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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

Experience: Understanding Long-Term Evolving Patterns of Shared Electric Vehicle NetworksDec 02 2018Due to the ever-growing concerns on the air pollution and energy security, many cities have started to update their taxi fleets with electric ones. Although environmentally friendly, the rapid promotion of electric taxis raises problems to both taxi drivers ... More

Two-sample Statistics Based on Anisotropic KernelsSep 14 2017Aug 30 2018The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed test can be ... 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

Low Rank plus Sparse Decomposition of ODFs for Improved Detection of Group-level Differences and Variable Correlations in White MatterMar 15 2018A novel approach is presented for group statistical analysis of diffusion weighted MRI datasets through voxelwise Orientation Distribution Functions (ODF). Recent advances in MRI acquisition make it possible to use high quality diffusion weighted protocols ... 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

Identifying Mild Traumatic Brain Injury Patients From MR Images Using Bag of Visual WordsOct 18 2017Feb 14 2018Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests are used to both assess the patient condition and to monitor the patient progress. This work aims ... More

A Machine Learning Approach For Identifying Patients with Mild Traumatic Brain Injury Using Diffusion MRI ModelingAug 27 2017While diffusion MRI has been extremely promising in the study of MTBI, identifying patients with recent MTBI remains a challenge. The literature is mixed with regard to localizing injury in these patients, however, gray matter such as the thalamus and ... More

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

Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph LaplacianOct 25 2018The extraction of clusters from a dataset which includes multiple clusters and another significant portion of "background" samples is a task of practical importance. The traditional spectral clustering algorithm, relying on the leading $K$ eigenvectors ... More

A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Apr 11 2018Mild traumatic brain injury is a growing public health problem with an estimated incidence of over 1.7 million people annually in US. Diagnosis is based on clinical history and symptoms, and accurate, concrete measures of injury are lacking. This work ... More

MTBI Identification From Diffusion MR Images Using Bag of Adversarial Visual FeaturesJun 27 2018In this work, we propose bag of adversarial features (BAF) for identifying mild traumatic brain injury (MTBI) patients from their diffusion magnetic resonance images (MRI) (obtained within one month of injury) by incorporating unsupervised feature learning ... 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

Ensemble SamplingMay 20 2017Nov 22 2017Thompson sampling has emerged as an effective heuristic for a broad range of online decision problems. In its basic form, the algorithm requires computing and sampling from a posterior distribution over models, which is tractable only for simple special ... 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

Provable Estimation of the Number of Blocks in Block ModelsMay 24 2017Mar 18 2018Community detection is a fundamental unsupervised learning problem for unlabeled networks which has a broad range of applications. Many community detection algorithms assume that the number of clusters $r$ is known apriori. In this paper, we propose an ... 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

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

The Geometry of Nodal Sets and Outlier DetectionJun 05 2017Let $(M,g)$ be a compact manifold and let $-\Delta \phi_k = \lambda_k \phi_k$ be the sequence of Laplacian eigenfunctions. We present a curious new phenomenon which, so far, we only managed to understand in a few highly specialized cases: the family of ... More

Butterfly-Net: Optimal Function Representation Based on Convolutional Neural NetworksMay 18 2018Deep networks, especially Convolutional Neural Networks (CNNs), have been successfully applied in various areas of machine learning as well as to challenging problems in other scientific and engineering fields. This paper introduces Butterfly-Net, a low-complexity ... 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

DCFNet: Deep Neural Network with Decomposed Convolutional FiltersFeb 12 2018Jul 27 2018Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the Decomposed Convolutional ... More

Diffusion Variational AutoencodersMay 29 2019Variational autoencoders (VAEs) have become one of the most popular deep learning approaches to unsupervised learning and data generation. However, traditional VAEs suffer from the constraint that the latent space must distributionally match a simple ... More

On Matrix Rearrangement InequalitiesApr 10 2019Given two symmetric and positive semidefinite square matrices $A, B$, is it true that any matrix given as the product of $m$ copies of $A$ and $n$ copies of $B$ in a particular sequence must be dominated in the spectral norm by the ordered matrix product ... More

