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Non-Stationary Streaming PCAFeb 08 2019We consider the problem of streaming principal component analysis (PCA) when the observations are noisy and generated in a non-stationary environment. Given $T$, $p$-dimensional noisy observations sampled from a non-stationary variant of the spiked covariance ... More

Convergence Rates of Gradient Descent and MM Algorithms for Generalized Bradley-Terry ModelsJan 01 2019We show tight convergence rate bounds for gradient descent and MM algorithms for maximum likelihood estimation and maximum aposteriori probability estimation of a popular Bayesian inference method for generalized Bradley-Terry models. This class of models ... More

Non-Stationary Streaming PCAFeb 08 2019Mar 30 2019We consider the problem of streaming principal component analysis (PCA) when the observations are noisy and generated in a non-stationary environment. Given $T$, $p$-dimensional noisy observations sampled from a non-stationary variant of the spiked covariance ... More

Feature Selection via Block-Regularized RegressionJun 13 2012Identifying co-varying causal elements in very high dimensional feature space with internal structures, e.g., a space with as many as millions of linearly ordered features, as one typically encounters in problems such as whole genome association (WGA) ... More

Spin-Polarized to Valley-Polarized Transition in Graphene Bilayers at $ν=0$ in High Magnetic FieldsFeb 01 2011Jul 04 2011We investigate the transverse electric field ($E$) dependence of the $\nu$=0 quantum Hall state (QHS) in dual-gated graphene bilayers in high magnetic fields. The longitudinal resistivity ($\rho_{xx}$) measured at $\nu$=0 shows an insulating behavior ... More

Dielectric Thickness Dependence of Carrier Mobility in Graphene with HfO2 Top DielectricOct 05 2010We investigate the carrier mobility in mono- and bi-layer graphene with a top HfO2 dielectric, as a function of the HfO2 film thickness and temperature. The results show that the carrier mobility decreases during the deposition of the first 2-4 nm of ... More

Coulomb Drag and Magnetotransport in Graphene Double LayersJun 13 2012We review the fabrication and key transport properties of graphene double layers, consisting of two graphene monolayers placed in close proximity, independently contacted, and separated by an ultra-thin dielectric. We outline a simple band structure model ... More

Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mappingSep 08 2009Sep 28 2012We consider the problem of estimating a sparse multi-response regression function, with an application to expression quantitative trait locus (eQTL) mapping, where the goal is to discover genetic variations that influence gene-expression levels. In particular, ... More

Observational approaches to understanding dark energyDec 01 2007Illuminating the nature of dark energy is one of the most important challenges in cosmology today. In this review I discuss several promising observational approaches to understanding dark energy, in the context of the recommendations by the U.S. Dark ... More

Differentiating dark energy and modified gravity with galaxy redshift surveysOct 21 2007Apr 28 2008The observed cosmic acceleration today could be due to an unknown energy component (dark energy), or a modification to general relativity (modified gravity). If dark energy models and modified gravity models are required to predict the same cosmic expansion ... More

Lectures on Springer theories and orbital integralsFeb 03 2016These are the expanded lecture notes from the author's mini-course during the graduate summer school of the Park City Math Institute in 2015. The main topics covered are: geometry of Springer fibers, affine Springer fibers and Hitchin fibers; representations ... More

Modeling galaxy clustering on small scales to tighten constraints on dark energy and modified gravityJun 26 2016Oct 10 2016We present a new approach to measuring cosmic expansion history and growth rate of large scale structure using the anisotropic two dimensional galaxy correlation function (2DCF) measured from data; it makes use of the empirical modeling of small-scale ... More

Parallelism-Aware Memory Interference Delay Analysis for COTS Multicore SystemsJul 25 2014In modern Commercial Off-The-Shelf (COTS) multicore systems, each core can generate many parallel memory requests at a time. The processing of these parallel requests in the DRAM controller greatly affects the memory interference delay experienced by ... More

125 GeV Higgs bosons in two-Higgs-doublet modelsMay 14 2013Moriond 2013 ALTAS data at 125 GeV state appears to exhibit a substantial excess in the di-photon final state and in the ZZ decaying to four lepton channel, whereas which are more or less SM-like rate observed by CMS MVA analysis. We examine the maximum ... More

