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Observation of polarization quantum noise of laser radiation in Rb vapor cellAug 29 2005We present experimental study of polarization quantum noise of laser radiation passed through optically think vapor of Rb87. We observe a step-like noise spectrum. We discuss various factor which may result in such noise spectrum and prevent observation ... More

A novel absorption resonance for all-optical atomic clocksJan 18 2005We report an experimental study of an all-optical three-photon-absorption resonance (known as a "N-resonance") and discuss its potential application as an alternative to atomic clocks based on coherent population trapping (CPT). We present measurements ... More

Coherent population trapping resonances with linearly polarized light for all-optical miniature atomic clocksOct 25 2009Dec 26 2009We present a joint theoretical and experimental characterization of the coherent population trapping (CPT) resonance excited on the D1 line of 87Rb atoms by bichromatic linearly polarized laser light. We observe high-contrast transmission resonances (up ... More

Narrow-linewidth homogeneous optical emitters in diamond nanostructures via silicon ion implantationDec 11 2015Apr 25 2016The negatively-charged silicon-vacancy ($\mathrm{SiV}^{-}$) center in diamond is a bright source of indistinguishable single photons and a useful resource in quantum information protocols. Until now, $\mathrm{SiV}^{-}$ centers with narrow optical linewidths ... More

Realization of Coherent Optically Dense Media via Buffer-Gas CoolingMay 09 2008Feb 02 2009We demonstrate that buffer-gas cooling combined with laser ablation can be used to create coherent optical media with high optical depth and low Doppler broadening that offers metastable states with low collisional and motional decoherence. Demonstration ... More

Comparison of 87Rb N-resonances for D1 and D2 transitionsJan 11 2006We report an experimental comparison of three-photon-absorption resonances (known as "N-resonances") for the D_1 and D_2 optical transitions of thermal 87Rb vapor. We find that the D_2 N-resonance has better contrast, a broader linewidth, and a more symmetric ... More

Cancellation of light-shifts in an N-resonance clockSep 13 2005We demonstrate that first-order light-shifts can be cancelled for an all-optical, three-photon-absorption resonance ("N-resonance") on the D1 transition of Rb87. This light-shift cancellation enables improved frequency stability for an N-resonance clock. ... More

Indistinguishable photons from separated silicon-vacancy centers in diamondJun 17 2014Jul 01 2014We demonstrate that silicon-vacancy (SiV) centers in diamond can be used to efficiently generate coherent optical photons with excellent spectral properties. We show that these features are due to the inversion symmetry associated with SiV centers, and ... More

Induced Absorption Resonance on the Open Fg = 1 -> Fe = 2 Transition of the D1 Line of the 87Rb AtomDec 21 2005Induced absorption resonance on the open Fg=1 -> Fe = 2 transition of the D1 line of the 87Rb atom has been observed. The effect of atomic motion on the formation of the resonance has been revealed. The numerical calculations are in good agreement with ... More

Probing many-body dynamics on a 51-atom quantum simulatorJul 13 2017Nov 30 2017Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on ... More

High-fidelity control and entanglement of Rydberg atom qubitsJun 12 2018Individual neutral atoms excited to Rydberg states are a promising platform for quantum simulation and quantum information processing. However, experimental progress to date has been limited by short coherence times and relatively low gate fidelities ... More

Quantum interference of single photons from remote nitrogen-vacancy centers in diamondDec 16 2011Apr 11 2012We demonstrate quantum interference between indistinguishable photons emitted by two nitrogen-vacancy (NV) centers in distinct diamond samples separated by two meters. Macroscopic solid immersion lenses are used to enhance photon collection efficiency. ... More

Experimental Investigation of the Dark Pseudoresonance on the D1 Line of the 87Rb Atom Excited by a Linearly Polarized FieldDec 28 2005The measurements of the metrological characteristics (amplitude, width, and shift in the magnetic field) of the dark pseudoresonance, which was proposed by Kazakov et al. [quant-ph/0506167] as the reference resonance for an atomic frequency standard, ... More

