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Quantum, Nonlocal Aberration CancellationJun 11 2019Phase distortions, or aberrations, can negatively influence the performance of an optical imaging system. Through the use of position-momentum entangled photons, we nonlocally correct for aberrations in one photon's optical path by intentionally introducing ... More

A 3D Kinematic Study of the Northern Ejecta "Jet" of the Crab NebulaDec 09 2014Dec 11 2014We present [O III] 4959,5007 emission line spectra (FWHM = 40 km/s) of the Crab Nebula's northern ejecta `jet'. These data, along with a recent [O III] image of the Crab, are used to build 3-dimensional models of the jet and adjacent remnant nebulosity ... More

Topological Superconductivity in Two Dimensions with Mixed ChiralityMar 09 2015Nov 02 2015We find a mixed chirality $d$-wave superconducting state in the coexistence region between antiferromagnetism and interaction-driven superconductivity in lightly doped honeycomb materials. This state has a topological chiral $d+id$-wave symmetry in one ... More

The Scalar Sector and the Eta -> 3 Pi ProblemApr 17 2003First, recent work on light scalar mesons, which is of possible interest in connection with the strong coupling region of QCD is briefly discussed. Then a very short highlighting of a paper concerned with an application to the eta -> 3 pi problem is presented. ... More

Filling of magnetic-impurity-induced gap in topological insulators by potential scatteringFeb 23 2015May 27 2015We show that the energy gap induced by ferromagnetically aligned magnetic impurities on the surface of a topological insulator can be filled, due to scattering off the non-magnetic potential of the impurities. In both a continuum surface model and a three-dimensional ... More

Magnon Dirac materialsDec 15 2015Aug 15 2016We demonstrate how a Dirac-like magnon spectrum is generated for localized magnetic moments forming a two-dimensional honeycomb lattice. The Dirac crossing point is proven to be robust against magnon-magnon interactions, as these only shift the spectrum. ... More

Complementary Ansatz for the neutrino mass matrixApr 11 2000We propose a simple Ansatz for the three generation neutrino mass matrix $M_\nu$ which is motivated from an SO(10) grand unified theory. The Ansatz can be combined with information from neutrino oscillation experiments and bounds on neutrinoless double ... More

Supercurrent detection of topologically trivial zero-energy states in nanowire junctionsApr 08 2019We report the emergence of zero-energy states in the trivial phase of a short nanowire junction with strong spin-orbit coupling and magnetic field, formed by strong coupling between the nanowire and two superconductors. The zero-energy states appear in ... More

Narrow Transient Absorptions in Late-Time Optical Spectra of Type Ia Supernovae: Evidence for Large Clumps of Iron-Rich Ejecta?Oct 16 2018Nov 21 2018An examination of late-time, optical spectra of type Ia supernovae revealed surprisingly narrow absorption features which only become visible a few months after maximum light. These features, most clearly seen in the late-time spectra of the bright, recent ... More

Domain walls in a chiral d-wave superconductor on the honeycomb latticeMay 10 2017Jul 27 2017We perform a fully self-consistent study of domain walls between different chiral domains in chiral $d_{x^2-y^2} \pm id_{xy}-wave superconductors with an underlying honeycomb lattice structure. We investigate domain walls along all possible armchair and ... More

Evidence for a scalar kappa(900) resonance in pi-K scatteringApr 10 1998Motivated by the $1/N_c$ expansion, we study a simple model in which the pi-K scattering amplitude is the sum of a current-algebra contact term and resonance pole exchanges. This phenomenological model is crossing symmetric and, when a putative light ... More

A note on the discrepancy of matrices with bounded row and column sumsJul 08 2013Jul 19 2013A folklore result uses the Lovasz local lemma to analyze the discrepancy of hypergraphs with bounded degree and edge size. We generalize this result to the context of real matrices with bounded row and column sums.

