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Results for "Jiachen Hu"

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Canonical Basis for Type $A_4$ (II)-Polynomial Elements in One VariableSep 18 2003All the 62 monomial elements in the canonical basis B of the quantized enveloping algebra for type $A_4$ have been determined in [2]. According to Lusztig's idea [7], the elements in the canonical basis B consist of monomials and linear combinations of ... More
Distributed Bandit Learning: How Much Communication is Needed to Achieve (Near) Optimal RegretApr 12 2019We study the communication complexity of distributed multi-armed bandits (MAB) and distributed linear bandits for regret minimization. We propose communication protocols that achieve near-optimal regret bounds and result in optimal speed-up under mild ... More
Towards a Fatality-Aware Benchmark of Probabilistic Reaction Prediction in Highly Interactive Driving ScenariosSep 10 2018Autonomous vehicles should be able to generate accurate probabilistic predictions for uncertain behavior of other road users. Moreover, reactive predictions are necessary in highly interactive driving scenarios to answer "what if I take this action in ... More
A Question Answering Approach to Emotion Cause ExtractionAug 18 2017Sep 24 2017Emotion cause extraction aims to identify the reasons behind a certain emotion expressed in text. It is a much more difficult task compared to emotion classification. Inspired by recent advances in using deep memory networks for question answering (QA), ... More
CM3: Cooperative Multi-goal Multi-stage Multi-agent Reinforcement LearningSep 13 2018We propose CM3, a new deep reinforcement learning method for cooperative multi-agent problems where agents must coordinate for joint success in achieving different individual goals. We restructure multi-agent learning into a two-stage curriculum, consisting ... More
Learning Deep Mean Field Games for Modeling Large Population BehaviorNov 08 2017Apr 22 2018We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable model founded ... More
Generic Probabilistic Interactive Situation Recognition and Prediction: From Virtual to RealSep 09 2018Accurate and robust recognition and prediction of traffic situation plays an important role in autonomous driving, which is a prerequisite for risk assessment and effective decision making. Although there exist a lot of works dealing with modeling driver ... More
Sensing and Recognition When Primary User Has Multiple Power LevelsNov 22 2013In this paper, we present a new cognitive radio (CR) scenario when the primary user (PU) operates under more than one transmit power levels. Different from the existing studies where PU is assumed to have only one constant transmit power, the new consideration ... More
Precise Condition Synthesis for Program RepairAug 28 2016Oct 10 2016A well-known problem of automatic defect repair is overfitting: the system tends to overfit to the test suite and has a low precision. In this paper we aim to produce precise patches, that is, any patch we produce has a relatively high probability to ... More
Factorials of infinite cardinals in ZFOct 14 2018For a set $x$, let $\mathcal{S}(x)$ be the set of all permutations of $x$. We study several aspects of this notion in $\mathsf{ZF}$. The main results are as follows: (1) $\mathsf{ZF}$ proves that for all sets $x$, if $\mathcal{S}(x)$ is Dedekind infinite, ... More
A New Multiplicity Formula for the Weyl Modules of Type ASep 18 2003A monomial basis and a filtration of subalgebras for the universal enveloping algebra $U(g_l)$ of a complex simple Lie algebra $g_l$ of type $A_l$ is given in this note. In particular, a new multiplicity formula for the Weyl module $V(\lambda)$ of $U(g_l)$ ... More
Weakly Supervised Scene Parsing with Point-based Distance Metric LearningNov 06 2018Semantic scene parsing is suffering from the fact that pixel-level annotations are hard to be collected. To tackle this issue, we propose a Point-based Distance Metric Learning (PDML) in this paper. PDML does not require dense annotated masks and only ... More
Some observations on Karoubian complete strongly exceptional posets on the projective homogeneous varietiesNov 13 2009Dec 23 2009Let $\cP=G/P$ be a homogeneous projective variety with $G$ a reductive group and $P$ a parabolic subgroup. In positive characteristic we exhibit for $G$ of low rank a Karoubian complete strongly exceptional poset of locally free sheaves appearing in the ... More
