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The finite temperature QCD phase transition with domain wall fermionsNov 02 1999Results from the Columbia lattice group study of the QCD finite temperature phase transition with dynamical domain wall fermions on $16^3 \times 4$ lattices are presented. These results include an investigation of the U(1) axial symmetry breaking above ... More

Domain wall fermions and applicationsNov 15 2000Domain wall fermions provide a complimentary alternative to traditional lattice fermion approaches. By introducing an extra dimension, the amount of chiral symmetry present in the lattice theory can be controlled in a linear way. This results in improved ... More

The BlueGene/L SupercomputerDec 17 2002The architecture of the BlueGene/L massively parallel supercomputer is described. Each computing node consists of a single compute ASIC plus 256 MB of external memory. The compute ASIC integrates two 700 MHz PowerPC 440 integer CPU cores, two 2.8 Gflops ... More

Gauged And Ungauged: A Nonperturbative TestFeb 08 2018We study the thermodynamics of the `ungauged' D0-brane matrix model by Monte Carlo simulation. Our results appear to be consistent with the conjecture by Maldacena and Milekhin.

A numerical test of the continuum index theorem on the latticeFeb 06 1997The overlap formalism of chiral fermions provides a tool to measure the index, Q, of the chiral Dirac operator in a fixed gauge field background on the lattice. This enables a numerical measurement of the probability distribution, p(Q), in Yang-Mills ... More

Gap Domain Wall FermionsJun 22 2006Jul 03 2006I demonstrate that the chiral properties of Domain Wall Fermions (DWF) in the large to intermediate lattice spacing regime of QCD, 1 to 2 GeV, are significantly improved by adding to the action two standard Wilson fermions with supercritical mass equal ... More

Moebius Algorithm for Domain Wall and GapDW FermionsJun 15 2009Nov 10 2009The M\"obius domain wall action \cite{Brower:2004xi} is a generalization of Shamir's action, which gives exactly the same overlap fermion lattice action as the separation ($L_s$) between the domain walls is taken to infinity. The performance advantages ... More

Domain Wall Fermions and Chiral Symmetry Restoration RateSep 25 1997Domain Wall Fermions utilize an extra space time dimension to provide a method for restoring the regularization induced chiral symmetry breaking in lattice vector gauge theories even at finite lattice spacing. The breaking is restored at an exponential ... More

Chiral Symmetry Restoration in the Schwinger Model with Domain Wall FermionsMay 17 1997Dec 19 1997Domain Wall Fermions utilize an extra space time dimension to provide a method for restoring the regularization induced chiral symmetry breaking in lattice vector gauge theories even at finite lattice spacing. The breaking is restored at an exponential ... More

The $I=1$, $J=1$ channel of the O(4) $λφ^4_4$ theoryOct 27 1992A Monte Carlo simulation of the $O(4)$ $\lambda \phi^4$ theory in the broken phase is performed on a hypercubic lattice in search of an $I=1$, $J=1$ resonance. We investigate the region of the cutoff theory where the interaction is strong as it is there ... More

The staggered domain wall fermion methodJul 16 2002Oct 04 2002A different lattice fermion method is introduced. Staggered domain wall fermions are defined in 2n+1 dimensions and describe 2^n flavors of light lattice fermions with exact U(1) x U(1) chiral symmetry in 2n dimensions. As the size of the extra dimension ... More

Dynamical lattice QCD thermodynamics and the U(1)_A symmetry with domain wall fermionsMar 15 1999Apr 26 1999Results from numerical simulations of full, two flavor QCD thermodynamics at N_t=4 with domain wall fermions are presented. For the first time a numerical simulation of the full QCD phase transition displays a low temperature phase with spontaneous chiral ... More

The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theoryMar 09 1993We study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments we show that the critical exponent $\nu$ describing the vanishing of the physical mass at the critical ... More

A simulation of the Schwinger model in the overlap formalismMar 12 1995In the continuum, the single flavor massless Schwinger model has an exact global axial $U(1)$ symmetry in the sector of perturbative gauge fields. This symmetry is explicitly broken by gauge fields with nonzero topological charge inducing a nonzero expectation ... More

