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A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests have been used to both assess the patient condition and to monitor the patient progress. This ... More

Cosmological Information in Weak Lensing PeaksSep 28 2011Recent studies have shown that the number counts of convergence peaks N(kappa) in weak lensing (WL) maps, expected from large forthcoming surveys, can be a useful probe of cosmology. We follow up on this finding, and use a suite of WL convergence maps, ... More

The Spectrum of Random Inner-product Kernel MatricesFeb 14 2012Mar 22 2012We consider n-by-n matrices whose (i, j)-th entry is f(X_i^T X_j), where X_1, ...,X_n are i.i.d. standard Gaussian random vectors in R^p, and f is a real-valued function. The eigenvalue distribution of these random kernel matrices is studied at the "large ... More

Concentration of the Kirchhoff index for Erdos-Renyi graphsJul 24 2013May 29 2014Given an undirected graph, the resistance distance between two nodes is the resistance one would measure between these two nodes in an electrical network if edges were resistors. Summing these distances over all pairs of nodes yields the so-called Kirchhoff ... More

Deep Haar Scattering NetworksSep 30 2015An orthogonal Haar scattering transform is a deep network, computed with a hierarchy of additions, subtractions and absolute values, over pairs of coefficients. It provides a simple mathematical model for unsupervised deep network learning. It implements ... More

Marchenko-Pastur Law for Tyler's M-estimatorJan 15 2014Apr 01 2016This paper studies the limiting behavior of Tyler's M-estimator for the scatter matrix, in the regime that the number of samples $n$ and their dimension $p$ both go to infinity, and $p/n$ converges to a constant $y$ with $0<y<1$. We prove that when the ... More

Unsupervised Deep Haar Scattering on GraphsJun 09 2014Nov 03 2014The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown. We introduce a Haar scattering transform on graphs, which computes invariant signal descriptors. It is implemented with a deep ... More

On the Diffusion Geometry of Graph Laplacians and ApplicationsNov 09 2016We study directed, weighted graphs $G=(V,E)$ and consider the (not necessarily symmetric) averaging operator $$ (\mathcal{L}u)(i) = -\sum_{j \sim_{} i}{p_{ij} (u(j) - u(i))},$$ where $p_{ij}$ are normalized edge weights. Given a vertex $i \in V$, we define ... More

NIST: An Image Classification Network to Image Semantic RetrievalJul 02 2016This paper proposes a classification network to image semantic retrieval (NIST) framework to counter the image retrieval challenge. Our approach leverages the successful classification network GoogleNet based on Convolutional Neural Networks to obtain ... More

A Deep Learning Approach to Unsupervised Ensemble LearningFeb 06 2016We show how deep learning methods can be applied in the context of crowdsourcing and unsupervised ensemble learning. First, we prove that the popular model of Dawid and Skene, which assumes that all classifiers are conditionally independent, is {\em equivalent} ... More

Baryon impact on weak lensing peaks and power spectrum: low-bias statistics and self-calibration in future surveysOct 02 2012Peaks in two-dimensional weak lensing (WL) maps contain significant cosmological information, complementary to the WL power spectrum. This has recently been demonstrated using N-body simulations which neglect baryonic effects. Here we employ ray-tracing ... More

On explicit factors of Cyclotomic polynomials over finite fieldsNov 22 2010We study the explicit factorization of $2^n r$-th cyclotomic polynomials over finite field $\mathbb{F}_q$ where $q, r$ are odd with $(r, q) =1$. We show that all irreducible factors of $2^n r$-th cyclotomic polynomials can be obtained easily from irreducible ... More

Quantization of adiabatic pumped charge in the presence of superconducting leadFeb 20 2002We investigate the parametric electron pumping of a double barrier structure in the presence of a superconducting lead. The parametric pumping is facilitated by cyclic variation of the barrier heights $x_1$ and $x_2$ of the barriers. In the weak coupling ... More

Twisted Dirac Operators and the Noncommutative Residue for Manifolds with BoundaryApr 09 2014In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and twisted signature ... More

Non-flow correlations in a cluster modelDec 05 2008Jun 17 2010We derive analytical forms for nonflow contributions from cluster correlation to the measurement of two-particle elliptic flow (v2{2}). We estimate nonflow contribution from rho->pi+pi decays and find it is negative but not a major contributor to the ... More

