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On the slope conjecture of Barja and Stoppino for fibred surfacesApr 23 2015Apr 11 2017Let $f:\,S \to B$ be a locally non-trivial relatively minimal fibration of genus $g\geq 2$ with relative irregularity $q_f$. It was conjectured by Barja and Stoppino that the slope $\lambda_f\geq \frac{4(g-1)}{g-q_f}$. We prove the conjecture when $q_f$ ... More

On the slope of hyperelliptic fibrations with positive relative irregularityNov 28 2013Feb 11 2015Let $f:\, S \to B$ be a locally non-trivial relatively minimal fibration of hyperelliptic curves of genus $g\geq 2$ with relative irregularity $q_f$. We show a sharp lower bound on the slope $\lambda_f$ of $f$. As a consequence, we prove a conjecture ... More

On Shimura curves in the Torelli locus of curvesNov 22 2013Dec 02 2013Oort has conjectured that there do not exist Shimura curves lying generically in the Torelli locus of curves of genus $g \geq 8$. We show that there do not exist one-dimensional Shimura families of semi-stable curves of genus $g\geq 5$ of Mumford type. ... More

Localize energy in random media: A new phase stateNov 08 2000This Letter reports a new wave phenomenon. We show that wave energy can be stored in random media. Associated with such energy storage is a global collective behavior. The features depicted are so general that they may be observed in many random systems. ... More

A note on Shimura subvarieties in the hyperelliptic Torelli locusApr 21 2015We prove the non-existence of Shimura subvarieties of positive dimension contained generically in the hyperelliptic Torelli locus for curves of genus at least 8, which is an analogue of Oort's conjecture in the hyperelliptic case.

Riding on the Primary: A New Spectrum Sharing Paradigm for Wireless-Powered IoT DevicesJan 20 2018In this paper, a new spectrum sharing model referred to as riding on the primary (ROP) is proposed for wireless-powered IoT devices with ambient backscatter communication capabilities. The key idea of ROP is that the secondary transmitter harvests energy ... More

A note on the characteristic $p$ nonabelian Hodge theory in the geometric caseFeb 17 2012Oct 24 2012We provide a construction of associating a de Rham subbundle to a Higgs subbundle in characteristic $p$ in the geometric case. As applications, we obtain a Higgs semistability result and a $W_2$-unliftable result.

The Oort conjecture for Shimura curves of small unitary rankDec 11 2017We prove that a Shimura curve in the Siegel modular variety is not generically contained in the open Torelli locus as long as the rank of unitary part in its canonical Higgs bundle satisfies a numerical upper bound. As an application we show that the ... More

Singular Fibers and Kodaira DimensionsOct 25 2016Let $f:\,X \to \mathbb{P}^1$ be a non-isotrivial semi-stable family of varieties of dimension $m$ over $\mathbb{P}^1$ with $s$ singular fibers. Assume that the smooth fibers $F$ are minimal, i.e., their canonical line bundles are semiample. Then $\kappa(X)\leq ... More

Incentive Mechanisms for Motivating Mobile Data Offloading in Heterogeneous Networks: A Salary-Plus-Bonus ApproachFeb 08 2018In this paper, a salary-plus-bonus incentive mechanism is proposed to motivate WiFi Access Points (APs) to provide data offloading service for mobile network operators (MNOs). Under the proposed salary-plus-bonus scheme, WiFi APs are rewarded not only ... More

On the Oort conjecture for Shimura varieties of unitary and orthogonal typesOct 21 2014Jul 27 2015In this paper we study the Oort conjecture on Shimura subvarieties contained generically in the Torelli locus in the Siegel modular variety $\mathcal{A}_g$. Using the poly-stability of Higgs bundles on curves and the slope inequality of Xiao on fibred ... More

Transverse momentum broadening in semi-inclusive deep inelastic scattering at next-to-leading orderSep 04 2014Dec 26 2016Within the framework of higher-twist collinear factorization, transverse momentum broadening for the final hadrons in semi-inclusive deeply inelastic $e+A$ collisions is studied at the next-to-leading order (NLO) in perturbative QCD. Through explicit ... More

