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Interlinked Dual-Time Feedback Loops can Enhance Robustness to Stochasticity and Persistence of MemoryAug 29 2012Multiple interlinked positive feedback loops shape the stimulus responses of various biochemical systems, such as the cell cycle or intracellular calcium release. Recent studies with simplified models have identified two advantages of coupling fast and ... More

How Can Memories Last for Days, Years, or a Lifetime? Proposed Mechanisms for Maintaining Synaptic Potentiation and MemoryMar 13 2019With memory encoding reliant on persistent changes in the properties of synapses, a key question is how can memories be maintained from days to months or a lifetime given molecular turnover? It is likely that positive feedback loops are necessary to persistently ... More

Simulation of Drosophila Circadian Oscillations, Mutations, and Light Responses by a Model with VRI, PDP-1, and CLKJan 23 2004A model of Drosophila circadian rhythm generation was developed to represent feedback loops based on transcriptional regulation of per, Clk (dclock), Pdp-1, and vri (vrille). The model postulates that histone acetylation kinetics make transcriptional ... More

ISiCLE: A molecular collision cross section calculation pipeline for establishing large in silico reference libraries for compound identificationSep 22 2018Comprehensive and confident identifications of metabolites and other chemicals in complex samples will revolutionize our understanding of the role these chemically diverse molecules play in biological systems. Despite recent advances, metabolomics studies ... More

Fixation and consensus times on a network: a unified approachJan 20 2008Jan 05 2009We investigate a set of stochastic models of biodiversity, population genetics, language evolution and opinion dynamics on a network within a common framework. Each node has a state, 0 < x_i < 1, with interactions specified by strengths m_{ij}. For any ... More

The Lack of Halo Ultraluminous X-ray SourcesSep 11 2006The premise that Ultraluminous X-ray sources (ULXs) exist beyond the optical extent of nearby galaxies is investigated. A published catalog containing 41 ULX candidates located between 1 and ~3 times the standard D_{25} isophotal radius of their putative ... More

Conditionally Positive Functions and p-norm Distance MatricesJun 12 2010In Micchelli's paper "Interpolation of scattered data: distance matrices and conditionally positive functions", deep results were obtained concerning the invertibility of matrices arising from radial basis function interpolation. In particular, the Euclidean ... More

Preconditioned Conjugate Gradients, Radial Basis Functions and Toeplitz MatricesJun 12 2010Radial basis functions provide highly useful and flexible interpolants to multivariate functions. Further, they are beginning to be used in the numerical solution of partial differential equations. Unfortunately, their construction requires the solution ... More

The Interpolation Theory of Radial Basis FunctionsJun 12 2010In this dissertation, it is first shown that, when the radial basis function is a $p$-norm and $1 < p < 2$, interpolation is always possible when the points are all different and there are at least two of them. We then show that interpolation is not always ... More

The Distance to NGC 2264Jul 17 2009We determine the distance to the open cluster NGC 2264 using a statistical analysis of cluster member inclinations. We derive distance-dependent values of sin i (where i is the inclination angle) for 97 stars in NGC 2264 from the rotation periods, luminosities, ... More

Bootstrap Percolation on Complex NetworksMar 29 2010May 26 2010We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: $f$, the fraction of vertices initially activated, and $p$, the fraction of undamaged vertices in the graph. ... More

Heterogeneous-k-core versus Bootstrap Percolation on Complex NetworksDec 20 2010We introduce the heterogeneous-$k$-core, which generalizes the $k$-core, and contrast it with bootstrap percolation. Vertices have a threshold $k_i$ which may be different at each vertex. If a vertex has less than $k_i$ neighbors it is pruned from the ... More

Castelnuovo-Mumford regularity and arithmetic Cohen-Macaulayness of complete bipartite subspace arrangementsSep 10 2012Aug 04 2014We give the Castelnuovo-Mumford regularity of arrangements of (n-2)-planes in P^n whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen-Macaulay.

