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Online Computation with Untrusted AdviceMay 14 2019The advice model of online computation captures the setting in which the online algorithm is given some partial information concerning the request sequence. This paradigm allows to establish tradeoffs between the amount of this additional information ... More

Online Maximum Matching with RecourseJan 10 2018May 07 2018We study the online maximum matching problem in a model in which the edges are associated with a known recourse parameter $k$. An online algorithm for this problem has to maintain a valid matching while edges of the underlying graph are presented one ... More

Best-of-two-worlds analysis of online searchOct 18 2018In search problems, a mobile searcher seeks to locate a target that hides in some unknown position of the environment. Such problems are typically considered to be of an on-line nature, in that the input is unknown to the searcher, and the performance ... More

GPS Ionospheric mapping and tomography: A case of study in a geomagnetic stormMay 10 2011The ionosphere has been normally detected by traditional instruments, such as ionosonde, scatter radars, topside sounders onboard satellites and in situ rocket. However, most instruments are expensive and also restricted to either the bottomside ionosphere ... More

Symplectomorphism group of $T^*(G_\mathbb{C}/B)$ and the braid group I: a homotopy equivalence for $G_\mathbb{C}=SL_3(\mathbb{C})$Dec 01 2014Oct 02 2016For a semisimple Lie group $G_\mathbb{C}$ over $\mathbb{C}$, we study the homotopy type of the symplectomorphism group of the cotangent bundle of the flag variety and its relation to the braid group. We prove a homotopy equivalence between the two groups ... More

The Length of the Longest Common Subsequence of Two Independent Mallows PermutationsNov 11 2016The Mallows measure is a probability measure on $S_n$ where the probability of a permutation $\pi$ is proportional to $q^{l(\pi)}$ with $q > 0$ being a parameter and $l(\pi)$ the number of inversions in $\pi$. We prove a weak law of large numbers for ... More

When Convexity meets Parallelism - A Novel Geometric Structure and Its Application in an Optimization ProblemDec 12 2015Apr 08 2016We consider the following geometric optimization problem: given a convex polygon $P$, compute the parallelograms in $P$ with maximal area. To solve it, we invent a novel geometric structure, called $Nest(P)$, which is induced by $P$ and is an arrangement ... More

Nonuniform viscosity in the solar nebula and large masses of Jupiter and SaturnMay 06 2008I report a novel theory that nonuniform viscous frictional force in the solar nebula accounts for the largest mass of Jupiter and Saturn and their largest amount of H and He among the planets, two outstanding facts that are unsolved puzzles in our understanding ... More

Topological phases and edge states in a non-Hermitian trimerized optical latticeMar 18 2018Topologically engineered optical materials support robust light transport. Herein, the investigated non-Hermitian lattice is trimerized and inhomogeneously coupled using uniform intracell coupling. The topological properties of the coupled waveguide lattice ... More

Damped wave equations on compact hyperbolic surfacesDec 07 2017We prove exponential decay of energy for solutions of the damped wave equation on compact hyperbolic surfaces with regular initial data as long as the damping is nontrivial. The proof is based on a similar strategy as in Dyatlov-Jin and in particular, ... More

Control for Schrödinger equation on hyperbolic surfacesJul 17 2017Jun 28 2018We show that the any nonempty open set on a hyperbolic surface provides observability and control for the time dependent Schr\"odinger equation. The only other manifolds for which this was previously known are flat tori. The proof is based on the main ... More

Differential graded algebras over some reductive groupApr 06 2017We study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group with an injective central cocharacter. Besides describing the derived category of differential graded modules ... More

Kinematic Wave Models of Network Vehicular TrafficSep 03 2003The kinematic wave theory, originally proposed by (Lighthill and Whitham, 1955b; Richards, 1956), has been a good candidate for studying vehicular traffic. In this dissertation, we study kinematic wave models of network traffic, which are expected to ... More

