total 14424took 0.10s

Light Transport in Random Media with ${\cal PT}$-SymmetryMay 09 2012The scattering properties of randomly layered optical media with ${\cal PT}$-symmetric index of refraction are studied using the transfer-matrix method. We find that the transmitance decays exponentially as a function of the system size, with an enhanced ... More

Design of diamond microcavities for single photon frequency down-conversionApr 07 2015Apr 10 2015We propose monolithic diamond cavities that can be used to convert color-center Fock-state single photons from emission wavelengths to telecommunication bands. We present a detailed theoretical description of the conversion process, analyzing important ... More

Enhanced nonlinear frequency conversion and Purcell enhancement at exceptional pointsMay 21 2017Jun 03 2017We derive analytical formulas quantifying radiative emission from subwavelength emitters embedded in triply resonant nonlinear $\chi^{(2)}$ cavities supporting exceptional points (EP) made of dark and leaky modes. We show that the up-converted radiation ... More

Material Scaling and Frequency-Selective Enhancement of Near-Field Radiative Heat Transfer for Lossy Metals in Two Dimensions via Inverse DesignFeb 15 2018Aug 24 2018The super-Planckian features of radiative heat transfer in the near-field are known to depend strongly on both material and geometric design properties. However, the relative importance and interplay of these two facets, and the degree to which they can ... More

Topology optimization of freeform large-area metasurfacesFeb 08 2019We demonstrate optimization of optical metasurfaces over $10^5$--$10^6$ degrees of freedom in two and three dimensions, 100--1000+ wavelengths ($\lambda$) in diameter, with 100+ parameters per $\lambda^2$. In particular, we show how topology optimization, ... More

Inverse designed photonic fibers and metasurfaces for nonlinear frequency conversionNov 21 2017Typically, photonic waveguides designed for nonlinear frequency conversion rely on intuitive and established principles, including index guiding and band gap engineering, and are based on simple shapes with high degrees of symmetry. We show that recently ... More

Inverse design of third-order Dirac exceptional points in photonic crystalsMay 19 2016We propose a novel inverse-design method that enables brute-force discovery of photonic crystal (PhC) structures with complex spectral degeneracies. As a proof of principle, we demonstrate PhCs exhibiting third-order Dirac points formed by the \emph{accidental} ... More

Topology Optimized Multi-layered Meta-opticsJun 21 2017We propose a general topology optimization framework for metasurface inverse design that can automatically discover highly complex multi-layered meta-structures with increased functionalities. In particular, we present topology-optimized multi-layered ... More

Cavity-enhanced second harmonic generation via nonlinear-overlap optimizationMay 12 2015May 18 2015We describe an approach based on topology optimization that enables automatic discovery of wavelength-scale photonic structures for achieving high-efficiency second-harmonic generation (SHG). A key distinction from previous formulation and designs that ... More

Inverse Design of Compact Multimode Cavity CouplersMar 16 2018Sep 03 2018Efficient coupling between on-chip sources and cavities plays a key role in silicon photonics. However, despite the importance of this basic functionality, there are few systematic design tools to simultaneously control coupling between multiple modes ... More

Overlapping domains for topology optimization of large-area metasurfacesJun 12 2019We introduce an overlapping-domain approach to large-area metasurface design, in which each simulated domain consists of a unit cell and overlapping regions from the neighboring cells plus PML absorbers. We show that our approach generates greatly improved ... More

Overlapping domains for topology optimization of large-area metasurfacesJun 12 2019Aug 07 2019We introduce an overlapping-domain approach to large-area metasurface design, in which each simulated domain consists of a unit cell and overlapping regions from the neighboring cells plus PML absorbers. We show that our approach generates greatly improved ... More

Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversionJan 19 2017We exploit recently developed topology-optimization techniques to design complex, wavelength-scale resonators for enhancing various nonlinear $\chi^{(2)}$ and $\chi^{(3)}$ frequency conversion processes. In particular, we demonstrate aperiodic, multi-track ... More

400%/W second harmonic conversion efficiency in $\mathrm{14 μ m}$-diameter gallium phosphide-on-oxide resonatorsOct 10 2018Second harmonic conversion from 1550~nm to 775~nm with an efficiency of 400% W$^{-1}$ is demonstrated in a gallium phosphide (GaP) on oxide integrated photonic platform. The platform consists of doubly-resonant, phase-matched ring resonators with quality ... More