Is there a $ρ$ in the O(4) $λφ^4_4$ theory?Apr 08 1992A Monte Carlo simulation of the O(4) $\lambda \phi^4$ theory in the broken phase is performed on a hypercubic lattice in search of an I=1, J=1 resonance. The region of the cutoff theory where the interaction is strong is investigated since it is there ... More

Large $N$ analysis of the Higgs mass triviality boundJul 22 1992We calculate the triviality bound on the Higgs mass in scalar field theory models whose global symmetry group $SU(2)_L \times SU(2)_{\rm custodial} \approx O(4)$ has been replaced by $O(N)$ and $N$ has been taken to infinity. Limits on observable cutoff ... More

Interacting staggered domain wall fermionsAug 22 2002The behavior of staggered domain wall fermions in the presence of gauge fields is presented. In particular, their response to gauge fields with nontrivial topology is discussed.

Random Walks and the Correlation Length Critical Exponent in Scalar Quantum Field TheoryApr 08 1992The distance scale for a quantum field theory is the correlation length $\xi$, which diverges with exponent $\nu$ as the bare mass approaches a critical value. If $t=m^{2}-m_{c}^{2}$, then $\xi=m_{P}^{-1} \sim t^{-\nu}$ as $t \to 0$. The two-point function ... More

The algebra of local unitary invariants of identical particlesJul 12 2011We investigate the properties of the inverse limit of the algebras of local unitary invariant polynomials of quantum systems containing various types of fermionic and/or bosonic particles as the dimensions of the single particle state spaces tend to infinity. ... More

An algebraically independent generating set of the algebra of local unitary invariantsFeb 14 2011We show that the inverse limit of the graded algebras of local unitary invariant polynomials of finite dimensional k-partite quantum systems is free, and give an algebraically independent generating set. The number of degree 2d invariants in the generating ... More

Approaching Conformality with Ten FlavorsApr 26 2012Jun 05 2012We present first results for lattice simulations, on a single volume, of the low-lying spectrum of an SU(3) Yang-Mills gauge theory with ten light fermions in the fundamental representation. Fits to the fermion mass dependence of various observables are ... More

Strongly interacting dynamics and the search for new physics at the LHCJan 15 2016Jan 28 2016We present results for the spectrum of a strongly interacting SU(3) gauge theory with $N_f = 8$ light fermions in the fundamental representation. Carrying out non-perturbative lattice calculations at the lightest masses and largest volumes considered ... More

Regularization dependence of the Higgs mass triviality boundOct 22 1992We calculate the triviality bound on the Higgs mass in scalar field theory models whose global symmetry group $SU(2)_L \times SU(2)_{\rm custodial} \approx O(4)$ has been replaced by $O(N)$ and $N$ has been taken to infinity. Limits on observable cutoff ... More

Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavorsJul 23 2018Jan 16 2019We present our lattice studies of SU(3) gauge theory with $N_f$ = 8 degenerate fermions in the fundamental representation. Using nHYP-smeared staggered fermions we study finite-temperature transitions on lattice volumes as large as $L^3 \times N_t = 48^3 ... More

Controlling Residual Chiral Symmetry Breaking in Domain Wall Fermion SimulationsFeb 16 2009At stronger gauge-field couplings, the domain wall fermion (DWF) residual mass, a measure of chiral symmetry breaking, grows rapidly. This measure is largely due to near zero fermion eigenmodes of logarithm of the 4D transfer matrix along the fifth dimension, ... More

Zamolodchikov integrability via rings of invariantsJun 17 2015Sep 05 2016Zamolodchikov periodicity is periodicity of certein recursions associated with box products $X \square Y$ of two finite type Dynkin diagrams. We suggest an affine analog of Zamolodchikov periodicity, which we call Zamolodchikov integrability. We conjecture ... More

Non-Crossing TableauxJul 08 2006Jul 18 2006In combinatorics there is a well-known duality between non-nesting and non-crossing objects. In algebra there are many objects which are standard, for example Standard Young Tableaux, Standard Monomials, Standard Bitableaux. We adopt a point of view that ... More

On plethysm conjectures of Stanley and Foulkes: the $2 \times n$ caseJun 26 2004We prove Stanley's plethysm conjecture for the $2 \times n$ case, which composed with the work of Black and List provides another proof of Foulkes conjecture for the $2 \times n$ case. We also show that the way Stanley formulated his conjecture, it is ... More

