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Some new results on sample path optimality in ergodic control of diffusionsMay 12 2016We present some new results on sample path optimality for the ergodic control problem of a class of non-degenerate diffusions controlled through the drift. The hypothesis most often used in the literature to ensure the existence of an a.s.\ sample path ... More

On the Non-Uniqueness of Solutions to the Average Cost HJB for Controlled Diffusions with Near-Monotone CostsSep 21 2013We present a theorem for verification of optimality of controlled diffusions under the average cost criterion with near-monotone running cost, without invoking any blanket stability assumptions. The implications of this result to the policy iteration ... More

A variational formula for risk-sensitive control of diffusions in $\mathbb{R}^d$Oct 02 2018We address the variational problem for the generalized principal eigenvalue on $\mathbb{R}^d$ of linear and semi-linear elliptic operators associated with nondegenerate diffusions controlled through the drift. We establish the Collatz-Wielandt formula ... More

Ergodic Diffusion Control of Multiclass Multi-Pool Networks in the Halfin-Whitt RegimeMay 16 2015Aug 19 2015We consider Markovian multiclass multi-pool networks with heterogeneous server pools, each consisting of many statistically identical parallel servers, where the bipartite graph of customer classes and server pools forms a tree. Customers form their own ... More

Infinite Horizon Risk-Sensitive Control of Diffusions Without Any Blanket Stability AssumptionsJan 03 2016We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely near-monotonicity, and show ... More

Average cost optimal control under weak hypotheses: Relative value iterationsFeb 04 2019We study the well-posedness of the Bellman equation for the ergodic control problem for a controlled Markov process in $R^d$ for a near-monotone cost and establish convergence results for the associated 'relative value iteration' algorithm which computes ... More

On uniform stability of certain parallel server networks with no abandonment in the Halfin-Whitt regimeJul 10 2019In this paper we show that a large class of parallel server networks, with $\sqrt n$-safety staffing, and no abandonment, in the Halfin-Whitt regime are exponentially ergodic and their invariant probability distributions are tight. This includes all networks ... More

On uniform exponential ergodicity of Markovian multiclass many-server queues in the Halfin-Whitt regimeDec 09 2018May 10 2019We study ergodic properties of Markovian multiclass many-server queues which are uniform over scheduling policies, as well as the size n of the system. The system is heavily loaded in the Halfin-Whitt regime, and the scheduling policies are work-conserving ... More

A counterexample to a nonlinear version of the Krein-Rutman theorem by R. MahadevanFeb 13 2018In this short note we present a simple counterexample to a nonlinear version of the Krein-Rutman theorem reported in [Nonlinear Anal. 11 (2007), 3084-3090]. Correct versions of this theorem, and related results for superadditive maps are also presented. ... More

Infinite horizon asymptotic average optimality for large-scale parallel server networksJun 13 2017Jan 23 2018We study infinite-horizon asymptotic average optimality for parallel server network with multiple classes of jobs and multiple server pools in the Halfin-Whitt regime. Three control formulations are considered: 1) minimizing the queueing and idleness ... More

Infinite Horizon Risk-Sensitive Control of Diffusions Without Any Blanket Stability AssumptionsJan 03 2016Nov 04 2016We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely near-monotonicity, and show ... More

Infinite Horizon Average Optimality of the N-network Queueing Model in the Halfin-Whitt RegimeFeb 10 2016We study the infinite horizon optimal control problem for N-network queueing systems, which consist of two customer classes and two server pools, under average (ergodic) criteria in the Halfin-Whitt regime. We consider three control objectives: 1) minimizing ... More

Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptionsJan 03 2016Aug 16 2017We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely near-monotonicity, and show ... More

A variational formula for risk-sensitive control of diffusions in $\mathbb{R}^d$Oct 02 2018Jun 06 2019We address the variational problem for the generalized principal eigenvalue on $\mathbb{R}^d$ of linear and semilinear elliptic operators associated with nondegenerate diffusions controlled through the drift. We establish the Collatz-Wielandt formula ... More

