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Hierarchical multiscale finite element method for multi-continuum mediaJun 11 2019Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of model reduction. One of the approaches is multi-continuum technique, where ... More

Topology & arithmetic geometry of moduli for elliptic Lefschetz fibrationsJul 11 2016We consider the moduli space $\mathcal{L}_{g, \mu}$ of holomorphic genus g Lefschetz fibrations over $\mathbb{CP}{}^{1}$ with $\mu \in \mathbb{N}$ number of singular fibers. After establishing a basic relationship between the moduli $\mathcal{L}_{g, \mu}$ ... More

Activation of zero-error classical capacity in low-dimensional quantum systemsJun 11 2018Channel capacities of quantum channels can be nonadditive even if one of two quantum channels has no channel capacity. We call this phenomenon \emph{activation} of the channel capacity. In this paper, we show that when we use a quantum channel on a qubit ... More

Product number counting statistics from stochastic bursting birth-death processesMar 15 2019Mar 21 2019Bursting and non-renewal processes are common phenomena in birth-death process, yet no theory can quantitatively describe a non-renewal birth process with bursting. Here, we present a theoretical model that yields the product number counting statistics ... More

Fourier multiplier theorems for Triebel-Lizorkin spacesDec 06 2017Nov 23 2018In this paper we study sharp generalizations of $\dot{F}_p^{0,q}$ multiplier theorem of Mikhlin-H\"ormander type. The class of multipliers that we consider involves Herz spaces $K_u^{s,t}$. Plancherel's theorem proves $\widehat{L_s^2}=K_2^{s,2}$ and we ... More

Boundedness of pseudo-differential operators of type (0,0) on Triebel-Lizorkin and Besov spacesSep 06 2018In this work we study the boundedness of pseudo-differential operators corresponding to $a\in\mathcal{S}_{0,0}^{m}$ on Triebel-Lizorkin spaces $F_p^{s,q}$ and Besov spaces $B_p^{s,q}$. We also discuss the sharpness of our estimates in a certain sense. ... More

Étale topology of the space of rational functions and the moduli stack of stable elliptic surfacesDec 31 2018Feb 03 2019Motivated by the enumeration of the moduli stack of morphisms $\mathrm{Hom}_n(\mathbb{P}^1,\mathcal{P}(a,b))$, where $\mathcal{P}(a,b)$ is the 1-dimensional $(a,b)$ weighted projective stack, over $\mathrm{char}(\mathbb{F}_q)$ not dividing $a$ or $b$ ... More

On the boundedness of Pseudo-differential operators on Triebel-Lizorkin and Besov spacesFeb 29 2016Nov 26 2018In this work we show endpoint boundedness properties of pseudo-differential operators of type $(\rho,\rho)$, $0<\rho<1$, on Triebel-Lizorkin and Besov spaces. Our results are sharp and they also cover operators defined by compound symbols.

Fourier multipliers on a vector-valued function spaceApr 26 2019In this work we will study a vector-valued version of Hormander's multiplier theorem. Our result improves the result of Triebel and extends to the case p=infinity in the scale of Triebel-Lizorkin space.

Unique fiber sum decomposability of genus 2 Lefschetz fibrationsJul 14 2015Oct 23 2015By applying the lantern relation substitutions to the positive relation of the genus two Lefschetz fibration over $\mathbb{S}^{2}$. We show that $K3\#2 \overline{\mathbb{CP}}{}^{2}$ can be rationally blown down along seven disjoint copies of the configuration ... More

Equivalence of (quasi-)norms on a vector-valued function space and its applications to multilinear operatorsMar 21 2019Apr 27 2019In this paper we present (quasi-)norm equivalence on a vector-valued function space $L^p_A(l^q)$ and extend the equivalence to $p=\infty$ and $0<q<\infty$ in the scale of Triebel-Lizorkin space, motivated by Fraizer-Jawerth. By applying the results, we ... More