Analytic formula for the Geometric Phase of an Asymmetric TopJul 10 2018Feb 21 2019The motion of a handle spinning in space has an odd behavior. It seems to unexpectedly flip back and forth in a periodic manner as seen in a popular YouTube video. As an asymmetrical top, its motion is completely described by the Euler equations and the ... More

Algebraic Structures and Algorithms for Matching and Matroid Problems (Preliminary Version)Jan 09 2006Basic path-matchings, introduced by Cunningham and Geelen (FOCS 1996), are a common generalization of matroid intersection and non-bipartite matching. The main results of this paper are a new algebraic characterization of basic path-matching problems ... More

Saturated Graphs of Prescribed Minimum DegreeJul 24 2014Dec 15 2016A graph $G$ is $H$-saturated if it contains no copy of $H$ as a subgraph but the addition of any new edge to $G$ creates a copy of $H$. In this paper we are interested in the function sat$_{t}(n,p)$, defined to be the minimum number of edges that a $K_{p}$-saturated ... More

Dense random regular digraphs: singularity of the adjacency matrixMar 24 2014Aug 02 2015Fix $c\in (0,1)$ and let $\Gamma$ be a $\lfloor c n\rfloor$-regular digraph on $n$ vertices drawn uniformly at random. We prove that when $n$ is large, the (non-symmetric) adjacency matrix $M$ of $\Gamma$ is invertible with high probability. The proof ... More

Fluid-Structure Interaction for the Classroom: Interpolation, Hearts, and Swimming!Aug 23 2018While students may find spline interpolation easily digestible, based on their familiarity with continuity of a function and its derivatives, some of its inherent value may be missed when students only see it applied to standard data interpolation exercises. ... More

Discrepancy properties for random regular digraphsOct 21 2014Oct 26 2015For the uniform random regular directed graph we prove concentration inequalities for (1) codegrees and (2) the number of edges passing from one set of vertices to another. As a consequence, we can deduce discrepancy properties for the distribution of ... More

Lower bounds for the smallest singular value of structured random matricesAug 26 2016May 18 2018We obtain lower tail estimates for the smallest singular value of random matrices with independent but non-identically distributed entries. Specifically, we consider $n\times n$ matrices with complex entries of the form \[ M = A\circ X + B = (a_{ij}\xi_{ij} ... More

The circular law for random regular digraphsMar 16 2017Aug 07 2017Let $\log^Cn\le d\le n/2$ for a sufficiently large constant $C>0$ and let $A_n$ denote the adjacency matrix of a uniform random $d$-regular directed graph on $n$ vertices. We prove that as $n$ tends to infinity, the empirical spectral distribution of ... More

The circular law for random regular digraphs with random edge weightsAug 02 2015Sep 08 2017We consider random $n\times n$ matrices of the form $Y_n=\frac1{\sqrt{d}}A_n\circ X_n$, where $A_n$ is the adjacency matrix of a uniform random $d$-regular directed graph on $n$ vertices, with $d=\lfloor p n\rfloor$ for some fixed $p \in (0,1)$, and $X_n$ ... More

Kaon-nucleon and D-nucleon scattering in the quark model, including spin-orbit interactionsMar 01 2002Interactions of charmed and strange mesons with baryonic matter can be calculated in the nonrelativistic quark potential model. For KN scattering data exists, and the theoretical results for S-waves are in approximate agreement with experiment. Here we ... More

Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes systemMay 17 2017We study the chemotaxis-fluid system \begin{align*} \left\{ \begin{array}{r@{\,}c@{\,}c@{\ }l@{\quad}l@{\quad}l@{\,}c} n_{t}&+&u\cdot\!\nabla n&=\Delta n-\nabla\!\cdot(\frac{n}{c}\nabla c),\ &x\in\Omega,& t>0, c_{t}&+&u\cdot\!\nabla c&=\Delta c-nc,\ &x\in\Omega,& ... More

Global very weak solutions to a chemotaxis-fluid system with nonlinear diffusionDec 01 2017Jun 06 2018We consider the chemotaxis-fluid system \begin{align}\label{star}\tag{$\diamondsuit$} \left\{ \begin{array}{r@{\,}c@{\,}c@{\ }l@{\quad}l@{\quad}l@{\,}c} n_{t}&+&u\cdot\!\nabla n&=\Delta n^m-\nabla\!\cdot(n\nabla c),\ &x\in\Omega,& t>0,\\ c_{t}&+&u\cdot\!\nabla ... More