Multi-Cell Interference Exploitation: A New Dimension in Cell CoordinationJan 13 2019In this paper, we propose a series of novel coordination schemes for multi-cell downlink communication. Starting from full base station (BS) coordination, we first propose a fully-coordinated scheme to exploit beneficial effects of both inter-cell and ... More

On the minimal number of singular fibers with non-compact Jacobians for families of curves over $\mathbb P^1$Sep 23 2014Let $f:X \to \mathbb{P}^1$ be a non-isotrivial family of semi-stable curves of genus $g\geq 1$ defined over an algebraically closed field $k$ with $s_{nc}$ singular fibers whose Jacobians are non-compact. We prove that $s_{nc}\geq 5$ if $k=\mathbb C$ ... More

Next-to-Leading QCD Factorization for Semi-Inclusive Deep Inelastic Scattering at Twist-4Oct 24 2013Mar 14 2014Within the framework of a high-twist approach, we calculate the next-to-leading order (NLO) perturbative QCD corrections to the transverse momentum broadening in semi-inclusive hadron production in deeply inelastic $e+A$ collisions, as well as lepton ... More

On Higgs bundles over Shimura varieties of ball quotient typeOct 25 2016We prove the generic exclusion of certain Shimura varieties of unitary and orthogonal types from the Torelli locus. The proof relies on a slope inequality on surface fibration due to G. Xiao, and the main result implies that certain Shimura varieties ... More

Self-Reinforced Cascaded Regression for Face AlignmentNov 23 2017Cascaded regression is prevailing in face alignment thanks to its accuracy and robustness, but typically demands manually annotated examples having low discrepancy between shape-indexed features and shape updates. In this paper, we propose a self-reinforced ... More

Incentive Mechanism Design for Heterogeneous Peer-to-Peer Networks: A Stackelberg Game ApproachJul 24 2014With high scalability, high video streaming quality, and low bandwidth requirement, peer-to-peer (P2P) systems have become a popular way to exchange files and deliver multimedia content over the internet. However, current P2P systems are suffering from ... More

On the slope conjecture of Barja and Stoppino for fibred surfacesApr 23 2015Let $f:\,S \to B$ be a locally non-trivial relatively minimal fibration of genus $g\geq 2$ with relative irregularity $q_f$. It was conjectured by Barja and Stoppino that the slope $\lambda_f\geq \frac{4(g-1)}{g-q_f}$. We prove the conjecture when $q_f$ ... More

A Rocket Model of Neutrino Jet for Pulsar KickSep 03 2003Sep 11 2003On the basis of the neutrino emission from the isotropic $^1$S$_0$ neutron superfluid vortexes in neutron star interiors, we propose a rocket model of neutrino jet for the observed pulsar kick.

The Oort conjecture on Shimura curves in the Torelli locus of curvesMay 19 2014Aug 18 2014Oort has conjectured that there do not exist Shimura curves contained generically in the Torelli locus of genus-$g$ curves when $g$ is large enough. In this paper we prove the Oort conjecture for Shimura curves of Mumford type and Shimura curves parameterizing ... More

On the Severi type inequalities for irregular surfacesApr 24 2015Apr 27 2015Let $X$ be a minimal surface of general type and maximal Albanese dimension with irregularity $q\geq 2$. We show that $K_X^2\geq 4\chi(\mathcal O_X)+4(q-2)$ if $K_X^2<\frac92\chi(\mathcal O_X)$, and also obtain the characterization of the equality. As ... More

A Trust-based Pollution Attack Prevention Scheme in Peer-to-Peer Streaming NetworksJul 24 2014Nowadays, peer-to-peer (P2P) streaming systems have become a popular way to deliver multimedia content over the internet due to their low bandwidth requirement, high video streaming quality, and flexibility. However, P2P streaming systems are vulnerable ... More

