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Non-hydrodynamic transport in trapped unitary Fermi gasesAug 05 2015Nov 19 2015Many strongly coupled fluids are known to share similar hydrodynamic transport properties. In this work we argue that this similarity could extend beyond hydrodynamics to transient dynamics through the presence of non-hydrodynamic modes. We review non-hydrodynamic ... More

Towards Improved Testing For Deep LearningFeb 17 2019The growing use of deep neural networks in safety-critical applications makes it necessary to carry out adequate testing to detect and correct any incorrect behavior for corner case inputs before they can be actually used. Deep neural networks lack an ... More

Learning 6-DOF Grasping Interaction via Deep Geometry-aware 3D RepresentationsAug 24 2017Jun 15 2018This paper focuses on the problem of learning 6-DOF grasping with a parallel jaw gripper in simulation. We propose the notion of a geometry-aware representation in grasping based on the assumption that knowledge of 3D geometry is at the heart of interaction. ... More

When random search is not enough: Sample-Efficient and Noise-Robust Blackbox Optimization of RL PoliciesMar 07 2019Interest in derivative-free optimization (DFO) and "evolutionary strategies" (ES) has recently surged in the Reinforcement Learning (RL) community, with growing evidence that they match state of the art methods for policy optimization tasks. However, ... More

Data-Efficient Learning for Sim-to-Real Robotic Grasping using Deep Point Cloud Prediction NetworksJun 21 2019Training a deep network policy for robot manipulation is notoriously costly and time consuming as it depends on collecting a significant amount of real world data. To work well in the real world, the policy needs to see many instances of the task, including ... More

New methods to find patches of invisible integer lattice pointsMay 08 2018It is a surprising fact that the proportion of integer lattice points visible from the origin is $\frac{6}{\pi^2}$ (approximately 60 percent). Hence approximately 40 percent of the integer lattice is hidden from the origin. Since 1971, many have studied ... More

Time-Contrastive Networks: Self-Supervised Learning from VideoApr 23 2017Mar 20 2018We propose a self-supervised approach for learning representations and robotic behaviors entirely from unlabeled videos recorded from multiple viewpoints, and study how this representation can be used in two robotic imitation settings: imitating object ... More

RL-RRT: Kinodynamic Motion Planning via Learning Reachability Estimators from RL PoliciesJul 10 2019This paper addresses two challenges facing sampling-based kinodynamic motion planning: a way to identify good candidate states for local transitions and the subsequent computationally intractable steering between these candidate states. Through the combination ... More

RL-RRT: Kinodynamic Motion Planning via Learning Reachability Estimators from RL PoliciesJul 10 2019Jul 12 2019This paper addresses two challenges facing sampling-based kinodynamic motion planning: a way to identify good candidate states for local transitions and the subsequent computationally intractable steering between these candidate states. Through the combination ... More

Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motionMar 29 2009Jul 14 2009We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation of motion that ... More

Provably Robust Blackbox Optimization for Reinforcement LearningMar 07 2019Jul 08 2019Interest in derivative-free optimization (DFO) and "evolutionary strategies" (ES) has recently surged in the Reinforcement Learning (RL) community, with growing evidence that they can match state of the art methods for policy optimization problems in ... More

Long-Range Indoor Navigation with PRM-RLFeb 25 2019Long-range indoor navigation requires guiding robots with noisy sensors and controls through cluttered environments along paths that span a variety of buildings. We achieve this with PRM-RL, a hierarchical robot navigation method in which reinforcement ... More

Quantum Computing Simulation Optimizations and Operational Errors on Various 2-qubit Multiplier CircuitsAug 15 2002Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates. Additionally, ... More

Multi-period Time Series Modeling with Sparsity via Bayesian Variational InferenceJul 03 2017Oct 23 2018In this paper, we use augmented the hierarchical latent variable model to model multi-period time series, where the dynamics of time series are governed by factors or trends in multiple periods. Previous methods based on stacked recurrent neural network ... More

