Dynamic Morse decompositions for semigroups of homeomorphisms and control systems

In this paper, we introduce the concept of dynamic Morse decomposition for an action of a semigroup of homeomorphisms. Conley has shown in [5, Sec. 7] that the concepts of Morse decomposition and dynamic Morse decompositions are equivalent for flows in metric spaces. Here, we show that a Morse decomposition for an action of a semigroup of homeomorphisms of a compact topological space is a dynamic Morse decomposition. We also define Morse decompositions and dynamic Morse decompositions for control systems on manifolds. Under certain condition, we show that the concept of dynamic Morse decomposition for control system is equivalent to the concept of Morse decomposition.

Combinatorial identities and quantum state densities of supersymmetric sigma models on N-folds

There is a remarkable connection between the number of quantum states of conformal theories and the sequence of dimensions of Lie algebras. In this paper, we explore this connection by computing the asymptotic expansion of the elliptic genus and the microscopic entropy of black holes associated with (supersymmetric) sigma models. The new features of these results are the appearance of correct prefactors in the state density expansion and in the coefficient of the logarithmic correction to the entropy.

Combinatorial synthesis and directed evolution applied to the production of alpha-helix forming antimicrobial peptides analogues

Antimicrobial peptides (AMPs) are effector molecules of innate immune systems found in different groups of organisms, including microorganisms, plants, insects, amphibians and humans. These peptides exhibit several structural motifs but the most abundant AMPs assume an amphipathic alpha-helical structure. The alpha-helix forming antimicrobial peptides are excellent candidates for protein engineering leading to an optimization of their biological activity and target specificity. Nowadays several approaches are available and this review deals with the use of combinatorial synthesis and directed evolution in order to provide a high-throughput source of antimicrobial peptides analogues with enhanced lytic activity and specificity.

A natural combinatorial chemistry strategy in acylpolyamine toxins from Nephilinae orb-web spiders

The present study shows how nature combined a small number of chemical building blocks to synthesize the acylpolyamine toxins in the venoms of Nephilinae orb-web spiders. Considering these structures in four parts, it was possible to rationalize a way to represent the natural combinatorial chemistry involved in the synthesis of these toxins: an aromatic moiety is connected through a linker amino acid to a polyamine chain, which in turn may be connected to an optional tail. The polyamine chains were classified into seven subtypes (from A to G) depending on the way the small chemical blocks are combined. These polyamine chains may be connected to one of the three possible chromophore moieties: 2,4-dihydroxyphenyl acetic acid, or 4-hydroxyindole acetic acid, or even with the indole acetic group. The connectivity between the aryl moiety and the polyamine chain is usually made through an asparagine residue; optionally a tail may be attached to the polyamine chain; nine different types of tails were identified among the 72 known acylpolyamine toxin structures. The combinations of three chromophores, two types of amino acid linkers, seven sub-types of polyamine backbone, and nine options of tails results in 378 different structural possibilities. However, we detected only 91 different toxin structures, which may represent the most successful structural trials in terms of efficiency of prey paralysis/death.

Combinatorial and geometrical properties of a class of tilings

In this paper, we consider a tiling generated by a Pisot unit number of degree d >= 3 which has a finite expansible property. We compute the states of a finite automaton which recognizes the boundary of the central tile. We also prove in the case d = 3 that the interior of each tile is simply connected.

A combinatorial approach for transmission expansion & reactive power planning

A metaheuristic technique for solving the short-term transmission network expansion and reactive power planning problems, at the same time, in regulated power systems using the AC model is presented. The problem is solved using a real genetic algorithm (RGA). For each topology proposed by RGA an indicator is employed to identify the weak buses for new reactive power sources allocation. The fitness function is calculated using the cost of each configuration as well as constraints deviation of an AC optimal power flow (OPF) in which the minimum reactive generation of new reactive sources and the active power losses are objectives. With allocation of reactive power sources at load buses, the circuit capacity increases and the cost of installation could be decreased. The method is tested in a well known test system, presenting good results when compared with other approaches. © 2011 IEEE.

