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Interpretation of parabolic arcs in pulsar secondary spectraMar 25 2004Pulsar dynamic spectra sometimes show organised interference patterns; these patterns have been shown to have power spectra which often take the form of parabolic arcs, or sequences of inverted parabolic arclets whose apexes themselves follow a parabolic ... More

Cross-Bifix-Free Codes Within a Constant Factor of OptimalitySep 03 2012Mar 11 2013A cross-bifix-free code is a set of words in which no prefix of any length of any word is the suffix of any word in the set. Cross-bifix-free codes arise in the study of distributed sequences for frame synchronization. We provide a new construction of ... More

Where do the Progenitors of Millisecond Pulsars come from?Dec 06 2011Observations of a large population of Millisecond Pulsars (MSPs) show a wide divergence in the orbital periods (from approximately hours to a few months). In the standard view, Low-Mass X-Ray Binaries (LMXBs) are considered as progenitors for some MSPs ... More

Investigation of Some Physical Properties of Accretion Induced Collapse in Producing Millisecond PulsarsJan 18 2012Jan 20 2012We investigate some physical characteristics of Millisecond Pulsar (MSP) such as magnetic fields, spin periods and masses, that are produced by Accretion Induced Collapse (AIC) of an accreting white dwarf (WD) in stellar binary systems. We also investigate ... More

Pressure-induced Superconductivity in Crystalline Boron NanowiresApr 08 2009We report high-pressure induced superconductivity in boron nanowires (BNWs) with rhombohedral crystal structure. Obviously different from bulk rhombohedral boron, these BNWs show a semiconductor-metal transition at much lower pressure than bulk boron. ... More

An innovative way of etching MoS2: Characterization and mechanistic investigationMar 01 2013We report a systematic study of the etching of MoS2 crystals by using XeF2 as a gaseous reactant. By controlling the etching process, monolayer MoS2 with uniform morphology can be obtained. The Raman and photoluminescence spectra of the resulting material ... More

Graphene-Silicon Layered Structures on Single-crystalline Ir(111) Thin FilmsMar 02 2015Single-crystalline transition metal films are ideal playing fields for the epitaxial growth of graphene and graphene-base materials. Graphene-silicon layered structures were successfully constructed on Ir(111) thin film on Si substrate with an yttria-stabilized ... More

Binary Pulsars in Magnetic Field versus Spin Period DiagramApr 09 2013We analyzed 186 binary pulsars (BPSRs) in the magnetic field versus spin period (B-P) diagram, where their relations to the millisecond pulsars (MSPs) can be clearly shown. Generally, both BPSRs and MSPs are believed to be recycled and spun-up in binary ... More

Existence, uniqueness and stability of transition fronts of nonlocal equations in time heterogeneous bistable mediaJul 14 2015Jan 07 2016The present paper is devoted to the study of existence, uniqueness and stability of transition fronts of nonlocal dispersal evolution equations in time heterogeneous media of bistable type under the unbalanced condition. We first study space nonincreasing ... More

Transition fronts in nonlocal Fisher-KPP equations in time heterogeneous mediaJul 14 2015Nov 19 2015The present paper is devoted to the study of transition fronts of nonlocal Fisher-KPP equations in time heterogeneous media. We first construct transition fronts with prescribed interface location functions, which are natural generalizations of front ... More

Stability, Uniqueness and Recurrence of Generalized Traveling Waves in Time Heterogeneous Media of Ignition TypeAug 17 2014Apr 21 2015The present paper is devoted to the study of stability, uniqueness and recurrence of generalized traveling waves of reaction-diffusion equations in time heterogeneous media of ignition type, whose existence has been proven by the authors of the present ... More

Regularity and stability of transition fronts in nonlocal equations with time heterogeneous ignition nonlinearityJan 09 2015The present paper is devoted to the investigation of various properties of transition fronts in nonlocal equations in heterogeneous media of ignition type, whose existence has been established by the authors of the present paper in a previous work. It ... More

Observation of Majorana conductance plateau by scanning tunneling spectroscopyApr 12 2019Majorana zero-modes (MZMs) are spatially-localized zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold great promise for topological quantum computing. Due to its particle-antiparticle equivalence, an MZM exhibits perfect ... More