Thermal radiation from optically driven Kerr ($χ^{(3)}$) photonic cavitiesMar 12 2015We study thermal radiation from nonlinear ($\chi^{(3)}$) photonic cavities coupled to external channels and subject to incident monochromatic light. Our work extends related work on nonlinear mechanical oscillators [Phys. Rev. Lett. 97, 110602 (2006)] ... More

Experimental observation of the dual behavior of ${\cal PT}$-symmetric scatteringMay 10 2012We investigate experimentally parity-time (${\cal PT}$) symmetric scattering using $LRC$ circuits in an inductively coupled ${\cal PT}$- symmetric pair connected to transmission line leads. In the single-lead case, the ${\cal PT}$-symmetric circuit acts ... More

Inverse design of large-area metasurfacesAug 13 2018Dec 14 2018We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and demultiplexers. To optimize ... More

Unidirectional Invisibility induced by PT-Symmetric Periodic StructuresAug 11 2011We show that parity-time (PT) symmetric Bragg periodic structures, near the spontaneous PT - symmetry breaking point, can act as unidirectional invisible media. In this regime, the re flection from one end is diminished while it is enhanced from the other. ... More

High-efficiency degenerate four wave-mixing in triply resonant nanobeam cavitiesNov 16 2013We demonstrate high-efficiency, degenerate four-wave mixing in triply resonant Kerr $\chi^(3)$ photonic crystal (PhC) nanobeam cavities. Using a combination of temporal coupled mode theory and nonlinear finite-difference time-domain (FDTD) simulations, ... More

Outlook for inverse design in nanophotonicsJan 20 2018Recent advancements in computational inverse design have begun to reshape the landscape of structures and techniques available to nanophotonics. Here, we outline a cross section of key developments at the intersection of these two fields: moving from ... More

Topology-optimized Dual-Polarization Dirac ConesMay 10 2017Sep 21 2017We apply a large-scale computational technique, known as topology optimization, to the inverse design of photonic Dirac cones. In particular, we report on a variety of photonic crystal geometries, realizable in simple isotropic dielectric materials, which ... More

Transition from subbarrier to deep subbarrier regimes in heavy-ion fusion reactionsApr 04 2012We analyze the recent experimental data of heavy-ion fusion cross sections available up to deep subbarrier energies in order to discuss the threshold incident energy for a deep subbarrier fusion hindrance phenomenon. To this end, we employ a one-dimensional ... More

On Loops in the Hyperbolic Locus of the Complex Hénon Map and Their MonodromiesApr 23 2007We prove John Hubbard's conjecture on the topological complexity of the hyperbolic horseshoe locus of the complex H\'enon map. Indeed, we show that there exist several non-trivial loops in the locus which generate infinitely many mutually different monodromies. ... More

Revivals in the attractive BEC in a double-well potential and their decoherenceOct 28 2010Oct 29 2010We study the dynamics of ultracold attractive atoms in a weakly linked two potential wells. We consider an unbalanced initial state and monitor dynamics of the population difference between the two wells. The average imbalance between wells undergoes ... More

Integrated high quality factor lithium niobate microdisk resonatorsOct 09 2014Lithium Niobate (LN) is an important nonlinear optical material. Here we demonstrate LN microdisk resonators that feature optical quality factor ~ 100,000, realized using robust and scalable fabrication techniques, that operate over a wide wavelength ... More

Interference of Fock states in a single measurementMar 29 2007We study analytically the structure of an arbitrary order correlation function for a pair of Fock states and prove without any approximations that in a single measurement of particle positions interference effects must occur as experimentally observed ... More

Self-bound Bose-Fermi liquids in lower dimensionsAug 14 2018Mar 29 2019We study weakly interacting mixtures of ultracold atoms composed of bosonic and fermionic species in 2D and 1D. When interactions between particles are appropriately tuned, self-bound quantum liquids can be formed. We show that while formation of these ... More

The influence of the interaction between quasiparticles on parametric resonance in Bose-Einstein quasicondensatesApr 23 2018We perform a simulation of the experiment [1] where the temporal modification of the effective one dimensional interaction constant was used to create pairs of atoms with opposite velocities. The simulations clearly demonstrate huge impact of interaction ... More

Adaptively Compressed Exchange OperatorJan 26 2016Jan 27 2016The Fock exchange operator plays a central role in modern quantum chemistry. The large computational cost associated with the Fock exchange operator hinders Hartree-Fock calculations and Kohn-Sham density functional theory calculations with hybrid exchange-correlation ... More