Experimental preparation of pure superposition states of atoms via elliptically polarized bichromatic radiationDec 13 2005We propose a simple and effective way of creating pure dark superposition states. The generation of pure states is carried out by using bichromatic radiation with controllable polarization ellipticity. We derived analytic formulas for polarization elipticity ... More

Ultra-Slow Light and Enhanced Nonlinear Optical Effects in a Coherently Driven Hot Atomic GasApr 07 1999We report the observation of small group velocities of order 90 meters per second, and large group delays of greater than 0.26 ms, in an optically dense hot rubidium gas (~360 K). Media of this kind yield strong nonlinear interactions between very weak ... More

Feedback spectroscopy of atomic resonancesJan 30 2013Feb 11 2013We propose a non-standard spectroscopic technique that uses a feedback control of the input probe field parameters to significantly increase the contrast and quality factor of the atomic resonances. In particular, to apply this technique for the dark ... More

Parametric Self-Oscillation via Resonantly Enhanced Multiwave MixingApr 08 1999We demonstrate an efficient nonlinear process in which Stokes and anti-Stokes components are generated spontaneously in a Raman-like, near resonant media driven by low power counter-propagating fields. Oscillation of this kind does not require optical ... More

Stationary pulses of light in an atomic mediumNov 13 2003Nov 17 2003Physical processes that could facilitate coherent control of light propagation are now actively explored. In addition to fundamental interest, these efforts are stimulated by possibilities to develop, for example, a quantum memory for photonic states. ... More

Nonlinear optics with stationary pulses of lightOct 20 2004We show that the recently demonstrated technique for generating stationary pulses of light [Nature {\bf 426}, 638 (2003)] can be extended to localize optical pulses in all three spatial dimensions in a resonant atomic medium. This method can be used to ... More

EIT-based Vector Magnetometry in Linear Polarized LightApr 22 2010May 24 2010We develop a generalized principle of EIT vector magnetometry based on high-contrast EIT-resonances and the symmetry of atom-light interaction in the linearly polarized bichromatic fields. Operation of such vector magnetometer on the D1 line of 87Rb has ... More

Photon-mediated interactions between quantum emitters in a diamond nanocavityJul 11 2018Photon-mediated interactions between quantum systems are essential for realizing quantum networks and scalable quantum information processing. We demonstrate such interactions between pairs of silicon-vacancy (SiV) color centers strongly coupled to a ... More

Robust nonabelian ground states and continuous quantum phase transitions in a half filled bilayer graphene Landau levelNov 22 2016In a topological quantum bit, quantum information is protected from decoherence by the energy gap separating the nonabelian vacuum from higher energy modes. Experimental systems predicted to harbor nonabelions range from p-wave superfluids to superconducting ... More

Dynamic optical bistability in resonantly enhanced Raman generationApr 11 2004We report observations of novel dynamic behavior in resonantly-enhanced stimulated Raman scattering in Rb vapor. In particular, we demonstrate a dynamic hysteresis of the Raman scattered optical field in response to changes of the drive laser field intensity ... More

Observation of fractional Chern insulators in a van der Waals heterostructureJun 19 2017Nov 27 2017Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to ... More

Pure superposition states of atoms generated by a bichromatic elliptically polarized filedMar 03 2005We find specific polarizations of components of a bichromatic field, which allow one to prepare pure superposition states of atoms, using the coherent population trapping effect. These $m$$-$$m$ states are prepared in the system of Zeeman substates of ... More

Shaping quantum pulses of light via coherent atomic memoryJun 14 2004We describe a technique for generating pulses of light with controllable photon numbers, propagation direction, timing, and pulse shapes. The technique is based on preparation of an atomic ensemble in a state with a desired number of atomic spin excitations, ... More

Coherence and Raman sideband cooling of a single atom in an optical tweezerSep 13 2012We investigate quantum control of a single atom in an optical tweezer trap created by a tightly focused optical beam. We show that longitudinal polarization components in the dipole trap arising from the breakdown of the paraxial approximation give rise ... More

Generation and manipulation of Schrödinger cat states in Rydberg atom arraysMay 14 2019May 15 2019Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging, since such states are extremely fragile. Using a programmable quantum ... More