RotDCF: Decomposition of Convolutional Filters for Rotation-Equivariant Deep NetworksMay 17 2018Explicit encoding of group actions in deep features makes it possible for convolutional neural networks (CNNs) to handle global deformations of images, which is critical to success in many vision tasks. This paper proposes to decompose the convolutional ... 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

Defending against Adversarial Images using Basis Functions TransformationsMar 28 2018Apr 16 2018We study the effectiveness of various approaches that defend against adversarial attacks on deep networks via manipulations based on basis function representations of images. Specifically, we experiment with low-pass filtering, PCA, JPEG compression, ... More

Transfer matrix method for the analysis of space-time modulated media and systemsMay 25 2019Space-time modulation adds another powerful degree of freedom to the manipulation of classical wave systems. It opens the door for complex control of wave behavior beyond the reach of stationary systems, such as nonreciprocal wave transport and realization ... 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

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

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

In-phase Synchronization of Two Coupled MetronomesMay 01 2018This paper used multi-scale method and KBM method to get approximate solution of coupled Van der Pol oscillators, based on which, researchers investigated the impact several parameters have on the prerequisite of synchronization and the time it takes ... More

New Braided $T$-Categories over Hopf (co)quasigroupsJan 22 2017Let $H$ be a Hopf quasigroup with bijective antipode and let $Aut_{HQG}(H)$ be the set of all Hopf quasigroup automorphisms of $H$. We introduce a category ${_{H}\mathcal{YDQ}^{H}}(\alpha,\beta)$ with $\alpha,\beta\in Aut_{HQG}(H)$ and construct a braided ... More

Characterization of Hopf QuasigroupsFeb 26 2019In this paper, we first discuss some properties of the Galois linear maps. We provide some equivalent conditions for Hopf algebras and Hopf (co)quasigroups as its applications. Then let $H$ be a Hopf quasigroup with bijective antipode and $G$ be the set ... More

Dirichlet Forms Constructed from Annihilation Operators on Bernoulli FunctionalsFeb 09 2017The annihilation operators on Bernoulli functionals (Bernoulli annihilators, for short) and their adjoint operators satisfy a canonical anti-commutation relation (CAR) in equal-time. As a mathematical structure, Dirichlet forms play an important role ... More

Recognizing number of communities and detecting community structures in complex networksMar 18 2018Recognizing number of communities and detecting community structures of complex network are discussed in this paper. As a visual and feasible algorithm, block model has been successfully applied to detect community structures in complex network. In order ... 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

On the Design of Constant Modulus Probing Waveforms with Good Correlation Properties for MIMO Radar via Consensus-ADMM ApproachJan 16 2019In this paper, we design constant modulus probing waveforms with good correlation properties for collocated multi-input multi-output (MIMO) radar systems. The main content is as follows: first, we formulate the design problem as a fourth order polynomial ... More

An Improved Cost Function for Hierarchical Cluster TreesDec 06 2018Dec 17 2018Hierarchical clustering has been a popular method in various data analysis applications. It partitions a data set into a hierarchical collection of clusters, and can provide a global view of (cluster) structure behind data across different granularity ... More

Indicators of Hopf algebras in positive characteristicApr 18 2017Feb 19 2019The notion of $n$-th indicator for a finite-dimensional Hopf algebra was introduced by Kashina, Montgomery and Ng as gauge invariance of the monoidal category of its representations. The properties of these indicators were further investigated by Shimizu. ... 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

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

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

Deterministic Analysis of Weighted BPDN With Partially Known Support InformationMar 03 2019In this paper, with the aid of the powerful Restricted Isometry Constant (RIC), a deterministic (or say non-stochastic) analysis, which includes a series of sufficient conditions (related to the RIC order) and their resultant error estimates, is established ... More

Topological Inference of Manifolds with BoundaryOct 12 2018Given a set of data points sampled from some underlying space, there are two important challenges in geometric and topological data analysis when dealing with sampled data: reconstruction -- how to assemble discrete samples into global structures, and ... More

The parameters of a family of linear codesMar 09 2019A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the sense that ... More