On parameter loci of the Hénon familyJan 07 2015Feb 29 2016We characterize the hyperbolic horseshoe locus and the maximal entropy locus of the H\'enon family defined on $\mathbb{R}^2$. More specifically, we show that (i) the two parameter loci are both connected and simply connected (by adding their corresponding ... More

Properties of atomic pairs produced in the collision of Bose-Einstein condensatesMar 16 2017Collisions of Bose-Einstein condensates can be used as a mean to generate correlated pairs of atoms. The scattered massive particles, in analogy to photon pairs in quantum optics, might be used in the violation of Bell's inequalities, demonstration of ... More

Micromagnetics of shape anisotropy based permanent magnetsDec 13 2013Mar 26 2014In the search for rare-earth free permanent magnets, various ideas related to shape anisotropy are being pursued. In this work we assess the limits of shape contributions to the reversal stability using micromagnetic simulations. In a first series of ... More

Randomized estimation of spectral densities of large matrices made accurateApr 29 2015Nov 23 2015For a large Hermitian matrix $A\in \mathbb{C}^{N\times N}$, it is often the case that the only affordable operation is matrix-vector multiplication. In such case, randomized method is a powerful way to estimate the spectral density (or density of states) ... More

Localized spectrum slicingNov 22 2014Nov 23 2015Given a sparse Hermitian matrix $A$ and a real number $\mu$, we construct a set of sparse vectors, each approximately spanned only by eigenvectors of $A$ corresponding to eigenvalues near $\mu$. This set of vectors spans the column space of a localized ... More

Hidden Markov Models on Variable Blocks with a Modal Clustering Algorithm and ApplicationsJun 28 2016Motivated by high-throughput single-cell cytometry data with applications to vaccine development and immunological research, we consider statistical clustering in large-scale data that contain multiple rare clusters. We propose a new hierarchical mixture ... More

Robust Determination of the Chemical Potential in the Pole Expansion and Selected Inversion Method for Solving Kohn-Sham density functional theoryAug 14 2017Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi ... More

Bold Feynman diagrams and the Luttinger-Ward formalism via Gibbs measures. Part I: Perturbative approachSep 09 2018Many-body perturbation theory (MBPT) is widely used in quantum physics, chemistry, and materials science. At the heart of MBPT is the Feynman diagrammatic expansion, which is, simply speaking, an elegant way of organizing the combinatorially growing number ... More

The technique of inverse Mellin transform for processes occurring in a background magnetic fieldOct 25 2002We develop the technique of inverse Mellin transform for processes occurring in a background magnetic field. We show by analyticity that the energy (momentum) derivatives of a field theory amplitude at the zero energy (momentum) is equal to the Mellin ... More

The inclusive B->eta' X_s decay and b-> sg* form factorsOct 25 1999We compute the branching ratio of inclusive $B \to \eta' X_s$ decay based upon the QCD anomaly mechanism: $b\to s+g^*\to s+g+\eta'$. To obtain a reliable $B \to \eta' X_s$ branching ratio, we calculate the $b\to s+g^*$ form factors up to the next-to-leading-logarithmic(NLL) ... More

A posteriori error estimates for discontinuous Galerkin methods using non-polynomial basis functions. Part II: Eigenvalue problemsMar 14 2016We present the first systematic work for deriving a posteriori error estimates for general non-polynomial basis functions in an interior penalty discontinuous Galerkin (DG) formulation for solving eigenvalue problems associated with second order linear ... More

Information MechanicsMay 03 2016Nov 10 2016Despite the wide usage of information as a concept in science, we have yet to develop a clear & concise scientific definition. This paper is aimed at laying the foundations for a new theory concerning the mechanics of information alongside its intimate ... More

Some weak versions of the $M_{1}$-spacesFeb 18 2013We mainly introduce some weak versions of the $M_{1}$-spaces, and study some properties about these spaces. The mainly results are that: (1) If $X$ is a compact scattered space and $i(X)\leq 3$, then $X$ is an $s$-$m_{1}$-space; (2) If $X$ is a strongly ... More

Uniform bases at non-isolated points and mapsJun 21 2011In this paper, the authors mainly discuss the images of spaces with an uniform base at non-isolated points, and obtain the following main results: (1)\ Perfect maps preserve spaces with an uniform base at non-isolated points; (2)\ Open and closed maps ... More