Determinations of |V_ub| and |V_cb| from measurements of B -> X_u,c\ellνdifferential decay ratesApr 07 1998Jul 01 1999Methods are described in the framework of light-cone expansion which allow one to determine the Cabibbo-Kobayashi-Maskawa matrix elements |V_ub| and |V_cb| from measurements of the differential decay rates as a function of the scaling variables in the ... More

Calculation of the semileptonic decay width of the $Λ_b$ baryonSep 25 1997We extend the approach based on the light-cone expansion and the heavy quark effective theory to the inclusive semileptonic decay of an unpolarized $b$-flavored hadron. It is applied to calculate the semileptonic decay width of the $\Lambda_b$ baryon ... More

Real-time Magnetometer Disturbance Estimation via Online Nonlinear ProgrammingNov 02 2018Feb 27 2019Magnetometer is a significant sensor for integrated navigation. However, it suffers from many kinds of unknown dynamic magnetic disturbances. We study the problem of online estimating such disturbances via a nonlinear optimization aided by intermediate ... More

Vehicle Classification Based on Seismic Signatures with Weighted Intrinsic Mode FunctionsFeb 24 2019Seismic signal is used for vehicle classification widely. However, this task becomes difficult as a result of various noises. To solve the problem, this paper proposes a novel de-noising algorithm which evolves from a nonparametric adaptive tool named ... More

Emergent Supersymmetry in the Marginal Deformations of N=4 SYMJan 08 2016Oct 24 2016We study the one loop renormalization group flow of the marginal deformations of N=4 SYM theory using the a-function. We found that in the planar limit some non-supersymmetric deformations flow to the supersymmetric infrared fixed points described by ... More

A general convergence analysis on inexact Newton method for nonlinear inverse problemsOct 17 2010We consider the inexact Newton methods $$ x_{n+1}^\d=x_n^\d-g_{\a_n}(F'(x_n^\d)^* F'(x_n^\d)) F'(x_n^\d)^* (F(x_n^\d)-y^\d) $$ for solving nonlinear ill-posed inverse problems $F(x)=y$ using the only available noise data $y^\d$ satisfying $\|y^\d-y\|\le ... More

Iterated Eisenstein τ-integrals and Multiple Eisenstein L-seriesJan 04 2019In this paper we study iterated Eisenstein {\tau}-integrals and multiple Eisenstein L-series, they are functions on the complex upper half plane and form two Q-algebras. They reduce to iterated Eisenstein integrals and multiple Hecke L-functions with ... More

Computational Investigations on Polymerase Actions in Gene Transcription and Replication Combining Physical Modeling and Atomistic SimulationsNov 26 2015Polymerases are protein enzymes that move along nucleic acid chains and catalyze template-based polymerization reactions during gene transcription and replication. The polymerases also substantially improve transcription or replication fidelity through ... More

Representing the big tilting sheaves as holomorphic Morse branesFeb 24 2016Feb 28 2016We introduce Morse branes in the Fukaya category of a holomorphic symplectic manifold, with the goal of constructing tilting objects in the category. We give a construction of a class of Morse branes in the cotangent bundles, and apply it to give the ... More

Efficient fidelity control by stepwise nucleotide selection in polymerase elongationApr 11 2014Polymerases select nucleotides before incorporating them for chemical synthesis during gene replication or transcription. How the selection proceeds stepwise efficiently to achieve sufficiently high fidelity and speed is essential for polymerase function. ... More

Dynamics of stellar and HI streams in the Milky Way haloOct 20 2011Stellar streams are key players in many aspects of Milky Way studies and, in particular, studying their orbital dynamics is crucial for furthering our understanding of the Milky Way's gravitational potential. Although this is not a trivial task when faced ... More

The 1856 Lemma of Cayley RevisitedJul 12 2004Jul 20 2004The result of the classical invariant theory (CIT) commonly referred to as Lemma of Cayley is reviewed and its analogue in the invariant theory of Killing tensors (ITKT) defined in pseudo-Riemannian spaces of constant curvature is formulated and proven. ... More

