Minimum Entropy Orientations

We study graph orientations that minimize the entropy of the in-degree sequence. The problem of finding such an orientation is an interesting special case of the minimum entropy set cover problem previously studied by Halperin and Karp [Theoret. Comput. Sci., 2005] and by the current authors [Algorithmica, to appear]. We prove that the minimum entropy orientation problem is NP-hard even if the graph is planar, and that there exists a simple linear-time algorithm that returns an approximate solution with an additive error guarantee of 1 bit. This improves on the only previously known algorithm which has an additive error guarantee of log_2 e bits (approx. 1.4427 bits).Comment: Referees' comments incorporate

Entropy-driven phase transition in a system of long rods on a square lattice

The isotropic-nematic (I-N) phase transition in a system of long straight rigid rods of length k on square lattices is studied by combining Monte Carlo simulations and theoretical analysis. The process is analyzed by comparing the configurational entropy of the system with the corresponding to a fully aligned system, whose calculation reduces to the 1D case. The results obtained (1) allow to estimate the minimum value of k which leads to the formation of a nematic phase and provide an interesting interpretation of this critical value; (2) provide numerical evidence on the existence of a second phase transition (from a nematic to a non-nematic state) occurring at density close to 1 and (3) allow to test the predictions of the main theoretical models developed to treat the polymers adsorption problem.Comment: 14 pages, 6 figures. Accepted for publication in JSTA

Critical behavior of long straight rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

The critical behavior of long straight rigid rods of length $k$ ($k$-mers) on square and triangular lattices at intermediate density has been studied. A nematic phase, characterized by a big domain of parallel $k$-mers, was found. This ordered phase is separated from the isotropic state by a continuous transition occurring at a intermediate density $\theta_c$. Two analytical techniques were combined with Monte Carlo simulations to predict the dependence of $\theta_c$ on $k$, being $\theta_c(k) \propto k^{-1}$. The first involves simple geometrical arguments, while the second is based on entropy considerations. Our analysis allowed us also to determine the minimum value of $k$ ($k_{min}=7$), which allows the formation of a nematic phase on a triangular lattice.Comment: 23 pages, 5 figures, to appear in The Journal of Chemical Physic

Electronic and Magnetic Properties of Electron-doped Superconductor, Sm_{1.85}Ce_{0.15}CuO_{4-delta}

Temperature-dependent magnetization (M(T)) and specific heat (C_p(T)) measurements were carried out on single crystal Sm_{1.85}Ce_{0.15}CuO_{4-delta} (T_c = 16.5 K). The magnetic anisotropy in the static susceptibility, chi {equiv} M/H, is apparent not only in its magnitude but also in its temperature dependence, with chi_{perp} for H{perp}c larger than chi_{parallel} for H{parallel}c. For both field orientations, chi does not follow the Curie-Weiss behavior due to the small energy gap of the J = 7/2 multiplet above the J = 5/2 ground-state multiplet. However, with increasing temperature, chi_{parallel}(T) exhibits a broad minimum near 100 K and then a slow increase while chi_{perp}(T) shows a monotonic decrease. A sharp peak in C_p(T) at 4.7 K manifests an antiferromagnetic ordering. The electronic contribution, gamma, to C_p(T) is estimated to be gamma = 103.2 (7) mJ/moleSmK^2. The entropy associated with the magnetic ordering is much smaller than Rln2, where R is the gas constant, which is usually expected for the doublet ground state of Sm^{+3}. The unusual magnetic and electronic properties evident in M(T) and C_p(T) are probably due to a strong anisotropic interaction between conduction electrons and localized electrons at Sm^{+3} sites.Comment: 5 pages, 5 encapsulated postscript figures, late

Triangular Trimers on the Triangular Lattice: an Exact Solution

A model is presented consisting of triangular trimers on the triangular lattice. In analogy to the dimer problem, these particles cover the lattice completely without overlap. The model has a honeycomb structure of hexagonal cells separated by rigid domain walls. The transfer matrix can be diagonalised by a Bethe Ansatz with two types of particles. This leads two an exact expression for the entropy on a two-dimensional subset of the parameter space.Comment: 4 pages, REVTeX, 5 EPS figure