A New Currency of the Future: The Novel Commodity Money with Attenuation Coefficient Based on the Logistics Cost of AnchorJun 22 2016In this paper, we reveal the attenuation mechanism of anchor of the commodity money from the perspective of logistics warehousing costs, and propose a novel Decayed Commodity Money (DCM) for the store of value across time and space. Considering the logistics ... More

Rapidity Correlation Structures from Causal HydrodynamicsAug 18 2016Viscous diffusion can broaden the rapidity dependence of two-particle transverse momentum fluctuations. Surprisingly, measurements at RHIC by the STAR collaboration demonstrate that this broadening is accompanied by the appearance of unanticipated structure ... More

Rapidity Correlation Structure in Nuclear CollisionsJun 08 2016Aug 17 2016We show that measurements of the rapidity dependence of transverse momentum correlations can be used to determine the characteristic time $\tau_\pi$ that dictates the rate of isotropization of the stress energy tensor, as well as the shear viscosity $\nu ... More

Information MechanicsMay 03 2016Jul 30 2016Despite the wide usage of the concept of information, we have yet to develop a unified scientific definition. Inspired by Shannon's and Boltzmann's work, by investigating information's role in various working processes, we recognised that information's ... More

An Item Recommendation Approach by Fusing Images based on Neural NetworksJul 04 2019There are rich formats of information in the network, such as rating, text, image, and so on, which represent different aspects of user preferences. In the field of recommendation, how to use those data effectively has become a difficult subject. With ... More

Decay estimates of discretized Green's functions for Schrödinger type operatorsNov 25 2015Jun 15 2016For a sparse non-singular matrix $A$, generally $A^{-1}$ is a dense matrix. However, for a class of matrices, $A^{-1}$ can be a matrix with off-diagonal decay properties, i.e. $\lvert A^{-1}_{ij}\rvert$ decays fast to $0$ with respect to the increase ... More

Bold Feynman diagrams and the Luttinger-Ward formalism via Gibbs measures. Part II: Non-perturbative analysisSep 09 2018Many-body perturbation theory (MBPT) is widely used in quantum physics, chemistry, and materials science. At the heart of MBPT is the Feynman diagrammatic expansion, which is, simply speaking, an elegant way of organizing the combinatorially growing number ... More

Variational structure of Luttinger-Ward formalism and bold diagrammatic expansion for Euclidean lattice field theoryNov 20 2017The Luttinger-Ward functional was proposed more than five decades ago to provide a link between static and dynamic quantities in a quantum many-body system. Despite its widespread usage, the derivation of the Luttinger-Ward functional remains valid only ... More

Sparsity pattern of the self-energy for classical and quantum impurity problemsFeb 13 2019We prove that for various impurity models, in both classical and quantum settings, the self-energy matrix is a sparse matrix with a sparsity pattern determined by the impurity sites. In the quantum setting, such a sparsity pattern has been known since ... More

Globally Constructed Adaptive Local Basis Set for Spectral Projectors of Second Order Differential OperatorsJul 23 2017Jun 01 2018Spectral projectors of second order differential operators play an important role in quantum physics and other scientific and engineering applications. In order to resolve local features and to obtain converged results, typically the number of degrees ... More

Strong-Field QED and the Inverse Mellin TransformFeb 10 2002We introduce the technique of inverse Mellin transform in a problem of strong-field QED. We show that the {\it moments} of pair production width in a uniform background magnetic field are proportional to the derivatives of photon polarization function ... More

A posteriori error estimates for discontinuous Galerkin methods using non-polynomial basis functions. Part I: Second order linear PDEFeb 05 2015Jun 17 2015We present the first systematic work for deriving a posteriori error estimates for general non-polynomial basis functions in an interior penalty discontinuous Galerkin (DG) formulation for solving second order linear PDEs. Our residual type upper and ... More

A Stochastic Generalized Ginzburg-Landau Equation Driven by Jump NoiseDec 26 2017This paper is concerned with the stochastic generalized Ginzburg-Landau equation driven by a multiplicative noise of jump type. By a prior estimate, weak convergence and monotonicity technique, we prove the existence and uniqueness of the solution of ... More

