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Texture Segmentation Based Video Compression Using Convolutional Neural NetworksFeb 08 2018There has been a growing interest in using different approaches to improve the coding efficiency of modern video codec in recent years as demand for web-based video consumption increases. In this paper, we propose a model-based approach that uses texture ... More

UV and EUV Emissions at the Flare Foot-points Observed by AIAMay 29 2013A solar flare is composed of impulsive energy release events by magnetic reconnection, which forms and heats flare loops. Recent studies have revealed a two-phase evolution pattern of UV 1600\AA\ emission at the feet of these loops: a rapid pulse lasting ... More

Conjugacy Search Problem for Relatively Hyperbolic GroupsNov 23 2012The asymptotic bound for a length-based attack on the Conjugacy Search Problem in relatively hyperbolic groups is cubic for hyperbolic elements and a "small" polynomial for parabolic elements, depending on the Conjugacy Search Problem for the peripheral ... More

The Possibility of Inflation in Asymptotically Safe GravityAug 30 2011Jun 13 2012We examine the inflationary modes in the cubic curvature theories in the context of asymptotically safe gravity. On the phase space of the Hubble parameter, there exists a critical point which corresponds to the slow-roll inflation in Einstein frame. ... More

Avalanche localization and crossover scaling in amorphous plasticityJul 08 2013Sep 25 2013We perform large scale simulations of a two dimensional lattice model for amorphous plasticity with random local yield stresses and long-range quadrupolar elastic interactions. We show that as the external stress increases towards the yielding phase transition, ... More

Effects of thermal inflation on small scale density perturbationsMar 31 2015May 09 2015In cosmological scenarios with thermal inflation, extra eras of moduli matter domination, thermal inflation and flaton matter domination exist between primordial inflation and the radiation domination of Big Bang nucleosynthesis. During these eras, cosmological ... More

Fair division and generalizations of Sperner- and KKM-type resultsJan 18 2017We treat problems of fair division, their various interconnections, and their relations to Sperner's lemma and the KKM theorem as well as their variants. We prove extensions of Alon's necklace splitting result in certain regimes and relate it to hyperplane ... More

Sulfidic Anion Concentrations on Early Earth for Surficial Origins-of-Life ChemistryJan 23 2018A key challenge in origin-of-life studies is understanding the environmental conditions on early Earth under which abiogenesis occurred. While some constraints do exist (e.g., zircon evidence for surface liquid water), relatively few constraints exist ... More

Size effects in dislocation depinning models for plastic yieldJan 24 2013Typically, the plastic yield stress of a sample is determined from a stress-strain curve by defining a yield strain and reading off the stress required to attain it. However, it is not a priori clear that yield strengths of microscale samples measured ... More

Mouse Pose Estimation From Depth ImagesNov 24 2015We focus on the challenging problem of efficient mouse 3D pose estimation based on static images, and especially single depth images. We introduce an approach to discriminatively train the split nodes of trees in random forest to improve their performance ... More

Black hole complementarity with local horizons and Horowitz-Maldacena's proposalSep 09 2008Dec 19 2008To implement the consistent black hole complementarity principle, we need two assumptions: first, there exists a singularity near the center, and second, global horizons are the same as local horizons. However, these assumptions are not true in general. ... More

Robust unravelings for resonance fluorescenceFeb 24 2000Monitoring the fluorescent radiation of an atom unravels the master equation evolution by collapsing the atomic state into a pure state which evolves stochastically. A robust unraveling is one that gives pure states that, on average, are relatively unaffected ... More

Semi-classical black holes with large N re-scaling and information loss problemJul 03 2009Aug 02 2011We consider semi-classical black holes and related re-scalings with N massless fields. For a given semi-classical solution of an N = 1 universe, we can find other solution of a large N universe by the re-scaling. After the re-scaling, any curvature quantity ... More

Can the Horowitz-Maldacena proposal be an alternative to the firewall?Nov 11 2008Oct 11 2013Recently, there have been discussions that black hole complementarity is inconsistent and that the firewall is required to prohibit the observation of duplicated information. It is thought that if the Horowitz-Maldacena proposal works as a selection principle, ... More