Infinite Horizon Average Optimality of the N-network Queueing Model in the Halfin-Whitt RegimeFeb 10 2016Sep 30 2016We study the infinite horizon optimal control problem for N-network queueing systems, which consist of two customer classes and two server pools, under average (ergodic) criteria in the Halfin-Whitt regime. We consider three control objectives: 1) minimizing ... More

Infinite Horizon Average Optimality of the N-network Queueing Model in the Halfin-Whitt RegimeFeb 10 2016Aug 28 2017We study the infinite horizon optimal control problem for N-network queueing systems, which consist of two customer classes and two server pools, under average (ergodic) criteria in the Halfin-Whitt regime. We consider three control objectives: 1) minimizing ... More

`Controlled' versions of the Collatz-Wielandt and Donsker-Varadhan formulaeMar 26 2019This is an overview of the work of the authors and their collaborators on the characterization of risk sensitive costs and rewards in terms of an abstract Collatz-Wielandt formula and in case of rewards, also a controlled version of the Donsker-Varadhan ... More

A Relative Value Iteration Algorithm for Non-degenerate Controlled DiffusionsOct 06 2011The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton-Jacobi-Bellman (HJB) equation. A nonlinear ... More

Controlled equilibrium selection in stochastically perturbed dynamicsApr 19 2015Apr 16 2017We consider a dynamical system with finitely many equilibria and perturbed by small noise, in addition to being controlled by an `expensive' control. The controlled process is optimal for an ergodic criterion with a running cost that consists the sum ... More

On Solutions of Mean Field Games with Ergodic CostOct 29 2015A general class of mean field games are considered where the governing dynamics are controlled diffusions in $\mathbb{R}^d$. The optimization criterion is the long time average of a running cost function. Under various sets of hypotheses, we establish ... More

On a Class of Stochastic Differential Equations With Jumps and Its PropertiesJan 23 2014Oct 05 2015We study stochastic differential equations with jumps with no diffusion part. We provide some basic stochastic characterizations of solutions of the corresponding non-local partial differential equations and prove the Harnack inequality for a class of ... More

Strict monotonicity of principal eigenvalues of elliptic operators in $\mathbb{R}^d$ and risk-sensitive controlApr 09 2017Jan 31 2018This paper studies the eigenvalue problem on $\mathbb{R}^d$ for a class of second order, elliptic operators of the form $\mathscr{L} = a^{ij}\partial_{x_i}\partial_{x_j} + b^{i}\partial_{x_i} + f$, associated with non-degenerate diffusions. We show that ... More

On the Capacity of Interference Channels with Degraded Message setsMay 17 2006This paper is motivated by a sensor network on a correlated field where nearby sensors share information, and can thus assist rather than interfere with one another. A special class of two-user Gaussian interference channels (IFCs) is considered where ... More

On the Capacity of Gaussian Weak Interference Channels with Degraded Message setsMay 17 2006This paper is motivated by a sensor network on a correlated field where nearby sensors share information, and can thus assist rather than interfere with one another. We consider a special class of two-user Gaussian interference channels (IFCs) where one ... More

Controlled equilibrium selection in stochastically perturbed dynamicsApr 19 2015Aug 30 2016We consider a dynamical system with finitely many equilibria and perturbed by small noise, in addition to being controlled by an `expensive' control. The controlled process is optimal for an ergodic criterion with a running cost that consists the sum ... More

Resource Allocation: Realizing Mean-Variability-Fairness TradeoffsJul 11 2012Oct 09 2012Network Utility Maximization (NUM) provides a key conceptual framework to study reward allocation amongst a collection of users/entities across disciplines as diverse as economics, law and engineering. In network engineering, this framework has been particularly ... More