A lower bound for the rank of a universal quadratic form with integer coefficients in a totally real number fieldAug 04 2018We show that if $K$ is a monogenic, primitive, totally real number field, that contains units of every signature, then there exists a lower bound for the rank of integer universal quadratic forms defined over $K$. In particular, we extend the work of ... More

A_2-web immanantsDec 16 2007We describe the rank 3 Temperley-Lieb-Martin algebras in terms of Kuperberg's A_2-webs. We define consistent labelings of webs, and use them to describe the coefficients of decompositions into irreducible webs. We introduce web immanants, inspired by ... More

The Veldkamp space of multiple qubitsJun 19 2009Jan 24 2010We introduce a point-line incidence geometry in which the commutation relations of the real Pauli group of multiple qubits are fully encoded. Its points are pairs of Pauli operators differing in sign and each line contains three pairwise commuting operators ... More

Special entangled quantum systems and the Freudenthal constructionFeb 13 2009Mar 17 2009We consider special quantum systems containing both distinguishable and identical constituents. It is shown that for these systems the Freudenthal construction based on cubic Jordan algebras naturally defines entanglement measures invariant under the ... More

Entanglement distillation from Greenberger-Horne-Zeilinger sharesMar 12 2016Mar 30 2016We study the problem of converting a product of Greenberger-Horne-Zeilinger (GHZ) states shared by subsets of several parties in an arbitrary way into GHZ states shared by every party. Our result is that if SLOCC transformations are allowed, then the ... More

Precision lattice test of the gauge/gravity duality at large-$N$Jun 15 2016We pioneer a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-$N$ and continuum limits of the gauge theory are taken for the first time at various temperatures $0.4 \leq T \leq 1.0$. As a way to directly test the gauge/gravity ... More

Supergravity from D0-brane Quantum MechanicsJun 15 2016The gauge/gravity duality conjecture claims the equivalence between gauge theory and superstring/M-theory. In particular, the one-dimensional gauge theory of D0-branes and type IIA string theory should agree on properties of hot black holes. Type IIA ... More

Anomalous Chiral Symmetry Breaking above the QCD Phase TransitionJul 08 1998We study the anomalous breaking of U_A(1) symmetry just above the QCD phase transition for zero and two flavors of quarks, using a staggered fermion, lattice discretization. The properties of the QCD phase transition are expected to depend on the degree ... More

Gluinos condensing at the CCNI: 4096 CPUs weigh inJul 13 2008Jul 31 2008We report preliminary results of lattice super-Yang-Mills computations using domain wall fermions, performed at an actual rate of 1000 Gflop/s, over the course of six months, using two BlueGene/L racks at Rensselaer's CCNI supercomputing center. This ... More

Nuclear Parity Violation from Lattice QCDNov 06 2015The electroweak interaction at the level of quarks and gluons are well understood from precision measurements in high energy collider experiments. Relating these fundamental parameters to Hadronic Parity Violation in nuclei however remains an outstanding ... More

Magnetic monopole plasma phase in (2+1)d compact quantum electrodynamics with fermionic matterMay 16 2011Jul 28 2011We present the first evidence from lattice simulations that the magnetic monopoles in three dimensional compact quantum electrodynamics (cQED3) with N_f=2 and N_f= 4 four-component fermion flavors are in a plasma phase. The evidence is based mainly on ... More

Lattice super-Yang-Mills using domain wall fermions in the chiral limitOct 31 2008Dec 09 2008Lattice N=1 super-Yang-Mills theory formulated using Ginsparg-Wilson fermions provides a rigorous non-perturbative definition of the continuum theory that requires no fine-tuning as the lattice spacing is reduced to zero. Domain wall fermions are one ... More

Effects of Content Popularity on the Performance of Content-Centric Opportunistic Networking: An Analytical Approach and ApplicationsJan 20 2016Mobile users are envisioned to exploit direct communication opportunities between their portable devices, in order to enrich the set of services they can access through cellular or WiFi networks. Sharing contents of common interest or providing access ... More

Dual Filtered GraphsOct 28 2014May 02 2016We define a K-theoretic analogue of Fomin's dual graded graphs, which we call dual filtered graphs. The key formula in the definition is DU-UD= D + I. Our major examples are K-theoretic analogues of Young's lattice, of shifted Young's lattice, and of ... More