Amplitude analysis of the anomalous decay $η'\toπ^+π^-γ$Dec 06 2017Feb 07 2018In this paper we perform an amplitude analysis of $\eta'\to\pi^+\pi^-\gamma$ and confront it with the latest BESIII data. Based on the final-state interaction theorem, we represent the amplitude in terms of an Omn\'es function multiplied by a form factor ... More

Selective-Candidate Framework with Similarity Selection Rule for Evolutionary OptimizationDec 18 2017Jan 07 2019This paper proposes a generic selective-candidate framework with similarity selection rule (SCSS) for performance enhancement of well-established evolutionary optimization algorithms. It is done by using a more efficient selective searching direction. ... More

Estimating the Distribution of Random Parameters in a Diffusion Equation Forward Model for a Transdermal Alcohol BiosensorAug 13 2018We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the blood alcohol ... More

Correlation between Dzyaloshinskii Moriya interaction and spin mixing conductance at antiferromagnet / ferromagnet interfaceApr 14 2018Jul 19 2018The rich interaction phenomena at antiferromagnet (AFM)/ ferromagnet (FM) interfaces are key ingredients in AFM spintronics, where many underlying mechanisms remain unclear. Here we report a correlation observed between interfacial Dzyaloshinskii-Moriya ... More

Scaling of Dzyaloshinskii Moriya interaction at heavy metal and ferromagnetic metal interfacesSep 12 2017The Dzyaloshinskii Moriya Interaction (DMI) at the heavy metal (HM) and ferromagnetic metal (FM) interface has been recognized as a key ingredient in spintronic applications. Here we investigate the chemical trend of DMI on the 5d band filling (5d^3~5d^10) ... More

On a question of Ekedahl and SerreMar 30 2017Jun 13 2017In this paper we study various aspects of the Ekedahl-Serre problem. We formulate questions of Ekedahl-Serre type and Coleman-Oort type for general weakly special subvarieties in the Siegel moduli space, propose a conjecture relating these two questions, ... More

Finiteness of hyperelliptic and superelliptic curves with CM JacobiansNov 25 2016In this paper we study the Coleman-Oort conjecture for superelliptic curves, i.e., curves defined by affine equations $y^n=F(x)$ with $F$ a separable polynomial. We prove that up to isomorphism there are at most finitely many superelliptic curves of fixed ... More

A renormalizable supersymmetric SO(10) model with natural doublet-triplet splittingOct 21 2014Dec 08 2014We propose a renormalizable supersymmetric SO(10) model where the doublet-triplet splitting problem is solved using the Dimopoulos-Wilczek mechanism. An unwanted coupling is forbidden through a filter sector. To suppress proton decay without spoiling ... More

Price-Based Resource Allocation for Spectrum-Sharing Femtocell Networks: A Stackelberg Game ApproachMar 11 2011This paper investigates the price-based resource allocation strategies for the uplink transmission of a spectrum-sharing femtocell network, in which a central macrocell is underlaid with distributed femtocells, all operating over the same frequency band ... More

Origins of the Isospin Violation of Dark Matter InteractionsJul 18 2011Nov 06 2012Light dark matter (DM) with a large DM-nucleon spin-independent cross section and furthermore proper isospin violation (ISV) $f_n/f_p\approx-0.7$ may provide a way to understand the confusing DM direct detection results. Combing with the stringent astrophysical ... More

Full-Duplex Wireless-Powered Communication Network with Energy CausalityApr 02 2014In this paper, we consider a wireless communication network with a full-duplex hybrid access point (HAP) and a set of wireless users with energy harvesting capabilities. The HAP implements the full-duplex through two antennas: one for broadcasting wireless ... More

Dzyaloshinskii Moriya interaction across antiferromagnet / ferromagnet interfaceJun 02 2017The antiferromagnet (AFM) / ferromagnet (FM) interfaces are of central importance in recently developed pure electric or ultrafast control of FM spins, where the underlying mechanisms remain unresolved. Here we report the direct observation of Dzyaloshinskii ... More