On the Capacity of Multiple Access Channels with State Information and FeedbackJun 03 2006In this paper, the multiple access channel (MAC) with channel state is analyzed in a scenario where a) the channel state is known non-causally to the transmitters and b) there is perfect causal feedback from the receiver to the transmitters. An achievable ... More

On uniform exponential ergodicity of Markovian multiclass many-server queues in the Halfin-Whitt regimeDec 09 2018We study ergodic properties of Markovian multiclass many-server queues which are uniform over scheduling policies, as well as the size n of the system. The system is heavily loaded in the Halfin-Whitt regime, and the scheduling policies are work-conserving ... More

Ergodic control of multi-class $M/M/N+M$ queues in the Halfin-Whitt regimeApr 07 2014Oct 29 2015We study a dynamic scheduling problem for a multi-class queueing network with a large pool of statistically identical servers. The arrival processes are Poisson, and service times and patience times are assumed to be exponentially distributed and class ... More

Ergodicity of Lévy-driven SDEs arising from multiclass many-server queuesJul 30 2017Sep 21 2018We study the ergodic properties of a class of multidimensional piecewise Ornstein-Uhlenbeck processes with jumps, which contains the limit of the queueing processes arising in multiclass many-server queues with heavy-tailed arrivals and/or asymptotically ... More

Certain Liouville properties of eigenfunctions of elliptic operatorsAug 31 2017Aug 30 2018We present certain Liouville properties of eigenfunctions of second-order elliptic operators with real coefficients, via an approach that is based on stochastic representations of positive solutions, and criticality theory of second-order elliptic operators. ... More

Rate of convergence in Wasserstein distance of piecewise-linear Lévy-driven SDEsJul 10 2019In this paper, we study the rate of convergence under the Wasserstein metric of a broad class of multidimensional piecewise Ornstein-Uhlenbeck processes with jumps. These are governed by stochastic differential equations having a piecewise linear drift, ... More

On uniqueness of solutions to viscous HJB equations with a subquadratic nonlinearity in the gradientJun 27 2019Uniqueness of positive solutions to viscous Hamilton-Jacobi-Bellman (HJB) equations of the form $-\Delta u(x) + \frac{1}{\gamma} |D{u}(x)|^\gamma = f(x) - \lambda$, with $f$ a coercive function and $\lambda$ a constant, in the subquadratic case, that ... More

Optimal control of Markov-modulated multiclass many-server queuesAug 13 2018We study multiclass many-server queues for which the arrival, service and abandonment rates are all modulated by a common finite-state Markov process. We assume that the system operates in the "averaged" Halfin-Whitt regime, which means that it is critically ... More

Relative Value Iteration for Stochastic Differential GamesOct 30 2012Apr 02 2013We study zero-sum stochastic differential games with player dynamics governed by a nondegenerate controlled diffusion process. Under the assumption of uniform stability, we establish the existence of a solution to the Isaac's equation for the ergodic ... More

Risk-Sensitive Control and an Abstract Collatz-Wielandt FormulaDec 20 2013Apr 21 2015The "value" of infinite horizon risk-sensitive control is the principal eigenvalue of a certain positive operator. This facilitates the use of Chang's extension of the Collatz-Wielandt formula to derive a variational characterization thereof. For the ... More

Aspiration Learning in Coordination GamesOct 19 2011We consider the problem of distributed convergence to efficient outcomes in coordination games through dynamics based on aspiration learning. Under aspiration learning, a player continues to play an action as long as the rewards received exceed a specified ... More

Ergodic control of a class of jump diffusions with finite Lévy measures and rough kernelsJan 23 2018Jan 24 2018We study the ergodic control problem for a class of jump diffusions in $\mathbb{R}^d$, which are controlled through the drift with bounded controls. The Levy measure is finite, but has no particular structure; it can be anisotropic and singular. Moreover, ... More

