Via Hexagons to Squares in Ferrofluids: Experiments on Hysteretic Surface Transformations under Variation of the Normal Magnetic Field

We report on different surface patterns on magnetic liquids following the Rosensweig instability. We compare the bifurcation from the flat surface to a hexagonal array of spikes with the transition to squares at higher fields. From a radioscopic mapping of the surface topography we extract amplitudes and wavelengths. For the hexagon--square transition, which is complex because of coexisting domains, we tailor a set of order parameters like peak--to--peak distance, circularity, angular correlation function and pattern specific amplitudes from Fourier space. These measures enable us to quantify the smooth hysteretic transition. Voronoi diagrams indicate a pinning of the domains. Thus the smoothness of the transition is roughness on a small scale.Comment: 17 pages, 14 figure

Optimal CDMA signatures: a finite-step approach

A description of optimal sequences for direct-sequence code division multiple access is a byproduct of recent characterizations of the sum capacity. The paper restates the sequence design problem as an inverse singular value problem and shows that it can be solved with finite-step algorithms from matrix analysis. Relevant algorithms are reviewed and a new one-sided construction is proposed that obtains the sequences directly instead of computing the Gram matrix of the optimal signatures

Finite-step algorithms for constructing optimal CDMA signature sequences

A description of optimal sequences for direct-spread code-division multiple access (DS-CDMA) is a byproduct of recent characterizations of the sum capacity. This paper restates the sequence design problem as an inverse singular value problem and shows that the problem can be solved with finite-step algorithms from matrix theory. It proposes a new one-sided algorithm that is numerically stable and faster than previous methods

Dual description of the superconducting phase transition

The dual approach to the Ginzburg-Landau theory of a Bardeen-Cooper-Schrieffer superconductor is reviewed. The dual theory describes a grand canonical ensemble of fluctuating closed magnetic vortices, of arbitrary length and shape, which interact with a massive vector field representing the local magnetic induction. When the critical temperature is approached from below, the magnetic vortices proliferate. This is signaled by the disorder field, which describes the loop gas, developing a non-zero expectation value in the normal conducting phase. It thereby breaks a {\it global} U(1) symmetry. The ensuing Goldstone field is the magnetic scalar potential. The superconducting-to-normal phase transition is studied by applying renormalization group theory to the dual formulation. In the regime of a second-order transition, the critical exponents are given by those of a superfluid with a reversed temperature axis.Comment: Latex + Postscript file

Translation-invariance of two-dimensional Gibbsian point processes

The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with two-body interaction, where the interesting cases of singular, hard-core and discontinuous interaction are included. We start with the special case of pure hard core repulsion in order to show how to treat hard cores in general.Comment: 44 pages, 6 figure

Genomics analysis on the responses of E. coli cells to varying environmental conditions

The natural living environments of E. coli cells are diverse, varying from mammalian gastrointestinal tracts and soil. Each environment might require distinct metabolic pathways and transporter systems, and long-term evolution has established elaborate regulatory system for E. coli cells to quickly adapt to the changing conditions. Sensing outside stresses and then adopting a different phenotype enable them to take advantage of any possible nutrients and defend against hostile environment. A lot of regulatory mechanisms have been identified by genetic, biochemical and molecular biology methods, and our study aim to build a systematic view on the response of the whole genome to four different environmental conditions. We used statistical tests including Pearson’s tests and Spearman’s tests and multiple testing adjustments to identify feature genes that are induced or repressed significantly across treatment levels. The feature genes identified were partially supported by previous literatures, and some of the novel genes not found in any previous studies may infer a potential research blind spot. Additionally, we compared the correlation tests to the implementation of machine learning algorithms, and discussed the advantage and drawbacks of each method.Statistic

Probability around the Quantum Gravity. Part 1: Pure Planar Gravity

In this paper we study stochastic dynamics which leaves quantum gravity equilibrium distribution invariant. We start theoretical study of this dynamics (earlier it was only used for Monte-Carlo simulation). Main new results concern the existence and properties of local correlation functions in the thermodynamic limit. The study of dynamics constitutes a third part of the series of papers where more general class of processes were studied (but it is self-contained), those processes have some universal significance in probability and they cover most concrete processes, also they have many examples in computer science and biology. At the same time the paper can serve an introduction to quantum gravity for a probabilist: we give a rigorous exposition of quantum gravity in the planar pure gravity case. Mostly we use combinatorial techniques, instead of more popular in physics random matrix models, the central point is the famous $\alpha =-7/2$ exponent.Comment: 40 pages, 11 figure