The Stokes limit in a three-dimensional chemotaxis-Navier-Stokes systemFeb 17 2019We consider initial-boundary value problems for the $\kappa$-dependent family of chemotaxis-(Navier--)Stokes systems \begin{align*} \left\{ \begin{array}{r@{\,}c@{\,}c@{\ }l@{\quad}l@{\quad}l@{\,}c} n_{t}&+&u\cdot\!\nabla n&=\Delta n-\nabla\!\cdot(n\nabla ... More

Global solvability of chemotaxis-fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensionsJul 06 2018In this work we extend a recent result to chemotaxis fluid systems which include matrix-valued sensitivity functions $S(x,n,c):\Omega\times[0,\infty)^2\to\mathbb{R}^{3\times3}$ in addition to the porous medium type diffusion, which were discussed in the ... More

Sublinear signal production in a two-dimensional Keller-Segel-Stokes systemFeb 01 2016We study the chemotaxis-fluid system \begin{align*} \left\{\begin{array}{r@{\,}l@{\quad}l@{\,}c} n_{t}&=\Delta n-\nabla\!\cdot(n\nabla c)-u\cdot\!\nabla n,\ &x\in\Omega,& t>0,\\ c_{t}&=\Delta c-c+f(n)-u\cdot\!\nabla c,\ &x\in\Omega,& t>0,\\ u_{t}&=\Delta ... More

Blow-up of weak solutions to a chemotaxis system under influence of an external chemoattractantOct 24 2015We study nonnnegative radially symmetric solutions of the parabolic-elliptic Keller-Segel whole space system \begin{align*} \left\{\begin{array}{c@{\,}l@{\quad}l@{\,}c} u_{t}&=\Delta u-\nabla\!\cdot(u\nabla v),\ &x\in\mathbb{R}^n,& t>0,\\ 0 &=\Delta v+u+f(x),\ ... More

Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivityMay 18 2017May 19 2017We investigate the parabolic-elliptic Keller-Segel model \begin{align*}\left\{\begin{array}{r@{\,}l@{\quad}l@{\quad}l@{\,}c} u_{t}&=\Delta u-\,\chi\nabla\!\cdot(\frac{u}{v}\nabla v),\ &x\in\Omega,& t>0,\\ 0&=\Delta v-\,v+u,\ &x\in\Omega,& t>0,\\ \frac{\partial ... More

Boundedness in a Keller-Segel system with external signal productionJul 27 2015We study the Neumann initial-boundary problem for the chemotaxis system \begin{align*} \left\{\begin{array}{c@{\,}l@{\quad}l@{\,}c} u_{t}&=\Delta u-\nabla\!\cdot(u\nabla v),\ &x\in\Omega,& t>0,\\ v_{t}&=\Delta v-v+u+f(x,t),\ &x\in\Omega,& t>0,\\ \frac{\partial ... More

On the Upper Limit of SeparabilityAug 30 2017We propose an approach to rapidly find the upper limit of separability between datasets that is directly applicable to HEP classification problems. The most common HEP classification task is to use $n$ values (variables) for an object (event) to estimate ... More

Neural Networks as a tool for parameter estimation in mega-pixel data setsAug 14 2001We present a neural net algorithm for parameter estimation in the context of large cosmological data sets. Cosmological data sets present a particular challenge to pattern-recognition algorithms since the input patterns (galaxy redshift surveys, maps ... More

On the Lusternik-Schnirelmann category of a simplicial mapJun 03 2016In this paper, we study the Lusternik-Schnirelmann category of a simplicial map between simplicial complexes, generalizing the simplicial category of a complex to that of a map. Several properties of this new invariant are shown, including its relevance ... More

