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Pressure-induced enhancement of non-polar to polar transition temperature in metallic LiOsO$_3$Jun 02 2018Jun 06 2018LiOsO$_3$ undergoes a continuous transition from a centrosymmetric $R\bar{3}c$ structure to a polar $R3c$ structure at $T_s=140$~K. By combining transport measurements and first-principles calculations, we find that $T_s$ is enhanced by applied pressure, ... More

Nonsaturating large magnetoresistance in the high carrier density nonsymmorphic metal CrPMar 14 2019The band structure of high carrier density metal CrP features an interesting crossing at the Y point of the Brillouin zone. The crossing, which is protected by the nonsymmorphic symmetry of the space group, results in a hybrid, semi-Dirac-like energy-momentum ... More

Angular dependence of the upper critical field in the high-pressure $1T'$ phase of MoTe$_2$Mar 13 2019Superconductivity in the type-II Weyl semimetal candidate MoTe$_2$ has attracted much attention due to the possible realization of topological superconductivity. Under applied pressure, the superconducting transition temperature is significantly enhanced, ... More

Multipole order and global/site symmetry in the hidden order phase of URu2Si2Sep 19 2014Oct 20 2014On the basis of group theory and the first-principles calculations, we investigate high-rank multipole orderings in URu2Si2, which have been proposed as a genuine primary order parameter in the hidden order phase below 17.5K. We apply Shubnikov group ... More

The mass distribution of dwarf spheroidal galaxies from stellar kinematics: Draco, Ursa Minor and FornaxFeb 08 2007We model three dSph galaxies, Draco, Ursa Minor and Fornax, as axisymmetric stellar systems embedded in spherical dark-matter potentials, which are in dynamical equilibrium without significant external tidal forces. We construct non-parametric two- and ... More

Emergent loop-nodal s$_\pm$-wave superconductivity in CeCu$_2$Si$_2$: similarities to the iron-based superconductorsApr 28 2015Heavy-fermion superconductors are prime candidates for novel electron-pairing states due to the spin-orbital coupled degrees of freedom and electron correlations. Superconductivity in CeCu$_2$Si$_2$ discovered in 1979, which is a prototype of unconventional ... More

Active Sensing of Social NetworksJan 21 2016This paper develops an active sensing method to estimate the relative weight (or trust) agents place on their neighbors' information in a social network. The model used for the regression is based on the steady state equation in the linear DeGroot model ... More

Key Exchange Protocol in the Trusted Data Servers ContextSep 11 2015The aim of this technical report is to complement the work in [To et al. 2014] by proposing a Group Key Exchange protocol so that the Querier and TDSs (and TDSs themselves) can securely create and exchange the shared key. Then, the security of this protocol ... More

Attractors for semilinear wave equations with localized damping and external forcesMay 08 2019This paper is concerned with long-time dynamics of semilinear wave equations defined on bounded domains of $\mathbb{R}^3$ with cubic nonlinear terms and locally distributed damping. The existence of regular finite-dimensional global attractors established ... More

Magnetically Driven Warping and Precession of Accretion Disks: Implications for "Exotic" Stellar VariabilitiesNov 13 2002The inner region of the accretion disk around a magnetized star is subjected to magnetic torques that induce warping and precession of the disk. These torques arise from interactions between the stellar field and the induced electric currents in the disk. ... More

Secular Instability of g-Modes in Rotating Neutron StarsJun 29 1998Apr 09 1999Gravitational radiation tends to drive gravity modes in rotating neutron stars unstable. For an inviscid star, the instability sets in when the rotation frequency is about 0.7 times the corresponding mode frequency of the nonrotating star. Neutron stars ... More

Tidal Stablization of Neutron Stars and White DwarfsMay 16 1996What happens to a neutron star or white dwarf near its maximum mass limit when it is brought into a close binary orbit with a companion? Such situation may occur in the progenitors of Type Ia supernovae and in coalescing neutron star binaries. Using an ... More

