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
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
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.
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
Testing a class of non-Kerr metrics with hot spots orbiting SgrA$^*$Nov 10 2014Dec 19 2014SgrA$^*$, the supermassive black hole candidate at the Galactic Center, exhibits flares in the X-ray, NIR, and sub-mm bands that may be interpreted within a hot spot model. Light curves and images of hot spots orbiting a black hole are affected by a number ... More
Long-wavelength deformations and vibrational modes in empty and liquid-filled microtubules and nanotubes: A theoretical studyApr 27 2017We propose a continuum model to predict long-wavelength vibrational modes of empty and liquid-filled tubules that are very hard to reproduce using the conventional force-constant matrix approach based on atomistic ab initio calculation. We derive simple ... More
Continuum approach for long-wavelength acoustic phonons in quasi-2D structuresOct 04 2016As an alternative to atomistic calculations of long-wavelength acoustic modes of atomically thin layers, which are known to converge very slowly, we propose a quantitatively predictive and physically intuitive approach based on continuum elasticity theory. ... More
Epidemic Variability in Hierarchical Geographical Networks with Human Activity PatternsApr 03 2012Recently, some studies have revealed that non-Poissonian statistics of human behaviors stem from the hierarchical geographical network structure. On this view, we focus on epidemic spreading in the hierarchical geographical networks, and study how two ... More
Multigrid Backprojection Super-Resolution and Deep Filter VisualizationSep 25 2018Jan 29 2019We introduce a novel deep-learning architecture for image upscaling by large factors (e.g. 4x, 8x) based on examples of pristine high-resolution images. Our target is to reconstruct high-resolution images from their downscale versions. The proposed system ... More
Is Twisted Bilayer Graphene Stable under Shear?Nov 01 2018In twisted bilayer graphene (TBLG), extremely small deviations from the magic twist angle $\theta_m{\approx}1.08^\circ$ change its electronic structure near the Fermi level drastically, causing a meV-wide flat band to appear or disappear. In view of such ... 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
Microscopic Mechanism of the Helix-to-Layer Transformation in Elemental Group VI SolidsJul 19 2018We study the conversion of bulk Se and Te, consisting of intertwined a helices, to structurally very dissimilar, atomically thin two-dimensional (2D) layers of these elements. Our ab initio calculations reveal that previously unknown and unusually stable ... More
Super-pixel cloud detection using Hierarchical Fusion CNNOct 19 2018Cloud detection plays a very important role in the process of remote sensing images. This paper designs a super-pixel level cloud detection method based on convolutional neural network (CNN) and deep forest. Firstly, remote sensing images are segmented ... 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
An audio CAPTCHA to distinguish humans from computersJun 12 2013CAPTCHAs are employed as a security measure to differentiate human users from bots. A new sound-based CAPTCHA is proposed in this paper, which exploits the gaps between human voice and synthetic voice rather than relays on the auditory perception of human. ... More
Joint Face Alignment and 3D Face Reconstruction with Application to Face RecognitionAug 09 2017Dec 22 2018Face alignment and 3D face reconstruction are traditionally accomplished as separated tasks. By exploring the strong correlation between 2D landmarks and 3D shapes, in contrast, we propose a joint face alignment and 3D face reconstruction method to simultaneously ... 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
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
Designing isoelectronic counterparts to layered group V semiconductorsMay 29 2015In analogy to III-V compounds, which have significantly broadened the scope of group IV semiconductors, we propose IV-VI compounds as isoelectronic counterparts to layered group V semiconductors. Using {\em ab initio} density functional theory, we study ... More
Knowledge Graph Embedding with Entity Neighbors and Deep Memory NetworkAug 11 2018Knowledge Graph Embedding (KGE) aims to represent entities and relations of knowledge graph in a low-dimensional continuous vector space. Recent works focus on incorporating structural knowledge with additional information, such as entity descriptions, ... 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
Dimension-free estimates for the vector-valued variational operatorsJul 25 2018Sep 03 2018In this paper, We study dimension-free $L^p$ estimates for UMD lattice-valued $q$-variations of Hardy-Littlewood averaging operators associated with the Euclidean balls.
