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A Smoother Way to Train Structured Prediction ModelsFeb 08 2019We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and paves the way for ... More

Data Driven Resource Allocation for Distributed LearningDec 15 2015In distributed machine learning, data is dispatched to multiple machines for processing. Motivated by the fact that similar data points are often belonging to the same or similar classes, and more generally, classification rules of high accuracy tend ... More

A Markov Chain Theory Approach to Characterizing the Minimax Optimality of Stochastic Gradient Descent (for Least Squares)Oct 25 2017Jul 21 2018This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and by sharply ... More

Data Driven Resource Allocation for Distributed LearningDec 15 2015Dec 15 2016In distributed machine learning, data is dispatched to multiple machines for processing. Motivated by the fact that similar data points often belong to the same or similar classes, and more generally, classification rules of high accuracy tend to be "locally ... More

The Phases of QCD in Heavy Ion Collisions and Compact StarsSep 05 2000Sep 14 2000I review arguments for the existence of a critical point in the QCD phase diagram as a function of temperature and baryon chemical potential. I describe how heavy ion collision experiments at the SPS and RHIC can discover the tell-tale signatures of such ... More

Traversing the QCD Phase Transition: Quenching Out of Equilibrium vs. Slowing Out of Equilibrium vs. Bubbling Out of EquilibriumMay 11 2000May 15 2000I review arguments for the existence of a critical point E in the QCD phase diagram as a function of temperature T and baryon chemical potential \mu. I describe how heavy ion collision experiments at the SPS and RHIC can discover the tell-tale signatures ... More

Crystalline Color SuperconductivitySep 14 2001We give an introduction crystalline color superconductivity, arguing that it is likely to occur wherever quark matter in which color-flavor locking does not occur is found. We survey the properties of this form of quark matter, and argue that its presence ... More

Collision Induced Decays of Electroweak Solitons: Fermion Number Violation with Two Initial ParticlesAug 23 1996This paper presents work done in collaboration with E. Farhi, J. Goldstone, and A. Lue which is described in full in Ref. [1]. We consider a variant of the standard electroweak theory in which the Higgs sector has been modified so that there is a classically ... More

Emergence of long wavelength pion oscillations following a rapid QCD phase transitionAug 28 1993To model the dynamics of the chiral order parameter in a far from equilibrium QCD phase transition, we consider quenching in the O(4) linear sigma model. We summarize arguments and numerical evidence which show that in the period immediately following ... More

Seshadri constants on surfaces with Picard number 1Aug 16 2016Let $X$ be a smooth projective surface with Picard number 1. Let $L$ be the ample generator of the N\'eron-Severi group of $X$. Given an integer $r\ge 2$, we prove lower bounds for the Seshadri constant of $L$ at $r$ general points in $X$.

On K_2 of 1-dimensional local ringsFeb 12 2004We study K_2 of one-dimensional local domains over a field of characteristic 0, introduce a conjecture, and show that this conjecture implies Geller's conjecture. We also show that Berger's conjecture implies Geller's conjecture, and hence verify it in ... More

Cobordism of flag bundlesJul 07 2010Let $G$ be a connected linear algebraic group over a field $k$ of characteristic zero. For a principal $G$-bundle $\pi: E \to X$ over a scheme $X$ of finite type over $k$ and a parabolic subgroup $P$ of $G$, we describe the rational algebraic cobordism ... More

Riemann-Roch For Equivariant K-TheoryJun 09 2009The goal of this paper is to prove the Riemann-Roch isomorphism for the higher equivariant K-theory of varieties with action of a linear algebraic group.

Limit Set Intersection Theorem for Graph of Relatively Hyperbolic GroupsDec 13 2018Dec 14 2018Let $G$ be a relatively hyperbolic group that admits a decomposition into a finite graph of relatively hyperbolic groups structure with quasi-isomterically (qi) embedded condition. We prove that the set of conjugates of all the vertex and edge groups ... More

Taut Foliations, Positive 3-Braids, and the L-Space ConjectureSep 11 2018We construct taut foliations in every closed 3-manifold obtained by $r$-framed Dehn surgery along a positive 3-braid knot $K$ in $S^3$, where $r < 2g(K)-1$ and $g(K)$ denotes the Seifert genus of $K$. This confirms a prediction of the L-space Conjecture. ... More

