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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

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 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

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

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 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

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

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

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

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

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

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

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

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

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

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

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

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

Single quantum realization of a collision of two Bose--Einstein condensatesJun 13 2006We propose a method for simulating a single realization of a collision of two Bose--Einstein condensates. Recently in Zi\'{n} {\it et al.} (Phys. Rev. Lett. {\bf 94}, 200401 (2005)) we introduced a quantum model of an incoherent elastic scattering in ... 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

A Knowledge-based Automated Debugger in Learning SystemJan 12 2001Currently, programming instructors continually face the problem of helping to debug students' programs. Although there currently exist a number of debuggers and debugging tools in various platforms, most of these projects or products are crafted through ... 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

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

Anomalies in the Relaxation of Small Magnetic Particles at Very Low TemperaturesSep 03 1996The magnetization relaxation rate of small gamma-Fe2O3 particles dispersed in a silica matrix has been measured from 60 mK to 5 K. It shows a minimum around 150 mK, that can be discussed in terms of either thermal or quantum relaxation regime.

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

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

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

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

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

$π$-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

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

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

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

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

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

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

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

Elliptic preconditioner for accelerating the self consistent field iteration in Kohn-Sham density functional theoryJun 11 2012May 09 2013We discuss techniques for accelerating the self consistent field (SCF) iteration for solving the Kohn-Sham equations. These techniques are all based on constructing approximations to the inverse of the Jacobian associated with a fixed point map satisfied ... More

An Approach to the High-level Maintenance Planning for EMU Trains Based on Simulated AnnealingApr 10 2017A high-speed train needs high-level maintenance when its accumulated running mileage or time reaches predefined threshold. The date of delivering an Electric Multiple Unit (EMU) train to maintenance ranges within a time window rather than be a fixed date. ... 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

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

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

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

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

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

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

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

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

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

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

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

A state sum invariant for regular isotopy of links having a polynomial number of statesApr 26 2008The state sum regular isotopy invariant of links which I introduce in this work is a generalization of the Jones Polynomial. So it distinguishes any pair of links which are distinguishable by Jones'. This new invariant, denoted {\em VSE-invariant} is ... More

A 3-Variable BracketMay 14 2008Kauffman's bracket is an invariant of regular isotopy of knots and links which since its discovery in 1985 it has been used in many different directions: (a) it implies an easy proof of the invariance of (in fact, it is equivalent to) the Jones polynomial; ... More

Manolescu correction terms and even Dehn surgeryJul 18 2016Oct 27 2016We discuss the behavior of Manolescu's correction terms under Dehn surgery with coefficient the reciprocal of a non-zero even number. We provide some applications to homology cobordism, Seifert fibered surgeries and concordance invariants.

Performance of leader-follower multi-agent systems in directed networksJun 07 2016We consider leader-follower multi-agent systems in which the leader executes the desired trajectory and the followers implement the consensus algorithm subject to stochastic disturbances. The performance of the leader-follower systems is quantified by ... More

Compiling Causal Theories to Successor State Axioms and STRIPS-Like SystemsJun 24 2011We describe a system for specifying the effects of actions. Unlike those commonly used in AI planning, our system uses an action description language that allows one to specify the effects of actions using domain rules, which are state constraints that ... More

Nilpotent Elements of Vertex AlgebrasJul 10 2011Using the method of commutative algebra, we show that the set $\mathfrak{R}$ of nilpotent elements of a vertex algebra $V$ forms an ideal, and $V/\mathfrak{R}$ has no nonzero nilpotent elements.

The Zero-Coupon Rate Model for Derivatives PricingJun 04 2016The aim of this paper is to present a dual-term structure model of interest rate derivatives in order to solve the two hardest problems in financial modeling: the exact volatility calibration of the entire swaption matrix, and the calculation of bucket ... More

A new proof of the $\mathfrak{sl}_{2}$ action on the triplet vertex algebraNov 09 2013Nov 20 2013Let $\mathcal {W}(p)$ be the triplet vertex algebra of central charge $c_{p}=1-\frac{6(p-1)^{2}}{p}$, $p\geq2$. As a Virasoro module, we have $$\mathcal {W}(p)=\bigoplus_{n=0} ^{\infty}(2n+1) L(c_{p}, n^{2}p+np-n).$$ It was pointed out in \cite{am1} that ... More

Weighted norm inequalities, spectral multipliers and Littlewood-Paley operators in the Schrödinger settingsMar 02 2012In this paper, we establish a good-$\lz$ inequality with two parameters in the Schr\"odinger settings. As it's applications, we obtain weighted estimates for spectral multipliers and Littlewood-Paley operators and their commutators in the Schr\"odinger ... More

Extrapolation from $A_\fz^{ρ,\fz}$, vector-valued inequalities and applications in the Schrödinger settingsSep 01 2011In this paper, we generalize the $A_\fz$ extrapolation theorem in \cite{cmp} and the $A_p$ extrapolation theorem of Rubio de Francia to Schr\"odinger settings. In addition, we also establish the weighted vector-valued inequalities for Schr\"odinger type ... More

