Results for "Dan Liu"

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Extremes of Spherical Fractional Brownian MotionJun 08 2018Feb 25 2019Let $\{B_\beta (x), x \in \mathbb{S}^N\}$ be a fractional Brownian motion on the $N$-dimensional unit sphere $\mathbb{S}^N$ with Hurst index $\beta$. We study the excursion probability $\mathbb{P}\{\sup_{x\in T} B_\beta(x) > u \}$ and obtain the asymptotics ... More
On the multipliers of repelling periodic points of entire functionsJan 24 2017Dec 01 2017We give a lower bound for the multipliers of repelling periodic points of entire functions. The bound is deduced from a bound for the multipliers of fixed points of composite entire functions.
Effect of Net Charge on the Relative Stability of 2D Boron AllotropesJan 24 2019We study the effect of electron doping on the bonding character and stability of two-dimensional (2D) structures of elemental boron, called borophene, which is known to form many stable allotropes. Our {\em ab initio} calculations for the neutral system ... More
ND^(*) and NB^(*) interactions in a chiral quark modelAug 17 2015ND and ND^* interactions become a hot topic after the observation of new charmed hadrons \Sigma_c(2800) and \Lambda_c(2940)^+. In this letter, we have preliminary investigated S-wave ND and ND^* interactions with possible quantum numbers in the chiral ... More
Threshold dynamics and ergodicity of an SIRS epidemic model with Markovian switchingJul 20 2017This paper studies the spread dynamics of a stochastic SIRS epidemic model with nonlinear incidence and varying population size, which is formulated as a piecewise deterministic Markov process. A threshold dynamic determined by the basic reproduction ... More
Multiple Entropy Measures for Multipartite Quantum EntanglementMay 26 2007Jun 22 2007A new entanglement measure, the multiple entropy measures (MEMS), is proposed to quantify quantum entanglement of multi-partite quantum state. The MEMS is vector-like with $m=[N/2]$, the integer part of $N/2$, components: $[S_1, S_2,..., S_m]$, and the ... More
A Novel Way of Identifying Cyber PredatorsDec 11 2017Recurrent Neural Networks with Long Short-Term Memory cell (LSTM-RNN) have impressive ability in sequence data processing, particularly for language model building and text classification. This research proposes the combination of sentiment analysis, ... More
Multiple D2-Brane Action from M2-BranesJul 08 2008We study the detail derivation of the multiple D2-brane effective action from multiple M2-branes in the Bagger-Lambert-Gustavsson (BLG) theory and the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory by employing the novel Higgs mechanism. We show explicitly ... More
Two-dimensional Mechanical Metamaterials with Unusual Poisson Ratio BehaviorDec 08 2018We design two-dimensional (2D) mechanical metamaterials that may be deformed substantially at little or no energy cost. Examples of such deformable structures are assemblies of rigid isosceles triangles hinged in their corners on the macro-scale, or polymerized ... More
Study of Unflavored Light Mesons with $J^{PC}=2^{--}$Jan 11 2019Mar 06 2019The unflavored light meson families, namely $\omega_2$, $\rho_2$, and $\phi_2$, are studied systematically by investigating the spectrum and the two-body strong decays allowed by Okubo-Zweig-Iizuka rule. Including the four experimentally observed states ... More
Magnetic nanotubes: A new material platform to realize robust spin-Seebeck effect and perfect thermal spin-filtering effectAug 31 2018To construct reliable material platforms and to uncover new rules to realize spin-Seebeck effect (SSE) and thermal spin-filtering effect (SFE) are core topics in spin caloritronics. Here we design several single-layer boron-nitrogen nanotubes (BNNTs) ... More
3D Face Reconstruction via Cascaded Regression in Shape SpaceSep 21 2015Oct 20 2016State-of-the-art methods reconstruct three dimensional (3D) face shape from a single image either by fitting 3D face model to the input image or by warping to a reference shape. However, they are often difficult to apply in real-world applications due ... More
Extraordinary transmission caused by symmetry breakingNov 18 2011Jan 29 2012The terahertz transmission properties of symmetrical and asymmetrical annular apertures arrays (AAAs) are investigated both experimentally and numerically. It is found that only odd order resonant modes are observed for the symmetrical structures but ... More
Regression-based Hypergraph Learning for Image Clustering and ClassificationMar 14 2016Inspired by the recently remarkable successes of Sparse Representation (SR), Collaborative Representation (CR) and sparse graph, we present a novel hypergraph model named Regression-based Hypergraph (RH) which utilizes the regression models to construct ... More
Efficient quantum circuit for singular value thresholdingNov 24 2017Jan 18 2019Singular value thresholding (SVT) operation is a fundamental core module in many mathematical models in computer vision and machine learning, particularly for many nuclear norm minimizing-based problems. We presented a quantum SVT (QSVT) algorithm which ... More