Quantizing G-connections via the tangent groupoidOct 16 2012A description of the space of G-connections using the tangent groupoid is given. As the tangent groupoid parameter is away from zero, the G-connections act as convolution operators on a Hilbert space. The gauge action is examined in the tangent groupoid ... More

Ferromagnetism of electrons in solid quark cluster starsDec 14 2015In this paper we are trying to solve the problem of the origin of strong magnetic fields in the framework of solid quark-cluster stars. We propose that, under the Coulomb repulsion, the electrons inside the stars could spontaneously magnetized and become ... More

An extremal problem on potentially $K_{m}-P_{k}$-graphic sequencesSep 24 2004Jul 07 2006A sequence $S$ is potentially $K_{m}-P_{k}$ graphical if it has a realization containing a $K_{m}-P_{k}$ as a subgraph. Let $\sigma(K_{m}-P_{k}, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $\sigma(S)\geq \sigma(K_{m}-P_{k}, ... More

The smallest degree sum that yields potentially $C_k$-graphical sequenceJun 06 2002Aug 22 2004In this paper we consider a variation of the classical Tur\'{a}n-type extremal problems. Let $S$ be an $n$-term graphical sequence, and $\sigma(S)$ be the sum of the terms in $S$. Let $H$ be a graph. The problem is to determine the smallest even $l$ such ... More

A Generalization of Aztec DragonsApr 01 2015Oct 28 2015Aztec dragons are lattice regions first introduced by James Propp, which have the number of tilings given by a power of $2$. This family of regions has been investigated further by a number of authors. In this paper, we consider a generalization of the ... More

Proof of a conjecture of Kenyon and Wilson on semicontiguous minorsJul 09 2015Jul 31 2018Kenyon and Wilson showed how to test if a circular planar electrical network with $n$ nodes is well-connected by checking the positivity of $\binom{n}{2}$ central minors of the response matrix. Their test is based on the fact that any contiguous minor ... More

Tiling enumeration of doubly-intruded halved hexagonsDec 31 2017Feb 08 2019Inspired by Propp's intruded Aztec diamond regions, we consider halved hexagons in which two aligned arrays of triangular holes have been removed from their boundaries. Unlike the intruded Aztec diamonds (whose numbers of domino tilings contain some large ... More

New aspects of regions whose tilings are enumerated by perfect powersSep 24 2013Dec 04 2013In 2003, Ciucu presented a unified way to enumerate tilings of lattice regions by using a certain Reduction Theorem (Ciucu, Perfect Matchings and Perfect Powers, Journal of Algebraic Combinatorics, 2003). In this paper we continue this line of work by ... More

First-principles study of magnetic properties in Fe-ladder compound BaFe2S3Jul 21 2015We study the magnetic, structural, and electronic properties of the recently discovered iron- based superconductor BaFe2S3 based on density functional theory with the generalized gradient approximation. The calculations show that the magnetic alignment ... More

Estimation of the Hurst and the stability indices of a $H$-self-similar stable processJun 18 2015Oct 18 2017In this paper we estimate both the Hurst and the stable indices of a H-self-similar stable process. More precisely, let $X$ be a $H$-sssi (self-similar stationary increments) symmetric $\alpha$-stable process. The process $X$ is observed at points $\frac{k}{n}$, ... More

Singular limit and long-time dynamics of Bresse systemsNov 20 2015Oct 07 2016The Bresse system is a valid model for arched beams which reduces to the classical Timoshenko system when the arch curvature $\ell=0$. Our first result shows the Timoshenko system as a singular limit of the Bresse system as $\ell \to 0$. The remaining ... More

A $q$-enumeration of generalized plane partitionsFeb 05 2015Aug 04 2015MacMahon proved a simple product formula for the generating function of the plane partitions fitting in a given rectangular box. The theorem implies the number of lozenge tilings of a semi-regular hexagon on the triangular lattice. By investigating the ... More

Lozenge tilings of a halved hexagon with an array of triangles removedOct 20 2016Proctor's work on staircase plane partitions yields an enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Recently, Rohatgi extended this tiling enumeration by proving an exact tiling formula for a halved hexagon with a triangle ... More

Word and Document Embeddings based on Neural Network ApproachesNov 18 2016Data representation is a fundamental task in machine learning. The representation of data affects the performance of the whole machine learning system. In a long history, the representation of data is done by feature engineering, and researchers aim at ... More

A proof to the Riemann HypothesisAug 08 2016Dec 05 2018The properties of several functions are employed to investigate the zeros of the Riemann zeta function $\zeta(a+bi)$. We show that if $0<a<1$, the zeros of the zeta function have the form $\frac{1}{2}+ib$ where $i=\sqrt{-1}$.