Spherically symmetric solutions in Covariant Horava-Lifshitz GravityOct 18 2010Mar 25 2011We study the most general case of spherically symmetric vacuum solutions in the framework of the Covariant Horava Lifshitz Gravity, for an action that includes all possible higher order terms in curvature which are compatible with power-counting normalizability ... More

Crystals and total positivity on orientable surfacesAug 11 2010We develop a combinatorial model of networks on orientable surfaces, and study weight and homology generating functions of paths and cycles in these networks. Network transformations preserving these generating functions are investigated. We describe ... More

Lattice Schwarzian Boussinesq equation and two-component systemsFeb 26 2012Mar 15 2012Various new two-component systems related to the lattice Schwarzian Boussinesq equation are constructed in a systematic way from conservation laws. Their multidimensional consistency is demonstrated, Lax pairs, symmetries and conservation laws are derived ... More

Symmetries and conservation laws of lattice Boussinesq equationsDec 29 2011Sequences of canonical conservation laws and generalized symmetries for the lattice Boussinesq and the lattice modified Boussinesq systems are successively derived. The interpretation of these symmetries as differential-difference equations leads to corresponding ... More

Fast DD-classification of functional dataMar 05 2014Jan 28 2016A fast nonparametric procedure for classifying functional data is introduced. It consists of a two-step transformation of the original data plus a classifier operating on a low-dimensional hypercube. The functional data are first mapped into a finite-dimensional ... More

Possible solution of the Coriolis attenuation problemNov 05 1996The most consistently useful simple model for the study of odd deformed nuclei, the particle-rotor model (strong coupling limit of the core-particle coupling model) has nevertheless been beset by a long-standing problem: It is necessary in many cases ... More

K-theoretic Poirier-Reutenauer bialgebraApr 16 2014We use the K-Knuth equivalence of Buch and Samuel to define a K-theoretic analogue of the Poirier-Reutenauer Hopf algebra. As an application, we rederive the K-theoretic Littlewood-Richardson rules of Thomas and Yong and of Buch and Samuel.

Signature of a universal statistical description for drift-wave plasma turbulenceAug 19 2010This Letter provides a theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events. Specifically, nonlinear gyrokinetic simulations of ion-temperature-gradient turbulence produce time ... More

The classification of Zamolodchikov periodic quiversMar 12 2016Feb 28 2017Zamolodchikov periodicity is a property of certain discrete dynamical systems associated with quivers. It has been shown by Keller to hold for quivers obtained as products of two Dynkin diagrams. We prove that the quivers exhibiting Zamolodchikov periodicity ... More

Quivers with subadditive labelings: classification and integrabilityJun 15 2016Mar 07 2017Strictly subadditive, subadditive and weakly subadditive labelings of quivers were introduced by the second author, generalizing Vinberg's definition for undirected graphs. In our previous work we have shown that quivers with strictly subadditive labelings ... More

The asymptotic spectrum of LOCC transformationsJul 13 2018Aug 16 2018We study exact, non-deterministic conversion of multipartite pure quantum states into one-another via local operations and classical communication (LOCC) and asymptotic entanglement transformation under such channels. In particular, we consider the maximal ... More

Analysing the Effects of Routing Centralization on BGP Convergence TimeMay 28 2016Software-defined networking (SDN) has improved the routing functionality in networks like data centers or WANs. Recently, several studies proposed to apply the SDN principles in the Internet's inter-domain routing as well. This could offer new routing ... More

P-partition products and fundamental quasi-symmetric function positivitySep 08 2006We show that certain differences of products of $P$-partition generating functions are positive in the basis of fundamental quasi-symmetric functions L_\alpha. This result interpolates between recent Schur positivity and monomial positivity results of ... More

Derivation and assessment of strong coupling core-particle model from the Kerman-Klein-Dönau-Frauendorf theoryAug 08 1996We review briefly the fundamental equations of a semi-microscopic core-particle coupling method that makes no reference to an intrinsic system of coordinates. We then demonstrate how an intrinsic system can be introduced in the strong coupling limit so ... More

Total positivity in loop groups II: Chevalley generatorsJun 02 2009Dec 06 2009This is the second in a series of papers developing a theory of total positivity for loop groups. In this paper, we study infinite products of Chevalley generators. We show that the combinatorics of infinite reduced words underlies the theory, and develop ... More