Algebraic G-theory in motivic homotopy categoriesJun 11 2018Jul 07 2018We prove that algebraic G-theory in is representable in unstable and stable motivic homotopy categories; in the stable category we identify it with the Borel-Moore theory associated to algebraic K-theory, and show that such an identification is compatible ... More

On 1-factorizations of Bipartite Kneser GraphsApr 28 2017Apr 03 2019It is a challenging open problem to construct an explicit 1-factorization of the bipartite Kneser graph $H(v,t)$, which contains as vertices all $t$-element and $(v-t)$-element subsets of $[v]:=\{1,\ldots,v\}$ and an edge between any two vertices when ... More

The Limit of the Empirical Measure of the Product of Two Independent Mallows PermutationsFeb 01 2017Feb 24 2019The Mallows measure is a probability measure on $S_n$ where the probability of a permutation $\pi$ is proportional to $q^{l(\pi)}$ with $q > 0$ being a parameter and $l(\pi)$ the number of inversions in $\pi$. We show the convergence of the random empirical ... More

Higher Spin Gravity and Exact HolographyMar 31 2013Apr 13 2013In this talk, we present some direct evidences of the Higher Spin/Vector Model correspondence. There are two particular examples we would like to address on. The first example concerns a constructive approach of four dimensional higher spin theory from ... More

Characterizing the structure of A when the ratio |2A|/|A| is bounded by 3+epsilonApr 09 2005Let N be the set all of non-negative integers, let A be a finite subset of N, and let (2A) be the set of all numbers of form a+b for each a and b in A. The arithmetic structure of A was accurately characterized by Freiman when (i) |2A|<3|A|-3, (ii) |2A|=3|A|-3, ... More

Center and Universal R-matrix for Quantized Borcherds SuperalgebrasOct 19 1998We construct a nondegenerate symmetric bilinear form on quantized enveloping algebras associated to Borcherds superalgebras. With this, we study its center and its universal R-matrix.

PHENIX Measurement of High-$p_T$ Hadron-hadron and Photon-hadron Azimuthal CorrelationsMay 07 2007High-$p_T$ hadron-hadron correlations have been measured with the PHENIX experiment in $\Cu$ and $\pp$ collisions at $\sqrt{s_{NN}}=200$ GeV. A comparison of the jet widths and yields between the two colliding systems allows us to study the medium effect ... More

High pT gamma-hadron and pi0-hadron correlations in sqrt(sNN)=200GeV Au+Au collisions in PHENIXNov 17 2005Feb 08 2006This poster presents the PHENIX results on high-p_T gamma-hadron and pi0-hadron correlations and shows the modification of away side jet shape by the medium. By comparing their jet shapes and yields, we see some evidence of the direct gamma contribution ... More

Fast community detection by SCORENov 25 2012Nov 27 2014Consider a network where the nodes split into $K$ different communities. The community labels for the nodes are unknown and it is of major interest to estimate them (i.e., community detection). Degree Corrected Block Model (DCBM) is a popular network ... More

Constructing Types in Differentially Closed Fields that are Analysable in the ConstantsAug 04 2017Analysability of finite $U$-rank types are explored both in general and in the theory $\mathrm{DCF}_0$. The well-known fact that the equation $\delta(\mathrm{log}\delta x)=0$ is analysable in but not almost internal to the constants is generalized to ... More

Scattering properties of anti-parity-time symmetric non-Hermitian systemSep 27 2018We investigate the scattering properties of an anti-parity-symmetric non-Hermitian system. The anti-parity-symmetric scattering center possesses imaginary nearest-neighbor hoppings and real onsite potentials, it has been experimentally realized through ... More

Scattering Resonances of Convex Obstacles for general boundary conditionsJan 19 2014We study the distribution of resonances for smooth strictly convex obstacles under general boundary conditions. We show that under a pinched curvature condition for the boundary of the obstacle, the resonances are separated into cubic bands and the distribution ... More