A Hybridized Weak Galerkin Finite Element Method for the Biharmonic EquationFeb 05 2014This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element boundaries. The Lagrange multiplier ... More

An Efficient Numerical Scheme for the Biharmonic Equation by Weak Galerkin Finite Element Methods on Polygonal or Polyhedral MeshesSep 22 2013This paper presents a new and efficient numerical algorithm for the biharmonic equation by using weak Galerkin (WG) finite element methods. The WG finite element scheme is based on a variational form of the biharmonic equation that is equivalent to the ... More

Simplification of protein representation from the contact potentials between residuesOct 19 2000Based on the concept of energy landscape a picture of the mismatch between the reduced interaction matrix of residues and the matrix of statistical contact potentials is presented. For the Miyazawa and Jernigan (MJ) matrix, rational groupings of 20 kinds ... More

Global existence of weak solution for the 2-D Ericksen-Leslie systemMay 03 2013Jun 04 2013We prove the global existence of weak solution for two dimensional Ericksen-Leslie system with the Leslie stress and general Ericksen stress under the physical constrains on the Leslie coefficients. We also prove the local well-posedness of the Ericksen-Leslie ... More

Classification of pointed Hopf algebras of dimension $p^2$ over any algebraically closed fieldDec 21 2012Mar 12 2015Let $p$ be a prime. We complete the classification on pointed Hopf algebras of dimension $p^2$ over an algebraically closed field $k$. When $\text{char}k \neq p$, our result is the same as the well-known result for $\text{char}k=0$. When $\text{char}k=p$, ... More

Uniformly bounded components of normalityMar 05 2007Jun 09 2007Suppose that $f(z)$ is a transcendental entire function and that the Fatou set $F(f)\neq\emptyset$. Set $$B_1(f):=\sup_{U}\frac{\sup_{z\in U}\log(|z|+3)}{\inf_{w\in U}\log(|w|+3)}$$ and $$B_2(f):=\sup_{U}\frac{\sup_{z\in U}\log\log(|z|+30)}{\inf_{w\in ... More

Global well-posedness and scattering for Derivative Schrödinger equationSep 20 2009Jun 11 2010In this paper we study the Cauchy problem for the elliptic and non-elliptic derivative nonlinear Schr\"odinger equations in higher spatial dimensions ($n\geq 2$) and some global well-posedness results with small initial data in critical Besov spaces $B^s_{2,1}$ ... More

Modeling study on the validity of a possibly simplified representation of proteinsJun 23 2000The folding characteristics of sequences reduced with a possibly simplified representation of five types of residues are shown to be similar to their original ones with the natural set of residues (20 types or 20 letters). The reduced sequences have a ... More

Study of the single neutral top-pion production process at $γγ$ colliderOct 29 2005Nov 18 2005$\gamma\gamma\to \Pi_t^0$ is the major production mechanism of neutral top-pion at the linear colliders. In this paper, we calculate the cross section of the process $\gamma\gamma \to \Pi^0_t$ and discuss the potential to observe the neutral top-pion ... More

Exploring the Systematic Uncertainties of Type Ia Supernovae as Cosmological ProbesJun 27 2013Jul 26 2013We explore the systematic uncertainties of using Type Ia supernovae (SNe Ia) as cosmological probes, using the Supernova Legacy Survey Three Year data (SNLS3). We focus on studying the possible evolution of the stretch-luminosity parameter $\alpha$ and ... More

WISE Detection of the Galactic Low-Mass X-Ray BinariesApr 14 2014We report on the results from our search for the Wide-field Infrared Survey Explorer detection of the Galactic low-mass X-ray binaries. Among 187 binaries catalogued in Liu et al. (2007), we find 13 counterparts and two candidate counterparts. For the ... More

Neural Network-Based Abstract Generation for Opinions and ArgumentsJun 09 2016We study the problem of generating abstractive summaries for opinionated text. We propose an attention-based neural network model that is able to absorb information from multiple text units to construct informative, concise, and fluent summaries. An importance-based ... More