Exploiting product molecule number to consider reaction rate fluctuation in elementary reactionsMar 15 2019Mar 18 2019In many chemical reactions, reaction rate fluctuation is inevitable. Reaction rates are different whenever chemical reaction occurs due to their dependence on the number of reaction events or the product number. As such, understanding the impact of rate ... More

On the boundedness of Pseudo-differential operators on Triebel-Lizorkin and Besov spacesFeb 29 2016Oct 17 2016In this work we show endpoint boundedness properties of pseudo-differential operators on Triebel-Lizorkin and Besov spaces. We assume that the symbols belong to H\"ormander's class $\mathcal{S}_{\rho,\rho}^{m}$, $0<\rho<1$. Our results also covers operators ... More

A certain vector-valued function space and its applications to multilinear operatorsMar 21 2019In this paper we present several (quasi-)norm equivalences involving $L^p(l^q)$ norm of a certain vector-valued functions and extend the equivalences to $p=\infty$ and $0<q<\infty$ in the scale of Triebel-Lizorkin spaces, motivated by Fraizer, Jawerth. ... More

Some maximal inequalities on Triebel-Lizorkin spaces for $p=\infty$Oct 03 2017Nov 26 2018In this work we give some maximal inequalities in Triebel-Lizorkin spaces, which are "$\dot{F}_{\infty}^{s,q}$-variants" of Fefferman-Stein vector-valued maximal inequality and Peetre's maximal inequality. We will give some applications of the new maximal ... More

Sharp estimates for pseudo-differential operators of type (1,1) on Triebel-Lizorkin and Besov spacesOct 02 2017Nov 23 2018Pseudo-differential operators of type $(1,1)$ and order $m$ are continuous from $F_p^{s+m,q}$ to $F_p^{s,q}$ if $s>d/\min{(1,p,q)}-d$ for $0<p<\infty$, and from $B_p^{s+m,q}$ to $B_{p}^{s,q}$ if $s>d/\min{(1,p)}-d$ for $0<p\leq\infty$. In this work we ... More

Real Grassmann Polylogarithms and Chern ClassesJul 18 1994In this paper we define real grassmann polylogarithms, which are real single valued analogues of the grassmann polylogarithms (or higher logarithms) defined by Hain and MacPherson. We prove the existence of all such real grassmann polylogs, at least generically. ... More

Lantern substitution and new symplectic 4-manifolds with ${b_{2}}^{+} = 3$Jul 03 2012May 24 2014Motivated by the construction of H. Endo and Y. Gurtas, changing a positive relator in Dehn twist generators of the mapping class group by using lantern substitutions, we show that 4-manifold $K3#2\CPb$ equipped with the genus two Lefschetz fibration ... More

Arithmetic of the moduli of semistable elliptic surfacesJul 11 2016Apr 07 2019We prove a new sharp asymptotic with the lower order term of zeroth order on $\mathcal{Z}_{\mathbb{F}_q(t)}(\mathcal{B})$ for counting the semistable elliptic curves over $\mathbb{F}_q(t)$ by the bounded height of discriminant $\Delta(X)$. The precise ... More

Crossing the cosmological constant barrier with kinetically interacting double quintessenceFeb 06 2009We examine the plausibility of crossing the cosmological constant ($\L$) barrier in a two-field quintessence model of dark energy, involving a kinetic interaction between the individual fields. Such a kinetic interaction may have its origin in the four ... More

Arithmetic of the moduli of semistable elliptic surfacesJul 11 2016Sep 18 2017We consider the moduli of nonsingular semistable elliptic fibrations over $\mathbb{P}^{1}$, also known as semistable elliptic surfaces, with $12n$ nodal singular fibers and a distinguished section. We establish a bijection of $K$-points between the moduli ... More

Statistical Mechanics of Membrane Protein Conformation: A Homopolymer ModelJul 01 1998The conformation and the phase diagram of a membrane protein are investigated via grand canonical ensemble approach using a homopolymer model. We discuss the nature and pathway of $\alpha$-helix integration into the membrane that results depending upon ... More

