Fully Analyzing an Algebraic Polya Urn Model

This paper introduces and analyzes a particular class of Polya urns: balls are of two colors, can only be added (the urns are said to be additive) and at every step the same constant number of balls is added, thus only the color compositions varies (the urns are said to be balanced). These properties make this class of urns ideally suited for analysis from an "analytic combinatorics" point-of-view, following in the footsteps of Flajolet-Dumas-Puyhaubert, 2006. Through an algebraic generating function to which we apply a multiple coalescing saddle-point method, we are able to give precise asymptotic results for the probability distribution of the composition of the urn, as well as local limit law and large deviation bounds.Comment: LATIN 2012, Arequipa : Peru (2012

An Interesting Class of Operators with unusual Schatten-von Neumann behavior

We consider the class of integral operators Q_\f on $L^2(\R_+)$ of the form (Q_\f f)(x)=\int_0^\be\f (\max\{x,y\})f(y)dy. We discuss necessary and sufficient conditions on $\phi$ to insure that $Q_{\phi}$ is bounded, compact, or in the Schatten-von Neumann class \bS_p, $1<p<\infty$. We also give necessary and sufficient conditions for $Q_{\phi}$ to be a finite rank operator. However, there is a kind of cut-off at $p=1$, and for membership in \bS_{p}, $0<p\leq1$, the situation is more complicated. Although we give various necessary conditions and sufficient conditions relating to Q_{\phi}\in\bS_{p} in that range, we do not have necessary and sufficient conditions. In the most important case $p=1$, we have a necessary condition and a sufficient condition, using $L^1$ and $L^2$ modulus of continuity, respectively, with a rather small gap in between. A second cut-off occurs at $p=1/2$: if \f is sufficiently smooth and decays reasonably fast, then \qf belongs to the weak Schatten-von Neumann class \wS{1/2}, but never to \bS_{1/2} unless \f=0. We also obtain results for related families of operators acting on $L^2(\R)$ and $\ell^2(\Z)$. We further study operations acting on bounded linear operators on $L^{2}(\R^{+})$ related to the class of operators Q_\f. In particular we study Schur multipliers given by functions of the form $\phi(\max\{x,y\})$ and we study properties of the averaging projection (Hilbert-Schmidt projection) onto the operators of the form Q_\f.Comment: 87 page

Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs

General upper tail estimates are given for counting edges in a random induced subhypergraph of a fixed hypergraph H, with an easy proof by estimating the moments. As an application we consider the numbers of arithmetic progressions and Schur triples in random subsets of integers. In the second part of the paper we return to the subgraph counts in random graphs and provide upper tail estimates in the rooted case.Comment: 15 page

Functional characterization and structure-guided mutational analysis of the transsulfuration enzyme cystathionine γ-lyase from toxoplasma gondii

Sulfur-containing amino acids play essential roles in many organisms. The protozoan parasite Toxoplasma gondii includes the genes for cystathionine β-synthase and cystathionine γ-lyase (TgCGL), as well as for cysteine synthase, which are crucial enzymes of the transsulfuration and de novo pathways for cysteine biosynthesis, respectively. These enzymes are specifically expressed in the oocyst stage of T. gondii. However, their functionality has not been investigated. Herein, we expressed and characterized the putative CGL from T. gondii. Recombinant TgCGL almost exclusively catalyses the α,γ-hydrolysis of L-cystathionine to form L-cysteine and displays marginal reactivity toward L-cysteine. Structure-guided homology modelling revealed two striking amino acid differences between the human and parasite CGL active-sites (Glu59 and Ser340 in human to Ser77 and Asn360 in toxoplasma). Mutation of Asn360 to Ser demonstrated the importance of this residue in modulating the specificity for the catalysis of α,β-versus α,γ-elimination of L-cystathionine. Replacement of Ser77 by Glu completely abolished activity towards L-cystathionine. Our results suggest that CGL is an important functional enzyme in T. gondii, likely implying that the reverse transsulfuration pathway is operative in the parasite; we also probed the roles of active-site architecture and substrate binding conformations as determinants of reaction specificity in transsulfuration enzymes

Monotone graph limits and quasimonotone graphs

The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a symmetric function $W$ on $[0,1]$, i.e., a kernel or graphon. In this context it is natural to wish to relate specific properties of the sequence to specific properties of the kernel. Here we show that the kernel is monotone (i.e., increasing in both variables) if and only if the sequence satisfies a `quasi-monotonicity' property defined by a certain functional tending to zero. As a tool we prove an inequality relating the cut and $L^1$ norms of kernels of the form $W_1-W_2$ with $W_1$ and $W_2$ monotone that may be of interest in its own right; no such inequality holds for general kernels.Comment: 38 page

Searching for young Jupiter analogs around AP Col: L-band high-contrast imaging of the closest pre-main sequence star