Molecular Constraints on Synaptic Tagging and Maintenance of Long-Term Potentiation: A Predictive ModelJun 16 2012Aug 03 2012Protein synthesis-dependent, late long-term potentiation (LTP) and depression (LTD) at glutamatergic hippocampal synapses are well characterized examples of long-term synaptic plasticity. Persistent increased activity of the enzyme protein kinase M (PKM) ... More

Stable furry black holes in $\mathfrak{su}(\infty)$ anti-de Sitter Einstein-Yang-Mills theory, characterised by an infinitude of global chargesFeb 10 2019We present solutions to classical field equations for purely magnetic $\mathfrak{su}(\infty)$ Einstein-Yang-Mills theory in asymptotically Anti-de Sitter space. These solutions are found to be stable under linear, time-dependent perturbations. Recent ... More

Functionals of Exponential Brownian Motion and Divided DifferencesJun 10 2010We provide a surprising new application of classical approximation theory to a fundamental asset-pricing model of mathematical finance. Specifically, we calculate an analytic value for the correlation coefficient between exponential Brownian motion and ... More

On the existence of topological dyons and dyonic black holes in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groupsJul 26 2017May 17 2018Here we study the global existence of `hairy' dyonic black hole and dyon solutions to four dimensional, anti-de Sitter Einstein-Yang-Mills theories for a general simply-connected and semisimple gauge group $G$, for so-called topologically symmetric systems, ... More

Dyonic black holes in $\mathfrak{su}(\infty)$ anti-de Sitter Einstein-Yang-Mills theory, characterised by an infinite set of global chargesDec 13 2018We here investigate static, spherically symmetric solutions to $\mathfrak{su}(\infty)$ Einstein-Yang-Mills theory with a negative cosmological constant $\Lambda$ in the case of dyonic solutions, which possess a non-trivial electric sector of the gauge ... More

Simulations Suggest Pharmacological Methods for Rescuing Long-Term PotentiationAug 08 2014Congenital cognitive dysfunctions are frequently due to deficits in molecular pathways that underlie synaptic plasticity. For example, Rubinstein-Taybi syndrome (RTS) is due to a mutation in cbp, encoding the histone acetyltransferase CREB-binding protein ... More

Bistable MAP Kinase Activity: A Plausible Mechanism Contributing to Maintenance of Late Long-Term PotentiationFeb 18 2008Bistability of MAP kinase (MAPK) activity has been suggested to contribute to several cellular processes, including differentiation and long-term synaptic potentiation. A recent model (48) predicts bistability due to interactions of the kinases and phosphatases ... More

A Model of the Roles of Essential Kinases in the Induction and Expression of Late Long-Term PotentiationJan 03 2006The induction of late long-term potentiation (L-LTP) involves complex interactions among second messenger cascades. To gain insights into these interactions, a mathematical model was developed for L-LTP induction in the CA1 region of the hippocampus. ... More

Paradoxical LTP maintenance with inhibition of protein synthesis and the proteasome suggests a novel protein synthesis requirement for early LTP reversalAug 20 2018The transition from early long-term potentiation (E-LTP) to late LTP (L-LTP) involves protein synthesis and degradation. L-LTP is blocked by inhibiting either protein synthesis or proteasome-dependent degradation prior to and during a tetanic stimulus, ... More

Surface and corner free energies of the self-dual Potts modelJun 06 2016Jan 26 2017We consider the bulk, vertical surface, horizontal surface and corner free energies $f_b, f_s, f'_s, f_c$ of the anisotropic self-dual $Q$-state Potts model for $Q > 4$. $f_b$ was calculated in 1973[1]. For $Q<4$, $f_s, f'_s$ were calculated in 1989[2]. ... More

Applying the Cluster Method to Count Occurrences of Generalized Permutation PatternsMay 29 2009We apply ideas from the cluster method to q-count the permutations of a multiset according to the number of occurrences of certain generalized patterns, as defined by Babson and Steingrimsson. In particular, we consider those patterns with three letters ... More