Time Series Compression Based on Adaptive Piecewise Recurrent AutoencoderJul 23 2017Aug 16 2017Time series account for a large proportion of the data stored in financial, medical and scientific databases. The efficient storage of time series is important in practical applications. In this paper, we propose a novel compression scheme for time series. ... More

Weighted sampling of outer productsOct 16 2014This note gives a simple analysis of the randomized approximation scheme for matrix multiplication of Drineas et al (2006) with a particular sampling distribution over outer products. The result follows from a matrix version of Bernstein's inequality. ... More

Frequency dependent conductivity of vortex cores in type II superconductorsAug 26 1992This paper is relevant to the recent optical transmission experiments of Karrai et al. for vortices in high Tc superconductors. We begin with a substantial review and introduction. The microscopic response of vortices is calculated from the Bogoliubov-deGennes ... More

Anomaly Detection on Graph Time SeriesAug 09 2017Nov 01 2017In this paper, we use variational recurrent neural network to investigate the anomaly detection problem on graph time series. The temporal correlation is modeled by the combination of recurrent neural network (RNN) and variational inference (VI), while ... More

Two classes of number fields with a non-principal Euclidean idealJun 17 2017This paper introduces two classes of totally real quartic number fields, one of biquadratic extensions and one of cyclic extensions, each of which has a non-principal Euclidean ideal. It generalizes techniques of Graves used to prove that the number field ... More

Optimized Treatment Schedules for Chronic Myeloid LeukemiaApr 17 2016Over the past decade, several targeted therapies (e.g. imatinib, dasatinib, nilotinib) have been developed to treat Chronic Myeloid Leukemia (CML). Despite an initial response to therapy, drug resistance remains a problem for some CML patients. Recent ... More

Lattice Boltzmann simulations of a two-dimensional Fermi gas at unitarityJul 21 2015We present fully nonlinear dissipative fluid dynamics simulations of a trapped two-dimensional Fermi gas at unitarity using a Lattice Boltzmann algorithm. We are able to simulate non-harmonic trapping potentials, temperature-dependent viscosities as well ... More

Applying Text Mining to Protest Stories as Voice against Media CensorshipDec 29 2018Data driven activism attempts to collect, analyze and visualize data to foster social change. However, during media censorship it is often impossible to collect such data. Here we demonstrate that data from personal stories can also help us to gain insights ... More

Class 2 Moufang loops, small Frattini Moufang loops, and code loopsNov 20 1996Let $L$ be a Moufang loop which is centrally nilpotent of class 2. We first show that the nuclearly-derived subloop (normal associator subloop) $L^*$ of $L$ has exponent dividing 6. It follows that $L_p$ (the subloop of $L$ of elements of $p$-power order) ... More

A general approach for analyzing baseline power spectral densities: Zwanzig-Mori projection operators and the generalized Langevin equationAug 06 2009There continues to be widespread interest in 1/f^(alpha) behavior in baseline power spectral densities (PSD's) but its origins remain controversial. Zwanzig-Mori projection operators provide a rigorous, common starting place for building a theory of PSD's ... More

Characterizing Classes of Potential Outliers through Traffic Data Set Data Signature 2D nMDS ProjectionFeb 24 2017This paper presents a formal method for characterizing the potential outliers from the data signature projection of traffic data set using Non-Metric Multidimensional Scaling (nMDS) visualization. Previous work had only relied on visual inspection and ... More

ATP concentration regulates enzyme kineticsJun 09 2014Adenosine 5'-triphosphate (ATP) is the nearly ubiquitous "energy currency" of living organisms, and thus is a crucial participant in the majority of enzymatic reactions. The standard models in enzyme kinetics generally ignore the temporal dynamics of ... More

Visual Content Privacy Leaks on Social Media NetworksJun 22 2018With the growth and accessibility of mobile devices and internet, the ease of posting and sharing content on social media networks (SMNs) has increased exponentially. Many users post images that contain "privacy leaks" regarding themselves or someone ... More