Thermodynamic Effects of Single-Qubit Operations in Silicon-Based Quantum ComputingApr 18 2017Silicon-based quantum logic is a promising technology to implement universal quantum computing. It is widely believed that a millikelvin cryogenic environment will be necessary to accommodate silicon-based qubits. This prompts a question of the ultimate ... More

Neural networks as a tool for parameter estimation in astrophysical dataDec 14 2001We present a neural net algorithm for parameter estimation in the context of large cosmological data sets. Cosmological data sets present a particular challenge to pattern-recognition algorithms since the input patterns (galaxy redshift surveys, maps ... More

Cosheaf Theoretical Constructions in Networks and Persistent HomologyDec 15 2016Persistent homology has recently emerged as a powerful technique in topological data analysis for analyzing the emergence and disappearance of topological features throughout a filtered space, shown via persistence diagrams. Additionally, (co)sheaves ... More

Statistical Power, the Bispectrum and the Search for Non-Gaussianity in the CMB AnisotropyOct 17 2000We use simulated maps of the cosmic microwave background anisotropy to quantify the ability of different statistical tests to discriminate between Gaussian and non-Gaussian models. Despite the central limit theorem on large angular scales, both the genus ... More

Field Ordering and Energy Density in Texture CosmologyJul 12 1995We use numerical simulations of the time evolution of global textures to investigate the relationship between ordering dynamics and energy density in an expanding universe. Events in which individual textures become fully wound are rare. The energy density ... More

Interfacial Effects of Al-Termination on Spin Transport in Magnetic Tunnel JunctionsOct 23 2009Experiments have shown that the tunneling current in a Co/Al$_2$O$_3$ magnetic tunneling junction (MTJ) is positively spin polarized, opposite to what is intuitively expected from standard tunneling theory which gives the spin polarization as exclusively ... More

Granular Superconductor in a honeycomb lattice as a realization of Bosonic Dirac MaterialNov 17 2015Mar 21 2016We examine the low energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in honeycomb lattice structure. Using the example of graphene we present the evidence for the engineered ... More

Light forces in ultracold photoassociationNov 17 2006We study the time-resolved photoassociation of ultracold sodium in an optical dipole trap. The photoassociation laser excites pairs of atoms to molecular states of large total angular momentum at high intensities (above 20 kW/cm$^{2}$). Such transitions ... More

Investigating the Light Scalar MesonsOct 26 2001Oct 26 2001We first briefly review a treatment of the scalars in meson meson scattering based on a non-linear chiral Lagrangian, with unitarity implemented by a "local" modification of the scalar propagators. It is shown that the main results are confirmed by a ... More

A Distance Estimate to the Cygnus Loop Based on the Distances to Two Stars Located Within the RemnantNov 06 2017Nov 25 2017Underlying nearly every quantitative discussion of the Cygnus Loop supernova remnant is uncertainty about its distance. Here we present optical images and spectra of nebulosities around two stars whose mass-loss material appears to have interacted with ... More

Exploring Io's atmospheric composition with APEX: first measurement of 34SO2 and tentative detection of KClAug 23 2013The composition of Io's tenuous atmosphere is poorly constrained. Only the major species SO2 and a handful of minor species have been positively identified, but a variety of other molecular species should be present, based on thermochemical equilibrium ... More

Learning and Tracking the 3D Body Shape of Freely Moving Infants from RGB-D sequencesOct 17 2018Statistical models of the human body surface are generally learned from thousands of high-quality 3D scans in predefined poses to cover the wide variety of human body shapes and articulations. Acquisition of such data requires expensive equipment, calibration ... More

Unitarized pseudoscalar meson scattering amplitudes in three flavor linear sigma modelsDec 21 2000The three flavor linear sigma model is studied as a ``toy model'' for understanding the role of possible light scalar mesons in the \pi \pi, \pi K and \pi \eta scattering channels. The approach involves computing the tree level partial wave amplitude ... More

Spinor Dynamics in an Antiferromagnetic Spin-1 CondensateApr 06 2007Apr 13 2007We observe coherent spin oscillations in an antiferromagnetic spin-1 Bose-Einstein condensate of sodium. The variation of the spin oscillations with magnetic field shows a clear signature of nonlinearity, in agreement with theory, which also predicts ... More

