Cover-Encodings of Fitness Landscapes

The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a feature of the typically rugged landscapes encountered arrest the progress of the search process. Another way of tackling optimization problems is by the use of heuristic approximations to estimate a global cost minimum. Here we present a combination of these two approaches by using cover-encoding maps which map processes from a larger search space to subsets of the original search space. The key idea is to construct cover-encoding maps with the help of suitable heuristics that single out near-optimal solutions and result in landscapes on the larger search space that no longer exhibit trapping local minima. We present cover-encoding maps for the problems of the traveling salesman, number partitioning, maximum matching and maximum clique; the practical feasibility of our method is demonstrated by simulations of adaptive walks on the corresponding encoded landscapes which find the global minima for these problems.Comment: 15 pages, 4 figure

Hybrid Courses in Aeronautical Science Curriculums

This article focuses on the need to address learning styles of NetGeners with an emphasis on aviation students. A brief history of aviation training generations as posited by Kearns (2010) is reviewed after which the author\u27s experience creating a university hybrid or blended course on Crew Resource Management is discussed. This article was supported in part by a grant from Embry-Riddle Aeronautical University\u27s Center for Teaching and Learning Excellence

The Moduli Space of the N=2N=2 Supersymmetric G2G_{2} Yang-Mills Theory

We present the hyper-elliptic curve describing the moduli space of the N=2 supersymmetric Yang-Mills theory with the $G_2$ gauge group. The exact monodromies and the dyon spectrum of the theory are determined. It is verified that the recently proposed solitonic equation is also satisfied by our solution.Comment: Complete set of monodromies are included. To be published in Phys.lett.

Holomorphic Anomaly in Gauge Theories and Matrix Models

We use the holomorphic anomaly equation to solve the gravitational corrections to Seiberg-Witten theory and a two-cut matrix model, which is related by the Dijkgraaf-Vafa conjecture to the topological B-model on a local Calabi-Yau manifold. In both cases we construct propagators that give a recursive solution in the genus modulo a holomorphic ambiguity. In the case of Seiberg-Witten theory the gravitational corrections can be expressed in closed form as quasimodular functions of Gamma(2). In the matrix model we fix the holomorphic ambiguity up to genus two. The latter result establishes the Dijkgraaf-Vafa conjecture at that genus and yields a new method for solving the matrix model at fixed genus in closed form in terms of generalized hypergeometric functions.Comment: 34 pages, 2 eps figures, expansion at the monopole point corrected and interpreted, and references adde

Divergent Time Scale in Axelrod Model Dynamics

We study the evolution of the Axelrod model for cultural diversity. We consider a simple version of the model in which each individual is characterized by two features, each of which can assume q possibilities. Within a mean-field description, we find a transition at a critical value q_c between an active state of diversity and a frozen state. For q just below q_c, the density of active links between interaction partners is non-monotonic in time and the asymptotic approach to the steady state is controlled by a time scale that diverges as (q-q_c)^{-1/2}.Comment: 4 pages, 5 figures, 2-column revtex4 forma

Patterning the insect eye: from stochastic to deterministic mechanisms

While most processes in biology are highly deterministic, stochastic mechanisms are sometimes used to increase cellular diversity, such as in the specification of sensory receptors. In the human and Drosophila eye, photoreceptors sensitive to various wavelengths of light are distributed randomly across the retina. Mechanisms that underlie stochastic cell fate specification have been analysed in detail in the Drosophila retina. In contrast, the retinas of another group of dipteran flies exhibit highly ordered patterns. Species in the Dolichopodidae, the "long-legged" flies, have regular alternating columns of two types of ommatidia (unit eyes), each producing corneal lenses of different colours. Individual flies sometimes exhibit perturbations of this orderly pattern, with "mistakes" producing changes in pattern that can propagate across the entire eye, suggesting that the underlying developmental mechanisms follow local, cellular-automaton-like rules. We hypothesize that the regulatory circuitry patterning the eye is largely conserved among flies such that the difference between the Drosophila and Dolichopodidae eyes should be explicable in terms of relative interaction strengths, rather than requiring a rewiring of the regulatory network. We present a simple stochastic model which, among its other predictions, is capable of explaining both the random Drosophila eye and the ordered, striped pattern of Dolichopodidae.Comment: 24 pages, 4 figure

Possible indicators for low dimensional superconductivity in the quasi-1D carbide Sc3CoC4

The transition metal carbide Sc3CoC4 consists of a quasi-one-dimensional (1D) structure with [CoC4]_{\inft} polyanionic chains embedded in a scandium matrix. At ambient temperatures Sc3CoC4 displays metallic behavior. At lower temperatures, however, charge density wave formation has been observed around 143K which is followed by a structural phase transition at 72K. Below T^onset_c = 4.5K the polycrystalline sample becomes superconductive. From Hc1(0) and Hc2(0) values we could estimate the London penetration depth ({\lambda}_L ~= 9750 Angstroem) and the Ginsburg-Landau (GL) coherence length ({\xi}_GL ~= 187 Angstroem). The resulting GL-parameter ({\kappa} ~= 52) classifies Sc3CoC4 as a type II superconductor. Here we compare the puzzling superconducting features of Sc3CoC4, such as the unusual temperature dependence i) of the specific heat anomaly and ii) of the upper critical field H_c2(T) at T_c, and iii) the magnetic hysteresis curve, with various related low dimensional superconductors: e.g., the quasi-1D superconductor (SN)_x or the 2D transition-metal dichalcogenides. Our results identify Sc3CoC4 as a new candidate for a quasi-1D superconductor.Comment: 4 pages, 5 figure

Heisenberg Dimer Single Molecule Magnets in a Strong Magnetic Field

We calculate the static and dynamic properties of single crystal, single molecule magnets consisting of equal spin $S=1/2$ or 5/2 dimers. The spins in each dimer interact with each other via the Heisenberg exchange interaction and with the magnetic induction ${\bf B}$ via the Zeeman interaction, and interdimer interactions are negligible. For antiferromagnetic couplings, the static magnetization and specific heat exhibit interesting low temperature $T$ and strong ${\bf B}$ quantum effects. We calculate the frequency spectrum of the Fourier transform of the real part of the time autocorrelation function ${\cal C}_{11}(t)$ for arbitrary $T, {\bf B}$, and compare our results with those obtained for classical spins. We also calculate the inelastic neutron magnetic dynamical structure factor $S({\bf q},\omega)$ at arbitrary $T, {\bf B}$.Comment: 11 pages, 14 figures, submitted to Phys. Rev.