Face Identification with Second-Order PoolingJun 26 2014Sep 17 2014Automatic face recognition has received significant performance improvement by developing specialised facial image representations. On the other hand, generic object recognition has rarely been applied to the face recognition. Spatial pyramid pooling ... More

Minimum Accretion Rate for Millisecond Pulsar Formation in Binary SystemMar 30 2013186 binary pulsars are shown in the magnetic field versus spin period (B-P) dia- gram, and their relations to the millisecond pulsars can be clearly seen. We declaim a minimum accretion rate for the millisecond pulsar formation both from the observation ... More

Existence, uniqueness and stability of transition fronts of nonlocal equations in time heterogeneous bistable mediaJul 14 2015Apr 01 2017The present paper is devoted to the study of existence, uniqueness and stability of transition fronts of nonlocal dispersal evolution equations in time heterogeneous media of bistable type under the unbalanced condition. We first study space nonincreasing ... More

Regularity of transition fronts in nonlocal dispersal evolution equationsApr 10 2015Nov 12 2015It is known that solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal equations. In the present paper, ... More

A New Set of Parameters of High-Mass X-ray Binaries Found with their Cyclotron LinesAug 16 2018Jan 11 2019We have derived new physical quantities for several High-Mass X-ray Binaries (HMXBs) with supergiant (SG) companions through their cyclotron lines. The parameters are: the terminal velocity of the wind, the mass loss rate of the donor, the effective temperature ... More

Could bright gamma-ray burst optical transients have been recorded historically?Oct 27 2011The brightest optical flash from a gamma-ray burst (GRB) was, briefly, a naked-eye object. Several other GRBs have produced optical transients only slightly fainter. We argue that, based upon the recently accumulated data from hundreds of GRB transients, ... More

Transition fronts in nonlocal equations with time heterogeneous ignition nonlinearityOct 17 2014Jul 09 2015The present paper is devoted to the study of transition fronts in nonlocal reaction-diffusion equations with time heterogeneous nonlinearity of ignition type. It is proven that such an equation admits space monotone transition fronts with finite speed ... More

Transition Fronts in Time Heterogeneous and Random Media of Ignition TypeJul 28 2014Dec 18 2015The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous media admit ... More

Quantum Dilaton Gravity in the Light-cone GaugeSep 18 1992Recently, models of two-dimensional dilaton gravity have been shown to admit classical black-hole solutions that exhibit Hawking radiation at the semi-classical level. These classical and semi-classical analyses have been performed in conformal gauge. ... More

Parametrizing an integer linear program by an integerOct 05 2015Nov 07 2016We consider a family of integer linear programs in which the coefficients of the constraints and objective function are polynomials of an integer parameter $t.$ For $\ell$ in $\mathbb{Z}_+,$ we define $f_\ell(t)$ to be the $\ell^{\text{th}}$ largest value ... More

Elections and statistics: the case of "United Russia", 2009-2012Apr 02 2012The election statistics analysis does not confirm the assumption of correct ballot counting (a survey).

Equation of State for Proto-Neutron StarFeb 26 2012Physics of the Equation of State (EoS) for proto-neutron star (PNS) concerns properties of neutron rich matter at finite temperature over wide range of densities. In this contribution we discuss the structure of PNS inner crust in a relativisitc mean ... More

Typical behavior of the harmonic measure in critical Galton-Watson trees with infinite variance offspring distributionMar 03 2016We study the typical behavior of the harmonic measure in large critical Galton-Watson trees whose offspring distribution is in the domain of attraction of a stable distribution with index $\alpha\in (1,2]$. Let $\mu_n$ denote the hitting distribution ... More

Analytic torsion, dynamical zeta functions and orbital integralsFeb 01 2016The purpose of this article is to prove an identity between the analytic torsion and the value at zero of a dynamical zeta function associated with an acyclic unitarily flat vector bundle on a closed locally symmetric reductive manifold, which solves ... More

Funk Metrics and R-Flat SpraysSep 05 2001The well-known Funk metric F(x,y) is projectively flat with constant flag curvature K=-1/4 and the Hilbert metric H(x,y):=(F(x,y)+F(x,-y))/2 is projectively flat with constant curvature K=-1. These metrics are the special solutions to Hilbert's Fourth ... More