Convergence of The Relative Value Iteration for the Ergodic Control Problem of Nondegenerate Diffusions under Near-Monotone CostsMar 04 2013Apr 02 2013We study the relative value iteration for the ergodic control problem under a near-monotone running cost structure for a nondegenerate diffusion controlled through its drift. This algorithm takes the form of a quasilinear parabolic Cauchy initial value ... More

A variational characterization of the risk-sensitive average reward for controlled diffusions on $\mathbb{R}^d$Mar 20 2019We address the variational formulation of the risk-sensitive reward problem for non-degenerate diffusions on $\mathbb{R}^d$ controlled through the drift. We establish a variational formula on the whole space and also show that the risk-sensitive value ... More

Uniform polynomial rates of convergence for a class of Lévy-driven controlled SDEs arising in multiclass many-server queuesJan 26 2019We study the ergodic properties of a class of controlled stochastic differential equations (SDEs) driven by $\alpha$-stable processes which arise as the limiting equations of multiclass queueing models in the Halfin-Whitt regime that have heavy-tailed ... More

Gapped spin Hamiltonian motivated by quantum teleportationOct 07 2014We construct a Hamiltonian whose ground state encodes a time-independent emulation of quan- tum teleportation. We calculate properties of the Hamiltonian, using exact diagonalization and a mean-field theory, and argue that it has a gap. The system exhibits ... More

Fault-tolerant, Universal Adiabatic Quantum ComputationMar 30 2014Quantum computation has revolutionary potential for speeding computational tasks such as factoring and simulating quantum systems, but the task of constructing a quantum computer is daunting. Adiabatic quantum computation and other ``hands-off" approaches ... More

Evidence for Line Broadening by Electron Scattering in the Broad Line Region of NGC 4395Jan 30 2006A high quality Keck spectrum of the Halpha line in NGC 4395 reveals symmetric exponential wings, fv\propto e^{-v/sigma}, with sigma~500km/s. The wings extend out to >2500km/s from the line core, and down to a flux density of <10^-3 of the peak flux density. ... More

Lyman $α$ Absorption as a Sensitive Probe of the H I Column in Cooling FlowsSep 24 1996X-ray spectra of a significant fraction of cooling flow (CF) clusters of galaxies indicate the presence of a large column of ``cold'' absorbing gas. The physical nature of the absorbing medium remains a mystery. Searches for H I absorption using the 21 ... More

The Ionizing Continuum of QuasarsOct 15 1998The ionizing continuum shape of quasars is generally not directly observable, but indirect arguments, based on photoionization models and thin accretion disk models suggest that it should peak in the extreme UV, and drop steeply into the soft X-ray regime. ... More

Why the Decision Theoretic Perspective Misrepresents Frequentist Inference: 'Nuts and Bolts' vs. Learning from DataNov 03 2012Aug 01 2016The primary objective of this paper is to revisit and make a case for the merits of R.A. Fisher's objections to the decision-theoretic framing of frequentist inference. It is argued that this framing is congruent with the Bayesian but incongruent with ... More

The Two Envelope Problem: a Paradox or Fallacious Reasoning?Jan 01 2013The primary objective of this note is to revisit the two envelope problem and propose a simple resolution. It is argued that the paradox arises from the ambiguity associated with the money content $x of the chosen envelope. When X=x is observed it is ... More

L^p change of variables inequalities on manifoldsApr 02 2010Nov 28 2011We prove two-sided inequalities for the $L^p$-norm of a pushforward or pullback (with respect to an orientation-preserving diffeomorphism) on oriented volume and Riemannian manifolds. For a function or density on a volume manifold, these bounds depend ... More

"The Waters I am Entering No One yet Has Crossed": Alexander Friedman and the Origins of Modern CosmologyFeb 06 2013Ninety years ago, in 1922, Alexander Friedman (1888-1925) demonstrated for the first time that the General Relativity equations admit non-static solutions and thus the Universe may expand, contract, collapse, and even be born. The fundamental equations ... More