Geometric-progression-free sets over quadratic number fieldsDec 02 2014Nov 14 2015A problem of recent interest has been to study how large subsets of the natural numbers can be while avoiding 3-term geometric progressions. Building on recent progress on this problem, we consider the analogous problem over quadratic number fields. We ... More

The Gould-Hopper Polynomials in the Novikov-Veselov equationNov 07 2010May 17 2011We use the Gould-Hopper (GH) polynomials to investigate the Novikov-Veselov (NV) equation. The root dynamics of the $\sigma$-flow in the NV equation is studied using the GH polynomials and then the Lax pair is found. In particulr, when $N=3,4,5$, one ... More

On the water-bag model of dispersionless KP hierarchy (II)Feb 07 2007Aug 24 2007We construct the bi-Hamiltonian structure of the waterbag model of dKP and establish the third-order Hamiltonian operator associated with the waterbag model. Also, the symmetries and conserved densities of rational type are discussed.

Quantum Corrections in Collective Field TheoryOct 13 1993We review and extend the computation of scattering amplitudes of tachyons in the $c=1$ matrix model using a manifestly finite prescription for the collective field hamiltonian. We give further arguments for the exactness of the cubic hamiltonian by demonstrating ... More

Dynamical stability of the quantum Lifshitz theory in 2+1 DimensionsMay 22 2012Feb 11 2013The role of magnetic and electric perturbations to the quantum Lifshitz model in 2+1 dimensions are examined in this paper. The quantum Lifshitz model is an effective field theory for quantum multicritical systems, that include generalized 2D quantum ... More

Quark Confinement, New Cosmic Expansion and General Yang-Mills SymmetryAug 24 2016We discuss a unified model of quark confinement and new cosmic expansion with linear potentials based on a general $(SU_3)_{color} \times (U_1)_{baryon}$ symmetry. The phase functions in the usual gauge transformations are generalized to new `action integrals'. ... More

Grounding Spatio-Semantic Referring Expressions for Human-Robot InteractionJul 18 2017The human language is one of the most natural interfaces for humans to interact with robots. This paper presents a robot system that retrieves everyday objects with unconstrained natural language descriptions. A core issue for the system is semantic and ... More

Convergence Rates for Differentially Private Statistical EstimationJun 27 2012Differential privacy is a cryptographically-motivated definition of privacy which has gained significant attention over the past few years. Differentially private solutions enforce privacy by adding random noise to a function computed over the data, and ... More

Physical limits on information processingJul 12 2006Aug 04 2006We derive a fundamental upper bound on the rate at which a device can process information (i.e., the number of logical operations per unit time), arising from quantum mechanics and general relativity. In Planck units a device of volume V can execute no ... More

Entanglement entropy, black holes and holographyOct 03 2005We observe that the entanglement entropy resulting from tracing over a subregion of an initially pure state can grow faster than the surface area of the subregion (indeed, proportional to the volume), in contrast to examples studied previously. The pure ... More

A speculative relation between the cosmological constant and the Planck massJun 16 2004We propose the relation $M_\Lambda \sim (M_{Pl} M_U)^{1/2}$ where $M_\Lambda$, $M_{Pl},$ and $M_U$ denote the mass scale associated with the cosmological constant, the gravitational interaction, and the size of the universe respectively.