N= 4 Supersymmetric Quantum Mechanical Model: Novel SymmetriesJun 19 2016Mar 03 2017We discuss a set of novel discrete symmetry transformations of the N = 4 supersymmetric quantum mechanical model of a charged particle moving on a sphere in the background of Dirac magnetic monopole. The usual five continuous symmetries (and their conserved ... More

Positivity of line bundles on general blow ups of $\mathbb{P}^2$Jul 23 2015Oct 19 2016Let $X$ be the blow up of $\mathbb{P}^2$ at $r$ general points $p_1,\ldots,p_r \in \mathbb{P}^2$. We study line bundles on $X$ given by plane curves of degree $d$ passing through $p_i$ with multiplicity $m_i$. We establish conditions for ampleness, very ... More

The QCD Tricritical Point: Beyond Monotony in Heavy Ion PhysicsAug 18 1998I first sketch recent developments concerning the phase diagram of strongly interacting matter as a function of temperature and baryon density, obtained using a model for two-flavor QCD in which the interaction between quarks is modelled on that induced ... More

Three-Flavor QCD at High Density: Color Flavor Locking and Chiral Symmetry BreakingJul 09 1998We propose a symmetry breaking scheme for QCD with three massless quarks at high baryon density wherein the color and flavor SU(3)_{color}xSU(3)_{L}xSU(3)_{R} symmetries are broken down to the diagonal subgroup SU(3)_{color+L+R} by the formation of a ... More

Extension of $ν$MSM model and possible explanations of recent astronomical and collider observationsDec 21 2015Here I present the extension to ${\nu}$MSM model by adding a $U(1)'$ gauge symmetry under which right-handed fermions including sterile neutrinos and exotic Higgs scalar are charged. This model explains 3.5 keV line observed by XMM-Newton telescope as ... More

Absolutely continuous spectrum and spectral transition for some continuous random operatorsFeb 21 2011In this paper we consider two classes of random Hamiltonians on $L^2(\RR^d)$ one that imitates the lattice case and the other a Schr\"odinger operator with non-decaying, non-sparse potential both of which exhibit a.c. spectrum. In the former case we also ... More

The Shapley Value of Digraph GamesJan 06 2017Jun 07 2017In this paper the Shapley value of digraph (directed graph) games are considered. Digraph games are transferable utility (TU) games with limited cooperation among players, where players are represented by nodes. A restrictive relation between two adjacent ... More

Toroidalization of Locally Toroidal Morphisms from N-folds to SurfacesMar 28 2008Jul 14 2008The toroidalization conjecture of D. Abramovich, K. Karu, K. Matsuki, and J. Wlodarczyk asks whether any given morphism of nonsingular varieties over an algebraically closed field of characteristic zero can be modified into a toroidal morphism. Following ... More

Formation and Destruction of Autocatalytic Sets in an Evolving Network ModelMar 28 2004I analyse a model of an evolving network represented as a directed graph; each node corresponds to one molecular species and the links to catalytic interactions between species. Over short timescales the graph remains fixed while relative populations ... More

Seshadri constants on surfaces with Picard number 1Aug 16 2016Oct 19 2016Let $X$ be a smooth projective surface with Picard number 1. Let $L$ be the ample generator of the N\'eron-Severi group of $X$. Given an integer $r\ge 2$, we prove lower bounds for the Seshadri constant of $L$ at $r$ general points in $X$.

Equivariant K-theory and Higher Chow Groups of Smooth VarietiesJun 17 2009For a quasi-projective variety $X$ over a field, with the action of a split torus, we construct a spectral sequence relating the equivariant and the ordinary higher Chow groups. We then completely describe the equivariant higher Chow groups of smooth ... More

The Chiral Phase Transition in QCD: Critical Phenomena and Long Wavelength Pion OscillationsApr 16 1995May 07 1995In QCD with two massless quarks, the chiral phase transition is plausibly in the same universality class as the classical O(4) magnet. To test this hypothesis, critical exponents characterizing the behaviour of universal quantities near the 2nd order ... More

Mapping the QCD Phase DiagramAug 15 1999I review recent theoretical developments which show how a key qualitative feature of the QCD phase diagram, namely a critical point which in a sense defines the landscape which heavy ion collision experiments are seeking to map, can be discovered. The ... More