Discovery of Hubble's Law: an Example of Type III ErrorMar 24 2014Recently much attention has been paid to the discovery of Hubble's law: the linear relation between the rate of recession of the distant galaxies and distance to them. Though we now mention several names associated with this law instead of one, the motivation ... More

Mimicking Time Evolution within a Quantum Ground State: Ground-State Quantum Computation, Cloning, and TeleportationDec 09 2003Ground-state quantum computers mimic quantum mechanical time evolution within the amplitudes of a time-independent quantum state. We explore the principles that constrain this mimicking. A no-cloning argument is found to impose strong restrictions. It ... More

Some Comments related to AGN Radio LoudnessDec 16 2003Dec 24 2003The bimodality of the AGN radio loudness distribution, and the relation of radio loudness and black hole mass were recently disputed. A closer look at the existing data suggests possible resolutions of these disputes, as further described below.

Another look at Black Hole SpinsMar 21 2019Do black holes rotate, and if yes, how fast? This question is fundamental and has broad implications, but still remains open. There are significant observational challenges in current spin determinations, and future facilities offer prospects for precision ... More

What Can We Learn from the Smallest AGN?Feb 21 2007Quite a few things. In particular, reverberation mapping of NGC 4395, the lowest luminosity type 1 Active Galactic Nucleus (AGN, L_bol~10^40 erg/s) revealed a size of only ~1 light hour for the C IV broad line region (BLR), which is by far the smallest ... More

Where do statistical models come from? Revisiting the problem of specificationOct 27 2006R. A. Fisher founded modern statistical inference in 1922 and identified its fundamental problems to be: specification, estimation and distribution. Since then the problem of statistical model specification has received scant attention in the statistics ... More

ICU Disparnumerophobia and Triskaidekaphobia: The 'Irrational Care Unit'?Jul 01 2019Whilst evidence-based medicine is the cornerstone of modern practice, it is likely that clinicians are influenced by cultural biases. This work set out to look for evidence of number preference in invasive mechanical ventilatory therapy as a concrete ... More

Quadratic twists of abelian varieties with real multiplicationOct 11 2017Jan 09 2018Let $F$ be a totally real number field and $A/F$ a principally polarized abelian variety with real multiplication by the ring of integers $\mathcal{O}$ of a totally real field. Assuming $A$ admits an $\mathcal{O}$-linear 3-isogeny over $F$, we prove that ... More

Unitarity of supersymmetric SL(2,R)/U(1) and no-ghost theorem for fermionic strings in AdS(3) x NJan 16 2003Feb 16 2003The unitarity of the NS supersymmetric coset SL(2,R)/U(1) is studied for the discrete representations. The results are applied to the proof of the no-ghost theorem for fermionic strings in AdS(3) x N in the NS sector. A no-ghost theorem is proved for ... More

Geometric visualization of the Brewster angle from dielectric--magnetic interfaceMar 29 2005A geometric visualization is presented for the Brewster angle for a plane wave reflecting from an interface. The surface is assumed isotropic but it is allowed to display both dielectric and magnetic susceptibility, and hence the Brewster (polarizing) ... More

On The Nature of Low Luminosity Narrow Line AGNFeb 26 2003There is clear observational evidence that some narrow line (type 2) AGN have a hidden broad line region (BLR), and are thus intrinsically broad line (type 1) AGN. Does this AGN unification applies for all type 2 AGN? Indirect arguments suggest that some ... More

Optical, UV, and X-ray Clues to the Nature of Narrow Line AGNsMay 08 2000AGNs with narrow Balmer lines show various extreme properties. In particular, rapid X-ray variability, steep X-ray spectra, peculiar optical and UV line ratios, and possibly peculiar line profiles. Since all these phenomena occur together they are likely ... More