Regularization of Chiral Gauge TheoriesMar 10 1995Mar 09 1996We propose a nonperturbative formulation of chiral gauge theories. The method involves a `pre-regulation' of the gauge fields, which may be implemented on a lattice, followed by a computation of the chiral fermion determinant in the form of a functional ... More

On the genetic architecture of intelligence and other quantitative traitsAug 14 2014Aug 30 2014How do genes affect cognitive ability or other human quantitative traits such as height or disease risk? Progress on this challenging question is likely to be significant in the near future. I begin with a brief review of psychometric measurements of ... More

Factorization of unitarity and black hole firewallsAug 26 2013Nov 05 2013Unitary black hole evaporation necessarily involves a late-time superposition of decoherent states, including states describing distinct spacetimes (e.g., different center of mass trajectories of the black hole). Typical analyses of the black hole information ... More

Spacetime topology change and black hole informationAug 25 2006Nov 09 2006Topology change -- the creation of a disconnected baby universe -- due to black hole collapse may resolve the information loss paradox. Evolution from an early time Cauchy surface to a final surface which includes a slice of the disconnected region can ... More

Entropy Bounds and Dark EnergyMar 03 2004May 05 2004Entropy bounds render quantum corrections to the cosmological constant $\Lambda$ finite. Under certain assumptions, the natural value of $\Lambda$ is of order the observed dark energy density $\sim 10^{-10} {\rm eV}^4$, thereby resolving the cosmological ... More

Quintessence and Thermal MatterFeb 23 2004Jun 16 2004We investigate the effects of thermal interactions on tracking models of quintessence. We show that even Planck-suppressed interactions between matter and the quintessence field can alter its evolution. The dark energy equation of state is in many cases ... More

Neutron Star Vortex Dynamics and Magnetic Field Decay: Implications for High Density Nuclear MatterMar 13 1999We investigate the effect of the density-dependent proton and neutron gaps on vortex dynamics in neutron stars. We argue that the persistence of neutron star magnetic fields on timescales of $10^9$ y suggests a superconducting gap curve with local maximum ... More

Zero Energy Configurations in General RelativityJan 29 1998Jan 31 1998We investigate the ratio of gravitational binding energy to rest mass in general relativity. For N pointlike masses, an upper bound on the magnitude of this ratio can be derived using the second law of black hole dynamics. Only as N approaches infinity ... More

Quantum Scattering and Classical SolutionsJun 06 1994I discuss a formalism for computing quantum scattering amplitudes using a semiclassical expansion of a functional integral representation for the S-matrix. The classical background for the expansion is determined by solving the equations of motion subject ... More

Minimizer of an isoperimetric ratio on a metric on $\R^2$ with finite total areaJan 25 2010Apr 09 2011Let $g=(g_{ij})$ be a complete Riemmanian metric on $\R^2$ with finite total area and $I_g=\inf_{\gamma}I(\gamma)$ with $I(\gamma)=L(\gamma)(A_{in}(\gamma)^{-1}+A_{out}(\gamma)^{-1})$ where $\gamma$ is any closed simple curve in $\R^2$, $L(\gamma)$ is ... More

Monte Carlo Simulations of Lattice Models for Single Polymer SystemsMar 03 2015Single linear polymer chains in dilute solutions under good solvent conditions are studied by Monte Carlo simulations with the pruned-enriched Rosenbluth method up to the chain length $N \sim {\cal O}(10^4)$. Based on the standard simple cubic lattice ... More

New Development of Monte Carlo Techniques for Studying Bottle-brush PolymersJul 07 2011Due to the complex characteristics of bottle-brush polymers, it became a challenge to develop an efficient algorithm for studying such macromolecules under various solvent conditions or some constraints in the space by using computer simulations. In the ... More

Some Identities Involving Three Kinds of Counting NumbersNov 02 2009In this note, we present several identities involving binomial coefficients and the two kind of Stirling numbers.

