Graph Compression with Side Information at the Decoder

In this paper, we study the problem of graph compression with side information at the decoder. The focus is on the situation when an unlabelled graph (which is also referred to as a structure) is to be compressed or is available as side information. For correlated Erd\H{o}s-R\'enyi weighted random graphs, we give a precise characterization of the smallest rate at which a labelled graph or its structure can be compressed with aid of a correlated labelled graph or its structure at the decoder. We approach this problem by using the entropy-spectrum framework and establish some convergence results for conditional distributions involving structures, which play a key role in the construction of an optimal encoding and decoding scheme. Our proof essentially uses the fact that, in the considered correlated Erd\H{o}s-R\'enyi model, the structure retains most of the information about the labelled graph. Furthermore, we consider the case of unweighted graphs and present how the optimal decoding can be done using the notion of graph alignment.Comment: 21 pages, 2 figures, submitted to the IEEE Journal on Selected Areas in Information Theor

Patterning of the Drosophila retina by the morphogenetic furrow

Pattern formation is the process by which cells within a homogeneous epithelial sheet acquire distinctive fates depending upon their relative spatial position to each other. Several proposals, starting with Alan Turing’s diffusion-reaction model, have been put forth over the last 70 years to describe how periodic patterns like those of vertebrate somites and skin hairs, mammalian molars, fish scales, and avian feather buds emerge during development. One of the best experimental systems for testing said models and identifying the gene regulatory networks that control pattern formation is the compound eye of the fruit fly, Drosophila melanogaster. Its cellular morphogenesis has been extensively studied for more than a century and hundreds of mutants that affect its development have been isolated. In this review we will focus on the morphogenetic furrow, a wave of differentiation that takes an initially homogeneous sheet of cells and converts it into an ordered array of unit eyes or ommatidia. Since the discovery of the furrow in 1976, positive and negative acting morphogens have been thought to be solely responsible for propagating the movement of the furrow across a motionless field of cells. However, a recent study has challenged this model and instead proposed that mechanical driven cell flow also contributes to retinal pattern formation. We will discuss both models and their impact on patterning

Rate-distortion function of the stochastic block model

The stochastic block model (SBM) is extensively used to model networks in which users belong to certain communities. In recent years, the study of information-theoretic compression of such networks has gained attention, with works primarily focusing on lossless compression. In this work, we address the lossy compression of SBM graphs by characterizing the rate-distortion function under a Hamming distortion constraint. Specifically, we derive the conditional rate-distortion function of the SBM with community membership as side information to both the encoder and decoder. We approach this problem as the classical Wyner-Ziv lossy problem by minimising mutual information of the graph and its reconstruction conditioned on community labels. Lastly, we also derive the rate-distortion function of the Erdὄs-Rényl (ER) random graph model

Effects of Oxygen Partial Pressure on the Surface Tension of Liquid Nickel

The NASA Marshall Space Flight Center's electrostatic levitation (ESL) laboratory has been recently upgraded with an oxygen partial pressure controller. This system allows the oxygen partial pressure within the vacuum chamber to be measured and controlled, theoretically in the range from 1036 to 100 bar. The oxygen control system installed in the ESL laboratory's main chamber consists of an oxygen sensor, oxygen pump, and a control unit. The sensor is a potentiometric device that determines the difference in oxygen activity in two gas compartments (inside the chamber and the air outside of the chamber) separated by an electrolyte, which is yttriastabilized zirconia. The pump utilizes coulometric titration to either add or remove oxygen. The system is controlled by a desktop control unit, which can also be accessed via a computer. The controller performs temperature control for the sensor and pump, PID-based current loop, and a control algorithm. Oxygen partial pressure has been shown to play a significant role in the surface tension of liquid metals. Oxide films or dissolved oxygen may lead to significant changes in surface tension. The effects of oxygen partial pressure on the surface tension of undercooled liquid nickel will be analyzed, and the results will be presented. The surface tension will be measured at several different oxygen partial pressures while the sample is undercooled. Surface tension will be measured using the oscillating drop method. While undercooled, each sample will be oscillated several times consecutively to investigate how the surface tension behaves with time while at a particular oxygen partial pressure

X-ray study of structural domains in the near-surface region of SrTiO₃ substrates with Y_0.6Pr_0.4Ba₂Cu₃O₇/La_2/3Ca_1/3MnO₃ superlattices grown on top