Soft Cache Hits and the Impact of Alternative Content Recommendations on Mobile Edge CachingSep 30 2016Caching popular content at the edge of future mobile networks has been widely considered in order to alleviate the impact of the data tsunami on both the access and backhaul networks. A number of interesting techniques have been proposed, including femto-caching ... More

Discrete solitons in infinite reduced wordsJun 03 2016Jan 27 2017We consider a discrete dynamical system where the roles of the states and the carrier are played by translations in an affine Weyl group of type $A$. The Coxeter generators are enriched by parameters, and the interactions with the carrier are realized ... More

Intrinsic energy is a loop Schur functionMar 20 2010Jul 24 2014We give an explicit subtraction-free formula for the energy function in tensor products of Kirillov-Reshetikhin crystals for symmetric powers of the standard representation of U_q'(\hat sl_n). The energy function is shown to be the tropicalization of ... More

Linear Laurent phenomenon algebrasJun 12 2012Oct 18 2012In [LP] we introduced Laurent phenomenon algebras, a generalization of cluster algebras. Here we give an explicit description of Laurent phenomenon algebras with a linear initial seed arising from a graph. In particular, any graph associahedron is shown ... More

Automatic Classification of Variable Stars in Catalogs with missing dataOct 29 2013We present an automatic classification method for astronomical catalogs with missing data. We use Bayesian networks, a probabilistic graphical model, that allows us to perform inference to pre- dict missing values given observed data and dependency relationships ... More

Combinatorial Hopf algebras and K-homology of GrassmaniansMay 15 2007Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be thought of as K-theoretic analogues of the by now classical ``square'' of Hopf algebras ... More

The classification of Zamolodchikov periodic quiversMar 12 2016Apr 01 2016Zamolodchikov periodicity is a property of certain discrete dynamical systems associated with quivers. It has been shown by Keller to hold for quivers obtained as products of two Dynkin diagrams. We prove that the quivers exhibiting Zamolodchikov periodicity ... More

Tensor diagrams and cluster algebrasOct 05 2012May 18 2015The rings of SL(V) invariants of configurations of vectors and linear forms in a finite-dimensional complex vector space V were explicitly described by Hermann Weyl in the 1930s. We show that when V is 3-dimensional, each of these rings carries a natural ... More

Cell transfer and monomial positivityMay 12 2005Dec 20 2006We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions ... More

Ising model and the positive orthogonal GrassmannianJul 09 2018Sep 29 2018We completely describe by inequalities the set of boundary correlation matrices of planar Ising networks embedded in a disk. Specifically, we build on a recent result of M.~Lis to give a simple bijection between such correlation matrices and points in ... More

Discrete solitons in infinite reduced wordsJun 03 2016We consider a discrete dynamical system where the roles of the states and the carrier are played by translations in an affine Weyl group of type $A$. The Coxeter generators are enriched by parameters, and the interactions with the carrier are realized ... More

Laurent phenomenon algebrasJun 12 2012Jan 21 2016We generalize Fomin and Zelevinsky's cluster algebras by allowing exchange polynomials to be arbitrary irreducible polynomials, rather than binomials.

Affine geometric crystals in unipotent loop groupsApr 13 2010We study products of the affine geometric crystal of type A corresponding to symmetric powers of the standard representation. The quotient of this product by the R-matrix action is constructed inside the unipotent loop group. This quotient crystal has ... More

A metric interpretation of reflexivity for Banach spacesApr 25 2016We define two metrics $d_{1,\alpha}$ and $d_{\infty,\alpha}$ on each Schreier family $\mathcal{S}_\alpha$, $\alpha<\omega_1$, with which we prove the following metric characterization of reflexivity of a Banach space $X$: $X$ is reflexive if and only ... More

Exact computation of the halfspace depthNov 25 2014Jan 12 2016For computing the exact value of the halfspace depth of a point w.r.t. a data cloud of $n$ points in arbitrary dimension, a theoretical framework is suggested. Based on this framework a whole class of algorithms can be derived. In all of these algorithms ... More

Application of the Kerman-Klein method to the solution of a spherical shell model for a deformed rare-earth nucleusFeb 19 1997Core-particle coupling models are made viable by assuming that core properties such as matrix elements of multipole and pairing operators and excitation spectra are known independently. From the completeness relation, it is seen, however, that these quantities ... More