Jammed disks in narrow channel: criticality and ordering tendenciesJul 23 2012Apr 17 2013A system of identical disks is confined to a narrow channel, closed off at one end by a stopper and at the other end by a piston. All surfaces are hard and frictionless. A uniform gravitational field is directed parallel to the plane of the disks and ... More
Two-dimensional phosphorus carbide: Competition between sp2 and sp3 bondingApr 19 2016We propose previously unknown allotropes of phosphorus carbide (PC) in the stable shape of an atomically thin layer. Different stable geometries, which result from the competition between sp2 bonding found in graphitic C and sp3 bonding found in black ... 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
Two novel approaches for photometric redshift estimation based on SDSS and 2MASS databasesJul 16 2007We investigate two training-set methods: support vector machines (SVMs) and Kernel Regression (KR) for photometric redshift estimation with the data from the Sloan Digital Sky Survey Data Release 5 and Two Micron All Sky Survey databases. We probe the ... 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
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
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
Disks in a narrow channel jammed by gravity and centrifuge: profiles of pressure, mass density and entropy densityDec 20 2013Apr 18 2014This work investigates jammed granular matter under conditions that produce heterogeneous mass distributions on a mesoscopic scale. We consider a system of identical disks that are confined to a narrow channel, open at one end and closed off at the other ... More
X-ray spectropolarimetric measurements of the Kerr metricApr 26 2015Aug 14 2015It is thought that the spacetime geometry around black hole candidates is described by the Kerr solution, but an observational confirmation is still missing. Today, the continuum-fitting method and the analysis of the iron K$\alpha$ line cannot unambiguously ... More
Extremal Entanglement For Triqubit Pure StatesAug 01 2004Feb 23 2005A complete analysis of entangled triqubit pure states is carried out based on a new simple entanglement measure. An analysis of all possible extremally entangled pure triqubit states with up to eight terms is shown to reduce, with the help of SLOCC transformations, ... More
On 3D Face Reconstruction via Cascaded Regression in Shape SpaceSep 21 2015Apr 18 2017Cascaded regression has been recently applied to reconstructing 3D faces from single 2D images directly in shape space, and achieved state-of-the-art performance. This paper investigates thoroughly such cascaded regression based 3D face reconstruction ... 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
Generalized Hofstadter model on a cubic optical lattice: From nodal bands to the three-dimensional quantum Hall effectApr 18 2017We propose that a tunable generalized three-dimensional Hofstadter Hamiltonian can be realized by engineering the Raman-assisted hopping of ultracold atoms in a cubic optical lattice. The Hamiltonian describes a periodic lattice system under artificial ... More
The USTC-NEL Speech Translation system at IWSLT 2018Dec 06 2018This paper describes the USTC-NEL system to the speech translation task of the IWSLT Evaluation 2018. The system is a conventional pipeline system which contains 3 modules: speech recognition, post-processing and machine translation. We train a group ... 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
Searching for hidden-charm baryonium signals in QCD sum rulesMay 24 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
Infer Implicit Contexts in Real-time Online-to-Offline RecommendationJul 08 2019Understanding users' context is essential for successful recommendations, especially for Online-to-Offline (O2O) recommendation, such as Yelp, Groupon, and Koubei. Different from traditional recommendation where individual preference is mostly static, ... 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
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
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
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
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
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
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
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
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
Nuclear geometry effect and transport coefficient in semi-inclusive lepton-production of hadrons off nucleiNov 03 2015Hadron production in semi-inclusive deep-inelastic scattering of leptons from nuclei is an ideal tool to determine and constrain the transport coefficient in cold nuclear matter. The leading-order computations for hadron multiplicity ratios are performed ... More
Roles of the spreading scope and effectiveness in spreading dynamics on multiplex networksApr 18 2016Nov 28 2017Comparing with single networks, the multiplex networks bring two main effects on the spreading process among individuals. First, the pathogen or information can be transmitted to more individuals through different layers at one time, which enlarges the ... 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
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
Discovering Communities of Malapps on Android-based Mobile Cyber-physical SystemsApr 05 2018Android-based devices like smartphones have become ideal mobile cyber-physical systems (MCPS) due to their powerful processors and variety of sensors. In recent years, an explosively and continuously growing number of malicious applications (malapps) ... 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
Quadratic Jahn-Teller effect of fullerene anionsMay 21 2018Jul 02 2018The quadratic Jahn-Teller effect of C$_{60}^{n-}$ ($n=$ 1-5) is investigated from the first principles. Employing the density functional theory calculations with hybrid functional, the quadratic vibronic coupling constants of C$_{60}^-$ were derived. ... More
The D-wave heavy-light mesons from QCD sum rulesOct 07 2014Dec 27 2014We study the D-wave c_bar s heavy meson doublets (1^-,2^-) and (2^-,3^-) using the method of QCD sum rule in the framework of heavy quark effective theory. Choosing the same threshold values omega_c around 2.7 Gev, we calculate the masses of the 1^- and ... More
Maximizing Mutual Information for TacotronAug 30 2019End-to-end speech synthesis method such as Tacotron, Tacotron2 and Transformer-TTS already achieves close to human quality performance. However compared to HMM-based method or NN-based frame-to-frame regression method, it is prone to some bad cases, such ... More
Cycle In Cycle Generative Adversarial Networks for Keypoint-Guided Image GenerationAug 02 2019In this work, we propose a novel Cycle In Cycle Generative Adversarial Network (C$^2$GAN) for the task of keypoint-guided image generation. The proposed C$^2$GAN is a cross-modal framework exploring a joint exploitation of the keypoint and the image data ... 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.