Non-flow, and what flow to subtract in jet-correlationOct 20 2009We derive analytical forms for non-flow contributions from cluster correlation to two-particle elliptic flow (v2{2}) measure. We also derive an analytical form for jet-correlation flow-background with the same cluster approach. We argue that the elliptic ... More

Geometrical quantities on a fuzzy sphereJul 12 2010In this paper, we consider the geometrical quantities on the fuzzy sphere from the spectral point of view, such as the area and the dimension. We find that, in contract to the standard sphere, the area and the dimension are the functions of the energy ... More

Discretization of div-curl Systems by Weak Galerkin Finite Element Methods on Polyhedral PartitionsJan 19 2015In this paper, the authors devise a new discretization scheme for div-curl systems defined in connected domains with heterogeneous media by using the weak Galerkin finite element method. Two types of boundary value problems are considered in the algorithm ... More

Extreme Negative Dependence and Risk AggregationJul 25 2014We introduce the concept of an extremely negatively dependent (END) sequence of random variables with a given common marginal distribution. The END structure, as a new benchmark for negative dependence, is comparable to comonotonicity and independence. ... More

Double Conformal Invariants and the Wodzicki ResidueJan 06 2011For compact real manifolds, a new double conformal invariant is constructed using the Wodzicki residue and the $d$ operator in the framework of Connes. In the flat case, we compute this double conformal invariant, and in some special cases, we also compute ... More

A Kastler-Kalau-Walze Type Theorem for 5-dimensional Manifolds with BoundaryApr 24 2014The Kastler-Kalau-Walze theorem, announced by Alain Connes, shows that the Wodzicki residue of the inverse square of the Dirac operator is proportional to the Einstein-Hilbert action of general relativity. In this paper, we prove a Kastler-Kalau-Walze ... More

Tailoring Thermal Radiative Properties with Film-Coupled Concave Grating MetamaterialsSep 25 2014This work numerically investigates the radiative properties of film-coupled metamaterials made of a two-dimensional metallic concave grating on a continuous metal film separated by an ultrathin dielectric spacer. Spectrally-selective absorption is demonstrated ... More

Coherent Optical DFT-Spread OFDMFeb 28 2011We consider application of the discrete Fourier transform-spread orthogonal frequency-division multiplexing (DFT-spread OFDM) technique to high-speed fiber optic communications. The DFT-spread OFDM is a form of single-carrier technique that possesses ... More

Magnetic interactions in FeSe studied by first principle calculationsOct 19 2015Based on first principle calculations we have investigated the evolution of magnetism in free-standing monolayer FeSe with respect to lattice constant and magnetism in bulk FeSe. The computational results show that the magnetic order in free-standing ... More

Identification of flow-background to subtract in jet-like azimuthal correlationJan 06 2009Jan 28 2010We derive an analytical form for flow-background to jet-like azimuthal correlation in a cluster approach. We argue that the elliptic flow parameter to use in jet-correlation background is that from two-particle method excluding non-flow correlation unrelated ... More

Almost Sure Existence of Global Weak Solutions to the 3D Incompressible Navier-Stokes EquationOct 31 2016In this paper we prove the almost sure existence of global weak solution to the 3D incompressible Navier-Stokes Equation for a set of large data in $\dot{H}^{-\alpha}(\mathbb{R}^{3})$ or $\dot{H}^{-\alpha}(\mathbb{T}^{3})$ with $0<\alpha\leq 1/2$. This ... More

Optimal Distributed Control for Networked Control Systems with DelaysDec 12 2013In networked control systems (NCS), sensing and control signals between the plant and controllers are typically transmitted wirelessly. Thus, the time delay plays an important role for the stability of NCS, especially with distributed controllers. In ... More

Distance Priors from Planck and Dark Energy Constraints from Current DataApr 16 2013Aug 29 2013We derive distance priors from Planck first data release, and examine their impact on dark energy constraints from current observational data. We give the mean values and covariance matrix of {R, l_a, \Omega_b h^2, n_s}, which give an efficient summary ... More

Plasmonic Light Trapping in an Ultrathin Photovoltaic Layer with Film-Coupled Metamaterial StructuresSep 11 2014Feb 04 2015A film-coupled metamaterial structure is numerically investigated for enhancing the light absorption in an ultrathin photovoltaic layer of crystalline gallium arsenide (GaAs). The top subwavelength concave grating and the bottom metallic film could not ... More