Towards a Global Springer Theory I: The affine Weyl group actionOct 13 2008Apr 22 2009We propose a generalization of Springer representations to the context of groups over a global function field. The global counterpart of the Grothendieck simultaneous resolution is the parabolic Hitchin fibration. We construct an action of the affine ... More

The spherical part of the local and global Springer actionsJun 11 2011The affine Weyl group acts on the cohomology (with compact support) of affine Springer fibers (local Springer theory) and of parabolic Hitchin fibers (global Springer theory). In this paper, we show that in both situations, the action of the center of ... More

Galois representations attached to moments of Kloosterman sums and conjectures of EvansAug 19 2013Sep 07 2013Kloosterman sums for a finite field arise as Frobenius trace functions of certain local systems defined over $\Gm$. The moments of Kloosterman sums calculate the Frobenius traces on the cohomology of tensor powers (or symmetric powers, exterior powers, ... More

Conditional Ergodic Averages for Asymptotically Additive PotentialsMay 07 2014Using an asymptotically additive sequence of continuous functions as a restrictive condition, this paper studies the relations of several ergodic averages for asymptotically additive potentials. Basic properties of conditional maximum ergodic averages ... More

One New Blowup Criterion for the 2D Full Compressible Navier-Stokes SystemOct 24 2012Jan 30 2013We establish a blowup criterion for the two-dimensional (2D) full compressible Navier-Stokes system. The criterion is given in terms of the divergence of the velocity field only, and is independent of the temperature. It is almost the same as that of ... More

Small Quarkonium states in an anisotropic QCD plasmaMay 16 2008We determine the hard-loop resummed propagator in an anisotropic QCD plasma in general covariant gauges and define a potential between heavy quarks from the Fourier transform of its static limit. We find that the potential exhibits angular dependence ... More

Testing 5d-6d dualities with fractional D-branesJul 26 20166d SCFTs compactified on a circle can often be studied from nonperturbative 5d super-Yang-Mills theories, using instanton solitons. However, the 5d Yang-Mills theories with 6d UV fixed points frequently have too many hypermultiplet matters, which makes ... More

Higher-order Alexander Invariants of Hypersurface ComplementsOct 12 2015We define the higher-order Alexander modules $A_{n,i}(\mathcal{U})$ and higher-order degrees $\delta_{n,i}(\mathcal{U})$ which are invariants of a complex hypersurface complement $\mathcal{U}$. These invariants come from the module structure of the homology ... More

Toroidal AdS Charged Branes and Toda EquationsOct 15 2009In this note, we consider the equations of motion for charged branes in AdS space and show that they can be cast into one-dimensional coupled Toda type. Then we solve the equations of motion to construct static charged AdS brane solutions which are invariant ... More

Brane Solutions with TensionMay 27 2009Nov 09 2009In this note, we apply a special metric ansatz to simplify the equations of motion for gravitational systems. Then we construct charged brane solutions in $D=n+p+2$ dimensions which have spherical symmetry of $S^n$ and translational symmetry along $p$ ... More

Non-Supersymmetric Unattractors in Born-Infeld Black HolesJun 14 2007We investigate unattractor behavior in non-extremal black holes in Einstein-Born-Infeld-Dilaton theory of gravity in four-dimensional asymptotically flat spacetime. We obtain solutions which are non-singular near the horizon and dependent on the value ... More

Figure of Merit for Dark Energy Constraints from Current Observational DataMar 31 2008Choosing the appropriate figure of merit (FoM) for dark energy (DE) constraints is key in comparing different DE experiments. Here we show that for a set of DE parameters {f_i}, it is most intuitive to define FoM = 1/\sqrt{Cov(f1,f2,f3,...)}, where Cov(f1,f2,f3,...) ... More

Model-Independent Distance Measurements from Gamma-Ray Bursts and Constraints on Dark EnergySep 03 2008Dec 16 2008Gamma-Ray Bursts (GRB) are the most energetic events in the Universe, and provide a complementary probe of dark energy by allowing the measurement of cosmic expansion history that extends to redshifts greater than 6. Unlike Type Ia supernovae (SNe Ia), ... More

Reducts of the random bipartite graphJan 10 2011Aug 18 2011Let $\Gamma$ be the random bipartite graph, a countable graph with two infinite sides, edges randomly distributed between the sides, but no edges within a side. In this paper, we investigate the reducts of $\Gamma$ that preserve sides. We classify the ... More