Positivity of line bundles on special blow ups of $\mathbb{P}^2$Aug 19 2016Sep 27 2016Let $C \subset \mathbb{P}^2$ be an irreducible and reduced curve of degree $e > 0$. Let $X$ be the blow up of $\mathbb{P}^2$ at $r$ distinct points $p_1,\ldots,p_r \in C$. We study line bundles on $X$ and establish conditions for ampleness and $k$-very ... More

Representation Variety of Surface GroupsFeb 20 2017Apr 18 2017We give an exact formula for the dimension of the variety of homomorphisms from $S_g$ to $\mathit{any}$ semisimple real algebraic group, where $S_g$ is a surface group of genus $g \geq 2$.

Torsion elements of the Nottingham group of order $p^2$ and type $\langle 2, m \rangle$Oct 25 2017Apr 17 2018We classify torsion elements of order $p^2$ and type $\langle 2, m \rangle$ in the Nottingham group defined over a prime field of characteristic $p >0$.

Inner Cohomology of the General Linear GroupAug 07 2017Feb 20 2018The main theorem is incorrectly stated.

Murthy's conjecture on 0-cyclesNov 13 2015Mar 18 2019We show that the Levine-Weibel Chow group of 0-cycles $\CH^d(A)$ of a reduced affine algebra $A$ of dimension $d \ge 2$ over an algebraically closed field is torsion-free. Among several applications, it implies an affirmative solution to an old conjecture ... More

The motivic cobordism for group actionsJun 26 2012For a linear algebraic group $G$ over a field $k$, we define an equivariant version of the Voevodsky's motivic cobordism $MGL$. We show that this is an oriented cohomology theory with localization sequence on the category of smooth $G$-schemes and there ... More

Inner cohomology of $GL_n$Feb 20 2018Feb 22 2018We give an explicit description of the inner cohomology of an adelic locally symmetric space of a given level structure attached to the general linear group of prime rank $n$, with coefficients in a locally constant sheaf of complex vector spaces. We ... More

Positivity of line bundles on general blow ups of $\mathbb{P}^2$Jul 23 2015Nov 19 2015Let $X$ be the blow up of $\mathbb{P}^2$ at $r$ general points $p_1,\ldots,p_r \in \mathbb{P}^2$. We study line bundles on $X$ given by plane curves of degree $d$ passing through $p_i$ with multiplicity $m_i$. We establish conditions for ampleness, very ... More

Perspectives on the mathematics of biological patterning and morphogenesisOct 08 2016A central question in developmental biology is how size and position are determined. The genetic code carries instructions on how to control these properties in order to regulate the pattern and morphology of structures in the developing organism. Transcription ... More

Disorienting the Chiral Condensate at the QCD Phase TransitionMar 06 1997I sketch how long wavelength modes of the pion field can be amplified during the QCD phase transition. If nature had been kinder, and had made the pion mass significantly less than the critical temperature for the transition, then this phenomenon would ... More

Zero cycles on affine varietiesNov 13 2015We show that the Chow group of 0-cycles of an affine algebra of dimension at least two over an algebraically closed field is torsion-free. As consequences, we affirmatively answer a question of Murthy and derive several other applications.

Murthy's conjecture on 0-cyclesNov 13 2015Mar 22 2018We show that the Levine-Weibel Chow group of 0-cycles $\CH^d(A)$ of a reduced affine algebra $A$ of dimension $d \ge 2$ over an algebraically closed field is torsion-free. Among several applications, it implies an affirmative solution to an old conjecture ... More

JSON Web Token (JWT) based client authentication in Message Queuing Telemetry Transport (MQTT)Mar 07 2019This paper is an overview of JSON Web Token (JWT) and Transport Layer Security (TLS) as two primary approaches for authentication of the things on the Internet. JSON Web Token (JWT) is used extensively today for authorization and authentication within ... More

AC spectrum for a class of random operators at small disorderJul 11 2011In this paper we present a class of Anderson type operators with independent, non-stationary (non-decaying) random potentials supported on a subset of positive density in the odd-dimensional lattice and prove the existence of pure absolutely continuous ... More

Time dependent density functional theory for nonadiabatic electronic dynamicsJan 10 2009We show that the time dependent single electron, nuclear density matrix of an interacting electronic system coupled to nuclear degrees of freedom can be exactly reproduced by that of an electronic system with arbitrarily specified electron-electron interactions ... More