Bilinear endpoint estimates for Calderón commutator with rough kernelOct 26 2017In this paper, we establish some bilinear endpoint estimates of Calder\'on commutator $\mathcal{C}[\nabla A,f](x)$ with a homogeneous kernel when $\Omega\in L\log^+L(\mathbf{S}^{d-1})$. More precisely, we prove that $\mathcal{C}[\nabla A,f]$ maps $L^q(\mathbb{R}^d)\times ... More

The smallest degree sum that yields potentially K_{r+1}-Z-graphical SequencesAug 10 2006Nov 17 2009Let $K_{m}-H$ be the graph obtained from $K_{m}$ by removing the edges set $E(H)$ of the graph $H$ ($H$ is a subgraph of $K_{m}$). We use the symbol $Z_4$ to denote $K_4-P_2.$ A sequence $S$ is potentially $K_{m}-H$-graphical if it has a realization containing ... More

An extremal problem on potentially $K_{p,1,1}$-graphic sequencesAug 22 2004Jul 07 2006A sequence $S$ is potentially $K_{p,1,1}$ graphical if it has a realization containing a $K_{p,1,1}$ as a subgraph, where $K_{p,1,1}$ is a complete 3-partite graph with partition sizes $p,1,1$. Let $\sigma(K_{p,1,1}, n)$ denote the smallest degree sum ... More

A Lower Bound for the Number of Edges in a Graph Containing No Two Cycles of the Same LengthJun 06 2002Jun 07 2002In 1975, P. Erd\"{o}s proposed the problem of determining the maximum number $f(n)$ of edges in a graph of $n$ vertices in which any two cycles are of different lengths. In this paper, it is proved that $$f(n)\geq n+32t-1$$ for $t=27720r+169 (r\geq 1)$ ... More

Multilinear estimates for Calderón commutatorsDec 25 2017Aug 01 2018In this paper, we investigate the multilinear boundedness properties of the higher ($n$-th) order Calder\'on commutator for dimensions larger than two. We establish all multilinear endpoint estimates for the target space $L^{\frac{d}{d+n},\infty}(\mathbb{R}^d)$, ... More

A note on a 2-enumeration of antisymmetric monotone trianglesOct 29 2014Jul 18 2015In their unpublished work, Jockusch and Propp showed that a 2-enumeration of antisymmetric monotone triangles is given by a simple product formula. On the other hand, the author proved that the same formula counts the domino tilings of the quartered Aztec ... More

Enumeration of Hybrid Domino-Lozenge Tilings III: Centrally Symmetric TilingsSep 11 2016Dec 25 2018We use the subgraph replacement method to investigate new properties of the tilings of regions on the square lattice with diagonals drawn in. In particular, we show that the centrally symmetric tilings of a generalization of the Aztec diamond are always ... More

The rightness of the Riemann hypothesisAug 08 2016Aug 11 2016Applying the properties of increasing functions and the limitation theory of one variable, we show that the Riemann hypothesis is correct. Namely, it is proved that all zeros of {\zeta} function are 1/2+b_0i where b_0 represents many constants.