On Projectively Related Einstein MetricsOct 19 1999We study the following problem: given an Einstein metric on a manifold, characterize and study all Einstein metrics which are pointwise projective to the given one. By definition, two metrics are said to be pointwise projectively related if they have ... More

Extrapolation for the $L^p$ Dirichlet Problem in Lipschitz domainsJan 02 2018Let $\mathcal{L}$ be a second-order linear elliptic operator with complex coefficients. We show that if the $L^p$ Dirichlet problem for the elliptic system $\mathcal{L}(u)=0$ in a fixed Lipschitz domain $\Omega$ in $\mathbb{R}^d$ is solvable for some ... More

Scattering Theory of Schrödinger Operators with Random Sparse PotentialsMar 11 2014In this paper, we study the scattering theory of a class of continuum Schr\"{o}dinger operators with random sparse potentials. The existence and completeness of wave operators are proven by establishing the uniform boundedness of modified free resolvents ... More

A Lefschetz Hyperplane Theorem for non-Archimedean JacobiansOct 07 2016We establish a Lefschetz hyperplane theorem for the Berkovich analytifications of Jacobians of curves over an algebraically closed non-Archimedean field. Let $J$ be the Jacobian of a curve $X$, and let $W_d \subset J$ be the locus of effective divisor ... More

Successive filament eruptions within one solar breakout eventJan 08 2014The magnetic breakout model has been widely used to explain solar eruptive activities. Here, we apply it to explain successive filament eruptions occurred in a quadrupolar magnetic source region. Based on the high temporal and spatial resolution, multi-wavelengths ... More

Elections and statistics: the case of "United Russia", 2009-2018Apr 02 2012Jun 23 2018The election statistics analysis does not confirm the assumption of correct ballot counting (a survey).

Kolmogorov complexity as a languageFeb 26 2011The notion of Kolmogorov complexity (=the minimal length of a program that generates some object) is often useful as a kind of language that allows us to reformulate some notions and therefore provide new intuition. In this survey we provide (with minimal ... More

Existence, Uniqueness and Anisotropic-Decay-Caused Lifshitz Tails of the Integrated Density of Surface States for Random Surface ModelsSep 23 2012The current paper is devoted to the study of existence, uniqueness and Lifshitz tails of the integrated density of surface states (IDSS) for Schr\"{o}dinger operators with alloy type random surface potentials. We prove the existence and uniqueness of ... More

Rational curves on Fermat hypersurfacesNov 24 2011Sep 19 2012In this note we study rational curves on degree $p^r+1$ Fermat hypersurface in $\PP^{p^r+1}_k$, where $k$ is an algebraically closed field of characteristic $p$. The key point is that the presence of Frobenius morphism makes the behavior of rational curves ... More

Frobenius algebras and root systems: the trigonometric caseJan 25 2019We construct Frobenius structures on the $\mathbb{C}^{\times}$-bundle of the complement of a toric arrangement associated with a root system, by making use of a one-parameter family of torsion free and flat connections on it. This gives rise to a trigonometric ... More

Geometric structures on the complement of a toric mirror arrangementAug 30 2018We study geometric structures on the complement of a toric mirror arrangement associated with a root system. Inspired by those special hypergeometric functions found by Heckman-Opdam, as well as the work of Couwenberg-Heckman-Looijenga on geometric structures ... More

A renormalization group method by harmonic extensions and the classical dipole gasNov 10 2013Dec 13 2014In this paper we develop a new renormalization group method, which is based on conditional expectations and harmonic extensions, to study functional integrals related with small perturbations of Gaussian fields. In this new method one integrates Gaussian ... More

A Differential Topological View of Challenges in Learning with Feedforward Neural NetworksNov 26 2018Among many unsolved puzzles in theories of Deep Neural Networks (DNNs), there are three most fundamental challenges that highly demand solutions, namely, expressibility, optimisability, and generalisability. Although there have been significant progresses ... More

Stability of transition waves and positive entire solutions of Fisher-KPP equations with time and space dependenceSep 14 2016Mar 21 2017This paper is concerned with the stability of transition waves and strictly positive entire solutions of random and nonlocal dispersal evolution equations of Fisher-KPP type with general time and space dependence, including time and space periodic or ... More