Sequence-covering maps on generalized metric spacesJun 20 2011Let $f:X\rightarrow Y$ be a map. $f$ is a {\it sequence-covering map}\cite{Si1} if whenever $\{y_{n}\}$ is a convergent sequence in $Y$ there is a convergent sequence $\{x_{n}\}$ in $X$ with each $x_{n}\in f^{-1}(y_{n})$; $f$ is an {\it 1-sequence-covering ... More

Symmetry breaking in the collisions of double channel BEC solitonsJul 07 2013We investigate an attractive Bose-Einstein condensate in two coupled one dimensional channels. In this system a stable double channel soliton can be formed. It is symmetric for small interaction parameters and asymmetric for large ones. We study this ... More

Huge quantum particle number fluctuations in a two-component Bose gas in a double-well potentialApr 09 2010May 24 2011Two component Bose gas in a double well potential with repulsive interactions may undergo a phase separation transition if the inter-species interactions outweigh the intra-species ones. We analyze the transition in the strong interaction limit within ... More

The Dispersive Approach to Electroweak Processes in the Background Magnetic FieldNov 07 2000We propose a new method to compute amplitudes of electroweak processes in the strong background magnetic field, using $\gamma\to e^+e^-$ as an example. We show that the {\it moments} of $\gamma\to e^+e^-$ width are proportional to the derivatives of photon ... More

Like Sign Top Pair Production at LHCMay 26 1997Having a mass comparable to the weak scale, the top quark may have a sizable flavor changing couplings to Higgs bosons. We show that such couplings can be probed at the LHC through the parton subprocess $c(\bar c)g \to t (\bar t)A^0$, where the pseudoscalar ... More

Classification of degree three polynomial solutions to the Polubarinova-Galin equationSep 19 2013The Polubarinova-Galin equation is derived from zero-surface-tension Hele-Shaw flow driven by injection. In this paper, we classify degree three polynomial solutions to the Polubarinova-Galin equation into three categories: global solutions, solutions ... More

Large-time rescaling behaviors of Stokes and Hele-Shaw flows driven by injectionJun 04 2009In this paper, we give a precise description of the rescaling behaviors of global strong polynomial solutions to the reformulation of zero surface tension Hele-Shaw problem driven by injection, the Polubarinova-Galin equation, in terms of Richardson complex ... More

$π$-metrizable spaces and strongly $π$-metrizable spacesFeb 18 2013A space $X$ is said to be $\pi$-metrizable if it has a $\sigma$-discrete $\pi$-base. In this paper, we mainly give affirmative answers for two questions about $\pi$-metrizable spaces. The main results are that: (1) A space $X$ is $\pi$-metrizable if and ... More

Minimum tree-stretch of Hamming graphs and higher-dimensional gridsJul 22 2018The minimum stretch spaning tree problem for a grah G is to find a spaning tree T of G such as that the maximum distance in T between two adjacent vertices is minimized. The minimum value of this optimization problem gives rise to a grpah invariant {\sigma} ... More

Element orbitals for Kohn-Sham density functional theoryJan 27 2012May 01 2012We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized around an element, ... More

Fast real-time time-dependent hybrid functional calculations with the parallel transport gauge and the adaptively compressed exchange formulationSep 25 2018Feb 04 2019We present a new method to accelerate real time-time dependent density functional theory (rt-TDDFT) calculations with hybrid exchange-correlation functionals. For large basis set, the computational bottleneck for large scale calculations is the application ... More

The minimum stretch spanning tree problem for typical graphsDec 10 2017With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The problem has been ... More

Perturbation theorems for Hele-Shaw flows and their applicationsMay 21 2010In this work, we give a perturbation theorem for strong polynomial solutions to the zero surface tension Hele-Shaw equation driven by injection or suction, so called the Polubarinova-Galin equation. This theorem enables us to explore properties of solutions ... More

Uniform covers at non-isolated pointsJun 21 2011In this paper,\ the authors define a space with an uniform base at non-isolated points, give some characterizations of images of metric spaces by boundary-compact maps, and study certain relationship among spaces with special base properties.\ The main ... More

Convergence of adaptive compression methods for Hartree-Fock-like equationsMar 16 2017Nov 20 2017The adaptively compressed exchange (ACE) method provides an efficient way for solving Hartree-Fock-like equations in quantum physics, chemistry, and materials science. The key step of the ACE method is to adaptively compress an operator that is possibly ... More