The bulk, surface and corner free energies of the square lattice Ising modelJun 07 2016Jul 18 2016We use Kaufman's spinor method to calculate the bulk, surface and corner free energies $f_b, f_s, f_s', f_c$ of the anisotropic square lattice zero-field Ising model for the ordered ferromagnetic case. For $f_b, f_s, f'_s$ our results of course agree ... More

Two new young, wide magnetic + non-magnetic double-degenerate binary systemsNov 29 2011Abridged: We report the discovery of two, new, rare, wide, double-degenerate binaries that each contain a magnetic and a non-magnetic star. The components of SDSSJ092646.88+132134.5 + J092647.00+132138.4 and SDSSJ150746.48+521002.1 + J150746.80+520958.0 ... More

Hidden Black: Coherent Enhancement of Absorption in Strongly-scattering MediaAug 04 2011Oct 12 2011We show that a weakly absorbing, strongly scattering (white) medium can be made very strongly absorbing at any frequency within its strong-scattering bandwidth by optimizing the input electromagnetic field. For uniform absorption, results from random ... More

The Effect of Encounters on the Eccentricity of Binaries in ClustersJun 13 1995May 22 1996We derive analytical expressions for the change in the orbital eccentricity of a binary following a distant encounter with a third star on a hyperbolic or parabolic orbit. To establish the accuracy of these expressions, we present detailed comparisons ... More

Site dependent hydrogenation in Graphynes: A Fully Atomistic Molecular Dynamics InvestigationJan 19 2015Graphyne is a generic name for a carbon allotrope family of 2D structures, where acetylenic groups connect benzenoid rings, with the coexistence of sp and sp2 hybridized carbon atoms. In this work we have investigated, through fully atomistic reactive ... More

Forced oscillations of coronal loops driven by EIT wavesJul 08 2008We study the generation of transversal oscillations in coronal loops represented as a straight thin flux tube under the effect of an external driver modeling the global coronal EIT wave. We investigate how the generated oscillations depend on the nature ... More

The Generalized DMPK equation revisited: A systematic derivationMar 21 2013The Generalized Dorokov-Mello-Pereyra-Kumar (DMPK) equation has recently been used to obtain a family of very broad and highly asymmetric conductance distributions for three dimensional disordered conductors. However, there are two major criticisms of ... More

Trees with Equal Total Domination and Game Total Domination NumbersSep 10 2016In this paper, we continue the study of the total domination game in graphs introduced in [Graphs Combin. 31(5) (2015), 1453--1462], where the players Dominator and Staller alternately select vertices of $G$. Each vertex chosen must strictly increase ... More

Mesoscopic conductance and its fluctuations at non-zero Hall angleJan 10 1997We consider the bilocal conductivity tensor, the two-probe conductance and its fluctuations for a disordered phase-coherent two-dimensional system of non-interacting electrons in the presence of a magnetic field, including correctly the edge effects. ... More

Progress Towards the Total Domination Game $\frac{3}{4}$-ConjectureDec 09 2015In this paper, we continue the study of the total domination game in graphs introduced in [Graphs Combin. 31(5) (2015), 1453--1462], where the players Dominator and Staller alternately select vertices of $G$. Each vertex chosen must strictly increase ... More

Localized shocksSep 29 2014May 25 2016We study products of precursors of spatially local operators, $W_{x_{n}}(t_{n}) ... W_{x_1}(t_1)$, where $W_x(t) = e^{-iHt} W_x e^{iHt}$. Using chaotic spin-chain numerics and gauge/gravity duality, we show that a single precursor fills a spatial region ... More

The Effect of the Infrared Phase of the Discrete BFKL Pomeron on Transverse Momentum DiffusionMay 26 2016Imposing infrared boundary conditions on the BFKL equation with running coupling transforms the complex momentum w-plane cut present in the gluon Green function into an infinite series of positive Regge poles. In addition, a cut on the negative w line ... More

