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The saturation conjecture (after A. Knutson and T. Tao)Oct 30 1998In this exposition we give a simple and complete treatment of A. Knutson and T. Tao's recent proof (http://front.math.ucdavis.edu/math.RT/9807160) of the saturation conjecture, which asserts that the Littlewood-Richardson semigroup is saturated. The main ... More

Positivity determines the quantum cohomology of GrassmanniansMay 14 2019We prove that if X is a Grassmannian of type A, then the Schubert basis of the (small) quantum cohomology ring QH(X) is the only homogeneous deformation of the Schubert basis of the ordinary cohomology ring of X that multiplies with non-negative structure ... More

A Giambelli formula for even orthogonal GrassmanniansSep 29 2011Mar 29 2012Let X be an orthogonal Grassmannian parametrizing isotropic subspaces in an even dimensional vector space equipped with a nondegenerate symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in the singular and quantum ... More

Quantum Giambelli formulas for isotropic GrassmanniansDec 04 2008Let X be a symplectic or odd orthogonal Grassmannian which parametrizes isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove quantum Giambelli formulas which express an arbitrary Schubert class in the small ... More

A Giambelli formula for isotropic GrassmanniansNov 17 2008Aug 04 2010Let X be a symplectic or odd orthogonal Grassmannian parametrizing isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in H^*(X,Z) as a polynomial ... More

Eigenvalues of Hermitian matrices with positive sum of bounded rankNov 03 2004We give a minimal list of inequalities characterizing the possible eigenvalues of a set of Hermitian matrices with positive semidefinite sum of bounded rank. This answers a question of A. Barvinok.

Direct proof of the quantum Monk's formulaJul 27 2001Jul 29 2001We give a direct geometric proof of the quantum Monk's formula which relies only on classical Schubert calculus.

Mutations of puzzles and equivariant cohomology of two-step flag varietiesJan 14 2014Oct 29 2014We introduce a mutation algorithm for puzzles that is a three-direction analogue of the classical jeu de taquin algorithm for semistandard tableaux. We apply this algorithm to prove our conjectured puzzle formula for the equivariant Schubert structure ... More

Euler characteristics in the quantum $K$-theory of flag varietiesMar 06 2019We prove that the sheaf Euler characteristic of the product of a Schubert class and an opposite Schubert class in the quantum $K$-theory ring of a (generalized) flag variety $G/P$ is equal to $q^d$, where $d$ is the smallest degree of a rational curve ... More

Quantum cohomology of GrassmanniansJun 29 2001Jul 01 2001We give elementary proofs of the main theorems about (small) quantum cohomology of Grassmannians, including the quantum Giambelli and quantum Pieri formulas, the rim-hook algorithm, Siebert and Tian's presentation, and a recent theorem of Fulton and Woodward ... More

Quantum cohomology of partial flag manifoldsMar 19 2003We give elementary geometric proofs of the main theorems about the (small) quantum cohomology of partial flag varieties SL(n)/P, including the quantum Pieri and quantum Giambelli formulas and the presentation.

Alternating signs of quiver coefficientsJul 01 2003Dec 24 2003We prove K-theoretic generalizations of the component formulas of Knutson, Miller, and Shimozono, and deduce that K-theoretic quiver coefficients have alternating signs. We also prove new variants of the factor sequences conjecture, and a conjecture of ... More

Euler characteristics of cominuscule quantum K-theoryJan 23 2017We prove an identity relating the product of two opposite Schubert varieties in the (equivariant) quantum K-theory ring of a cominuscule flag variety to the minimal degree of a rational curve connecting the Schubert varieties. We deduce that the sum of ... More

Stable Grothendieck polynomials and K-theoretic factor sequencesJan 21 2006We formulate a nonrecursive combinatorial rule for the expansion of the stable Grothendieck polynomials of [Fomin-Kirillov '94] in the basis of stable Grothendieck polynomials for partitions. This gives a common generalization, as well as new proofs of ... More

Rational connectedness implies finiteness of quantum K-theoryMay 24 2013Let X be any generalized flag variety with Picard group of rank one. Given a degree d, consider the Gromov-Witten variety of rational curves of degree d in X that meet three general points. We prove that, if this Gromov-Witten variety is rationally connected ... More

