Solution of the Percus-Yevick equation for hard discs

We solve the Percus-Yevick equation in two dimensions by reducing it to a set of simple integral equations. We numerically obtain both the pair correlation function and the equation of state for a hard disc fluid and find good agreement with available Monte-Carlo calculations. The present method of resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure

The spectrum of large powers of the Laplacian in bounded domains

We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a useful numerical approach valid for any N. Finally, we discuss implications of this work and present its possible extensions for non integer N and for 3D Laplacian problems.Comment: 13 pages, 2 figure

Nonlinear field theories during homogeneous spatial dilation

The effect of a uniform dilation of space on stochastically driven nonlinear field theories is examined. This theoretical question serves as a model problem for examining the properties of nonlinear field theories embedded in expanding Euclidean Friedmann-Lema\^{\i}tre-Robertson-Walker metrics in the context of cosmology, as well as different systems in the disciplines of statistical mechanics and condensed matter physics. Field theories are characterized by the speed at which they propagate correlations within themselves. We show that for linear field theories correlations stop propagating if and only if the speed at which the space dilates is higher than the speed at which correlations propagate. The situation is in general different for nonlinear field theories. In this case correlations might stop propagating even if the velocity at which space dilates is lower than the velocity at which correlations propagate. In particular, these results imply that it is not possible to characterize the dynamics of a nonlinear field theory during homogeneous spatial dilation {\it a priori}. We illustrate our findings with the nonlinear Kardar-Parisi-Zhang equation

Void Formation and Roughening in Slow Fracture

Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Post mortem analysis of the resulting fracture surfaces of ductile and brittle materials on the $\mu$m-mm and the nm scales respectively, reveals self-affine cracks with anomalous scaling exponent $\zeta\approx 0.8$ in 3-dimensions and $\zeta\approx 0.65$ in 2-dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation and the fracture growth, culminating in estimates of the roughening exponents in 2-dimensions. In the simplest realization of the model we allow one void ahead of the crack, and address the robustness of the roughening exponent. Next we develop the theory further, to include two voids ahead of the crack. This development necessitates generalizing the method of iterated conformal maps to include doubly connected regions (maps from the annulus rather than the unit circle). While mathematically and numerically feasible, we find that the employment of the stress field as computed from elasticity theory becomes questionable when more than one void is explicitly inserted into the material. Thus further progress in this line of research calls for improved treatment of the plastic dynamics.Comment: 15 pages, 20 figure

Solution of the Percus-Yevick equation for hard hyperspheres in even dimensions

We solve the Percus-Yevick equation in even dimensions by reducing it to a set of simple integro-differential equations. This work generalizes an approach we developed previously for hard discs. We numerically obtain both the pair correlation function and the virial coefficients for a fluid of hyper-spheres in dimensions $d=4,6$ and 8, and find good agreement with available exact results and Monte-Carlo simulations. This paper confirms the alternating character of the virial series for $d \ge 6$, and provides the first evidence for an alternating character for $d=4$. Moreover, we show that this sign alternation is due to the existence of a branch point on the negative real axis. It is this branch point that determines the radius of convergence of the virial series, whose value we determine explicitly for $d=4,6,8$. Our results complement, and are consistent with, a recent study in odd dimensions [R.D. Rohrmann et al., J. Chem. Phys. 129, 014510 (2008)].Comment: Accepted for publication in J. Chem. Phys. (11 pages, 6 figures

Human Vav1 Expression in Hematopoietic and Cancer Cell Lines Is Regulated by c-Myb and by CpG Methylation

Vav1 is a signal transducer protein that functions as a guanine nucleotide exchange factor for the Rho/Rac GTPases in the hematopoietic system where it is exclusively expressed. Recently, Vav1 was shown to be involved in several human malignancies including neuroblastoma, lung cancer, and pancreatic ductal adenocarcinoma (PDA). Although some factors that affect vav1 expression are known, neither the physiological nor pathological regulation of vav1 expression is completely understood. We demonstrate herein that mutations in putative transcription factor binding sites at the vav1 promoter affect its transcription in cells of different histological origin. Among these sites is a consensus site for c-Myb, a hematopoietic-specific transcription factor that is also found in Vav1-expressing lung cancer cell lines. Depletion of c-Myb using siRNA led to a dramatic reduction in vav1 expression in these cells. Consistent with this, co-transfection of c-Myb activated transcription of a vav1 promoter-luciferase reporter gene construct in lung cancer cells devoid of Vav1 expression. Together, these results indicate that c-Myb is involved in vav1 expression in lung cancer cells. We also explored the methylation status of the vav1 promoter. Bisulfite sequencing revealed that the vav1 promoter was completely unmethylated in human lymphocytes, but methylated to various degrees in tissues that do not normally express vav1. The vav1 promoter does not contain CpG islands in proximity to the transcription start site; however, we demonstrated that methylation of a CpG dinucleotide at a consensus Sp1 binding site in the vav1 promoter interferes with protein binding in vitro. Our data identify two regulatory mechanisms for vav1 expression: binding of c-Myb and CpG methylation of 5′ regulatory sequences. Mutation of other putative transcription factor binding sites suggests that additional factors regulate vav1 expression as well