Nonparametric Additive Model-assisted Estimation for Survey DataJan 04 2011An additive model-assisted nonparametric method is investigated to estimate the finite population totals of massive survey data with the aid of auxiliary information. A class of estimators is proposed to improve the precision of the well known Horvitz-Thompson ... More

Hierarchical Spatial Sum-Product Networks for Action Recognition in Still ImagesNov 17 2015Jul 08 2016Recognizing actions from still images is popularly studied recently. In this paper, we model an action class as a flexible number of spatial configurations of body parts by proposing a new spatial SPN (Sum-Product Networks). First, we discover a set of ... More

Learning Fine-grained Features via a CNN Tree for Large-scale ClassificationNov 14 2015We propose a novel approach to enhance the discriminability of Convolutional Neural Networks (CNN). The key idea is to build a tree structure that could progressively learn fine-grained features to distinguish a subset of classes, by learning features ... More

Non-zero degree maps between 3-manifoldsApr 21 2003First the title could be also understood as ``3-manifolds related by non-zero degree maps" or "Degrees of maps between 3-manifolds" for some aspects in this survey talk. The topology of surfaces was completely understood at the end of 19th century, but ... More

Weak type estimates of Marcinkiewicz integrals on the weighted Hardy and Herz-type Hardy spacesDec 03 2010Jun 27 2012The Marcinkiewicz integral is essentially a Littlewood-Paley $g$-function, which plays a important role in harmonic analysis. In this article, by using the atomic decomposition theory of weighted Hardy spaces and homogeneous weighted Herz-type Hardy spaces, ... More

Some estimates of intrinsic square functions on weighted Herz-type Hardy spacesOct 06 2010Jan 11 2013In this paper, by using the atomic decomposition theory of weighted Herz-type Hardy spaces, we will obtain some strong type and weak type estimates for intrinsic square functions including the Lusin area function, Littlewood-Paley $\mathcal G$-function ... More

Boundedness of intrinsic square functions on the weighted weak Hardy spacesJul 05 2012In this paper, by using the atomic decomposition theorem for weighted weak Hardy spaces, we will show the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function ... More

On the De Giorgi type conjecture for an elliptic system modeling phase separationJul 23 2012Oct 04 2013In this paper we study the one dimensional symmetry problem of entire solutions to the problem \[\Delta u=uv^2,\Delta v=vu^2,u,v>0 \text{in} \mathbb{R}^n,\] for all $n\geq 2$. We prove that, if a solution $(u,v)$ is a local minimizer and has linear growth ... More

Framed and oriented links of codimension 2May 28 2002Jun 06 2002We discuss the relationship between the m-th homotopy group of the one-point union of r copies of the two-dimensional sphere and the m-th homotopy group of the one-point union of r+1 copies of the Thom space of the oriented two-dimensional universal vector ... More

The geometry of the Hilton splittingMay 22 2002One of the important theorems in homotopy theory is the Hilton splitting. In this paper we will construct all the Hilton homomorphisms by geometrical means and prove a family of sharper symmetry relations of linking coefficients which desuspend and generalize ... More

Isoperimetric inequality, $Q$-curvature and $A_p$ weightsJun 07 2013A well known question in differential geometry is to control the constant in isoperimetric inequality by intrinsic curvature conditions. In dimension 2, the constant can be controlled by the integral of the positive part of the Gaussian curvature. In ... More

Intrinsic square functions on the weighted Morrey spacesFeb 22 2011Aug 13 2012In this paper, we will study the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function on the weighted Morrey spaces $L^{p,\kappa}(w)$ for $1<p<\infty$ and $0<\kappa<1$. ... More

Endpoint estimates for commutators of intrinsic square functions in the Morrey type spacesNov 07 2010Jul 05 2014In this paper, the boundedness properties of commutators generated by $b$ and intrinsic square functions in the endpoint case are discussed, where $b\in BMO(\mathbb R^n)$. We first establish the weighted weak $L\log L$-type estimates for these commutator ... 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