Completion theorem for equivariant $K$-theoryJan 27 2012Nov 16 2015In this paper, we study the algebraic analogue of the topological Atiyah-Segal completion theorem. We verify this completion theorem for the algebraic equivariant $K$-theory of smooth projective schemes. We also show that the completion theorem fails ... More

Equivariant K-theory and Higher Chow Groups of SchemesJun 17 2009Nov 30 2016For a smooth quasi-projective scheme $X$ over a field $k$ with an action of a reductive group, we establish a spectral sequence connecting the equivariant and the ordinary higher Chow groups of $X$. For $X$ smooth and projective, we show that this spectral ... More

Torsion in the 0-cycle group with modulusJul 06 2016Feb 16 2018We show, for a smooth projective variety $X$ over an algebraically closed field $k$ with an effective Cartier divisor $D$, that the torsion subgroup $\CH_0(X|D)\{l\}$ can be described in terms of a relative {\'e}tale cohomology for any prime $l \neq p ... More

Gersten Conjecture For Equivariant K-theory And ApplicationsJun 22 2009For a reductive group scheme over a regular semi-local ring, we prove an equivarinat version of the Gersten conjecture. We draw some interesting consequences for the representation rings of such reductive group schemes. We also prove the rigidity for ... More

An Artin-Rees Theorem and applications to zero cyclesApr 10 2008We prove an Artin-Rees type theorem for algebraic cycles and give an application to zero cycles.

Positivity of line bundles on special blow ups of $\mathbb{P}^2$Aug 19 2016Jan 06 2017Let $C \subset \mathbb{P}^2$ be an irreducible and reduced curve of degree $e > 0$. Let $X$ be the blow up of $\mathbb{P}^2$ at $r$ distinct smooth points $p_1,\ldots,p_r \in C$. We study line bundles on $X$ and establish conditions for ampleness and ... More

Some Koszul Rings from GeometryMay 23 2009Jun 23 2009We give examples of Koszul rings that arise naturally in algebraic geometry. In the first part, we prove a general result on Koszul property associated to an ample line bundle on a projective variety. Specifically, we show how Koszul property of multiples ... More

How to Find the QCD Critical PointMar 31 1999The event-by-event fluctuations in heavy ion collisions carry information about the thermodynamic properties of the hadronic system at the time of freeze-out. By studying these fluctuations as a function of varying control parameters, such as the collision ... More

QCD at Finite Baryon Density: Chiral Symmetry Restoration and Color SuperconductivityMar 13 1998We use a variational procedure to study finite density QCD in an approximation in which the interaction between quarks is modelled by that induced by instantons. We find that uniform states with conventional chiral symmetry breaking have negative pressure ... More

N= 4 Supersymmetric Quantum Mechanical Model: Novel SymmetriesJun 19 2016We discuss a set of novel discrete symmetry transformations of the N = 4 supersymmetric quantum mechanical model of a charged particle moving on a sphere in the background of Dirac magnetic monopole. The usual five continuous symmetries (and their conserved ... More

On torsion in the 0-cycle group with modulusJul 06 2016We show for a smooth projective variety $X$ over an algebraically closed field $k$ with an effective Cartier divisor $D$ that the torsion subgroup $\CH_0(X|D)\{l\}$ can be described in terms of a relative {\'e}tale cohomology for any prime $l \neq p = ... More

Representation Variety of Fuchsian Groups in SO(p,q)Nov 11 2014Oct 14 2015We estimate the dimension of the variety of homomorphisms from $\Gamma$ to $ SO(p,q)$ with Zariski dense image, where $\Gamma$ is a Fuchsian group, and $SO(p,q)$ is the indefinite special orthogonal group with signature $(p,q)$.