A Simple and Space Efficient Segment Tree ImplementationJul 14 2018The segment tree is an extremely versatile data structure. In this paper, a new heap based implementation of segment trees is proposed. In such an implementation of segment tree, the structural information associated with the tree nodes can be removed ... More

Oseba: Optimization for Selective Bulk Analysis in Big Data ProcessingJul 12 2017Selective bulk analyses, such as statistical learning on temporal/spatial data, are fundamental to a wide range of contemporary data analysis. However, with the increasingly larger data-sets, such as weather data and marketing transactions, the data organization/access ... 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

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

On the boundary between qualitative and quantitative measures of causal effectsNov 13 2017Jul 09 2018Causal relationships among variables are commonly represented via directed acyclic graphs. There are many methods in the literature to quantify the strength of arrows in a causal acyclic graph. These methods, however, have undesirable properties when ... More

Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equationDec 15 2017Jan 24 2019We investigate the time-asymptotic stability of planar rarefaction wave for the three-dimensional Boltzmann equation, based on the micro-macro decomposition introduced in [24, 22] and our new observations on the underlying wave structures of the equation ... 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

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

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

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

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

Integrability of scalar curvature and normal metric on conformally flat manifoldsJul 14 2017On a manifold $(\mathbb{R}^n, e^{2u} |dx|^2)$, we say $u$ is normal if the $Q$-curvature equation that $u$ satisfies $(-\Delta)^{\frac{n}{2}} u = Q_g e^{nu}$ can be written as the integral form $u(x)=\frac{1}{c_n}\int_{\mathbb R^n}\log\frac{|y|}{|x-y|}Q_g(y)e^{nu(y)}dy+C$. ... More

Constructing Social Networks From Binary DataJun 11 2018Much of applied network analysis concerns with studying the existing relationships between a set of agents; however, little focus has been given to the considerations of how to represent observed phenomena as a network object. In the case of physical ... 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

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

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

Electron Transport in Dirac and Weyl SemimetalsSep 10 2018Recently, the Dirac and Weyl semimetals have attracted extensive attention in condensed matter physics due to both the fundamental interest and the potential application of a new generation of electronic devices. Here we review the exotic electrical transport ... 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

Free boundary problems of ecological models with nonlocal and local diffusionsDec 31 2018We study a class of free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of free boundary problems of reaction diffusion systems in there local diffusions are used to describe the population dispersal, ... More

Compatible Matrices of Spearman's Rank CorrelationOct 08 2018Oct 11 2018In this paper, we provide a negative answer to a long-standing open problem on the compatibility of Spearman's rho matrices. Following an equivalence of Spearman's rho matrices and linear correlation matrices for dimensions up to 9 in the literature, ... More

Thermalization of small quantum systems: From the zeroth law of thermodynamicsMay 15 2019Thermalization of isolated quantum systems has been studied intensively in recent years and significant progresses have been achieved. Here, we study thermalization of small quantum systems that interact with large chaotic environments under the consideration ... 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

Compatible Matrices of Spearman's Rank CorrelationOct 08 2018Apr 03 2019In this paper, we provide a negative answer to a long-standing open problem on the compatibility of Spearman's rho matrices. Following an equivalence of Spearman's rho matrices and linear correlation matrices for dimensions up to 9 in the literature, ... More

Octonion Algebra and Noise-Free Fully Homomorphic Encryption (FHE) SchemesJan 25 2016Mar 22 2016Brakerski showed that linearly decryptable fully homomorphic encryption (FHE) schemes cannot be secure in the chosen plaintext attack (CPA) model. In this paper, we show that linearly decryptable FHE schemes cannot be secure even in the ciphertext only ... More

Commercialization of fuel cells: myth or reality?Jan 19 2014Despite huge investment and efforts in the last decades, fuel cells are still known as a fledgling industry after 170 years of the first fuel cell. It becomes clear that these investment and efforts did not address the critical questions. Why upscaling ... More

Recent developments in weak-coupling color superconductivityApr 07 2004May 10 2004Recent developments in weak-coupling color superconductivity are reviewed. These developments are as follows. The mean field gap equation is solved for most common superconducting phases up to subleading order; BCS relation is found to be violated in ... More