The imaging X-ray detector for Lobster-ISSMay 07 2003Lobster-ISS is a revolutionary astrophysical X-ray all-sky monitor scheduled for deployment as an attached payload on the International Space Station (ISS) in 2009. Using a new wide field-of-view focusing optic, Lobster-ISS provides an order-of-magnitude ... More

Alternative Data Reduction Procedures for UVES: Wavelength Calibration and Spectrum AdditionDec 05 2008This paper addresses alternative procedures to the ESO supplied pipeline procedures for the reduction of UVES spectra of two quasar spectra to determine the value of the fundamental constant mu = Mp/Me at early times in the universe. The procedures utilize ... More

Bifurcations in valveless pumping techniques from a coupled fluid-structure-electrophysiology model in heart developmentSep 14 2017We explore an embryonic heart model that couples electrophysiology and muscle-force generation to flow induced using a $2D$ fluid-structure interaction framework based on the immersed boundary method. The propagation of action potentials are coupled to ... More

Calculation of the Anisotropic Coefficients of Thermal Expansion: A First-Principles ApproachMar 07 2019Predictions of the anisotropic coefficients of thermal expansion are needed to not only compare to experimental measurement, but also as input for macroscopic modeling of devices which operate over a large temperature range. While most current methods ... More

Pipage Rounding, Pessimistic Estimators and Matrix ConcentrationJul 08 2013Pipage rounding is a dependent random sampling technique that has several interesting properties and diverse applications. One property that has been particularly useful is negative correlation of the resulting vector. Unfortunately negative correlation ... More

Fluid-Structure Interaction for the Classroom: Speed, Accuracy, Convergence, and Jellyfish!Feb 20 2019When is good, good enough? This question lingers in approximation theory and numerical methods as a competition between accuracy and practicality. Numerical Analysis is traditionally where the rubber meets the road: students begin to use numerical algorithms ... More

Maker-Breaker Percolation Games I: Crossing GridsOct 11 2018Motivated by problems in percolation theory, we study the following 2-player positional game. Let $\Lambda_{m \times n}$ be a rectangular grid-graph with $m$ vertices in each row and $n$ vertices in each column. Two players, Maker and Breaker, play in ... More

Finding Better Active Learners for Faster Literature ReviewsDec 10 2016Feb 02 2018Literature reviews can be time-consuming and tedious to complete. By cataloging and refactoring three state-of-the-art active learning techniques from evidence-based medicine and legal electronic discovery, this paper finds and implements FASTREAD, a ... More

Naut your everyday jellyfish model: Exploring how tentacles and oral arms impact locomotionAug 09 2019Jellyfish - majestic, energy efficient, and one of the oldest species that inhabits the oceans. It is perhaps the second item, their efficiency, that has captivated scientists for decades into investigating their locomotive behavior. Yet, no one has specifically ... More

Singular Points of High Multiplicity for Septic CurvesJun 26 2019For real irreducible algebraic curves of the seventh degree, there are 22 types of singular points of multiplicity six, 174 types of singular points of multiplicity five, and at least 182 types of singular points of multiplicity four. For complex irreducible ... More

Self-assembling DNA-caged particles: nanoblocks for hierarchical self-assemblyJul 24 2008Nov 24 2008DNA is an ideal candidate to organize matter on the nanoscale, primarily due to the specificity and complexity of DNA based interactions. Recent advances in this direction include the self-assembly of colloidal crystals using DNA grafted particles. In ... More

Statistical Mechanics of DNA-Mediated Colloidal AggregationJun 15 2006Feb 27 2007We present a statistical mechanical model of aggregation in colloidal systems with DNA mediated interactions. We obtain a general result for the two-particle binding energy in terms of the hybridization free energy $\Delta G$ of DNA and two model dependent ... More

Singular Points of Real Quintic Curves Via Computer AlgebraJun 30 2008There are 42 types of real singular points for irreducible real quintic curves and 49 types of real singular points for reducible real quintic curves. The classification of real singular points for irreducible real quintic curves is originally due to ... More

