinematic chains.

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  • In recent years, classical antibody-based affinity reagents have been challenged by novel types of binding proteins developed by combinatorial protein engineering principles. One of these classes of binding proteins of non-Ig origin are the so-called affibody binding proteins, functionally selected from libraries of a small (6 kDa), non-cysteine three-helix bundle domain used as a scaffold.

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  • To facilitate the process of proteindesign and learn the basic rules that control the structure and stability of proteins, combinatorial methods have been developed to select or screen proteins with desired properties from libraries of mutants. One such method uses phage-display and proteo-lysis to select stably folded proteins. This method does not rely on specific properties of proteins for selection. There-fore, in principle it can be applied to any protein.

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  • Haematopoiesis, the differentiation of haematopoietic stem cells and progenitors into various lineages, involves complex interactions of transcription factors that modulate the expression of downstream genes and mediate proliferation and differentiation signals. Commitment of pluripotent haematopoietic stem cells to the erythroid lineage induces erythropoiesis, the production of red blood cells. This process involves a concerted progression through an erythroid burst forming unit (BFU-E), an erythroid colony forming unit (CFU-E), proerythroblast and an erythroblast....

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  • Modern tools in proteomics require access to large arrays of specific bind-ers for use in multiplex array formats, such as microarrays, to decipher complex biological processes. Combinatorial protein libraries offer a solu-tion to the generation of collections of specific binders, but unit operations in the process to isolate binders from such libraries must be automatable to ensure an efficient procedure.

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  • Chapter 1: Analysis of Algorithms considers the general motivations for algorithmic analysis and relationships among various approaches to studying performance characteristics of algorithms. This chapter includes contents: History and motivation, a scientific approach, example: Quicksort, resources.

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