Cascaded Regressor based 3D Face Reconstruction from a Single Arbitrary View ImageSep 21 2015State-of-the-art methods reconstruct three-dimensional (3D) face shapes from a single image by fitting 3D face models to input images or by directly learning mapping functions between two-dimensional (2D) images and 3D faces. However, they are often difficult ... More
PixelLink: Detecting Scene Text via Instance SegmentationJan 04 2018Most state-of-the-art scene text detection algorithms are deep learning based methods that depend on bounding box regression and perform at least two kinds of predictions: text/non-text classification and location regression. Regression plays a key role ... More
Quantum walks on regular uniform hypergraphsSep 15 2017Sep 23 2017Quantum walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information stored inherently. ... More
Automatic Performance Debugging of SPMD Parallel ProgramsFeb 23 2010Automatic performance debugging of parallel applications usually involves two steps: automatic detection of performance bottlenecks and uncovering their root causes for performance optimization. Previous work fails to resolve this challenging issue in ... More
Similarity Analysis in Automatic Performance Debugging of SPMD Parallel ProgramsJun 07 2009Different from sequential programs, parallel programs possess their own characteristics which are difficult to analyze in the multi-process or multi-thread environment. This paper presents an innovative method to automatically analyze the SPMD programs. ... More
Taxonomy of particles in Ising spin chainsApr 04 2011Aug 10 2011The statistical mechanics of particles with shapes on a one-dimensional lattice is investigated in the context of the $s=1$ Ising chain with uniform nearest-neighbor coupling, quadratic single-site potential, and magnetic field, which supports four distinct ... More
Interlinking motifs and entropy landscapes of statistically interacting particlesAug 15 2011Apr 26 2012The s=1/2 Ising chain with uniform nearest-neighbor and next-nearest-neighbor coupling is used to construct a system of floating particles characterized by motifs of up to six consecutive local spins. The spin couplings cause the assembly of particles ... More
Unusually stable helical coil allotrope of phosphorusDec 01 2016We have identified an unusually stable helical coil allotrope of phosphorus. Our ab initio Density Functional Theory calculations indicate that the uncoiled, isolated straight 1D chain is equally stable as a monolayer of black phosphorus dubbed phosphorene. ... More
Polarimetric Convolutional Network for PolSAR Image ClassificationJul 09 2018Apr 03 2019The approaches for analyzing the polarimetric scattering matrix of polarimetric synthetic aperture radar (PolSAR) data have always been the focus of PolSAR image classification. Generally, the polarization coherent matrix and the covariance matrix obtained ... More
Extremality of graph entropy based on degrees of uniform hypergraphs with few edgesSep 27 2017Let $\mathcal{H}$ be a hypergraph with $n$ vertices. Suppose that $d_1,d_2,\ldots,d_n$ are degrees of the vertices of $\mathcal{H}$. The $t$-th graph entropy based on degrees of $\mathcal{H}$ is defined as $$ I_d^t(\mathcal{H}) =-\sum_{i=1}^{n}\left(\frac{d_i^{t}}{\sum_{j=1}^{n}d_j^{t}}\log\frac{d_i^{t}}{\sum_{j=1}^{n}d_j^{t}}\right) ... More
On the Chudnovsky-Seymour-Sullivan Conjecture on Cycles in Triangle-free DigraphsSep 14 2009For a simple digraph $G$ without directed triangles or digons, let $\beta(G)$ be the size of the smallest subset $X \subseteq E(G)$ such that $G\setminus X$ has no directed cycles, and let $\gamma(G)$ be the number of unordered pairs of nonadjacent vertices ... More
Neural Networks Models for Entity Discovery and LinkingNov 11 2016This paper describes the USTC_NELSLIP systems submitted to the Trilingual Entity Detection and Linking (EDL) track in 2016 TAC Knowledge Base Population (KBP) contests. We have built two systems for entity discovery and mention detection (MD): one uses ... More
Szegedy Quantum Walks with Memory on Regular GraphsMay 02 2019Quantum walks with memory(QWM) are a type of modified quantum walks that record the walker's latest path. The general model of coined QWM is presented in Phys. Rev. A 93, 042323 (2016). In this paper, we present general model of Szegedy QWM. Importantly, ... More
Automatic Performance Debugging of SPMD-style Parallel ProgramsMar 31 2011The simple program and multiple data (SPMD) programming model is widely used for both high performance computing and Cloud computing. In this paper, we design and implement an innovative system, AutoAnalyzer, that automates the process of debugging performance ... More
The Mason Test: A Defense Against Sybil Attacks in Wireless Networks Without Trusted AuthoritiesMar 24 2014Wireless networks are vulnerable to Sybil attacks, in which a malicious node poses as many identities in order to gain disproportionate influence. Many defenses based on spatial variability of wireless channels exist, but depend either on detailed, multi-tap ... More