Shilnikov problem in Filippov dynamical systemsApr 09 2015In this paper we introduce the concept of a sliding Shilnikov orbit for 3D Filippov systems. Versions of the Shilnikov's Theorems are provided for those systems. Specifically, we show that arbitrarily close to a sliding Shilnikov orbit there exist countable ... More

On the existence of soliton and hairy black hole solutions of su(N) Einstein-Yang-Mills theory with a negative cosmological constantAug 21 2008Oct 30 2008We study the existence of soliton and black hole solutions of four-dimensional su(N) Einstein-Yang-Mills theory with a negative cosmological constant. We prove the existence of non-trivial solutions for any integer N, with N-1 gauge field degrees of freedom. ... More

On the stability of soliton and hairy black hole solutions of ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory with a negative cosmological constantJan 29 2015Jan 25 2016We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant $\Lambda $. These solutions are described ... More

Topological black holes in ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory with a negative cosmological constantNov 16 2015Jan 07 2016We investigate the phase space of topological black hole solutions of ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory in anti-de Sitter space with a purely magnetic gauge potential. The gauge field is described by $N-1$ magnetic gauge field functions ... More

Artificial Intelligence for Interstellar TravelNov 15 2018Nov 19 2018The large distances involved in interstellar travel require a high degree of spacecraft autonomy, realized by artificial intelligence. The breadth of tasks artificial intelligence could perform on such spacecraft involves maintenance, data collection, ... More

Component masses of young, wide, non-magnetic white dwarf binaries in the SDSS DR7Mar 17 2014We present a spectroscopic component analysis of 18 candidate young, wide, non-magnetic, double-degenerate binaries identified from a search of the Sloan Digital Sky Survey Data Release 7 (DR7). All but two pairings are likely to be physical systems. ... More

Radiative Corrections to Chargino Production with Polarized BeamsDec 26 2000We show that radiative corrections to chargino production in electron-positron annihilation with polarized beams can be large especially in the case of right handed electrons. In addition, there is some dependency on the squark masses that allows us to ... More

First Demonstration of a Scintillating Xenon Bubble Chamber for Detecting Dark Matter and Coherent Elastic Neutrino-Nucleus ScatteringFeb 28 2017Jun 08 2017A 30-g xenon bubble chamber, operated at Northwestern University in June and November 2016, has for the first time observed simultaneous bubble nucleation and scintillation by nuclear recoils in a superheated liquid. This chamber is instrumented with ... More

Interacting Quantum Dot Coupled to a Kondo Spin: A Universal Hamiltonian StudyFeb 26 2008We study a mesoscopic interacting quantum dot described by the "universal Hamiltonian" that is coupled to a Kondo spin. The ferromagnetic exchange interaction within the dot leads to a stepwise increase of the ground state spin; this Stoner staircase ... More

A Galactic Ring of Minimum Stellar Density Near the Solar Orbit RadiusAug 02 2013We analyse the secular effects of a long-lived Galactic spiral structure on the stellar orbits with mean radii close to the corotation resonance. By test-particle simulations and different spiral potential models with parameters constrained on observations, ... More

The EMC effect still puzzles after 30 yearsMay 30 2013Thirty years ago, high-energy muons at CERN revealed the first hints of an effect that puzzles experimentalists and theorists alike to this day.

A Study of Ultra-Luminous X-ray Sources from the Chandra Archive of GalaxiesFeb 11 2003The more than 80 nearby galaxies imaged with the Chandra Advanced CCD Imaging Spectrometer have been analyzed in a search for Ultra-Luminous X-ray (ULX) sources. The sample of galaxies span the range of Hubble morphological types and include galaxies ... More

Eigenvalues and Eigenfunctions of the Scalar Laplace Operator on Calabi-Yau ManifoldsMay 23 2008Jul 10 2008A numerical algorithm for explicitly computing the spectrum of the Laplace-Beltrami operator on Calabi-Yau threefolds is presented. The requisite Ricci-flat metrics are calculated using a method introduced in previous papers. To illustrate our algorithm, ... More

