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Sparticles in Motion - getting to the line in compressed scenarios with the Recursive Jigsaw ReconstructionJul 28 2016The observation of light super-partners from a supersymmetric extension to the Standard Model is an intensely sought-after experimental outcome, providing an explanation for the stabilization of the electroweak scale and indicating the existence of new ... More

Multizeta values: Lie algebras and periods on $\mathfrak{M}_{0,n}$Nov 13 2009This thesis is a study of algebraic and geometric relations between multizeta values. In chapter 2, we prove a result which gives the dimension of the associated depth-graded pieces of the double shuffle Lie algebra in depths 1 and 2. In chapters 3 and ... More

Baryonic and Non-Baryonic Dark MatterAug 01 2000Cosmological nucleosynthesis calculations imply that there should be both non-baryonic and baryonic dark matter. Recent data suggest that some of the non-baryonic dark matter must be "hot" (i.e. massive neutrinos) and there may also be evidence for "cold" ... More

A polygonal presentation of $Pic(\overline{\mathfrak{M}}_{0,n})$Nov 13 2009In the first section of this article, we recall Keel's well-known presentation of $Pic(\overline{\mathfrak{M}}_{0,n})$ using irreducible boundary divisors of $\overline{\mathfrak{M}}_{0,n}$ as generators, and describe a basis for $Pic(\overline{\mathfrak{M}}_{0,n})$ ... More

Two-generator subgroups of right-angled Artin groups are quasi-isometrically embeddedDec 01 2014Oct 13 2015We show that non-abelian two-generator subgroups of right-angled Artin groups are quasi-isometrically embedded free groups. This provides an alternate proof of a theorem of A. Baudisch: that all two-generator subgroups are free or free abelian. Additionally, ... More

Primordial black holes as dark matter and generators of cosmic structureJan 23 2019Primordial black holes (PBHs) could provide the dark matter but a variety of constraints restrict the possible mass windows to $10^{16} - 10^{17}$g, $10^{20} - 10^{24}$g and $10 - 10^3M_{\odot}$. The last possibility is of special interest in view of ... More

Non Trivial Effects in Heavy Nuclear Systems due to Charge RearrangementSep 27 2003Dec 04 2003In this report we propose that a charge rearrangement within heavy ions may occur during fusion reactions, lowering the Coulomb barrier as the nuclear systems approach each other. In this situation a modified Gamow factor has been calculated, which emphasizes ... More

Periods on the moduli space of genus 0 curvesNov 13 2009This report outlines a combinatorial recipe for computing the bases, whose elements are oriented polygons, of two cohomology spaces associated to multizeta values: the top dimensional de Rham cohomology of moduli spaces of genus 0 complex pointed curves ... More

Super-Razor and Searches for Sleptons and Charginos at the LHCOct 17 2013Direct searches for electroweak pair production of new particles at the LHC are a difficult proposition, due to the large background and low signal cross sections. We demonstrate how these searches can be improved by a combination of new razor variables ... More

Mixing inequalities in Riesz spacesJul 14 2017Various topics in stochastic processes have been considered in the abstract setting of Riesz spaces, for example martingales, martingale convergence, ergodic theory, AMARTS, Markov processes and mixingales. Here we continue the relaxation of conditional ... More

Primordial black holes as a probe of the early universe and a varying gravitational constantFeb 22 2001Mar 20 2001We discuss recent developments in the study of primordial black holes, focussing particularly on their formation and quantum evaporation. Such studies can place important constraints on models of the early Universe. An especially interesting development ... More

Primordial Black Holes and Quantum EffectsFeb 06 2014Primordial black holes (PBHs) are of special interest because of the crucial role of quantum effects in their formation and evaporation. This means that they provide a unique probe of the early universe, high-energy physics and quantum gravity. We highlight ... More

On the initial-value problem of the Maxwell-Lorentz equationsJul 06 2010Oct 03 2010We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell's equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and constraints, and ... More

Local Variance Gamma and Explicit Calibration to Option PricesAug 10 2013Jan 31 2014In some options markets (e.g. commodities), options are listed with only a single maturity for each underlying. In others, (e.g. equities, currencies), options are listed with multiple maturities. In this paper, we provide an algorithm for calibrating ... More