The UV Properties of I Zw 1Oct 18 1998IZw1 is the prototype narrow line quasar. This type of AGNs show a number of common peculiar characteristics whose physical origin is not yet well understood. Here, I review the results of a detailed study by Laor et al. (1997b) of the UV emission properties ... More

Critically damped quantum searchOct 02 2008Although measurement and unitary processes can accomplish any quantum evolution in principle, thinking in terms of dissipation and damping can be powerful. We propose a modification of Grover's algorithm in which the idea of damping plays a natural role. ... More

Variational Monte Carlo for Interacting Electrons in Quantum DotsMay 03 2005We use a variational Monte Carlo algorithm to solve the electronic structure of two-dimensional semiconductor quantum dots in external magnetic field. We present accurate many-body wave functions for the system in various magnetic field regimes. We show ... More

A Note on the Viability of Gaseous Ionization in Active Galaxies by Fast ShocksFeb 12 1998Observational evidence suggest that shocks may affect the spatial and velocity distributions of gas in the NLR/ENLR of some active galaxies. It thus seemed plausible that shocks may also energize the NLR. The observed emission line ratios strongly favor ... More

What is the Broad Line Region?Dec 16 2003What is the Broad Line Region (BLR) made of? What determines its location? Why is it sometimes missing? What controls its properties? Some recent results and new approaches which may shed light on these issues are briefly described.

On Black Hole Masses and Radio Loudness in AGNSep 13 2000The distribution of radio to optical fluxes in AGN is bimodal. The physical origin for this bimodality is not understood. In this Letter I describe observational evidence, based on the Boroson & Green PG quasar sample, that the radio loudness bimodality ... More

On fixed-gap adiabatic quantum computationFeb 04 2010Jan 21 2014Quantum computation has revolutionary potential for speeding algorithms and for simulating quantum systems such as molecules. We report here a quantum computer design that performs universal quantum computation within a single non-degenerate ground state ... More

BRST Quantization of String Theory in AdS(3)Apr 28 2003Aug 21 2003We study the BRST quantization of bosonic and NSR strings propagating in AdS(3) x N backgrounds. The no-ghost theorem is proved using the Frenkel-Garland-Zuckerman method. Regular and spectrally-flowed representations of affine SL(2,R) appear on an equal ... More

Quantum vortex tunneling: Microscopic theory and application to d-wave superconductorsJul 25 2001Sep 26 2003We present a microscopic approach to the quantum tunneling of vortices. The formalism characterizes the rate at which a many-body superconducting state with a vortex in one location makes a transition to a second many-body superconducting state with a ... More

On The Linearity of The Black Hole - Bulge Mass Relation in Active and in Nearby GalaxiesJan 23 2001Analysis of PG quasar observations suggests a nonlinear relation between the black hole mass, M_BH, and the bulge mass, M_bulge, although a linear relation, as proposed for nearby galaxies, cannot be ruled out. New M_BH values for nearby galaxies from ... More

On Quasar Masses and Quasar Host GalaxiesJul 27 1998The mass of massive black holes in quasar cores can be deduced using the typical velocities of Hb-emitting clouds in the Broad Line Region (BLR) and the size of this region. However, this estimate depends on various assumptions and is susceptible to large ... More

Revisiting Simpson's Paradox: a statistical misspecification perspectiveMay 07 2016May 13 2016The primary objective of this paper is to revisit Simpson's paradox using a statistical misspecification perspective. It is argued that the reversal of statistical associations is sometimes spurious, stemming from invalid probabilistic assumptions imposed ... More

Revisiting the Neyman-Scott model: an Inconsistent MLE or an Ill-defined Model?Jan 26 2013The Neyman and Scott (1948) model is widely used to demonstrate a serious weakness of the Maximum Likelihood (ML) method: it can give rise to inconsistent estimators. The primary objective of this paper is to revisit this example with a view to demonstrate ... More

