Results for "Anders S. Buch"

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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
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 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
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
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
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
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
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
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
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
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
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
A qualitative quantum rate model for hydrogen transfer in soybean lipoxygenaseDec 09 2016Nov 04 2017The hydrogen transfer reaction catalysed by soybean lipoxygenase (SLO) has been the focus of intense study following observations of a high kinetic isotope effect (KIE). Today high KIEs are generally thought to indicate departure from classical rate theory ... 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.
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
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.
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
Distributed Robust Stability Analysis of Interconnected Uncertain SystemsNov 06 2012This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic constraints. This ... More
Robust Stability Analysis of Sparsely Interconnected Uncertain SystemsNov 11 2013In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems ... 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
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
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
Distributed Robustness Analysis of Interconnected Uncertain Systems Using Chordal DecompositionFeb 10 2014Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions. Aside from the heavy computational cost of solving centralized robust stability analysis techniques, privacy requirements in the network can also introduce ... More
Distributed Semidefinite Programming with Application to Large-scale System AnalysisApr 29 2015Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled problem has an inherent ... 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
Scalable Dissipative Preparation of Many-Body EntanglementJan 26 2015Sep 09 2016We present a technique for the dissipative preparation of highly entangled multiparticle states of atoms coupled to common oscillator modes. By combining local spontaneous emission with coherent couplings we engineer many-body dissipation that drives ... More
Elementary test for non-classicality based on measurements of position and momentumAug 04 2015We generalise a non-classicality test described by Kot et al. [Phys. Rev. Lett. 108, 233601 (2010)], which can be used to rule out any classical description of a physical system. The test is based on measurements of quadrature operators and works by proving ... 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
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
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
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
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
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
Interfacing superconducting qubits and single optical photons using molecules in waveguidesJul 21 2016Apr 06 2017We propose an efficient light-matter interface at optical frequencies between a single photon and a superconducting qubit. The desired interface is based on a hybrid architecture composed of an organic molecule embedded inside an optical waveguide and ... More
Electro-optomechanical equivalent circuits for quantum transductionOct 27 2017Jun 14 2018Using the techniques of optomechanics, a high-$Q$ mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of classical signals ... More
Photon Scattering from a System of Multi-Level Quantum Emitters. II. Application to Emitters Coupled to a 1D WaveguideJan 09 2018In a preceding paper we introduced a formalism to study the scattering of low intensity fields from a system of multi-level emitters embedded in a $3$D dielectric medium. Here we show how this photon-scattering relation can be used to analyze the scattering ... 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
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
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
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
Characterization of topological states on a lattice with Chern numberJun 06 2007Dec 04 2007We study Chern numbers to characterize the ground state of strongly interacting systems on a lattice. This method allows us to perform a numerical characterization of bosonic fractional quantum Hall (FQH) states on a lattice where conventional overlap ... More
Distributed Interior-point Method for Loosely Coupled ProblemsDec 19 2013In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first order methods. ... More
Distributed Primal-dual Interior-point Methods for Solving Loosely Coupled Problems Using Message PassingFeb 23 2015Jun 29 2015In this paper, we propose a distributed algorithm for solving loosely coupled problems with chordal sparsity which relies on primal-dual interior-point methods. We achieve this by distributing the computations at each iteration, using message-passing. ... 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.
Nearly quantum limited nanoSQUIDs based on cross-type Nb/AlOx/Nb junctionsMay 17 2017We report on the development of nearly quantum limited SQUIDs with miniature pickup loop dimensions. The implemented high quality and low capacitance cross-type Nb/AlOx/Nb Josephson junctions offer large $I_CR_N$-products and therefore enable an exceptional ... More
Long-lived non-classical correlations for scalable quantum repeaters at room temperatureJan 10 2018Heralded single-photon sources with on-demand readout are promising candidates for quantum repeaters enabling long-distance quantum communication. The need for scalability of such systems requires simple experimental solutions, thus favouring room-temperature ... 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
Counting non-standard binary representationsSep 03 2015Let $\mathcal{A}$ be a finite subset of $\mathbb{N}$ including $0$ and $f_\mathcal{A}(n)$ be the number of ways to write $n=\sum_{i=0}^{\infty}\epsilon_i2^i$, where $\epsilon_i\in\mathcal{A}$. We consider asymptotics of the summatory function $s_\mathcal{A}(r,m)$ ... More
Spikes as regularizersNov 18 2016We present a confidence-based single-layer feed-forward learning algorithm SPIRAL (Spike Regularized Adaptive Learning) relying on an encoding of activation spikes. We adaptively update a weight vector relying on confidence estimates and activation offsets ... More
Subword counting and the incidence algebraFeb 10 2015Mar 11 2015The Pascal matrix, $P$, is an upper diagonal matrix whose entries are the binomial coefficients. In 1993 Call and Velleman demonstrated that it satisfies the beautiful relation $P=\exp(H)$ in which $H$ has the numbers 1, 2, 3, etc. on its superdiagonal ... More
Tempo-Invariant Processing of Rhythm with Convolutional Neural NetworksApr 22 2018Apr 28 2018Rhythm patterns can be performed with a wide variation of tempi. This presents a challenge for many music information retrieval (MIR) systems; ideally, perceptually similar rhythms should be represented and processed similarly, regardless of the specific ... More
Deep Layered Learning in MIRApr 18 2018Dec 10 2018Deep learning has boosted the performance of many music information retrieval (MIR) systems in recent years. Yet, the complex hierarchical arrangement of music makes end-to-end learning hard for some MIR tasks - a very deep and flexible processing chain ... More
The Ground State Energy of a Dilute Bose Gas in Dimension n >3Jan 23 2014Mar 24 2014We consider a Bose gas in spatial dimension $n>3$ with a repulsive, radially symmetric two-body potential $V$. In the limit of low density $\rho$, the ground state energy per particle in the thermodynamic limit is shown to be $(n-2)|\mathbb S^{n-1}|a^{n-2}\rho$, ... 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
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
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
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 Dirichlet problem for p-harmonic functions on the topologist's combApr 05 2013In this paper we study the Perron method for solving the p-harmonic Dirichlet problem on the topologist's comb. For functions which are bounded and continuous at the accessible points, we obtain invariance of the Perron solutions under arbitrary perturbations ... 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
Multi-Adaptive Galerkin Methods for ODEs II: Implementation and ApplicationsMay 12 2012Continuing the discussion of the multi-adaptive Galerkin methods mcG(q) and mdG(q) presented in [A. Logg, SIAM J. Sci. Comput., 24 (2003), pp. 1879-1902], we present adaptive algorithms for global error control, iterative solution methods for the discrete ... More
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
Projective lines as groupoids with projection structureOct 20 2013The coordinate projective line over a field is seen as a groupoid with a further `projection' structure. We investigate conversely to what extent such an, abstractly given, groupoid may be coordinatized by a suitable field constructed out of the geometry. ... More
Fibrations as Eilenberg-Moore algebrasDec 05 2013We give an elementary exposition of some fundamental facts about fibered (or rather opfibered) categories, in terms of monads and 2-categories. The account avoids any mention of category-valued functors and pseudofunctors.