Generation and manipulation of Schrödinger cat states in Rydberg atom arraysMay 14 2019Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging, since such states are extremely fragile. Using a programmable quantum ... More

Trapping and manipulation of isolated atoms using nanoscale plasmonic structuresMay 22 2009We propose and analyze a scheme to interface individual neutral atoms with nanoscale solid-state systems. The interface is enabled by optically trapping the atom via the strong near-field generated by a sharp metallic nanotip. We show that under realistic ... More

Efficient all-optical switching using slow light within a hollow fiberJan 03 2009We demonstrate a fiber-optical switch that is activated at tiny energies corresponding to few hundred optical photons per pulse. This is achieved by simultaneously confining both photons and a small laser-cooled ensemble of atoms inside the microscopic ... More

Laser-cooled atoms inside a hollow-core photonic-crystal fiberApr 27 2011Apr 28 2011We describe the loading of laser-cooled rubidium atoms into a single-mode hollow-core photonic-crystal fiber. Inside the fiber, the atoms are confined by a far-detuned optical trap and probed by a weak resonant beam. We describe different loading methods ... More

Emergent Dirac gullies and gully-symmetry breaking quantum Hall states in ABA trilayer grapheneMay 02 2018Jul 19 2018We report on quantum capacitance measurements of high quality, graphite- and hexagonal boron nitride encapsulated Bernal stacked trilayer graphene devices. At zero applied magnetic field, we observe a number of electron density- and electrical displacement-tuned ... More

Robust fractional quantum Hall states and continuous quantum phase transitions in a half-filled bilayer graphene Landau levelNov 22 2016Apr 28 2017Nonabelian anyons offer the prospect of storing quantum information in a topological qubit protected from decoherence, with the degree of protection determined by the energy gap separating the topological vacuum from its low lying excitations. Originally ... More

Thermodynamics of the ferromagnetic phase transition in nearly half metallic CoS2 at high pressuresOct 15 2013The volume change and heat capacity at the ferromagnetic phase transition in CoS2 were measured at high pressures using X-rays generated by the Argonne synchrotron light source and by ac-calorimetry, respectively. The transition entropy, calculated on ... More

Features of Magneto-Optical Resonances in an Elliptically Polarized Traveling Light WaveOct 09 2006The parameters of nonlinear absorption magneto-optical resonances in the Hanle configuration have been studied as functions of the ellipticity of a traveling light wave. It has been found that these parameters (amplitude, width, and amplitude-to-width ... More

Circuit Depth ReductionsNov 12 2018Dec 13 2018The best known circuit lower bounds against unrestricted circuits remained around $3n$ for several decades. Moreover, the only known technique for proving lower bounds in this model, gate elimination, is inherently limited to proving lower bounds of less ... More

Inflationary Birefringence and BaryogenesisApr 03 2016A decade ago, the first leptogenesis model based on inflation was proposed, where the complex phase of the inflaton field carries lepton number. If the inflaton field is an axion, it can couple to gravitational waves and gauge fields via. Chern-Simons ... More

$S^1 \times S^2$ wormholes and topological chargeDec 16 1993I investigate solutions to the Euclidean Einstein-matter field equations with topology $S^1 \times S^2 \times R$ in a theory with a massless periodic scalar field and electromagnetism. These solutions carry winding number of the periodic scalar as well ... More

Subgaussian rates of convergence of means in directed first passage percolationJan 07 2011May 18 2011We consider directed first passage percolation on the integer lattice, with time constant $\mu$ and passage time $a_{0n}$ from the origin to $(n,0,...,0)$. It is shown that under certain conditions on the passage time distribution, $Ea_{0n} - n\mu = O(n^{1/2}(\log\log ... More

A repetition-free hypersequent calculus for first-order rational Pavelka logicDec 12 2018Jan 28 2019We present a hypersequent calculus $\text{G}^3\text{\L}\forall$ for first-order infinite-valued {\L}ukasiewicz logic and for an extension of it, first-order rational Pavelka logic; the calculus is intended for bottom-up proof search. In $\text{G}^3\text{\L}\forall$, ... More