Inner Market as a "Black Box"Jun 20 2001Each market has its singular characteristic. Its inner structure is directly responsible for the observed distributions of returns though this fact is widely overlooked. Big orders lead to doubling the tails. The behavior of a market maker with many or ... More

FZZ ScatteringJun 08 2006Nov 03 2006We study the duality between the two dimensional black hole and the sine-Liouville conformal field theories via exact operator quantization of a classical scattering problem. The ideas are first illustrated in Liouville theory, which is dual to itself ... More

Liouville theory without an actionJan 26 2006Jun 08 2006We show that the crossing symmetry of the four-point function in the Liouville conformal field theory on the sphere contains more information than what was hitherto considered. Under certain assumptions, it provides the special structure constants that ... More

Nonlinear coupling of nano mechanical resonators to Josephson quantum circuitsMay 01 2006We propose a technique to couple the position operator of a nano mechanical resonator to a SQUID device by modulating its magnetic flux bias. By tuning the magnetic field properly, either linear or quadratic couplings can be realized, with a discretely ... More

Hadronic Production of TeV Gamma Ray Flares from BlazarsOct 30 1996Jan 13 1997We propose that TeV $\gamma$-ray emission from blazars is produced by collisions near the line of sight of high energy jet protons with gas targets (``clouds'') from the broad emission-line region (BLR). Intense TeV $\gamma$-ray flares (GRFs) are produced ... More

Attosecond neutron Compton scattering from protonsFeb 01 2007The effect of "anomalous" scattering of neutrons and electrons from protons in the electron-volt energy-transfer range is considered, and related experimental results are mentioned. A recent independent confirmation of this effect with a new data analysis ... More

Modern Telecommunications: A Playground for Physicists?May 04 2016This report summarizes some of the material that was presented by the author during the 2015 Les Houches Summerschool on "Random Matrices and Stochastic Processes". In these Lectures, various applications of Random Matrix Theory in modern telecommunications ... More

Trace formulae for Schrödinger operators with complex-valued potentials on cubic latticesSep 30 2016We consider Schr\"odinger operators with complex decaying potentials on the lattice. Using some classical results from Complex Analysis we obtain some trace formulae and using them estimate globally all zeros of the Fredholm determinant in terms of the ... More

On the negative spectrum of two-dimensional Schrödinger operators with radial potentialsAug 04 2011Dec 21 2011For a two-dimensional Schr\"odinger operator $H_{\alpha V}=-\Delta-\alpha V$ with the radial potential $V(x)=F(|x|), F(r)\ge 0$, we study the behavior of the number $N_-(H_{\alpha V})$ of its negative eigenvalues, as the coupling parameter $\alpha$ tends ... More

Radiative corrections to the Higgs boson decay rate $Γ(H\rightarrow ZZ)$ in the minimal supersymmetric modelJun 26 1992We consider radiative corrections to the decay rate $\Gamma(H\rightarrow ZZ)$ of the heavy {\it CP}-even Higgs boson of the minimal supersymmetric model to two $Z$ bosons. We perform a one loop Feynman diagram calculation in the on-mass-shell renormalization ... More

Metal enrichment by radiation pressure in active galactic nucleus outflows -- theory and observationsJul 30 2012Outflows from active galactic nuclei may be produced by absorption of continuum radiation by UV resonance lines of abundant metal ions, as observed in broad absorption line quasars (BALQs). The radiation pressure exerted on the metal ions is coupled to ... More

Topological Entanglement Entropy and HolographyMay 13 2008May 30 2008We study the entanglement entropy in confining theories with gravity duals using the holographic prescription of Ryu and Takayanagi. The entanglement entropy between a region and its complement is proportional to the minimal area of a bulk hypersurface ... More

Tides Alone Cannot Explain Kepler Planets Close to 2:1 MMRAug 19 2015A number of Kepler planet pairs lie just wide of first-order mean motion resonances (MMRs). Tides have been frequently proposed to explain these pileups, but it is still an ongoing discussion. We contribute to this discussion by calculating an optimistic ... More