Polymer translocation induced by adsorptionFeb 10 1998We study the translocation of a flexible polymer through a pore in a membrane induced by its adsorption on \trans side of the membrane. When temperature $T$ is higher than $T_c$, the adsorption-desorption transition temperature, attractive interaction ... More

Self-similar occurrence of massless Dirac particles in graphene under magnetic fieldSep 11 2012Intricate interplay between the periodicity of the lattice structure and that of the cyclotron motion gives rise to a well-known self-similar fractal structure of the energy eigenvalue, known as the Hofstadter butterfly, for an electron moving in lattice ... More

Arithmetic of the moduli of semistable elliptic surfacesJul 11 2016Apr 25 2019We prove a new sharp asymptotic with the lower order term of zeroth order on $\mathcal{Z}_{\mathbb{F}_q(t)}(\mathcal{B})$ for counting the semistable elliptic curves over $\mathbb{F}_q(t)$ by the bounded height of discriminant $\Delta(X)$. The precise ... More

Polymer Release out of a Spherical Vesicle through a PoreFeb 10 1998Translocation of a polymer out of curved surface or membrane is studied via mean first passage time approach. Membrane curvature gives rise to a constraint on polymer conformation, which effectively drives the polymer to the outside of membrane where ... More

Non Local Detection of quantum dynamical processes in spin chainsJun 24 2016We study the dynamics of a one dimensional quantum spin chain evolving from unentangled or entangled initial state. At a given instant of time a quantum dynamical process (ex. measurement) is performed on a single spin at one end of the chain. The aim ... More

Synchronization in Harper dynamics: a classical `to' quantum perspectiveFeb 23 2019Measure synchronization is a well-known phenomenon in coupled classical Hamiltonian systems over last two decades. In this paper, synchronization for coupled Harper system is investigated in both classical and quantum contexts. The concept of measure ... More

Unifying Interacting Nodal Semimetals: A New Route to Strong CouplingDec 13 2018We propose a general framework for constructing a large set of nodal-point semimetals by tuning the number of linearly ($d_L$) and (at most) quadratically ($d_Q$) dispersing directions. By virtue of such a unifying scheme, we identify a new perturbative ... More

Galactic dynamo action in presence of stochastic alpha and shearSep 01 2008Oct 08 2008Using a one-dimensional $\alpha\omega$-dynamo model appropriate to galaxies, we study the possibility of dynamo action driven by a stochastic alpha effect and shear. To determine the field evolution, one needs to examine a large number of different realizations ... More

Coulomb interaction driven instabilities of sliding Luttinger liquidsMay 01 2017Aug 21 2017We study systems made of periodic arrays of one dimensional quantum wires, coupled by Coulomb interaction. Using bosonization an interacting metallic fixed point is obtained, which is shown to be a higher dimensional analogue of the Tomonaga-Luttinger ... More

Improved Reconciliation With Polar Codes In Quantum Key DistributionMay 14 2018Quantum key distribution (QKD) is a cryptographic system that generates an information-theoretically secure key shared by two legitimate parties. QKD consists of two parts: quantum and classical. The latter is referred to as classical post-processing ... More

Integrative Factorization of Bidimensionally Linked MatricesJun 09 2019Advances in molecular "omics'" technologies have motivated new methodology for the integration of multiple sources of high-content biomedical data. However, most statistical methods for integrating multiple data matrices only consider data shared vertically ... More

VeST: Very Sparse Tucker Factorization of Large-Scale TensorsApr 04 2019Apr 08 2019Given a large tensor, how can we decompose it to sparse core tensor and factor matrices such that it is easier to interpret the results? How can we do this without reducing the accuracy? Existing approaches either output dense results or give low accuracy. ... More

Entropy production estimates for the polyatomic ellipsoidal BGK modelAug 02 2017Aug 16 2017We study the entropy production estimate for the polyatomic ellipsoidal BGK model, which is a relaxation type kinetic model describing the time evolution of polyatomic particle systems. An interesting dichotomy is observed between $0<\theta\leq 1$ and ... More

Cauchy problem for the ellipsoidal BGK model for polyatomic particlesAug 08 2017We establish the existence and uniqueness of mild solutions for the polyatomic ellipsoidal BGK model, which is a relaxation type kinetic model describing the evolution of polyatomic gaseous system at the mesoscopic level.