Moduli of mathematical instanton vector bundles with odd c_2 on projective spaceJan 15 2011Sep 03 2011The problem of irreducibility of the moduli space I_n of rank-2 mathematical instanton vector bundles with arbitrary positive second Chern class n on the projective 3-space is considered. The irreducibility of I_n was known for small values of n: Barth ... More

M-theory Calabi-Yau Quantum MechanicsNov 30 2009This thesis explores an exotic class of M-theory compactifications in which the compact manifold is taken to be a Calabi-Yau five-fold. The resulting effective theory is a one-dimensional N=2 super-mechanics model that exhibits peculiar features of one-dimensional ... More

Pricing with coherent riskMay 02 2006This paper deals with applications of coherent risk measures to pricing in incomplete markets. Namely, we study the No Good Deals pricing technique based on coherent risk. Two forms of this technique are presented: one defines a good deal as a trade with ... More

Separated-occurrence inequalities for dependent percolation and Ising modelsOct 01 2002Separated-occurrence inequalities are variants for dependent lattice models of the van den Berg-Kesten inequality for independent models. They take the form $P(A \circ_r B) \leq (1 + ce^{-\epsilon r})P(A)P(B)$, where $A \circ_r B$ is the event that $A$ ... More

Hierarchy and size distribution function of star formation regions in the spiral galaxy NGC 628Jun 03 2014Jun 21 2014Hierarchical structures and size distribution of star formation regions in the nearby spiral galaxy NGC 628 are studied over a range of scale from 50 to 1000 pc using optical images obtained with 1.5 m telescope of the Maidanak Observatory. We found hierarchically ... More

Brane Gas Cosmology, M-theory and Little String TheoryDec 13 2002We generalize the Brane Gas Cosmological Scenario to M-theory degrees of freedom, namely $M5$ and $M2$ branes. Without brane intersections, the Brandenberger Vafa(BV) arguments applied to M-theory degrees of freedom generically predict a large 6 dimensional ... More

The Sterile Neutrino Field and Late Time AccelerationJun 12 2013We show that when the neutrino minimal standard model ($\nu MSM$) with a light sterile neutrino has a long range interaction between the neutrino vacuum charge density and a dark U(1) gauge potential, late time acceleration is dynamically realized. Moreover, ... More

Is Cosmic Parity Violation Responsible for the Anomalies in the WMAP Data?Jan 06 2006Aug 04 2006This research demonstrates that parity violation in general relativity can simultaneously explain the observed loss in power and alignment at a preferred axis ('Axis of Evil')in the low multipole moments of the WMAP data. This observational possibility ... More

Geometrical modeling of dendritic structuresSep 09 2018Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the same equilibrium ... More

About tilings of the type of Penrose of the two-dimensional sphere, which modellings quasicrystalsApr 23 2018The problem of constructing a limit series of Penrose type partitions of a two-dimensional sphere is solved, which makes it possible to model quasicrystals possessing a point icosahedral group symmetry Ih. Images of polyhedron models are given (the number ... More

Isogravity: Toward an Electroweak and Gravitational UnificationJun 29 2007We present a model that unites the electroweak interaction with general relativity without specifying a space-time metric. This is made possible by embedding the kinetic terms for gravity and electroweak theory using one $\SL$ connection variable. The ... More

Inflation from D-\bar{D} brane annihilationMay 03 2001We demonstrate that the initial conditions for inflation are met when D5 and \bar{D}5 branes annihilate. This scenario uses Sen's conjecture that a co-dimension two vortex forms on the worldvolume of the annihilated 5-brane system. Analogous to a "Big ... More

On The Varying Speed of Light in a Brane-Induced FRW UniverseDec 06 1999Oct 26 2000We investigate a string/M theoretic realization of the varying speed of light scenario. We consider a 3+1 dimensional probe-brane universe in the background of a black hole in the bulk formed by a stack of branes, in the spirit of Kiritsis (hep-th/9906206). ... More

On The Apparent Narrowing of Radio Recombination Lines at High Principal Quantum NumbersDec 08 2011Jan 17 2012We critically analyze the Bell et al. findings on "anomalous" widths of high-order Hydrogen radio recombination lines in the Orion Nebula at 6 GHz. We review their method of modified frequency switching and show that the way this method is used for large ... More

Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with $G_2$-structureDec 22 2015Mar 09 2016We study $\mathfrak{g}$-valued Yang-Mills fields on cylinders $Z(G/H)=\mathbb{R} \times G/H$, where G/H is a compact seven-dimensional coset space with $G_2$-structure, $\mathfrak{g}$ is the Lie algebra of G, and Z(G/H) inherits a Spin(7)-structure. After ... More

The spectral gap of the 2-D stochastic Ising model with nearly single-spin boundary conditionsAug 29 2000We establish upper bounds for the spectral gap of the stochastic Ising model at low temperature in an N-by-N box, with boundary conditions which are ``plus'' except for small regions at the corners which are either free or ``minus.'' The spectral gap ... More

Affine highest weight categories and affine quasihereditary algebrasMay 13 2014Jun 03 2014Koenig and Xi introduced {\em affine cellular algebras}. Kleshchev and Loubert showed that an important class of {\em infinite dimensional} algebras, the KLR algebras $R(\Gamma)$ of finite Lie type $\Gamma$, are (graded) affine cellular; in fact, the ... More

Radiation of a quantum localized sourceNov 19 1999New effective operators, describing the photons with given polarization at given position with respect to a source are proposed. These operators can be used to construct the near and intermediate zones quantum optics. It is shown that the use of the conventional ... More

Scientific works citation analysisFeb 14 2014Several questions of scientometrics parameters organization are considered. Two new indices for scientific works citation analysis are proposed. They provide more detailed and reliable scientific significance assessment of individual authors and scientific ... More

Cuspidal systems for affine Khovanov-Lauda-Rouquier algebrasOct 24 2012Dec 10 2012A cuspidal system for an affine Khovanov-Lauda-Rouquier algerba $R_\al$ yields a theory of standard modules. This allows us to classify the irreducible modules over $R_\al$ up to the so-called imaginary modules. We make a conjecture on reductions modulo ... More

Sending Quantum Information with Gaussian StatesSep 10 1998Quantum information characteristics, such as quantum mutual information, loss, noise and coherent information are explicitly calculated for Bosonic attenuation/amplification channel with input Gaussian state. The coherent information is shown to be negative ... More

A Theory of Neutrino Oscillations and Late Time AccelerationNov 26 2009We provide a microphysical model that connects neutrino oscillations to dark energy, which has predictions of Lorentz and CPT violating neutrino oscillations. We argue that the DE is a BCS condensate of flavored neutrinos. As neutrinos propigate in their ... More

The Fedosov manifolds and magnetic monopoleApr 21 2010Aug 10 2010A non-symplectic generalization of Hamiltonian mechanics is considered. It allows include into consideration "non-Lagrange" systems, such as theory of charged particle in the field of magnetic monopole. The corresponding generalization for the Fedosov ... More

Excursions and local limit theorems for Bessel-like random walksDec 23 2009Sep 03 2010We consider reflecting random walks on the nonnegative integers with drift of order 1/x at height x. We establish explicit asymptotics for various probabilities associated to such walks, including the distribution of the hitting time of 0 and first return ... More

A Universal Characterisation of Codescent ObjectsSep 05 2017In this work we define a 2-dimensional analogue of extranatural transformation and use these to characterise codescent objects. They will be seen as universal objects amongst extrapseudonatural transformations in a similar manner in which coends are universal ... More

Families with infants: speeding up algorithms for NP-hard problems using FFTOct 08 2014Assume that a group of people is going to an excursion and our task is to seat them into buses with several constraints each saying that a pair of people does not want to see each other in the same bus. This is a well-known coloring problem and it can ... More

Measurable entanglementDec 22 2005Amount of entanglement carried by a quantum bipartite state is usually evaluated in terms of concurrence (see Ref. 1). We give a physical interpretation of concurrence that reveals a way of its direct measurement and discuss possible generalizations.