Gromov-Witten invariants on GrassmanniansJun 27 2003We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a two-step flag variety. We also give symplectic and orthogonal analogues of this result; in these cases the two-step ... More

K-theory of minuscule varietiesJun 23 2013Based on Thomas and Yong's K-theoretic jeu de taquin algorithm, we prove a uniform Littlewood-Richardson rule for the K-theoretic Schubert structure constants of all minuscule homogeneous spaces. Our formula is new in all types. For the main examples ... More

Littlewood-Richardson rules for GrassmanniansJun 27 2003We give elementary and short proofs of the Littlewood-Richardson rules for type A Grassmannians and maximal isotropic Grassmannians, based on the corresponding Pieri rules.

Grothendieck polynomials and quiver formulasJun 27 2003Fulton's universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear combinations ... More

Schubert Polynomials and Quiver FormulasNov 19 2002The work of Buch and Fulton established a formula for a general kind of degeneracy locus associated to an oriented quiver of type $A$. The main ingredients in this formula are Schur determinants and certain integers, the quiver coefficients, which generalize ... More

On a conjectured formula for quiver varietiesSep 15 1999In our joint paper with W. Fulton (math.AG/9804041) we prove a formula for the cohomology class of a quiver variety. This formula involves a new class of generalized Littlewood-Richardson coefficients, all of which surprisingly seem to be non-negative. ... More

Stanley symmetric functions and quiver varietiesSep 16 1999In our joint paper with W. Fulton (math.AG/9804041) we prove a formula for the cohomology class of a quiver variety. This formula is general enough to give new expressions for all known types of Schubert polynomials. In the present paper we discuss the ... More

Specializations of Grothendieck polynomialsAug 11 2003We prove a formula for double Schubert and Grothendieck polynomials specialized to two rearrangements of the same set of variables. Our formula generalizes the usual formulas for Schubert and Grothendieck polynomials in terms of RC-graphs, and it gives ... More

Chern class formulas for quiver varietiesApr 07 1998In this paper a formula is proved for the general degeneracy locus associated to an oriented quiver of type A_n. Given a finite sequence of vector bundles with maps between them, these loci are described by putting rank conditions on arbitrary composites ... More

Positivity of quiver coefficients through Thom polynomialsNov 12 2003Let r be an orbit of the quiver representation of type A_n (equioriented case). In this paper we study the Poincare dual of the closure of r (a.c.a. Thom polynomial/degeneracy loci formula) in equivariant cohomology. Using general Thom polynomial theory ... More

Quantum Pieri rules for isotropic GrassmanniansSep 29 2008We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the classical ... More

Quantum K-theory of GrassmanniansOct 06 2008Jun 13 2009We show that (equivariant) K-theoretic 3-point Gromov-Witten invariants of genus zero on a Grassmann variety are equal to triple intersections computed in the ordinary (equivariant) K-theory of a two-step flag manifold, thus generalizing an earlier result ... More

A Littlewood-Richardson rule for the K-theory of GrassmanniansApr 21 2000Aug 15 2000We prove an explicit combinatorial formula for the structure constants of the Grothendieck ring of a Grassmann variety with respect to its basis of Schubert structure sheaves. We furthermore relate K-theory of Grassmannians to a bialgebra of stable Grothendieck ... More

Quiver coefficients of Dynkin typeAug 25 2007We study the Grothendieck classes of quiver cycles, i.e. invariant closed subvarieties of the representation space of a quiver. For quivers without oriented loops we show that the class of a quiver cycle is determined by quiver coefficients, which generalize ... More

Angles in hyperbolic lattices : The pair correlation densitySep 19 2014Oct 14 2014It is well known that the angles in a lattice acting on hyperbolic $n$-space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we determine, among other ... More

Grothendieck classes of quiver varietiesApr 02 2001We prove a formula for the structure sheaf of a quiver variety in the Grothendieck ring of its embedding variety. This formula generalizes and gives new expressions for Grothendieck polynomials. We furthermore conjecture that the coefficients in our formula ... More