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

Torsion points on the cohomology jump loci of compact Kähler manifoldsDec 23 2013Nov 30 2015We prove that each irreducible component of the cohomology jump loci of rank one local systems over a compact K\"ahler manifold contains at least one torsion point. This generalizes a theorem of Simpson for smooth complex projective varieties. An immediate ... More

Rational curves on hypersurfacesOct 12 2014In this paper, we prove three related results; (1) Extension of our result in [10] to all generic hypersurfaces. More precisely, the normal sheaf of a generic rational map $c_0$ to a generic hypersurface $X_0$ of $\mathbf P^n, n\geq 4$ has a vanishing ... More

Decoherence of the two-level system coupled to a fermionic reservoir and the information transfer from it to the environmentDec 24 2010Feb 01 2011We study the evolution of reduced density matrix of an impurity coupled to a Fermi sea after the coupling is switched on at time $t=0$. We find the non-diagonal elements of the reduced density matrix decay exponentially, and the decay constant is the ... More

Belief Revision in Probability TheoryMar 06 2013In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit conditions and the implicit conditions of probability assignments `me properly distinguished, it follows ... More

Electron spin and the origin of Bio-homochirality I. Extant enzymatic reaction modelSep 05 2013Jul 05 2016In this paper, I tentatively put forward a new hypothesis that the emergence of a single chiral form of biomolecules in living organisms is specifically determined by the electron spin state during their enzyme-catalyzed synthesis processes. Specifically ... More

Some issues about neutrino processes in color superconducting quark matterJul 10 2006Several relevant issues in computing neutrino emissivity in Urca processes in color superconducting quark matter are addressed. These include: (1) The constraint on $u$ quark abundance is given from electric neutrality and the triangle relation among ... More

Some properties of Hamiltonian homeomorphisms on closed aspherical surfacesFeb 07 2016Jun 13 2016On closed symplectically aspherical manifolds, Schwarz proved a classical result that the action function of a nontrivial Hamiltonian diffeomorphism is not constant by using Floer homology. In this article, we generalize Schwarz's theorem to the $C^0$-case ... More

Optimality of Myopic Policy for Restless Multiarmed Bandit with Imperfect ObservationJan 31 2016We consider the scheduling problem concerning N projects. Each project evolves as a multi-state Markov process. At each time instant, one project is scheduled to work, and some reward depending on the state of the chosen project is obtained. The objective ... More

Content-based Multi-media Retrieval TechnologyAug 15 2012This paper gives a summary of the content-based Image Retrieval and Content-based Audio Retrieval, which are two parts of the Content-based Retrieval. Content-based Retrieval is the retrieval based on the features of the content. Generally, it is a way ... More

Iterated Function Systems with Economic ApplicationsSep 21 2012This work's purpose is to understand the dynamics of some social systems whose properties can be captured by certain iterated function systems. To achieve this intension, we start from the theory of iterated function systems, and then we study two specific ... More

On the linear operation of cloned dynamical systems and its Lyapunov exponentsNov 10 2013Mar 16 2014The cloned dynamical system theory is introduced and the Lyapunov exponents of this system are qualitatively proven to be same as the original dynamical system. This property indicates that these two systems have the same error propagation speed in the ... More

Duality in infinite dimensional Fock representationsOct 28 1997We construct and study in detail various dual pairs acting on some Fock representations between a finite dimensional Lie group and a completed infinite rank affine algebra associated to an infinite affine Cartan matrix. We give explicit decompositions ... More

Improved Results on Robust Stability of Multivariable Interval Control SystemsNov 01 2002For interval polynomial matrices, we identify the minimal testing set, whose stability can guarantee that of the whole uncertain set. Our results improve the conclusions given by Kamal and Dahleh.

Poincaré-type Inequalities for Singular Stable-Like Dirichlet FormsAug 29 2015This paper is concerned with a class of singular stable-like Dirichlet forms on $\R^d$, which are generated by $d$ independent copies of a one-dimensional symmetric $\alpha$-stable process, and whose L\'evy jump kernel measure is concentrated on the union ... More

H-infinity Performance of Interval SystemsNov 01 2002In this paper, we study $H^{\infty}$ performance of interval systems. We prove that, for an interval system, the maximal $H^{\infty}$ norm of its sensitivity function is achieved at twelve (out of sixteen) Kharitonov vertices.