Constructing a counterexample to the black hole complementarityFeb 12 2008Nov 10 2008We propose a regular black hole whose inside generates a de Sitter space and then is finally frustrated into a singularity. It is a modified model which was suggested originally by Frolov, Markov, and Mukhanov. In our model, we could adjust a regular ... More

A Novel Approach to Formulae Production and Overconfidence Measurement to Reduce Risk in Spreadsheet ModellingMar 12 2008Research on formulae production in spreadsheets has established the practice as high risk yet unrecognised as such by industry. There are numerous software applications that are designed to audit formulae and find errors. However these are all post creation, ... More

Vertex dynamics in finite two dimensional square spin icesApr 15 2010Jun 05 2010Local magnetic ordering in artificial spin ices is discussed from the point of view of how geometrical frustration controls dynamics and the approach to steady state. We discuss the possibility of using a particle picture based on vertex configurations ... More

Covering Array Bounds Using Analytical TechniquesMay 12 2014A $t$-covering array with entries from the alphabet ${\cal Q}=\{0,1,\ldots,q-1\}$ is a $k\times n$ stack, so that for any choice of $t$ (typically non-consecutive) columns, each of the $q^{t}$ possible $t$-letter words over ${\cal Q}$ appear at least ... More

Disorder regimes and equivalence of disorder types in artificial spin iceOct 07 2011The field-induced dynamics of artificial spin ice are determined in part by interactions between magnetic islands, and the switching characteristics of each island. Disorder in either of these affects the response to applied fields. Numerical simulations ... More

Set K-Cover Algorithms for Energy Efficient Monitoring in Wireless Sensor NetworksNov 20 2003Wireless sensor networks (WSNs) are emerging as an effective means for environment monitoring. This paper investigates a strategy for energy efficient monitoring in WSNs that partitions the sensors into covers, and then activates the covers iteratively ... More

The Validity of the Super-Particle Approximation during Planetesimal FormationDec 31 2009Jan 08 2010The formation mechanism of planetesimals in protoplanetary discs is hotly debated. Currently, the favoured model involves the accumulation of meter-sized objects within a turbulent disc, followed by a phase of gravitational instability. At best one can ... More

Diversity enabling equilibration: disorder and the ground state in artificial spin iceAug 02 2011Nov 16 2011We report a novel approach to the question of whether and how the ground state can be achieved in square artificial spin ices where frustration is incomplete. We identify two types of disorder: quenched disorder in the island response to fields and disorder ... More

A network model for field and quenched disorder effects in artificial spin iceDec 09 2011Apr 11 2012We have performed a systematic study of the effects of field strength and quenched disorder on the driven dynamics of square artificial spin ice. We construct a network representation of the configurational phase space, where nodes represent the microscopic ... More

Differential-algebraic jet spaces preserve internality to the constantsNov 14 2013This paper concerns the model theory of jet spaces (i.e., higher-order tangent spaces) in differentially closed fields. Suppose p is the generic type of the jet space to a finite dimensional differential-algebraic variety at a generic point. It is shown ... More

Full Numerical Simulations of Catastrophic Small Body CollisionsNov 02 2008The outcome of collisions between small icy bodies, such as Kuiper belt objects, is poorly understood and yet a critical component of the evolution of the trans-Neptunian region. The expected physical properties of outer solar system materials (high porosity, ... More

H-Representation of the Kimura-3 PolytopeSep 15 2014Dec 09 2015Given a group-based Markov model on a tree, one can compute the vertex representation of a polytope which describes the associated toric variety. The half-space representation, however, is not easily computable. In the case of $\mathbb{Z}_2$ or $\mathbb{Z}_2\times\mathbb{Z}_2$, ... More

How structure sculpts function: unveiling the contribution of anatomical connectivity to the brain's spontaneous correlation structureDec 07 2016Intrinsic brain activity is characterized by highly structured co-activations between different regions, whose origin is still under debate. In this paper, we address the question whether it is possible to unveil how the underlying anatomical connectivity ... More

Fault Modelling in System-of-Systems ContractsApr 30 2014Oct 07 2014The nature of Systems of Systems (SoSs), large complex systems composed of independent, geographically distributed and continuously evolving constituent systems, means that faults are unavoidable. Previous work on defining contractual specifications of ... More