Yarkovsky-Driven Spreading of the Eureka Family of Mars TrojansDec 04 2014Out of nine known stable Mars Trojans, seven appear to be members of an orbital grouping including the largest Trojan, Eureka. In order to test if this could be a genetic family, we simulated the long term evolution of a tight orbital cluster centered ... More

Discovery of a Transient X-ray Source in the Compact Stellar Nucleus of NGC 2403Feb 28 2007We report the discovery of an X-ray source coincident with the nuclear star cluster at the dynamical center of the nearby late-type spiral galaxy NGC 2403. The X-ray luminosity of this source varies from below detection levels, ~1e35 erg/s in the 0.5-8.0 ... More

Probing F-theory With Multiple BranesDec 05 1996We study multiple 3-branes on an F theory orientifold. The world-volume theory of the 3-branes is d=4, N=2 Sp(2k) gauge theory with an antisymmetric tensor and four flavors of matter in the fundamental. The solution of this gauge theory is found for vanishing ... More

Strong Interactions in Multimode Random LasersMay 29 2008Unlike conventional lasers, diffusive random lasers (DRLs) have no resonator to trap light and no high-Q resonances to support lasing. Due to this lack of sharp resonances the DRL has presented a challenge to conventional laser theory. We present a theory ... More

Steady-State Ab Initio Laser Theory for N-level LasersNov 09 2011We show that Steady-state Ab initio Laser Theory (SALT) can be applied to find the stationary multimode lasing properties of an N-level laser. This is achieved by mapping the N-level rate equations to an effective two-level model of the type solved by ... More

Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zonesJul 14 2016This work is devoted to study the existence of periodic solutions for a family of discontinuous differential systems $Z(x,y;\epsilon)$ with many zones. We show that for $\epsilon$ sufficiently small the averaged functions at any order control the existence ... More

The slice spectral sequence for the $C_{4}$ analog of real $K$-theoryFeb 26 2015Feb 02 2016We describe the slice spectral sequence of a 32-periodic $C_{4}$-spectrum $K_{[2]}$ related to the $C_{4}$ norm ${N_{C_{2}}^{C_{4}}MU_{\bf R}}$ of the real cobordism spectrum $MU_{\bf R}$. We will give it as a spectral sequence of Mackey functors converging ... More

On the super domination number of graphsMay 02 2017Apr 23 2018The open neighbourhood of a vertex $v$ of a graph $G$ is the set $N(v)$ consisting of all vertices adjacent to $v$ in $G$. For $D\subseteq V(G)$, we define $\overline{D}=V(G)\setminus D$. A set $D\subseteq V(G)$ is called a super dominating set of $G$ ... More

Polarization state of radiation from a photonic crystal slabAug 07 2017We point out that the polarization state of radiation from a photonic crystal slab is strongly constrained by the direct non-resonant scattering process. The phase difference between the two linearly-polarized components in the far field can be predicted ... More

Evolution on a smooth landscapeJul 24 1996We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation functions that ... More

An Area-Efficient FPGA Overlay using DSP Block based Time-multiplexed Functional UnitsJun 21 2016Coarse grained overlay architectures improve FPGA design productivity by providing fast compilation and software-like programmability. Throughput oriented spatially configurable overlays typically suffer from area overheads due to the requirement of one ... More

Semiclassical theory of the emission properties of wave-chaotic resonant cavitiesJul 08 1999We develop a perturbation theory for the lifetime and emission intensity for isolated resonances in asymmetric resonant cavities. The inverse lifetime $\Gamma$ and the emission intensity $I(\theta)$ in the open system are expressed in terms of matrix ... More

Molecular Dynamics Simulations of Ballistic Penetration of Pentagraphene SheetsJan 16 2018The superior mechanical properties and low density of carbon nanostructures make them promising ballistic protection materials, stimulating investigations on their high-strain-rate behavior. Recent experiments and simulations revealed graphene possesses ... More

