An electron backscatter diffraction study of geesops: a broader view of trilobite vision?

The calcite eyes of trilobites have been studied for over 100 years using methods including light microscopy (e.g. Clarke 1889; Campbell 1975; Towe 1973; Clarkson 1979 and Bruton and Haas 2003) and more recently cathodoluminescence (CL) imaging coupled with scanning electron microscopy (SEM) of samples etched in EDTA (Miller and Clarkson 1980). This work has provided a great deal of information on the mechanisms by which lenses collected light, drawing attention to the importance of the crystallographic orientation of lens calcite for focusing, and leading to sophisticated models of trilobite vision (Clarkson and Levi-Setti, 1975; Gál et al., 2000). The morphology and mode of life of phacopids, in particular Geesops, are well understood (Bruton and Haas, 2003a; 2003b) but observations on the internal structure of their lenses contradict the generally accepted models for image formation by schizochroal eyes. Recent technological advances have given new impetus to the analysis of crystalline materials and especially important has been electron backscatter diffraction (EBSD). This is a SEM-based technique that can be used to accurately ‘map’ variations in the crystallographic orientation of a sample down to the sub-micrometre scale by recording on a sensitive camera Kikuchi patterns that are formed by diffraction of an electron beam when focused on a polished sample tilted at 70°. Although this technique has been understood for over 50 years (Alam et al., 1954) and has been extensively used in disciplines such as metallography (Humphreys, 2001), until recently its Earth Science applications were limited to studies of structural geology and petrology (Nuchter and Stockhert, 2007). Recent applications of EBSD to biomineralisation research (Dalbeck and Cusack, 2006; Griesshaber et al., 2007) have mapped the crystal orientation and microstructure of calcite shells and in 2006 Lee et al. were able to apply this technique to investigating the microstructure of lenses in the schizochroal eye of Dalmanites. This paper describes results of an EBSD study of eyes of Geesops schlotheimi (Bronn, 1825) combined with more traditional microscopy techniques to reveal new aspects of trilobite lens structure

Charged stripes from alternating static magnetic field

We motivate and perform a calculation of the energy of a cold fluid of charged fermions in the presence of a striped magnetic background. We find that a non-trivial value for the doping density on the walls is preferredComment: RevTeX, 3 pages, 3 encapsulated PostScript figure

The sign problem in Monte Carlo simulations of frustrated quantum spin systems

We discuss the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of ``semi-frustrated'' systems (Heisenberg models with ferromagnetic couplings $J_z(r) < 0$ along the $z$-axis and antiferromagnetic couplings $J_{xy}(r)=-J_z(r)$ in the $xy$-plane, for arbitrary distances $r$) the sign problem present for algorithms operating in the $z$-basis can be solved within a recent ``operator-loop'' formulation of the stochastic series expansion method (a cluster algorithm for sampling the diagonal matrix elements of the power series expansion of ${\rm exp}(-\beta H)$ to all orders). The solution relies on identification of operator-loops which change the configuration sign when updated (``merons'') and is similar to the meron-cluster algorithm recently proposed by Chandrasekharan and Wiese for solving the sign problem for a class of fermion models (Phys. Rev. Lett. {\bf 83}, 3116 (1999)). Some important expectation values, e.g., the internal energy, can be evaluated in the subspace with no merons, where the weight function is positive definite. Calculations of other expectation values require sampling of configurations with only a small number of merons (typically zero or two), with an accompanying sign problem which is not serious. We also discuss problems which arise in applying the meron concept to more general quantum spin models with frustrated interactions.Comment: 13 pages, 16 figure

Quantum Monte Carlo with Directed Loops

We introduce the concept of directed loops in stochastic series expansion and path integral quantum Monte Carlo methods. Using the detailed balance rules for directed loops, we show that it is possible to smoothly connect generally applicable simulation schemes (in which it is necessary to include back-tracking processes in the loop construction) to more restricted loop algorithms that can be constructed only for a limited range of Hamiltonians (where back-tracking can be avoided). The "algorithmic discontinuities" between general and special points (or regions) in parameter space can hence be eliminated. As a specific example, we consider the anisotropic S=1/2 Heisenberg antiferromagnet in an external magnetic field. We show that directed loop simulations are very efficient for the full range of magnetic fields (zero to the saturation point) and anisotropies. In particular for weak fields and anisotropies, the autocorrelations are significantly reduced relative to those of previous approaches. The back-tracking probability vanishes continuously as the isotropic Heisenberg point is approached. For the XY-model, we show that back-tracking can be avoided for all fields extending up to the saturation field. The method is hence particularly efficient in this case. We use directed loop simulations to study the magnetization process in the 2D Heisenberg model at very low temperatures. For LxL lattices with L up to 64, we utilize the step-structure in the magnetization curve to extract gaps between different spin sectors. Finite-size scaling of the gaps gives an accurate estimate of the transverse susceptibility in the thermodynamic limit: chi_perp = 0.0659 +- 0.0002.Comment: v2: Revised and expanded discussion of detailed balance, error in algorithmic phase diagram corrected, to appear in Phys. Rev.