ESE: Efficient Speech Recognition Engine with Sparse LSTM on FPGADec 01 2016Feb 20 2017Long Short-Term Memory (LSTM) is widely used in speech recognition. In order to achieve higher prediction accuracy, machine learning scientists have built larger and larger models. Such large model is both computation intensive and memory intensive. Deploying ... More

An intrinsic link between long-term UV/optical variations and X-ray loudness in quasarsOct 09 2018Oct 12 2018Observations have shown that UV/optical variation amplitude of quasars depend on several physi- cal parameters including luminosity, Eddington ratio, and likely also black hole mass. Identifying new factors which correlate with the variation is essential ... More

Structural and electronic properties of uranium-encapsulated Au14 cageDec 26 2013The structural properties of the uranium-encapsulated nano-cage U@Au14 are predicted using density functional theory. The presence of the uranium atom makes the Au14 structure more stable than the empty Au14-cage, with a triplet ground electronic state ... More

The Supersymmetric Standard Models with Decay and Stable Dark MattersJan 19 2010Aug 31 2010We propose two supersymmetric Standard Models (SMs) with decaying and stable dark matter (DM) particles. To explain the SM fermion masses and mixings and have a heavy decay DM particle S, we consider the Froggatt-Nielsen mechanism by introducing an anomalous ... More

Long Short-Term AttentionOct 30 2018In order to learn effective features from temporal sequences, the long short-term memory (LSTM) network is widely applied. A critical component of LSTM is the memory cell, which is able to extract, process and store temporal information. Nevertheless, ... More

Outcome-Driven Clustering of Acute Coronary Syndrome Patients using Multi-Task Neural Network with AttentionMar 01 2019Cluster analysis aims at separating patients into phenotypically heterogenous groups and defining therapeutically homogeneous patient subclasses. It is an important approach in data-driven disease classification and subtyping. Acute coronary syndrome ... More

A renormalizable supersymmetric SO(10) modelApr 08 2015Jun 03 2015A realistic grand unified model has never been constructed in the literature due to three major difficulties: the seesaw mechanism without spoiling gauge coupling unification, the doublet-triplet splitting and the proton decay suppression. We propose ... More

Asteroseismic analysis of the CoRoT target HD49933Nov 25 2013Dec 05 2013The frequency ratios and of HD 49933 exhibit an increase at high frequencies. This behavior also exists in the ratios of other stars, which is considered to result from the low signal-to-noise ratio and the larger line width at the high-frequency end ... More

Exact Simulation of Wishart Multidimensional Stochastic Volatility ModelSep 02 2013In this article, we propose an exact simulation method of the Wishart multidimensional stochastic volatility (WMSV) model, which was recently introduced by Da Fonseca et al. \cite{DGT08}. Our method is based onanalysis of the conditional characteristic ... More

Present Status of Diffusive Shock AccelerationDec 26 2000Diffusive shock acceleration (DSA) is now widely accepted as the model to explain the production of cosmic rays (CRs) in a wide range of astrophysical environments. Despite initial successes of the theory in explaining the energetics and the spectrum ... More

Re-acceleration model for the `Sausage' Radio RelicJul 02 2016The Sausage radio relic is the arc-like radio structure in the cluster CIZA J2242.8+5301, whose observed properties can be best understood by synchrotron emission from relativistic electrons accelerated at a merger-driven shock. However, there remain ... More

Re-acceleration model for the "Toothbrush" Radio RelicMar 24 2016The Toothbrush radio relic associated the merging cluster 1RXS J060303.3 is presumed to be produced by relativistic electrons accelerated at merger-driven shocks. Since the shock Mach number inferred from the observed radio spectral index, $M_{radio}\approx ... More

Radio emission from weak spherical shocks in the outskirts of galaxy clustersFeb 10 2015In Kang (2015) we calculated the acceleration of cosmic-ray electrons and the ensuing radio synchrotron emission at weak spherical shocks that are expected to form in the outskirts of galaxy clusters.There we demonstrated that, at decelerating spherical ... More