Quantum Stabilizer Codes from Maximal CurvesNov 12 2013A curve attaining the Hasse-Weil bound is called a maximal curve. Usually classical error-correcting codes obtained from a maximal curve have good parameters. However, the quantum stabilizer codes obtained from such classical error-correcting codes via ... More

Resonance-free Region in scattering by a strictly convex obstacleAug 27 2012Sep 01 2012We prove the existence of a resonance free region in scattering by a strictly convex obstacle with the Robin boundary condition. More precisely, we show that the scattering resonances lie below a cubic curve which is the same as in the case of the Neumann ... More

Parameter Extension Simulation of Turbulent FlowsApr 24 2019Parameter extension simulation (PES) as a mathematical method for simulating turbulent flows has been proposed in the study. It is defined as a calculation of the turbulent flow for the desired parameter values with the help of a reference solution. A ... More

Finding all Maximal Area Parallelograms in a Convex PolygonNov 01 2017Sep 03 2018Polygon inclusion problems have been studied extensively in geometric optimization. In this paper, we consider the variant of computing the maximum area parallelograms (MAPs) and all the locally maximal area parallelograms (LMAPs) in a given convex polygon. ... More

B -> K(K^*)X: Decay Distributions, Branching Ratios and CP AsymmetriesApr 20 2001We discuss an improved theoretical description of the semi-inclusive B meson decays $B\to K(K^*)X$. The decay distributions are calculated. Their branching ratios are found to be appreciable. The CP asymmetries in the neutral B modes $\bar{B^0}\to K^-(K^{*-})X$ ... More

Determining |V_{ub}| from the sum rule for semileptonic B decayNov 18 1999Jun 05 2000A precise determination of |V_{ub}| can be obtained exploiting the sum rule for inclusive charmless semileptonic B-meson decays. The sum rule is derived on the basis of light-cone expansion and b-flavored quantum number conservation. The sum rule does ... More

Extracting |V_{ub}| from the inclusive charmless semileptonic branching ratio of b hadronsOct 21 1998Feb 17 1999We calculate the inclusive charmless semileptonic decay width of the B meson using a QCD-based approach. This approach is able to account for both dynamic and kinematic effects of nonperturbative QCD. The charmless semileptonic decay width is found to ... More

Inclusive Heavy Hadron Decays and Light-Cone DynamicsJun 27 2000The governing role of light-cone dynamics in inclusive heavy hadron decay processes is demonstrated. Nonperturbative QCD effects on the processes can be systematically calculated using light-cone expansion and heavy quark effective theory. The applications ... More

A Hamiltonian $\coprod\limits_n BO(n)$-action, stratified Morse theory and the $J$-homomorphismFeb 18 2019Apr 06 2019We use sheaves of spectra to quantize a Hamiltonian $\coprod\limits_n BO(n)$-action on $\varinjlim\limits_{N}T^*\mathbf{R}^N$ that naturally arises from Bott periodicity. We employ the category of correspondences developed in [GaRo] to give an enrichment ... More

Boundary Regularity for Asymptotically Hyperbolic Metrics with Smooth Weyl CurvatureJan 14 2018In this paper, we study the regularity of asymptotically hyperbolic metrics with Einstein condition near boundary and Weyl curvature smooth enough in arbitrary dimension. Following Michael Anderson's method, we show that $C^{m,\alpha}$ conformally compact ... More

Symplectomorphism group of $T^*(G_\mathbb{C}/B)$ and the braid group I: a homotopy equivalence for $G_\mathbb{C}=SL_3(\mathbb{C})$Dec 01 2014Feb 18 2019For a semisimple Lie group $G_\mathbb{C}$ over $\mathbb{C}$, we study the homotopy type of the symplectomorphism group of the cotangent bundle of the flag variety and its relation to the braid group. We prove a homotopy equivalence between the two groups ... More

A Note on the External-Field Method in QCD Sum RulesAug 12 1996Nov 12 1996The external-field method has been used extensively in the QCD sum-rule approach to explore various hadron static properties. In the traditional formalism of this method, the transitions from the ground state hadron to excited states are not exponentially ... More

Large deviation for diffusions and Hamilton--Jacobi equation in Hilbert spacesFeb 28 2006Large deviation for Markov processes can be studied by Hamilton--Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify that limit of the transformed ... More

Crystal graphs for basic representations of the quantum affine algebra $U_q(C_2^{(1)})$Nov 11 1999We give a realization of crystal graphs for basic representations of the quantum affine algebra $U_q(C_2^{(1)})$ in terms of new combinatorial objects called the Young walls.