Disentanglement via entanglement: A unified method for Wannier localizationMar 20 2017Jun 05 2018The Wannier localization problem in quantum physics is mathematically analogous to finding a localized representation of a subspace corresponding to a nonlinear eigenvalue problem. While Wannier localization is well understood for insulating materials ... More

Elastic scattering losses from colliding BEC'sDec 05 2005Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently ... More

Boltzmann-Langevin Approach to Pre-equilibrium Correlations in Nuclear CollisionsDec 23 2016Mar 28 2017Correlations born before the onset of hydrodynamic flow can leave observable traces on the final state particles. Measurement of these correlations can yield important information on the isotropization and thermalization process. Starting from a Boltzmann-like ... More

Quantum Dynamics with the Parallel Transport GaugeApr 06 2018The dynamics of a closed quantum system is often studied with the direct evolution of the Schrodinger equation. In this paper, we propose that the gauge choice (i.e. degrees of freedom irrelevant to physical observables) of the Schrodinger equation can ... More

Rapidity correlations test stochastic hydrodynamicsNov 02 2016We show that measurements of the rapidity dependence of transverse momentum correlations can be used to determine the characteristic time $\tau_{\pi}$ that dictates the rate of isotropization of the stress energy tensor, as well as the shear viscosity ... More

Parallel Transport Time-Dependent Density Functional Theory Calculations with Hybrid Functional on SummitMay 03 2019Real-time time-dependent density functional theory (rt-TDDFT) with hybrid exchange-correlation functional has wide-ranging applications in chemistry and material science simulations. However, it can be thousands of times more expensive than a conventional ... More

Probing the coupling of heavy dark matter to nucleons by detecting neutrino signature from the Earth coreApr 02 2014We argue that the detection of neutrino signature from the Earth core is an ideal approach for probing the coupling of heavy dark matter ($m_{\chi}>10^{4}$ GeV) to nucleons. We first note that direct searches for dark matter (DM) in such a mass range ... More

Average coherence and its typicality for random mixed quantum statesJul 08 2016Wishart ensemble is a useful and important random matrix model used in diverse fields. By realizing induced random mixed quantum states as Wishart ensemble with a fixed trace one, using matrix integral technique we give a fast track to the average coherence ... More

A short note on integral representation of equally positive integer indexed harmonic sums at infinityNov 13 2016We identify the partition-theoretic generalization of Riemann-zeta function and the equally positive integer indexed harmonic sums at infinity, to obtain the generating function and the integral representation of the latter. The special cases coincide ... More

The Results From The NICMOS Parallel Imaging and Grism SurveyJun 28 1999We present the results of a survey which utilizes the NICMOS Camera 3 Parallel grism and imaging observations of random fields. We have identified 33 H$\alpha$ emission-line galaxies at 0.75<z<1.9. The inferred co-moving number density of these objects ... More

A Constructive Proof On the Compositionality of LinearizabilityDec 29 2014Mar 26 2015Linearizability is the strongest correctness property for both shared memory and message passing concurrent systems. One promising nature of linearizability is the compositionality: a history(execution) is linearizable if and only if each object subhistory ... More

The Rohlin property for automorphisms on simple C*-algebrasFeb 23 2006Jan 27 2010We study a general Kishimoto's problem for automorphisms on simple C*-algebras with tracial rank zero. Let $A$ be a unital separable simple C*-algebra with tracial rank zero and let $\alpha$ be an automorphism. Under the assumption that $\alpha$ has certain ... More

Classification of simple $C^*$-algebras of tracial topological rank zeroNov 13 2000We give a classification theorem for unital separable simple nuclear $C^*$-algebras with tracial topological rank zero which satisfy the Universal Coefficient Theorem. We prove that if $A$ and $B$ are two such $C^*$-algebras and $$ (K_0(A), K_0(A)_+, ... More

Bouchard-Klemm-Marino-Pasquetti Conjecture for $\mathbb{C}^3$Oct 20 2009In this paper, we give a proof of the Bouchard-Klemm-Marino-Pasquetti conjecture for a framed vertex, by using the symmetrized Cut-Join Equation developed in a previous paper.