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

A remote response of ATP hydrolysisApr 28 2013ATP-hydrolysis is the basic energy source of many physiological processes, but there is a lack of knowledge regarding its biological role other than energy transfer and thermogenesis. Not all the energy released by ATP-hydrolysis could be used in powering ... More

The Whittaker-Shintani functions for symplectic groupsNov 15 2012In this note, we give a formula for the Whittaker-Shintani functions for the p-adic symplectic groups, which is a generalization of the Zonal spherical functions and Whittaker functions. We then use the formula to give an alternative proof of a conjecture ... More

Nonlocal symmetries and conservation laws of the coupled Hirota equationJan 15 2015Using the lax pair, nonlocal symmetry of the coupled Hirota equation is obtained. By introducing an appropriate auxiliary dependent variable the nonlocal symmetry is successfully localized to a Lie point symmetry. For the closed prolongation, one-dimensional ... More

A genus-4 topological recursion relation for Gromov-Witten invariantsAug 18 2016In this paper, we give a new genus-4 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds via Pixton's relations on the moduli space of curves. As an application, we prove Pixton's relations imply a known topological ... More

On Schauder Equivalence RelationsNov 02 2014In this paper, we study Schauder equivalence relations, which are Borel equivalence relations generated by Banach spaces with basic sequences. We prove that the set of equivalence relations generated by basic sequences has boundaries. Then we show that ... More

Nuclearity of semigroup C*-algebras and the connection to amenabilityFeb 29 2012May 11 2012We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*-algebras as C*-algebras of ... More

An efficient search algorithm for inverting the sweep map on rational Dyck pathsMay 04 2015Given a coprime pair $(m,n)$ of positive integers, rational $(m,n)$-Dyck paths are lattice paths in the $m\times n$ rectangle that never go below the diagonal. The sweep map of a rational $(m,n)$-Dyck paths $D$ is the rational Dyck path $\Phi(D)$ obtained ... More

Bound States via Higgs Exchanging and Resonant Di-HiggsJun 05 2016Sep 18 2016The standard model (SM)-like Higgs boson $h$ has spin zero and light mass around weak scale, so it has the potential to mediate a new and relatively strong force for the particle $\phi$ in the new physics (NP) sector; then $\phi$ may form bound state ... More

Irreducibility algorithm for the Weierstrass polynomials of two complex variables and the Puiseux expansions: Part[A], Part[B], Part[C]Jul 28 2014It is very fundamental to study irreducible plane curve singularities in algebraic geometry. The contents of the paper consist of three parts, called Part[A], Part[B] and Part[C] with Good Appendix. Our aim is to prove by Part[B] and Part[C] that a complete ... More

$\mathbb{Z}_{2}$-equivariant Heegaard Floer cohomology of knots in $S^{3}$ as a strong Heegaard invariantOct 03 2018The $\mathbb{Z}_{2}$-equivariant Heegaard Floer cohomlogy $\widehat{HF}_{\mathbb{Z}_{2}}(\Sigma(K))$ of a knot $K$ in $S^{3}$, constructed by Hendricks, Lipshitz, and Sarkar, is an isotopy invariant which is defined using bridge diagrams of $K$ drawn ... More

Single-orbital realization of high temperature $s^\pm$ superconductivity in the square-octagon latticeDec 31 2017Jan 16 2019We propose possible high-temperature superconductivity with singlet $s^\pm$-wave pairing symmetry in the octagraphene, i.e. a monolayer of carbon atoms arranged into the square-octagon lattice. Starting from a tight-binding model which well describes ... More

Growth strategy of microbes on mixed carbon sourcesMar 26 2017Mar 02 2019A classic problem in microbiology is that bacteria display two types of growth behavior when cultured on a mixture of two carbon sources: the two sources are sequentially consumed one after another (diauxie) or they are simultaneously consumed (co-utilization). ... More