Topological Sigma B Model in 4-DimensionsMay 16 2008Sep 10 2008We propose a 4-dimensional version of topological sigma B-model, governing maps from a smooth compact 4-manifold M to a Calabi-Yau target manifold X. The theory depends on on complex structure of X, while is independent of Kaehler metric of X. The theory ... More

Optimization of the pulse width and injection time in a double-pass laser amplifierMay 03 2018We have optimized the input pulse width and injection time to achieve the highest possible output pulse energy in a double-pass laser amplifier. For this purpose, we have extended the modified Frantz-Nodvik equation by simultaneously including both spontaneous ... More

Cleaned Three-Year WMAP CMB Map: Magnitude of the Quadrupole and Alignment of Large Scale ModesAug 05 2006[Abridged] We have produced a cleaned map of the Wilkinson Microwave Anisotropy Probe (WMAP) 3-year data using an improved foreground subtraction technique. We perform an internal linear combination (ILC) to subtract the Galactic foreground emission from ... More

Instabilities of Weyl-loop semi-metalsAug 29 2016We study Weyl-loop semi-metals with short range interactions, focusing on the possible interaction driven instabilities. We introduce an $\epsilon$ expansion regularization scheme by means of which the possible instabilities may be investigated in an ... More

Multiple kinetic k-essence, phantom barrier crossing and stabilityJun 26 2008Feb 09 2009We investigate models of dark energy with purely kinetic multiple k-essence sources that allow for the crossing of the phantom divide line, without violating the conditions of stability. It is known that with more than one kinetic k-field one can possibly ... More

Gravitational Redshift in Einstein-Kalb-Ramond Spacetime and Randall-Sundrum ScenarioJun 05 2003Feb 28 2004It is shown that the gravitational redshift as predicted by Einstein's theory, is modified in presence of second rank antisymmetric tensor (Kalb-Ramond) field in a string inspired background spacetime.In presence of extra dimensions, the Randall-Sundrum ... More

Surface Light Field FusionSep 06 2018We present an approach for interactively scanning highly reflective objects with a commodity RGBD sensor. In addition to shape, our approach models the surface light field, encoding scene appearance from all directions. By factoring the surface light ... More

Dynamic behaviors in directed networksSep 11 2006Motivated by the abundance of directed synaptic couplings in a real biological neuronal network, we investigate the synchronization behavior of the Hodgkin-Huxley model in a directed network. We start from the standard model of the Watts-Strogatz undirected ... More

Distribution of Korean Family NamesJul 13 2004The family name distribution in Korea is investigated in comparison with previous studies in other countries. In Korea, both the family name and its birthplace, where the ancestor of the family originated, are commonly used to distinguish one family name ... More

VeST: Very Sparse Tucker Factorization of Large-Scale TensorsApr 04 2019Given a large tensor, how can we decompose it to sparse core tensor and factor matrices such that it is easier to interpret the results? How can we do this without reducing the accuracy? Existing approaches either output dense results or give low accuracy. ... More

On a Positive decomposition of entropy production functional for the polyatomic BGK modelAug 16 2017In this paper, we show that the entropy production functional for the polyatomic ellipsoidal BGK model can be decomposed into two non-negative parts. Two applications of this property: the $H$-theorem for the polyatomic BGK model and the weak compactness ... More

VeST: Very Sparse Tucker Factorization of Large-Scale TensorsApr 04 2019Apr 09 2019Given a large tensor, how can we decompose it to sparse core tensor and factor matrices such that it is easier to interpret the results? How can we do this without reducing the accuracy? Existing approaches either output dense results or give low accuracy. ... More