Fake News Mitigation via Point Process Based InterventionMar 22 2017Jun 19 2017We propose the first multistage intervention framework that tackles fake news in social networks by combining reinforcement learning with a point process network activity model. The spread of fake news and mitigation events within the network is modeled ... More
A study of the strong gravity region of the black hole in GS 1354-645Jul 26 2018Oct 01 2018It is thought that the spacetime metric around astrophysical black holes is well described by the Kerr solution of Einstein's gravity. However, a robust observational evidence of the Kerr nature of these objects is still lacking. Here we fit the X-ray ... More
Double-bosonization and Majid's conjecture, (I): rank-induction of $ABCD$May 11 2015Dec 20 2015Majid developed in \cite{majid3} his double-bosonization theory to construct $U_q(\mathfrak g)$ and expected to generate inductively not just a line but a tree of quantum groups starting from a node. In this paper, the authors confirm the Majid's first ... More
Double-bosonization and Majid's Conjecture, (III): type-crossing and inductions of $E_6$ and $E_7$, $E_8$Jan 17 2016Feb 05 2016Double-bosonization construction in Majid \cite{majid1} is expectedly allowed to generate a tree of quantum groups. Some main branches of the tree in \cite{HH1, HH2} have been depicted how to grow up. This paper continues to elucidate the type-crossing ... More
Symplectic group and Heisenberg group in p-adic quantum mechanicsFeb 06 2015Feb 16 2015This paper treats mathematically some problems in p-adic quantum mechanics. We first deal with p-adic symplectic group corresponding to the symmetry on the classical phase space. By the filtrations of isotropic subspaces and almost self-dual lattices ... More
An Efficient Steady-State Solver for Microflows with High-Order Moment ModelAug 14 2018In [Z. Hu, R. Li, and Z. Qiao. Acceleration for microflow simulations of high-order moment models by using lower-order model correction. J. Comput. Phys., 327:225-244, 2016], it has been successfully demonstrated that using lower-order moment model correction ... More
Fractional diffusion in Gaussian noisy environmentFeb 19 2015We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic partial equations of the following form: $D_t^\alpha u(t, x)=\textit{B}u+u\cdot W^H$, where $D_t^\alpha$ is the fractional derivative of ... More
A substructuring preconditioner with vertex-related interface solvers for elliptic-type equations in three dimensionsJan 11 2018In this paper we propose a variant of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the proposed preconditioner, we use the simplest coarse solver associated with the ... More
Double-bosonization and Majid's Conjecture, (II): cases of irregular $R$-matrices and type-crossings of $F_4$, $G_2$Dec 29 2015The purpose of the paper is to build up the related theory of weakly quasitriangular dual pairs suitably for non-standard $R$-matrices (irregular), and establish the generalized double-bosonization construction theorem for irregular $R$, which generalize ... More
Substructuring preconditioners with novel interface solvers for general elliptic-type equations in three dimensionsNov 27 2016In this paper we propose two variants of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the new preconditioners, we use the simplest coarse solver associated with the ... More
Asymptotic properties of covariate-adaptive randomizationOct 17 2012Balancing treatment allocation for influential covariates is critical in clinical trials. This has become increasingly important as more and more biomarkers are found to be associated with different diseases in translational research (genomics, proteomics ... More
Interaction-aware Multi-agent Tracking and Probabilistic Behavior Prediction via Adversarial LearningApr 04 2019In order to enable high-quality decision making and motion planning of intelligent systems such as robotics and autonomous vehicles, accurate probabilistic predictions for surrounding interactive objects is a crucial prerequisite. Although many research ... More
Double-bosonization and Majid's Conjecture, (IV): Type-Crossings from $A$ to $BCD$May 11 2015Dec 20 2015Both in Majid's double-bosonization theory and in Rosso's quantum shuffle theory, the rank-inductive and type-crossing construction for $U_q(\mathfrak g)$'s is still a remaining open question. In this paper, working with Majid's framework, based on our ... More