BOP: Benchmark for 6D Object Pose EstimationAug 24 2018We propose a benchmark for 6D pose estimation of a rigid object from a single RGB-D input image. The training data consists of a texture-mapped 3D object model or images of the object in known 6D poses. The benchmark comprises of: i) eight datasets in ... More

Towards Error Handling in a DSL for Robot Assembly TasksDec 15 2014This work-in-progress paper presents our work with a domain specific language (DSL) for tackling the issue of programming robots for small-sized batch production. We observe that as the complexity of assembly increases so does the likelihood of errors, ... More

Pieri rules for the K-theory of cominuscule GrassmanniansMay 14 2010We prove Pieri formulas for the multiplication with special Schubert classes in the K-theory of all cominuscule Grassmannians. For Grassmannians of type A this gives a new proof of a formula of Lenart. Our formula is new for Lagrangian Grassmannians, ... More

Curve neighborhoods of Schubert varietiesMar 25 2013A previous result of the authors with Chaput and Perrin states that the union of all rational curves of fixed degree passing through a Schubert variety in a homogeneous space G/P is again a Schubert variety. In this paper we identify this Schubert variety ... More

Reduced-Complexity Semidefinite Relaxations of Optimal Power Flow ProblemsAug 30 2013Dec 06 2013We propose a new method for generating semidefinite relaxations of optimal power flow problems. The method is based on chordal conversion techniques: by dropping some equality constraints in the conversion, we obtain semidefinite relaxations that are ... More

Improving intermolecular interactions in DFTB3 using extended polarization from chemical-potential equalizationJul 01 2015Semi-empirical quantum mechanical methods traditionally expand the electron density in a minimal, valence-only electron basis set. The minimal-basis approximation causes molecular polarization to be underestimated, and hence intermolecular interaction ... More

A Chevalley formula for the equivariant quantum K-theory of cominuscule varietiesApr 26 2016We prove a type-uniform Chevalley formula for multiplication with divisor classes in the equivariant quantum $K$-theory ring of any cominuscule flag variety $G/P$. We also prove that multiplication with divisor classes determines the equivariant quantum ... More

A Chevalley formula for the equivariant quantum K-theory of cominuscule varietiesApr 26 2016Jun 08 2017We prove a type-uniform Chevalley formula for multiplication with divisor classes in the equivariant quantum $K$-theory ring of any cominuscule flag variety $G/P$. We also prove that multiplication with divisor classes determines the equivariant quantum ... More

Projected Gromov-Witten varieties in cominuscule spacesDec 09 2013A projected Gromov-Witten variety is the union of all rational curves of fixed degree that meet two opposite Schubert varieties in a homogeneous space X = G/P. When X is cominuscule we prove that the map from a related Gromov-Witten variety is cohomologically ... More

Projected Gromov-Witten varieties in cominuscule spacesDec 09 2013Jun 08 2017A projected Gromov-Witten variety is the union of all rational curves of fixed degree that meet two opposite Schubert varieties in a homogeneous space X = G/P. When X is cominuscule we prove that the map from a related Gromov-Witten variety is cohomologically ... More

Performance Analysis of Physical Layer Network Coding for Two-way Relaying over Non-regenerative Communication SatellitesMar 12 2017Two-way relaying is one of the major applications of broadband communication satellites, for which an efficient technique is Physical Layer Network Coding (PLNC). Earlier studies have considered satellites employing PLNC with onboard processing. This ... More

Rotational Subgroup Voting and Pose Clustering for Robust 3D Object RecognitionSep 07 2017It is possible to associate a highly constrained subset of relative 6 DoF poses between two 3D shapes, as long as the local surface orientation, the normal vector, is available at every surface point. Local shape features can be used to find putative ... More

Quiver coefficients are Schubert structure constantsNov 21 2003We give an explicit natural identification between the quiver coefficients of Buch and Fulton, decomposition coefficients for Schubert polynomials, and the Schubert structure constants for flag manifolds. This is also achieved in K-theory where we give ... More