Metallic state in bosonic systems with continuously degenerate minimaMar 15 2018A continuously degenerate minima of the single particle dispersion is realized in the presence of an isotropic spin-orbit coupling above one dimension. The unit codimension of the dispersion-minima leads to a divergent density of states which enhances ... More

The role of the Yoshizawa effect in the Archontis dynamoFeb 16 2009Jun 16 2009The generation of mean magnetic fields is studied for a simple non-helical flow where a net cross helicity of either sign can emerge. This flow, which is also known as the Archontis flow, is a generalization of the Arnold--Beltrami--Childress flow, but ... More

Does curvature-dilaton coupling with Kalb Ramond field lead to an accelerating Universe ?Jul 08 2002Dec 02 2003In this work we show that the Universe evolving in a spacetime with torsion (originated from a second rank antisymmetric Kalb-Ramond field) and dilaton is free from any big bang singularity and can have acceleration during the evolution. Both the matter ... More

Spherically Symmetric Solutions of Gravitational Field Equations in Kalb-Ramond BackgroundFeb 22 2001Static spherically symmetric solution in a background spacetime with torsion is derived explicitly. The torsion considered here is identified with the field strength of a second rank antisymmetric tensor field namely the Kalb-Ramond field and the proposed ... More

Loschmidt echo of local dynamical processes in integrable and non integrable spin chainsOct 23 2018The Loschmidt echo is investigated to track the effect of the local QDP. It is also quite sensitive to whether the background dynamics is integrable or not. For the integrable case, viz. the Heisenberg model, the Loschmidt echo depends on the parameters ... More

Remotely detecting the signal of a local decohering process in spin chainsJun 24 2016Feb 08 2017We study the dynamics of a one dimensional quantum spin chain evolving from unentangled or entangled initial state. At a given instant of time a quantum dynamical process (ex. measurement) is performed on a single spin at one end of the chain, decohering ... More

Green Heron Swarm Optimization Algorithm - State-of-the-Art of a New Nature Inspired Discrete Meta-HeuristicsOct 14 2013Many real world problems are NP-Hard problems are a very large part of them can be represented as graph based problems. This makes graph theory a very important and prevalent field of study. In this work a new bio-inspired meta-heuristics called Green ... More

Interference of the signal from a local dynamical process with the quantum state propagation in spin chainsMay 30 2018Oct 09 2018The effect of a local instantaneous quantum dynamical process (QDP), either unitary or non-unitary, on the quantum state transfer through a unitary Hamiltonian evolution is investigated for both integrable and non-integrable dynamics. There are interference ... More

Ask Me Anything: A Conversational Interface to Augment Information Security WorkersJul 18 2017Security products often create more problems than they solve, drowning users in alerts without providing the context required to remediate threats. This challenge is compounded by a lack of experienced personnel and security tools with complex interfaces. ... More

Curvature of the Universe and Observed Gravitational Lens Image Separations Versus RedshiftFeb 20 1997In a flat, k=0 cosmology with galaxies that approximate singular isothermal spheres, gravitational lens image separations should be uncorrelated with source redshift. But in an open k=-1 cosmology such gravitational lens image separations become smaller ... More

Symmetrizers and antisymmetrizers for the BMW algebraSep 02 2011Jul 18 2012Let $n\in\mathds{N}$ and $B_n(r,q)$ be the generic Birman-Murakami-Wenzl algebra with respect to indeterminants $r$ and $q$. It is known that $B_n(r,q)$ has two distinct linear representations generated by two central elements of $B_n(r,q)$ called the ... More

A Survey on Rankin-Cohen DeformationsSep 24 2009This is a survey about recent progress in Rankin-Cohen deformations. We explain a connection between Rankin-Cohen brackets and higher order Hankel forms.