Observation of electromagnetically induced Talbot effect in an atomic systemAug 01 2016Nov 29 2016We experimentally demonstrate the Talbot effect resulting from the repeated self-reconstruction of a spatially intensity-modulated probe field under the Fresnel near-field regime. By launching the probe beam into an optically induced atomic lattice (established ... More
Channel is more important than effectiveness in spreading dynamics on multiplex networksApr 18 2016Jun 21 2016In this paper we will study a spreading process on multiplex networks with link overlapping. For overlapping links, a node can transfer the information or pathogen to the same nodes through different layers, which increases epidemic effectiveness between ... More
First principles study of the vibronic coupling in positively charged C$_{60}^+$May 01 2019The orbital vibronic coupling parameters for C$_{60}^{+}$ are derived by using density functional theory calculations with hybrid B3LYP functional. The obtained parameters tend to be stronger than the estimates within local density approximation. Based ... More
Distributed Learning over Unreliable NetworksOct 17 2018May 16 2019Most of today's distributed machine learning systems assume {\em reliable networks}: whenever two machines exchange information (e.g., gradients or models), the network should guarantee the delivery of the message. At the same time, recent work exhibits ... More
Three-Dimensional Radiotherapy Dose Prediction on Head and Neck Cancer Patients with a Hierarchically Densely Connected U-net Deep Learning ArchitectureMay 25 2018Feb 04 2019The treatment planning process for patients with head and neck (H&N) cancer is regarded as one of the most complicated due to large target volume, multiple prescription dose levels, and many radiation-sensitive critical structures near the target. Treatment ... More
Two Birds with One Stone: Transforming and Generating Facial Images with Iterative GANNov 16 2017Mar 07 2018Generating high fidelity identity-preserving faces with different facial attributes has a wide range of applications. Although a number of generative models have been developed to tackle this problem, there is still much room for further improvement.In ... More
MFDL: A Multicarrier Fresnel Penetration Model based Device-Free Localization System leveraging Commodity Wi-Fi CardsJul 21 2017Device-free localization plays an important role in many ubiquitous applications. Among the different technologies proposed, Wi-Fi based technology using commercial devices has attracted much attention due to its low cost, ease of deployment, and high ... More
Scale Invariant Fully Convolutional Network: Detecting Hands EfficientlyJun 11 2019Existing hand detection methods usually follow the pipeline of multiple stages with high computation cost, i.e., feature extraction, region proposal, bounding box regression, and additional layers for rotated region detection. In this paper, we propose ... More
Searching for hidden-charm baryonium signals in QCD sum rulesMay 24 2016Nov 04 2016We give an explicit QCD sum rule investigation to hidden-charm baryonium states with the quark content $u\bar u d\bar d c\bar c$, spin $J=0/1/2/3$, and of both positive and negative parities. We systematically construct the relevant local hidden-charm ... More
Dynamical Jahn-Teller effect in the first excited C$_{60}^-$May 26 2019The Jahn-Teller problems of C$_{60}$ anions involving $t_{1g}$ next lowest unoccupied molecular orbital (NLUMO) were theoretically investigated. The orbital vibronic coupling parameters for the $t_{1g}$ orbitals were derived from the Kohn-Sham orbital ... More
Geographic Trough Filling for Internet DatacentersAug 28 2011To reduce datacenter energy consumption and cost, current practice has considered demand-proportional resource provisioning schemes, where servers are turned on/off according to the load of requests. Most existing work considers instantaneous (Internet) ... More
Synthetic spin-orbit coupling and topological polaritons in Janeys-Cummings latticesJan 25 2018May 09 2019The interaction between a photon and a qubit in the Janeys-Cummings (JC) model generates a kind of quasiparticle called polariton. While they are widely used in quantum optics, difficulties in engineering controllable coupling of them severely limit their ... More
Perceive Your Users in Depth: Learning Universal User Representations from Multiple E-commerce TasksMay 28 2018Tasks such as search and recommendation have become increas- ingly important for E-commerce to deal with the information over- load problem. To meet the diverse needs of di erent users, person- alization plays an important role. In many large portals ... More
An Empirical Scaling formula for fragments production in projectile fragmentation reactionsMay 21 2017A scaling phenomenon in the cross section for fragments has been found in the projectile fragmentation reaction, and an empirical scaling formula is proposed by considering the dependence of cross section on the size and asymmetry of the reaction system ... More