The relativistic Doppler effect: when a zero frequency shift or a red shift exists for sources approaching the observerJun 23 2010Oct 24 2012It is shown without making use of Lorentz transformation that there exists a phenomenon of relativistic zero-frequency shift in Doppler effect for a plane wave in free space, observed in two inertial frames of relative motion, and the zero shift takes ... More

A Perspective on Deep ImagingSep 10 2016The combination of medical imaging and deep learning promises to empower not only image analysis but also image reconstruction. The latter perspective is considered in this perspective article to develop low- and high-hanging image reconstruction techniques. ... More

Stock price direction prediction by directly using prices data: an empirical study on the KOSPI and HSISep 27 2013Jul 13 2016The prediction of a stock market direction may serve as an early recommendation system for short-term investors and as an early financial distress warning system for long-term shareholders. Many stock prediction studies focus on using macroeconomic indicators, ... More

A Brief Review of Social-Force Model in Psychological PrinciplesMay 17 2016Jul 18 2016To well understand crowd behavior, microscopic models have been developed in recent decades, in which an individual's behavioral/psychological status can be modeled and simulated. A well-known model is the social-force model innovated by physical scientists. ... More

Passivity-Based Adaptive Control for Visually Servoed Robotic SystemsJun 29 2015May 08 2016This paper investigates the visual servoing problem for robotic systems with uncertain kinematic, dynamic, and camera parameters. We first present the passivity properties associated with the overall kinematics of the system, and then propose two passivity-based ... More

On the Geodesic Centers of Polygonal DomainsJul 20 2016In this paper, we study the problem of computing Euclidean geodesic centers of a polygonal domain $\mathcal{P}$ with a total of $n$ vertices. We discover many interesting observations. We give a necessary condition for a point being a geodesic center. ... More

An Improved Algorithm for Diameter-Optimally Augmenting Paths in a Metric SpaceAug 16 2016Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ such that the diameter of the resulting graph is minimized. Previously (in ICALP 2015) the problem was solved in $O(n\log^3 n)$ time. ... More

On the global $2$-holonomy for a $2$-connection on a $2$-bundleDec 29 2015A crossed module constitutes a strict $2$-groupoid $\mathcal{G}$ and a $\mathcal{G}$-valued $2$-cocycle on a manifold defines a $2$-bundle. A $2$-connection on this $2$-bundle is given by a Lie algebra $\mathfrak g$ valued $1$-form $A $ and a Lie algebra ... More

Measuring free energy in parallel tempering Monte CarloJan 13 2015An efficient approach of measuring the absolute free energy in parallel tempering Monte Carlo using the exponential averaging method is discussed and the results are compared with those of population annealing Monte Carlo using the three-dimensional Edwards-Anderson ... More

On passage to over-groups of finite indices of the Farrell-Jones conjectureDec 05 2015We use the controlled algebra approach to study the problem that whether the Farrell-Jones conjecture is closed under passage to over-groups of finite indices. Our study shows that this problem is closely related to a general problem in algebraic $K$- ... More

Relative Definability of $n$-GenericsNov 28 2015A set $G \subseteq \omega$ is $n$-generic for a positive integer $n$ if and only if every $\Sigma^0_n$ formula of $G$ is decided by a finite initial segment of $G$ in the sense of Cohen forcing. It is shown here that every $n$-generic set $G$ is properly ... More

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

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

The normal bundle of a rational curve on a generic quintic threefoldAug 30 2015This is another proof of the same result in [9]. Let $X_0$ be a generic quintic hypersurface in $\mathbf P^4$ over $\mathbb C$ and $c_0$ a regular map $\mathbf P^1\to X_0$ that is generically one-to-one to its image. In this paper, we show (1) $c_0$ must ... More

A Process Algebra for GamesDec 03 2013Jul 13 2015Using formal tools in computer science to describe games is an interesting problem. We give games, exactly two person games, an axiomatical foundation based on the process algebra ACP (Algebra of Communicating Process). A fresh operator called opponent's ... More