Operad bimodules, and composition products on Andre-Quillen filtrations of algebrasFeb 22 2016If O is a reduced operad in symmetric spectra, an O-algebra I can be viewed as analogous to the augmentation ideal of an augmented algebra. Implicit in the literature on Topological Andre-Quillen homology is that such an I admits a canonical (and homotopically ... More

Combinatorics of certain higher $q,t$-Catalan polynomials: chains, joint symmetry, and the Garsia-Haiman formulaNov 09 2012Jun 22 2013The higher $q,t$-Catalan polynomial $C^{(m)}_n(q,t)$ can be defined combinatorially as a weighted sum of lattice paths contained in certain triangles, or algebraically as a complicated sum of rational functions indexed by partitions of $n$. This paper ... More

Graph Sparsification by Edge-Connectivity and Random Spanning TreesMay 03 2010Aug 09 2010We present new approaches to constructing graph sparsifiers --- weighted subgraphs for which every cut has the same value as the original graph, up to a factor of $(1 \pm \epsilon)$. Our first approach independently samples each edge $uv$ with probability ... More

Nested quantum Dyck paths and nabla(s_lambda)May 31 2007We conjecture a combinatorial formula for the monomial expansion of the image of any Schur function under the Bergeron-Garsia nabla operator. The formula involves nested labeled Dyck paths weighted by area and a suitable "diagonal inversion" statistic. ... More

Colloids with key-lock interactions: non-exponential relaxation, aging and anomalous diffusionFeb 23 2007Jul 17 2007The dynamics of particles interacting by key-lock binding of attached biomolecules are studied theoretically. Experimental realizations of such systems include colloids grafted with complementary single-stranded DNA (ssDNA), and particles grafted with ... More

How to build nanoblocks using DNA scaffoldsApr 23 2008Jun 02 2008In recent years there have been a number of proposals to utilize the specificity of DNA based interactions for potential applications in nanoscience. One interesting direction is the self-assembly of micro- and nanoparticle clusters using DNA scaffolds. ... More

Atom laser dynamicsMar 29 2001An ideal atom laser would produce an atomic beam with highly stable flux and energy. In practice the stability is likely to be limited by technical noise and nonlinear dynamical effects. We investigate the dynamics of an atom laser using a comprehensive ... More

Direct Extragalactic Distance Determination Using X-Ray ScatteringJul 20 2004We examine the feasibility of using dust-scattered X-rays for direct determination of distances to nearby galaxies with bright background AGNs, QSOs, or GRBs. We show how the Chandra X-Ray Observatory could be used to determine the distance to M31 to ... More

On wave equations of the $p$-Laplacian type with supercritical nonlinearitiesJul 02 2018This article focuses on a quasilinear wave equation of $p$-Laplacian type: \[ u_{tt} - \Delta_p u -\Delta u_t = f(u) \] in a bounded domain $\Omega \subset \mathbb{R}^3$ with a sufficiently smooth boundary $\Gamma=\partial \Omega$ subject to a generalized ... More

Protoplanetary Disk Masses from Radiative Transfer Modeling: A Case Study in TaurusMar 19 2019Measuring the masses of protoplanetary disks is crucial for understanding their planet-forming potential. Typically, dust masses are derived from (sub-)millimeter flux density measurements plus assumptions for the opacity, temperature, and optical depth ... More

The redshift evolution of X-ray and Sunyaev-Zel'dovich scaling relations in the FABLE simulationsApr 30 2019Aug 16 2019We study the redshift evolution of the X-ray and Sunyaev-Zel'dovich (SZ) scaling relations for galaxy groups and clusters in the FABLE suite of cosmological hydrodynamical simulations. Using an expanded sample of $27$ high-resolution zoom-in simulations, ... More

Submodular Functions: Learnability, Structure, and OptimizationAug 12 2010Aug 22 2012Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In this work we study ... More