Nonlinear filtering in target tracking using cooperative mobile sensorsAug 09 2011Collaborative signal processing and sensor deployment have been among the most important research tasks in target tracking using networked sensors. In this paper, the mathematical model is formulated for single target tracking using mobile nonlinear scalar ... More
A study for testing the Kerr metric with AGN iron line eclipsesMar 14 2016Apr 21 2016Recently, two of us have studied iron line reverberation mapping to test black hole candidates, showing that the time information in reverberation mapping can better constrain the Kerr metric than the time-integrated approach. Motivated by this finding, ... More
Testing the Kerr Nature of Black Hole Candidates using Iron Line Spectra in the CPR FrameworkApr 08 2015Sep 05 2015The iron K$\alpha$ line commonly observed in the X-ray spectrum of both stellar-mass and supermassive black hole candidates originates from X-ray fluorescence of the inner accretion disk. Accordingly, it can be used to map the spacetime geometry around ... More
Testing the Kerr metric with the iron line and the KRZ parametrizationJul 17 2016Sep 05 2016The spacetime geometry around astrophysical black holes is supposed to be well approximated by the Kerr metric, but deviations from the Kerr solution are predicted in a number of scenarios involving new physics. Broad iron K$\alpha$ lines are commonly ... More
Generic Vehicle Tracking Framework Capable of Handling Occlusions Based on Modified Mixture Particle FilterSep 20 2018Accurate and robust tracking of surrounding road participants plays an important role in autonomous driving. However, there is usually no prior knowledge of the number of tracking targets due to object emergence, object disappearance and false alarms. ... More
Using iron line reverberation and spectroscopy to distinguish Kerr and non-Kerr black holesJun 22 2014Apr 21 2015The iron K$\alpha$ line commonly observed in the X-ray spectrum of both stellar-mass and supermassive black hole candidates is produced by the illumination of a cold accretion disk by a hot corona. In this framework, the activation of a new flaring region ... More
Coronary Calcium Detection using 3D Attention Identical Dual Deep Network Based on Weakly Supervised LearningNov 10 2018Coronary artery calcium (CAC) is biomarker of advanced subclinical coronary artery disease and predicts myocardial infarction and death prior to age 60 years. The slice-wise manual delineation has been regarded as the gold standard of coronary calcium ... More
Testing the Kerr nature of black hole candidates using iron line reverberation mapping in the CPR frameworkJan 05 2016Jun 09 2016The iron K$\alpha$ line commonly observed in the X-ray spectrum of black hole candidates is produced by X-ray fluorescence of the inner accretion disk. This line can potentially be quite a powerful tool to probe the spacetime geometry around these objects ... More
Testing the no-hair theorem with the continuum-fitting and the iron line methods: a short reviewNov 24 2015Feb 23 2016The continuum-fitting and the iron line methods are leading techniques capable of probing the spacetime geometry around astrophysical black hole candidates and testing the no-hair theorem. In the present paper, we review the two approaches, from the astrophysical ... More
Testing the Kerr black hole hypothesis: comparison between the gravitational wave and the iron line approachesMar 15 2016Jul 14 2016The recent announcement of the detection of gravitational waves by the LIGO/Virgo collaboration has opened a new window to test the nature of astrophysical black holes. Konoplya & Zhidenko have shown how the LIGO data of GW 150914 can constrain possible ... More
High Density Reflection Spectroscopy I. A case study of GX~339-4Jan 07 2019We present a broad band spectral analysis of the black hole binary GX~339-4 with NuSTAR and Swift using high density reflection model. The observations were taken when the source was in low flux hard states (LF) during the outbursts in 2013 and 2015, ... More
Relative Geometric Invariant Theory and Universal Moduli SpacesApr 25 1995We expose in detail the principle that the relative geometric invariant theory of equivariant morphisms is related to the GIT for linearizations near the boundary of the $G$-effective ample cone. We then apply this principle to construct and reconstruct ... More