Quantum Noise for Faraday Light Matter InterfacesDec 22 2011Jun 19 2012In light matter interfaces based on the Faraday effect quite a number of quantum information protocols have been successfully demonstrated. In order to further increase the performance and fidelities achieved in these protocols a deeper understanding ... More

Efficient quantum computation in a network with probabilistic gates and logical encodingDec 20 2016A new approach to efficient quantum computation with probabilistic gates is proposed and analyzed in both a local and non-local setting. It combines heralded gates previously studied for atom or atom-like qubits with logical encoding from linear optical ... More

Operators in Machine Learning: Response Properties in Chemical SpaceJul 23 2018Aug 23 2018The role of response operators is well established in quantum mechanics. We investigate their use for universal quantum machine learning models of response properties in molecules. After introducing a theoretical basis, we present and discuss numerical ... More

Distributed Solutions for Loosely Coupled Feasibility Problems Using Proximal Splitting MethodsJun 28 2013In this paper, we consider convex feasibility problems where the underlying sets are loosely coupled, and we propose several algorithms to solve such problems in a distributed manner. These algorithms are obtained by applying proximal splitting methods ... More

High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayersSep 28 2005We use quantum Monte Carlo (stochastic series expansion) and finite-size scaling to study the quantum critical points of two S=1/2 Heisenberg antiferromagnets in two dimensions: a bilayer and a Kondo-lattice-like system (incomplete bilayer), each with ... More

Data collapse in the critical region using finite-size scaling with subleading correctionsMay 08 2005We propose a treatment of the subleading corrections to finite-size scaling that preserves the notion of data collapse. This approach is used to extend and improve the usual Binder cumulant analysis. As a demonstration, we present results for the two- ... More

Photon Scattering from a System of Multi-Level Quantum Emitters. I. FormalismJan 09 2018We introduce a formalism to solve the problem of photon scattering from a system of multi-level quantum emitters. Our approach provides a direct solution of the scattering dynamics. As such the formalism gives the scattered fields amplitudes in the limit ... More

How well do STARLAB and NBODY compare? II: Hardware and accuracyJan 27 2012Most recent progress in understanding the dynamical evolution of star clusters relies on direct N-body simulations. Owing to the computational demands, and the desire to model more complex and more massive star clusters, hardware calculational accelerators, ... More

How well do STARLAB and NBODY4 compare? I: Simple modelsFeb 26 2009Feb 27 2009N-body simulations are widely used to simulate the dynamical evolution of a variety of systems, among them star clusters. Much of our understanding of their evolution rests on the results of such direct N-body simulations. They provide insight in the ... More

Quantum nondemolition measurement of mechanical motion quantaJan 08 2018May 28 2018The fields of opto- and electromechanics have facilitated numerous advances in the areas of precision measurement and sensing, ultimately driving the studies of mechanical systems into the quantum regime. To date, however, the quantization of the mechanical ... More

Square summability of variations and convergence of the transfer operatorDec 05 2006In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [13], we prove that the sequence of iterates of the transfer operator converges under square summability of variations ... More

A formula for non-equioriented quiver orbits of type ADec 03 2004Jan 19 2006We prove a positive combinatorial formula for the equivariant class of an orbit closure in the space of representations of an arbitrary quiver of type $A$. Our formula expresses this class as a sum of products of Schubert polynomials indexed by a generalization ... More

In search of inliers: 3d correspondence by local and global votingAug 23 2017We present a method for finding correspondence between 3D models. From an initial set of feature correspondences, our method uses a fast voting scheme to separate the inliers from the outliers. The novelty of our method lies in the use of a combination ... More

A $q$-analogue of the FKG inequality and some applicationsJun 07 2009Aug 21 2009Let $L$ be a finite distributive lattice and $\mu : L \to {\mathbb R}^{+}$ a log-supermodular function. For functions $k: L \to {\mathbb R}^{+}$ let $$E_{\mu} (k; q) \defeq \sum_{x\in L} k(x) \mu (x) q^{{\mathrm rank}(x)} \in {\mathbb R}^{+}[q].$$ We ... More

Commutation StructuresNov 02 2005For a fixed object X in a monoidal category, an X-commutation structure on an object A is just a map from XA to AX. We study aspects of such structure in case A has a dual.