Cohesive sets and rainbowsMar 14 2013We study the strength of $\RRT^3_2$, Rainbow Ramsey Theorem for colorings of triples, and prove that $\RCA + \RRT^3_2$ implies neither $\WKL$ nor $\RRT^4_2$. To this end, we establish some recursion theoretic properties of cohesive sets and rainbows for ... More

The Definability Strength of Combinatorial PrinciplesAug 07 2014Aug 11 2014We introduce the definability strength of combinatorial principles. In terms of definability strength, a combinatorial principle is strong if solving a corresponding combinatorial problem could help in simplifying the definition of a definable set. We ... More

Precision Arithmetic: A New Floating-Point ArithmeticJun 25 2006Apr 12 2014A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional floating-point arithmetic. ... More

Rigidity of entire convex self-shrinking solutions to Hessian quotient flowOct 28 2016We prove that every entire strictly convex self-shrinking solution on $\mathbb{R}^n$ to the Hessian quotient flow must be quadratic. This result includes the rigidity theorem for entire self-shrinking solutions to Lagrangian mean curvature flow in pseudo-Euclidean ... More

Consistency Analysis of Nearest Subspace ClassifierJan 24 2015The Nearest subspace classifier (NSS) finds an estimation of the underlying subspace within each class and assigns data points to the class that corresponds to its nearest subspace. This paper mainly studies how well NSS can be generalized to new samples. ... More

A Recipe for Construction of the Critical Vertices for Left-Sector Stability of Interval PolynomialsFeb 23 2002For the left-sector stability of interval polynomials, it suffices to check a subset of its vertex polynomials. This paper provides a recipe for construction of these critical vertices. Illustrative examples are presented.

Notes on Rainbow Distinguished Point MethodJun 02 2015Jun 03 2015This paper clarifies the method described in our previous paper (DOI: 978-3-319-02726-5\_21), namely rainbow distinguished point method, and give revised theoretical and experimental results which shows rainbow distinguished point method behaves inferiorly ... More

Rigidity of entire self-shrinking solutions to Kähler-Ricci flow on complex planeFeb 01 2016Oct 24 2016We show that every entire self-shrinking solution on $\mathbb{C}^1$ to the K\"ahler-Ricci flow must be generated from a quadratic potential.

On Column Selection in Approximate Kernel Canonical Correlation AnalysisFeb 05 2016We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nystr\"om approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the training set. When ... More

On Invariants of $\text{C}^*$-algebras with the ideal propertyOct 04 2015Oct 12 2016In this paper, we consider $\text{C}^*$-algebras with the ideal property (the ideal property unifies the simple and real rank zero cases). We define two categories related the invariants of the $\text{C}^*$-algebras with the ideal property. And we showed ... More

Topological Rigidity for FJ by the Infinite Cyclic GroupDec 03 2015Feb 17 2016We call a group FJ if it satisfies the $K$- and $L$-theoretic Farrell-Jones conjecture with coefficients in $\mathbb Z$. We show that if $G$ is FJ, then the simple Borel conjecture (in dimensions $\ge 5$) holds for every group of the form $G\rtimes\mathbb ... More

Monomial Difference IdealsJan 06 2016Jun 16 2016In this paper, basic properties of monomial difference ideals are studied. We prove the finitely generated property of well-mixed difference ideals generated by monomials. Furthermore, a finite prime decomposition of radical well-mixed monomial difference ... More

Some conjectures on modular representations of affine $\mathfrak{sl}_2$ and Virasoro algebraAug 29 2016We conjecture an explicit bound on the prime characteristic of a field, under which the Weyl modules of affine $\mathfrak{sl}_2$ and the minimal series modules of Virasoro algebra remain irreducible, and Goddard-Kent-Olive coset construction for affine ... More

Uniform regularity and vanishing dissipation limit for the full compressible Navier-Stokes system in 3-D bounded domainAug 17 2015In the present paper, we study the uniform regularity and vanishing dissipation limit for the full compressible Navier-Stokes system whose viscosity and heat conductivity are allowed to vanish at different order. The problem is studied in a 3-D bounded ... More

Effective Computation of Stochastic Protein Kinetic Equation by Reducing Stiffness via Variable TransformationNov 13 2014The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such situation, we provide ... More

Total destruction of Lagrangian toriMar 05 2014For an integrable Tonelli Hamiltonian with $d\ (d\geq 2)$ degrees of freedom, we show that all of the Lagrangian tori can be destroyed by analytic perturbations which are arbitrarily small in the $C^{d-\delta}$ topology.