Mullineux involution and twisted affine Lie algebrasDec 05 2005Apr 02 2006We use Naito-Sagaki's work [S. Naito & D. Sagaki, J. Algebra 245 (2001) 395--412, J. Algebra 251 (2002) 461--474] on Lakshmibai-Seshadri paths fixed by diagram automorphisms to study the partitions fixed by Mullineux involution. We characterize the set ... More
Branching rules for Hecke Algebras of Type $D_{n}$Dec 09 2005In this paper we study the branching problems for Hecke algebra $\H(D_n)$ of type $D_n$. We explicitly describe the decompositions of the socle of the restriction of each irreducible $\H(D_n)$-representation to $\H(D_{n-1})$ into irreducible modules by ... More
Ramification and nearby cycles for l-adic sheaves on relative curvesJul 05 2013Deligne and Kato proved a formula computing the dimension of the nearby cycles complex of an l-adic sheaf on a relative curve over an excellent strictly henselian trait. In this article, we reprove this formula using Abbes-Saito's ramification theory. ... More
Crossing the Phantom Divide: Dark Energy Internal Degrees of FreedomOct 28 2004Jan 27 2005Dark energy constraints have forced viable alternatives that differ substantially from a cosmological constant Lambda to have an equation of state w that evolves across the phantom divide set by Lambda. Naively, crossing this divide makes the dark energy ... More
Self-Consistency and Calibration of Cluster Number Count Surveys for Dark EnergyJan 21 2003Cluster number counts offer sensitive probes of the dark energy if and only if the_evolution_ of the cluster mass versus observable relation(s) is well calibrated. We investigate the potential for internal calibration by demanding consistency in the counts ... More
Dark Synergy: Gravitational Lensing and the CMBAug 06 2001Power spectra and cross-correlation measurements from the weak gravitational lensing of the cosmic microwave background (CMB) and the cosmic shearing of faint galaxies images will help shed light on quantities hidden from the CMB temperature anisotropies: ... More
CMB Anisotropies: A Decadal SurveyFeb 29 2000We review the theoretical implications of the past decade of CMB anisotropy measurements, which culminated in the recent detection of the first feature in the power spectrum, and discuss the tests available to the next decade of experiments. The current ... More
Structure Formation with Generalized Dark MatterJan 24 1998May 26 1998The next generation of cosmic microwave background (CMB) experiments, galaxy surveys, and high-redshift observations can potentially determine the nature of the dark matter observationally. With this in mind, we introduce a phenomenological model for ... More
Generalized Slow Roll for TensorsMay 08 2014The recent BICEP2 detection of degree scale CMB B-mode polarization, coupled with a deficit of observed power in large angle temperature anisotropy, suggest that the slow-roll parameter $\epsilon_H$, the fractional variation in the Hubble rate per efold, ... More
On metastability in nearly-elastic systemsFeb 02 2012We consider a nearly-elastic model system with one degree of freedom. In each collision with the "wall", the system can either lose or gain a small amount of energy due to stochastic perturbation. The weak limit of the corresponding slow motion, which ... More
A trick: why \hatγ< γ(=3) in [1=arXiv:cond-mat/0106096]?Oct 22 2008In this paper, first a theorem on the partial sum of a particular series is given. Then, based on it, the origin of obvious simulation deviation from theory is explained: i) why the numerically estimated \hat\gamma (degree exponent) in [1=arXiv:cond-mat/0106096] ... More
Power Spectrum Tomography with Weak LensingApr 13 1999Upcoming weak lensing surveys on wide fields will provide the opportunity to reconstruct the structure along the line of sight tomographically by employing photometric redshift information about the source distribution. We define power-spectrum statistics, ... More
A new family of efficient conforming mixed finite elements on both rectangular and cuboid meshes for linear elasticity in the symmetric formulationNov 19 2013Jan 21 2015A new family of mixed finite elements is proposed for solving the classical Hellinger-Reissner mixed problem of the elasticity equations. For two dimensions, the normal stress of the matrix-valued stress field is approximated by an enriched Brezzi-Douglas-Fortin-Marini ... More
The probability that random positive integers are k-wise relatively primeAug 07 2012An s-tuple of positive integers are k-wise relatively prime if any k of them are relatively prime. Exact formula is obtained for the probability that s positive integers are k-wise relatively prime.