On the uniform equidistribution of closed horospheres in hyperbolic manifoldsMar 17 2011We prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. This extends earlier results by Hejhal and Str\"ombergsson in dimension 2. Our proofs use spectral methods, and ... More
Monads and extensive quantitiesMar 30 2011If T is a commutative monad on a cartesian closed category, then there exists a natural T-bilinear pairing from T(X) times the space of T(1)-valued functions on X ("integration"), as well as a natural T-bilinear action on T(X) by the space of these functions. ... More
A linear threshold for uniqueness of solutions to random jigsaw puzzlesJan 17 2017Aug 15 2018We consider a problem introduced by Mossel and Ross [Shotgun assembly of labeled graphs, arXiv:1504.07682]. Suppose a random $n\times n$ jigsaw puzzle is constructed by independently and uniformly choosing the shape of each "jig" from $q$ possibilities. ... More
Multiadaptive Galerkin Methods for ODEs III: A Priori Error EstimatesMay 14 2012The multiadaptive continuous/discontinuous Galerkin methods mcG(q) and mdG(q) for the numerical solution of initial value problems for ordinary differential equations are based on piecewise polynomial approximation of degree q on partitions in time with ... More
A comparison theorem for $f$-vectors of simplicial polytopesMay 12 2006Nov 07 2006Let $f_i(P)$ denote the number of $i$-dimensional faces of a convex polytope $P$. Furthermore, let $S(n,d)$ and $C(n,d)$ denote, respectively, the stacked and the cyclic $d$-dimensional polytopes on $n$ vertices. Our main result is that for every simplicial ... More
Random walks, arrangements, cell complexes, greedoids, and self-organizing librariesMay 01 2008The starting point is the known fact that some much-studied random walks on permutations, such as the Tsetlin library, arise from walks on real hyperplane arrangements. This paper explores similar walks on complex hyperplane arrangements. This is achieved ... More
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
Limitations of two-level emitters as non-linearities in two-photon controlled phase gatesDec 14 2016Apr 04 2017We investigate the origin of imperfections in the fidelity of a two-photon controlled-phase gate based on two-level-emitter non-linearities. We focus on a passive system that operates without external modulations to enhance its performance. We demonstrate ... More
Long-distance entanglement distribution using individual atoms in optical cavitiesApr 14 2015Jul 20 2015Individual atoms in optical cavities can provide an efficient interface between stationary qubits and flying qubits (photons), which is an essentiel building block for quantum communication. Furthermore, cavity assisted controlled-not (CNOT) gates can ... 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 Allophiles Improve Entropic AssemblyJun 25 2015We investigate a class of "shape allophiles" that fit together like puzzle pieces as a method to access and stabilize desired structures by controlling directional entropic forces. Squares are cut into rectangular halves, which are shaped in an allophilic ... 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.
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
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
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
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
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
Fast Entanglement Distribution with Atomic Ensembles and Fluorescent DetectionJul 22 2009Nov 09 2009Quantum repeaters based on atomic ensemble quantum memories are promising candidates for achieving scalable distribution of entanglement over long distances. Recently, important experimental progress has been made towards their implementation. However, ... More
Distributed Quantum Computation Based-on Small Quantum RegistersSep 28 2007Nov 21 2007We describe and analyze an efficient register-based hybrid quantum computation scheme. Our scheme is based on probabilistic, heralded optical connection among local five-qubit quantum registers. We assume high fidelity local unitary operations within ... More
Spin-Photon Entangling DiodeFeb 28 2007Mar 05 2007We propose a semiconductor device that can electrically generate entangled electron spin-photon states, providing a building block for entanglement of distant spins. The device consists of a p-i-n diode structure that incorporates a coupled double quantum ... More
Mediated Digraphs and Quantum NonlocalityNov 30 2004Mar 09 2006A digraph D=(V,A) is mediated if, for each pair x,y of distinct vertices of D, either xy belongs to A or yx belongs to A or there is a vertex z such that both xz,yz belong to A. For a digraph D, DELTA(D) is the maximum in-degree of a vertex in D. The ... More