On the Complexity of Computing the Topology of Real Algebraic Space CurvesJan 28 2019In this paper, we present a deterministic algorithm to find a strong generic position for an algebraic space curve. We modify our existing algorithm for computing the topology of an algebraic space curve and analyze the bit complexity of the algorithm. ... More

Discrete Green functions of the SDFEM on Shishkin triangular meshesAug 18 2015Jun 12 2016We propose estimates of the discrete Green function for the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes.

A method to establish GPS grid ionospheric correction modelOct 10 2010Oct 12 2010The ionospheric influence is one of the largest error sources in GPS positioning and navigation after closing the Selective Availability (SA). Therefore, it is available to establish a real time ionospheric correction model to eliminate or mitigate the ... More

Evolution of Giant Molecular Clouds in Nearby GalaxiesMay 20 2013Studies of GMC evolution in galactic disks were limited to local, predominantly atom-rich small galaxies in the past, but have now been expanded to typical spiral galaxies with a rich molecular content. The evolution appears quite different between the ... More

Stochastic Optimization of Smooth LossNov 30 2013In this paper, we first prove a high probability bound rather than an expectation bound for stochastic optimization with smooth loss. Furthermore, the existing analysis requires the knowledge of optimal classifier for tuning the step size in order to ... More

A variational Bayesian method for inverse problems with impulsive noiseSep 12 2011We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness ... More

Real-time Magnetometer Disturbance Estimation via Online Nonlinear ProgrammingNov 02 2018Magnetometer is a significant sensor for integrated navigation. However, it suffers from many kinds of unknown dynamic magnetic disturbances. We study the problem of online estimating such disturbances via a nonlinear optimization aided by intermediate ... More

A Hamiltonian $\coprod\limits_n BO(n)$-action, stratified Morse theory and the $J$-homomorphismFeb 18 2019Feb 19 2019We use sheaves of spectra to quantize a Hamiltonian $\coprod\limits_n BO(n)$-action on $\varinjlim\limits_{N}T^*\mathbf{R}^N$ that naturally arises from Bott periodicity. We employ the category of correspondences developed in [GaRo] to give an enrichment ... More

Maximal Parallelograms in Convex Polygons and a Novel Geometric StructureDec 12 2015Nov 30 2018We propose a novel geometric structure induced by any given convex polygon $P$, called $Nest(P)$, which is an arrangement of $\Theta(n^2)$ segments, each of which is parallel to an edge of $P$, where $n$ denotes the number of edges of $P$. This structure ... More

Unions of 1-factors in $r$-graphsSep 06 2015The generalized Berge-Fulkerson conjecture states that every $r$-graph has $2r$ 1-factors such that each edge is contained in precisely two of them. This conjecture is shown to be equivalent to the statement that every $r$-graph can be covered by $2r-1$ ... More

Baryon QCD sum rules in an external isovector-scalar field and baryon isospin mass splittingsJun 12 1995Within the QCD sum-rule approach in an external field, we calculate the baryon matrix element of isovector-scalar current, $H_{\rm B}=\langle B|\overline{u}u- \overline{d}d|B\rangle/2M_{\rm B}$, for octet baryons, which appears in the response of the ... More

Dimension result and KPZ formula for two-dimensional multiplicative cascade processesMay 28 2010Sep 25 2012We prove a Hausdorff dimension result for the image of two-dimensional multiplicative cascade processes, and we obtain from this result a KPZ-type formula which normally has one point of phase transition.