On 0-cycles with modulusApr 13 2015Nov 16 2015Given a smooth surface $X$ over a field and an effective Cartier divisor $D$, we provide an exact sequence connecting $CH_0(X,D)$ and the relative $K$-group $K_0(X,D)$. We use this exact sequence to answer a question of Kerz and Saito whenever $X$ is ... More

Equivariant Cobordism for Torus ActionsOct 29 2010We study the equivariant cobordism theory of schemes for torus actions. We give the explicit relation between the equivariant and the ordinary cobordism of schemes with torus action. We deduce analogous results for action of arbitrary connected linear ... More

Equivariant cobordism of schemesJun 16 2010Oct 25 2010We study the equivariant cobordism theory of schemes for action of linear algebraic groups. We compare the equivariant cobordism theory for the action of a linear algebraic groups with similar groups for the action of tori and deduce some consequences ... More

On The Negative K-Theory of Schemes in Finite CharacteristicNov 03 2008We study the negative $K$-theory of singular varieties over a field of positive characteristic and in particular, prove the vanishing of $K_i(X)$ for $i < -d-2$ for a $k$-variety of dimension $d$.

Quantum equations for vibrational dynamics on metal surfacesJul 05 2006A first-principles treatment of the vibrational dynamics of molecular chemisorbates on metal surfaces is presented. It is shown that the mean field quantum evolution of the vibrational position operator is determined by a quantum Langevin equation with ... More

Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum-classical limitFeb 25 2007This work identifies geometric effects on dynamics due to nonadiabatic couplings in Born Oppenheimer systems and provides a systematic method for deriving corrections to mixed quantum-classical methods. Specifically, an exact path integral formulation ... More

0-cycles on singular schemes and class field theoryFeb 05 2015We show that the Chow group of 0-cycles on a singular projective scheme $X$ over a finite field describes the abelian extensions of its function field which are unramified over the regular locus of $X$. As a consequence, we obtain the Bloch-Quillen formula ... More

Completions of Higher Equivariant K-theoryJun 15 2009The goal of this paper is to prove a version of the non-abelian localization theorem for the rational equivariant K-theory of a smooth variety $X$ with the action of a linear algebraic group $G$. We then use this to prove a Riemann-Roch theorem which ... More

Continuity of integrated density of states -- independent randomnessSep 14 2006Sep 19 2006In this paper we discuss the continuity properties of the integrated density of states for random models based on that of the single site distribution. Our results are valid for models with independent randomness with arbitrary free parts. In particular ... More

A cdh approach to zero-cycles on singular varietiesMar 01 2010We study the Chow group of zero-cycles on singular varieties using the cdh topology. We define the cdh versions of the zero-cycles and albanese maps. We prove results comparing these groups for a singular variety with the similar groups on the resolution ... More

Stability, convergence and Hopf bifurcation analyses of the classical car-following modelJul 29 2016Mar 29 2018Reaction delays play an important role in determining the qualitative dynamical properties of a platoon of vehicles traversing a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of the Classical Car-Following ... More

The Modified Optimal Velocity Model: Stability Analyses and Design GuidelinesJun 29 2017Jul 20 2017Reaction delays are important in determining the qualitative dynamical properties of a platoon of vehicles traveling on a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of the Modified Optimal Velocity Model ... More

Impact of delayed acceleration feedback on the classical car-following modelMay 24 2018Delayed feedback plays a vital role in determining the qualitative dynamical properties of a platoon of vehicles driving on a straight road. Motivated by the positive impact of Delayed Acceleration Feedback (DAF) in various scenarios, in this paper, we ... More

Mass-Induced Crystalline Color SuperconductivityDec 14 2001Jan 09 2002We demonstrate that crystalline color superconductivity may arise as a result of pairing between massless quarks and quarks with nonzero mass m_s. Previous analyses of this phase of cold dense quark matter have all utilized a chemical potential difference ... More

Illuminating Dense Quark MatterJul 19 2001We imagine shining light on a lump of cold dense quark matter, in the CFL phase and therefore a transparent insulator. We calculate the angles of reflection and refraction, and the intensity of the reflected and refracted light. Although the only potentially ... More

Stressed pairing in conventional color superconductors is unavoidableDec 02 2005Jan 18 2006At sufficiently high densities, cold dense three-flavor quark matter is in the color-flavor locked (CFL) phase, in which all nine quarks pair in a particularly symmetric fashion. Once the heaviness of the strange quark (mass $m_s$) and the requirements ... More

Multiple Signal Classification Algorithm (MUSICAL) for super-resolution fluorescence microscopyNov 28 2016Super-resolution microscopy is providing unprecedented insights into biology by resolving details much below the diffraction limit. State-of-the-art Single Molecule Localization Microscopy (SMLM) techniques for super-resolution are restricted by long ... More