Regional economic status inference from information flow and talent mobilityFeb 14 2019Novel data has been leveraged to estimate socioeconomic status in a timely manner, however, direct comparison on the use of social relations and talent movements remains rare. In this letter, we estimate the regional economic status based on the structural ... More
Structured Attention Guided Convolutional Neural Fields for Monocular Depth EstimationMar 29 2018Recent works have shown the benefit of integrating Conditional Random Fields (CRFs) models into deep architectures for improving pixel-level prediction tasks. Following this line of research, in this paper we introduce a novel approach for monocular depth ... More
Joint time and frequency dissemination network over delay-stabilized fiber optic linksJan 22 2015A precise fiber-based time and frequency dissemination scheme for multiple users with a tree-like branching topology is proposed. Through this scheme, ultra-stable signals can be easily accessed online anywhere along the fiber without affecting other ... More
Epitaxial Growth of Two-Dimensional StaneneJun 04 2015Ultrathin semiconductors present various novel electronic properties. The first experimental realized two-dimensional (2D) material is graphene. Searching 2D materials with heavy elements bring the attention to Si, Ge and Sn. 2D buckled Si-based silicene ... More
Hermitian forms for affine Hecke algebrasDec 11 2013Mar 18 2015We study star operations for Iwahori-Hecke algebras and invariant hermitian forms for finite dimensional modules over (graded) affine Hecke algebras with a view towards a unitarity algorithm.
Coordinating Multiple Sources for Service Restoration to Enhance Resilience of Distribution SystemsOct 16 2018Jan 15 2019When a major outage occurs on a distribution system due to extreme events, microgrids, distributed generators, and other local resources can be used to restore critical loads and enhance resiliency. This paper proposes a decision-making method to determine ... More
Manipulating Steady Heat Conduction by Sensu-shaped Thermal MetamaterialsDec 01 2014The ability to design the control of heat flow has innumerable benefits in the design of electronic systems such as thermoelectric energy harvesters, solid-state lighting, and thermal imagers, where the thermal design plays a key role in performance and ... More
A Two-Layer Distributed Control Method for Islanded Networked Microgrid SystemsOct 19 2018Mar 29 2019This paper presents a two-layer, four-level distributed control method for networked microgrid (NMG) systems, taking into account the proprietary nature of microgrid (MG) owners. The proposed control architecture consists of a MG-control layer and a NMG-control ... More
Strong Coherent Light Amplification with Double Electromagnetically Induced Transparency CoherencesJul 29 2017We experimentally demonstrate coherent amplification of probe field in a tripod-type atoms driven by strong coupling, signal and weak probe fields. We suppress linear and nonlinear atomic absorptions for resonant and near resonant probe via double electromagnetically ... More
Quantum simulation of exotic PT-invariant topological nodal loop bands with ultracold atoms in an optical latticeJan 04 2016Apr 20 2016Since the well-known PT symmetry has its fundamental significance and implication in physics, where PT denotes the combined operation of space-inversion P and time-reversal T, it is extremely important and intriguing to completely classify exotic PT-invariant ... More
Normal-dispersion Microcombs Enabled by Controllable Mode InteractionsMar 20 2015We demonstrate a scheme incorporating dual coupled microresonators through which mode interactions are intentionally introduced and controlled for Kerr frequency comb (microcomb) generation in the normal dispersion region. Microcomb generation, repetition ... More
Topology Of Real And Angle Valued Maps And Graph Representations (A Brief Survey)May 20 2012(lecture delivered at the Congress of the Romanian mathematicians, Brasov, June 2011) Using graph representations a new class of computable topological invariants associated with a tame real or angle valued map were recently introduced, providing a theory ... More
Low-Luminosity Active Galactic Nuclei: Are They UV-Faint and Radio Loud?Feb 12 2007Mar 14 2007Low-luminosity AGNs are perceived to be radio loud and devoid of a ``big blue bump'', indicating a transition from a radiatively efficient, geometrically thin, accretion disc in high-luminosity AGNs, to a geometrically thick, radiatively inefficient accretion ... More
Quasar Lensing Statistics and Omega_Lambda: What Went Wrong?Jan 23 2005In the pre-WMAP, pre-Supernova-Ia-Hubble-diagram era, quasar lensing statistics stubbornly indicated low values of Omega_Lambda. In contrast, a number of recent lensing statistics studies either find the data support the standard Lambda-CDM picture, or ... More
Reverberation Mapping and Broad-Line Region ModelsSep 25 1996I review what we have learned about the BLR from reverberation mapping, point to some problems and complications that have emerged, and outline some future directions.