Model-Independent Measurements of Cosmic Expansion and Growth at z=0.57 Using the Anisotropic Clustering of CMASS Galaxies From the Sloan Digital Sky Survey Data Release 9Apr 21 2014Jul 07 2014We analyze the anisotropic two dimensional galaxy correlation function (2DCF) of the CMASS galaxy sample from the Sloan Digital Sky Survey Data Release 9 (DR9) of the Baryon Oscillation Spectroscopic Survey (BOSS) data. Modeling the 2DCF fully including ... More

A Tale Of Two Amplitudes In High Energy PhysicsMay 27 2013(abbreviated) I will describe my work on proton Compton scattering in a Unified Proton-Delta theory and on the computation of scattering amplitudes in Yang-Mills theory. We study proton Compton scattering in the first resonance region in an effective ... More

The Frenet-Serret formulas of a discrete centroaffine curveJan 25 2016In this paper, we build the fundamental theory of a discrete centroaffine curve. For a discrete plane curve, we define its first and second centroaffine curvatures which are invariant under the affine transformation. Using the centroaffine curvatures, ... More

Space time symmetry in quantum mechanicsFeb 26 2014Mar 12 2014New prescription to treat position and time equally in quantum mechanics is presented. Using this prescription, we could successfully derive some interesting formulae such as time-of-arrival for a free particle and quantum tunneling formula. The physical ... More

Towards a Global Springer Theory III: Endoscopy and Langlands dualityApr 22 2009We prove three new results about the global Springer action defined in \cite{GSI}. The first one determines the support of the perverse cohomology sheaves of the parabolic Hitchin complex, which serves as a technical tool for the next results. The second ... More

Permanence of a general discrete-time two-species-interaction model with non-monotonic per capita growth ratesFeb 28 2011Combined with all density-dependent factors, the per capita growth rate of a species may be non-monotonic. One important consequence is that species may suffer from weak Allee effects or strong Allee effects. In this paper, we study the permanence of ... More

Horseshoes for $\mathcal{C}^{1+α}$ mappings with hyperbolic measuresNov 25 2014We present here a construction of horseshoes for any $\mathcal{C}^{1+\alpha}$ mapping $f$ preserving an ergodic hyperbolic measure $\mu$ with $h_{\mu}(f)>0$ and then deduce that the exponential growth rate of the number of periodic points for any $\mathcal{C}^{1+\alpha}$ ... More

Weights of mixed tilting sheaves and geometric Ringel dualityMay 10 2008Nov 22 2008We describe several general methods for calculating weights of mixed tilting sheaves. We introduce a notion called "non-cancellation property" which implies a strong uniqueness of mixed tilting sheaves and enables one to calculate their weights effectively. ... More

Orientation data for local P2Sep 06 2018In this note, we show that the canonical orientation data on the quiver hearts are compatible under the autoequivalence $\_\otimes\pi^*O(1)$, and hence glue to give an orientation data for the stack of coherent sheaves on local P2.

Towards a Global Springer Theory II: the double affine actionApr 22 2009We construct an action of the graded double affine Hecke algebra (DAHA) on the parabolic Hitchin complex, extending the affine Weyl group action constructed in \cite{GSI}. In particular, we get representations of the degenerate DAHA on the cohomology ... More

The fundamental lemma of Jacquet-Rallis in positive characteristicsJan 07 2009Oct 28 2009We prove both the group version and the Lie algebra version of the Fundamental Lemma appearing in a relative trace formula of Jacquet-Rallis in the function field case when the characteristic is greater than the rank of the relevant groups.

Moving frame and integrable system of the discrete centroaffine curves in R^3Jan 25 2016Nov 27 2016Any two equivalent discrete curves must have the same invariants at the corresponding points under an affine transformation. In this paper, we construct the moving frame and invariants for the discrete centroaffine curves, which could be used to discriminate ... More

The effects of Zn Impurity on the Properties of Doped Cuprates in the Normal StateMay 14 2004We study the interplay of quantum impurity, and collective spinon and holon dynamics in Zn doped high-T$_c$ cuprates in the normal state. The two-dimensional t-t$^{\prime}$-J models with one and a small amount of Zn impurity are investigated within a ... More

Matrix Models for Deconfinement and Their Perturbative CorrectionsSep 23 2014Nov 27 2014Matrix models for the deconfining phase transition in $SU(N)$ gauge theories have been developed in recent years. With a few parameters, these models are able to reproduce the lattice results of the thermodynamic quantities in the semi-quark gluon plasma(QGP) ... More