We investigated with synchrotron x-ray diffraction and reflectometry the formation of structural domains in the near-surface region of single crystalline SrTiO₃ (001) substrates with Y0.6Pr0.4Ba₂Cu₃O₇/La2/3Ca1/3MnO₃ superlattices grown on top. We find that the antiferrodistortive cubic to tetragonal transition, which occurs at TSTO=104  K in the bulk and at a considerably higher temperature of at least 120 K in the surface region of SrTiO₃, has only a weak influence on the domain formation. The strongest changes occur instead in the vicinity of the tetragonal to orthorhombic transition in SrTiO₃ around 65 K where pronounced surface facets develop that reach deep (at least several micrometers) into the SrTiO₃ substrate. These micrometer-sized facets are anisotropic and tilted with respect to one another by up to 0.5° along the shorter direction. Finally, we find that a third structural transition below 30 K gives rise to significant changes in the spread of the c-axis parameters. Overall, our data provide evidence for a strong mutual interaction between the structural properties of the SrTiO₃ surface and the multilayer grown on top

Stride-level analysis of mouse open field behavior using deep-learning-based pose estimation.

Gait and posture are often perturbed in many neurological, neuromuscular, and neuropsychiatric conditions. Rodents provide a tractable model for elucidating disease mechanisms and interventions. Here, we develop a neural-network-based assay that adopts the commonly used open field apparatus for mouse gait and posture analysis. We quantitate both with high precision across 62 strains of mice. We characterize four mutants with known gait deficits and demonstrate that multiple autism spectrum disorder (ASD) models show gait and posture deficits, implying this is a general feature of ASD. Mouse gait and posture measures are highly heritable and fall into three distinct classes. We conduct a genome-wide association study to define the genetic architecture of stride-level mouse movement in the open field. We provide a method for gait and posture extraction from the open field and one of the largest laboratory mouse gait and posture data resources for the research community

Adsorption transition of a self-avoiding polymer chain onto a rigid rod

The subject of this work is the adsorption transition of a long flexible self-avoiding polymer chain onto a rigid thin rod. The rod is represented by a cylinder of radius R with a short-ranged attractive surface potential for the chain monomers. General scaling results are obtained by using renormalization group arguments in conjunction with available results for quantum field theories with curved boundaries [McAvity and Osborn 1993 Nucl. Phys. B 394, 728]. Relevant critical exponents are identified and estimated using geometric arguments.Comment: 19 pages, 4 figures. To appear in: J. Phys.: Condens. Matter, special issue dedicated to Lothar Schaefer on the occasion of his 60th birthda

Critical specific heats of the N-vector spin models on the sc and the bcc lattices

We have computed through order $\beta^{21}$ the high-temperature expansions for the nearest-neighbor spin correlation function $G(N,\beta)$ of the classical N-vector model, with general N, on the simple-cubic and on the body-centered-cubic lattices. For this model, also known in quantum field theory as the lattice O(N) nonlinear sigma model, we have presented in previous papers extended expansions of the susceptibility, of its second field derivative and of the second moment of the correlation function. Here we study the internal specific energy and the specific heat $C(N,\beta)$, obtaining new estimates of the critical parameters and therefore a more accurate direct test of the hyperscaling relation $d \nu(N)=2 - \alpha(N)$ on a range of values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the classical Heisenberg model]. By the newly extended series, we also compute the universal combination of critical amplitudes usually denoted by $R^+_{\xi}(N)$, in fair agreement with renormalization group estimates.Comment: 15 pages, latex, no figure

Critical fluctuations and breakdown of Stokes-Einstein relation in the Mode-Coupling Theory of glasses

We argue that the critical dynamical fluctuations predicted by the mode-coupling theory (MCT) of glasses provide a natural mechanism to explain the breakdown of the Stokes-Einstein relation. This breakdown, observed numerically and experimentally in a region where MCT should hold, is one of the major difficulty of the theory, for which we propose a natural resolution based on the recent interpretation of the MCT transition as a bona fide critical point with a diverging length scale. We also show that the upper critical dimension of MCT is d_c=8.Comment: Proceedings of the workshop on non-equilibrium phenomena in supercooled fluids, glasses and amorphous materials (17-22 September, 2006, Pisa