Temperley-Lieb pfaffinants and Schur $Q$-positivity conjecturesDec 28 2006We study pfaffian analogues of immanants, which we call pfaffinants. Our main object is the TL-pfaffinants which are analogues of Rhoades and Skandera's TL-immanants. We show that TL-pfaffinants are positive when applied to planar networks and explain ... More

Quivers with subadditive labelings: classification and integrabilityJun 15 2016Strictly subadditive, subadditive and weakly subadditive labelings of quivers were introduced by the second author, generalizing Vinberg's definition for undirected graphs. In our previous work we have shown that quivers with strictly subadditive labelings ... More

Webs on surfaces, rings of invariants, and clustersAug 08 2013We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of three-dimensional vectors, covectors, and matrices. The construction uses Kuperberg's calculus of webs on marked surfaces with ... More

Exponential loss of memory for the 2-dimensional Allen-Cahn equation with small noiseAug 13 2018We prove an asymptotic coupling theorem for the $2$-dimensional Allen--Cahn equation perturbed by a small space-time white noise. We show that with overwhelming probability two profiles that start close to the minimisers of the potential of the deterministic ... More

Quivers with additive labelings: classification and algebraic entropyApr 17 2017May 09 2017We show that Zamolodchikov dynamics of a recurrent quiver has zero algebraic entropy only if the quiver has a weakly subadditive labeling, and conjecture the converse. By assigning a pair of generalized Cartan matrices of affine type to each quiver with ... More

Puzzles in $K$-homology of GrassmanniansJan 23 2018Knutson, Tao, and Woodward formulated a Littlewood-Richardson rule for the cohomology ring of Grassmannians in terms of puzzles. Vakil and Wheeler-Zinn-Justin have found additional triangular puzzle pieces that allow one to express structure constants ... More

Families of Integrable EquationsJun 03 2011Oct 28 2011We present a method to obtain families of lattice equations. Specifically we focus on two of such families, which include 3-parameters and their members are connected through B\"acklund transformations. At least one of the members of each family is integrable, ... More

Y-meshes and generalized pentagram mapsMar 06 2015Feb 03 2016We introduce a rich family of generalizations of the pentagram map sharing the property that each generates an infinite configuration of points and lines with four points on each line. These systems all have a description as $Y$-mutations in a cluster ... More

A family of bijections between G-parking functions and spanning treesJul 22 2003Jun 30 2004For a directed graph G on vertices {0,1,...,n}, a G-parking function is an n-tuple (b_1,...,b_n) of non-negative integers such that, for every non-empty subset U of {1,...,n}, there exists a vertex j in U for which there are more than b_j edges going ... More

Spherically symmetric solutions, Newton's Law and IR limit λ->1, in Covariant Horava Lifshitz GravityAug 05 2011Aug 26 2015In this note we examine whether spherically symmetric solutions in Covariant Horava Lifshitz Gravity can reproduce Newton's Law in the IR limit \lambda->1. We adopt the position that the auxiliary field A is independent of the space-time metric [10,11], ... More

Total positivity in loop groups I: whirls and curlsDec 04 2008Dec 06 2009This is the first of a series of papers where we develop a theory of total positivity for loop groups. In this paper, we completely describe the totally nonnegative part of the polynomial loop group GL_n(\R[t,t^{-1}]), and for the formal loop group GL_n(\R((t))) ... More

Inverse problem in cylindrical electrical networksApr 26 2011In this paper we study the inverse Dirichlet-to-Neumann problem for certain cylindrical electrical networks. We define and study a birational transformation acting on cylindrical electrical networks called the electrical $R$-matrix. We use this transformation ... More

Electrical networks and Lie theoryMar 17 2011Jan 21 2016We introduce a new class of "electrical" Lie groups. These Lie groups, or more precisely their nonnegative parts, act on the space of planar electrical networks via combinatorial operations previously studied by Curtis-Ingerman-Morrow. The corresponding ... More

On products of sl_n characters and support containmentAug 04 2006Let $\lambda$, $\mu$, $\nu$ and $\rho$ be dominant weights of $\mathfrak{sl_n}$ satisfying $\lambda + \mu = \nu + \rho$. Let $V_{\lambda}$ denote the highest weight module corresponding to $\lambda$. Lam, Postnikov, Pylyavskyy conjectured a sufficient ... More