Entanglement and quantum fluctuationsJul 16 2003We discuss maximum entangled states of quantum systems in terms of quantum fluctuations of all essential measurements responsible for manifestation of entanglement. Namely, we consider maximum entanglement as a property of states, for which quantum fluctuations ... More

Simulation and analytical approach to the identification of significant factorsJun 04 2014We develop our previous works concerning the identification of the collection of significant factors determining some, in general, non-binary random response variable. Such identification is important, e.g., in biological and medical studies. Our approach ... More

Representation theory and cohomology of Khovanov-Lauda-Rouquier algebrasJan 23 2014This expository paper is based on the lectures given at the program `Modular Representation Theory of Finite and $p$-adic Groups' at the National University of Singapore. We are concerned with recent results on representation theory and cohomology of ... More

Coding Theorems for Quantum ChannelsSep 10 1998The more than thirty years old issue of the (classical) information capacity of quantum communication channels was dramatically clarified during the last years, when a number of direct quantum coding theorems was discovered. The present paper gives a ... More

Comparing several calculi for first-order infinite-valued Łukasiewicz logicDec 13 2018From the viewpoint of provability, we compare some Gentzen-type hypersequent calculi for first-order infinite-valued {\L}ukasiewicz logic and for first-order rational Pavelka logic with each other and with H\'ajek's Hilbert-type calculi for these logics. ... More

Cube-root boundary fluctuations for droplets in random cluster modelsAug 29 2000For a family of bond percolation models on Z^{2} that includes the Fortuin-Kasteleyn random cluster model, we consider properties of the ``droplet'' that results, in the percolating regime, from conditioning on the existence of an open dual circuit surrounding ... More

Equilibrium with coherent riskMay 02 2006This paper is the continuation of "Pricing with coherent risk" and deals with further applications of coherent risk measures to problems of finance. First, we study the optimization problem. Three forms of this problem are considered. Furthermore, the ... More

About discrete groups of symmetry of similarity of Euclidean spaceFeb 28 2019Starting from the classical results of Shubnikov and Zamorzayev, computer models of shapes are implemented, which allow to visualize the action of discrete subgroups of continuous topological groups. The action is visualize by performing partitions of ... More

The Effect of Disorder on Polymer Depinning TransitionsSep 30 2006We consider a polymer, with monomer locations modeled by the trajectory of a Markov chain, in the presence of a potential that interacts with the polymer when it visits a particular site 0. We assume that probability of an excursion of length $n$ is given ... More

Ivy on the ceiling: first-order polymer depinning transitions with quenched disorderDec 21 2006We consider a polymer, with monomer locations modeled by the trajectory of an underlying Markov chain, in the presence of a potential thatinteracts with the polymer when it visits a particular site 0. Disorder is introduced by having the interaction vary ... More

Controlled random walk with a target siteMar 15 2013We consider a simple random walk W_i in 1 or 2 dimensions, in which the walker may choose to stand still for a limited time. The time horizon is n, the maximum consecutive time steps which can be spent standing still is m_n and the goal is to maximize ... More

Flexoelectric effect in finite samplesOct 03 2011Static flexoelectric effect in a finite sample of a solid is addressed in terms of phenomenological theory for the case of a thin plate subjected to bending. It has been shown that despite an explicit asymmetry inherent to the bulk constitutive electromechanical ... More

Entangled States and Local MeasurementsMar 20 2002We show that the maximum entanglement in a composite system corresponds to the maximum uncertainty and maximum correlation of local measurements.

General entanglementDec 23 2005The paper contains a brief review of an approach to quantum entanglement based on analysis of dynamic symmetry of systems and quantum uncertainties, accompanying the measurement of mean value of certain basic observables. The latter are defined in terms ... More

Collapsing Superstring ConjectureSep 23 2018In the Shortest Common Superstring (SCS) problem, one is given a collection of strings, and needs to find a shortest string containing each of them as a substring. SCS admits $2\frac{11}{23}$-approximation in polynomial time. While this algorithm and ... More

Nonlinear Relaxation Dynamics in Elastic Networks and Design Principles of Molecular MachinesMay 17 2007Analyzing nonlinear conformational relaxation dynamics in elastic networks corresponding to two classical motor proteins, we find that they respond by well-defined internal mechanical motions to various initial deformations and that these motions are ... More