The Gravitational Sine-Gordon ModelDec 03 1992We use matrix model results to investigate the Sine-Gordon model coupled to two dimensional gravity. For relevant (in the RG sense) potentials, we show that the $c=1$ string, which appears in the ultraviolet limit of this model, flows to a set of decoupled ... More

Informatic error-disturbance relation in the qubit caseOct 16 2014Oct 28 2014In 1927, Heisenberg heuristically disclosed the tradeoff between the error in the measurement and the caused disturbance on another complementary observable. In the quantum theory, most of uncertainty relations are proposed to reveal the amount of unavoidable ... More

Information causality and non-locality swapping are equivalent from emergence of quantum correlationsDec 14 2009Jan 17 2010Is information causality a new physical principle? To answer this question, we first analytically derive the criteria of emergence of quantum correlations from information causality. Then it is shown that, as emergence criteria of quantum correlations, ... More

Air Flow Analysis of a Rotating Cylinder through Numerical SimulationOct 24 2018The complete flow field surrounding a rotating cylinder is calculated by solving the Navier-Stokes equations using the finite difference method. The numerical simulation is performed on a transformed rectilinear grid, with axes representing the radial ... More

Laplacian Controllability of Interconnected GraphsAug 09 2018In this work we consider the Laplacian controllability of a graph constructed by interconnecting a finite number of single-input Laplacian controllable graphs. We first study the interconnection realized by the composite graph of two connected simple ... More

Global Spread of Infectious DiseasesJun 25 2003We develop simple models for the global spread of infectious diseases, emphasizing human mobility via air travel and the variation of public health infrastructure from region to region. We derive formulas relating the total and peak number of infections ... More

Quantum Production of Black HolesMar 16 2002Aug 07 2002We give a path integral expression for the quantum amplitude to produce a black hole from particle collisions. When expanded about an appropriate classical solution it yields the leading order contribution to the production amplitude in a curvature expansion. ... More

Complementarity and Chiral Fermions in SU(2) gauge TheoriesFeb 08 1993Complementarity - the absence of a phase boundary separating the Higgs and confinement phases of a gauge theory - can be violated by the addition of chiral fermions. We utilize chiral symmetry violating fermion correlators such as $ \langle \bps \psi ... More

On the origin of probability in quantum mechanicsOct 04 2011Mar 28 2012I give a brief introduction to many worlds or "no wavefunction collapse" quantum mechanics, suitable for non-specialists. I then discuss the origin of probability in such formulations, distinguishing between objective and subjective notions of probability. ... More

Physical consequences of the QED theta angleDec 14 2010We describe a simple gedanken experiment which illustrates the physical effects of the QED theta angle, a fundamental parameter of Nature that has yet to be measured. The effects are manifest in quantum phases analogous to those in the Aharonov-Bohm effect, ... More

White holes and eternal black holesJul 17 2010Nov 16 2011We investigate isolated white holes surrounded by vacuum, which correspond to the time reversal of eternal black holes that do not evaporate. We show that isolated white holes produce quasi- thermal Hawking radiation. The time reversal of this radiation, ... More

Bayesian Learning of Conditional Kernel Mean Embeddings for Automatic Likelihood-Free InferenceMar 03 2019In likelihood-free settings where likelihood evaluations are intractable, approximate Bayesian computation (ABC) addresses the formidable inference task to discover plausible parameters of simulation programs that explain the observations. However, they ... More

Parameter identification in Markov chain choice modelsJun 02 2017Jul 25 2017This work studies the parameter identification problem for the Markov chain choice model of Blanchet, Gallego, and Goyal used in assortment planning. In this model, the product selected by a customer is determined by a Markov chain over the products, ... More

A lower bound for the scalar curvature of the standard solution of the Ricci flowDec 15 2006In this paper we will give a rigorous proof of the lower bound for the scalar curvature of the standard solution of the Ricci flow conjectured by G. Perelman. We will prove that the scalar curvature $R$ of the standard solution satisfies $R(x,t)\ge C_0/(1-t)\quad\forall ... More

Another proof of Ricci flow on incomplete surfaces with bounded above Gauss curvatureNov 10 2010We give a simple proof of an extension of the existence results of Ricci flow of G.Giesen and P.M.Topping [GiT1],[GiT2], on incomplete surfaces with bounded above Gauss curvature without using the difficult Shi's existence theorem of Ricci flow on complete ... More