Ryu-Takayanagi Area as an Entanglement Edge TermApr 25 2017Aug 13 2017I argue that an analogy between emergent gauge theories and the bulk in AdS/CFT suggests that the Ryu-Takayanagi area term is a boundary entropy, counting the number of ways UV degrees of freedom in the bulk can satisfy an emergent gauge constraint for ... More

PRINCIPAR---An Efficient, Broad-coverage, Principle-based ParserJul 27 1994We present an efficient, broad-coverage, principle-based parser for English. The parser has been implemented in C++ and runs on SUN Sparcstations with X-windows. It contains a lexicon with over 90,000 entries, constructed automatically by applying a set ... More

Zeta Functions for Elliptic Curves I. Counting BundlesFeb 04 2012To count bundles on curves, we study zetas of elliptic curves and their zeros. There are two types, i.e., the pure non-abelian zetas defined using moduli spaces of semi-stable bundles, and the group zetas defined for special linear groups. In lower ranks, ... More

Geometry of NumbersFeb 07 2011Feb 23 2011We develop a global cohomology theory for number fields by offering topological cohomology groups, an arithmetical duality, a Riemann-Roch type theorem, and two types of vanishing theorem. As applications, we study moduli spaces of semi-stable lattices, ... More

Stability and ArithmeticApr 08 2009Nov 04 2009Stability plays a central role in arithmetic. In this article, we explain some basic ideas and present certain constructions for such studies. There are two aspects: namely, general Class Field Theories for Riemann surfaces using semi-stable parabolic ... More

Codes and StabilityJun 12 2018We introduce new yet easily accessible codes for elements of $GL_r(A)$ with $A$ the adelic ring of a (dimension one) function field over a finite field. They are linear codes, and coincide with classical algebraic geometry codes when $r=1$. Basic properties ... More

Non-Abelian L Function for Number FieldsDec 01 2004This is an integrated part of our Geo-Arithmetic Program. In this paper we introduce and hence study non-abelian zeta functions and more generally non-abelian $L$-functions for number fields, based on geo-arithmetical cohomology, geo-arithmetical truncation ... More

Constructions of Non-Abelian Zeta Functions for CurvesFeb 08 2001In this paper, we introduce (local and) global non-abelian zeta functions for general curves. As an example, we compute the so-called rank two zeta functions for genus two curves by studying non-abelian Brill-Noether loci and their infinitesimal structures. ... More

Non-Abelian Zeta Function, Fokker-Planck Equation and Projectively Flat ConnectionMar 08 2019Over the moduli space of rank $n$ semi-stable lattices is a universal family of tori. Along the fibers, there are natural differential operators and differential equations, particularly, the heat equations and the Fokker-Planck equations in statistical ... More

The Parameterized Complexity of k-BicliqueJun 14 2014Nov 01 2014Given a graph $G$ and a parameter $k$, the $k$-biclique problem asks whether $G$ contains a complete bipartite subgraph $K_{k,k}$. This is the most easily stated problem on graphs whose parameterized complexity is still unknown. We provide an fpt-reduction ... More

Mass Bounds in Mirror-Fermion ModelsSep 08 1995Numerical simulations are performed on different lattice sizes of chiral U(1) and SU(2) scalar-fermion models with explicit mirror pairs of fermions in the broken symmetry phase. Relevance of these models to the electroweak theory is discussed. Shift ... More

A Comprehensive Framework for Dynamic Bike Rebalancing in a Large Bike Sharing NetworkJun 07 2018Bike sharing is a vital component of a modern multi-modal transportation system. However, its implementation can lead to bike supply-demand imbalance due to fluctuating spatial and temporal demands. This study proposes a comprehensive framework to develop ... More

A Simple Gap-producing Reduction for the Parameterized Set Cover ProblemFeb 11 2019Apr 26 2019Given an $n$-vertex bipartite graph $I=(S,U,E)$, the goal of set cover problem is to find a minimum sized subset of $S$ such that every vertex in $U$ is adjacent to some vertex of this subset. It is NP-hard to approximate set cover to within a $(1-o(1))\ln ... More

Nash equilibrium payoffs for stochastic differential games with jumps and coupled nonlinear cost functionalsAug 18 2011Jul 18 2013In this paper we investigate Nash equilibrium payoffs for two-player nonzero-sum stochastic differential games whose cost functionals are defined by a system of coupled backward stochastic differential equations. We obtain an existence theorem and a characterization ... More

Minimal Homeomorphisms and Approximate Conjugacy in MeasureJan 18 2005Apr 26 2005Let X be an infinite compact metric space with finite covering dimension. Let $\afhpa,\bt: X\to X$ be two minimal homeomorphisms. Suppose that the range of $K_0$-groups of both crossed product C*-algebras s are dense in the space of real affine continuous ... More