Using pseudo-parabolic and fractional equations for option pricing in jump diffusion modelsFeb 09 2010In mathematical finance a popular approach for pricing options under some Levy model is to consider underlying that follows a Poisson jump diffusion process. As it is well known this results in a partial integro-differential equation (PIDE) that usually ... More

Concerning the Representability of Self-Reference in ArithmeticSep 05 2011Jan 27 2012Terms in arithmetic of the form s in the formula s=t(< s >), with t a term with one free variable and < s > a numeral denoting the G\"odel number of s, are examined by writing the explicit definition of the encoding functions whose representation they ... More

FX Options in Target ZoneDec 04 2015Jul 28 2016In this note we discuss - in what is intended to be a pedagogical fashion - FX option pricing in target zones with attainable boundaries. The boundaries must be reflecting. The no-arbitrage requirement implies that the differential (foreign minus domestic) ... More

Geometric Local Variance Gamma modelSep 19 2018Dec 25 2018This paper describes another extension of the Local Variance Gamma model originally proposed by P. Carr in 2008, and then further elaborated on by Carr and Nadtochiy, 2017 (CN2017), and Carr and Itkin, 2018 (CI2018). As compared with the latest version ... More

Complete graph decompositions and p-groupoidsApr 09 2019We study P-groupoids that arise from certain decompositions of complete graphs. We show that left distributive P-groupoids are distributive, quasigroups. We characterize P-groupoids when the corresponding decomposition is a Hamiltonian decomposition for ... More

Bessel processes, the integral of geometric Brownian motion, and Asian optionsNov 17 2003This paper is motivated by questions about averages of stochastic processes which originate in mathematical finance, originally in connection with valuing the so-called Asian options. Starting with research of Yor's in 1992, these questions about exponential ... More

The Black Hole Uncertainty Principle CorrespondenceFeb 06 2014The Black Hole Uncertainty Principle correspondence proposes a connection between the Uncertainty Principle on microscopic scales and black holes on macroscopic scales. This is manifested in a unified expression for the Compton wavelength and Schwarzschild ... More

Baryonic Dark Matter in GalaxiesAug 01 2000Cosmological nucleosynthesis calculations imply that many of the baryons in the Universe must be dark. We discuss the likelihood that some of these dark baryons may reside in the discs or halos of galaxies. If they were in the form of compact objects, ... More

Spherically symmetric self-similar solutions and their astrophysical and cosmological applicationsMar 02 2000We discuss spherically symmetric perfect fluid solutions of Einstein's equations which have equation of state ($p=\alpha \mu$) and which are self-similar in the sense that all dimensionless variables depend only upon $z\equiv r/t$. For each value of $\alpha$, ... More

ADOL - Markovian approximation of rough lognormal modelApr 19 2019In this paper we apply Markovian approximation of the fractional Brownian motion (BM), known as the Dobric-Ojeda (DO) process, to the fractional stochastic volatility model where the instantaneous variance is modelled by a lognormal process with drift ... More

Robust replication of barrier-style claims on price and volatilityAug 04 2015We show how to price and replicate a variety of barrier-style claims written on the $\log$ price $X$ and quadratic variation $\<X\>$ of a risky asset. Our framework assumes no arbitrage, frictionless markets and zero interest rates. We model the risky ... More

Primordial Black Holes - Recent DevelopmentsApr 01 2005Recent developments in the study of primordial black holes (PBHs) will be reviewed, with particular emphasis on their formation and evaporation. PBHs could provide a unique probe of the early Universe, gravitational collapse, high energy physics and quantum ... More

A classification of spherically symmetric self-similar dust modelsMar 02 2000We classify all spherically symmetric dust solutions of Einstein's equations which are self-similar in the sense that all dimensionless variables depend only upon $z\equiv r/t$. We show that the equations can be reduced to a special case of the general ... More

Recent developments in the search for baryonic dark matterFeb 22 2001Mar 20 2001Cosmological nucleosynthesis calculations imply that many of the baryons in the Universe must be dark. We discuss the likelihood that some of these dark baryons may reside in galaxies as Massive Compact Halo Objects (MACHOs), the remnants of a first generation ... More

Primordial Black Holes With Multi-Modal Mass SpectraNov 15 2018A mechanism for generating primordial black hole mass spectra with many spikes is proposed and investigated. This mechanism relies on the choice of non-Bunch-Davies vacua, these leading to oscillatory features in the inflationary power spectrum. This ... More