Observational Probes of Dark EnergyJan 10 2012Jan 12 2012The cause for the observed acceleration in the expansion of the universe is unknown, and referred to as "dark energy" for convenience. Dark energy could be an unknown energy component, or a modification of Einstein's general relativity. This dictates ... More

Gluon Propagator and Heavy Quark Potential in an Anisotropic QCD PlasmaSep 23 2008The hard-loop resummed propagator in an anisotropic QCD plasma in general linear gauges are computed. We get the explicit expressions of the gluon propagator in covariant gauge, Coulomb gauge and temporal axial gauge. Considering one gluon exchange, the ... More

Many worlds interpretation for double slit experimentMay 29 2014As is well known, the double slit experiment contains every key concepts of quantum mechanics such as phase effect, probability wave, quantum interference, quantum superposition. In this article, I will clarify the meaning of quantum superposition in ... More

Path integral approach on Schrodinger's catOct 30 2013Jan 24 2014From the following thought experiments, it is demonstrated that the collapse of wave function of an isolated system is possible without external observer. It will be shown that the analysis by Feynman path integral method supports this conclusion. The ... More

An optimal estimate for electric fields on the shortest line segment between two spherical insulators in three dimensionsApr 28 2015Dec 13 2015We consider a gradient estimate for a conductivity problem whose inclusions are two neighboring insulators in three dimensions. When inclusions with an extreme conductivity (insulators or perfect conductors) are closely located, the gradient can be concentrated ... More

Domain Walls in AdS-Einstein-scalar GravityDec 19 2010Apr 26 2011In this note, we will show that the supergravity theory which is dual to ABJM field theory can be consistently reduced to scalar-coupled AdS-Einstein gravity and then consider the reflection symmetric domain wall and its small fluctuation. This domain ... More

Epipelagic representations and rigid local systemsJan 29 2014We construct automorphic representations for quasi-split groups $G$ over the function field $F=k(t)$ one of whose local components is an epipelagic representation in the sense of Reeder and Yu. We also construct the attached Galois representations under ... More

Meaning of delayed choice experiment and quantum uncertaintyApr 22 2014By slight modifying of the delayed-choice experiment, it is argued that the quantum wave function must be interpreted as real physical entity; With this interpretation in mind, multiple least action paths due to uncertainty leads us to new perspective ... More

Robust constraints on dark energy and gravity from galaxy clustering dataFeb 23 2012Apr 24 2012Galaxy clustering data provide a powerful probe of dark energy. We examine how the constraints on the scaled expansion history of the universe, x_h(z)=H(z)s (with s denoting the sound horizon at the drag epoch), and the scaled angular diameter distance, ... More

Reducts of the Generalized Random Bipartite GraphJul 20 2011Let \Gamma be the generalized random bipartite graph that has two sides Rl and Rr with edges for every pair of vertices between R1 and Rr but no edges within each side, where all the edges are randomly colored by three colors P1; P2; P3. In this paper, ... More

Distance Measurements from Supernovae and Dark Energy ConstraintsOct 14 2009Nov 10 2009Constraints on dark energy from current observational data are sensitive to how distances are measured from Type Ia supernova (SN Ia) data. We find that flux-averaging of SNe Ia can be used to test the presence of unknown systematic uncertainties, and ... More

Clarifying Forecasts of Dark Energy Constraints from Baryon Acoustic OscillationsApr 14 2009Dec 03 2009The measurement of baryon acoustic oscillations (BAO) from a galaxy redshift survey provides one of the most promising methods for probing dark energy. In this paper, we clarify the assumptions that go into the forecasts of dark energy constraints from ... More

Discrete Time Harness ProcessesJun 06 2015Jun 09 2015We study the invariant measures and fluctuation limits of discrete-time harness processes in one spatial dimension. We construct one essential ergodic (under spatial shifts) invariant measure of the increment process derived from harness process, and ... More

Goresky-MacPherson calculus for the affine flag varietiesDec 28 2007We use the fixed point arrangement technique developed by Goresky-MacPherson to calculate the part of the equivariant cohomology of the affine flag varieties generated by degree 2. This turns out to be a quadric cone. We also describe the spectrum of ... More