A sampling theorem on shift-invariant spaces associated with the fractional Fourier transform domainFeb 10 2013As a generalization of the Fourier transform, the fractional Fourier transform was introduced and has been further investigated both in theory and in applications of signal processing. We obtain a sampling theorem on shift-invariant spaces associated ... More

The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifoldsApr 28 2009In this paper, we discuss the Yang-Mills functional and a certain family of its critical points on quantum Heisenberg manifolds using noncommutative geometrical methods developed by A. Connes and M. Rieffel. In our main result, we construct a certain ... More

Transverse momentum broadening at NLO and QCD evolution of $\hat q$Jul 31 2014Within the framework of a high-twist approach, we show the first complete next-to-leading order calculation of transverse momentum broadening in semi-inclusive deeply inelastic $e+A$ scattering and Drell-Yan dilepton production in $p+A$ collisions. We ... More

Local invariant for scale structures on mapping spacesAug 01 2011Scale structures were introduced by H. Hofer, K. Wysocki, and E. Zehnder as a new concept of a smooth structure in infinite dimensions. We prove that scale structures on mapping spaces are completely determined by the dimension of domain manifolds. As ... More

Hajós-like theorem for signed graphsFeb 27 2017The paper designs five graph operations, and proves that every signed graph with chromatic number $q$ can be obtained from all-positive complete graphs $(K_q,+)$ by repeatedly applying these operations. This result gives a signed version of the Haj\'os ... More

Bulk Cluster Decomposition in AdS/CFT and A No-Go Theorem for Correlators in Microstates of Extremal Black HolesMay 13 2013May 19 2013Applying the thermo-field double formalism to extremal black holes in AdS with a macroscopic horizon, we show that (1) there exists a natural basis for the degenerate microstates of an extremal black hole, and (2) cluster decomposition in the bulk implies ... More

Generalized Rabinowitz Floer homology and coisotropic intersectionsMar 04 2010May 29 2012In this paper, we extend Rabinowitz Floer homology theory which has been established and extensively studied for hypersurfaces to coisotropic submanifolds of higher codimension. With this generalized version of Rabinowitz Floer homology theory, we explore ... More

Mechanisms leading to a warmer climate on high obliquity planetsMar 09 2019Mar 13 2019High obliquity planets have been suggested to be warmer than their low obliquity equivalents when the climate is cold, and the ice-albedo feedback has been suggested to play a dominant role. In this study, we first find the warming under high obliquity ... More

Longitudinal RF capture simulation and BPM signal estimationNov 06 2016Nov 16 2016In this paper, the theoretical aspects behind longitudinal RF capture are reviewed and the capture process is simulated via a program based on this theory. Four kinds of cases with different initial distribution and capture curve are considered, i.e. ... More

Mobile Data Offloading through A Third-Party WiFi Access Point: An Operator's PerspectiveAug 22 2014WiFi offloading is regarded as one of the most promising techniques to deal with the explosive data increase in cellular networks due to its high data transmission rate and low requirement on devices. In this paper, we investigate the mobile data offloading ... More

Ergodic Sum-Rate Maximization for Fading Cognitive Multiple Access Channels without Successive Interference CancellationMar 03 2014In this paper, the ergodic sum-rate of a fading cognitive multiple access channel (C-MAC) is studied, where a secondary network (SN) with multiple secondary users (SUs) transmitting to a secondary base station (SBS) shares the spectrum band with a primary ... More

Transverse momentum broadening in semi-inclusive deep inelastic scattering at next-to-leading orderSep 04 2014Within the framework of higher-twist collinear factorization, transverse momentum broadening for the final hadrons in semi-inclusive deeply inelastic $e+A$ collisions is studied at the next-to-leading order (NLO) in perturbative QCD. Through explicit ... More

Random Access Analysis for Massive IoT Networks under A New Spatio-Temporal Model: A Stochastic Geometry ApproachApr 06 2017Jul 04 2018Massive Internet of Things (mIoT) has provided an auspicious opportunity to build powerful and ubiquitous connections that faces a plethora of new challenges, where cellular networks are potential solutions due to their high scalability, reliability, ... More

