AUTOMATED MORPHOLOGICAL CLASSIFICATION OF APM GALAXIES BY SUPERVISED ARTIFICIAL NEURAL NETWORKS

We train Artificial Neural Networks to classify galaxies based solely on the morphology of the galaxy images as they appear on blue survey plates. The images are reduced and morphological features such as bulge size and the number of arms are extracted, all in a fully automated manner. The galaxy sample was first classified by 6 independent experts. We use several definitions for the mean type of each galaxy, based on those classifications. We then train and test the network on these features. We find that the rms error of the network classifications, as compared with the mean types of the expert classifications, is 1.8 Revised Hubble Types. This is comparable to the overall rms dispersion between the experts. This result is robust and almost completely independent of the network architecture used.Comment: The full paper contains 25 pages, and includes 22 figures. It is available at ftp://ftp.ast.cam.ac.uk/pub/hn/apm2.ps . The table in the appendix is available on request from [email protected]. Mon. Not. R. Astr. Soc., in pres

Universal statistical properties of poker tournaments

We present a simple model of Texas hold'em poker tournaments which retains the two main aspects of the game: i. the minimal bet grows exponentially with time; ii. players have a finite probability to bet all their money. The distribution of the fortunes of players not yet eliminated is found to be independent of time during most of the tournament, and reproduces accurately data obtained from Internet tournaments and world championship events. This model also makes the connection between poker and the persistence problem widely studied in physics, as well as some recent physical models of biological evolution, and extreme value statistics.Comment: Final longer version including data from Internet and WPT tournament

Hydration of an apolar solute in a two-dimensional waterlike lattice fluid

In a previous work, we investigated a two-dimensional lattice-fluid model, displaying some waterlike thermodynamic anomalies. The model, defined on a triangular lattice, is now extended to aqueous solutions with apolar species. Water molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three equivalent bonding arms. Bond formation depends both on orientation and local density. The insertion of inert molecules displays typical signatures of hydrophobic hydration: large positive transfer free energy, large negative transfer entropy (at low temperature), strong temperature dependence of the transfer enthalpy and entropy, i.e., large (positive) transfer heat capacity. Model properties are derived by a generalized first order approximation on a triangle cluster.Comment: 9 pages, 5 figures, 1 table; submitted to Phys. Rev.

Kinetics of Heterogeneous Single-Species Annihilation

We investigate the kinetics of diffusion-controlled heterogeneous single-species annihilation, where the diffusivity of each particle may be different. The concentration of the species with the smallest diffusion coefficient has the same time dependence as in homogeneous single-species annihilation, A+A-->0. However, the concentrations of more mobile species decay as power laws in time, but with non-universal exponents that depend on the ratios of the corresponding diffusivities to that of the least mobile species. We determine these exponents both in a mean-field approximation, which should be valid for spatial dimension d>2, and in a phenomenological Smoluchowski theory which is applicable in d<2. Our theoretical predictions compare well with both Monte Carlo simulations and with time series expansions.Comment: TeX, 18 page

Nonlinear Integral-Equation Formulation of Orthogonal Polynomials

The nonlinear integral equation P(x)=\int_alpha^beta dy w(y) P(y) P(x+y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions P(x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic equations for the coefficients of the polynomials. Interestingly, the set of polynomial solutions is orthogonal with respect to the measure x w(x). The nonlinear integral equation can be used to specify all orthogonal polynomials in a simple and compact way. This integral equation provides a natural vehicle for extending the theory of orthogonal polynomials into the complex domain. Generalizations of the integral equation are discussed.Comment: 7 pages, result generalized to include integration in the complex domai

Vibrational dynamics of confined granular material

By means of two-dimensional contact dynamics simulations, we analyze the vibrational dynamics of a confined granular layer in response to harmonic forcing. We use irregular polygonal grains allowing for strong variability of solid fraction. The system involves a jammed state separating passive (loading) and active (unloading) states. We show that an approximate expression of the packing resistance force as a function of the displacement of the free retaining wall from the jamming position provides a good description of the dynamics. We study in detail the scaling of displacements and velocities with loading parameters. In particular, we find that, for a wide range of frequencies, the data collapse by scaling the displacements with the inverse square of frequency, the inverse of the force amplitude and the square of gravity. Interestingly, compaction occurs during the extension of the packing, followed by decompaction in the contraction phase. We show that the mean compaction rate increases linearly with frequency up to a characteristic frequency and then it declines in inverse proportion to frequency. The characteristic frequency is interpreted in terms of the time required for the relaxation of the packing through collective grain rearrangements between two equilibrium states

A lattice model of hydrophobic interactions

Hydrogen bonding is modeled in terms of virtual exchange of protons between water molecules. A simple lattice model is analyzed, using ideas and techniques from the theory of correlated electrons in metals. Reasonable parameters reproduce observed magnitudes and temperature dependence of the hydrophobic interaction between substitutional impurities and water within this lattice.Comment: 7 pages, 3 figures. To appear in Europhysics Letter

Addition-Deletion Networks

We study structural properties of growing networks where both addition and deletion of nodes are possible. Our model network evolves via two independent processes. With rate r, a node is added to the system and this node links to a randomly selected existing node. With rate 1, a randomly selected node is deleted, and its parent node inherits the links of its immediate descendants. We show that the in-component size distribution decays algebraically, c_k ~ k^{-beta}, as k-->infty. The exponent beta=2+1/(r-1) varies continuously with the addition rate r. Structural properties of the network including the height distribution, the diameter of the network, the average distance between two nodes, and the fraction of dangling nodes are also obtained analytically. Interestingly, the deletion process leads to a giant hub, a single node with a macroscopic degree whereas all other nodes have a microscopic degree.Comment: 8 pages, 5 figure

Random Geometric Series

Integer sequences where each element is determined by a previous randomly chosen element are investigated analytically. In particular, the random geometric series x_n=2x_p with 0<=p<=n-1 is studied. At large n, the moments grow algebraically, n^beta(s) with beta(s)=2^s-1, while the typical behavior is x_n n^ln 2. The probability distribution is obtained explicitly in terms of the Stirling numbers of the first kind and it approaches a log-normal distribution asymptotically.Comment: 6 pages, 2 figure

Discrete Analog of the Burgers Equation

We propose the set of coupled ordinary differential equations dn_j/dt=(n_{j-1})^2-(n_j)^2 as a discrete analog of the classic Burgers equation. We focus on traveling waves and triangular waves, and find that these special solutions of the discrete system capture major features of their continuous counterpart. In particular, the propagation velocity of a traveling wave and the shape of a triangular wave match the continuous behavior. However, there are some subtle differences. For traveling waves, the propagating front can be extremely sharp as it exhibits double exponential decay. For triangular waves, there is an unexpected logarithmic shift in the location of the front. We establish these results using asymptotic analysis, heuristic arguments, and direct numerical integration.Comment: 6 pages, 5 figure