Formation of planetary debris discs around white dwarfs II: Shrinking extremely eccentric collisionless ringsMay 22 2015The formation channel of the tens of compact debris discs which orbit white dwarfs (WDs) at a distance of one Solar radius remains unknown. Asteroids that survive the giant branch stellar phases beyond a few au are assumed to be dynamically thrust towards ... More

Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering dataOct 19 2016We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude with a fixed ... More

Formula of Volume of Revolution with Integration by Parts and ExtensionSep 04 2016A calculation formula of volume of revolution with integration by parts of definite integral is derived based on monotone function, and extended to a general case that curved trapezoids is determined by continuous, piecewise strictly monotone and differential ... More

A class of cyclic codes whose dual have five zerosFeb 07 2015In this paper, a family of cyclic codes over $\mathbb{F}_{p}$ whose duals have five zeros is presented, where $p$ is an odd prime. Furthermore, the weight distributions of these cyclic codes are determined.

Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering dataOct 19 2016Nov 10 2016We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude with a fixed ... More

An Online Approach to Dynamic Channel Access and Transmission SchedulingApr 04 2015Making judicious channel access and transmission scheduling decisions is essential for improving performance as well as energy and spectral efficiency in multichannel wireless systems. This problem has been a subject of extensive study in the past decade, ... More

To Stay Or To Switch: Multiuser Dynamic Channel AccessSep 14 2013In this paper we study opportunistic spectrum access (OSA) policies in a multiuser multichannel random access cognitive radio network, where users perform channel probing and switching in order to obtain better channel condition or higher instantaneous ... More

Modeling the distribution of distance data in Euclidean spaceJun 20 2016Phylogenetic inference-the derivation of a hypothesis for the common evolutionary history of a group of species- is an active area of research at the intersection of biology, computer science, mathematics, and statistics. One assumes the data contains ... More

Formation of planetary debris discs around white dwarfs I: Tidal disruption of an extremely eccentric asteroidSep 08 201425%-50% of all white dwarfs (WDs) host observable and dynamically active remnant planetary systems based on the presence of close-in circumstellar dust and gas and photospheric metal pollution. Currently-accepted theoretical explanations for the origin ... More

Avalanches, loading and finite size effects in 2D amorphous plasticity: results from a finite element modelNov 10 2014Feb 11 2015Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand - where the concept of linear lattice defects ... More

Critical Reviews of Causal Patch Measure over the MultiverseMar 13 2009Dec 01 2009In this talk, the causal patch measure based on black hole complementarity is critically reviewed. By noticing the similarities between the causal structure of an inflationary dS space and that of a black hole, we have considered the complementarity principle ... More

The Formation of the Collisional Family around the Dwarf Planet HaumeaMar 30 2010Haumea, a rapidly rotating elongated dwarf planet (~ 1500 km in diameter), has two satellites and is associated with a "family" of several smaller Kuiper Belt objects (KBOs) in similar orbits. All members of the Haumea system share a water ice spectral ... More

Physical effects of collisions in the Kuiper beltMay 27 2007Collisions are a major modification process over the history of the Kuiper Belt. Recent work illuminates the complex array of possible outcomes of individual collisions onto porous, volatile bodies. The cumulative effects of such collisions on the surface ... More

Avoidance and Coalescence of Delamination PatternsMar 31 2014Delamination of coatings and thin films from substrates generates a fascinating variety of patterns, from circular blisters to wrinkles and labyrinth domains, in a way that is not completely understood. We report on large-scale numerical simulations of ... More

Overfitting Bayesian Mixture Models with an Unknown Number of ComponentsFeb 18 2015Aug 24 2015This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov ... More

Novel Sampling Design for Respondent-driven SamplingJun 01 2016Aug 11 2016Respondent-driven sampling (RDS) is a type of chain referral sampling popular for sampling hidden and/or marginalized populations. As such, even under the ideal sampling assumptions, the performance of RDS is restricted by the underlying social network: ... More

Erosive Hit-and-Run Impact Events: Debris UnboundNov 16 2015Oct 31 2016Erosive collisions among planetary embryos in the inner solar system can lead to multiple remnant bodies, varied in mass, composition and residual velocity. Some of the smaller, unbound debris may become available to seed the main asteroid belt. The makeup ... More