A Complete Sample of ULX Host GalaxiesAug 05 2011Aug 19 2011One hundred seven ultraluminous X-ray (ULX) sources with 0.3-10.0 keV luminosities in excess of 1e39 erg/s are identified in a complete sample of 127 nearby galaxies. The sample includes all galaxies within 14.5 Mpc above the completeness limits of both ... More

An X-ray View of Star Formation in the Central 3 kpc of NGC 2403Dec 28 2009Archival Chandra observations are used to study the X-ray emission associated with star formation in the central region of the nearby SAB(s)cd galaxy NGC 2403. The distribution of X-ray emission is compared to the morphology visible at other wavelengths ... More

Constraining Satellite Galaxy Stellar Mass Loss and Predicting Intrahalo Light I: Framework and Results at Low RedshiftJan 11 2012Jun 06 2013We introduce a new technique that uses galaxy clustering to constrain how satellite galaxies lose stellar mass and contribute to the diffuse "intrahalo light" (IHL). We implement two models that relate satellite galaxy stellar mass loss to the detailed ... More

A Cosmic Coincidence: The Power-Law Galaxy Correlation FunctionJan 26 2011Jun 02 2011We model the evolution of galaxy clustering through cosmic time to investigate the nature of the power-law shape of xi(r), the galaxy two-point correlation function. Departures from a power law are mainly governed by galaxy pair counts on small scales, ... More

s$_\pm$ pairing near a Lifshitz transitionMar 11 2016Observation of robust superconductivity in some of the iron based superconductors in the vicinity of a Lifshitz point where a spin density wave instability is suppressed as the {hole} band drops below the Fermi energy raise questions for spin-fluctuation ... More

Gate Coupling to Nanoscale ElectronicsDec 16 2008May 07 2009The realization of single-molecule electronic devices, in which a nanometer-scale molecule is connected to macroscopic leads, requires the reproducible production of highly ordered nanoscale gaps in which a molecule of interest is electrostatically coupled ... More

Effective pairing interaction in a system with an incipient bandJan 29 2019The nature and mechanism of superconductivity in the extremely electron-doped FeSe based superconductors continues to be a matter of debate. In these systems, the hole-like band has moved below the Fermi energy, and various spin-fluctuation theories involving ... More

The Slice Spectral Sequence for certain $RO(C_{p^n})$-graded Suspensions of $H\underline{\mathbb Z}$Oct 20 2015We study the slice filtration and associated spectral sequence for a family of $RO(C_{p^{n}})$-graded suspensions of the Eilenberg-MacLane spectrum for the constant Mackey functor $\underline{\mathbb Z}$. Since $H\underline{\mathbb Z}$ is the zero slice ... More

Homological obstructions to string orientationsOct 12 2008We observe that the Poincare duality isomorphism for a string manifold is an isomorphism of modules over the subalgebra A(2) of the modulo 2 Steenrod algebra. In particular, the pattern of the operations Sq^1, Sq^2, and Sq^4 on the cohomology of a string ... More

Gravity Modes Reveal the Internal Rotation of a Post-mass Transfer Gamma Doradus/Delta Scuti Hybrid Pulsator in Kepler Eclipsing Binary KIC 9592855Apr 12 2017Oct 31 2017We report the discovery of a post-mass transfer Gamma Doradus/Delta Scuti hybrid pulsator in the eclipsing binary KIC~9592855. This binary has a circular orbit, an orbital period of 1.2 days, and contains two stars of almost identical masses ($M_1=1.72M_{\odot}, ... More

Total Dominating Sequences in GraphsJan 27 2016A vertex in a graph totally dominates another vertex if they are adjacent. A sequence of vertices in a graph $G$ is called a total dominating sequence if every vertex $v$ in the sequence totally dominates at least one vertex that was not totally dominated ... More

Morphing of Geometric Composites via Residual SwellingApr 12 2015May 30 2015Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such ... More

Supporting Online Material for "Strong Interactions in Multimode Random Lasers"May 29 2008This preprint contains the Supporting Online Material for our paper ''Strong Interactions in Multimode Random Lasers'', Science 320, 643 (2008) (also available at: arXiv:0805.4496).