Generic unipotent standard modulesSep 29 2009Apr 19 2012Using Lusztig's geometric classification, we find the reducibility points of a standard module for the affine Hecke algebra, in the case when the inducing data is generic. This recovers the known result of Muic-Shahidi for representations of split p-adic ... More
Unitary equivalences for reductive p-adic groupsSep 28 2009Apr 07 2011We establish a transfer of unitarity for a Bernstein component of the category of smooth representations of a reductive p-adic group to the associated Hecke algebra, in the framework of the theory of types, whenever the Hecke algebra is an affine Hecke ... More
Non-trivial topology in a layered Dirac nodal-line semimetal candidate SrZnSb$_2$ with distorted Sb square netsJul 06 2018Aug 23 2019Dirac states hosted by Sb/Bi square nets are known to exist in the layered antiferromagnetic AMnX$_2$ (A = Ca/Sr/Ba/Eu/Yb, X=Sb/Bi) material family the space group to be P4/nmm or I4/mmm. In this paper, we present a comprehensive study of quantum transport ... More
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
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
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
Hydration lubrication of polyzwitterionic brushes leads to nearly friction- and adhesion-free droplet motionJun 17 2019Jul 02 2019Recently, there has been much progress in the design and application of oil-repellent superoleophobic surfaces. Polyzwitterionic brush surfaces are of particular interest, because of their ability to repel oil under water, even in the absence of micro-/nano-structures. ... 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
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
Estimating the trace-free Ricci tensor in Ricci flowNov 07 2007An important and natural question in the analysis of Ricci flow singularity formation in dimensions four and above is as follows: What are the weakest conditions that provide control of the norm of the Riemann curvature tensor? In this short note, we ... More
The Schlesinger System and the Riemann-Hilbert ProblemSep 16 2003We generalize some classical results for the Schlesinger system of partial differential equations and give the explicit form of its solution, associated with rational matrix functions in general position.