A Semi-linear Energy Critical Wave Equation With ApplicationsJan 01 2015In this work we consider a semi-linear energy critical wave equation in ${\mathbb R}^d$ ($3\leq d \leq 5$) \[ \partial_t^2 u - \Delta u = \pm \phi(x) |u|^{4/(d-2)} u, \qquad (x,t)\in {\mathbb R}^d \times {\mathbb R} \] with initial data $(u, \partial_t ... More

Scattering of solutions to the defocusing energy sub-critical semi-linear wave equation in 3DDec 02 2015In this paper we consider a semi-linear, energy sub-critical, defocusing wave equation $\partial_t^2 u - \Delta u = - |u|^{p -1} u$ in the 3-dimensional space with $p \in [3,5)$. We prove that if initial data $(u_0, u_1)$ are radial so that $\|\nabla ... More

Typical behavior of the harmonic measure in critical Galton-Watson trees with infinite variance offspring distributionMar 03 2016Feb 25 2017We study the typical behavior of the harmonic measure in large critical Galton-Watson trees whose offspring distribution is in the domain of attraction of a stable distribution with index $\alpha\in (1,2]$. Let $\mu_n$ denote the hitting distribution ... More

A stochastic-variational model for soft Mumford-Shah segmentationOct 23 2005In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte-Carlo or other stochastic algorithms. ... More

Generic Image Classification Approaches Excel on Face RecognitionSep 22 2013Sep 30 2013The main finding of this work is that the standard image classification pipeline, which consists of dictionary learning, feature encoding, spatial pyramid pooling and linear classification, outperforms all state-of-the-art face recognition methods on ... More

Conic Kähler-Einstein metrics along simple normal crossing divisors on Fano manifoldsMar 21 2016We prove that on one K\"{a}hler-Einstein Fano manifold without holomorphic vector fields, there exists a unique conical K\"{a}hler-Einstein metric along a simple normal crossing divisor with admissible prescribed cone angles. We also establish a curvature ... More

Recent $J/ψ$ Results from BESIINov 17 2004The studies on the multi-quark candidates, light scalar mesons and excited baryon states at BES are presented, based on $5.8 \times 10^7$ $J/\psi$ data collected with BESII detector. The measurements of some $J/\psi$ and $\eta_c$ decays are presented ... More

J/psi Radiative DecaysSep 16 2002The previous results of J/psi radiative decays from MARKIII, DM2, Crystal Ball and BESI are briefly reviewed in this talk. The main part of this talk focuses on presenting the recent results from BESII 58 million J/psi data, including the Partial Wave ... More

On some generalized Rapoport-Zink spacesNov 28 2016We enlarge the class of Rapoport-Zink spaces of Hodge type by modifying the centers of the associated $p$-adic reductive groups. These such-obtained Rapoport-Zink spaces are called of abelian type. The class of Rapoport-Zink spaces of abelian type is ... More

Weil-Petersson Teichmüller spaceApr 11 2013Oct 30 2017The paper presents some recent results on the Weil-Petersson geometry theory of the universal Teichm\"uller space, a topic which is important in Teichm\"uller theory and has wide applications to various areas such as mathematical physics, differential ... More

Are random axioms useful?Sep 26 2011Oct 16 2011The famous G\"odel incompleteness theorem says that for every sufficiently rich formal theory (containing formal arithmetic in some natural sense) there exist true unprovable statements. Such statements would be natural candidates for being added as axioms, ... More

Axiomatic approach to the theory of algorithms and relativized computabilityNov 15 2018It is well known that many theorems in recursion theory can be "relativized". This means that they remain true if partial recursive functions are replaced by functions that are partial recursive relative to some fixed oracle set. Uspensky formulates three ... More

Motives of Noncommutative ToriMar 09 2014In this article, we propose a way of seeing the noncommutative tori in the category of noncommutative motives. As an algebra, the noncommutative torus is lack the smoothness property required to define a noncomutative motive. Thus, instead of working ... More

The Coleman-Weinberg Mechanism and First Order Phase TransitionsMar 26 1993Aug 06 1993Revised and reduced the size of the text. Removed figure 2 in previous text. So, old figure 3 and 4 become new figure 2 and 3, respectively. Added figure 4 for first order phase transition observation in the strong coupling region. Postscript files for ... More