Birhythmicity, Synchronization, and Turbulence in an Oscillatory System with Nonlocal Inertial CouplingFeb 09 2005We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial coupling, the system ... More

Nonlinear Behavior of Baryon Acoustic Oscillations from the Zel'dovich Approximation Using a Non-Fourier Perturbation ApproachFeb 06 2012Apr 10 2012Baryon acoustic oscillations are an excellent technique to constrain the properties of dark energy in the Universe. In order to accurately characterize the dark energy equation of state, we must understand the effects of both the nonlinearities and redshift ... More

Diffusion-induced instability and chaos in random oscillator networksFeb 21 2009We demonstrate that diffusively coupled limit-cycle oscillators on random networks can exhibit various complex dynamical patterns. Reducing the system to a network analog of the complex Ginzburg-Landau equation, we argue that uniform oscillations can ... More

A semidefinite program for unbalanced multisection in the stochastic block modelJul 20 2015We analyze semidefinite programming (SDP) algorithms that exactly recover community structure in graphs generated from the stochastic block model. In this model, a graph is randomly generated on a vertex set that is partitioned into multiple communities ... More

Cosmological Parameters from Redshift-Space CorrelationsMar 20 2002Apr 15 2002We estimate how clustering in large-scale redshift surveys can constrain various cosmological parameters. Depth and sky coverage of modern redshift surveys are greater than ever, opening new possibilities for statistical analysis. We have constructed ... More

Weak containment of measure preserving group actionsNov 23 2016We survey recent progress in the theory of weak containment of measure preserving group actions.

Role of gravity waves in vertical coupling during sudden stratospheric warmingsSep 02 2016Gravity waves are primarily generated in the lower atmosphere, and can reach thermospheric heights in the course of their propagation. This paper reviews the recent progress in understanding the role of gravity waves in vertical coupling during sudden ... More

Spectral Methods from Tensor NetworksNov 02 2018A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although they are not ... More

Weak containment of measure preserving group actionsNov 23 2016Feb 27 2019We survey recent progress in the theory of weak containment of measure preserving group actions.

Protoplanetary dust porosity and FU Orionis Outbursts: Solving the mystery of Earth's missing volatilesApr 15 2014The Earth is known to be depleted in volatile lithophile elements in a fashion that defies easy explanation. We resolve this anomaly with a model that combines the porosity of collisionally grown dust grains in protoplanetary disks with heating from FU ... More

Construction of Fredholm representations and a modification of the Higson-Roe coronaSep 14 2007Feb 16 2008The Fredholm representation theory is well adapted to construction of homotopy invariants of non simply connected manifolds on the base of generalized Hirzebruch formula. Earlier a natural family of the Fredholm representations was constructed that lead ... More

Effects of Sampling on Measuring Galaxy Count ProbabilitiesAug 09 1995We investigate in detail the effects of sampling on our ability to accurately reconstruct the distribution of galaxies from galaxy surveys. We use a simple probability theory approach, Bayesian classifier theory and Bayesian transition probabilities. ... More

Cumulant Correlators from the APMFeb 01 1997Dec 23 1998This work presents a set of new statistics, the cumulant correlators, aimed at high precision analysis of the galaxy distribution. They form a symmetric matrix, $Q_{NM}$, related to moment correlators the same way as cumulants are related to the moments ... More

Probabilistic Cross-Identification of Astronomical SourcesJul 11 2007Feb 11 2008We present a general probabilistic formalism for cross-identifying astronomical point sources in multiple observations. Our Bayesian approach, symmetric in all observations, is the foundation of a unified framework for object matching, where not only ... More

The spectral gap of the 2-D stochastic Ising model with mixed boundary conditionsAug 25 2000We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an n-by-n box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary spins over ... More

How many Turing degrees are there?Jan 28 2000A Borel equivalence relation on a Polish space is said to be countable if all of its equivalence classes are countable. Standard examples of countable Borel equivalence relations (on the space of subsets of the integers) that occur in recursion theory ... More