Notes on the construction of the moduli space of curvesMay 22 1998The purpose of these notes is to give an introduction to Deligne-Mumford stacks and their moduli spaces, with emphasis on the moduli problem for curves. The paper has 4 sections. In section 1 we discuss the general problem of constructing a moduli "space" ... More
Notes on Actions of Sets and Groups and Generalized Affine SpacesJul 13 2016Nov 17 2016Some well-known and less well-known or new notions related to group actions are surveyed. Some of these notions are used to generalize affine spaces. Actions are seen as functions with values in transformation monoids
The Taylor coefficients of the Jacobi theta constant $θ_3$Jul 16 2018Oct 17 2018We study the Taylor expansion around the point $x=1$ of a classical modular form, the Jacobi theta constant $\theta_3$. This leads naturally to a new sequence $(d(n))_{n=0}^\infty=1,1,-1,51,849,-26199,\ldots$ of integers, which arise as the Taylor coefficients ... More
Higher order matching polynomials and d-orthogonalitySep 09 2009Nov 16 2009We show combinatorially that the higher-order matching polynomials of several families of graphs are d-orthogonal polynomials. The matching polynomial of a graph is a generating function for coverings of a graph by disjoint edges; the higher-order matching ... More
Periodic points in random substitution subshiftsAug 17 2018We study various aspects of periodic points for random substitution subshifts. In order to do so, we introduce a new property for random substitutions called the disjoint images condition. We provide a procedure for determining the property for compatible ... More
Projections and Phase retrievalJun 01 2015We characterize collections of orthogonal projections for which it is possible to reconstruct a vector from the magnitudes of the corresponding projections. As a result we are able to show that in an $M$-dimensional real vector space a vector can be reconstructed ... More
Equivariant geometry and the cohomology of the moduli space of curvesJun 11 2010Aug 05 2011In this expository article we give a categorical definition of the integral cohomology ring of a stack. We show that for quotient stacks the categorical cohomology may be identified with equivariant cohomology. Via this identification we show that for ... More
The automorphism group of the pants complexJan 31 2002We show that the automorphism group of the complex of pants decompositions for a surface is isomorphic to the mapping class group for that surface.
A Universal Model of Global Civil UnrestJun 21 2012Civil unrest is a powerful form of collective human dynamics, which has led to major transitions of societies in modern history. The study of collective human dynamics, including collective aggression, has been the focus of much discussion in the context ... More
Is the CMB telling us that dark matter is weaker than weakly interacting?Jul 02 2013If moduli, or other long-lived heavy states, decay in the early universe in part into light and feebly interacting particles (such as axions), these decay products could account for the additional energy density in radiation that is suggested by recent ... More
Probing Supersymmetric Parameters With Astrophysical ObservationsJun 28 2006A wide range of techniques have been developed to search for particle dark matter, including direct detection, indirect detection, and collider searches. The prospects for the detection of neutralino dark matter is quite promising for each of these three ... More
Probing Exotic Physics With Cosmic NeutrinosOct 07 2005Traditionally, collider experiments have been the primary tool used in searching for particle physics beyond the Standard Model. In this talk, I will discuss alternative approaches for exploring exotic physics scenarios using high energy and ultra-high ... More
Fragmentation and Dijet Mass ResolutionJan 30 2004At the LHC the overlap of minimum bias events and the jet energy deposits in a calorimeter causes a degradation in the dijet mass resolution. Guided by QCD, a judicious set of cuts can be developed to mitigate this degradation.