Strategies to reduce the number of variables and the combinatorial search space of the multistage transmission expansion planning problem

This paper proposes strategies to reduce the number of variables and the combinatorial search space of the multistage transmission expansion planning problem (TEP). The concept of the binary numeral system (BNS) is used to reduce the number of binary and continuous variables related to the candidate transmission lines and network constraints that are connected with them. The construction phase of greedy randomized adaptive search procedure (GRASP-CP) and additional constraints, obtained from power flow equilibrium in an electric power system are employed for more reduction in search space. The multistage TEP problem is modeled like a mixed binary linear programming problem and solved using a commercial solver with a low computational time. The results of one test system and two real systems are presented in order to show the efficiency of the proposed solution technique. © 1969-2012 IEEE.

A semigroups theory approach to a model of suspension bridges

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Goppa codes over certain semigroups

A Goppa code is described in terms of a polynomial, known as Goppa polynomial, and in contrast to cyclic codes, where it is difficult to estimate the minimum Hamming distance d from the generator polynomial. Furthermore, a Goppa code has the property that d ≥ deg(h(X))+1, where h(X) is a Goppa polynomial. In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm.

Combinatorial-topological framework for the analysis of global dynamics

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

Huckebein is part of a combinatorial repression code in the anterior blastoderm

The hierarchy of the segmentation cascade responsible for establishing the Drosophila body plan is composed by gap, pair-rule and segment polarity genes. However, no pair-rule stripes are formed in the anterior regions of the embryo. This lack of stripe formation, as well as other evidence from the literature that is further investigated here, led us to the hypothesis that anterior gap genes might be involved in a combinatorial mechanism responsible for repressing the cis-regulatory modules (CRMs) of hairy (h), even-skipped (eve), runt (run), and fushi-tarazu (ftz) anterior-most stripes. In this study, we investigated huckebein (hkb), which has a gap expression domain at the anterior tip of the embryo. Using genetic methods we were able to detect deviations from the wild-type patterns of the anterior-most pair-rule stripes in different genetic backgrounds, which were consistent with Hkb-mediated repression. Moreover, we developed an image processing tool that, for the most part, confirmed our assumptions. Using an hkb misexpression system, we further detected specific repression on anterior stripes. Furthermore, bioinformatics analysis predicted an increased significance of binding site clusters in the CRMs of h 1, eve 1, run 1 and ftz 1 when Hkb was incorporated in the analysis, indicating that Hkb plays a direct role in these CRMs. We further discuss that Hkb and Slp1, which is the other previously identified common repressor of anterior stripes, might participate in a combinatorial repression mechanism controlling stripe CRMs in the anterior parts of the embryo and define the borders of these anterior stripes. (C) 2011 Elsevier Inc. All rights reserved.

Structural analysis of combinatorial optimization problem characteristics and their resolution using hybrid approaches

Many combinatorial problems coming from the real world may not have a clear and well defined structure, typically being dirtied by side constraints, or being composed of two or more sub-problems, usually not disjoint. Such problems are not suitable to be solved with pure approaches based on a single programming paradigm, because a paradigm that can effectively face a problem characteristic may behave inefficiently when facing other characteristics. In these cases, modelling the problem using different programming techniques, trying to ”take the best” from each technique, can produce solvers that largely dominate pure approaches. We demonstrate the effectiveness of hybridization and we discuss about different hybridization techniques by analyzing two classes of problems with particular structures, exploiting Constraint Programming and Integer Linear Programming solving tools and Algorithm Portfolios and Logic Based Benders Decomposition as integration and hybridization frameworks.

Intrinsic ordering, combinatorial numbers and reliability engineering

[EN]A new algorithm for evaluating the top event probability of large fault trees (FTs) is presented. This algorithm does not require any previous qualitative analysis of the FT. Indeed, its efficiency is independent of the FT logic, and it only depends on the number n of basic system components and on their failure probabilities. Our method provides exact lower and upper bounds on the top event probability by using new properties of the intrinsic order relation between binary strings. The intrinsic order enables one to select binary n-tuples with large occurrence probabilities without necessity to evaluate them. This drastically reduces the complexity of the problem from exponential (2n binary n-tuples) to linear (n Boolean variables)...