Webs of Lagrangian Tori in Projective Symplectic ManifoldsJan 11 2012Jan 13 2012For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperk\"ahler manifold is a fiber of an almost holomorphic ... More

Brauer algebras, symplectic Schur algebras and Schur-Weyl dualityMar 24 2005Sep 28 2005In this paper we prove Schur-Weyl duality between the symplectic group and Brauer algebra over an arbitrary infinite field $K$. We show that the natural homomorphism from the Brauer algebra $B_n(-2m)$ to the endomorphism algebra of tensor space $(K^{2m})^{\otimes ... More

Constraining Torsion in Maximally symmetric (sub)spacesJun 03 2013We look into the general aspects of space-time symmetries in presence of torsion, and how the latter is affected by such symmetries. Focusing in particular to space-times which either exhibit maximal symmetry on their own, or could be decomposed to maximally ... More

Parareal methods for highly oscillatory dynamical systemsMar 06 2015Nov 18 2015We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the system using an ... More

Constraining Torsion in Maximally symmetric (sub)spacesJun 03 2013Aug 17 2017We look into the general aspects of space-time symmetries in presence of torsion, and how the latter is affected by such symmetries. Focusing in particular to space-times which either exhibit maximal symmetry on their own, or could be decomposed to maximally ... More

Dynamical system analysis of dark energy models in scalar coupled metric-torsion theoriesFeb 04 2017Aug 17 2017We study the phase space dynamics of cosmological models in the theoretical formulations of non-minimal metric-torsion couplings with a scalar field, and investigate in particular the critical points which yield stable solutions exhibiting cosmic acceleration ... More

Analytical Theory of Strongly Correlated Wigner Crystals in the Lowest Landau LevelJun 23 2015In this work, we present an analytical theory of strongly correlated Wigner crystals (WCs) in the lowest Landau level (LLL) by constructing an approximate, but accurate effective two-body interaction for composite fermions (CFs) participating in the WCs. ... More

Scale Space Approximation in Convolutional Neural Networks for Retinal Vessel SegmentationJun 24 2018Oct 18 2018Retinal images have the highest resolution and clarity among medical images. Thus, vessel analysis in retinal images may facilitate early diagnosis and treatment of many chronic diseases. In this paper, we propose a novel multi-scale residual convolutional ... More

The initial conditions and evolution of isolated galaxy models: effects of the hot gas haloDec 30 2012We construct several Milky Way-like galaxy models containing a gas halo (as well as gaseous and stellar disks, a dark matter halo, and a stellar bulge) following either an isothermal or an NFW density profile with varying mass and initial spin. In addition, ... More

Accurate calculations of magnetic dipole and electric quadrupole hyperfine coupling constants of 6 P_{3/2} state of Cesium atom : A Relativistic Coupled Cluster approachJun 18 2004We report the magnetic dipole and electric quadrupole hyperfine coupling constants of 6 P_{3/2} state of ^{133} Cs(I= {7/2}) obtained from the relativistic coupled cluster (RCC) method. To our knowledge, no prior electric quadrupole hyperfine CC calculation ... More

Effects of partial triple excitations in atomic coupled cluster calculationsJul 24 2007In this article we study the effects of higher body excitations in the relativistic CC calculations for atoms and ions with one valence electron using Fock-space CCSD, CCSD(T) and its unitary variants. The present study demonstrates that CCSD(T) estimates ... More

Phase Plane Analysis of Metric-Scalar Torsion Model for Interacting Dark EnergyNov 21 2016We study the phase space dynamics of the non-minimally coupled Metric-Scalar-Torsion model in both Jordan and Einstein frames. We specifically check for the existence of critical points which yield stable solutions representing the current state of accelerated ... More

An Inexpensive Arterial Pressure Wave Sensor and its application in different physiological conditionDec 08 2005Arterial Blood Pressure wave monitoring is considered to be important in assessment of cardiovascular system. We developed a novel pulse wave detection system using low frequency specific piezoelectric material as pressure wave sensor. The transducer ... More