Iron-Based Superconductors as Parity Odd SuperconductorsJan 27 2013Apr 01 2013Parity is a fundamental quantum number to classify a state of matter. Materials rarely possess ground states with odd parity. We show that the superconducting state in iron-based superconductors is classified as an odd parity s-wave spin-singlet pairing ... More
Combinatorial Modelling and Learning with Prediction MarketsJan 18 2012Combining models in appropriate ways to achieve high performance is commonly seen in machine learning fields today. Although a large amount of combinatorial models have been created, little attention is drawn to the commons in different models and their ... More
Local Donaldson-Thomas invariants of Blowups of surfacesAug 30 2011Using the degeneration formula for Donaldson-Thomas invariants, we proved a formula for the change of Donaldson-Thomas invariants of local surfaces under blowing up along points.
Weighted vector-valued estimates for a non-standard Calderón-Zygmund operatorFeb 25 2016In this paper, the author considers the weighted vector-valued estimate for the operator defined by $$T_Af(x)={\rm p.\,v.}\int_{\mathbb{R}^n}\frac{\Omega(x-y)}{|x-y|^{n+1}}\big(A(x)-A(y)-\nabla A(y)\big)f(y){\rm d}y,$$ where $\Omega$ is homogeneous of ... More
Itô's formula, the stochastic exponential and change of measure on general time scalesSep 19 2016We provide an It\^{o}'s formula for stochastic dynamical equation on general time scales. Based on this It\^{o}'s formula we give a closed form expression for stochastic exponential on general time scales. We then demonstrate a Girsanov's change of measure ... More
S-duality transformation of $\mathcal{N}$ $=4$ SYM theory at the operator levelMar 04 2019We consider the $ SL(2,Z) $ transformation of the gauge invariant operators and states in $\mathcal{N}$ $=4$ SYM theory. Duality requires the $ SU(2,2|4) $ generators with the dual coupling constants are related by a unitary transformation $ S $ up to ... More
Deformation of exceptional collectionsMay 10 2018Oct 08 2018We show that in a smooth family of complete varieties, the existence of full exceptional collection on a fiber preserves for the fibers in a neighborhood. Then we show that the noncommutative deformations of a strong exceptional collection of vector bundles ... More
A System Architecture for Software-Defined Industrial Internet of ThingsJul 31 2015Wireless sensor networks have been a driving force of the Industrial Internet of Things (IIoT) advancement in the process control and manufacturing industry. The emergence of IIoT opens great potential for the ubiquitous field device connectivity and ... More
Some relations between the topological and geometric filtration for smooth projective varietiesMar 09 2006In the first part of this paper, we show that the assertion "T_pH_k(X,Q)=G_pH_k(X,Q)" (which is called the Friedlander-Mazur conjecture) is a birationally invariant statement for smooth projective varieties X when p=dim(X)-2 and when p=1. We also establish ... More
Birational invariants defined by Lawson homologyNov 29 2005Mar 08 2006New birational invariants for a projective manifold are defined by using Lawson homology. These invariants can be highly nontrivial even for projective threefolds. Our techniques involve the weak factorization theorem of Wlodarczyk and tools developed ... More
Ammonia, Water Clouds and Methane Abundances of Giant Exoplanets and Opportunities for Super-Earth ExoplanetsDec 24 2014Future direct-imaging exoplanet missions such as WFIRST/AFTA, Exo-C, and Exo-S will measure the reflectivity of exoplanets at visible wavelengths. The exoplanets to be observed will be located further away from their parent stars than is Earth from the ... More
