Spatial Mixing of Coloring Random Graphs

We study the strong spatial mixing (decay of correlation) property of proper $q$-colorings of random graph $G(n, d/n)$ with a fixed $d$. The strong spatial mixing of coloring and related models have been extensively studied on graphs with bounded maximum degree. However, for typical classes of graphs with bounded average degree, such as $G(n, d/n)$, an easy counterexample shows that colorings do not exhibit strong spatial mixing with high probability. Nevertheless, we show that for $q\ge\alpha d+\beta$ with $\alpha>2$ and sufficiently large $\beta=O(1)$, with high probability proper $q$-colorings of random graph $G(n, d/n)$ exhibit strong spatial mixing with respect to an arbitrarily fixed vertex. This is the first strong spatial mixing result for colorings of graphs with unbounded maximum degree. Our analysis of strong spatial mixing establishes a block-wise correlation decay instead of the standard point-wise decay, which may be of interest by itself, especially for graphs with unbounded degree

Two-subband system in quantizing magnetic field: Probing many-body gap by non-equilibrium phonons

We study the many-body effects in a two-subband quasi-two-dimensional electron system in a quantizing magnetic field at filling factor three. A manifestation of these effects in the phonon absorption spectroscopy is discussed. The electron system is mapped onto a two-level system with the separation between levels determined by the intersubband splitting and the cyclotron energy. The electron-electron interaction enhances the excitation gap, which exists at all values of the interlevel splitting. This results in a single-peak structure of the phonon absorption rate as a function of magnetic field, instead of the double-peak structure for non-interacting electrons.Comment: 9 pages, 3 figure

Content-Based Image Retrieval of Skin Lesions by Evolutionary Feature Synthesis

Abstract. This paper gives an example of evolved features that improve image retrieval performance. A content-based image retrieval system for skin lesion images is presented. The aim is to support decision making by retrieving and displaying relevant past cases visually similar to the one under examination. Skin lesions of five common classes, including two non-melanoma cancer types, are used. Colour and texture features are extracted from lesions. Evolutionary algorithms are used to create composite features that optimise a similarity matching function. Experiments on our database of 533 images are performed and results are compared to those obtained using simple features. The use of the evolved composite features improves the precision by about 7%.

Quantum railroads and directed localization at the juncture of quantum Hall systems

The integer quantum Hall effect (QHE) and one-dimensional Anderson localization (AL) are limiting special cases of a more general phenomenon, directed localization (DL), predicted to occur in disordered one-dimensional wave guides called "quantum railroads" (QRR). Here we explain the surprising results of recent measurements by Kang et al. [Nature 403, 59 (2000)] of electron transfer between edges of two-dimensional electron systems and identify experimental evidence of QRR's in the general, but until now entirely theoretical, DL regime that unifies the QHE and AL. We propose direct experimental tests of our theory.Comment: 11 pages revtex + 3 jpeg figures, to appear in Phys. Rev.

Squark-, Slepton- and Neutralino-Chargino coannihilation effects in the low-energy effective MSSM

Within the low-energy effective Minimal Supersymmetric extension of the Standard Model (effMSSM) we calculate the neutralino relic density taking into account slepton-neutralino, squark-neutralino and neutralino/chargino- neutralino coannihilation channels. By including squark (stop and sbottom) coannihilation channels we extend our comparative study to all allowed coannihilations and obtain the general result that all of them give sizable contributions to the reduction of the neutralino relic density. Due to these coannihilation processes some models (mostly with large neutralino masses) enter into the cosmologically interesting region for relic density, but other models leave this region. Nevertheless, in general, the predictions for direct and indirect dark matter detection rates are not strongly affected by these coannihilation channels in the effMSSM.Comment: 14 pages, 10 figures, corrected and to be published in Phys. Rev.

Cold Dark Matter detection in SUSY models at large tan(beta)

We study the direct detection rate for SUSY cold dark matter (CDM) predicted by the minimal supersymmetric standard model with universal boundary conditions and large values for tan(beta). The relic abundance of the lightest supersymmetric particle (LSP), assumed to be approximately a bino, is obtained by including its coannihilations with the next-to-lightest supersymmetric particle (NLSP), which is the lightest s-tau. The cosmological constraint on this quantity severely limits the allowed SUSY parameter space, especially in the case the CP-even Higgs has mass of around 114 GeV. We find that for large tan(beta) it is possible to find a subsection of the allowed parameter space, which yields detectable rates in the currently planned experiments.Comment: Changes in text and figure

Talk the talk, walk the walk: Defining Critical Race Theory in research

Over the last decade there has been a noticeable growth in published works citing Critical Race Theory (CRT). This has led to a growth in interest in the UK of practical research projects utilising CRT as their framework. It is clear that research on 'race' is an emerging topic of study. What is less visible is a debate on how CRT is positioned in relation to methodic practice, substantive theory and epistemological underpinnings. The efficacy of categories of data gathering tools, both traditional and non-traditional is a discussion point here to explore the complexities underpinning decisions to advocate a CRT framework. Notwithstanding intersectional issues, a CRT methodology is recognisable by how philosophical, political and ethical questions are established and maintained in relation to racialised problematics. This paper examines these tensions in establishing CRT methodologies and explores some of the essential criteria for researchers to consider in utilising a CRT framework. © 2012 Copyright Taylor and Francis Group, LLC

Slepton and Neutralino/Chargino Coannihilations in MSSM

Within the low-energy effective Minimal Supersymmetric extension of Standard Model (effMSSM) we calculated the neutralino relic density taking into account slepton-neutralino and neutralino-chargino/neutralino coannihilation channels. We performed comparative study of these channels and obtained that both of them give sizable contributions to the reduction of the relic density. Due to these coannihilation processes some models (mostly with large neutralino masses) enter into the cosmologically interesting region for relic density, but other models leave this region. Nevertheless, in general, the predictions for direct and indirect dark matter detection rates are not strongly affected by these coannihilation channels in the effMSSM.Comment: 12 pages, 9 figures, revte

What if Supersymmetry Breaking Unifies beyond the GUT Scale?

We study models in which soft supersymmetry-breaking parameters of the MSSM become universal at some unification scale, $M_{in}$, above the GUT scale, \mgut. We assume that the scalar masses and gaugino masses have common values, $m_0$ and $m_{1/2}$ respectively, at $M_{in}$. We use the renormalization-group equations of the minimal supersymmetric SU(5) GUT to evaluate their evolutions down to \mgut, studying their dependences on the unknown parameters of the SU(5) superpotential. After displaying some generic examples of the evolutions of the soft supersymmetry-breaking parameters, we discuss the effects on physical sparticle masses in some specific examples. We note, for example, that near-degeneracy between the lightest neutralino and the lighter stau is progressively disfavoured as $M_{in}$ increases. This has the consequence, as we show in $(m_{1/2}, m_0)$ planes for several different values of $\tan \beta$, that the stau coannihilation region shrinks as $M_{in}$ increases, and we delineate the regions of the $(M_{in}, \tan \beta)$ plane where it is absent altogether. Moreover, as $M_{in}$ increases, the focus-point region recedes to larger values of $m_0$ for any fixed $\tan \beta$ and $m_{1/2}$. We conclude that the regions of the $(m_{1/2}, m_0)$ plane that are commonly favoured in phenomenological analyses tend to disappear at large $M_{in}$.Comment: 24 pages with 11 eps figures; references added, some figures corrected, discussion extended and figure added; version to appear in EPJ