Characteristic time scales for diffusion processes through layers and across interfacesJan 16 2018Apr 12 2018This paper presents a simple tool for characterising the timescale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, ... More

Calculating how long it takes for a diffusion process to effectively reach steady state without computing the transient solutionApr 21 2017Jul 11 2017Mathematically, it takes an infinite amount of time for the transient solution of a diffusion equation to transition from initial to steady state. Calculating a \textit{finite} transition time, defined as the time required for the transient solution to ... More

The Compton-Schwarzschild correspondence from extended de Broglie relationsMay 26 2015Apr 05 2016The Compton wavelength gives the minimum radius within which the mass of a particle may be localized due to quantum effects, while the Schwarzschild radius gives the maximum radius within which the mass of a black hole may be localized due to classial ... More

Preparation of entangled and antiferromagnetic states by dissipative Rydberg pumpingApr 23 2013Jun 06 2013We propose and analyze an approach for preparation of high fidelity entanglement and antiferromagnetic states using Rydberg mediated interactions with dissipation. Using asymmetric Rydberg interactions the two-atom Bell singlet is a dark state of the ... More

The separate universe problem: 40 years onMay 14 2014The claim that an overdense (positive curvature) region in the early universe cannot extend beyond some maximum scale and remain part of our universe, first made 40 years ago, has recently been questioned by Kopp et al. Their analysis is elucidating and ... More

Quantum teleportation between nanomechanical modesDec 19 2005We study a quantum teleportation scheme between two nanomechanical modes without local interaction. The nanomechanical modes are linearly coupled to and connected by the continuous variable modes of a superconducting circuit consisting of a transmission ... More

Spacetime structure of self-similar spherically symmetric perfect fluid solutionsSep 24 2002Dec 09 2002We classify all spherically symmetric and homothetic spacetimes that are allowed kinematically by constructing them from a small number of building blocks. We then restrict attention to a particular dynamics, namely perfect fluid matter with the scale-free ... More

Limits of sympathetic cooling of fermions: The role of the heat capacity of the coolantOct 28 2003Jun 16 2004The sympathetic cooling of an initially degenerate Fermi gas by either an ideal Bose gas below $T_c$ or an ideal Boltzmann gas is investigated. It is shown that the efficiency of cooling by a Bose gas below $T_c$ is by no means reduced when its heat capacity ... More

Dynamics of a matter-wave bright soliton in an expulsive potentialMay 29 2002May 31 2002The stability regimes and nonlinear dynamics of bright solitons created in a harmonic potential which is transversely attractive and longitudinally expulsive are presented. This choice of potential is motivated by the recent creation of a matter-wave ... More

The Compton-Schwarzschild relations in higher dimensionsNov 07 2016In three spatial dimensions, the Compton wavelength $(R_C \propto M$) and Schwarzschild radius $(R_S \propto M^{-1}$) are dual under the transformation $M \rightarrow M_{P}^2/M$, where $M_{P}$ is the Planck mass. This suggests that there is a fundamental ... More

Emergent topological properties in interacting one-dimensional systems with spin-orbit couplingApr 20 2015Jul 27 2015We present analysis of a single channel interacting quantum wire problem in the presence of spin-orbit interaction. The spin-orbit coupling breaks the spin-rotational symmetry from SU(2) to U(1) and breaks inversion symmetry. The low-energy theory is ... More

A THz time-domain susceptibility for superconductors including strong-current effectsJul 19 2013Oct 08 2013Finite-difference time-domain methods are increasingly being used to develop, model and analyze the response of materials, including engineered metamaterials that may contain superconductors. Though simple and useful expressions for the time-domain susceptibility ... More

Graph Neural Processes: Towards Bayesian Graph Neural NetworksFeb 26 2019We introduce Graph Neural Processes (GNP), inspired by the recent work in conditional and latent neural processes. A Graph Neural Process is defined as a Conditional Neural Process that operates on arbitrary graph data. It takes features of sparsely observed ... More

Modelling mass diffusion for a multi-layer sphere immersed in a semi-infinite medium: application to drug deliveryJan 16 2018We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing ... More