Global Hopf bifurcation for differential-algebraic equations with state dependent delayMay 10 2017Aug 29 2017We develop a global Hopf bifurcation theory for differential equations with a state-dependent delay governed by an algebraic equation, using the $S^1$-equivariant degree. We apply the global Hopf bifurcation theory to a model of genetic regulatory dynamics ... More
Left-orderability and cyclic branched coveringsNov 13 2013Jul 01 2014We provide an alternative proof of a sufficient condition for the fundamental group of the $n^{th}$ cyclic branched cover of $S^3$ along a prime knot $K$ to be left-orderable, which is originally due to Boyer-Gordon-Watson. As an application of this sufficient ... More
Reduction and duality in generalized geometryDec 29 2005Nov 14 2006Extending our reduction construction in \cite{Hu} to the Hamiltonian action of a Poisson Lie group, we show that generalized K\"ahler reduction exists even when only one generalized complex structure in the pair is preserved by the group action. We show ... More
Hamiltonian symmetries and reduction in generalized geometrySep 05 2005Nov 14 2006A closed 3-form $H \in \Omega^3_0(M)$ defines an extension of $\Gamma(TM)$ by $\Omega^2_0(M)$. This fact leads to the definition of the group of $H$-twisted Hamiltonian symmetries $\Ham(M, \JJ; H)$ as well as Hamiltonian action of Lie group and moment ... More
On generalized Kähler geometry on compact Lie groupsJan 05 2015We present some fundamental facts about a class of generalized K\"ahler structures defined by invariant complex structures on compact Lie groups. The main computational tool is the BH-to-GK spectral sequences that relate the bi-Hermitian data to generalized ... More
The Generalized Hodge conjecture for 1-cycles and codimension two algebraic cyclesNov 30 2005Apr 04 2006In this paper, we prove that the statement: ``The (Generalized) Hodge Conjecture holds for codimension-two cycles on a smooth projective variety $X$" is a birationally invariant statement, that is, if the statement is true for $X$, it is also true for ... More
Deep Learning for Ranking Response Surfaces with Applications to Optimal Stopping ProblemsJan 11 2019In this paper, we propose deep learning algorithms for ranking response surfaces, with applications to optimal stopping problems in financial mathematics. The problem of ranking response surfaces is motivated by estimating optimal feedback policy maps ... More
On Additive invariants of actions of additive and multiplicative groupsDec 03 2009Oct 26 2010The additive invariants of an algebraic variety is calculated in terms of those of the fixed point set under the action of additive and multiplicative groups, by using Bialynicki-Birula's fixed point formula for a projective algebraicset with a G_m-action ... More
The Lawson-Yau Formula and its generalizationSep 17 2008Dec 08 2008The Euler characteristic of Chow varieties of algebraic cycles of a given degree in complex projective spaces was computed by Blaine Lawson and Stephen Yau by using holomorphic symmetries of cycles spaces. In this paper we compute this in a direct and ... More
Valuative multiplier idealsJun 04 2014The main goal of this paper is to construct an algebraic analogue of quasi-plurisubharmonic function (qpsh for short) from complex analysis and geometry. We define a notion of qpsh function on a valuation space associated to a quite general scheme. We ... More
The implications of Galilean invariance for classical point particle lagrangiansDec 29 2011We explore the implications of the requirement of Galilean invariance for classical point particle lagrangians, in which the space is not assumed to be flat to begin with. We show that for the free, time-independent lagrangian, this requirement is equivalent ... More
Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domainsOct 28 2010Oct 22 2012Let $R$ be a 2-dimensional normal excellent henselian local domain in which 2 is invertible and let $L$ and $k$ be respectively its fraction field and residue field. Let $\Omega_R$ be the set of rank 1 discrete valuations of $L$ corresponding to codimension ... More
BMW algebra, quantized coordinate algebra and type C Schur--Weyl dualityAug 22 2007Nov 17 2009We prove an integral version of the Schur--Weyl duality between the specialized Birman--Murakami--Wenzl algebra $B_n(-q^{2m+1},q)$ and the quantum algebra associated to the symplectic Lie algebra sp_{2m}. In particular, we deduce that this Schur--Weyl ... More
Which Way?Apr 06 2016I report the result of a which-way experiment based on Young's double-slit experiment. It reveals which slit photons go through while retaining the (self) interference of all the photons collected. The idea is to image the slits using a lens with a narrow ... More
Optimal Softening for N-Body Halo SimulationsJul 10 2005Nov 16 2005We propose to determine the optimal softening length in N-body halo simulations by minimizing the ensemble-average acceleration error at a small radius r0. This strategy ensures that the error never exceeds the optimal value beyond r0. Furthermore, we ... More
The Large-Scale Structure of the Universe in One DimensionAug 20 2004(Abridged) I investigate statistical properties of one-dimensional fields in the universe such as the Lyman alpha forest and inverted line-of-sight densities. Because of gravitational clustering, the cosmic density field is already quite non-Gaussian ... More
A Dichotomous Analysis of Unemployment WelfareAug 26 2018Jan 15 2019In an economy which could not accommodate the full employment of its labor force, it employs some labor but does not employ others. The bipartition of the labor force is random, and we characterize it by a compound Beta-Binomial probability distribution ... More
Hausdorff dimension of concentration for isentropic compressible Navier-Stokes equationsJun 22 2016Jun 30 2018The concentration phenomenon of the kinetic energy, $\rho|\mathbf{u}|^2$, associated to isentropic compressible Navier-Stokes equations, is addressed in $\mathbb{R}^n$ with $n=2,3$ and the adiabatic constant $\gamma\in[1,\frac{n}{2}]$. Except a space-time ... More
On the Crepant Resolution Conjecture for Gromov-Witten Gravitational Ancestors in All Genera for Surface SingularitiesAug 05 2013Dec 15 2013We state a version of the crepant resolution conjecture for total ancestor potentials for surface singularities, and reduce the conjecture to the quantum McKay correspondence conjecture of J.Bryan and A.Gholampour and a vanishing conjecture for Hurwitz-Hodge ... More
Spin-Based Quantum Dot Quantum ComputingNov 01 2004We present a brief overview of the current theoretical and experimental progresses in the study of quantum dot-based quantum computing schemes, then focus on the spin-based varieties, which are generally regarded as the most scalable because of the relatively ... More
Lawson Homology for Abelian VarietiesOct 16 2011In this paper we introduce the Fourier-Mukai transform for Lawson homology of abelian varieties and prove an inversion theorem for the Lawson homology as well as the morphic cohomology of abelian varieties. As applications, we obtain the direct sum decomposition ... More
The Euler number of a $C^*$-invariant subvariety in $P^n$Oct 20 2017In this note we show that the Euler number of a projective variety $C^*$-equivariantly embedded into a projective space $P^n$ is bounded by $n+1$, as conjectured by Carrell and Sommese.