On the Hessian of Shape Matching EnergyApr 08 2016Apr 13 2016In this technical report we derive the analytic form of the Hessian matrix for shape matching energy. Shape matching is a useful technique for meshless deformation, which can be easily combined with multiple techniques in real-time dynamics. Nevertheless, ... More

Hitchin type moduli stacks in automorphic representation theorySep 06 2018In the study of automorphic representations over a function field, Hitchin moduli stack and its variants naturally appear and their geometry helps the comparison of trace formulae. We give a survey on applications of this observation to a relative fundamental ... More

Livšic Measurable Rigidity Theorem for \mathcal{C}^1 Generic Volume-preserving SystemsOct 31 2014In this paper, we prove that for $\mathcal{C}^1$ generic volume-preserving Anosov diffeomorphisms of a compact Riemannian manifold, Liv\v{s}ic measurable rigidity theorem holds. We also prove that for $\mathcal{C}^1$ generic volume-preserving Anosov flows ... More

Rigidity in automorphic representations and local systemsMay 13 2014We introduce the notion of rigidity for automorphic representations of groups over global function fields. We construct the Langlands parameters of rigid automorphic representations explicitly as local systems over open curves. We expect these local systems ... More

Modeling Waveform Shapes with Random Eects Segmental Hidden Markov ModelsJul 11 2012In this paper we describe a general probabilistic framework for modeling waveforms such as heartbeats from ECG data. The model is based on segmental hidden Markov models (as used in speech recognition) with the addition of random effects to the generative ... More

$Z/m$-graded Lie algebras and perverse sheaves, IIApr 03 2016We consider a fixed block for the equivariant perverse sheaves with nilpotent support in the $1$-graded ccomponent of a semisimple cyclically graded Lie algebra. We give a combinatorial parametrization of the simple objects in that block.

How Sensitive Are Weak Lensing Statistics to Dark Energy Content?Jun 27 2002Oct 04 2002Future weak lensing surveys will directly probe the clustering of dark matter, in addition to providing a test for various cosmological models. Recent studies have provided us with the tools which can be used to construct the complete probability distribution ... More

Joint estimation of quantile planes over arbitrary predictor spacesJul 11 2015In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parametrization that characterizes any collection of non-crossing ... More

New massive conformal gravityFeb 09 2014We investigate the new massive conformal gravity which is not invariant under conformal transformations, in comparison to the massive conformal gravity. We find five polarization modes of gravitational waves propagating on the Minkowski spacetimes. The ... More

Thermodynamics of unparticle-enhanced black holesOct 13 2010Oct 21 2010This article has been withdrawn by arXiv administrators because it plagiarises arXiv:1006.4556 (published in Phys. Lett. B 693, 129 (2010)).

Does entropic force always imply the Newtonian force law?Mar 26 2010Jan 19 2011We study the entropic force by introducing a bound $S \le A^{3/4}$ between entropy and area which was derived by imposing the non-gravitational collapse condition. In this case, applying a modified entropic force to this system does not lead to the Newtonian ... More

Chiral gravitational waves from z=2 Hořava-Lifshitz gravityNov 04 2009Dec 24 2009We construct the chiral gravitational waves from the $z=2$ Ho\v{r}ava-Lifshitz gravity with gravitational Chern-Simons term in the de Sitter and Minkowski backgrounds. These gravitational waves which show a feature of the Ho\v{r}ava-Lifshitz gravity may ... More

Controlled nanostructures at La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ thin film surfaces formed by STM lithographyApr 21 2009Nanoscale lithography on La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ (LSMO) thin film surfaces has been performed by scanning tunneling microscopy under ambient conditions. From line-etching experiments we found that the line depth is increasing in a step-wise fashion ... More

Entropy of black holes in the deformed Hořava-Lifshitz gravityAug 28 2009Jan 13 2010We find the entropy of Kehagias-Sfetsos black hole in the deformed Ho\v{r}ava-Lifshitz gravity by using the first law of thermodynamics. When applying generalized uncertainty principle (GUP) to Schwarzschild black hole, the entropy $S=A/4+(\pi/\omega)\ln(A/4)$ ... More

Generalized uncertainty principle and Hořava-Lifshitz gravityJul 30 2009Aug 13 2009We explore a connection between generalized uncertainty principle (GUP) and modified Ho\v{r}ava-Lifshitz (HL) gravity. The GUP density function may be replaced by the cutoff function for the renormalization group of modified Ho\v{r}ava-Lifshitz gravity. ... More