Analysis of Parasitic Signals in the Method of Recoil Nuclei Applied to Direct Observation of the Th-229m Isomeric StateJul 08 2014We carry out necessary theoretical justifications for the method of recoil nuclei in application to direct observation of the Th-229m isomeric state. We consider Cherenkov radiation, phosphorescence and fluorescence in the crystal plate which is used ... More

Spectral Gap for the Stochastic Quantization Equation on the 2-dimensional TorusSep 27 2016We study the long time behavior of the stochastic quantization equation. Extending recent results by Mourrat and Weber we first establish a strong non-linear dissipative bound that gives control of moments of solutions at all positive times independent ... More

$R$-systemsSep 02 2017Birational toggling on Gelfand-Tsetlin patterns appeared first in the study of geometric crystals and geometric Robinson-Schensted-Knuth correspondence. Based on these birational toggle relations, Einstein and Propp introduced a discrete dynamical system ... More

On non-multiaffine consistent-around-the-cube lattice equationsJun 01 2011Sep 30 2011We show that integrable involutive maps, due to the fact they admit three integrals in separated form, can give rise to equations, which are consistent around the cube and which are not in the multiaffine form assumed in papers [1, 2]. Lattice models, ... More

The Real 3x+1 ProblemOct 22 2004Jul 06 2006In this work, we introduce another extension U of the 3n+1 function to the real line. We propose a conjecture about the U-trajectories that generalizes the famous 3n+1 (or Collatz) conjecture. We then prove our main result about the iterates of U (which ... More

Asymptotic Hecke algebras and Lusztig-Vogan bijection via affine matrix-ball constructionFeb 18 2019Affine matrix-ball construction (abbreviated AMBC) was developed by Chmutov, Lewis, Pylyavskyy, and Yudovina as an affine generalization of Robinson-Schensted correspondence. We show that AMBC gives a simple way to compute a distinguished (or Duflo) involution ... More

Two-Nucleon Higher Partial-Wave Scattering from Lattice QCDAug 04 2015We present a determination of nucleon-nucleon scattering phase shifts for l>=0. The S,P,D and F phase shifts for both the spin-triplet and spin-singlet channels are computed for the first time with lattice Quantum ChromoDynamics. This required the design ... More

Toward the Chiral Limit of QCD: Quenched and Dynamical Domain Wall FermionsDec 10 1998Dec 14 1998A serious difficulty in conventional lattice field theory calculations is the coupling between the chiral and continuum limits. With both staggered and Wilson fermions, the chiral limit cannot be realized without first taking the limit of vanishing lattice ... More

Two-nucleon scattering in multiple partial wavesNov 06 2015We determine scattering phase shifts for S,P,D, and F partial wave channels in two-nucleon systems using lattice QCD methods. We use a generalization of Luscher's finite volume method to determine infinite volume phase shifts from a set of finite volume ... More

Staggered domain wall fermionsOct 19 2001Staggered Domain Wall Fermions (SDWF) combine the attractive chiral properties of staggered fermions with those of domain wall fermions. SDWF describe four flavors with exact U(1)xU(1) flavor chiral symmetry. An extra lattice dimension is introduced and ... More

Three-Qubit Operators, the Split Cayley Hexagon of Order Two and Black HolesAug 28 2008Sep 11 2008The set of 63 real generalized Pauli matrices of three-qubits can be factored into two subsets of 35 symmetric and 28 antisymmetric elements. This splitting is shown to be completely embodied in the properties of the Fano plane; the elements of the former ... More

A reflexive HI space with the hereditary Invariant Subspace PropertyNov 15 2011Jun 18 2013A reflexive hereditarily indecomposable Banach space $\mathfrak{X}_{_{^\text{ISP}}}$ is presented, such that for every $Y$ infinite dimensional closed subspace of $\mathfrak{X}_{_{^\text{ISP}}}$ and every bounded linear operator $T:Y\rightarrow Y$, the ... More

${\mathbb{Z}}_N$ graded discrete Lax pairs and discrete integrable systemsNov 22 2014We introduce a class of ${\mathbb{Z}}_N$ graded discrete Lax pairs, with $N\times N$ matrices, linear in the spectral parameter. We give a classification scheme for such Lax pairs and the associated discrete integrable systems. We present two potential ... More