Primordial Black Holes as a Probe of Cosmology and High Energy PhysicsOct 29 2003Recent developments in the study of primordial black holes (PBHs) will be reviewed, with particular emphasis on their formation and evaporation. PBHs could provide a unique probe of the early Universe, gravitational collapse, high energy physics and quantum ... More

Primordial Black Holes: Do They Exist and Are They Useful?Nov 26 2005Recent developments in the study of primordial black holes (PBHs) are reviewed, with particular emphasis on their formation and evaporation. It is still not clear whether PBHs formed but, if they did, they could provide a unique probe of the early Universe, ... More

Primordial Black Holes as Generators of Cosmic StructuresJan 02 2018Jun 23 2018Primordial black holes (PBHs) could provide the dark matter in various mass windows below $10^2 M_{\odot}$ and those of $30 M_{\odot}$ might explain the LIGO events. PBHs much larger than this might have important consequences even if they provide only ... More

Strong correlation effects in single-wall carbon nanotubesNov 07 2008We present an overview of strong correlations in single-wall carbon nanotubes, and an introduction to the techniques used to study them theoretically. We concentrate on zigzag nanotubes, although universality dictates that much ofthe theory can also be ... More

Rear-surface integral method for calculating thermal diffusivity from laser flash experimentsSep 15 2018The laser flash method for measuring thermal diffusivity of solids involves subjecting the front face of a small sample to a heat pulse of radiant energy and recording the resulting temperature rise on the opposite (rear) surface. For the adiabatic case, ... More

Geometries, the principle of duality, and algebraic groupsMar 10 2005Sep 09 2005Jacques Tits gave a general recipe for producing an abstract geometry from a semisimple algebraic group. This expository paper describes a uniform method for giving a concrete realization of Tits's geometry and works through several examples. We also ... More

Super-horizon primordial black holesAug 04 2005Aug 24 2005We discuss a new class of solutions to the Einstein equations which describe a primordial black hole (PBH) in a flat Friedmann background. Such solutions arise if a Schwarzschild black hole is patched onto a Friedmann background via a transition region. ... More

Higher-order quantum bright solitons in Bose-Einstein condensates show truly quantum emergent behaviorDec 16 2016When an interaction quench by a factor of four is applied to an attractive Bose-Einstein condensate, a higher-order quantum bright soliton exhibiting robust oscillations is predicted in the semiclassical limit by the Gross-Pitaevskii equation. Combining ... More

On flips of unitary buildings I: Classification of flipsDec 10 2010We classify flips of buildings arising from non-degenerate unitary spaces of dimension at least 4 over finite fields of odd characteristic in terms of their action on the underlying vector space. We also construct certain geometries related to flips and ... More

Upper limits on the size of a primordial black holeDec 06 2004May 11 2005We provide precise constraints on the size of any black holes forming in the early Universe for a variety of formation scenarios. In particular, we prove that the size of the apparent horizon of a primordial black hole formed by causal processes in a ... More

On the Linear Independence of RootsMar 19 2007Sep 14 2007A set of real $n$th roots that is pairwise linearly independent over the rationals must also be linearly independent. We show how this result may be extended to more general fields.

Nucleation of superfluid-light domains in a quenched dynamicsFeb 03 2018Aug 15 2018Strong correlation effects emerge from light-matter interactions in coupled resonator arrays, such as the Mott-insulator to superfluid phase transition of atom-photon excitations. We demonstrate that the quenched dynamics of a finite-sized complex array ... More

Doubly magic optical trapping for Cs atom hyperfine clock transitionsJun 13 2014Sep 19 2016We analyze doubly magic trapping of Cs hyperfine transitions including previously neglected contributions from the ground state hyperpolarizability and the interaction of the laser light and a static magnetic field. Extensive numerical searches do not ... More

Growth of primordial black holes in a universe containing a massless scalar fieldDec 06 2004May 11 2005The evolution of primordial black holes in a flat Friedmann universe with a massless scalar field is investigated in fully general relativistic numerical relativity. A primordial black hole is expected to form with a scale comparable to the cosmological ... More

Does Compton/Schwarzschild duality in higher dimensions exclude TeV quantum gravity?Aug 25 2018Dec 31 2018In three spatial dimensions, the Compton wavelength $(R_C \propto M^{-1}$) and Schwarzschild radius $(R_S \propto M$) are dual under the transformation $M \rightarrow M_{P}^2/M$, where $M_{P}$ is the Planck mass. This suggests that there could be a fundamental ... More