Logarithmic conformal field theory approach to topologically massive gravityAug 14 2008We study the topologically massive gravity at the chiral point (chiral gravity) by using the logarithmic conformal field theory. Two new tensor fields of $\psi^{new}$ and $X$ are introduced for a candidate of propagating physical field at the chiral point. ... More

Conformally Dual to InflationDec 16 2011It is showed by a conformal rescaling that the inflationary background can be dual to a slowly expanding background, which is almost Minkowski and described by a conformal field theory conformally coupled to gravity. It is proved that the primordial curvature ... More

Primordial Perturbation in Horava-Lifshitz CosmologyApr 27 2009May 22 2009Recently, Ho\v{r}ava has proposed a renormalizable theory of gravity with critical exponent z=3 in the UV. This proposal might imply the scale invariant primordial perturbation can be generated in any expansion of early universe with a\sim t^n and n>1/3, ... More

Tunnelling for Large NOct 21 2008In this brief note, by applying the stochastic approach to multiple fields, we estimate the probability of tunneling between vacua in a landscape with $\cal N$ fields. We find that the probability can be enhanced by large $\cal N$. When $\cal N$ saturates ... More

Island Cosmology in the LandscapeDec 27 2007Jun 11 2008In the eternally inflationary background driven by the metastable vacua of the landscape, it is possible that some local quantum fluctuations with the null energy condition violation can be large enough to stride over the barriers among different vacua, ... More

Seeding of Primordial Perturbations During a Decelerated ExpansionSep 19 2006May 09 2007A scalar field with a modified dispersion relation may seed, under certain conditions, the primordial perturbations during a decelerated expansion. In this note we examine whether and how these perturbations can be responsible for the structure formation ... More

Entropy of Microwave Background Radiation in Observable UniverseJun 05 2006Jul 17 2006We show that the cosmological constant at late time places a bound on the entropy of microwave background radiation deposited in the future event horizon of a given observer, $S\leq S_{\Lambda_0}^{3/4}$. This bound is independent of the energy scale of ... More

On Dualities Of Primordial Perturbation SpectraApr 01 2004Feb 16 2005In this paper, we discuss the dualities of the primordial perturbation spectra from various expanding/contracting phases for full space of parameter $w\equiv {p\over \rho}$ of state equation.

Proliferation in CycleJan 18 2009Jun 11 2009In the contracting phase with w\simeq 0, the scale invariant spectrum of curvature perturbation is given by the increasing mode of metric perturbation. In this paper, it is found that if the contracting phase with w\simeq 0 is included in each cycle of ... More

Primordial Perturbations Spectra in a Holographic PhaseFeb 13 2007Jul 04 2007In this paper, we suppose that the universe begins in a holographic thermal equilibrium phase with the diverged correlation length, and the phase transition to the radiation phase of standard cosmology goes with the abrupt reducing of correlation length. ... More

On Perturbation Spectra of N-flationJun 08 2006Aug 07 2006In this note we study the adiabatic perturbation spectrum of N-flation with power law potential. We show that the scalar spectrum of N-flation is generally redder than that of its corresponding single field. The result obtained for that with unequal massive ... More

Z/m-graded Lie algebras and perverse sheaves, IFeb 16 2016Sep 30 2016We give a block decomposition of the equivariant derived category arising from a cyclically graded Lie algebra. This generalizes certain aspects of the generalized Springer correspondence to the graded setting.

Charged coherent states related to su_{q}(2) covarianceJun 16 2003A new kind of q-deformed charged coherent states is constructed in Fock space of two-mode q-boson system with su_{q}(2) covariance and a resolution of unity for these states is derived. We also present a simple way to obtain these coherent states using ... More

Hall algebras and quantum groups associated to Dynkin quiversMay 01 2016May 04 2016For Dynkin quivers, we find the Laurent polynomials $\widetilde{X}_{a, c}^{b}(v)$ and use $\widetilde{X}_{a, c}^{b}(v)$ to construct the Hall algebra $\hc_v(\cc(\cp))$ over $\mz[v, v^{-1}]$, where $\widetilde{X}_{a, c}^{b}(|\mf_q|)$'s are structure constants ... More