Enumeration of Hybrid Domino-Lozenge Tilings III: Symmetric TilingsSep 11 2016We use the subgraph replacement method to investigate new properties of regions on the square lattice with diagonals drawn in. In particular, we show that cyclically symmetric tilings of a generalization of the Aztec diamond are always enumerated by a ... More

Proof of a conjecture of Kenyon and Wilson on semicontiguous minorsJul 09 2015Oct 26 2015Kenyon and Wilson showed how to test if a circular planar electrical network with $n$ nodes is well-connected by checking the positivity of $\binom{n}{2}$ central minors of the response matrix (arXiv:1411.7425). Their test is based on the fact that any ... More

Matter in Strong Magnetic FieldsSep 20 2000Jan 24 2001The properties of matter are significantly modified by strong magnetic fields, $B>>2.35\times 10^9$ Gauss ($1 G =10^{-4} Tesla$), as are typically found on the surfaces of neutron stars. In such strong magnetic fields, the Coulomb force on an electron ... More

Transonic Magnetic Slim Accretion Disks and kilo-Hertz Quasi-Periodic Oscillations in Low-Mass X-Ray BinariesNov 12 1997Feb 24 1998The inner regions of accretion disks of weakly magnetized neutron stars are affected by general relativity and stellar magnetic fields. Even for field strengths sufficiently small so that there is no well-defined magnetosphere surrounding the neutron ... More

Theory of Disk Accretion onto Magnetic StarsFeb 09 2014Disk accretion onto magnetic stars occurs in a variety of systems, including accreting neutron stars (with both high and low magnetic fields), white dwarfs, and protostars. We review some of the key physical processes in magnetosphere-disk interaction, ... More

Merging neutron star binaries: equation of state and electrodynamicsDec 25 2012Merging neutron star (NS) binaries may be detected by ground-based gravitational wave (GW) interferometers (e.g. LIGO/VIRGO) within this decade and may also generate electromagnetic radiation detectable by wide-field, fast imaging telescopes that are ... More

Tidal Dissipation in Planet-Hosting Stars: Damping of Spin-Orbit Misalignment and Survival of Hot JupitersSep 22 2011Jun 19 2012Observations of hot Jupiters around solar-type stars with very short orbital periods (~day) suggest that tidal dissipation in such stars is not too efficient so that these planets can survive against rapid orbital decay. This is consistent with recent ... More

Neutron Star Kicks and Supernova AsymmetryDec 19 2003Observations over the last decade have shown that neutron stars receive a large kick velocity (of order a hundred to a thousand km/s) at birth. The physical origin of the kicks and the related supernova asymmetry is one of the central unsolved mysteries ... More

Warping of Accretion Disks with Magnetically Driven Outflows: A Possible Origin for Jet PrecessionMay 31 2003Current theoretical models for the outflows/jets from AGN, X-ray binaries and young stellar objects involve large-scale magnetic fields threading an underlying accretion disk. We suggest that such a disk is subjected to warping instability and retrograde ... More

Physics of Neutron Star KicksDec 27 1999It is no longer necessary to `sell' the idea of pulsar kicks, the notion that neutron stars receive a large velocity (a few hundred to a thousand km s$^{-1}$) at birth. However, the origin of the kicks remains mysterious. We review the physics of different ... More

Magnetically Driven Warping, Precession and Resonances in Accretion DisksApr 09 1999Dec 27 1999The inner region of the accretion disk onto a rotating magnetized central star (neutron star, white dwarf or T Tauri star) is subjected to magnetic torques which induce warping and precession of the disk. The origin of these torques lies in the interaction ... More

Superfluidity of Hydrogenlike Gas in a Strong Magnetic Field ?May 10 1995The recent claim that in a strong magnetic field hydrogenlike gas (e.g., excitons in certain semiconductors, neutron star surface layers) becomes superfluid is refuted. Molecules form by strong covalent bond along the magnetic field axis, which prohibits ... More

Resonant Oscillations and Tidal Heating in Coalescing Binary Neutron StarsApr 25 1994Tidal interaction in a coalescing neutron star binary can resonantly excite the g-mode oscillations of the neutron star when the frequency of the tidal driving force equals the intrinsic g-mode frequencies. We study the g-mode oscillations of cold neutron ... More

An extremal problem on potentially $K_{m}-C_{4}$-graphic sequencesSep 03 2004Jul 07 2006A sequence $S$ is potentially $K_{m}-C_{4}$-graphical if it has a realization containing a $K_{m}-C_{4}$ as a subgraph. Let $\sigma(K_{m}-C_{4}, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $\sigma(S)\geq \sigma(K_{m}-C_{4}, ... More