Drug delivery from microcapsules: how can we estimate the release time?Jan 24 2019Predicting the release performance of a drug delivery device is an important challenge in pharmaceutics and biomedical science. In this paper, we consider a multi-layer diffusion model of drug release from a composite spherical microcapsule into an external ... More

Primordial black holes and gravitational memoryMar 02 2000We discuss the various ways in which primordial black holes may have formed in the early Universe and how the effects of such black holes can be used to place constraints on cosmological models. We show that such constraints may be severely modified if ... More

Primordial Black Holes as Dark MatterJul 20 2016Aug 08 2016The possibility that the dark matter comprises primordial black holes (PBHs) is considered, with particular emphasis on the currently allowed mass windows at $10^{16}$ -- $10^{17}\,$g, $10^{20}$ -- $10^{24}\,$g and $1$ -- $10^{3}\,M_{\odot}$. The Planck ... More

Persistence of black holes through a cosmological bounceApr 19 2011We discuss whether black holes could persist in a universe which recollapses and then bounces into a new expansion phase. Whether the bounce is of classical or quantum gravitational origin, such cosmological models are of great current interest. In particular, ... More

Self-Similarity in General Relativity \endtitleJun 09 1998The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the ``first'' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classes of self-similar solutions ... More

Metastable quantum phase transitions in a periodic one-dimensional Bose gas: II. Many-body theoryOct 15 2009May 10 2010We show that quantum solitons in the Lieb-Liniger Hamiltonian are precisely the yrast states. We identify such solutions clearly with Lieb's type II excitations from weak to strong interactions, clarifying a long-standing question of the physical meaning ... More

The nonlinear Dirac equation in Bose-Einstein condensates: Superfluid fluctuations and emergent theories from relativistic linear stability equationsFeb 26 2015Oct 07 2015We present the theoretical and mathematical foundations of stability analysis for a Bose-Einstein condensate (BEC) at Dirac points of a honeycomb optical lattice. The combination of s-wave scattering for bosons and lattice interaction places constraints ... More

Group Theoretic Bases for Tribimaximal MixingJan 04 2007Mar 20 2007Present data on neutrino masses and mixing favor the highly symmetric tribimaximal neutrino mixing matrix which suggests an underlying flavor symmetry. A systematic study of non-abelian finite groups of order $g \leq 31$ reveals that tribimaximal mixing ... More

Can a primordial black hole or wormhole grow as fast as the universe?Mar 17 2010This review addresses the issue of whether there are physically realistic self-similar solutions in which a primordial black hole is attached to an exact or asymptotically Friedmann model for an equation of state of the form $p=(\gamma-1)\rho c^2$. In ... More

Driven two-component Bose-Einstein condensate in optical latticesOct 28 2016Nov 02 2016We explore quantum many-body physics of a driven Bose-Einstein condensate and present exact results for the Rabi-Bogoliubov spectrum and amplitudes of the condensate. We find a gap in the spectrum of elementary excitations that amounts to the effective ... More

Transport through nanostructures: Finite time vs. finite sizeJul 29 2013Aug 26 2013Numerical simulations and experiments on nanostructures out of equilibrium usually exhibit strong finite size and finite measuring time $t_m$ effects. We discuss how these affect the determination of the full counting statistics for a general quantum ... More

Superconductivity and Charge Density Wave in a Quasi-One-Dimensional Spin Gap SystemNov 14 2001Jan 24 2002We consider a model of spin-gapped chains weakly coupled by Josephson and Coulomb interactions. Combining such non-perturbative methods as bosonization and Bethe ansatz to treat the intra-chain interactions with the Random Phase Approximation for the ... More

Pricing Variance Swaps on Time-Changed Markov ProcessesMay 02 2017We prove that the variance swap rate equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving ... More

Robust replication of barrier-style claims on price and volatilityAug 04 2015May 03 2017We show how to price and replicate a variety of barrier-style claims written on the $\log$ price $X$ and quadratic variation $\langle X \rangle$ of a risky asset. Our framework assumes no arbitrage, frictionless markets and zero interest rates. We model ... More