Anthropic Likelihood for the Cosmological Constant and the Primordial Density Perturbation AmplitudeOct 14 2011Jan 12 2012Weinberg et al. calculated the anthropic likelihood of the cosmological constant using a model assuming that the number of observers is proportional to the total mass of gravitationally collapsed objects, with mass greater than a certain threshold, at ... More

Electromagnetically induced coherent backscatteringJun 06 2006We demonstrate a strong coherent backward wave oscillation using forward propagating fields only. This is achieved by applying laser fields to an ultra-dispersive medium with proper chosen detunings to excite a molecular vibrational coherence that corresponds ... More

On the arithmetic of the endomorphism ring End($\mathbb{Z}_{p}\times\mathbb{Z}_{p^{m}}$)May 03 2016For a prime $p$, let $E_{p,p^m}=\{\begin{pmatrix}a&b\\p^{m-1}c&d\end{pmatrix}|a,b,c\in\mathbb{Z}_{p},~\mathrm{and}~d\in \mathbb{Z}_{p^{m}}\}$. We first establish a ring isomorphism from $\mathrm{End}(\mathbb{Z}_p\times\mathbb{Z}_p^m)$ onto $E_{p,p^m}$. ... More

A blow-up criterion for the compressible liquid crystals systemNov 19 2010Nov 23 2010In this paper, we establish a blow-up criterion for the compressible liquid crystals equations in terms of the gradient of the velocity only, similar to the Beale-Kato-Majda criterion \cite{majda} for ideal incompressible flows and the criterion obtained ... More

$T$-adic exponential sums of polynomials in one variableNov 03 2009The $T$-adic exponential sum of a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function of the T-adic exponential ... More

The Dynamic Behavior of Quantum Statistical Entropy in 5D Ricci-flat Black String with Thin-layer ApproachNov 05 2008In this paper, the statistical-mechanical entropies of 5D Ricci-flat black string is calculated through the wave modes of the quantum field with improved thin-layer brick-wall method. The modes along the fifth dimension are semi-classically quantized ... More

Erosive Hit-and-Run Impact Events: Debris UnboundNov 16 2015Erosive collisions among planetary embryos in the inner solar system can lead to multiple remnant bodies, varied in mass, composition and residual velocity. Some of the smaller, unbound debris may become available to seed the main asteroid belt. The makeup ... More

Fixed point structure of the conformal factor field in quantum gravityMay 24 2016Oct 15 2016The $\mathcal{O}(\partial^2)$ background independent flow equations for conformally reduced gravity are shown to be equivalent to flow equations naturally adapted to scalar field theory with a wrong sign kinetic term. This sign change is shown to have ... More

How not to build Tatooine: the difficulty of in situ formation of circumbinary planets Kepler 16b, Kepler 34b and Kepler 35bJun 15 2012We study planetesimal evolution in circumbinary disks, focusing on the three systems Kepler 16, 34 and 35 where planets have been discovered recently. We show that for circumbinary planetesimals, in addition to secular forcing, eccentricities evolve on ... More

Learning Deep Neural Network Policies with Continuous Memory StatesJul 05 2015Sep 23 2015Policy learning for partially observed control tasks requires policies that can remember salient information from past observations. In this paper, we present a method for learning policies with internal memory for high-dimensional, continuous systems, ... More

Twisted exponential sums of polynomials in one variableDec 10 2009The twisted $T$-adic exponential sum associated to a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function ... More

Exploiting Unlabeled Data for Neural Grammatical Error DetectionNov 28 2016Nov 29 2016Identifying and correcting grammatical errors in the text written by non-native writers has received increasing attention in recent years. Although a number of annotated corpora have been established to facilitate data-driven grammatical error detection ... More

Matrix-Product Complementary dual CodesApr 13 2016Linear complementary dual codes (LCD) are linear codes satisfying $C\cap C^{\perp}=\{0\}$. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal matrices. Some ... More

Derivations from the even parts into the odd parts for Lie superalgebras W and SSep 08 2005Let $\mathcal{W}$ and $\mathcal{S}$ denote the even parts of the general Witt superalgebra $W$ and the special superalgebra $S$ over a field of characteristic $ p>3,$ respectively. In this note, using the method of reduction on $\mathbb{Z}$-gradations, ... More

Maximal graded subalgebras of Witt and Special superalgebrasNov 18 2009Mar 08 2010This paper has been withdrawn by the author due to that the main results and approaches are closedly parallel to the ones in Lie algebra case.

