Near-optimal design of Global Positioning System (GPS) networks using the Tabu Search technique

This paper describes an optimization technique based on an heuristic procedure which is applied to analyse and improve the efficiency of the design of Global Positioning System (GPS) surveying networks. GPS is a valuable survey tool because of its ability to increase the accuracy, speed and flexibility of a survey. A GPS network can be defined as a number of stations, which are co-ordinated by a series of sessions, formed by placing receivers on stations. The goal is to select the best order in which these sessions can be organised to give the best possible schedule. Generally, solving large networks to optimality requires impractical computational time. This paper proposes a Tabu Search technique which provides optimal or near-optimal solutions for large networks with an acceptable amount of computational effort. Computational results for several case studies with known and unknown optimal schedules have been presented to assess the performance of the proposed technique.     

Dendrimers and combinatorial chemistry—tools for fluorescent enhancement in protease assays

FRET based systems are some of the best methods available to detect and monitor proteolytic activity. To enhance fluorescent signals and hence assay sensitivity, two different systems were developed using two different dendrimeric constructs. In the first case, a triple branched dendrimer bearing three dansyl groups was used to enhance assay sensitivity and showed a significant enhancement of fluorescence following enzymatic cleavage. In another example, a tris-fluorescein probe, that undergoes self-quenching, was utilized in a combinatorial library synthesis to map the substrate specificity of proteases.     

Branch and win: OR tree search algorithms for solving combinatorial optimisation problems

Currently, most combinatorial optimisation problems have to be solved, if the optimum solution is sought, using general techniques to explore the space of feasible solutions and, more specifically, through exploratory enumerative procedures in trees and search graphs. We propose Branch and Win, a general formulation for understanding and synthesising the different tree search procedures that have been presented in the literature of operations research as well as in that of artificial intelligence. Several general ideas are also presented, whose application allows designing new hybrid search algorithms, in order to implement the procedure.     

Interpolation by a Game

We introduce a notion of a real game (a generalisation of the Karchmer-Wigderson game (cf. [3]) and of real communication complexity, and relate this complexity to the size of monotone real formulas and circuits. We give an exponential lower bound for tree-like monotone protocols (defined in [4, Definition 2.2]) of small real communication complexity solving the monotone communication complexity problem associated with the bipartite perfect matching problem. This work is motivated by a research in interpolation theorems for prepositional logic (by a problem posed in [5, Section 8], in particular). Our main objective is to extend the communication complexity approach of [4, 5] to a wider class of proof systems. In this direction we obtain an effective interpolation in a form of a protocol of small real communication complexity. Together with the above mentioned lower bound for tree-like protocols this yields as a corollary a lower bound on the number of steps for particular semantic derivations of Hall's theorem (these include tree-like cutting planes proofs for which an exponential lower bound was demonstrated in [2]).     

A Relationship Among Gentzen's Proof-Reduction,Kirby-Paris' Hydra Game and Buchholz's Hydra Game

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φ_ω (0) (while that of PA or of Kirby-Paris' Game is φ₁ (0) = ?₀) in the Veblen hierarchy of ordinals.     

A four-parameter partition identity

We present a new partition identity and give a combinatorial proof of our result. This generalizes a result of Andrews in which he considers the generating function for partitions with respect to size, number of odd parts, and number of odd parts of the conjugate. 2000 Mathematics Subject Classification Primary—05A17; Secondary—11P81     

清除树脂在组合化学中的应用

清除树脂是一种特殊的固相试剂。近五年，它们被广泛的用于平行液相法合成组合化学库，简化液相组合化学库的纯化操作。本文综述了清除树脂在纯化操作中的使用策略。根据清除纯化原理，介绍了共价键型和离子键型两类清除树脂。给出了清除树脂在组合化学中的具体应用实例。最后对清除树脂的发展作了展望。     

Combinatorial Synthesis and Multidimensional NMR Spectroscopy: An Approach to Understanding Protein–Ligand Interactions

Combinatorial chemistry is a laboratory emulation of natural recombination and selection processes. Strategies in this developing discipline involve the generation of diverse, molecular libraries through combinatorial synthesis and the selection of compounds that possess a desired property. Such approaches can facilitate the identification of ligands that bind to biological receptors, promoting our chemical understanding of cellular processes. This article illustrates that the coupling of combinatorial synthesis, multidimensional NMR spectroscopy, and biochemical methods has enhanced our understanding of a protein receptor used commonly in signal transduction, the Src Homology 3 (SH3) domain. This novel approach to studying molecular recognition has revealed a set of rules that govern SH3–ligand interactions, allowing models of receptor–ligand complexes to be constructed with only a knowledge of the polypeptide sequences. Combining combinatorial synthesis with structural methods provides a powerful new approach to understanding how proteins bind their ligands in general.     

Combinatorial synthesis of amino acid- and peptide-carbohydrate conjugates on solid phase

Carbohydrates are useful polyfunctional scaffold molecules which allow the selective attachment of a number of different side chains. The combinatorial solid phase synthesis of diverse amino acid or peptide conjugates of a polyfunctional glucose scaffold based on a set of selectively removable and orthogonally stable protecting groups is described. The resulting carbohydrate-peptide hybrids constitute potential turn mimetics.