Vector Boson Fusion and Quartic Boson CouplingsJun 17 2003One of the goals of the upcoming experiments at the LHC is the exploration of electroweak symmetry breaking in all aspects. In particular, the self-couplings of the vector gauge bosons are completely specified in the Standard Model, as are the couplings ... More
Quantization of heterotic strings in a Goedel/Anti de Sitter spacetime and chronology protectionOct 16 2003Jan 22 2004We show that a Goedel-like deformation of AdS3 in heterotic string theory can be realized as an exact string background. Indeed this class of solutions is obtained as an exactly marginal deformation of the conformal field theory describing the NS5/F1 ... More
Some aspects of profinite group theoryMar 29 2007A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.
The Chow ring of a Fulton-MacPherson compactificationJun 19 2015We give a short proof of a presentation of the Chow ring of the Fulton-MacPherson compactification of n points on an algebraic variety. The result can be found already in Fulton and MacPherson's original paper. However, there is an error in one of the ... More
Asymptotic Control for a Class of Piecewise Deterministic Markov Processes Associated to Temperate VirusesMay 28 2015We aim at characterizing the asymptotic behavior of value functions in the control of piece-wise deterministic Markov processes (PDMP) of switch type under nonexpansive assumptions. For a particular class of processes inspired by temperate viruses, we ... More
Volume and Self-Intersection of Differences of Two Nef ClassesMay 13 2015Let $\{\alpha\}$ and $\{\beta\}$ be nef cohomology classes of bidegree $(1,\,1)$ on a compact $n$-dimensional K\"ahler manifold $X$ such that the difference of intersection numbers $\{\alpha\}^n - n\,\{\alpha\}^{n-1}.\,\{\beta\}$ is positive. We solve ... More
A refinement of Betti numbers and homology in the presence of a continuous function II (the case of an angle valued map)Mar 06 2016Mar 25 2016This paper is a sequel of [2]. We propose a refinement of the Novikov-Betti numbers and of the Novikov homology (w.r. to a specified field) of a pair consisting of a compact ANR and a degree one integral cohomology class in the presence of a continuous ... More
Effects of the ISM on Detection of Low-frequency Gravitational WavesOct 30 2013Time variable delays due to radio wave propagation in the ionized interstellar medium are a substantial source of error in pulsar timing array efforts. We describe the physical origin of these effects, discussing dispersive and scattering effects separately. ... More
T-Duality in Gauged Linear Sigma-Models with TorsionJun 27 2013Oct 13 2015(0,2) gauged linear sigma models with torsion, corresponding to principal torus bundles over warped CY bases, provide a useful framework for getting exact statements about perturbative dualities in the presence of fluxes. In this context we first study ... More
A gradient estimate for harmonic functions sharing the same zerosJun 03 2013Let u, v be two harmonic functions in the disk of radius two which have exactly the same set Z of zeros. We observe that the gradient of \log |u/v| is bounded in the unit disk by a constant which depends on Z only. In case Z is empty this goes back to ... More
A Lower Bound for Generalized Dominating NumbersJan 30 2014May 04 2014We show a new proof for the fact that when $\kappa$ and $\lambda$ are infinite cardinals satisfying $\lambda ^ \kappa = \lambda$, the cofinality of the set of all functions from $\lambda$ to $\kappa$ ordered by everywhere domination is $2^\lambda$. An ... More
Quantities, Dimensions and Dimensional AnalysisAug 21 2014Apr 16 2015Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of dimensional analysis ... More
Weak Distributivity Implying DistributivityOct 08 2014Mar 21 2016Let $\mathbb{B}$ be a complete Boolean algebra. We show, as an application of a previous result of the author, that if $\lambda$ is an infinite cardinal and $\mathbb{B}$ is weakly $(\lambda^\omega, \omega)$-distributive, then $\mathbb{B}$ is $(\lambda, ... More
The solution to the Kadison--Singer Problem: yet another presentationJan 02 2015In the summer of 2013 Marcus, Spielman, and Srivastava gave a surprising and beautiful solution to the Kadison--Singer problem. The current presentation is slightly more didactical than other versions that have appeared since; it hopes to contribute to ... More
The topological version of free entropySep 04 2002Notions of topological free entropy and of free capacity are introduced in the $C^*$-algebra context. Basic properties, basic problems and connections to potential theory and random matrix theory are discussed.