A note on potentially $K_4-e$ graphical sequencesAug 11 2003A sequence $S$ is potentially $K_4-e$ graphical if it has a realization containing a $K_4-e$ as a subgraph. Let $\sigma(K_4-e, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $\sigma(S)\geq \sigma(K_4-e, n)$ is ... More

Lozenge tilings of hexagons with central holes and dentsMar 07 2018Jan 04 2019Ciucu showed that the number of a hexagon in which a chain of equilateral triangles of alternating orientations, called a `\emph{fern}', has been removed in the center is given by a simple product formula (Adv. Math. 2017). In the first part of this paper, ... More

Proof of a refinement of Blum's conjecture on hexagonal dungeonsMar 18 2014Apr 01 2015Matt Blum conjectured that the number of tilings of a hexagonal dungeon with side-lengths $a,2a,b,a,2a,b$ (for $b\geq2a$) equals $13^{2a^2}14^{\lfloor a^2/2\rfloor}$. Ciucu and the author of the present paper proved the conjecture by using Kuo's graphical ... More

A simple proof for the number of tilings of quartered Aztec diamondsSep 26 2013We get four quartered Aztec diamonds by dividing an Aztec diamond region by two zigzag cuts passing its center. W. Jockusch and J. Propp (in an unpublished work) found that the number of tilings of quartered Aztec diamonds is given by simple product formulas. ... More

A New Proof for a Triple Product Formula for Plane PartitionsOct 06 2017Stanley generalized MacMahon's classical theorem by proving a product formula for the norm-trace generating function for plane partition with unbounded parts. In his recent work on biothorgonal polynomials, Kamioka proved a finite analogue of Stanley's ... More

Strict Deformation Quantisation of the G-connections via Lie GroupoidJan 17 2014Motivated by the compactification process of the space of connections in loop quantum gravity literature. A description of the space of G-connections using the tangent groupoid is given. As the tangent groupoid parameter is away from zero, the G-connections ... More

Solar Obliquity Induced by Planet Nine: Simple CalculationAug 04 2016Bailey et al.~(2016) and Gomes et al.~(2016) recently suggested that the 6 degree misalignment between the Sun's rotational equator and the orbital plane of the major planets may be produced by the forcing from the hypothetical Planet Nine on an inclined ... More

Dynamics of PSR J0045-7319/B-star Binary and Neutron Star FormationApr 14 1997Recent timing observations have revealed the presence of orbital precession due to spin-orbit coupling and rapid orbital decay due to dynamical tidal interaction in the PSR J0045-7319/B-star binary system. They can be used to put concrete constraints ... More

Dynamical Tides in Rotating Binary StarsApr 14 1997We study the effect of rotation on the excitation of internal oscillation modes of a star by the external gravitational potential of its companion. Unlike the nonrotating case, there are difficulties with the usual mode decomposition for rotating stars ... More

Physics in Very Strong Magnetic Fields: Introduction and OverviewNov 28 2014This paper provides an introduction to a number of astrophysics problems related to strong magnetic fields. The first part deals with issues related to atoms, condensed matter and high-energy processes in very strong magnetic fields, and how these issues ... More

Global Nonradial Instabilities of Dynamically Collapsing Gas SpheresApr 05 2000Apr 18 2000Self-similar solutions provide good descriptions for the gravitational collapse of spherical clouds or stars when the gas obeys a polytropic equation of state, $p=K\rho^\gamma$ (with $\gamma\le 4/3$). We study the behaviors of nonradial perturbations ... More

Orbital Decay of the PSR J0045-7319/B Star Binary System: Age of Radio Pulsar and Initial Spin of Neutron StarMay 16 1996Recent timing observations of PSR J0045-7319 reveal that the neutron star/B star binary orbit is decaying on a time scale of $|\Porb/\dot\Porb|=0.5$ Myr, shorter than the characteristic age ($\tau_c=3$ Myr) of the pulsar (Kaspi et al.~1996a). We study ... More