On the positional and orientational order of water and methanol around indole: a study on the microscopic origin of solubility

Although they are both highly polar liquids, there are a number of compounds, such as many pharmaceuticals, which show vastly different solubilities in methanol compared with water. From theories of the hydrophobic effect, it might be predicted that this enhanced solubility is due to association between drugs and the less polar -CH3 groups on methanol. In this work, detailed analysis on the atomic structural interactions between water, methanol and the small molecule indole – which is a precursor to many drugs and is sparingly soluble in water yet highly soluble in methanol – reveal that indole preferentially interacts with both water and methanol via electrostatic interactions rather than with direction interactions to the –CH3 groups. The presence of methanol hydrogen bonds with p electrons of the benzene ring of indole can explain the increase in solubility of indole in methanol relative to water. In addition, the excess entropy calculations performed here suggest that this solvation is enthalpically rather than entropically driven.Postprint (author's final draft

The Nature of the Chemical Process. 1. Symmetry Evolution - Revised Information Theory, Similarity Principle and Ugly Symmetry

Three laws of information theory have been proposed. Labeling by introducing nonsymmetry and formatting by introducing symmetry are defined. The function L (L=lnw, w is the number of microstates, or the sum of entropy and information, L=S+I) of the universe is a constant (the first law of information theory). The entropy S of the universe tends toward a maximum (the second law law of information theory). For a perfect symmetric static structure, the information is zero and the static entropy is the maximum (the third law law of information theory). Based on the Gibbs inequality and the second law of the revised information theory we have proved the similarity principle (a continuous higher similarity-higher entropy relation after the rejection of the Gibbs paradox) and proved the Curie-Rosen symmetry principle (a higher symmetry-higher stability relation) as a special case of the similarity principle. Some examples in chemical physics have been given. Spontaneous processes of all kinds of molecular interaction, phase separation and phase transition, including symmetry breaking and the densest molecular packing and crystallization, are all driven by information minimization or symmetry maximization. The evolution of the universe in general and evolution of life in particular can be quantitatively considered as a series of symmetry breaking processes. The two empirical rules - similarity rule and complementarity rule - have been given a theoretical foundation. All kinds of periodicity in space and time are symmetries and contribute to the stability. Symmetry is beautiful because it renders stability. However, symmetry is in principle ugly because it is associated with information loss.Comment: 29 pages, 14 figure

Two-dimensional lattice-fluid model with water-like anomalies

We investigate a lattice-fluid model defined on a two-dimensional triangular lattice, with the aim of reproducing qualitatively some anomalous properties of water. Model molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three bonding arms. Bond formation depends both on orientation and local density. We work out phase diagrams, response functions, and stability limits for the liquid phase, making use of a generalized first order approximation on a triangle cluster, whose accuracy is verified, in some cases, by Monte Carlo simulations. The phase diagram displays one ordered (solid) phase which is less dense than the liquid one. At fixed pressure the liquid phase response functions show the typical anomalous behavior observed in liquid water, while, in the supercooled region, a reentrant spinodal is observed.Comment: 9 pages, 1 table, 7 figure

Modeling a Sensor to Improve its Efficacy

Robots rely on sensors to provide them with information about their surroundings. However, high-quality sensors can be extremely expensive and cost-prohibitive. Thus many robotic systems must make due with lower-quality sensors. Here we demonstrate via a case study how modeling a sensor can improve its efficacy when employed within a Bayesian inferential framework. As a test bed we employ a robotic arm that is designed to autonomously take its own measurements using an inexpensive LEGO light sensor to estimate the position and radius of a white circle on a black field. The light sensor integrates the light arriving from a spatially distributed region within its field of view weighted by its Spatial Sensitivity Function (SSF). We demonstrate that by incorporating an accurate model of the light sensor SSF into the likelihood function of a Bayesian inference engine, an autonomous system can make improved inferences about its surroundings. The method presented here is data-based, fairly general, and made with plug-and play in mind so that it could be implemented in similar problems.Comment: 18 pages, 8 figures, submitted to the special issue of "Sensors for Robotics