Aspects of line operators of class S theoriesDec 11 2013Geometric picture of line operators of N=2 class S theories was found by imposing closure condition on operator product expansion (OPE) of line operators. In this paper, we first identify the geometric representation of ordinary Wilson-'t Hooft line operators ... More
Three dimensional Seiberg-like duality and tropical cluster algebraNov 04 2013Nov 19 2013Seiberg-like duality of three dimensional N=2 Chern-Simons-Matter quiver gauge theory is shown to have a chiral double tropical cluster algebra structure. We use cluster algebra results to study combinatorial aspects of these theories such as classification, ... More
BPS spectrum, wall crossing and quantum dilogarithm identityNov 29 2012BPS spectrum with finite number of states are found for higher rank four dimensional N=2 theory engineered from six dimensional A_{N-1} (2,0) theory on a Riemann surface with various kinds of defects. The wall crossing formula is interpreted as the quantum ... More
General Argyres-Douglas TheoryApr 10 2012Jul 12 2016We construct a large class of Argyres-Douglas type theories by compactifying six dimensional (2,0) A_N theory on a Riemann surface with irregular singularities. We give a complete classification for the choices of Riemann surface and the singularities. ... More
On Group-Like MagmoidsFeb 16 2019May 06 2019A magmoid is a non-empty set with a partial binary operation; group-like magmoids generalize group-like magmas such as semigroups, monoids and groups. In this article, we first consider the many ways in which the notions of associative multiplication, ... More
Excursion Probabilities of Isotropic and Locally Isotropic Gaussian Random Fields on ManifoldsApr 29 2015May 01 2015Let $X= \{X(p), p\in M\}$ be a centered Gaussian random field, where $M$ is a smooth Riemannian manifold. For a suitable compact subset $D\subset M$, we obtain the approximations to excursion probability $\mathbb{P}\{\sup_{p\in D} X(p) \ge u \}$, as $u\to ... More
A Criterion for the Viability of Stochastic Semilinear Control Systems via the Quasi-Tangency ConditionNov 02 2008May 08 2009In this paper we study a criterion for the viability of stochastic semilinear control systems on a real, separable Hilbert space. The necessary and sufficient conditions are given using the notion of stochastic quasi-tangency. As a consequence, we prove ... More
Riemann Surfaces and 3-Regular GraphsFeb 17 2002In this thesis we consider a way to construct a rich family of compact Riemann Surfaces in a combinatorial way. Given a 3-regualr graph with orientation, we construct a finite-area hyperbolic Riemann surface by gluing triangles according to the combinatorics ... More
Alternative to Morse-Novikov Theory for closed 1-form (I)Mar 01 2019Apr 04 2019This paper extends the Alternative to Morse-Novikov Theory we have proposed in [1] from real- and angle-valued map to closed 1-forms. For a topological closed 1-form on a compact ANR, a concept generalizing closed differential 1-form on a compact manifold, ... More
Barcodes in level and sub level persistence and Morse-Novikov theoryMay 31 2018In this note we recall the relations between the barcodes in level and sub-level persistence and make precise their relation with the Morse-Novikov complex of a Morse real- or angle-valued map. The results in this papers are implicit in my previous work(w.collaborators), ... More
The effect of curvature on convexity properties of harmonic functions and eigenfunctionsDec 19 2011Jul 25 2012We give a proof of the Donnelly-Fefferman growth bound of Laplace-Beltrami eigenfunctions which is probably the easiest and the most elementary one. Our proof also gives new quantitative geometric estimates in terms of curvature bounds which improve and ... More
On the Inner Radius of Nodal DomainsNov 14 2005Dec 20 2006Let M be a closed Riemannian manifold. We consider the inner radius of a nodal domain for a large eigenvalue \lambda. We give upper and lower bounds on the inner radius of the type C/\lambda^k. Our proof is based on a local behavior of eigenfunctions ... More
The 2-color Rado number of $x_1+x_2+\cdots +x_n=y_1+y_2+\cdots +y_k$Feb 24 2014Mar 10 2014In 1982, Beutelspacher and Brestovansky determined the 2-color Rado number of the equation $$x_1+x_2+\cdots +x_{m-1}=x_m$$ for all $m\geq 3.$ Here we extend their result by determining the 2-color Rado number of the equation $$x_1+x_2+\cdots +x_n=y_1+y_2+\cdots ... More