Doob-Martin compactification of a Markov chain for growing random words sequentially

We consider a Markov chain that iteratively generates a sequence of random finite words in such a way that the $n^{\mathrm{th}}$ word is uniformly distributed over the set of words of length $2n$ in which $n$ letters are $a$ and $n$ letters are $b$: at each step an $a$ and a $b$ are shuffled in uniformly at random among the letters of the current word. We obtain a concrete characterization of the Doob-Martin boundary of this Markov chain. Writing $N(u)$ for the number of letters $a$ (equivalently, $b$) in the finite word $u$, we show that a sequence $(u_n)_{n \in \mathbb{N}}$ of finite words converges to a point in the boundary if, for an arbitrary word $v$, there is convergence as $n$ tends to infinity of the probability that the selection of $N(v)$ letters $a$ and $N(v)$ letters $b$ uniformly at random from $u_n$ and maintaining their relative order results in $v$. We exhibit a bijective correspondence between the points in the boundary and ergodic random total orders on the set $\{a_1, b_1, a_2, b_2, \ldots \}$ that have distributions which are separately invariant under finite permutations of the indices of the $a'$s and those of the $b'$s. We establish a further bijective correspondence between the set of such random total orders and the set of pairs $(\mu,\nu)$ of diffuse probability measures on $[0,1]$ such that $\frac{1}{2}(\mu+\nu)$ is Lebesgue measure: the restriction of the random total order to $\{a_1, b_1, \ldots, a_n, b_n\}$ is obtained by taking $X_1, \ldots, X_n$ (resp. $Y_1, \ldots, Y_n$) i.i.d. with common distribution $\mu$ (resp. $\nu$), letting $(Z_1, \ldots, Z_{2n})$ be $\{X_1, Y_1, \ldots, X_n, Y_n\}$ in increasing order, and declaring that the $k^{\mathrm{th}}$ smallest element in the restricted total order is $a_i$ (resp. $b_j$) if $Z_k = X_i$ (resp. $Z_k = Y_j$).Comment: 24 pages, revised to deal with reviewer's comment

DFacTo: Distributed Factorization of Tensors

We present a technique for significantly speeding up Alternating Least Squares (ALS) and Gradient Descent (GD), two widely used algorithms for tensor factorization. By exploiting properties of the Khatri-Rao product, we show how to efficiently address a computationally challenging sub-step of both algorithms. Our algorithm, DFacTo, only requires two sparse matrix-vector products and is easy to parallelize. DFacTo is not only scalable but also on average 4 to 10 times faster than competing algorithms on a variety of datasets. For instance, DFacTo only takes 480 seconds on 4 machines to perform one iteration of the ALS algorithm and 1,143 seconds to perform one iteration of the GD algorithm on a 6.5 million x 2.5 million x 1.5 million dimensional tensor with 1.2 billion non-zero entries.Comment: Under review for NIPS 201

Correct Effective Potential of Supersymmetric Yang-Mills Theory on M^4\times S^1

We study an ${\cal N}=1$ supersymmetric Yang-Mills theory defined on $M^4\times S^1$. The vacuum expectation values for adjoint scalar field in vector multiplet, though important, has been overlooked in evaluating one-loop effective potential of the theory. We correctly take the vacuum expectation values into account in addition to the Wilson line phases to give an expression for the effective potential, and gauge symmetry breaking is discussed. In evaluating the potential, we employ the Scherk-Schwarz mechanism and introduce bare mass for gaugino in order to break supersymmetry. We also obtain masses for the scalars, the adjoint scalar, and the component gauge field for the $S^1$ direction in case of the SU(2) gauge group. We observe that large supersymmetry breaking gives larger mass for the scalar. This analysis is easily applied to the $M^4\times S^1/Z_2$ case.Comment: 12 pages, 1 figur

Impact of the recent results by the CMS and ATLAS Collaborations at the CERN Large Hadron Collider on an effective Minimal Supersymmetric extension of the Standard Model

We discuss the impact for light neutralinos in an effective Minimal Supersymmetric extension of the Standard Model of the recent results presented by the CMS and ATLAS Collaborations at the CERN Large Hadron Collider for a search of supersymmetry in proton-proton collisions at a center-of-mass energy of 7 TeV with an integrated luminosity of 35 inverse pb. We find that, in the specific case of light neutralinos, efficiencies for the specific signature searched by ATLAS (jets+missing transverse energy and an isolated lepton) imply a lower sensitivity compared to CMS (which searches for jets +missing transverse energy). Focusing on the CMS bound, if squark soft masses of the three families are assumed to be degenerate, the combination of the ensuing constraint on squark and gluino masses with the experimental limit on the b to s + gamma decay imply a lower bound on the neutralino mass that can reach the value of 11.9 GeV, depending on the gluino mass. On the other hand, when the universality condition among squark soft parameters is relaxed, the lower bound on the neutralino mass is not constrained by the CMS measurement and then remains at the value 7.5 GeV derived in previous papers.Comment: 6 pages, 6 figures, typeset with ReVTeX4. A version of the paper with full resolution figures can be found at http://www.to.infn.it/~scopel/cms_mssm2.pd