Multi-Adaptive Galerkin Methods for ODEs IMay 12 2012We present multi-adaptive versions of the standard continuous and discontinuous Galerkin methods for ODEs. Taking adaptivity one step further, we allow for individual time-steps, order and quadrature, so that in particular each individual component has ... More

Calculus of extensive quantitiesMay 17 2011We show how a commutative monad gives rise to a theory of extensive quantities, including (under suitable further conditions) a differential calculus of such. The relationship to Schwartz distributions is dicussed. The paper is a companion to the author's ... More

Pregroupoids and their enveloping groupoidsFeb 03 2005We prove that the forgetful functor from groupoids to pregroupoids has a left adjoint, with the front adjunction injective. Thus we get an enveloping groupoid for any pregroupoid. We prove that the category of torsors is equivalent to that of pregroupoids. ... More

Accessibility percolation and first-passage site percolation on the unoriented binary hypercubeJan 09 2015Inspired by biological evolution, we consider the following so-called accessibility percolation problem: The vertices of the unoriented $n$-dimensional binary hypercube are assigned independent $U(0, 1)$ weights, referred to as fitnesses. A path is considered ... More

The Kellogg property and boundary regularity for p-harmonic functions with respect to the Mazurkiewicz boundary and other compactificationsMay 05 2017Oct 30 2018In this paper boundary regularity for p-harmonic functions is studied with respect to the Mazurkiewicz boundary and other compactifications. In particular, the Kellogg property (which says that the set of irregular boundary points has capacity zero) is ... More

The puzzle conjecture for the cohomology of two-step flag manifoldsJan 08 2014Jun 24 2016We prove a conjecture of Knutson asserting that the Schubert structure constants of the cohomology ring of a two-step flag variety are equal to the number of puzzles with specified border labels that can be created using a list of eight puzzle pieces. ... More

Finiteness of cominuscule quantum K-theoryNov 30 2010Jun 15 2012The product of two Schubert classes in the quantum K-theory ring of a homogeneous space X = G/P is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on X. We show that if X is cominuscule, then this power series ... More

The Expanded Giant Metrewave Radio TelescopeJan 03 2019With 30 antennas and a maximum baseline length of 25 km, the Giant Metrewave Radio Telescope (GMRT) is the premier low-frequency radio interferometer today. We have carried out a study of possible expansions of the GMRT, via adding new antennas and installing ... More

Infinitesimal cubical structure, and higher connectionsMay 30 2007In the context of Synthetic Differential Geometry, we describe a notion of higher connection with values in a cubical groupoid. We do this by exploiting a certain structure of cubical complex derived from the first neighbourhood of the diagonal of a manifold. ... More

The dual fibration in elementary termsJan 08 2015We give an elementary construction of the dual fibration of a fibration. It does not use the non-elementary notion of (pseudo-) functor into the category of categories.

A Lipschitz metric for conservative solutions of the two-component Hunter--Saxton systemFeb 26 2015We establish the existence of conservative solutions of the initial value problem of the two-component Hunter--Saxton system on the line. Furthermore we investigate the stability of these solutions by constructing a Lipschitz metric.

Duality for generic algebrasDec 20 2014We prove that double dualization into the generic algebra for an algebraic theory has some Gelfand- or Stone- duality properties

Shotgun edge assembly of random jigsaw puzzlesMay 23 2016May 25 2016In recent work by Mossel and Ross, it was asked how large $q$ has to be for a random jigsaw puzzle with $q$ different shapes of "jigs" to have exactly one solution. The jigs are assumed symmetric in the sense that two jigs of the same type always fit ... More

Wireless Bidirectional Relaying using Physical Layer Network Coding with Heterogeneous PSK ModulationMar 12 2017In bidirectional relaying using Physical Layer Network Coding (PLNC), it is generally assumed that users employ same modulation schemes in the Multiple Access phase. However, as observed by Zhang et al., it may not be desirable for the users to always ... More