Upper Beurling Density of Systems formed by Translates of finite Sets of Elements in $L^p(\R^d)$Mar 28 2012In this paper, we prove that if a finite disjoint union of translates $\bigcup_{k=1}^n\{f_k(x-\gamma)\}_{\gamma\in\Gamma_k}$ in $L^p(\R^d)$ $(1<p<\infty)$ is a $p'$-Bessel sequence for some $1<p'<\infty$, then the disjoint union $\Gamma=\bigcup_{k=1}^n\Gamma_k$ ... More

Quantum Manifestation of Elastic Constants in NanostructuresSep 05 2012Generally, there are two distinct effects in modifying the properties of low-dimensional nanostructures: surface effect (SS) due to increased surface-volume ratio and quantum size effect (QSE) due to quantum confinement in reduced dimension. The SS has ... More

Higher Toda Mechanics and Spectral CurvesJun 01 2003For each one of the Lie algebras $\mathfrak{gl}_{n}$ and $\widetilde {\mathfrak{gl}}_{n}$, we constructed a family of integrable generalizations of the Toda chains characterized by two integers $m_{+}$ and $m_{-}$. The Lax matrices and the equations of ... More

Group Learning and Opinion Diffusion in a Broadcast NetworkSep 14 2013We analyze the following group learning problem in the context of opinion diffusion: Consider a network with $M$ users, each facing $N$ options. In a discrete time setting, at each time step, each user chooses $K$ out of the $N$ options, and receive randomly ... More

Ehrhart polynomials of lattice-face polytopesDec 28 2005There is a simple formula for the Ehrhart polynomial of a cyclic polytope. The purpose of this paper is to show that the same formula holds for a more general class of polytopes, lattice-face polytopes. We develop a way of decomposing any d-dimensional ... More

Pólya conjecture for the Neumann eigenvaluesNov 08 2014Feb 13 2015For a given bounded domain $\Omega\subset {\Bbb R}^n$ with $C^1$-smooth boundary, we prove the P\'olya conjecture for the Neumann eigenvalues. In other words, we prove that \begin{eqnarray*} \mu_{k+1}\le \frac{(2\pi)^2k^{2/n}}{(\omega_n \cdot \mbox{vol}\, ... More

Uniqueness of scatterer in inverse acoustic obstacle scattering with a single incident plane waveOct 11 2016Oct 17 2016In this paper, we give a simple proof for uniqueness of the scatterer in inverse obstacle scattering problem for acoustic wave with a single incident plane wave. Ramm in \cite{Ram1} showed that the acoustic scattering amplitude $A(\beta, {\alpha}_0, k_0)$, ... More

Model-based Differential Private Data SynthesisJun 26 2016We propose model-based based differential private data synthesis (modips) for releasing individual-level data with strong privacy guarantee. The modips technique is an original framework to integrate differential privacy -- a concept discussed largely ... More

Bridge the gap between network-based inference method and global ranking method in personal recommendationJul 15 2015In this paper, we study the relationship between the network-based inference method and global ranking method in personal recommendation. By some theoretical analysis, we prove that the recommendation result under the global ranking method is the limit ... More

Mixture Diffusion for Asset PricingOct 05 2016Oct 12 2016This paper proposes a general form of mixture diffusion process to model asset price dynamics, using a mixture of infinite number of parametric diffusions. We show that the underlying asset price dynamics of the risk-neutral probability density distributions ... More

Uniqueness of scatterer in inverse acoustic obstacle scattering with a single incident plane waveOct 11 2016Oct 19 2016In this paper, we give a simple proof for uniqueness of the scatterer in inverse obstacle scattering problem for acoustic wave with a single incident plane wave. Ramm in \cite{Ram1} showed that the acoustic scattering amplitude $A(\beta, {\alpha}_0, k_0)$, ... More

Twisted K-homology,Geometric cycles and T-dualityNov 06 2014Nov 14 2014Twisted $K$-homology corresponds to $D$-branes in string theory. In this paper we compare two different models of geometric twisted $K$-homology and get their equivalence. Moreover, we give another description of geometric twisted $K$-homology using bundle ... More