Supersymmetric Vacua in Random Supergravity

We determine the spectrum of scalar masses in a supersymmetric vacuum of a general N=1 supergravity theory, with the Kahler potential and superpotential taken to be random functions of N complex scalar fields. We derive a random matrix model for the Hessian matrix and compute the eigenvalue spectrum. Tachyons consistent with the Breitenlohner-Freedman bound are generically present, and although these tachyons cannot destabilize the supersymmetric vacuum, they do influence the likelihood of the existence of an `uplift' to a metastable vacuum with positive cosmological constant. We show that the probability that a supersymmetric AdS vacuum has no tachyons is formally equivalent to the probability of a large fluctuation of the smallest eigenvalue of a certain real Wishart matrix. For normally-distributed matrix entries and any N, this probability is given exactly by P = exp(-2N^2|W|^2/m_{susy}^2), with W denoting the superpotential and m_{susy} the supersymmetric mass scale; for more general distributions of the entries, our result is accurate when N >> 1. We conclude that for |W| \gtrsim m_{susy}/N, tachyonic instabilities are ubiquitous in configurations obtained by uplifting supersymmetric vacua.Comment: 26 pages, 6 figure

Signaling Mechanisms of Vav3, a Guanine Nucleotide Exchange Factor and Androgen Receptor Coactivator, in Physiology and Prostate Cancer Progression

The Rho GTPase guanine nucleotide exchange factor (GEF) Vav3 is the third member of the Vavfamily of GEFS and is activated by tyrosine phosphorylation. Through stimulation of Rho GTPaseactivity, Vav3 promotes cell migration, invasion, and other cellular processes. Work from our laboratory first established that Vav3 is upregulated in models of castration-resistant prostate cancer progression and enhances androgen receptor as well as androgen receptor splice variant activity. Recent analysis of clinical specimens supports Vav3 as a potential biomarker of aggressive prostate cancer. Consistent with a role in promoting castration-­resistant disease, Vav3 is a versatile enhancer of androgen receptor by both ligand-dependent and ligand-independent mechanisms and as such impacts established pathways of androgen receptor reactivation in advanced prostate cancer. Distinct Vav3 domains and mechanisms participate in ligand-dependent and -independent androgen receptor coactivation. To provide a physiologic context, we review Vav3 actions elucidated by gene knockout studies. This chapter describes the pervasive role of Vav3 in progression of prostate cancer to castration resistance. We discuss the mechanisms by which prostate cancer cells exploit Vav3 signaling to promote androgen receptor activity under different hormonal milieus, which are relevant to clinical prostate cancer. Lastly, we review the data on the emerging role for Vav3 in other cancers ranging from leukemias to gliomas.https://nsuworks.nova.edu/hpd_medsci_faculty_books/1002/thumbnail.jp

Finding consistent disease subnetworks across microarray datasets

<p>Abstract</p> <p>Background</p> <p>While contemporary methods of microarray analysis are excellent tools for studying individual microarray datasets, they have a tendency to produce different results from different datasets of the same disease. We aim to solve this reproducibility problem by introducing a technique (SNet). SNet provides both quantitative and descriptive analysis of microarray datasets by identifying specific connected portions of pathways that are significant. We term such portions within pathways as “subnetworks”.</p> <p>Results</p> <p>We tested SNet on independent datasets of several diseases, including childhood ALL, DMD and lung cancer. For each of these diseases, we obtained two independent microarray datasets produced by distinct labs on distinct platforms. In each case, our technique consistently produced almost the same list of significant nontrivial subnetworks from two independent sets of microarray data. The gene-level agreement of these significant subnetworks was between 51.18% to 93.01%. In contrast, when the same pairs of microarray datasets were analysed using GSEA, t-test and SAM, this percentage fell between 2.38% to 28.90% for GSEA, 49.60% tp 73.01% for t-test, and 49.96% to 81.25% for SAM. Furthermore, the genes selected using these existing methods did not form subnetworks of substantial size. Thus it is more probable that the subnetworks selected by our technique can provide the researcher with more descriptive information on the portions of the pathway actually affected by the disease.</p> <p>Conclusions</p> <p>These results clearly demonstrate that our technique generates significant subnetworks and genes that are more consistent and reproducible across datasets compared to the other popular methods available (GSEA, t-test and SAM). The large size of subnetworks which we generate indicates that they are generally more biologically significant (less likely to be spurious). In addition, we have chosen two sample subnetworks and validated them with references from biological literature. This shows that our algorithm is capable of generating descriptive biologically conclusions.</p