Gradient estimates for a nonlinear parabolic equation under Ricci flowJun 25 2008Let $(M,g(t))$, $0\le t\le T$, be a n-dimensional complete noncompact manifold, $n\ge 2$, with bounded curvatures and metric $g(t)$ evolving by the Ricci flow $\frac{\partial g_{ij}}{\partial t}=-2R_{ij}$. We will extend the result of L. Ma and Y. Yang ... More

A Generalization of Gauge Symmetry, Fourth-Order Gauge Field Equations and Accelerated Cosmic-ExpansionFeb 14 2014A generalization of the usual gauge symmetry leads to fourth-order gauge field equations, which imply a new constant force independent of distances. The force associated with the new $U_1$ gauge symmetry is repulsive among baryons. Such a constant force ... More

A model of unified quantum chromodynamics and Yang-Mills gravityAug 11 2011Based on a generalized Yang-Mills framework, gravitational and strong interactions can be unified in analogy with the unification in the electroweak theory. By gauging $T(4) \times [SU(3)]_{color} $ in flat space-time, we have a unified model of chromo-gravity ... More

A Unified Gravity-Electroweak Model Based on a Generalized Yang-Mills FrameworkJun 10 2011Gravitational and electroweak interactions can be unified in analogy with the unification in the Weinberg-Salam theory. The Yang-Mills framework is generalized to include space-time translational group T(4), whose generators $T_{\mu}(=\p/\p x^{\mu})$ ... More

An elementary proof of the convergence of Ricci flow on compact surfacesMay 16 2007Jun 03 2009This paper has been withdrawn by the author for further modification.

Phase Transition and Acoustic Localization in Arrays of Air-Bubbles in WaterJun 23 2000Wave localization is a ubiquitous phenomenon. It refers to situations that transmitted waves in scattering media are trapped in space and remain confined in the vicinity of the initial site until dissipated. Here we report a phase transition from acoustically ... More

Viscous singular shock profiles for the Keyfitz-Kranzer systemDec 03 2015It was shown by Schecter (2004, J. Differential Equations, 205, 185-210), using the methods of Geometric Singular Perturbation Theory, that the Dafermos regularization $u_t+f(u)_x= \epsilon tu_{xx}$ for the Keyfitz-Kranzer system admits an unbounded family ... More

Global behaviour of solutions of the fast diffusion equationOct 17 2017Dec 20 2017We will extend a recent result of B.~Choi and P.~Daskalopoulos (\cite{CD}). For any $n\ge 3$, $0<m<\frac{n-2}{n}$, $m\ne\frac{n-2}{n+2}$, $\beta>0$ and $\lambda>0$, we prove the higher order expansion of the radially symmetric solution $v_{\lambda,\beta}(r)$ ... More

On the Sustainability of Electrical VehiclesNov 23 2013Many perceive electric vehicles (EVs) to be eco-environmentally sustainable because they are free of emissions of toxic and greenhouse gases to the environment. However, few have questioned the sustainability of the electric power required to drive these ... More

Diameter-based Interactive Structure SearchJun 05 2019In this work, we introduce \emph{interactive structure search}, a generic framework that encompasses many interactive learning settings, both explored and unexplored. We show that a recently developed active learning algorithm of~\citet{TD17} can be adapted ... More

Existence and asymptotic behaviour of solutions of the very fast diffusion equationSep 16 2011Let n>2, $0<m\le (n-2)/n$, p>\max(1,(1-m)n/2), and $0\le u_0\in L_{loc}^p(R^n)$ satisfy $\liminf_{R\to\infty}R^{-n+\frac{2}{1-m}}\int_{|x|\le R}u_0\,dx=\infty$. We prove the existence of unique global classical solution of $u_t=\frac{n-1}{m}\Delta u^m$, ... More

The emergence of 4-cycles in polynomial maps over the extended integersJul 13 2015Let $f(x) \in \mathbb{Z}[x]$; for each integer $\alpha$ it is interesting to consider the number of iterates $n_{\alpha}$, if possible, needed to satisfy $f^{n_{\alpha}}(\alpha) = \alpha$. The sets $\{\alpha, f(\alpha), \ldots, f^{n_{\alpha} - 1}(\alpha), ... More