A new two weight estimates for a vector-valued positive operatorMar 23 2015Mar 24 2015We give a new characterization of the two weight inequality for a vector-valued positive operator. Our characterization has a different flavor than the one of Scurry's and H\"{a}nninen's. The proof can be essentially derived from the scalar-valued case. ... More

The Bellman functions of the Carleson Embedding Theorem and the Doob's martingale inequalityNov 20 2014Feb 11 2015Evaluation of the Bellman functions is a difficult task. The exact Bellman functions of the dyadic Carleson Embedding Theorem 1.1 and the dyadic maximal operators are obtained in [3] and [4]. Actually, the same Bellman functions also work for the tree-like ... More

Markets are Dead, Long Live MarketsFeb 04 2005Researchers have long proposed using economic approaches to resource allocation in computer systems. However, few of these proposals became operational, let alone commercial. Questions persist about the economic approach regarding its assumptions, value, ... More

Lozenge tilings of a halved hexagon with an array of triangles removed from the boundary, part IISep 07 2017Proctor's work on staircase plane partitions yields an enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi later extended this tiling enumeration to a halved hexagon with a triangle cut off from the boundary. In the previous ... More

Generating function of the tilings of Aztec rectangle with holesFeb 04 2014Apr 01 2015We consider a generating function of the domino tilings of an Aztec rectangle with several boundary unit squares removed. Our generating function involves two statistics: the rank of the tiling and half number of vertical dominoes as in the Aztec diamond ... More

A Generalization of Aztec Diamond Theorem, Part IIOct 04 2013Oct 30 2015The author gave a proof of a generalization of the Aztec diamond theorem for a family of $4$-vertex regions on the square lattice with southwest-to-northeast diagonals drawn in (Electron. J. Combin., 2014) by using a bijection between tilings and non-intersecting ... More

Enumeration of Hybrid Domino-Lozenge TilingsSep 20 2013We solve and generalize an open problem posted by James Propp (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999) on the number of tilings of quasi-hexagonal regions on the square lattice with every third diagonal ... More

On the numbers of perfect matchings of trimmed Aztec rectanglesApr 01 2015We consider several new families of graphs obtained from Aztec rectangle and augmented Aztec rectangle graphs by trimming two opposite corners. We prove that the perfect matchings of these new graphs are enumerated by powers of $2$, $3$, $5$, and $11$. ... More

A $q$-enumeration of lozenge tilings of a hexagon with four adjacent triangles removed from the boundaryFeb 05 2015Apr 10 2017MacMahon proved a simple product formula for the generating function of plane partitions fitting in a given box. The theorem implies a $q$-enumeration of lozenge tilings of a semi-regular hexagon on the triangular lattice. In this paper we generalize ... More

A $q$-enumeration of lozenge tilings of a hexagon with three dentsFeb 20 2015Oct 03 2015We $q$-enumerate lozenge tilings of a hexagon with three bowtie-shaped regions have been removed from three non-consecutive sides. The unweighted version of the result generalizes a problem posed by James Propp on enumeration of lozenge tilings of a hexagon ... More

Double Aztec RectanglesNov 01 2014Sep 29 2015We investigate the connection between lozenge tilings and domino tilings by introducing a new family of regions obtained by attaching two different Aztec rectangles. We prove a simple product formula for the generating functions of the tilings of the ... More

Buser-Sarnak invariant and projective normality of abelian varietiesMar 03 2010We show that a general $n$-dimensional polarized abelian variety $(A,L)$ of a given polarization type and satisfying $ h^0(A, L) \geq \dfrac{8^n}{2} \cdot \dfrac{n^n}{n !}$ is projectively normal. In the process, we also obtain a sharp lower bound for ... More

An extremal problem on potentially $K_{p_{1},p_{2},...,p_{t}}$-graphic sequencesAug 24 2004A sequence $S$ is potentially $K_{p_{1},p_{2},...,p_{t}}$ graphical if it has a realization containing a $K_{p_{1},p_{2},...,p_{t}}$ as a subgraph, where $K_{p_{1},p_{2},...,p_{t}}$ is a complete t-partite graph with partition sizes $p_{1},p_{2},...,p_{t} ... More