Making the cut: improved ranking and selection for large-scale inferenceDec 19 2013Sep 08 2015Identifying leading measurement units from a large collection is a common inference task in various domains of large-scale inference. Testing approaches, which measure evidence against a null hypothesis rather than effect magnitude, tend to overpopulate ... More

A test for dependence between two point processes on the real lineAug 17 2014Dec 20 2014Many scientific questions rely on determining whether two sequences of event times are associated. This article introduces a likelihood ratio test which can be parameterised in several ways to detect different forms of dependence. A common finite-sample ... More

Kinetic limitations of cooperativity based drug delivery systemsAug 17 2007Mar 07 2008We study theoretically a novel drug delivery system that utilizes the overexpression of certain proteins in cancerous cells for cell specific chemotherapy. The system consists of dendrimers conjugated with "keys" (ex: folic acid) which "key-lock" bind ... More

Subdivision of Maps of Digital ImagesJun 07 2019With a view towards providing tools for analyzing and understanding digitized images, various notions from algebraic topology have been introduced into the setting of digital topology. In the ordinary topological setting, invariants such as the fundamental ... More

A Combinatorial Approach to the Symmetry of $q,t$-Catalan NumbersFeb 02 2016The \emph{$q,t$-Catalan numbers} $C_n(q,t)$ are polynomials in $q$ and $t$ that reduce to the ordinary Catalan numbers when $q=t=1$. These polynomials have important connections to representation theory, algebraic geometry, and symmetric functions. Haglund ... More

Short proofs for generalizations of the Lovász Local Lemma: Shearer's condition and cluster expansionNov 18 2017The Lov\'asz Local Lemma is a seminal result in probabilistic combinatorics. It gives a sufficient condition on a probability space and a collection of events for the existence of an outcome that simultaneously avoids all of those events. Over the years, ... More

Don't be jelly: Exploring effective jellyfish locomotionApr 19 2019Jellyfish have been called one of the most energy-efficient animals in the world due to the ease in which they move through their fluid environment, by product of their morphological, muscular, and material properties. We investigated jellyfish locomotion ... More

Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearityJan 26 2012Apr 19 2012In this paper we analyze the classical solution set ({\lambda},u), for {\lambda}>0, of a one-dimensional prescribed mean curvature equation on the interval [-L,L]. It is shown that the solution set depends on the two parameters, {\lambda} and L, and undergoes ... More

Maker-Breaker Percolation Games II: Escaping to InfinityJun 29 2019Let $\Lambda$ be an infinite connected graph, and let $v_0$ be a vertex of $\Lambda$. We consider the following positional game. Two players, Maker and Breaker, play in alternating turns. Initially all edges of $\Lambda$ are marked as unsafe. On each ... More

Effects of the non-uniform initial environment and the guide field on the plasmoid instabilityJul 08 2013Effects of non-uniform initial mass density and temperature on the plasmoid instability are studied via 2.5-dimensional resistive magnetohydrodynamic(MHD) simulations. Our results indicate that the development of the plasmoid instability is apparently ... More

Singular Points of Reducible Sextic CurvesJul 01 2008There are 106 individual types of singular points for reducible complex sextic curves.

Singular points of real quartic curves via computer algebraJul 02 2007There are thirteen types of singular points for irreducible real quartic curves and seventeen types of singular points for reducible real quartic curves. This classification is originally due to D.A. Gudkov. There are nine types of singular points for ... More

Error-proof programmable self-assembly of DNA-nanoparticle clustersApr 16 2005Feb 27 2007We study theoretically a new generic scheme of programmable self-assembly of nanoparticles into clusters of desired geometry. The problem is motivated by the feasibility of highly selective DNA-mediated interactions between colloidal particles. By analyzing ... More

Bayesian estimation of the latent dimension and communities in stochastic blockmodelsApr 06 2019Apr 13 2019Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the community structure ... More

Expressive Body Capture: 3D Hands, Face, and Body from a Single ImageApr 11 2019To facilitate the analysis of human actions, interactions and emotions, we compute a 3D model of human body pose, hand pose, and facial expression from a single monocular image. To achieve this, we use thousands of 3D scans to train a new, unified, 3D ... More