Weakly dynamic dark energy via metric-scalar couplings with torsionNov 02 2016Aug 17 2017We study the dynamical aspects of dark energy in the context of a non-minimally coupled scalar field with curvature and torsion. Whereas the scalar field acts as the source of the trace mode of torsion, a suitable constraint on the torsion pseudo-trace ... More

Relativistic coupled-cluster calculation of core ionization potential using the Fock space eigenvalue independent partitioning techniqueApr 16 2004Jul 13 2004In this paper we have applied the cluster-expansion ansatz for the wave operator \Omega which incorporates the orbital relaxation and correlation effects in an efficient manner. We have used both ordinary and normal ordered cluster operator (\Omega) to ... More

Branching ratios of radiative transitions in O VIJul 24 2007We study the branching ratios of the allowed and forbidden radiative transitions among the first few (9) fine structure levels of O VI using relativistic coupled cluster theory. We find irregular patterns for a number of transitions with in $n$-complexes ... More

Quasi-Local Strange MetalMay 28 2014Mar 23 2015One of the key factors that determine the fates of quantum many-body systems in the zero temperature limit is the competition between kinetic energy that delocalizes particles in space and interaction that promotes localization. While one dominates over ... More

The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regressionApr 25 2018This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp `phase transition'. We introduce an explicit boundary curve $h_{\text{MLE}}$, ... More

Reentrant phase transition in a predator-prey modelJul 11 2008May 30 2009We numerically investigate the six-species predator-prey game in complex networks as well as in $d$-dimensional hypercubic lattices with $d=1,2,..., 6$. The interaction topology of the six species contains two loops, each of which is composed of cyclically ... More

Virtual Interpolation Point Method for Viscous Flows in Complex GeometriesJan 25 2014Feb 04 2014A new approach for simulating flows over complex geometries is developed by introducing an accurate virtual interpolation point scheme as well as a virtual local stencil approach. The present method is based on the concept of point collocation on a virtual ... More

Weakly dynamic dark energy via metric-scalar couplings with torsionNov 02 2016We study the dynamical aspects of dark energy in the context of a non-minimally coupled scalar field with curvature and torsion. Whereas the scalar field acts as the source of the trace mode of torsion, a suitable constraint on the pseudo-trace of the ... More

Chiral non-Fermi LiquidsOct 28 2013Jul 21 2014A non-Fermi liquid state without time-reversal and parity symmetries arises when a chiral Fermi surface is coupled with a soft collective mode in two space dimensions. The full Fermi surface is described by a direct sum of chiral patch theories, which ... More

A modern maximum-likelihood theory for high-dimensional logistic regressionMar 19 2018Jun 16 2018Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there are formulas ... More

Anisotropic Non-Fermi LiquidsJun 21 2016Jul 27 2016We study non-Fermi liquid states that arise at the quantum critical points associated with the spin density wave (SDW) and charge density wave (CDW) transitions in metals with twofold rotational symmetry. We use the dimensional regularization scheme, ... More

The Minimum Gap-opening Planet Mass in an Irradiated Circumstellar Accretion DiskMay 23 2007Aug 02 2007We consider the minimum mass planet, as a function of radius, that is capable of opening a gap in an $\alpha$-accretion disk. We estimate that a half Jupiter mass planet can open a gap in a disk with accretion rate $\dot M \la 10^{-8} M_\odot$/yr for ... More

The Horizon Run N-body Simulation: Baryon Acoustic Oscillations and Topology of Large Scale Structure of the UniverseDec 08 2008Jun 09 2009In support of the new Sloan III survey, which will measure the baryon oscillation scale using the luminous red galaxies (LRGs), we have run the largest N-body simulation to date using $4120^3 = 69.9$ billion particles, and covering a volume of $(6.592 ... More

Transformation of Morphology and Luminosity Classes of the SDSS GalaxiesAug 30 2007Oct 23 2007We present a unified picture on the evolution of galaxy luminosity and morphology. Galaxy morphology is found to depend critically on the local environment set up by the nearest neighbor galaxy in addition to luminosity and the large scale density. When ... More