Resolution for Sheaf of Differential Operators on Smooth Free Geometric Quotient of Linear Action of Algebraic GroupSep 13 1996Sep 16 1996We obtain a global resolution for the sheaf of differential operators on smooth geometric quotients of free linear actions of algebraic groups. The terms of our resolution involve symmetric and alternating powers of vector bundles easily constructed geometrically ... More

Relative trace formulae toward Bessel and Fourier-Jacobi periods of unitary groupsDec 21 2010We propose a relative trace formula approach and state the corresponding fundamental lemma toward the global restriction problem involving Bessel or Fourier-Jacobi periods of unitary groups $\mathrm{U}_n\times\mathrm{U}_m$, extending the work of Jacquet-Rallis ... More

Smooth crossed products induced by minimal unique ergodic diffeomorphisms on odd spheresApr 06 2016For minimal unique ergodic diffeomorphisms $\alpha_n$ of $S^{2n+1} (n>0)$ and $\alpha_m$ of $S^{2m+1}(m>0)$, the $C^*$-crossed product algebra $C(S^{2n+1})\rtimes_{\alpha_n} \mathbb{Z}$ is isomorphic to $C(S^{2m+1})\rtimes_{\alpha_m} \mathbb{Z}$ even ... More

Comptage des multiplicités dans une hypersurfaceJun 30 2016Jul 11 2016In this paper, we give an upper bound of a sum of a function of multiplicity over a reduced projective hypersurface over a finite field.

Stationarity of Stochastic Linear Equations with Additive Noise and Delays in the Unbounded Drift TermsFeb 10 2014This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a consequence, the associated ... More

Heat kernel and moduli spaces IIDec 01 1996Apr 15 1997In this paper we continue our study on the moduli spaces of flat G-bundles, for any semi-simple Lie group G, over a Riemann surface by using heat kernel and Reidemeister torsion. Formulas for intersection numbers on the moduli spaces over a Riemann surface ... More

Lying-Over Theorem on Left Commutative RngsNov 26 2005We introduce the notion of a graded integral element, prove the counterpart of the lying-over theorem on commutative algebra in the context of left commutative rngs, and use the Hu-Liu product to select a class of noncommutative rings.

On Extension of Ginzburg-Jiang-Soudry Correspondence to Certain Automorphic Forms on $Sp_{4mn}(\BA)$ and $\wt{Sp}_{4mn \pm 2n}(\BA)$Sep 24 2013Let $F$ be a number field, and $\BA=\BA_F$. In this paper, first, we provide a family of global Arthur parameters confirming all parts of a general conjecture on the relation between the structure of Fourier coefficients and the structure of global Arthur ... More

On quadratic distinction of automorphic sheavesFeb 17 2011We prove a geometric version of a classical result on the characterization of an irreducible cuspidal automorphic representation of $\mathrm{GL}_n(\mathbb{A}_E)$ being the base change of a stable cuspidal packet of the quasi-split unitary group associated ... More

The Weyl-type asymptotic formula for biharmonic Steklov eigenvalues with Dirichlet boundary condition on Riemannian manifoldsDec 20 2009Jan 31 2011Let $\Omega$ be a bounded domain with $C^2$-smooth boundary in an $n$-dimensional oriented Riemannian manifold. It is well-known that for the bi-harmonic equation $\Delta^2 u=0$ in $\Omega$ with the $0$-Dirichlet boundary condition, there exists an infinite ... More

A Simple Converse Proof and a Unified Capacity Formula for Channels with Input ConstraintsJul 01 2008Given the single-letter capacity formula and the converse proof of a channel without constraints, we provide a simple approach to extend the results for the same channel but with constraints. The resulting capacity formula is the minimum of a Lagrange ... More

The L-functions of twisted Witt extensionsSep 18 2004Nov 25 2005The L-function of a non-degenerate twisted Witt extension is proved to be a polynomial. Its Newton polygon is proved to lie above the Hodge polygon of that extension. And the Newton polygons of the Gauss-Heilbronn sums are explicitly determined, generalizing ... More

Piecewise Interference and Stability of Branched FlowSep 01 2014The defining feature of chaos is its hypersensitivity to small perturbations. However, we report a stability of branched flow against large perturbations where the classical trajectories are chaotic, showing that strong perturbations are largely ignored ... More

Optimal control problems with state constraint governed by Navier-Stokes equationsMay 18 2010This work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by Navier-Stokes equations with state constraint in 3-D. Strong results in 2-D also are given.