A common origin for baryons and dark matterApr 25 2019The origin of the baryon asymmetry of the Universe (BAU) and the nature of dark matter are two of the most challenging problems in cosmology. We propose a scenario in which the gravitational collapse of large inhomogeneities at the quark-hadron epoch ... More

Evolutionary genomics of transposable elements in Saccharomyces cerevisiaeSep 01 2012Saccharomyces cerevisiae is one of the premier model systems for studying the genomics and evolution of transposable elements. The availability of the S. cerevisiae genome led to many insights into its five known transposable element families (Ty1-Ty5) ... More

A complete classification of spherically symmetric perfect fluid similarity solutionsJan 18 1999We classify all spherically symmetric perfect fluid solutions of Einstein's equations with equation of state p/mu=a which are self-similar in the sense that all dimensionless variables depend only upon z=r/t. For a given value of a, such solutions are ... More

Spatial Dependence of Entropy in Trapped Ultracold Bose GasesJun 25 2009We find a new physical regime in the trapped Bose-Hubbard Hamiltonian using time-evolving block decimation. Between Mott-insulating and superfluid phases, the latter induced by trap compression, a spatially self-organized state appears in which non-local ... More

The nonlinear Dirac equation in Bose-Einstein condensates: Vortex solutions and spectra in a weak harmonic trapFeb 19 2015Nov 03 2015We analyze the vortex solution space of the $(2 +1)$-dimensional nonlinear Dirac equation for bosons in a honeycomb optical lattice at length scales much larger than the lattice spacing. Dirac point relativistic covariance combined with s-wave scattering ... More

Infrared Searches for Dark Matter in the Form of Brown DwarfsSep 02 1993Brown dwarfs, stars with insufficient mass to burn hydrogen, could contribute to the dark matter in the Galactic disk, galactic halos or even a background critical density. We consider the detectability of such brown dwarfs in various scenarios, extending ... More

Limits on primordial black holes from $μ$ distortions in cosmic microwave backgroundOct 18 2017Feb 24 2018If primordial black holes (PBHs) form directly from inhomogeneities in the early Universe, then the number in the mass range $10^5 -10^{12}M_{\odot}$ is severely constrained by upper limits to the $\mu$ distortion in the cosmic microwave background (CMB). ... More

Dipole-dipole interactions in optical lattices do not follow an inverse cube power lawMar 06 2013Jul 17 2013We study the effective dipole-dipole interactions in ultracold quantum gases on optical lattices as a function of asymmetry in confinement along the principal axes of the lattice. In particular, we study the matrix elements of the dipole-dipole interaction ... More

Cosmological wormholesJan 08 2009Mar 03 2009Motivated by the cosmological wormhole solutions obtained from our recent numerical investigations, we provide a definition of a wormhole which applies to dynamical situations. Our numerical solutions do not have timelike trapping horizons but they are ... More

Full counting statistics in the not-so-long-time limitMay 13 2014The full counting statistics of charge transport is the probability distribution $p_n(t_m)$ that $n$ electrons have flown through the system in measuring time $t_m$. The cumulant generating function (CGF) of this distribution $F(\chi,t_m)$ has been well ... More

Vortices and Ring Solitons in Bose-Einstein CondensatesAug 20 2004Oct 19 2006The form and stability properties of axisymmetric and spherically symmetric stationary states in two and three dimensions, respectively, are elucidated for Bose-Einstein condensates. These states include the ground state, central vortices, and radial ... More

Vortices in attractive Bose-Einstein condensates in two dimensionsAug 23 2004Mar 28 2006The form and stability of quantum vortices in Bose-Einstein condensates with attractive atomic interactions is elucidated. They appear as ring bright solitons, and are a generalization of the Townes soliton to nonzero winding number $m$. An infinite sequence ... More

Pseudograph associahedraMay 14 2010Given a simple graph G, the graph associahedron KG is a simple polytope whose face poset is based on the connected subgraphs of G. This paper defines and constructs graph associahedra in a general context, for pseudographs with loops and multiple edges, ... More

Organic Molecules and Water in the Inner Disks of T Tauri StarsApr 01 2011We report high signal-to-noise Spitzer IRS spectra of a sample of eleven classical T Tauri stars. Molecular emission from rotational transitions of H2O and OH and ro-vibrational bands of simple organic molecules (CO2, HCN, C2H2) is common among the sources ... More