Weighted norm inequalities for commutators of Littlewood-Paley functions related to Schrödinger operatorsSep 01 2011Let $L=-\Delta+V$ be a Schr\"{o}dinger operator, where $\Delta $ is the Laplacian operator on $\rz$, while the nonnegative potential $V$ belongs to certain reverse H\"{o}lder class. In this paper, we establish some weighted norm inequalities for commutators ... More

On Bernoulli Numbers and Its PropertiesAug 06 2004Oct 10 2004In this survey paper, I first review the history of Bernoulli numbers, then examine the modern definition of Bernoulli numbers and the appearance of Bernoulli numbers in expansion of functions. I revisit some properties of Bernoulli numbers and the history ... More

Adiabatic State Conversion and Pulse Transmission in Optomechanical SystemsNov 09 2011Apr 16 2012Optomechanical systems with strong coupling can be a powerful medium for quantum state engineering. Here, we show that quantum state conversion between cavity modes with different wavelengths can be realized with high fidelity by adiabatically varying ... More

Analyzing Signal Attenuation in PFG Anomalous Diffusion via a Modified Gaussian Phase Distribution Approximation Based on Fractal Derivative ModelSep 15 2016Pulsed field gradient (PFG) has been increasingly employed to study anomalous diffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). However, the analysis of PFG anomalous diffusion is complicated. In this paper, a fractal ... More

Exponential rank and exponential length for Z-stable simple C*-algebrasJan 03 2013Feb 12 2013Let $A$ be a unital separable simple ${\cal Z}$-stable C*-algebra which has rational tracial rank at most one and let $u\in U_0(A),$ the connected component of the unitary group of $A.$ We show that, for any $\epsilon>0,$ there exists a self-adjoint element ... More

On the passibility of a short-lived free Dirac particleMay 01 1998A time-decaying Dirac equation is suggested. For a free particle with rest mass about 0.5GeV, the live-time is about 10**(-25) second in the rest frame.

The velocity and angular momentum of a free Dirac electronApr 22 1998It is shown that, in Dirac theory, there is a spatial velocity of a free electron which commutes with the Hamiltonian, so it is a conserved quantity of the motion. Furthermore, there is a spatial orbital angular momentum which also commutes with the Hamiltonian ... More

Study of the Decoupling of Heavy Fermions in a Z_2 Scalar-Fermion ModelJan 19 1995According to one-loop perturbation theory, fermions whose masses are totally generated from Yukawa couplings do not decouple in the heavy mass limit. We investigate this issue nonperturbatively in a 4-dimensional $Z_2$ scalar-fermion model with staggered ... More

Furstenberg Transformations and Approximate ConjugacyMay 02 2005Let $\alpha$ and $\beta$ be two Furstenberg transformations on 2-torus associated with irrational numbers $\theta_1,$ $\theta_2,$ integers $d_1, d_2$ and Lipschitz functions $f_1$ and $f_2.$ We show that $\alpha$ and $\beta$ are approximately conjugate ... More

Extensions by simple $C^*$-algebras -- Quasidiagonal extensionsJan 19 2004Let $A$ be an amenable separable \CA and $B$ be a non-unital but $\sigma$-unital simple \CA with continuous scale. We show that two essential extensions $\tau_1$ and $\tau_2$ of $A$ by $B$ are approximately unitarily equivalent if and only if $$ [\tau_1]=[\tau_2] ... More

Simple nuclear $C^*$-algebras of tracial topological rank oneJan 19 2004Nov 11 2004We give a classification theorem for unital separable nuclear simple \CA s with tracial rank no more than one. Let $A$ and $B$ be two unital separable simple nuclear \CA s with $TR(A), TR(B)\le 1$ which satisfy the universal coefficient theorem. We show ... More

Classification of simple C*-algebras and higher dimensional noncommutative toriNov 24 2003We show that unital simple C*-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C^-algebras can be classified by their ordered $K$-theory. We apply this classification result to show that certain simple crossed ... More

Remarks on some majorization inequalitiesDec 31 2012Jan 02 2013This note revisits some majorization inequalities for eigenvalues, special attention is given to an elegant theorem of Hiroshima. An extension of the special case of Hiroshima's theorem is presented. Some discussion and open problems are also included. ... More

Curvature Free Rigidity for Higher Rank Three-ManifoldsAug 16 2016We prove two rigidity results for complete Riemannian three-manifolds of higher rank. Complete three-manifolds have higher spherical rank if an only if they are spherical space forms. Complete finite volume three-manifolds have higher hyperbolic rank ... More

On the anomalous superfluid hydrodynamicsApr 27 2011Jun 27 2011It has been shown by Son and Sur\'owka that the presence of anomaly in hydrodynamics with global U(1) symmetry can induce vortical and magnetic currents. The induced current is uniquely determined by anomaly from the existence of an entropy current with ... More

Some results on equivalence of multi-letter quantum finite automataJun 26 2011Jul 05 2013Two quantum finite automata are equivalent if for all input string $\omega$ over the input alphabet the two automata accept $\omega$ with equal probability. In [Theoret. Comput. Sci. 410 (2009) 3006-3017], it was shown that a $k_1$-letter QFA $\mathcal{A}_1$ ... More

A characterization of weighted local Hardy spacesMay 06 2010In this paper, we give a characterization of weighted local Hardy spaces $h^1_\wz(\rz)$ associated with local weights by using the truncated Reisz transforms, which generalizes the corresponding result of Bui in \cite{b}.