A characterization of virtually embedded subsurfaces in 3-manifoldsJun 18 2014Mar 26 2015The paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes an invariant due to Rubinstein and Wang. The subsurface is virtually embedded ... More

Inequality for Variance of Weighted Sum of Correlated Random Variables and WLLNSep 11 2012Dec 17 2014The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with sum of 1. We also give a novel proof with positive semidefinite matrix ... More

$\mathsf{RT}_2^2$ does not imply $\mathsf{WKL}_0$Feb 11 2016We prove that $\mathsf{RCA}_0+\mathsf{RT}_2^2\not\rightarrow \mathsf{WKL}_0$ by showing that for any set $C$ not of PA-degree and any set $A$, there exists an infinite subset $G$ of $A$ or $\bar{A}$, such that $G\oplus C$ is also not of PA-degree.

Lecture notes on thermodynamics of ideal string gases and its application in cosmologyDec 05 2014In these lecture notes I give a pedagogical introduction to the thermodynamics of ideal string gases. The computation of thermodynamic quantities in the canonical ensemble formalism will be shown in detail with explicit examples. Attention will be given ... More

Holographic renormalization in no-boundary quantum cosmologyDec 04 2014Dec 22 2014Recent results of Hartle-Hawking wave functions on asymptotic dS boundaries show non-normalizability, while the bulk origin is not clear. This paper attempts to addresse this problem by studying (Kerr-)dS_3 cosmology in Einstein gravity deformed by a ... More

Extracting the trustworthiest way to service provider in complex online social networksJun 18 2013In complex online social networks, it is crucial for a service consumer to extract the trustworthiest way to a target service provider from numerous social trust paths between them. The extraction of the trustworthiest way (namely, optimal social trust ... More

Robust Particle Filter by Dynamic Averaging of Multiple Noise ModelsSep 05 2016State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which may result in ... More

The intrinsic line width of the Fe Ka line of AGNAug 26 2016X-ray fluorescent lines are unique features of the reflection spectrum of the cold torus when irradiated by the central AGN. Their intrinsic line widths can be used to probe the line-emitting region. The line widths of the Fe \Ka line measured from the ... More

Recovery of inhomogeneities and buried obstaclesApr 06 2008In this paper we consider the unique determination of inhomogeneities together with possible buried obstacles by scattering measurements. Under the assumption that the buried obstacles have only planar contacts with the inhomogeneities, we prove that ... More

A Global Uniqueness for Formally Determined Inverse Electromagnetic Obstacle ScatteringJan 17 2008It is proved that a general polyhedral perfect conducting obstacle in $\mathbb{R}^3$, possibly consisting of finitely many solid polyhedra, is uniquely determined by the far-field pattern corresponding to a single incident wave. This improves earlier ... More

Existence and Uniqueness of Solutions to Nonlinear Evolution Equations with Locally Monotone OperatorsNov 02 2010In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators. In particular, ... More

Generalized Canonical Correlation Analysis and Its Application to Blind Source Separation Based on a Dual-Linear Predictor StructureMar 09 2014Blind source separation (BSS) is one of the most important and established research topics in signal processing and many algorithms have been proposed based on different statistical properties of the source signals. For second-order statistics (SOS) based ... More

Channel Equalization and Beamforming for Quaternion-Valued Wireless Communication SystemsMay 31 2015Quaternion-valued wireless communication systems have been studied in the past. Although progress has been made in this promising area, a crucial missing link is lack of effective and efficient quaternion-valued signal processing algorithms for channel ... More

Noise-Sustained Convective Instability in a Magnetized Taylor-Couette FlowAug 19 2008Oct 13 2008The helical magnetorotational instability of the magnetized Taylor-Couette flow is studied numerically in a finite cylinder. A distant upstream insulating boundary is shown to stabilize the convective instability entirely while reducing the growth rate ... More