Exponential clogging time for a one dimensional DLA

When considering DLA on a cylinder it is natural to ask how many particles it takes to clog the cylinder, e.g. modeling clogging of arteries. In this note we formulate a very simple DLA clogging model and establish an exponential lower bound on the number of particles arriving before clogging appears

Shape-based peak identification for ChIP-Seq

We present a new algorithm for the identification of bound regions from ChIP-seq experiments. Our method for identifying statistically significant peaks from read coverage is inspired by the notion of persistence in topological data analysis and provides a non-parametric approach that is robust to noise in experiments. Specifically, our method reduces the peak calling problem to the study of tree-based statistics derived from the data. We demonstrate the accuracy of our method on existing datasets, and we show that it can discover previously missed regions and can more clearly discriminate between multiple binding events. The software T-PIC (Tree shape Peak Identification for ChIP-Seq) is available at http://math.berkeley.edu/~vhower/tpic.htmlComment: 12 pages, 6 figure

Percolation in invariant Poisson graphs with i.i.d. degrees

Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme that is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components

A Sublinear Variance Bound for Solutions of a Random Hamilton Jacobi Equation

We estimate the variance of the value function for a random optimal control problem. The value function is the solution $w^\epsilon$ of a Hamilton-Jacobi equation with random Hamiltonian $H(p,x,\omega) = K(p) - V(x/\epsilon,\omega)$ in dimension $d \geq 2$. It is known that homogenization occurs as $\epsilon \to 0$, but little is known about the statistical fluctuations of $w^\epsilon$. Our main result shows that the variance of the solution $w^\epsilon$ is bounded by $O(\epsilon/|\log \epsilon|)$. The proof relies on a modified Poincar\'e inequality of Talagrand

Excited Random Walk in One Dimension

We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q=1-p. If the walk hops onto an empty site, there is no bias. For the 1-excited walk on the half-line (one cookie initially at each site), the probability of first returning to the starting point at time t scales as t^{-(2-p)}. Although the average return time to the origin is infinite for all p, the walk eats, on average, only a finite number of cookies until this first return when p<1/2. For the infinite line, the probability distribution for the 1-excited walk has an unusual anomaly at the origin. The positions of the leftmost and rightmost uneaten cookies can be accurately estimated by probabilistic arguments and their corresponding distributions have power-law singularities near the origin. The 2-excited walk on the infinite line exhibits peculiar features in the regime p>3/4, where the walk is transient, including a mean displacement that grows as t^{nu}, with nu>1/2 dependent on p, and a breakdown of scaling for the probability distribution of the walk.Comment: 14 pages, 13 figures, 2-column revtex4 format, for submission to J. Phys.

Phase Transitions on Nonamenable Graphs

We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees

The Five Factor Model of personality and evaluation of drug consumption risk

The problem of evaluating an individual's risk of drug consumption and misuse is highly important. An online survey methodology was employed to collect data including Big Five personality traits (NEO-FFI-R), impulsivity (BIS-11), sensation seeking (ImpSS), and demographic information. The data set contained information on the consumption of 18 central nervous system psychoactive drugs. Correlation analysis demonstrated the existence of groups of drugs with strongly correlated consumption patterns. Three correlation pleiades were identified, named by the central drug in the pleiade: ecstasy, heroin, and benzodiazepines pleiades. An exhaustive search was performed to select the most effective subset of input features and data mining methods to classify users and non-users for each drug and pleiad. A number of classification methods were employed (decision tree, random forest, $k$-nearest neighbors, linear discriminant analysis, Gaussian mixture, probability density function estimation, logistic regression and na{\"i}ve Bayes) and the most effective classifier was selected for each drug. The quality of classification was surprisingly high with sensitivity and specificity (evaluated by leave-one-out cross-validation) being greater than 70\% for almost all classification tasks. The best results with sensitivity and specificity being greater than 75\% were achieved for cannabis, crack, ecstasy, legal highs, LSD, and volatile substance abuse (VSA).Comment: Significantly extended report with 67 pages, 27 tables, 21 figure

A Deep WSRT 1.4 GHz Radio Survey of the Spitzer Space Telescope FLSv Region

The First Look Survey (FLS) is the first scientific product to emerge from the Spitzer Space Telescope. A small region of this field (the verification strip) has been imaged very deeply, permitting the detection of cosmologically distant sources. We present Westerbork Synthesis Radio Telescope (WSRT) observations of this region, encompassing a ~1 sq. deg field, centred on the verification strip (J2000 RA=17:17:00.00, DEC=59:45:00.000). The radio images reach a noise level of ~ 8.5 microJy/beam - the deepest WSRT image made to date. We summarise here the first results from the project, and present the final mosaic image, together with a list of detected sources. The effect of source confusion on the position, size and flux density of the faintest sources in the source catalogue are also addressed. The results of a serendipitous search for HI emission in the field are also presented. Using a subset of the data, we clearly detect HI emission associated with four galaxies in the central region of the FLSv. These are identified with nearby, massive galaxies.Comment: 9 pages, 6 figures (fig.3 in a separate gif file). Accepted for publication in A&A. The full paper and the related material can be downloaded from http://www.astron.nl/wsrt/WSRTsurveys/WFLS

Trapping in the random conductance model

We consider random walks on $\Z^d$ among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of the random walk conditioned to return back to the starting point at time $2n$. We show that in the situations when the heat kernel exhibits subdiffusive decay --- which is known to occur in dimensions $d\ge4$ --- the walk gets trapped for a time of order $n$ in a small spatial region. This shows that the strategy used earlier to infer subdiffusive lower bounds on the heat kernel in specific examples is in fact dominant. In addition, we settle a conjecture concerning the worst possible subdiffusive decay in four dimensions.Comment: 21 pages, version to appear in J. Statist. Phy

Gaussian multiplicative Chaos for symmetric isotropic matrices

Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985