A C++ library for Multimodal Deep LearningDec 22 2015Apr 12 2016MDL, Multimodal Deep Learning Library, is a deep learning framework that supports multiple models, and this document explains its philosophy and functionality. MDL runs on Linux, Mac, and Unix platforms. It depends on OpenCV.

Identifying Conditional Causal EffectsJul 11 2012This paper concerns the assessment of the effects of actions from a combination of nonexperimental data and causal assumptions encoded in the form of a directed acyclic graph in which some variables are presumed to be unobserved. We provide a procedure ... More

Generating Markov Equivalent Maximal Ancestral Graphs by Single Edge ReplacementJul 04 2012Maximal ancestral graphs (MAGs) are used to encode conditional independence relations in DAG models with hidden variables. Different MAGs may represent the same set of conditional independences and are called Markov equivalent. This paper considers MAGs ... More

A Criterion for Parameter Identification in Structural Equation ModelsJun 20 2012This paper deals with the problem of identifying direct causal effects in recursive linear structural equation models. The paper establishes a sufficient criterion for identifying individual causal effects and provides a procedure computing identified ... More

Identifying Dynamic Sequential PlansJun 13 2012We address the problem of identifying dynamic sequential plans in the framework of causal Bayesian networks, and show that the problem is reduced to identifying causal effects, for which there are complete identi cation algorithms available in the literature. ... More

PT-symmetric trimer systemsJan 02 2017May 09 2017We studied parity-time (PT) symmetric trimer systems that feature open and closed boundaries. The exceptional point is three-state coalescence at zero energy because of chiral symmetry in the open trimer; however, two-state coalescence appears in the ... More

Semiclassical Cauchy Estimates and ApplicationsFeb 21 2013In this note, we study solutions to semiclassical Schrodinger equations on a real analytic manifold with a real analytic potential and prove the semiclassical version of Cauchy estimates on derivatives. As an application, we use Donnelly and Fefferman's ... More

Explicit construction of optimal locally recoverable codes of distance 5 and 6 via binary constant weight codesAug 14 2018It was shown in \cite{GXY18} that the length $n$ of a $q$-ary linear locally recoverable code with distance $d\ge 5$ is upper bounded by $O(dq^3)$. Thus, it is a challenging problem to construct $q$-ary locally recoverable codes with distance $d\ge 5$ ... More

Asymmetric lasing at spectral singularitiesSep 27 2018Scattering coefficients can diverge at spectral singularities. In such situation, the stationary solution becomes a laser solution with outgoing waves only. We explore a parity-time (PT)-symmetric non-Hermitian two-arm Aharonov-Bohm interferometer consisting ... More

Inclusive breakup calculations in angular momentum basis: application to $^7$Li+$^{58}$NiDec 05 2017The angular momentum basis method is introduced to solve the inclusive breakup within the model proposed by Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985)]. This method is based on the geometric transformation between Jacobi coordinates, ... More

Landweber-Kaczmarz method in Banach spaces with inexact inner solversMar 24 2016In recent years Landweber(-Kaczmarz) method has been proposed for solving nonlinear ill-posed inverse problems in Banach spaces using general convex penalty functions. The implementation of this method involves solving a (nonsmooth) convex minimization ... More

Traffic Flow Models and Their Numerical SolutionsJun 10 2004In this thesis, Riemann problems and Godunov methods are developed for higher order traffic flow models. A rigorous analysis of the first order traffic flow model of inhomogeneous road is presented. A two-level simulation framework of network vehicular ... More

Existence of Weak Solutions to Kinetic Flocking Model with Cut-off Interaction FunctionOct 06 2015We prove the existence of weak solutions to kinetic flocking model with cut-off interaction function by using Schauder fixed pointed theorem and velocity averaging lemma. Under the natural assumption that the velocity support of the initial distribution ... More