Current noise enhancement: channel mixing and possible nonequilibrium phonon backaction in atomic-scale Au junctionsOct 05 2016We report measurements of the bias dependence of the Fano factor in ensembles of atomic-scale Au junctions at 77 K. Previous measurements of shot noise at room temperature and low biases have found good agreement of the Fano factor with the expectations ... More

Heisenberg model in a random field: phase diagram and tricritical behaviorMar 19 2002By using the differential operator technique and the effective field theory scheme we study the tricritical behavior of Heisenberg classical model of spin-1/2 in a random field. The phase diagram in the T-h plane on a square and simple cubic lattice for ... More

On the non-existence of elements of Kervaire invariant oneAug 26 2009May 25 2015We show that Kervaire invariant one elements in the homotopy groups of spheres exist only in dimensions at most 126. By Browder's Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14, 30, 62, and ... More

Ascent sequences avoiding pairs of patternsJun 16 2014Feb 15 2015Ascent sequences were introduced by Bousquet-Melou et al. in connection with (2+2)-avoiding posets and their pattern avoidance properties were first considered by Duncan and Steingrimsson. In this paper, we consider ascent sequences of length $n$ avoiding ... More

Enumeration schemes for vincular patternsAug 12 2011Jan 16 2012We extend the notion of an enumeration scheme developed by Zeilberger and Vatter to the case of vincular patterns (also called "generalized patterns" or "dashed patterns"). In particular we provide an algorithm which takes in as input a set $B$ of vincular ... More

Pattern avoidance by even permutationsJun 18 2011We study questions of even-Wilf-equivalence, the analogue of Wilf-equivalence when attention is restricted to pattern avoidance by permutations in the alternating group. Although some Wilf-equivalence results break when considering even-Wilf-equivalence ... More

Automatic Generation of Theorems and Proofs on Enumerating Consecutive-Wilf classesJan 20 2011This article, dedicated to Herbert Saul Wilf on the occaison of his forthcoming 80-th birthday, describes two complementary approaches to enumeration, the "positive" and the "negative", each with its advantages and disadvantages. Both approaches are amenable ... More

Stopping time convergence for processes associated with Dirichlet formsMay 27 2017Jun 29 2017Convergence is proved for solutions of Dirichlet problems in regions with many small excluded sets (holes), as the holes become smaller and more numerous. The problem is formulated in the context of Markov processes associated with general Dirichlet forms, ... More

Spitzer Observations of CO2 Ice Towards Field Stars in the Taurus Molecular CloudMay 17 2005We present the first Spitzer Infrared Spectrograph observations of the 15.2 micron bending mode of CO2 ice towards field stars behind a quiescent dark cloud. CO2 ice is detected towards 2 field stars (Elias 16, Elias 3) and a single protostar (HL Tau) ... More

Connecting Defects and Amorphization in UiO-66 and MIL-140 Metal-organic Frameworks: A Combined Experimental and Computational StudyOct 28 2015The mechanism and products of the structural collapse of the metal-organic frameworks (MOFs) UiO-66, MIL-140B and MIL-140C upon ball-milling are investigated through solid state 13C NMR and pair distribution function (PDF) studies, finding amorphization ... More

The evolution of galaxy formationDec 01 2011Our history of understanding galaxy formation could be traced through the development of individual ideas. A cynic might be tempted to suggest that new catchphrases are developed at a faster rate than genuine progress is made.