Necessary and Sufficient Conditions for the Solvability of the $L^p$ Dirichlet Problem On Lipschitz DomainsSep 26 2005We study the homogeneous elliptic systems of order $2\ell$ with real constant coefficients on Lipschitz domains in $R^n$, $n\ge 4$. For any fixed $p>2$, we show that a reverse H\"older condition with exponent $p$ is necessary and sufficient for the solvability ... More

Towards Semantic Big Graph Analytics for Cross-Domain Knowledge DiscoveryFeb 20 2019In recent years, the size of big linked data has grown rapidly and this number is still rising. Big linked data and knowledge bases come from different domains such as life sciences, publications, media, social web, and so on. However, with the rapid ... More

Global Well-posedness and Scattering of Defocusing Energy subcritical Nonlinear Wave Equation in dimension 3 with radial dataNov 09 2011The paper deals with the defocusing case of the energy subcritical non-linear wave equation in $R^3$. We assume the initial data is in the space $\dot{H}^s \times \dot{H}^{s-1}$ and radial. If $s=1$, this is the energy space and the scattering results ... More

Developments and Obstacles in Chinese eBook MarketJul 17 2012The purpose of this study was to provide insights into the eBook market in China through case studies on eBook companies and a survey research with individual eBook users. The information from three companies, Beijing Superstar Electric Company, Beijing ... More

I-method for Defocusing, Energy-Subcritical Non-linear Wave EquationMay 21 2012In this paper the author considers the global existence and well-posedness of the non-linear wave equation $\partial_t^2 u - \Delta u = -|u|^{p-1} u$ in 3-dimensional space, assuming that the initial data is in the space $(\dot{H}^s \cap \dot{H}^{s_p}) ... More

On stochastic stability of non-uniformly expanding interval mapsJul 13 2011Dec 17 2012We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic stability.

On some generalized Rapoport-Zink spacesNov 28 2016Dec 07 2017We enlarge the class of Rapoport-Zink spaces of Hodge type by modifying the centers of the associated $p$-adic reductive groups. These such-obtained Rapoport-Zink spaces are called of abelian type. The class of Rapoport-Zink spaces of abelian type is ... More

Perfectoid Shimura varieties of abelian typeJul 07 2015Sep 12 2016We prove that Shimura varieties of abelian type with infinite level at $p$ are perfectoid. As a corollary, the moduli spaces of polarized K3 surfaces with infinite level at $p$ are also perfectoid.

Location of the Path Supremum for Self-similar Processes with Stationary IncrementsApr 15 2016May 21 2016In this paper we consider the distribution of the location of the path supremum in a fixed interval for self-similar processes with stationary increments. To this end, a point process is constructed and its relation to the distribution of the location ... More

Prym-Tjurin Constructions on Cubic HypersurfacesNov 28 2011Oct 22 2013In this paper, we give a Prym-Tjurin construction for the cohomology and the Chow groups for a cubic hypersurface. On the space of lines meeting a given rational curve, there is the incidence correspondence. This correspondence induces an action on both ... More

Birational Chow-Künneth decompositionsJun 15 2016We study the notion of a birational Chow-K\"unneth decomposition, which is essentially a decomposition of the integral birational motive of a variety. The existence of a birational Chow-K\"unneth decomposition is stably birationally invariant and this ... More

Towards a Mathematical Understanding of the Difficulty in Learning with Feedforward Neural NetworksNov 17 2016Nov 21 2017Training deep neural networks for solving machine learning problems is one great challenge in the field, mainly due to its associated optimisation problem being highly non-convex. Recent developments have suggested that many training algorithms do not ... More

A Complete Equation of State for Astrophysical SimulationsDec 19 2015We construct a complete equation of state (EOS) covering a wide range of temperature, proton fraction, and baryon density for the use of astrophysical simulations. We employ the relativistic mean-field (RMF) theory to describe nuclear interactions and ... More

Typical behavior of the harmonic measure in critical Galton-Watson treesFeb 19 2015Mar 03 2016We study the typical behavior of the harmonic measure of balls in large critical Galton-Watson trees whose offspring distribution has finite variance. The harmonic measure considered here refers to the hitting distribution of height $n$ by simple random ... More

Traveling Wave Profiles for a Follow-the-Leader Model for Traffic Flow with Rough Road ConditionNov 06 2017Feb 05 2018We study a Follow-the-Leader (FtL) ODE model for traffic flow with rough road condition, and analyze stationary traveling wave profiles where the solutions of the FtL model trace along, near the jump in the road condition. We derive a discontinuous delay ... More

Cobordism invariants of the moduli space of stable pairsSep 16 2014May 29 2016For a quasi-projective scheme M which carries a perfect obstruction theory, we construct the virtual cobordism class of M. If M is projective, we prove that the corresponding Chern numbers of the virtual cobordism class are given by integrals of the Chern ... More

An analogue of Szego's limit theorem in free probability theoryJun 06 2007Aug 07 2007In the paper, we discuss orthogonal polynomials in free probability theory. Especially, we prove an analogue of of Szego's limit theorem in free probability theory.