Elements of a metric spectral theoryApr 02 2019This paper discusses a general method for spectral type theorems using metric spaces instead of vector spaces. Advantages of this approach are that it applies to genuinely non-linear situations and also to random versions. Metric analogs of operator norm, ... More

Unoriented first-passage percolation on the n-cubeFeb 12 2014Jun 05 2014The $n$-dimensional binary hypercube is the graph whose vertices are the binary $n$-tuples $\{0, 1\}^n$ and where two vertices are connected by an edge if they differ at exactly one coordinate. We prove that if the edges are assigned independent mean ... More

On the value distribution of the Epstein zeta function in the critical stripMay 13 2011We study the value distribution of the Epstein zeta function $E_n(L,s)$ for $0<s<\frac{n}{2}$ and a random lattice $L$ of large dimension $n$. For any fixed $c\in(1/4,1/2)$ and $n\to\infty$, we prove that the random variable $V_n^{-2c}E_n(\cdot,cn)$ has ... More

On the value distribution and moments of the Epstein zeta function to the right of the critical stripJun 09 2010Sep 08 2010We study the Epstein zeta function $E_n(L,s)$ for $s>\frac{n}{2}$ and determine for fixed $c>\frac{1}{2}$ the value distribution and moments of $E_n(\cdot,cn)$ (suitably normalized) as $n\to\infty$. We further discuss the random function $c\mapsto E_n(\cdot,cn)$ ... More

A Universal Density Matrix Functional from Molecular Orbital-Based Machine Learning: Transferability across Organic MoleculesJan 10 2019Apr 04 2019We address the degree to which machine learning can be used to accurately and transferably predict post-Hartree-Fock correlation energies. Refined strategies for feature design and selection are presented, and the molecular-orbital-based machine learning ... More

Adiabatic preparation of many-body states in optical latticesJun 14 2009May 11 2010We analyze a technique for the preparation of low entropy many body states of atoms in optical lattices based on adiabatic passage. In particular, we show that this method allows preparation of strongly correlated states as stable highest energy states ... More

Shape Driven Solid--Solid Transitions in ColloidsMar 02 2016Mar 12 2017Despite the fundamental importance of solid--solid transitions for metallurgy, ceramics, earth science, reconfigurable materials, and colloidal matter, the details of how materials transform between two solid structures are poorly understood. We introduce ... More

On the distribution of angles between the N shortest vectors in a random latticeDec 15 2010We determine the joint distribution of the lengths of, and angles between, the N shortest lattice vectors in a random n-dimensional lattice as n tends to infinity. Moreover we interpret the result in terms of eigenvalues and eigenfunctions of the Laplacian ... More

On the Poisson distribution of lengths of lattice vectors in a random latticeJan 20 2010Sep 08 2010We prove that the volumes determined by the lengths of the non-zero vectors $\pm\vecx$ in a random lattice L of covolume 1 define a stochastic process that, as the dimension n tends to infinity, converges weakly to a Poisson process on the positive real ... More

Note: Random-to-front shuffles on treesJan 27 2009A Markov chain is considered whose states are orderings of an underlying fixed tree and whose transitions are local "random-to-front" reorderings, driven by a probability distribution on subsets of the leaves. The eigenvalues of the transition matrix ... More

A cell complex in number theoryJan 29 2011Let De_n be the simplicial complex of squarefree positive integers less than or equal to n ordered by divisibility. It is known that the asymptotic rate of growth of its Euler characteristic (the Mertens function) is closely related to deep properties ... More

Most edge-orderings of $K_n$ have maximal altitudeMay 23 2016Mar 08 2018Suppose the edges of the complete graph on $n$ vertices are assigned a uniformly chosen random ordering. Let $X$ denote the corresponding number of Hamiltonian paths that are increasing in this ordering. It was shown in a recent paper by Lavrov and Loh ... More

On the dynamics of isometriesDec 29 2005We provide an analysis of the dynamics of isometries and semicontractions of metric spaces. Certain subsets of the boundary at infinity play a fundamental role and are identified completely for the standard boundaries of CAT(0)-spaces, Gromov hyperbolic ... More

First-passage percolation on Cartesian power graphsJun 29 2015Apr 17 2017We consider first-passage percolation on the class of "high-dimensional" graphs that can be written as an iterated Cartesian product $G\square G \square \dots \square G$ of some base graph $G$ as the number of factors tends to infinity. We propose a natural ... More

Upper and Lower Semimodularity of the Supercharacter Theory Lattices of Cyclic GroupsMar 07 2012We consider the lattice of supercharacter theories, in the sense of Diaconis and Isaacs, of the cyclic group of order n. We find necessary and sufficient conditions on n for that lattice to be upper or lower semimodular.

