Irreducibility testing over local fields

The purpose of this paper is to describe a method to determine whether a bivariate polynomial with rational coefficients is irreducible when regarded as an element in , the ring of polynomials with coefficients from the field of Laurent series in with rational coefficients. This is achieved by computing certain associated Puiseux expansions, and as a result, a polynomial-time complexity bound for the number of bit operations required to perform this irreducibility test is computed.

     

Bistable behaviour in squeezed vacua: II. Stability analysis and chaos

Linear stability analysis and (numerical) investigation of the periodic and chaotic self-pulsing behaviour are presented for the Maxwell-Bloch equations of a bistable model in contact with a squeezed vacuum field. Effect of the squeeze phase parameter on the period doubling bifurcation that preceeds chaos is examined for the adiabatic and non-adiabatic regimes.     

非线性时间序列互信息与Lempel-Ziv复杂度的相关性研究

为探究非线性动力学系统的互信息和复杂度的相关性，用Logistic映射、Lorenz模型和心电RR间期的非线性时间序列作为实验数据，计算多分段延时互信息和多分段Lempel-Ziv复杂度以及它们之间的相关系数.结果表明这些序列的互信息和复杂度呈强负相关，对Logistic方程生成的201个序列的不同段互信息和不同段复杂度之间的相关系数绝对值都大于0.9162，最大达0.9923；对94个心电RR间期序列都大于0.8555，最大达0.9860.研究还发现互信息比复杂度能更敏感地表现出非线性动力系统的特征. 关键词： 相关系数 互信息 Lempel-Ziv 复杂度 心电RR间期     

Boltzmann distribution of free energies in a finite-connectivity spin-glass system and the cavity approach

At sufficiently low temperatures, the configurational phase space of a large spin-glass system breaks into many separated domains, each of which is referred to as a macroscopic state. The system is able to visit all spin configurations of the same macroscopic state, while it can not spontaneously jump between two different macroscopic states. Ergodicity of the whole configurational phase space of the system, however, can be recovered if a temperature-annealing process is repeated an infinite number of times. In a heating-annealing cycle, the environmental temperature is first elevated to a high level and then decreased extremely slowly until a final low temperature T is reached. Different macroscopic states may be reached in different rounds of the annealing experiment; while the probability of finding the system in macroscopic state α decreases exponentially with the free energy F _α (T) of this state. For finite-connectivity spin glass systems, we use this free energy Boltzmann distribution to formulate the cavity approach of Mézard and Parisi [Eur. Phys. J. B, 2001, 20: 217] in a slightly different form. For the ±J spin-glass model on a random regular graph of degree K = 6, the predictions of the present work agree with earlier simulational and theoretical results.      

Combination of two basic types of synchronization in a coupled semiconductor laser system

Combination of two basic types of synchronization, anticipatory synchronization and lagged synchronization, is investigated numerically between two coupled semiconductor lasers. It is found that lagged synchronization produced by a backward coupling with a suitable delay can combine with the originally hidden anticipatory synchronization and produce a type of synchronization overcoming the original lagged synchronization produced by a forward coupling. We study the combination synchronization phenomenon when the delay of the backward coupling is different from that of the original anticipatory synchronization. Our results suggest that the synchronization combination phenomenon might allow an interpretation of an experimental observation by Sivaprakasam et al. [Phys. Rev. Lett. 87, 154101 (2001)] that the anticipating time is irrespective of the external-cavity round trip time, which to date remains to be understood.     

Inferring topological features of proteins from amino acid residue networks

Topological properties of native folds are obtained from statistical analysis of 160 low homology proteins covering the four structural classes. This is done analyzing one, two and three-vertex joint distribution of quantities related to the corresponding network of amino acid residues. Emphasis on the amino acid residue hydrophobicity leads to the definition of their center of mass as vertices in this contact network model with interactions represented by edges. The network analysis helps us to interpret experimental results such as hydrophobic scales and fraction of buried accessible surface area in terms of the network connectivity. Moreover, those networks show assortative mixing by degree. To explore the vertex-type dependent correlations, we build a network of hydrophobic and polar vertices. This procedure presents the wiring diagram of the topological structure of globular proteins leading to the following attachment probabilities between hydrophobic–hydrophobic 0.424(5), hydrophobic-polar 0.419(2) and polar–polar 0.157(3) residues.     

Structural complexity of disordered surfaces: Analyzing the porous silicon SFM patterns

This paper introduces a relative structural complexity measure for the characterization of disordered surfaces. Numerical solutions of 2d+1 KPZ equation and scanning force microscopy (SFM) patterns of porous silicon samples are analyzed using this methodology. The results and phenomenological interpretation indicate that the proposed measure is efficient for quantitatively characterize the structural complexity of disordered surfaces (and interfaces) observed and/or simulated in nano, micro and ordinary scales.     

FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension

We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully polynomial-time approximation scheme for the problem of maximizing or minimizing an arbitrary polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. A conference version of this article, containing a part of the results presented here, appeared in Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, Miami, FL, January 22–24, 2006, pp. 743–748. The first author gratefully acknowledges support from NSF grant DMS-0608785, a 2003 UC-Davis Chancellor’s fellow award, the Alexander von Humboldt foundation, and IMO Magdeburg. The remaining authors were supported by the European TMR network ADONET 504438.     

PSPACE complexity of modal logic <Emphasis Type="Italic">K D</Emphasis>45<Subscript>n</Subscript>

We study sequent calculus for multi-modal logic K D45_n and its complexity. We introduce a loop-check free sequent calculus. Loop-check is eliminated by using the marked modal operator □_i^•, which is used as an alternative to sequents with histories ([8], [3], [5]). All inference rules are invertible or semi-invertible. To get this, we use or branches beside common and branches. We prove the equivalence between known sequent calculus and our newly introduced efficient sequent calculus. We concentrate on the complexity analysis of the introduced sequent calculus for multi-modal logic K D45_n. We prove that the space complexity of the given calculus is polynomial (O(l ³)). We show the maximum height of the constructed derivation tree that leads to the reduction of the time and space complexity. We present a decision algorithm for multi-modal logic K D45_n and some nontrivial examples to improve the introduced loop-check free sequent calculus.