Optimizing DF Cognitive Radio Networks with Full-Duplex-Enabled Energy Access PointsNov 16 2016Mar 28 2017With the recent advances in radio frequency (RF) energy harvesting (EH) technologies, wireless powered cooperative cognitive radio network (CCRN) has drawn an upsurge of interest for improving the spectrum utilization with incentive to motivate joint ... More

Band renormalization and Fermi surface reconstruction in iron-based superconductorsJan 07 2009Using the fluctuation exchange approximation and a three-orbital model, we study the band renormalization, Fermi surface reconstruction and the superconducting pairing symmetry in the newly-discovered iron-based superconductors. We find that the inter-orbital ... More

Leptonic Charm DecaysJan 14 2011Jan 17 2011We review the recent experimental results on D and Ds meson leptonic decays from CLEO-c, Belle, and BABAR, which results in the decay constants f_D= (206.7 +- 8.9) MeV and f_Ds= (257.3 +- 5.3) MeV. The latter is an average obtained by the Heavy Flavor ... More

KPP Front Speeds in Random Shears and the Parabolic Anderson ProblemDec 19 2002We study the asymptotics of front speeds of the reaction-diffusion equations with Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity and zero mean stationary ergodic Gaussian shear advection on the entire plane. By exploiting connections of KPP front speeds ... More

Heegner Point Kolyvagin System and Iwasawa Main ConjectureAug 18 2014Nov 24 2014In this paper we prove an anticyclotomic Iwasawa main conjecture proposed by Perrin-Riou for Heegner points when the global sign is -1, using a recent work of the author on one divisibility of Iwasawa-Greenberg main conjecture for Rankin-Selberg p-adic ... More

Dedekind η-function and quantum groupsMay 02 2012Aug 10 2015We realize some powers of Dedekind $\eta$-function as traces on quantum coordinate algebras.

Quantum groups, q-Boson algebras and quantized Weyl algebrasApr 01 2010Sep 13 2010We give a unified construction of quantum groups, q-Boson algebras and quantized Weyl algebras and an action of quantum groups on quantized Weyl algebras. This enables us to give a conceptual proof of the semi-simplicity of the category $\mathcal{O}(B_q)$ ... More

On Whittaker modules over a class of algebras similar to $U(sl_{2})$Oct 29 2006Motivated by the study of invariant rings of finite groups on the first Weyl algebras $A_{1}$ (\cite{AHV}) and finding interesting families of new noetherian rings, a class of algebras similar to $U(sl_{2})$ were introduced and studied by Smith in \cite{S}. ... More

Well-posedness of strong solutions to the anelastic equations for viscous flowsMar 04 2019We address the local and global well-posedness issues of strong solutions to the anelastic equations for viscous flows. The density profile is taken to satisfy physical vacuum singularity, and the interaction of the density profile with the velocity fields ... More

Effective Non-vanishing of Asymptotic Adjoint SyzygiesMar 31 2012Apr 08 2014The purpose of this paper is to establish an effective non-vanishing theorem for the syzygies of an adjoint-type line bundle on a smooth variety, as the positivity of the embedding increases. Our purpose here is to show that for an adjoint type divisor ... More

Improved Online Wilson Score Interval Method for Community Answer Quality RankingSep 04 2018In this paper, a fast and easy-to-deploy method with a strong interpretability for community answer quality ranking is proposed. This method is improved based on the Wilson score interval method [Wilson, 1927], which retains its advantages and simultaneously ... More

On Irreducible weight representations of a new deformation $U_{q}(sl_{2})$ of $U(sl_{2})$Oct 29 2006Starting from a Hecke $R-$matrix, Jing and Zhang constructed a new deformation $U_{q}(sl_{2})$ of $U(sl_{2})$, and studied its finite dimensional representations in \cite{JZ}. Especically, this algebra is proved to be just a bialgebra, and all finite ... More