Alchemical and structural distribution based representation for improved QMLDec 22 2017We introduce a representation of any atom in any chemical environment for the generation of efficient quantum machine learning (QML) models of common electronic ground-state properties. The representation is based on scaled distribution functions explicitly ... More

One-way quantum repeater based on near-deterministic photon-emitter interfacesJul 11 2019We propose a novel one-way quantum repeater architecture based on photonic tree-cluster states. Encoding a qubit in a photonic tree-cluster protects the information from transmission loss and enables long-range quantum communication through a chain of ... More

Interface of the polarizable continuum model of solvation with semi-empirical methods in the GAMESS programMar 19 2013May 22 2013An interface between semi-empirical methods and the polarized continuum model (PCM) of solvation successfully implemented into GAMESS following the approach by Chudinov et al (Chem. Phys. 1992, 160, 41). The interface includes energy gradients and is ... More

Demonstration of suppressed phonon tunneling losses in phononic bandgap shielded membrane resonators for high-Q optomechanicsDec 30 2013Dielectric membranes with exceptional mechanical and optical properties present one of the most promising platforms in quantum opto-mechanics. The performance of stressed silicon nitride nanomembranes as mechanical resonators notoriously depends on how ... More

Using superlattice potentials to probe long-range magnetic correlations in optical latticesSep 02 2015Sep 04 2015In Pedersen et al. (2011) we proposed a method to utilize a temporally dependent superlattice potential to mediate spin-selective transport, and thereby probe long and short range magnetic correlations in optical lattices. Specifically this can be used ... More

Probing spatial spin correlations of ultracold gases by quantum noise spectroscopySep 01 2008Dec 11 2008Spin noise spectroscopy with a single laser beam is demonstrated theoretically to provide a direct probe of the spatial correlations of cold fermionic gases. We show how the generic many-body phenomena of anti-bunching, pairing, antiferromagnetic, and ... More

Holographic Resonant Laser Printing of metasurfaces using plasmonic templateAug 18 2017Jan 04 2018Laser printing with a spatial light modulator (SLM) has several advantages over conventional raster-writing and dot-matrix display (DMD) writing: multiple pixel exposure, high power endurance and existing software for computer generated holograms (CGH). ... More

EEG source imaging assists decoding in a face recognition taskApr 17 2017EEG based brain state decoding has numerous applications. State of the art decoding is based on processing of the multivariate sensor space signal, however evidence is mounting that EEG source reconstruction can assist decoding. EEG source imaging leads ... More

Unique Bernoulli g-measuresApr 05 2010We improve and subsume the conditions of Johansson and \"Oberg [18] and Berbee [2] for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique g-measures have Bernoulli natural ... More

Detection of weak microwave fields with an underdamped Josephson junctionMay 19 2016May 23 2016We have constructed a microwave detector based on the voltage switching of an underdamped Josephson junction, that is positioned at a current antinode of a {\lambda}/4 coplanar waveguide resonator. By measuring the switching current and the transmission ... More

Non-localized states and high hole mobility in amorphous germaniumAug 22 2019Covalent amorphous semiconductors, such as amorphous silicon (a-Si) and germanium (a-Ge), are commonly believed to have localized electronic states at the top of the valence band and the bottom of the conduction band. Electrical conductivity is thought ... More

Neural Networks for Full Phase-space Reweighting and Parameter TuningJul 18 2019Aug 17 2019Precise scientific analysis in collider-based particle physics is possible because of complex simulations that connect fundamental theories to observable quantities. The significant computational cost of these programs limits the scope, precision, and ... More