Influence of Fe, Ni, and Cu Doping on the Photocatalytic Efficiency of ZnS: Implications for Prebiotic ChemistryOct 04 2016The mineral sphalerite (ZnS) is a typical constituent at the periphery of submarine hydrothermal deposits on Earth. It has been frequently suggested to have played an important role in the prebiotic chemistry due to its prominent photocatalytic activity. ... More

On quaternionic complexes over unimodular quaternionic manifoldsOct 20 2016Penrose's two-spinor notation for $4$-dimensional Lorentzian manifolds can be extended to two-component notation for quaternionic manifolds, which is a very useful tool for calculation. We construct a family of quaternionic complexes over unimodular quaternionic ... More

Extremes of $q$-Ornstein-Uhlenbeck processesSep 01 2016The $q$-Ornstein-Uhlenbeck processes, $q\in(-1,1)$, are a family of stationary Markov processes that converge weakly to the standard Ornstein-Uhlenbeck process as $q$ tends to 1. It has been noticed recently that in terms of path properties, however, ... More

Simulation analysis of rectangular dielectric-loaded traveling wave amplifiers for THz-sourcesDec 16 2010Dec 30 2010Non-linear simulation results for a 220-GHz rectangular dielectric-loaded traveling wave amplifier are presented. Simulations are used to check a linear theory that is developed by phenomenological introduction of an effective dielectric parameter for ... More

Electric and Magnetic Walls on Dielectric InterfacesJul 20 2010Sufficient conditions of the existence of electric or magnetic walls on dielectric interfaces are given for a multizone uniform dielectric waveguiding system. If one of two adjacent dielectric zones supports a TEM field distribution while the other supports ... More

An Opinion Dynamics Model with Increasing Self-ConfidenceSep 19 2016We propose an opinion dynamics model in which agents gradually increase their own self-confidence while interacting with each other. The relations between the newly proposed model and existing works of social learning, inertial opinion dynamics, Bayesian ... More

New insight into light propagation and light-matter interactions with applications to experimental observationsJun 13 2013Sep 14 2016The paper provides a new understanding of light propagation and light-matter interactions by examining the physical implications of group velocity and energy conservation equation. The classical definition of group velocity has two flaws: (a) the group ... More

On the capacity of the binary adversarial wiretap channelMay 04 2016Jun 12 2016New bounds on the semantic secrecy capacity of the binary adversarial wiretap channel are established . Against an adversary which reads a $\rho_r$ fraction of the transmitted codeword and modifies a $\rho_w$ fraction of the codeword, we show an achievable ... More

Self-consistent theory for a plane wave in a moving medium and light-momentum criterionSep 11 2014Jun 29 2016A self-consistent theory is developed based on the principle of relativity for a plane wave in a moving non-dispersive, lossless, non-conducting, isotropic, uniform medium. A light-momentum criterion is set up for the first time, which states that the ... More

An exponential integrator scheme for time discretization of nonlinear stochastic wave equationDec 18 2013Nov 30 2014This work is devoted to convergence analysis of an exponential integrator scheme for semi-discretization in time of nonlinear stochastic wave equation. A unified framework is first set forth, which covers important cases of additive and multiplicative ... More

Semilinear substructural logics with the finite embeddability propertyAug 13 2016In this paper, three semilinear substructural logics ULw, IULw and HpsUL*w are constructed. Then the completeness of ULw and IULw with respect to classes of finite UL and IUL-algebras, respectively, is proved. Algebraically, non-integral ULw and IULw-algebras ... More

Tetravalent edge-transitive Cayley graphs of Frobenius groupsJun 24 2016Aug 29 2016In this paper, we give a characterization for a class of edge-transitive Cayley graphs, and provide methods for constructing Cayley graphs with certain symmetry properties. Also this study leads to construct and characterise a new family of half-transitive ... More