Greedy Strategy Works for Clustering with Outliers and Coresets ConstructionJan 24 2019We study the problems of clustering with outliers in high dimension. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithms with low complexities for the problems. Our ... More
A Proposed Algorithm for Minimum Vertex Cover Problem and its TestingOct 24 2016The paper presents an algorithm for minimum vertex cover problem, which is an NP-Complete problem. The algorithm computes a minimum vertex cover of each input simple graph. Tested by the attached MATLAB programs, Stage 1 of the algorithm is applicable ... More
Weighted vector-valued estimates for a non-standard Calderón-Zygmund operatorFeb 25 2016Sep 08 2017In this paper, the author considers the weighted vector-valued estimate for the operator defined by $$T_Af(x)={\rm p.\,v.}\int_{\mathbb{R}^n}\frac{\Omega(x-y)}{|x-y|^{n+1}}\big(A(x)-A(y)-\nabla A(y)\big)f(y){\rm d}y,$$ and the corresponding maximal operator ... More
Minimum Enclosing Ball Revisited: Stability and Sub-linear Time AlgorithmsApr 08 2019In this paper, we revisit the Minimum Enclosing Ball (MEB) problem and its robust version, MEB with outliers, in Euclidean space $\mathbb{R}^d$. Though the problem has been extensively studied before, most of the existing algorithms need at least linear ... More
Higher string topology on general spacesJan 08 2004In this paper, I give a generalized analogue of the string topology results of Chas and Sullivan, and of Cohen and Jones. For a finite simplicial complex $X$ and $k \geq 1$, I construct a spectrum $Maps(S^k, X)^{S(X)}$, and show that the corresponding ... More
The black hole mass-bulge mass correlation: bulges versus pseudo-bulgesAug 14 2009We investigate the scaling relations between the supermassive black holes mass (M_bh) and the host bulge mass in elliptical galaxies, classical bulges, and pseudo-bulges. We use two-dimensional image analysis software BUDDA to obtain the structural parameters ... More
Chiral corrections to heavy quark-diquark symmetry predictions for doubly heavy baryon zero-recoil semileptonic decayMay 21 2009Sep 21 2010This paper studies the leading chiral corrections to heavy quark-diquark symmetry predictions for doubly heavy baryon semileptonic decay form factors. We derive the coupling between heavy diquarks and weak current in the limit of heavy quark-diquark symmetry, ... More
Iron and nickel diffusion in subdwarf B starsSep 01 2011Pulsations in subdwarf B stars are attributed to radiative levitation of iron-group elements in the stellar envelope. Until now, only iron diffusion is accounted for in stellar models used for sdB seismology. However, nickel has also been suggested as ... More
Generalized Slow Roll for Non-Canonical Kinetic TermsApr 22 2011Jul 13 2011We show that the generalized slow-roll approach for calculating the power spectrum where the inflationary slow roll parameters are neither small nor slowly varying can be readily extended to models with non-canonical kinetic terms in the inflaton action. ... More
Concepts in CMB Anisotropy FormationNov 27 1995These lecture notes form a primer on the theory of cosmic microwave background (CMB) anisotropy formation. With emphasis on conceptual aspects rather than technical issues, we examine the physical foundations of anisotropy evolution in relativistic kinetic ... More
The dimension of automorphism groups of algebraic varieties with pseudo-effective log canonical divisorsNov 03 2016Let $(X,D)$ be a log smooth pair of dimension $n$ and $D$ a reduced effective divisor such that the log canonical divisor $K_X+D$ is pseudo-effective. Let $G$ be a connected (algebraic) subgroup of $\mathrm{Aut}(X,D)$. Then $G$ is a semi-abelian variety ... More
High Order Regularity Obstacle of Geodesics in Space of Kähler PotentialsAug 10 2018In this paper we address following questions regarding regularity of geodesics in space of K\"ahler potentials. First, is the regularity of a geodesic stable under smooth boundary value perturbation? Second, can we expect that any sufficiently regular ... More
A map from Lawson homology to Deligne CohomologyOct 02 2008Sep 30 2009A natural map from Lawson homology to Deligne cohomology groups for smooth complex projective varieties is constructed by using the Harvey-Lawson spark complexes. We also compare this to Abel-Jacobi type constructions by others.
A Holistic Framework for Open Low-Power Internet of Things Technology EcosystemsJun 12 2018The low-power Internet of Things (IoT) has been thriving because of the recent technological advancement and ecosystems meeting the vertical application requirements and market needs. An open IoT technology ecosystem of the low-power IoT has become increasingly ... More
The Independence under Sublinear ExpectationsJul 02 2011We show that, for two non-trivial random variables X and Y under a sublinear expectation space, if X is independent from Y and Y is independent from X, then X and Y must be maximally distributed.