Embedding Dimensions of Finite von Neumann AlgebrasApr 06 2006We introduce "embedding dimensions" of a family of generators of a finite von Neumann algebra when the von Neumann algebra can be faithfully embedded into the ultrapower of the hyperfinite II$_1$ factor. These embedding dimensions are von Neumann algebra ... More

On Voiculescu's Semicircular MatricesAug 17 2005Oct 03 2005Assume $\N$ is a von Neumann algebra of type II$_1$ with a tracial state $\tau_{\N}$, and $\M$ is the von Neumann algebra of the $n\times n$ matrices over $\N$ with the canonical tracial state $\tau_{\M}$. Let $\mathcal D_n$ be the subalgebra of $\M$ ... More

Maximal Injective Subalgebras of Tensor Products of Free Groups FactorsAug 16 2005Aug 25 2005In this article, we proved the following results. Let $L(F(n_i))$ be the free group factor on $n_i$ generators and $\lambda (g_{i})$ be one of standard generators of $L(F(n_i))$ for $1\le i\le N$. Let $\A_i$ be the abelian von Neumann subalgebra of $L(F(n_i))$ ... More

The parametric Frobenius problem and parametric exclusionOct 05 2015Nov 07 2016The Frobenius number of relatively prime positive integers $a_1, \ldots, a_n$ is the largest integer that is not a nononegative integer combination of the $a_i.$ Given positive integers $a_1, \ldots, a_n$ with $n \ge 2,$ the set of multiples of $\gcd(a_1, ... More

Weak embedding theorem and a proof of cycle double cover of bridgeless graphsDec 11 2017In this article, we give a positive answer to the cycle double cover conjecture. Ones who are mainly interesting in the proof of the conjecture can only read Sections 2 and 4.

A manual proof of the Four-colour TheoremOct 30 2017Jul 06 2018In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.

A uniformness conjecture of the Kolakoski sequence, graph connectivity, and correlationsMar 01 2017Apr 24 2017The Kolakoski sequence is the unique infinite sequence with values in $\{1,2\}$ and first term $1$ which equals the sequence of run-lengths of itself, we call this $K(1,2).$ We define $K(m,n)$ similarly. A well-known conjecture is that the limiting density ... More

Finite temperature magnon spectra in yttrium iron garnet from mean field approach in tight-binding modelDec 27 2017We study magnon spectra at finite temperature in yttrium iron garnet from tight-binding model with nearest neighboring exchange interaction. The spin reduction due to thermal magnon excitation are taken into account via the mean field approximation to ... More

Face Image Classification by Pooling Raw FeaturesJun 26 2014Sep 17 2014We propose a very simple, efficient yet surprisingly effective feature extraction method for face recognition (about 20 lines of Matlab code), which is mainly inspired by spatial pyramid pooling in generic image classification. We show that features formed ... More

On the cohomology of some simple Shimura varieties with bad reductionNov 02 2014We determine the Galois representations inside the $l$-adic cohomology of some quaternionic and related unitary Shimura varieties at ramified places. The main results generalize the previous works of Reimann and Kottwitz in this setting to arbitrary levels ... More

W-Infinity and String TheoryFeb 20 1992Feb 23 1992We review some recent developments in the theory of $W_\infty$. We comment on its relevance to lower-dimensional string theory.