Semi-inclusive nonleptonic decays B\to D_s^{(*)} XMar 18 2002We calculate the total and differential decay rates for the semi-inclusive nonleptonic decays $B\to D_s^{(*)} X_q$ ($q=c$ or $u$) under the factorization hypothesis. The initial bound state effect is treated using the light-cone expansion and the heavy ... More

Probing hadron structure and strong interactions with inclusive semileptonic decays of B mesonsAug 13 1998The study of inclusive semileptonic decays of $B$ mesons is analyzed from the viewpoint of probing hadron structure and strong interactions. General formulas for the differential decay rates are given in terms of the structure functions in arbitrary frame ... More

Heat kernel estimates for non-symmetric stable-like processesSep 08 2017Sep 12 2017Let $d\ge1$ and $0<\alpha<2$. Consider the integro-differential operator \[ \mathcal{L}f(x) =\int_{\mathbb{R}^{d}\backslash\{0\}}\left[f(x+h)-f(x)-\chi_{\alpha}(h)\nabla f(x)\cdot h\right]\frac{n(x,h)}{|h|^{d+\alpha}}\mathrm{d}h+\mathbf{1}_{\alpha>1}b(x)\cdot\nabla ... More

A Global Compact Result for a Fractional Elliptic Problem with Hardy term and critical non-linearity on the whole spaceMay 07 2019In this paper, we deal with a fractional elliptic equation with critical Sobolev nonlinearity and Hardy term $$ (-\Delta)^{\alpha} u-\mu\frac{u}{|x|^{2\alpha}}+a(x) u=|u|^{2^*-2}u+k(x)|u|^{q-2}u$$ $$ u\,\in\,H^\alpha({\mathbb R}^N),$$ where $2<q< 2^*$, ... More

An Alternative Method of Extracting $V_{bu}$ from Semi-leptonic B DecayMay 12 1994We propose a new method of extracting $V_{bu}$ from measurements of Semi-leptonic B decay which has much less theoretical uncertainties than conventional methods.

Representing the big tilting sheaves as holomorphic Morse branesFeb 24 2016Oct 02 2016We introduce Morse branes in the Fukaya category of a holomorphic symplectic manifold, with the goal of constructing tilting objects in the category. We give a construction of a class of Morse branes in the cotangent bundles, and apply it to give the ... More

Type Two Cuts, Bad Cuts and Very Bad CutsApr 24 1996Type two cuts, bad cuts and very bad cuts are introduced by Keisler and Leth for studying the relationship between Loeb measure and U-topology of a hyperfinite time line in an $\omega_1$-saturated nonstandard universe. The questions concerning the existence ... More

Theory on Structure and Coloring of Maximal Planar Graphs (I): Relationship between Structure and ColoringOct 16 2012Maximal planar graph refers to the planar graph with the most edges, which means no more edges can be added so that the resulting graph is still planar. The Four-Color Conjecture says that every planar graph without loops is 4-colorable. Indeed, in order ... More

GCN: a gaseous Galactic halo stream?Aug 18 2010We show that a string of HI clouds that form part of the high-velocity cloud complex known as GCN is a probable gaseous stream extending over more than 50 deg in the Galactic halo. The radial velocity gradient along the stream is used to deduce transverse ... More

Probe MachineSep 16 2015Feb 27 2016A novel computing model, called \emph{Probe Machine}, is proposed in this paper. Different from Turing Machine, Probe Machine is a fully-parallel computing model in the sense that it can simultaneously process multiple pairs of data, rather than sequentially ... More

A Branch-and-Bound Algorithm for MDL Learning Bayesian NetworksJan 16 2013This paper extends the work in [Suzuki, 1996] and presents an efficient depth-first branch-and-bound algorithm for learning Bayesian network structures, based on the minimum description length (MDL) principle, for a given (consistent) variable ordering. ... More

Final state interaction in decays B----->Kaon PionMay 06 1998May 07 1998We discuss the rescattering effects in decays $B\to \pi+K$. The picture we take is very simple: first, B decay into $K*\rho$, then $K*$ and $\rho$ go to kaon and pion by exchanging a pion. We find a up to ten percent CP violation asymmetry rate. We also ... More