Graphs without repeated cycle lengthsMay 12 2003In 1975, P. Erd\"{o}s proposed the problem of determining the maximum number $f(n)$ of edges in a graph of $n$ vertices in which any two cycles are of different lengths. In this paper, it is proved that $$f(n)\geq n+36t$$ for $t=1260r+169 (r\geq 1)$ and ... More

Ricci flow under local almost non-negative curvature conditionsApr 22 2018Jun 12 2018We find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative number. The curvature ... More

An Effective Compactness Theorem for Coxeter GroupsFeb 16 2009Through highly non-constructive methods, works by Bestvina, Culler, Feighn, Morgan, Paulin, Rips, Shalen, and Thurston show that if a finitely presented group does not split over a virtually solvable subgroup, then the space of its discrete and faithful ... More

On the number of edges in some graphsAug 05 2018Sep 30 2018In 1975, P. Erd\H{o}s proposed the problem of determining the maximum number $f(n)$ of edges in a graph with $n$ vertices in which any two cycles are of different lengths. The sequence $(c_1,c_2,\cdots,c_n)$ is the cycle length distribution of a graph ... More

A new proof for the number of lozenge tilings of quartered hexagonsOct 29 2014Apr 26 2015It has been proven that the lozenge tilings of a quartered hexagon on the triangular lattice are enumerated by a simple product formula. In this paper we give a new proof for the tiling formula by using Kuo's graphical condensation. Our result generalizes ... More

Segment-wise Description of the Dynamics of Traffic CongestionAug 05 2018We compare the point-wise and segment-wise descriptions of the traffic system. Using real data from the Taiwan highway system with a tremendous volume of segment-wise data, we find that the segment-wise description is much more informative of the evolution ... More

Star Formation Rate and Extinction in Faint z~4 Lyman-Break GalaxiesApr 14 2014Jul 24 2014We present a statistical detection of 1.5 GHz radio continuum emission from a sample of faint z~4 Lyman-break galaxies (LBGs). LBGs are key tracers of the high-redshift star formation history and important sources of UV photons that ionized the intergalactic ... More

Decentralized Projection-free Optimization for Convex and Non-convex ProblemsDec 05 2016Decentralized optimization algorithms have received much attention as fueled by the recent advances in network information processing and the tremendous amount of data that is generated by human activities. However, conventional decentralized algorithms ... More

First-principles theory of magnetic multipoles in condensed matter systemsFeb 03 2018The multipole concept, which characterizes the spacial distribution of scalar and vector objects by their angular dependence, has already become widely used in various areas of physics. In recent years it has become employed to systematically classify ... More

Coupled Decorated Membrane Resonators with Large Willis CouplingMar 09 2019Mar 17 2019We report the experimental studies on an acoustic scatterer consisting of a pair of coupled decorated membrane resonators (DMRs) that exhibits near extreme contrast in reflection asymmetry and strong Willis coupling coefficient with amplitude of 2.5 and ... More

Curvature-aided Incremental Aggregated Gradient MethodOct 24 2017We propose a new algorithm for finite sum optimization which we call the curvature-aided incremental aggregated gradient (CIAG) method. Motivated by the problem of training a classifier for a d-dimensional problem, where the number of training data is ... More

Non-asymptotic Analysis of Biased Stochastic Approximation SchemeFeb 02 2019Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions such as unbiased ... More

SUCAG: Stochastic Unbiased Curvature-aided Gradient Method for Distributed OptimizationMar 22 2018Oct 26 2018We propose and analyze a new stochastic gradient method, which we call Stochastic Unbiased Curvature-aided Gradient (SUCAG), for finite sum optimization problems. SUCAG constitutes an unbiased total gradient tracking technique that uses Hessian information ... More

Spectrins in Axonal Cytoskeletons: Dynamics Revealed by Extensions and FluctuationsDec 04 2013Jun 18 2014The macroscopic properties, the properties of individual components and how those components interact with each other are three important aspects of a composited structure. An understanding of the interplay between them is essential in the study of complex ... More