Rationality, universal generation and the integral Hodge conjectureFeb 23 2016We use the universal generation of 1-cycles to relate (stable) rationality to the integral Hodge conjecture. Applications are mainly given to cubic threefolds and cubic fourfolds. We show that if a generic cubic fourfold is stably rational, then a canonical ... More

Designing and Training Feedforward Neural Networks: A Smooth Optimisation PerspectiveNov 17 2016Despite the recent great success of deep neural networks in various applications, designing and training a deep neural network is still among the greatest challenges in the field. In this work, we present a smooth optimisation perspective on designing ... More

Convergence Rates and Hölder Estimates in Almost-Periodic Homogenization of Elliptic SystemsApr 23 2014Jun 24 2015For a family of second-order elliptic systems in divergence form with rapidly oscillating almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the coefficients. The ... More

Priority arguments and separation problemsNov 16 2018Different constructions in the recursion theory use the so-called priority arguments. A general scheme was suggested by A.~Lachlan. Based on his work, we define the notion of a priority-closed class of requirements. Then, for a specific priority construction, ... More

Decomposition ComplexityDec 03 2010We consider a problem of decomposition of a ternary function into a composition of binary ones from the viewpoint of communication complexity and algorithmic information theory as well as some applications to cellular automata.

On the Energy Subcritical, Non-linear Wave Equation with Radial Data for $p\in (3,5)$Aug 10 2012In this paper, we consider the wave equation in 3-dimensional space with an energy-subcritical nonlinearity, either in the focusing or defocusing case. We show that any radial solution of the equation which is bounded in the critical Sobolev space is ... More

Rest-frame Optical Properties of Luminous 1.5<z<3.5 Quasars: the Hbeta-[OIII] RegionNov 30 2015We study the rest-frame optical properties of 74 luminous (L_bol=10^46.2-48.2 erg/s), 1.5<z<3.5 broad-line quasars with near-IR (JHK) slit spectroscopy. Systemic redshifts based on the peak of the [OIII]5007 line reveal that redshift estimates from the ... More

The Mass of QuasarsFeb 11 2013I review the current status of quasar black hole (BH) mass estimations. Spectroscopic methods have been developed to estimate BH mass in broad line quasars to an accuracy of ~0.5 dex. Despite their popularity, significant issues and confusion remain regarding ... More

Fluctuation Induced First Order Phase TransitionsNov 17 1993We study a $U(N)\times U(N)$ symmetric scalar field model in four and three dimensions. First, using our data in four dimensions in the weak coupling region, we demonstrate explicitly that the observed first order phase transition is induced by quantum ... More

Data Sustainability and Reuse Pathways of Natural Resources and Environmental ScientistsMar 05 2018This paper presents a multifarious examination of natural resources and environmental scientists' adventures navigating the policy change towards open access and cultural shift in data management, sharing, and reuse. Situated in the institutional context ... More

Burgeoning Data Repository Systems, Characteristics and Development Strategies: Insights of Natural Resources and Environmental ScientistsMar 05 2018Nowadays, we have the emergence and abundance of many different data repositories and archival systems for scientific data discovery, use, and analysis. With the burgeoning data sharing platforms available, this study addresses how natural resources and ... More

On relations among 1-cycles on cubic hypersurfacesFeb 13 2011Feb 02 2012In this paper we give two explicit relations among 1-cycles modulo rational equivalence on a smooth cubic hypersurfaces $X$. Such a relation is given in terms of a (pair of) curve(s) and its secant lines. As the first application, we reprove Paranjape's ... More

Foliations and Rational Connectedness in Positive CharacteristicJun 04 2009Oct 17 2009In this paper, the technique of foliations in characteristic $p$ is used to investigate the difference between rational connectedness and separable rational connectedness in positive characteristic. The notion of being freely rationally connected is defined; ... More

Automatic Kolmogorov complexity and normality revisitedJan 31 2017Aug 28 2017It is well known that normality (all factors of given length appear in an infinite sequence with the same frequency) can be described as incompressibility via finite automata. Still the statement and proof of this result as given by Becher and Heiber ... More

The ternary Goldbach problem with primes in positive density setsFeb 27 2016Let $\mathcal{P}$ denote the set of all primes. $P_{1},P_{2},P_{3}$ are three subsets of $\mathcal{P}$. Let $\underline{\delta}(P_{i})$ $(i=1,2,3)$ denote the lower density of $P_{i}$ in $\mathcal{P}$, respectively. It is proved that if $\underline{\delta}(P_{1})>5/8$, ... More

Nonrationality of a generic cubic fourfoldJan 23 2016Jan 29 2016An error in Section 4 invalidates all the main results of the paper.