Quantum transport in coupled resonators enclosed synthetic magnetic fluxNov 30 2016Quantum transport properties are instrumental to understanding quantum coherent transport processes. Potential applications of quantum transport are widespread, in areas ranging from quantum information science to quantum engineering, and not restricted ... More

Flat band induced by the interplay of synthetic magnetic flux and non-HermiticityMar 06 2019A flat band is nondispersive and formed under destructive interference. Although flat bands are found in various Hermitian systems, to realize a flat band in non-Hermitian systems is an interesting task. Here, we propose a flat band in a parity-time symmetric ... More

Cohen-Macaulay differential graded modules and negative Calabi-Yau configurationsDec 10 2018In this paper, we introduce the class of Cohen-Macaulay (=CM) dg (=differential graded) modules over Gorenstein dg algebras and study their basic properties. We show that the category of CM dg modules forms a Frobenius extriangulated category, in the ... More

The Emergence of Supersymmetry in $γ_i$-deformed ${\cal N}=4$ super-Yang-Mills theoryNov 28 2013Dec 02 2013The $\gamma_i$-deformed $\mathcal{N}=4$ super-Yang-Mills theory is a non-supersymmetric deformation of the maximally-supersymmetric gauge theory in four dimensions which is conformally-invariant at the planar level. At the non-planar level non-trivial ... More

On the order optimality of the regularization via inexact Newton iterationsNov 08 2011Inexact Newton regularization methods have been proposed by Hanke and Rieder for solving nonlinear ill-posed inverse problems. Every such a method consists of two components: an outer Newton iteration and an inner scheme providing increments by regularizing ... More

Brownian Motion with Singular Time-Dependent DriftOct 14 2017In this paper we study weak solutions for the following type of stochastic differential equation \[ dX_{t}=dW_{t}+b(t, X_{t})dt, \quad t\ge s, \quad X_{s}=x, \] where $b: [0,\infty) \times \mathbb{R}^{d} \to \mathbb{R}^{d}$ is a measurable drift, $W=(W_{t})_{t ... More

Well-posedness of the martingale problem for non-local perturbations of Lévy-type generatorsAug 15 2017Let $L$ be a L\'evy-type generator whose L\'evy measure is controlled from below by that of a non-degenerate $\alpha$-stable ($0<\alpha<2$) process. In this paper, we study the martingale problem for the operator $\mathcal{L}_{t}=L+K_{t}$, with $K_{t}$ ... More

Motives for an elliptic curveAug 27 2017May 05 2018In this paper we describe the category of motives for an elliptic curve in the sense of Voevodsky as a derived category of dg modules over a commutative differential graded algebra in the category of representations over some reductive group.

The graph, range and level set singularity spectra of $b$-adic independent cascade functionNov 06 2009Jan 25 2010With the "iso-H\"older" sets of a function we naturally associate subsets of the graph, range and level set of the function. We compute the associated singularity spectra for a class of statistically self-similar multifractal functions, namely the $b$-adic ... More

Mathematical Proofs of Two Conjectures: The Four Color Problem and The Uniquely 4-colorable Planar GraphNov 09 2009Jan 18 2012The famous four color theorem states that for all planar graphs, every vertex can be assigned one of 4 colors such that no two adjacent vertices receive the same color. Since Francis Guthrie first conjectured it in 1852, it is until 1976 with electronic ... More

Well-posedness of Weak and Strong Solutions to the Kinetic Cucker-Smale ModelApr 24 2017We first prove the well-posedness of weak and strong solutions to the kinetic Cucker-Smale model in the Sobolev space with the initial data having compact velocity support. Then we study the kinetic Cucker-Smale model with noise. By introducing two weighted ... More

New unitarity triangles of quark mixing and CP violationNov 16 2000Unitarity of the Cabibbo-Kobayashi-Maskawa matrix gives rise to nine new unitarity triangles in the standard model.