Existence and uniqueness of the Hele-Shaw problem with injectionOct 16 2008May 21 2010This paper gives a new and short proof of existence and uniqueness of the Polubarinova-Galin equation. The existence proof is an application of the main theorem in Lin's paper. Furthermore, we can conclude that every strong solution can be approximated ... More

Large-time rescaling behaviors for large data to the Hele-Shaw problemOct 16 2008May 21 2010This paper addresses a rescaling behavior of some classes of global solutions to the zero surface tension Hele-Shaw problem with injection at the origin, $\{\Omega(t)\}_{t\geq 0}$. Here $\Omega(0)$ is a small perturbation of $f(B_{1}(0),0)$ if $f(\xi,t)$ ... More

A predictive A4 model, Charged Lepton Hierarchy and Tri-bimaximal Sum RuleApr 17 2008May 20 2008We propose a novel A4 model in which the Tri-Bimaximal (TB) neutrino mixing and the charged lepton mass hierarchy are reproduced simultaneously. At leading order, the residual symmetry of the neutrino sector is Z2 x Z2 which guarantees the TB mixing without ... More

Generalized geometry, equivariant $\bar{\partial}\partial$-lemma, and torus actionsJul 18 2006Mar 11 2007In this paper we first consider the Hamiltonian action of a compact connected Lie group on an $H$-twisted generalized complex manifold $M$. Given such an action, we define generalized equivariant cohomology and generalized equivariant Dolbeault cohomology. ... More

Examples of Non-Kähler Hamiltonian circle manifolds with the strong Lefschetz propertyAug 25 2004May 01 2006In this paper we construct six-dimensional compact non-K\"ahler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counter examples ... More

Triple correlations of Fourier coefficients of cusp formsJul 11 2016We treat an unbalanced shifted convolution sum of Fourier coefficients of cusp forms. As a consequence, we obtain an upper bound for correlation of three Hecke eigenvalues of holomorphic cusp forms $\sum_{H\leq h\leq 2H}W\big(\frac{h}{H}\big)\sum_{X\leq ... More

Universal Approach to Quantum Adiabaticity via Ancilla CavityFeb 07 2018A central challenge in the successful implementation of adiabatic quantum algorithms is to maintain the quantum adiabaticity during the entire evolution. However, the energy gap between the ground and the excited states of interacting many-body systems ... More

Performing Bayesian Risk Aggregation using Discrete Approximation Algorithms with Graph FactorizationJun 02 2015Risk aggregation is a popular method used to estimate the sum of a collection of financial assets or events, where each asset or event is modelled as a random variable. Applications, in the financial services industry, include insurance, operational risk, ... More

Weighted norm inequalities for pseudo-differential operators with smooth symbols and their commutatorsJun 24 2010We obtain weighted $L^p$ inequalities for pseudo-differential operators with smooth symbols and their commutators by using a class of new weight functions which include Muckenhoupt weight functions. Our results improve essentially some well-known results. ... More

The Range of Approximate Unitary Equivalence Classes of Homomorphisms from AH-algebrasJan 25 2008Let $C$ be a unital AH-algebra and $A$ be a unital simple C*-algebra with tracial rank zero. It has been shown that two unital monomorphisms $\phi, \psi: C\to A$ are approximately unitarily equivalent if and only if $$ [\phi]=[\psi] {\rm in} KL(C,A) and ... More

AF-embedding of crossed products of AH-algebras by $\Z$ and asymptotic AF-embeddingDec 18 2006Apr 30 2007Let $A$ be a unital AH-algebra and let $\alpha\in Aut(A)$ be an automorphism. A necessary condition for $A\rtimes_{\alpha}\Z$ being embedded into a unital simple AF-algebra is the existence of a faithful tracial state. If in addition, there is an automorphism ... More

The Bochner Formula via Volume VariationsJun 17 2013In this short paper, we re-derive the Bochner formula for the Laplacian by considering local variations of volume. The derivation is rooted in the fact that the Laplacian of a function measures the volume variation along the flow of the gradient vector ... More

SO(3) massive gravityMay 09 2013Aug 05 2014In this paper, we propose a massive gravity theory with 5 degrees of freedom. The mass term is constructed by 3 Stuckelberg scalar fields, which respects SO(3) symmetry in the fields' configuration. By the analysis on the linear cosmological perturbations, ... More

Large Hierarchy from Non-minimal CouplingMay 19 2014Jun 26 2014In this paper, a model is proposed to solve the gauge hierarchy problem. Beyond the standard model, we introduce an extra scalar field that non-minimally couples to gravity. The fundamental scale is set at weak scale and Planck scale emerges dynamically ... More

The Functional Determinant and the Partition Function in Geometric FlowsNov 21 2013We propose the use of the functional determinant of geometric operators in constructing an entropy functional associated to geometric flows. Our approach is based on the direct computation of the partition function, with a well-defined set of microstates ... More