Towards explainable metaheuristics: PCA for trajectory mining in evolutionary algorithms.

The generation of explanations regarding decisions made by population-based meta-heuristics is often a difficult task due to the nature of the mechanisms employed by these approaches. With the increase in use of these methods for optimisation in industries that require end-user confirmation, the need for explanations has also grown. We present a novel approach to the extraction of features capable of supporting an explanation through the use of trajectory mining - extracting key features from the populations of NDAs. We apply Principal Components Analysis techniques to identify new methods of population diversity tracking post-runtime after projection into a lower dimensional space. These methods are applied to a set of benchmark problems solved by a Genetic Algorithm and a Univariate Estimation of Distribution Algorithm. We show that the new sub-space derived metrics can capture key learning steps in the algorithm run and how solution variable patterns that explain the fitness function may be captured in the principal component coefficients

Non-deterministic solvers and explainable AI through trajectory mining.

Traditional methods of creating explanations from complex systems involving the use of AI have resulted in a wide variety of tools available to users to generate explanations regarding algorithm and network designs. This however has traditionally been aimed at systems that mimic the structure of human thought such as neural networks. The growing adoption of AI systems in industries has led to research and roundtables regarding the ability to extract explanations from other systems such as Non-Deterministic algorithms. This family of algorithms can be analysed but the explanation of events can often be difficult for non-experts to understand. Mentioned is a potential path to the generation of explanations that would not require expert-level knowledge to be correctly understood

Multi-population genetic algorithms with immigrants scheme for dynamic shortest path routing problems in mobile ad hoc networks

Copyright @ Springer-Verlag Berlin Heidelberg 2010.The static shortest path (SP) problem has been well addressed using intelligent optimization techniques, e.g., artificial neural networks, genetic algorithms (GAs), particle swarm optimization, etc. However, with the advancement in wireless communications, more and more mobile wireless networks appear, e.g., mobile ad hoc network (MANET), wireless mesh network, etc. One of the most important characteristics in mobile wireless networks is the topology dynamics, that is, the network topology changes over time due to energy conservation or node mobility. Therefore, the SP problem turns out to be a dynamic optimization problem in mobile wireless networks. In this paper, we propose to use multi-population GAs with immigrants scheme to solve the dynamic SP problem in MANETs which is the representative of new generation wireless networks. The experimental results show that the proposed GAs can quickly adapt to the environmental changes (i.e., the network topology change) and produce good solutions after each change.This work was supported by the Engineering and Physical Sciences Research Council(EPSRC) of UK under Grant EP/E060722/1

Partial structure learning by subset Walsh transform.

Estimation of distribution algorithms (EDAs) use structure learning to build a statistical model of good solutions discovered so far, in an effort to discover better solutions. The non-zero coefficients of the Walsh transform produce a hypergraph representation of structure of a binary fitness function; however, computation of all Walsh coefficients requires exhaustive evaluation of the search space. In this paper, we propose a stochastic method of determining Walsh coefficients for hyperedges contained within the selected subset of the variables (complete local structure). This method also detects parts of hyperedges which cut the boundary of the selected variable set (partial structure), which may be used to incrementally build an approximation of the problem hypergraph

A bivariate first order autoregressive time series model in exponential variables (BEAR (1))

A simple time series model for bivariate exponential variables having first-order auto-regressive structure is presented. The linear random coefficient difference equation model is an adaptation of the New Exponential Autoregressive model (NEAR (2)). The process is Markovian in the bivariate sense and has correlation structure analogous to that of the Gaussian AR(1) bivariate time series model. The model exhibits a full range of positive correlations and cross-correlations. With some modification in either the innovation or the random coefficients, the model admits some negative values for the cross- correlations. The marginal processes are shown to have correlation structure of ARMA (2,1) modelsPrepared for: Naval Postgraduate School Monterey, CAhttp://archive.org/details/bivariatefirstor00dewaNAN

In-medium kaon and antikaon properties in the quark-meson coupling model

The properties of the kaon, $K$, and antikaon, \kbar, in nuclear medium are studied in the quark-meson coupling (QMC) model. Employing a constituent quark-antiquark (MIT bag model) picture, their excitation energies in a nuclear medium at zero momentum are calculated within mean field approximation. The scalar, and the vector mesons are assumed to couple directly to the nonstrange quarks and antiquarks in the $K$ and \kbar mesons. It is demonstrated that the $\rho$ meson induces different mean field potentials for each member of the isodoublets, $K$ and \kbar, when they are embedded in asymmetric nuclear matter. Furthermore, it is also shown that this $\rho$ meson potential is repulsive for the $K^-$ meson in matter with a neutron excess, and renders $K^-$ condensation less likely to occur.Comment: Latex, 11 pages, 4 Postscript figures, a few typos which can be important for an interpretation (but not reflected in the results) are corrected, as published in (E) Phys. Lett. B 436 (1998) 45