A new approach to recent constructions of C*-algebras from modular index theoryAug 18 2014We present a new approach to C*-algebras recently constructed in the context of modular index theory by Carey, Phillips, Putnam and Rennie. It turns out that their constructions can be identified with full corners of ideals in semigroup C*-algebras. This ... More

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

The Ring of Malcev-Neumann Series and the Residue TheoremMay 07 2004We develop a theory of the field of double Laurent series, iterated Laurent series, and Malcev-Neumann series that applies to most constant term evaluation problems. These include (i) MacMahon's partition analysis, counting solutions of systems of linear ... More

A Euclid style algorithm for MacMahon's partition analysisAug 30 2012Apr 08 2015Solutions to a linear Diophantine system, or lattice points in a rational convex polytope, are important concepts in algebraic combinatorics and computational geometry. The enumeration problem is fundamental and has been well studied, because it has many ... More

Meromorphic cubic differentials and convex projective structuresMar 09 2015Extending the Labourie-Loftin correspondence, we establish, on any punctured oriented surface of finite type, a one-to-one correspondence between convex projective structures with specific types of ends and punctured Riemann surface structures endowed ... More

Mixture Diffusion for Asset PricingOct 05 2016Oct 30 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 distributions can be modeled ... More

Improved Non-Malleable Extractors, Non-Malleable Codes and Independent Source ExtractorsJul 30 2016In this paper we give improved constructions of several central objects in the literature of randomness extraction and tamper-resilient cryptography. Our main results are: (1) An explicit seeded non-malleable extractor with error $\epsilon$ and seed length ... More

The quasi-Poisson Goldman formulaJan 22 2013Feb 10 2013We prove a quasi-Poisson bracket formula for the space of representations of the fundamental groupoid of a surface with boundary, which generalizes Goldman's Poisson bracket formula. We also deduce a similar formula for quasi-Poisson cross-sections.

Iwasawa Main Conjecture for Rankin-Selberg $p$-adic $L$-functions: Non-Ordinary CaseDec 04 2014Dec 19 2017In this paper we prove that the $p$-adic $L$-function that interpolates the Rankin-Selberg product of a general weight two modular form which is unramified and non-ordinary at $p$, and an ordinary CM form of higher weight contains the characteristic ideal ... More

Statistical Regularity of Apollonian GasketsSep 03 2017Sep 10 2017Apollonian gaskets are formed by repeatedly filling the gaps between three mutually tangent circles with further tangent circles. In this paper we give explicit formulas for the the limiting pair correlation and the limiting nearest neighbor spacing of ... More

Diffusive shock acceleration with magnetic field amplification and Alfvenic driftSep 24 2012We explore how wave-particle interactions affect diffusive shock acceleration (DSA) at astrophysical shocks by performing time-dependent kinetic simulations, in which phenomenological models for magnetic field amplification (MFA), Alfvenic drift, thermal ... More

$H_{u,d}$-messenger Couplings Address the $μ/B_μ$ \& $A_t/m_{H_u}^2$ Problem and $(g-2)_μ$ PuzzleOct 19 2016Gauge mediated supersymmetry (SUSY)-breaking (GMSB) furnishes the best idea to overcome the flavor problem in SSMs, supersymmetric stand models (SM). However, implemented in the minimal SSM (MSSM), a very serious fine-tuning problem arises, owing to the ... More

Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert CalculusOct 18 2017May 16 2018The self-dual spaces of polynomials are related to Bethe vectors in the Gaudin model associated to the Lie algebras of types B and C. In this paper, we give lower bounds for the numbers of real self-dual spaces in intersections of Schubert varieties related ... More

Particle Acceleration at Structure Formation ShocksJun 12 2017Cosmological hydrodynamic simulations have demonstrated that shock waves could be produced in the intergalactic medium by supersonic flow motions during the course of hierarchical clustering of the large-scale-structure in the Universe. Similar to interplanetary ... More