Brane Inflation and Moduli Stabilization on Twisted ToriOct 24 2013Aug 08 2015We consider supergravity compactifications on 6-dimensional twisted tori, which are 5-torus fibrations of the circle. The motion of branes on such manifolds can lead to power-law potentials at low energy, that may be useful for inflation. We classify ... More

High-field magnetoresistance revealing scattering mechanisms in grapheneMay 02 2012Sep 13 2012We show that the type of charge carrier scattering significantly affects the high-field magnetoresistance of graphene nanoribbons. This effect has potential to be used in identifying the scattering mechanisms in graphene. The results also provide an explanation ... More

Exact diagonalization of the Hubbard model on graphics processing unitsApr 16 2012Jun 19 2012We solve the Hubbard model with the exact diagonalization method on a graphics processing unit (GPU). We benchmark our GPU program against a sequential CPU code by using the Lanczos algorithm to solve the ground state energy in two cases: a one-dimensional ... More

Control of a two-electron quantum ring with an external magnetic fieldFeb 04 2010We investigate the use of external time-dependent magnetic field for the control of the quantum states in a two-electron quantum ring. The hyperfine interaction of the confined electrons with surrounding nuclei couples the singlet state with the three ... More

Charge dynamics in two-electron quantum dotsMay 19 2010We investigate charge dynamics in a two-electron double quantum dot. The quantum dot is manipulated by using a time-dependent external voltage that induces charge oscillations between the dots. We study the dependence of the charge dynamics on the external ... More

A Gross-Kohnen-Zagier formula for Heegner-Drinfeld cyclesJul 01 2017Let $F$ be the field of rational functions on a smooth projective curve over a finite field, and let $\pi$ be an unramified cuspidal automorphic representation for $\mathrm{PGL}_2$ over $F$. We prove a variant of the formula of Yun and Zhang relating ... More

The modal logic of $σ$-centered forcing and related forcing classesJan 18 2017We consider the modality "$\varphi$ is true in every $\sigma$-centered forcing extension", denoted $\square\varphi$ and its dual "$\varphi$ is true in some $\sigma$-centered forcing extension", denoted $\lozenge\varphi$, (where $\varphi$ is a statement ... More

A Theory of Stationary Trees and the Balanced Baumgartner-Hajnal-Todorcevic Theorem for TreesDec 17 2013Building on early work by Stevo Todorcevic, we describe a theory of stationary subtrees of trees of successor-cardinal height. We define the diagonal union of subsets of a tree, as well as normal ideals on a tree, and we characterize arbitrary subsets ... More

Hierarchical Soft Actor-Critic: Adversarial Exploration via Mutual Information OptimizationJun 17 2019We describe a novel extension of soft actor-critics for hierarchical Deep Q-Networks (HDQN) architectures using mutual information metric. The proposed extension provides a suitable framework for encouraging explorations in such hierarchical networks. ... More

Ground-state of two-dimensional finite electron systems in the Quantum Hall regimeMar 09 2005May 20 2005We study electronic structures of quasi-two-dimensional finite electron systems in high magnetic fields. The solutions in the fractional quantum Hall regime are interpreted as quantum liquids of electrons and off-electron vortices. The ground states are ... More

The frequency dependence of scattering imprints on pulsar observationsJul 18 2016Aug 22 2016Observations of pulsars across the radio spectrum are revealing a dependence of the characteristic scattering time ($\tau$) on frequency, which is more complex than the simple power law with a theoretically predicted power law index. In this paper we ... More

Geodesics in a Graph of Perfect MatchingsJun 15 2013Sep 09 2014This paper studies geodesics in the graph $\mathscr{P}_{m}$, which has all perfect matchings in $K_{2m}$ as vertices with two perfect matchings connected by an edge if their symmetric difference is a cycle of length four. The diameter of $\mathscr{P}_{m}$, ... More