An introduction to linear stability analysis for deciphering spatial patterns in signaling networksJan 27 2015Jul 22 2016Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains are now widely ... More

IGM-Vis: Analyzing Intergalactic and Circumgalactic Medium Absorption Using Quasar Sightlines in a Cosmic Web ContextDec 17 2018Apr 25 2019We introduce IGM-Vis, a novel astrophysics visualization and data analysis application for investigating galaxies and the gas that surrounds them in context with their larger scale environment, the Cosmic Web. Environment is an important factor in the ... More

Asymptotic analysis of rogue waves in the KP-(I) equationMay 29 2016Inspired by the works of Y. Ohta and J. Yang, one constructs the rogue waves solutions in the KP-(I) equation using the Grammian determinants. It is shown that the number of lumps will depend on the real roots of Wronskian of the Hermite polynomials for ... More

A new Hedging algorithm and its application to inferring latent random variablesJun 30 2008We present a new online learning algorithm for cumulative discounted gain. This learning algorithm does not use exponential weights on the experts. Instead, it uses a weighting scheme that depends on the regret of the master algorithm relative to the ... More

Nonperturbative Decoupling and Effective Field TheoryOct 29 1993Nov 01 1993We examine recent claims that nonperturbative effects can prevent the decoupling of a heavy fermion whose mass arises from a Yukawa coupling to a scalar field. We show that in weakly coupled, four dimensional models such as the standard model with heavy ... More

Resource Allocation for Wireless Networks: A Distributed Optimization ApproachJun 08 2017We consider the multi-cell joint power control and scheduling problem in cellular wireless networks as a weighted sum-rate maximization problem. This formulation is very general and applies to a wide range of applications and QoS requirements. The problem ... More

Some results for the Perelman LYH-type inequalityJan 23 2008May 12 2008Let $(M,g(t))$, $0\le t\le T$, $\partial M\ne\phi$, be a compact $n$-dimensional manifold, $n\ge 2$, with metric $g(t)$ evolving by the Ricci flow such that the second fundamental form of $\partial M$ with respect to the unit outward normal of $\partial ... More

A simple proof on the non-existence of shrinking breathers for the Ricci flowSep 05 2005Jan 21 2006Suppose $M$ is a compact n-dimensional manifold, $n\ge 2$, with a metric $g_{ij}(x,t)$ that evolves by the Ricci flow $\partial_tg_{ij}=-2R_{ij}$ in $M\times (0,T)$. We will give a simple proof of a recent result of Perelman on the non-existence of shrinking ... More

A harmonic map flow associated with the standard solution of Ricci flowFeb 07 2007Let $(\Bbb{R}^n,g(t))$, $0\le t\le T$, $n\ge 3$, be a standard solution of the Ricci flow with radially symmetric initial data $g_0$. We will extend a recent existence result of P. Lu and G. Tian and prove that for any $t_0\in [0,T)$ there exists a solution ... More

Maximum principle and convergence of fundamental solutions for the Ricci flowNov 08 2007In this paper we will prove a maximum principle for the solutions of linear parabolic equation on complete non-compact manifolds with a time varying metric. We will prove the convergence of the Neumann Green function of the conjugate heat equation for ... More

Lattice Monte Carlo Simulations of Polymer MeltsMar 03 2015We use Monte Carlo simulations to study polymer melts consisting of fully flexible and moderately stiff chains in the bond fluctuation model at a volume fraction $0.5$. In order to reduce the local density fluctuations, we test a pre-packing process for ... More

The Interactions of Solitons in the Novikov-Veselov EquationOct 15 2013Aug 07 2014Using the reality condition of the solutions, one constructs the real Pfaffian N-solitons solutions of the Novikov-Veselov (NV) equation using the $\tan$ function and the Schur identity. By the minor-summation formula of the Pfaffian, we can study the ... More