Study of scalar mesons in chiral Lagrangian frameworksJan 16 2008We review two approaches to studying pseudoscalar meson-meson scattering amplitudes to beyond 1 GeV using non-linear and linear chiral Lagrangians. These approaches use two different unitarisation techniques - a generalised Breit Wigner prescription and ... More

A toolkit to describe and interactively display three-manifolds embedded in four-spaceJan 25 2012A data structure and toolkit are presented here that allow for the description and manipulation of mathematical models of three-manifolds and their interactive display from multiple viewpoints via the OpenGL 3D graphics package. The data structure and ... More

RKKY coupling in grapheneJan 22 2010May 12 2010We study the carrier-mediated exchange interaction, the so-called RKKY coupling, between two magnetic moments in graphene using exact diagonalization on the honeycomb lattice. By using the tight-binding nearest neighbor band structure of graphene we avoid ... More

Another look at the size of the low-surface brightness galaxy VCC 1661 in the Virgo ClusterOct 25 2016We present new wide-field images of the low-surface brightness Virgo Cluster dwarf galaxy VCC 1661. The extant literature lists a broad range of radii for this object, covering a factor of more than four, depending on the filters used and the details ... More

Measuring the Neutron's Mean Square Charge Radius Using Neutron InterferometrySep 14 2005The neutron is electrically neutral, but its substructure consists of charged quarks so it may have an internal charge distribution. In fact it is known to have a negative mean square charge radius (MSCR), the second moment of the radial charge density. ... More

Chemical Analysis of a Diffuse Cloud along a Line of Sight Toward W51: Molecular Fraction and Cosmic-Ray Ionization RateAug 15 2012Absorption lines from the molecules OH+, H2O+, and H3+ have been observed in a diffuse molecular cloud along a line of sight near W51 IRS2. We present the first chemical analysis that combines the information provided by all three of these species. Together, ... More

Spatially resolved images of reactive ions in the Orion BarApr 27 2017We report high angular resolution (4.9" x 3.0") images of reactive ions SH+, HOC+, and SO+ toward the Orion Bar photodissociation region (PDR). We used ALMA-ACA to map several rotational lines at 0.8 mm, complemented with multi-line observations obtained ... More

Driving Solar Giant Cells through the Self-Organization of Near-Surface PlumesApr 03 2018Global 3D simulations of solar giant-cell convection have provided significant insight into the processes which yield the Sun's observed differential rotation and cyclic dynamo action. However, as we move to higher resolution simulations a variety of ... More

A Survey of Low-Velocity Collisional Features in Saturn's F RingSep 12 2013Small (~50km scale), irregular features seen in Cassini images to be emanating from Saturn's F ring have been termed mini-jets by Attree et al. (2012). One particular mini-jet was tracked over half an orbital period, revealing its evolution with time ... More

Reducing Spontaneous Emission in Circuit Quantum Electrodynamics by a Combined Readout/Filter TechniqueApr 16 2015Oct 20 2015Physical implementations of qubits can be extremely sensitive to environmental coupling, which can result in decoherence. While efforts are made for protection, coupling to the environment is necessary to measure and manipulate the state of the qubit. ... More

On the dynamic suction pumping of blood cells in tubular heartsOct 11 2016Around the third week after gestation in embryonic development, the human heart consists only of a valvless tube, unlike a fully developed adult heart, which is multi-chambered. At this stage in development, the heart valves have not formed and so net ... More

Impact of Rigidity on Molecular Self-AssemblyOct 12 2018Jun 20 2019Rigid, cage-like molecules, like diamondoids, show unique self-assembly behavior, such as templating 1-D nanomaterial assembly via pathways that are typically blocked for such bulky substituents. We investigate molecular forces between diamondoids to ... More

Optical Flow Estimation using a Spatial Pyramid NetworkNov 03 2016Nov 21 2016We learn to compute optical flow by combining a classical spatial-pyramid formulation with deep learning. This estimates large motions in a coarse-to-fine approach by warping one image of a pair at each pyramid level by the current flow estimate and computing ... More