Probing the Galactic Dark Matter Mass Funtion Using Microlensing and Direct SearchesDec 02 1994If compact baryonic objects contribute significantly to the dark matter in our Galaxy, their mass function will present vital clues for galaxy formation theories and star formation processes in the early Universe. Here we discuss what one might expect ... More

Self-similar cosmological solutions with dark energy. II: black holes, naked singularities and wormholesJul 04 2007Jan 02 2008We use a combination of numerical and analytical methods, exploiting the equations derived in a preceding paper, to classify all spherically symmetric self-similar solutions which are asymptotically Friedmann at large distances and contain a perfect fluid ... More

Tolman-Bondi collapse in scalar-tensor theories as a probe of gravitational memoryDec 31 2001Oct 08 2002In cosmological models with a varying gravitational constant, it is not clear whether primordial black holes preserve the value of $G$ at their formation epoch. We investigate this question by using the Tolman-Bondi model to study the evolution of a background ... More

Limits of sympathetic cooling of fermions by zero temperature bosons due to particle lossesMay 19 2003Feb 23 2004It has been suggested by Timmermans [Phys. Rev. Lett. {\bf 87}, 240403 (2001)] that loss of fermions in a degenerate system causes strong heating. We address the fundamental limit imposed by this loss on the temperature that may be obtained by sympathetic ... More

An asymptotic analysis of spherically symmetric perfect fluid self-similar solutionsAug 01 2000The asymptotic properties of self-similar spherically symmetric perfect fluid solutions with equation of state p=alpha mu (-1<alpha<1) are described. We prove that for large and small values of the similarity variable, z=r/t, all such solutions must have ... More

Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensatesJun 19 2010Jan 05 2011We present relativistic linear stability equations (RLSE) for quasi-relativistic cold atoms in a honeycomb optical lattice. These equations are derived from first principles and provide a method for computing stabilities of arbitrary localized solutions ... More

The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and SymmetriesMar 20 2008We show that Bose-Einstein condensates in a honeycomb optical lattice are described by a nonlinear Dirac equation in the long wavelength, mean field limit. Unlike nonlinear Dirac equations posited by particle theorists, which are designed to preserve ... More

Metastable Quantum Phase Transitions in a Periodic One-dimensional Bose Gas: Mean-Field and Bogoliubov AnalysesJan 28 2009May 10 2010We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for \emph{metastable states} in \emph{finite size systems}. In particular, we treat the one-dimensional ... More

Primordial Black Holes as Dark MatterJul 20 2016Oct 07 2016The possibility that the dark matter comprises primordial black holes (PBHs) is considered, with particular emphasis on the currently allowed mass windows at $10^{16}$ - $10^{17}\,$g, $10^{20}$ - $10^{24}\,$g and $1$ - $10^{3}\,M_{\odot}$. The Planck ... More

Out of equilibrium dynamics with Matrix Product StatesMay 04 2012Theoretical understanding of strongly correlated systems in one spatial dimension (1D) has been greatly advanced by the density-matrix renormalization group (DMRG) algorithm, which is a variational approach using a class of entanglement-restricted states ... More

Primordial Black Holes as Dark MatterJul 20 2016Mar 22 2017The possibility that the dark matter comprises primordial black holes (PBHs) is considered, with particular emphasis on the currently allowed mass windows at $10^{16}$ - $10^{17}\,$g, $10^{20}$ - $10^{24}\,$g and $1$ - $10^{3}\,M_{\odot}$. The Planck ... More

Black holes as echoes of previous cosmic cyclesApr 10 2017The existence of exact solutions which represent a lattice of black holes at a scalar-field-dominated cosmological bounce suggests that black holes could persist through successive eras of a cyclic cosmology. Here we explore some remarkable cosmological ... More

Domain Adaptation through Synthesis for Unsupervised Person Re-identificationApr 26 2018Drastic variations in illumination across surveillance cameras make the person re-identification problem extremely challenging. Current large scale re-identification datasets have a significant number of training subjects, but lack diversity in lighting ... More

Topological Winding and Unwinding in Metastable Bose-Einstein CondensatesApr 24 2007Feb 12 2008Topological winding and unwinding in a quasi-one-dimensional metastable Bose-Einstein condensate are shown to be manipulated by changing the strength of interaction or the frequency of rotation. Exact diagonalization analysis reveals that quasidegenerate ... More