On Weyl modules over affine Lie algebras in prime characteristicOct 14 2013Jan 25 2016We construct a family of homomorphisms between Weyl modules for affine Lie algebras in characteristic p, which supports our conjecture on the strong linkage principle in this context. We also exhibit a large class of reducible Weyl modules beyond level ... More

Induced Lorentz-Violating Chern-Simons Term in QED and Anomalous Contributions to Effective Action ExpansionsJul 14 1999Aug 23 2000I present a unified formulation of anomalous contributions in quantum field theories by calculating directly the effective action using the background field and covariant-derivative expansion technique. I use this method to determine uniquely the induced ... More

On the definition and K-theory realization of a modular functorOct 18 2013Aug 10 2014We present a definition of a (super)-modular functor which includes certain interesting cases that previous definitions do not allow. We also introduce a notion of topological twisting of a modular functor, and construct formally a realization by a 2-dimensional ... More

Weak type (1,1) bound criterion for singular integral with rough kernel and its applicationsSep 11 2015In this paper, a weak type (1,1) bound criterion is established for singular integral operator with rough kernel. As some applications of this criterion, we prove some important operators with rough kernel in harmonic analysis, such as Calder\'on commutator, ... More

Low-Eccentricity Formation of Ultra-Short Period Planets in Multi-Planet SystemsJan 24 2019Recent studies suggest that ultra-short period planets (USPs), Earth-sized planets with sub-day periods, constitute a statistically distinct sub-sample of {\it Kepler} planets: USPs have smaller radii ($1-1.4R_\oplus$) and larger mutual inclinations with ... More

Polarization Evolution in A Strongly Magnetized Vacuum: QED Effect and Polarized X-ray Emission from Magnetized Neutron StarsMar 12 2009Apr 06 2009X-ray photons emitted from the surface or atmosphere of a magnetized neutron star is highly polarized. However, the observed polarization may be modified due to photon propagation through the star's magnetosphere. For photon frequencies much larger than ... More

Enhanced Black-Hole Mergers in Binary-Binary InteractionsSep 20 2018Dec 25 2018We study the orbital evolution of black hole (BH) binaries in quadruple systems, where the tertiary binary excites large eccentricity in the BH binary through Lidov-Kozai (LK) oscillations, causing the binary BHs to merge via gravitational radiation. ... More

Rossby Wave Instability in Accretion Discs with Large-Scale Poloidal Magnetic FieldsDec 06 2012We study the effect of large-scale magnetic fields on the non-axisymmetric Rossby wave instability (RWI) in accretion discs. The instability develops around a density bump, which is likely present in the transition region between the active zone and dead ... More

Axion-photon Propagation in Magnetized UniverseNov 11 2015May 26 2016Oscillations between photons and axion-like particles (ALP) travelling in intergalactic magnetic fields have been invoked to explain a number of astrophysical phenomena, or used to constrain ALP properties using observations. One example is the anomalous ... More

Tidal Novae in Compact Binary White DwarfsJun 03 2012Sep 20 2012Compact binary white dwarfs (WDs) undergoing orbital decay due to gravitational radiation can experience significant tidal heating prior to merger. In these WDs, the dominant tidal effect involves the excitation of outgoing gravity waves in the inner ... More

Corotational Instability of Inertial-Acoustic Modes in Black Hole Accretion Discs and Quasi-Periodic OscillationsOct 01 2008Nov 14 2008We study the global stability of non-axisymmetric p-modes (also called inertial-acoustic modes) trapped in the inner-most regions of accretion discs around black holes. We show that the lowest-order (highest-frequency) p-modes, with frequencies $\omega=(0.5-0.7) ... More

Density-Functional-Theory Calculations of Matter in Strong Magnetic Fields: II. Infinite Chains and Condensed MatterJul 12 2006Jan 05 2007We present new, ab initio calculations of the electronic structure of one-dimensional infinite chains and three-dimensional condensed matter in strong magnetic fields ranging from B=10^12 G to 2x10^15 G, appropriate for observed magnetic neutron stars. ... More