Multilevel Coding Schemes for Compute-and-Forward with Flexible DecodingDec 12 2011Dec 14 2011We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute and forward paradigm, we present a multilevel coding scheme that permits computation ... More

Joint Compute and Forward for the Two Way Relay Channel with Spatially Coupled LDPC CodesMay 26 2012We consider the design and analysis of coding schemes for the binary input two way relay channel with erasure noise. We are particularly interested in reliable physical layer network coding in which the relay performs perfect error correction prior to ... More

An MSE Based Ttransfer Chart to Analyze Iterative Decoding SchemesJun 14 2005An alternative to extrinsic information transfer (EXIT) charts called mean squared error (MSE) charts that use a measure related to the MSE instead of mutual information is proposed. Using the relationship between mutual information and minimum mean squared ... More

Multi-point Seshadri constants on ruled surfacesOct 25 2016Let $X$ be a surface and let $L$ be an ample line bundle on $X$. We first obtain a lower bound for the Seshadri constant $\varepsilon(X,L,r)$, when $r \ge 3$. We then assume that $X$ is a ruled surface and study Seshadri constants on $X$ in greater detail. ... More

Bellwethers: A Baseline Method For Transfer LearningMar 17 2017Jan 21 2018Software analytics builds quality prediction models for software projects. Experience shows that (a) the more projects studied, the more varied are the conclusions; and (b) project managers lose faith in the results of software analytics if those results ... More

K-theory and 0-cycles on schemesMar 02 2018Apr 26 2018We prove Bloch's formula for 0-cycles on affine schemes over algebraically closed fields. We prove this formula also for projective schemes over algebraically closed fields which are regular in codimension one. Several applications, including Bloch's ... More

Szego limit theorem on the latticeFeb 21 2011Jul 13 2012In this paper, we prove a Szeg\"{o} type limit theorem on $\ell^2(\ZZ^d)$. We consider operators of the form $H=\Delta+V$, $V$ multiplication by a positive sequence $\{V(n), n \in \ZZ^d\}$ with $V(n) \rightarrow \infty, |n| \rightarrow \infty $ on $\ell^2(\ZZ^d)$ ... More

From Prediction to Planning: Improving Software Quality with BELLTREEAug 17 2017Jul 20 2018The current generation of software analytics tools are mostly prediction algorithms (e.g. support vector machines, naive bayes, logistic regression, etc). While prediction is useful, after prediction comes planning about what actions to take in order ... More

Unconditionally stable, second-order schemes for gradient-regularized, non-convex, finite-strain elasticity modeling martensitic phase transformationsSep 11 2017Apr 20 2018In the setting of continuum elasticity martensitic phase transformations are characterized by a non-convex free energy density function that possesses multiple wells in strain space and includes higher-order gradient terms for regularization. Metastable ... More

BKM Lie superalgebra for the Z_5 orbifolded CHL stringNov 09 2010We study the Z_5-orbifolding of the CHL string theory by explicitly constructing the modular form tilde{Phi}_2 generating the degeneracies of the 1/4-BPS states in the theory. Since the additive seed for the sum form is a weak Jacobi form in this case, ... More

Generating Question-Answer HierarchiesJun 06 2019Jul 21 2019The process of knowledge acquisition can be viewed as a question-answer game between a student and a teacher in which the student typically starts by asking broad, open-ended questions before drilling down into specifics (Hintikka, 1981; Hakkarainen and ... More

Analogues of Gersten's conjecture for singular schemesAug 23 2015Jul 21 2016We formulate analogues, for Noetherian local $\mathbb Q$-algebras which are not necessarily regular, of the injectivity part of Gersten's conjecture in algebraic $K$-theory, and prove them in various cases. Our results suggest that the algebraic $K$-theory ... More

On weight initialization in deep neural networksApr 28 2017May 02 2017A proper initialization of the weights in a neural network is critical to its convergence. Current insights into weight initialization come primarily from linear activation functions. In this paper, I develop a theory for weight initializations with non-linear ... More

Wavy stripes and squares in zero P number convectionMar 29 2001A simple model to explain numerically observed behaviour of chaotically varying stripes and square patterns in zero Prandtl number convection in Boussinesq fluid is presented. The nonlinear interaction of mutually perpendicular sets of wavy rolls, via ... More