Assessing the Role of the Microbiome, Parasite Infections, and Movement in Avian Health

Avian health encompasses the physical, physiological, and behavioral well-being of birds. Assessing avian health is not only important for the conservation and management of wild birds and the recreational economy, but also for the management of infectious diseases that threaten public health and agriculture. Birds, comprising approximately 10,000 species and an estimated 50 billion individuals worldwide, are known to be involved in the spread of pathogens, some of which are zoonotic (from animals to humans), such as avian influenza and West Nile viruses. Individual measures of avian health may include physical measurements (e.g., body mass, wing length), pathogen infection status, the host-associated microbial community (the microbiome), and behavior (e.g., movement, migratory status). In particular, the microbiome is known to play diverse functional roles in individuals, including in immune function, growth, and physiology, however little is known about the relationships between the microbiome, pathogen infection, and fitness in wild birds. Here, we sought to evaluate indicators of avian health and the factors that drive them by (1) defining the “core” microbiome of mallard ducks (Anas platyrhynchos), (2) demonstrating the utility of microbiome data for pathogen detection in barn swallows (Hirundo rustica), (3) identifying predictors of parasite infection intensity and relationships with the microbiome in Maine waterfowl, and (4) examining whether trait variation (plumage coloration) predicts potential indicators of avian health (pathogen infection, microbiome, movement), and whether these health indicators affect reproductive success in barn owls (Tyto alba). We collected cloacal swabs from multiple wild bird species to characterize the cloacal bacterial microbiome through 16S rRNA sequencing. We also collected biological samples for the detection and/or quantification of pathogen infections: a cloacal swab in nutrient broth for Salmonella (barn swallows) and whole blood for avian haemosporidian parasite (all others). We recorded host ecological data (all species), as well as movement and/or reproductive data (barn owls only) and conducted statistical analyses to identify potential drivers of pathogen infection, microbiome diversity and composition, movement and/or fitness. We found that although six taxa were identified as part of the core cloacal microbiome of mallard ducks, they were not universally prominent across three represented flyways (Obj. 1). Rather, sampling location was found to significantly influence the bacterial microbiome alpha diversity (Chao1; χ2 = 71.218, p = 3.43e-16) of mallards. We also detected Salmonella in 23.1% (25) barn swallow samples and found a significant relationship between the presence of Salmonella and microbiome alpha diversity in swallows (Obj. 2). Location was the primary driver for avian haemosporidian parasite infection intensity in Maine waterfowl, followed by age (Obj. 3). While we found no consistent relationship between parasite infection and the avian microbiome across duck species, we did observe a significant relationship between parasite infection intensity and microbiome composition (beta diversity) using the weighted UniFrac measure (F = 3.02, p = 0.013). Finally, we found no relationship between plumage coloration and indicators of avian health in barn owls (Obj. 4). However, female owl movement, as reflected by home range area, was inversely related to measures of reproductive success (clutch size and fledge success. Furthermore, microbiome alpha diversity was significantly correlated with Julian laying date, such that individuals with higher microbiome diversity laid their eggs earlier, thereby potentially enhancing their reproductive potential. Collectively, this thesis evaluates multiple indicators of avian health, including the microbiome diversity, parasite infections, and movement ecology, and provides valuable insight into the ecological drivers and dynamics of host-microbe interactions

Giant phonon anomalies in the pseudo-gap phase of TiOCl

We report infrared and Raman spectroscopy results of the spin-1/2 quantum magnet TiOCl. Giant anomalies are found in the temperature dependence of the phonon spectrum, which hint to unusual coupling of the electronic degrees of freedom to the lattice. These anomalies develop over a broad temperature interval, suggesting the presence of an extended fluctuation regime. This defines a pseudo-gap phase, characterized by a local spin-gap. Below 100 K a dimensionality cross-over leads to a dimerized ground state with a global spin-gap of about 2$\Delta_{spin}\approx$~430 K.Comment: 4 pages, 3 figures, for further information see http://www.peter-lemmens.d