Adiabatic Limit and Deformations of Complex StructuresJan 13 2019Mar 14 2019Based on our recent adaptation of the adiabatic limit construction to the case of complex structures, we give a new proof of the fact, that we first proved in 2009 and 2010, that the deformation limiting manifold of any holomorphic family of Moishezon ... 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
Diffusion of Confidential Information on NetworksJan 01 2011Mar 11 2011This is a natural generalization of the previous work by Dan, "Modeling and Simulation of Diffusion Phenomena on Social Networks," to appear in The proceedings of 2011 Third International Conference on Computer Modeling and Simulation. In this paper, ... More
Resolution of singularities of complex algebraic varieties and their familiesNov 27 2017We discuss Hironaka's theorem on resolution of singularities in charactetistic 0 as well as more recent progress, both on simplifying and improving Hironaka's method of proof and on new results and directions on families of varieties, leading to joint ... More
Shortest paths in the Tower of Hanoi graph and finite automataOct 08 2003We present efficient algorithms for constructing a shortest path between two states in the Tower of Hanoi graph, and for computing the length of the shortest path. The key element is a finite-state machine which decides, after examining on the average ... More
Inflation and the Higgs ScalarDec 05 2014This note makes a self-contained exposition of the basic facts of big bang cosmology as they relate to inflation. The fundamental problems with that model are then explored. A quartic scalar potential model of inflation is evaluated which provides the ... More
Hot Hands, Streaks and Coin-flips: Numerical Nonsense in the New York TimesDec 29 2015The existence of "Hot Hands" and "Streaks" in sports and gambling is hotly debated, but there is no uncertainty about the recent batting-average of the New York Times: it is now two-for-two in mangling and misunderstanding elementary concepts in probability ... More
On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta functionMar 12 2015Oct 04 2016We derive new results about properties of the Witten zeta function associated with the group SU(3), and use them to prove an asymptotic formula for the number of n-dimensional representations of SU(3) counted up to equivalence. Our analysis also relates ... More
Coding in the automorphism group of a computably categorical structureMay 20 2019Using new techniques for controlling the categoricity spectrum of a structure, we construct a structure with degree of categoricity but infinite spectral dimension, answering a question of Bazhenov, Kalimulin and Yamaleev. Using the same techniques, we ... More
On simple derivations and the group of polynomial automorphismsAug 23 2018Sep 10 2018In the paper, we first give an equivalent statement about $\operatorname{Aut}({\bf K}[x_1,\ldots,x_n])_D=\{id\}$ and some properties of $D$ if $D$ is a simple derivation. Then we study the subgroup of ${\bf K}$-automorphisms of ${\bf K}[x_1,\ldots,x_n]$ ... More
Polynomial maps with nilpotent Jacobians in dimension three IOct 08 2017In this paper, we first prove that $u,v,h$ are linearly dependent over ${\bf K}$ if $JH$ is nilpotent and $H$ has the form: $H=(u(x,y,z),v(u,h),h(x,y))$ with $H(0)=0$ or $H=(u(x,y),v(u,h),h(x,y,z))$ with $H(0)=0$. Then we classify polynomial maps of the ... More
A Hamiltonian approach to implicit systems, generalized solutions and applications in optimizationAug 28 2014Oct 21 2016We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the usual implicit ... More
Explicit reduction theory for SU(2,1;Z[i])Jan 04 2006Let Gamma\D be an arithmetic quotient of a symmetric space of non-compact type. A spine D_0 is a Gamma-equivariant deformation retraction of D with dimension equal to the virtual cohomological dimension of Gamma. We explicitly construct a spine for the ... 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 2-color Rado Number of $x_1+x_2+\cdots +x_{m-1}=ax_m,$ IIJun 04 2013Jan 30 2014In the first installment of this series, we proved that, for every integer $a\geq 3$ and every $m\geq 2a^2-a+2$, the 2-color Rado number of $x_1 + x_2 + \cdots + x_{m-1} = ax_m$ is $\lceil\frac{m-1}{a} \lceil\frac{m-1}{a} \rceil\rceil$. Here we obtain ... More
Representation of One as the Sum of Unit FractionsFeb 23 2009Apr 15 2009One is expressed as the sum of the reciprocals of a certain set of integers. We give an elegant proof to the fact applying the polynomial theorem and basic calculus.
Bott--Kitaev periodic table and index theoryOct 04 2017We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev. An effective Hamiltonian determines the analytical index, which can be computed by a topological ... More
A Simple Proof of a Theorem by Uhlenbeck and YauNov 04 2003A subbundle of a Hermitian vector bundle $(E, h)$ can be metrically and differentiably defined by the orthogonal projection onto this subbundle. A weakly holomorphic subbundle of a Hermitian holomorphic bundle is, by definition, an orthogonal projection ... More
Faster Projection-free Convex Optimization over the SpectrahedronMay 20 2016Minimizing a convex function over the spectrahedron, i.e., the set of all positive semidefinite matrices with unit trace, is an important optimization task with many applications in optimization, machine learning, and signal processing. It is also notoriously ... More
Bijections from weighted Dyck paths to Schroeder pathsJun 10 2010Jun 11 2010Kim and Drake used generating functions to prove that the number of 2-distant noncrossing matchings, which are in bijection with little Schroeder paths, is the same as the weight of Dyck paths in which downsteps from even height have weight 2. This work ... More