Uniform Sobolev inequalities for manifolds evolving by Ricci flowAug 07 2007Let M be a compact n-dimensional manifold, $n\ge 2$, with metric g(t) evolving by the Ricci flow $\partial g_{ij}/\partial t=-2R_{ij}$ in (0,T) for some $T\in\Bbb{R}^+\cup\{\infty\}$ with $g(0)=g_0$. Let $\lambda_0(g_0)$ be the first eigenvalue of the ... More

Viscous singular shock profiles for a system of conservation laws modeling two-phase flowDec 01 2015This paper is concerned with singular shocks for a system of conservation laws modeling incompressible two-phase fluid flow. We prove the existence of viscous profiles using the Geometric Singular Perturbation Theory. Weak convergence and growth rates ... More

Exact decay rate of a nonlinear elliptic equation related to the Yamabe flowNov 14 2012Jan 12 2013Let 0<m<(n-2)/n, n>2, $\alpha=(2\beta +\rho)/(1-m)$ and $\beta>m\rho/(n-2-mn)$ for some constant $\rho>0$. Suppose v is a radially symmetric symmetric solution of $\frac{n-1}{m}\Delta v^m+\alpha v+\beta x\cdot\nabla v=0$, v>0, in $R^n$. When m=(n-2)/(n+2), ... More

Number and Stability of Relaxation Oscillations for Predator-Prey Systems with Small Death RatesJan 08 2018Oct 29 2018We consider planar systems of predator-prey models with small predator death rate $\epsilon>0$. Using geometric singular perturbation theory and Floquet theory, we derive characteristic functions that determines the location and the stability of relaxation ... More

On a Flywheel-Based Regenerative Braking System for Regenerative Energy RecoveryNov 23 2013This paper presents a unique flywheel-based regenerative energy recovery, storage and release system developed at the author's laboratory. It can recover and store regenerative energy produced by braking a motion generator with intermittent rotary velocity ... More

On Bifurcation Delay: An Alternative Approach Using Geometric Singular Perturbation TheoryApr 14 2016Jul 29 2016To explain the phenomenon of bifurcation delay, which occurs in planar systems of the form $\dot{x}=\epsilon f(x,z,\epsilon)$, $\dot{z}=g(x,z,\epsilon)z$, where $f(x,0,0)>0$ and $g(x,0,0)$ changes sign at least once on the $x$-axis, we use the Exchange ... More

Effect of three-particle correlations in low dimensional Hubbard modelsFeb 16 1993A simple approximation which captures some non-perturbative aspects of the one electron Green function of strongly interacting Fermion systems is developed. It provides a way to go one step beyond the usual dilute limit since particle-particle as well ... More

Existence and properties of ancient solutions of the Yamabe flowJun 09 2016Jun 11 2016Let $n\ge 3$ and $m=\frac{n-2}{n+2}$. We construct $5$-parameters, $4$-parameters, $3$-parameters ancient solutions of the equation $v_t=(v^m)_{xx}+v-v^m$, $v>0$, in $\mathbb{R}\times (-\infty,T)$ for some $T\in\mathbb{R}$. This equation arises in the ... More

Super fast vanishing solutions of the fast diffusion equationFeb 25 2019We will extend a recent result of B.Choi, P.Daskalopoulos and J.King. For any $n\ge 3$, $0<m<\frac{n-2}{n+2}$ and $\gamma>0$, we will construct subsolutions and supersolutions of the fast diffusion equation $u_t=\frac{n-1}{m}\Delta u^m$ in $\mathbb{R}^n\times ... More

Dynamics of cancer recurrenceJul 19 2013Mutation-induced drug resistance in cancer often causes the failure of therapies and cancer recurrence, despite an initial tumor reduction. The timing of such cancer recurrence is governed by a balance between several factors such as initial tumor size, ... More