Topology of COBE Microwave Background FluctuationsJan 16 1996We have measured the topology (genus) of the fluctuations in the cosmic microwave background seen in the recently completed (four-year) data set produced by the COBE satellite. We find that the genus is consistent with that expected from a random-phase ... More

Proof of the Gorenstein Interval Conjecture in low socle degreeApr 23 2018Jan 09 2019Roughly ten years ago, the following "Gorenstein Interval Conjecture" (GIC) was proposed: Whenever $(1,h_1,\dots,h_i,\dots,h_{e-i},\dots,h_{e-1},1)$ and $(1,h_1,\dots,h_i+\alpha,\dots,h_{e-i}+\alpha,\dots,h_{e-1},1)$ are both Gorenstein Hilbert functions ... More

Continuity of the Explosive Percolation TransitionMar 23 2011Jun 16 2011The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is found to be well ... More

Geometric phase at graphene edgeJan 21 2014We study the scattering phase shift of Dirac fermions at graphene edge. We find that when a plane wave of a Dirac fermion is reflected at an edge of graphene, its reflection phase is shifted by the geometric phase resulting from the change of the pseudospin ... More

Local and Tunable Geometric Phase of Dirac Fermions in a Topological JunctionOct 22 2012We discover a new type of geometric phase of Dirac fermions in solids, which is an electronic analogue of the Pancharatnam phase of polarized light. The geometric phase occurs in a local and nonadiabatic scattering event of Dirac fermions at a junction, ... More

Slopes of smooth curves on Fano manifoldsMay 24 2010Mar 10 2011Ross and Thomas introduced the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature K\"ahler metric. This paper presents a study of slope stability of Fano manifolds of dimension ... More

Existence and stability in a virtual interpolation method of the Stokes equationsJan 25 2014In this paper, we propose a new virtual interpolation point method to formulate the discrete Stokes equations. We form virtual staggered structure for the velocity and pressure from the actual computation node set. The virtual interpolation point method ... More

The rotation-vibration structure of the SO$_2$ $\mathrm{\tilde{C}}^1\mathrm{B}_2$ state explained by a new internal coordinate force fieldApr 22 2016A new quartic force field for the SO$_2$ $\tilde{\text{C}}$$^1$B$_2$ state has been derived, based on high resolution data from S$^{16}$O$_2$ and S$^{18}$O$_2$. Included are eight $b_2$ symmetry vibrational levels of S$^{16}$O$_2$ reported in the first ... More

Acoustic omni meta-atom for top-down, decoupled access to all octants of a wave parameter spaceJan 18 2016The common behavior of a wave is determined by wave parameters of its medium, which are generally associated with the characteristic oscillations of its corresponding elementary particles. In the context of metamaterials, the decoupled excitation of these ... More

Discovery of five low luminosity active galactic nuclei at the centre of the Perseus clusterNov 18 2016According to optical stellar kinematics observations, an over-massive black hole candidate has been reported by van den Bosch et al. (2012) in the normal early-type galaxy NGC 1277. This galaxy is located in the central region of the Perseus cluster. ... More

Flexible and Scalable Deep Learning with MMLSparkApr 11 2018In this work we detail a novel open source library, called MMLSpark, that combines the flexible deep learning library Cognitive Toolkit, with the distributed computing framework Apache Spark. To achieve this, we have contributed Java Language bindings ... More

Genus Topology of the Cosmic Microwave Background from the WMAP 3-Year DataOct 25 2006We have independently measured the genus topology of the temperature fluctuations in the cosmic microwave background seen in the Wilkinson Microwave Anisotropy Probe (WMAP) 3-year data. A genus analysis of the WMAP data indicates consistency with Gaussian ... More

Horizon Run 3: Topology as a Standard RulerOct 16 2013We study the Physically Self Bound Cold Dark Matter Halo distribution which we associate with the massive galaxies within the Horizon Run 3 to estimate the accuracy in determination of the cosmological distance scale measured by the topology analysis. ... More