Survival probability (heat content) and the lowest eigenvalue of Dirichlet Laplacian

We study the survival probability of a particle diffusing in a two-dimensional domain, bounded by a smooth absorbing boundary. The short-time expansion of this quantity depends on the geometric characteristics of the boundary, whilst its long-time asymptotics is governed by the lowest eigenvalue of the Dirichlet Laplacian defined on the domain. We present a simple algorithm for calculation of the short-time expansion for an arbitrary "star-shaped" domain. The coefficients are expressed in terms of powers of boundary curvature, integrated around the circumference of the domain. Based on this expansion, we look for a Pad\'e interpolation between the short-time and the long-time behavior of the survival probability, i.e. between geometric characteristics of the boundary and the lowest eigenvalue of the Dirichlet Laplacian.Comment: Accepted in IJMP

Changes in the secretory profile of NSCLC-associated fibroblasts after ablative radiotherapy: potential impact on angiogenesis and tumor growth

In the context of radiotherapy, collateral effects of ablative ionizing radiation (AIR) on stromal components of tumors remains understudied. In this work, cancer-associated fibroblasts (CAFs) isolated from freshly resected human lung tumors were exposed to AIR (1x18Gy) and analyzed for their release of paracrine factors. Inflammatory mediators and regulators of angiogenesis and tumor growth were analyzed by multiplex protein assays in conditioned medium (CM) from irradiated and non-irradiated CAFs. Additionally, the profile of secreted proteins was examined by proteomics. In functional assays, effects of CAF-CM on proliferative and migratory capacity of lung tumor cells (H-520/H-522) and endothelial cells (HUVECs), and on the tube-forming capacity of endothelial cells was assessed. Our data show that exposure of CAFs to ablative doses of ionizing radiation results in a) down-regulated release of angiogenic factors SDF-1, angiopoietin and thrombospondin-2; b) up-regulated release of growth factor bFGF from most donors, and c) unaffected expression-levels of HGF and inflammatory mediators IL-6, IL-8, IL-1ƒÒ and TNF-£. Conditioned medium from irradiated and control CAFs did not affect differently the proliferative or migratory capacity of tumor cells (H-520/H-522), whereas migratory capacity of endothelial HUVEC cells was partially reduced in the presence of irradiated CAF conditioned medium. Overall we conclude that AIR mediates a transformation on the secretory profile of CAFs that could influence the behavior of other cells in the tumor tissue and hence guide to some extent therapeutic outcomes. The downstream consequences of the changes observed in this study merits further investigations

Gain control in molecular information processing: Lessons from neuroscience

Statistical properties of environments experienced by biological signaling systems in the real world change, which necessitate adaptive responses to achieve high fidelity information transmission. One form of such adaptive response is gain control. Here we argue that a certain simple mechanism of gain control, understood well in the context of systems neuroscience, also works for molecular signaling. The mechanism allows to transmit more than one bit (on or off) of information about the signal independently of the signal variance. It does not require additional molecular circuitry beyond that already present in many molecular systems, and, in particular, it does not depend on existence of feedback loops. The mechanism provides a potential explanation for abundance of ultrasensitive response curves in biological regulatory networks.Comment: 10 pages, 5 figure

Entropy-based analysis of the number partitioning problem

In this paper we apply the multicanonical method of statistical physics on the number-partitioning problem (NPP). This problem is a basic NP-hard problem from computer science, and can be formulated as a spin-glass problem. We compute the spectral degeneracy, which gives us information about the number of solutions for a given cost $E$ and cardinality $m$. We also study an extension of this problem for $Q$ partitions. We show that a fundamental difference on the spectral degeneracy of the generalized ($Q>2$) NPP exists, which could explain why it is so difficult to find good solutions for this case. The information obtained with the multicanonical method can be very useful on the construction of new algorithms.Comment: 6 pages, 4 figure