Zero cycles with modulus and zero cycles on singular varietiesDec 15 2015Jun 16 2017Given a smooth variety $X$ and an effective Cartier divisor $D \subset X$, we show that the cohomological Chow group of 0-cycles on the double of $X$ along $D$ has a canonical decomposition in terms of the Chow group of 0-cycles ${\rm CH}_0(X)$ and the ... More

Algebraic cycles and crystalline cohomologyApr 30 2015Jul 13 2018We show that additive higher Chow groups of S. Bloch and H. Esnault of smooth varieties over an arbitrary field induce a Zariski sheaf of pro-differential graded algebras, whose Milnor range is isomorphic to the Zariski sheaf of the big de Rham-Witt complexes ... More

Localization and mobility edge for sparsely random potentialsMay 18 1998Nov 04 1998In this paper we consider sparsely random potentials in 5 or more dimensional cubic lattice and exhibit localized and extended states. We identify also the mobility edge for a class of potentials going to infinity at infinity. Our treatment includes a ... More

On Palindromic widths of graphs of groupsDec 05 2016Sep 24 2018We prove that the palindromic width of HNN extension of a group by proper associated subgroups is infinite. We also prove that the palindromic width of the amalgamated free product of two groups via a proper subgroup is infinite (except when the amalgamated ... More

Higher K-theory of Toric stacksOct 03 2012In this paper, we develop several techniques for computing the higher G-theory and K-theory of quotient stacks. Our main results for computing these groups are in terms of spectral sequences. We show that these spectral sequences degenerate in the case ... More

From Entropy and Jet Quenching to Deconfinement?Feb 18 2005The challenge of demonstrating that the matter produced in heavy ion collisions is a deconfined quark-gluon plasma, as predicted by lattice QCD calculations, is the challenge of measuring the number of thermodynamic degrees of freedom \nu ~ \epsilon/T^4 ... More

Bulk Viscosity and Cavitation in Boost-Invariant Hydrodynamic ExpansionAug 12 2009Feb 16 2010We solve second order relativistic hydrodynamics equations for a boost-invariant 1+1-dimensional expanding fluid with an equation of state taken from lattice calculations of the thermodynamics of strongly coupled quark-gluon plasma. We investigate the ... More

Absence of two-flavor color-superconductivity in compact starsMar 29 2002May 17 2002The simplest pattern of color superconductivity involves BCS pairing between up and down quarks. We argue that this ``2SC'' phase will not arise within a compact star. A macroscopic volume of quark matter must be electrically neutral and must be a color ... More

Emergence of Coherent Long Wavelength Oscillations After a Quench: Application to QCDMar 18 1993To model the dynamics of the chiral order parameter in a far from equilibrium phase transition, we consider quenching in the O(4) linear sigma model. We argue, and present numerical evidence, that in the period immediately following the quench long wavelength ... More

The mechano-chemistry of cytoskeletal force generationApr 01 2014Apr 23 2014In this communication, we propose a model to study the non-equilibrium process by which actin stress fibers develop force in contractile cells. The emphasis here is on the non-equilibrium thermodynamics, which is necessary to address the mechanics as ... More

Multilevel Coding Schemes for Compute-and-ForwardOct 05 2010Jul 27 2011We investigate techniques for designing modulation/coding schemes for the wireless two-way relaying channel. The relay is assumed to have perfect channel state information, but the transmitters are assumed to have no channel state information. We consider ... More

A thermodynamic approach to nonlinear ultrasonics for material state awareness and prognosisOct 03 2016We develop a thermodynamic framework for modeling nonlinear ultrasonic damage sensing and prognosis in materials undergoing progressive damage. The framework is based on the internal variable approach and relies on the construction of a pseudo-elastic ... More

Generating Question-Answer HierarchiesJun 06 2019The process of knowledge acquisition can be viewed as a question-answer game between a student and a teacher in which the student typically starts by asking broad, open-ended questions before drilling down into specifics (Hintikka, 1981; Hakkarainen and ... More

Cross-view image synthesis using geometry-guided conditional GANsAug 14 2018We address the problem of generating images across two drastically different views, namely ground (street) and aerial (overhead) views. Image synthesis by itself is a very challenging computer vision task and is even more so when generation is conditioned ... More