CMB ANISOTROPIES: AN OVERVIEWFeb 02 1995A brief outline of the current status of CMB anisotropies and what they might mean, heavily biased towards the perspective of Berkeley theorists. Based on a talk presented at the 17th Texas Symposium on Relativistic Astrophysics held in Munich, December ... More

Scaling limits of Markov branching trees and Galton-Watson trees conditioned on the number of vertices with out-degree in a given setMay 12 2011Sep 22 2013We generalize recent results of Haas and Miermont to obtain scaling limits of Markov branching trees whose size is specified by the number of nodes whose out-degree lies in a given set. We then show that this implies that the scaling limit of finite variance ... More

Explicit points on the Legendre curve IIIJun 25 2014Nov 24 2014We continue our study of the Legendre elliptic curve y^2=x(x+1)(x+t) over function fields K_d=F_p(\mu_d,t^{1/d}). When d=p^f+1, we have previously exhibited explicit points generating a subgroup V_d of E(K_d) of rank d-2 and of finite, p-power index. ... More

Many-anyon trial statesAug 17 2016The problem of bounding the (abelian) many-anyon ground-state energy from above, with a dependence on the statistics parameter which matches that of currently available lower bounds, is reduced to studying the correlation functions of Moore-Read (Pfaffian) ... More

Many-anyon trial statesAug 17 2016Dec 05 2016The problem of bounding the (abelian) many-anyon ground-state energy from above, with a dependence on the statistics parameter which matches that of currently available lower bounds, is reduced to studying the correlation functions of Moore-Read (Pfaffian) ... More

L-functions with large analytic rank and abelian varieties with large algebraic rank over function fieldsSep 25 2006The goal of this paper is to explain how a simple but apparently new fact of linear algebra together with the cohomological interpretation of L-functions allows one to produce many examples of L-functions over function fields vanishing to high order at ... More

A Leray-Serre spectral sequence for Lagrangian Floer theoryJan 26 2017Mar 26 2018We show tranversality and compactness for the moduli of pearly Morse trajectories on a Lagrangian in a compact symplectic fiber bundle with rational base and small monotone fibers. We then derive a spectral sequence in the vein of the classical Leray-Serre ... More

Transversality via gauge transformations for pseudo holomorphic disks in projectivized vector bundlesNov 26 2018We show that one can achieve transversality for lifts of holomorphic disks to a projectivized vector bundle by locally enlarging the structure group and considering the action of gauge transformations on the almost complex structure, which eases computation ... More

Geometric extensions of many-particle Hardy inequalitiesJan 13 2011Oct 12 2014Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy inequalities ... More

Weighted Supermembrane Toy ModelApr 29 2009Mar 25 2010A weighted Hilbert space approach to the study of zero-energy states of supersymmetric matrix models is introduced. Applied to a related but technically simpler model, it is shown that the spectrum of the corresponding weighted Hamiltonian simplifies ... More

Modelling resonances and orbital chaos in disk galaxies. Application to a Milky Way spiral modelAug 31 2016Oct 19 2016Context: Resonances in the stellar orbital motion under perturbations from spiral arms structure play an important role in the evolution of the disks of spiral galaxies. The epicyclic approximation allows the determination of the corresponding resonant ... More

Some spectral bounds for Schroedinger operators with Hardy-type potentialsNov 17 2009This note points out some bounds for the number of negative eigenvalues of Schroedinger operators with Hardy-type potentials, which follow from a simple coordinate transformation, and could prove useful in a spectral analysis of certain supersymmetric ... More

Adjusting for bias introduced by instrumental variable estimation in the Cox Proportional Hazards ModelNov 07 2017Instrumental variable (IV) methods are widely used for estimating average treatment effects in the presence of unmeasured confounders. However, the capability of existing IV procedures, and most notably the two-stage residual inclusion (2SRI) procedure ... More

Assouad type dimensions for partially affine spongesOct 13 2016Recently self-affine sponges have been shown to be interesting examples and counter-examples to several previously open problems. One class of recently discovered sponges are partially affine Bedford-McMullen sponges whose Assouad type dimensions cannot ... More