Theory of the striped superconductor

We define a distinct phase of matter, a "pair density wave" (PDW), in which the superconducting order parameter $\phi$ varies periodically as a function of position such that when averaged over the center of mass position, all components of $\phi$ vanish identically. Specifically, we study the simplest, unidirectional PDW, the "striped superconductor," which we argue may be at the heart of a number of spectacular experimental anomalies that have been observed in the failed high temperature superconductor, La$_{2-x}$ Ba$_x$CuO$_4$. We present a solvable microscopic model with strong electron-electron interactions which supports a PDW groundstate. We also discuss, at the level of Landau theory, the nature of the coupling between the PDW and other order parameters, and the origins and some consequences of the unusual sensitivity of this state to quenched disorder.Comment: 16 pages, 3 figures, 1 table; Journal ref. adde

High orders of Weyl series for the heat content

This article concerns the Weyl series of spectral functions associated with the Dirichlet Laplacian in a $d$-dimensional domain with a smooth boundary. In the case of the heat kernel, Berry and Howls predicted the asymptotic form of the Weyl series characterized by a set of parameters. Here, we concentrate on another spectral function, the (normalized) heat content. We show on several exactly solvable examples that, for even $d$, the same asymptotic formula is valid with different values of the parameters. The considered domains are $d$-dimensional balls and two limiting cases of the elliptic domain with eccentricity $\epsilon$: A slightly deformed disk ($\epsilon\to 0$) and an extremely prolonged ellipse ($\epsilon\to 1$). These cases include 2D domains with circular symmetry and those with only one shortest periodic orbit for the classical billiard. We analyse also the heat content for the balls in odd dimensions $d$ for which the asymptotic form of the Weyl series changes significantly.Comment: 20 pages, 1 figur

Grundstate Properties of the 3D Ising Spin Glass

We study zero--temperature properties of the 3d Edwards--Anderson Ising spin glass on finite lattices up to size $12^3$. Using multicanonical sampling we generate large numbers of groundstate configurations in thermal equilibrium. Finite size scaling with a zero--temperature scaling exponent $y = 0.74 \pm 0.12$ describes the data well. Alternatively, a descriptions in terms of Parisi mean field behaviour is still possible. The two scenarios give significantly different predictions on lattices of size $\ge 12^3$.Comment: LATEX 9pages,figures upon request ,SCRI-9

Phase Structure of Z(3)-Polyakov-Loop Models

We study effective lattice actions describing the Polyakov loop dynamics originating from finite-temperature Yang-Mills theory. Starting with a strong-coupling expansion the effective action is obtained as a series of Z(3)-invariant operators involving higher and higher powers of the Polyakov loop, each with its own coupling. Truncating to a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both approaches concerning the phase structure of the theories. The phase diagram exhibits both first and second order transitions between symmetric, ferromagnetic and anti-ferromagnetic phases with phase boundaries merging at three tricritical points. The critical exponents nu and gamma at the continuous transition between symmetric and anti-ferromagnetic phases are the same as for the 3-state Potts model.Comment: 20 pages, 22 figure

Effects of thermal fluctuation and the receptor-receptor interaction in bacterial chemotactic signalling and adaptation

Bacterial chemotaxis is controlled by the conformational changes of the receptors, in response to the change of the ambient chemical concentration. In a statistical mechanical approach, the signalling due to the conformational changes is a thermodynamic average quantity, dependent on the temperature and the total energy of the system, including both ligand-receptor interaction and receptor-receptor interaction. This physical theory suggests to biology a new understanding of cooperation in ligand binding and receptor signalling problems. How much experimental support of this approach can be obtained from the currently available data? What are the parameter values? What is the practical information for experiments? Here we make comparisons between the theory and recent experimental results. Although currently comparisons can only be semi-quantitative or qualitative, consistency is clearly shown. The theory also helps to sort a variety of data.Comment: 26 pages, revtex. Journal version. Analysis on another set of data on adaptation time is adde