The nearby M-dwarf AP Col was recently identified by Riedel et al. 2011 as a pre-main sequence star (age 12 - 50 Myr) situated only 8.4 pc from the Sun. The combination of its youth, distance, and intrinsically low luminosity make it an ideal target to search for extrasolar planets using direct imaging. We report deep adaptive optics observations of AP Col taken with VLT/NACO and Keck/NIRC2 in the L-band. Using aggressive speckle suppression and background subtraction techniques, we are able to rule out companions with mass m >= 0.5 - 1M_Jup for projected separations a>4.5 AU, and m >= 2 M_Jup for projected separations as small as 3 AU, assuming an age of 40 Myr using the COND theoretical evolutionary models. Using a different set of models the mass limits increase by a factor of ~2. The observations presented here are the deepest mass-sensitivity limits yet achieved within 20 AU on a star with direct imaging. While Doppler radial velocity surveys have shown that Jovian bodies with close-in orbits are rare around M-dwarfs, gravitational microlensing studies predict that ~17% of these stars host massive planets with orbital separations of 1-10 AU. Sensitive high-contrast imaging observations, like those presented here, will help to validate results from complementary detection techniques by determining the frequency of gas giant planets on wide orbits around M-dwarfs.Comment: Accepted for publication in ApJ, 6 pages text ApJ style (incl. references), 4 figures, 1 tabl

Rotordynamic coefficients and leakage flow of parallel grooved seals and smooth seals

Based on Childs finite length solution for annular plain seals an extension of the bulk flow theory is derived to calculate the rotordynamic coefficients and the leakage flow of seals with parallel grooves in the stator. Hirs turbulent lubricant equations are modified to account for the different friction factors in circumferential and axial direction. Furthermore an average groove depth is introduced to consider the additional circumferential flow in the grooves. Theoretical and experimental results are compared for the smooth constant clearance seal and the corresponding seal with parallel grooves. Compared to the smooth seal the direct and cross-coupled stiffness coefficients as well as the direct damping coefficients are lower in the grooved seal configuration. Leakage is reduced by the grooving pattern

Peculiar long-range superexchange in Cu2A2O7 (A = P, As, V) as a key element of the microscopic magnetic model

A microscopic magnetic model for alpha-Cu2P2O7 is evaluated in a combined theoretical and experimental study. Despite a dominant intradimer coupling J1, sizable interdimer couplings enforce long-range magnetic ordering at T_N=27 K. The spin model for alpha-Cu2P2O7 is compared to the models of the isostructural beta-Cu2V2O7 and alpha-Cu2As2O7 systems. As a surprise, coupled dimers in alpha-Cu2P2O7 and alternating chains in alpha-Cu2As2O7 contrast with a honeycomb lattice in beta-Cu2V2O7. We find that the qualitative difference in the coupling regime of these isostructural compounds is governed by the nature of AO4 side groups: d-elements (A = V) hybridize with nearby O atoms forming a Cu-O-A-O-Cu superexchange path, while for p-elements (A = P, As) the superexchange is realized via O-O edges of the tetrahedron. Implications for a broad range of systems are discussed.Comment: 8 pages, 5 figures, 1 table; discussion extende

Detection of the nearest Jupiter analog in radial velocity and astrometry data

© 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society.The presence of Jupiter is crucial to the architecture of the Solar System and models underline this to be a generic feature of planetary systems. We find the detection of the difference between the position and motion recorded by the contemporary astrometric satellite Gaia and its precursor Hipparcos can be used to discover Jupiter-like planets. We illustrate how observations of the nearby star $\varepsilon$ Indi A giving astrometric and radial velocity data can be used to independently find the orbit of its suspected companion. The radial velocity and astrometric data provide complementary detections which allow for a much stronger solution than either technique would provide individually. We quantify $\varepsilon$ Indi A b as the closest Jupiter-like exoplanet with a mass of 3 $M_{Jup}$ on a slightly eccentric orbit with an orbital period of 45 yr. While other long-period exoplanets have been discovered, $\varepsilon$ Indi A b provides a well constrained mass and along with the well-studied brown dwarf binary in orbit around $\varepsilon$ Indi A means that the system provides a benchmark case for our understanding of the formation of gas giant planets and brown dwarfs.Peer reviewe

AKLT Models with Quantum Spin Glass Ground States

We study AKLT models on locally tree-like lattices of fixed connectivity and find that they exhibit a variety of ground states depending upon the spin, coordination and global (graph) topology. We find a) quantum paramagnetic or valence bond solid ground states, b) critical and ordered N\'eel states on bipartite infinite Cayley trees and c) critical and ordered quantum vector spin glass states on random graphs of fixed connectivity. We argue, in consonance with a previous analysis, that all phases are characterized by gaps to local excitations. The spin glass states we report arise from random long ranged loops which frustrate N\'eel ordering despite the lack of randomness in the coupling strengths.Comment: 10 pages, 1 figur