Shtukas and the Taylor expansion of $L$-functionsDec 08 2015Jan 05 2016We define the Heegner--Drinfeld cycle on the moduli stack of Drinfeld Shtukas of rank two with $r$-modifications for an even integer $r$. We prove an identity between (1) The $r$-th central derivative of the quadratic base change $L$-function associated ... More

On the non-minimal character of the SMEFTDec 06 2016When integrating out unknown new physics sectors, what is the minimal character of the Standard Model Effective Field Theory (SMEFT) that can result? In this paper we focus on a particular aspect of this question: "How can one obtain only one dimension ... More

Moduli Interpretations for Noncongruence Modular CurvesOct 19 2015Aug 20 2016We define the notion of a $G$-structure for elliptic curves, where $G$ is a finite 2-generated group. When $G$ is abelian, a $G$-structure is the same as a classical congruence level structure. There is a natural action of $\text{SL}_2(\mathbb{Z})$ on ... More

Integral homology of loop groups via Langlands dual groupsSep 30 2009Let K be a connected compact Lie group, and G be its complexification. The homology of the based loop group \Omega K with integer coefficients is naturally a \ZZ-Hopf algebra. After possibly inverting 2 or 3, we identify H_*(\Omega K,\ZZ) with the Hopf ... More

Geometric Langlands correspondence for SL(2), PGL(2) over the pair of pantsOct 26 2016We establish the Geometric Langlands correspondence for rank one groups over the projective line with three points of tame ramification.

Galaxy clustering, CMB and supernova data constraints on $φ$CDM model with massive neutrinosJul 08 2015Dec 11 2015We investigate a scalar field dark energy model (i.e., $\phi$CDM model) with massive neutrinos, where the scalar field possesses an inverse power-law potential, i.e., $V(\phi)\propto {\phi}^{-\alpha}$ ($\alpha>0$). We find that the sum of neutrino masses ... More

Spectral action in Betti Geometric LanglandsNov 13 2016Aug 25 2017Let $X$ be a smooth projective curve, $G$ a reductive group, and $Bun_G(X)$ the moduli of $G$-bundles on $X$. For each point of $X$, the Satake category acts by Hecke modifications on sheaves on $Bun_G(X)$. We show for sheaves with nilpotent singular ... More

Reconstructing the weak lensing magnification distribution of Type Ia supernovaeJan 24 2019Weak lensing of Type Ia supernovae (SNe Ia) is a systematic uncertainty in the use of SNe Ia as standard candles, as well as an independent cosmological probe, if the corresponding magnification distribution can be extracted from data. We study the peak ... More

Primordial Power Spectrum ReconstructionFeb 07 2005Jan 11 2006In order to reconstruct the initial conditions of the universe it is important to devise a method that can efficiently constrain the shape of the power spectrum of primordial matter density fluctuations in a model-independent way from data. In an earlier ... More

On the canonical degrees of Gorenstein threefolds of general typeSep 16 2015Mar 16 2016Let $X$ be a Gorenstein minimal projective $3$-fold with at worst locally factorial terminal singularities. Suppose that the canonical map is generically finite onto its image. C. Hacon showed that the canonical degree is universally bounded by $576$. ... More

Universal coverings of Steinberg Lie algebras of small characteristicDec 09 2005It is well-known that the second homology group $H_2(\st)$ of the Steinberg Lie algebra $\st$ is trivial when $n\geq 5$. In this paper, we will work out $H_2(\st)$ explicitly for $n=3, 4$ which are not necessarily trivial. Consequently, we obtained $H_2(sl_n(R))$ ... More

Revisiting the dispersion measure of fast radio bursts associated with gamma-ray burst afterglowsJun 13 2014Nov 06 2014Some fast radio bursts (FRBs) are expected to be associated with the afterglow emission of gamma-ray bursts (GRBs), while a short-lived, supermassive neutron star (NS) forms during the GRBs. I investigate the possible contributions to the dispersion measure ... More

Expansion or extinction: deterministic and stochastic two-patch models with Allee effectsFeb 27 2010We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment, focusing on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes ... More

Cauchy problem for the Boltzmann-BGK model near a global MaxwellianSep 28 2010In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth solution if the ... More

An analytic formula determining quantum pointer basis and its application to a flying bulletFeb 23 2015Jun 12 2016We propose a general scheme determining the quantum pointer basis of a macroscopic object interacting with environment. Unlike the decoherence program, our pointer basis does not require robustness against entanglement, but require robustness on the object ... More