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Suppression of nonlinear Zeeman effect and heading error in earth-field-range alkali-vapor magnetometersAug 17 2017The nonlinear Zeeman effect can induce splitting and asymmetries of magnetic-resonance lines in the geophysical magnetic field range. This is a major source of "heading error" for scalar atomic magnetometers. We demonstrate a method to suppress the nonlinear ... More

Waveplate retarders based on overhead transparenciesFeb 25 2007Feb 28 2007We describe procedures for constructing inexpensive waveplates of desired retardation out of ordinary commercially available transparencies. Various relevant properties of the transparencies are investigated: the dependence of retardation on rotation ... More

Tailorable Dispersion in a Four-Wave Mixing LaserMay 08 2017We present experimental results demonstrating controllable dispersion in a ring laser by monitoring the lasing-frequency response to cavity-length variations. Pumping on an N-type level configuration in ${}^{87}$Rb, we tailor the intra-cavity dispersion ... More

Nondestructive in-line sub-picomolar detection of magnetic nanoparticles in flowing complex fluidsJan 17 2018Over the last decades, the use of magnetic nanoparticles in research and commercial applications has increased dramatically. However, direct detection of trace quantities remains a challenge in terms of equipment cost, operating conditions and data acquisition ... More

Remote sensing of geomagnetic fields and atomic collisions in the mesosphereFeb 09 2018Magnetic-field sensing has contributed to the formulation of the plate-tectonics theory, the discovery and mapping of underground structures on Earth, and the study of magnetism in other planets. Filling the gap between space-based and near-Earth observation, ... More

Constraints on exotic spin-dependent interactions between matter and antimatter from antiprotonic helium spectroscopyJan 01 2018Heretofore undiscovered spin-0 or spin-1 bosons can mediate exotic spin-dependent interactions between standard-model particles. Here we carry out the first search for semileptonic spin-dependent interactions between matter and antimatter. We compare ... More

Directional infrared emission resulting from cascade population inversion and four-wave mixing in Rb vapoursNov 01 2013Directional infrared emission at 1367 and 5230 nm is generated in Rb vapours that are step-wise excited by low-power resonant light. The mid-infrared radiation originating from amplified spontaneous emission on the 5D-6P transition consists of forward- ... More

Rules for collaborative scientific writingJun 21 2016Several years ago, one of us, having noticed that inexperienced scientists tend to make largely the same mistakes while writing their first papers, was compelled to write a one-page note summarizing some dos and don'ts intended to help take care of common ... More

Optimizing a Dynamical Decoupling Protocol for Solid-State Electronic Spin Ensembles in DiamondMay 04 2015Jul 14 2015We demonstrate significant improvements of the spin coherence time of a dense ensemble of nitrogen-vacancy (NV) centers in diamond through optimized dynamical decoupling (DD). Cooling the sample down to $77$ K suppresses longitudinal spin relaxation $T_1$ ... More

A Precessing Ferromagnetic Needle MagnetometerFeb 08 2016Apr 20 2016A ferromagnetic needle is predicted to precess about the magnetic field axis at a Larmor frequency $\Omega$ under conditions where its intrinsic spin dominates over its rotational angular momentum, $N\hbar \gg I\Omega$ ($I$ is the moment of inertia of ... More

Polarized alkali vapor with minute-long transverse spin-relaxation timeMay 10 2010We demonstrate lifetimes of atomic populations and coherences in excess of 60 seconds in alkali vapor cells with inner walls coated with an alkene material. This represents two orders of magnitude improvement over the best paraffin coatings. Such anti-relaxation ... More

Alkali-vapor magnetic resonance driven by fictitious radiofrequency fieldsSep 22 2014Sep 26 2014We demonstrate an all-optical $^{133}$Cs scalar magnetometer, operating in nonzero magnetic field,in which the magnetic resonance is driven by an effective oscillating magnetic field provided by the AC Stark shift of an intensity-modulated laser beam. ... More

Eddy current imaging with an atomic radio-frequency magnetometerMar 16 2016We use a radio-frequency $^{85}$Rb alkali-vapor cell magnetometer based on a paraffin-coated cell with long spin-coherence time and a small, low-inductance driving coil to create highly resolved conductivity maps of different objects. We resolve sub-mm ... More

Detection of the Meissner Effect with a Diamond MagnetometerNov 13 2009Sep 24 2010We examine the possibility of probing superconductivity effects in metal nanoclusters via diamond magnetometry. Metal nanoclusters have been proposed as constitutive elements of high T$_c$ superconducting nanostructured materials. Magnetometry based on ... More

Nonlinear processes responsible for mid-infrared and blue light generation in alkali vapoursOct 10 2013The nonlinear processes responsible for frequency up- and down-conversion of resonant low-intensity laser radiation in Rb vapour have been evaluated from the spatial and temporal properties of blue and mid-IR light resulting from wave mixing.

Optical polarization of nuclear ensembles in diamondFeb 06 2012Jan 21 2013We report polarization of a dense nuclear-spin ensemble in diamond and its dependence on magnetic field and temperature. The polarization method is based on the transfer of electron spin polarization of negatively charged nitrogen vacancy color centers ... More

Multi-Channel Data Acquisition System with Absolute Time SynchronizationNov 22 2013A low-cost, stand-alone Global-Positioning-System-time-synchronized data acquisition system is described. The constructed prototype allows recoding up to four analog signals with a 16-bit resolution in variable ranges and a maximum sampling rate of 1000 ... More

Sensitive optical atomic magnetometer based on nonlinear magneto-optical rotationMar 07 2010A self-oscillating magnetometer based on nonlinear magneto-optical rotation using amplitude-modulated pump light and unmodulated probe light (AM-NMOR) in 87Rb has been constructed and tested towards a goal of airborne detection of magnetic anomalies. ... More

Gyroscopes based on nitrogen-vacancy centers in diamondMay 01 2012Sep 04 2012We propose solid-state gyroscopes based on ensembles of negatively charged nitrogen-vacancy (${\rm NV^-}$) centers in diamond. In one scheme, rotation of the nitrogen-vacancy symmetry axis will induce Berry phase shifts in the ${\rm NV^{-}}$ electronic ... More

Search for ultralight scalar dark matter with atomic spectroscopyMar 24 2015Apr 08 2015We report new limits on ultralight scalar dark matter (DM) with dilaton-like couplings to photons that can induce oscillations in the fine-structure constant alpha. Atomic dysprosium exhibits an electronic structure with two nearly degenerate levels whose ... More

Efficient polarization of high-angular-momentum systemsAug 31 2016We propose methods of optical pumping that are applicable to open, high-angular-momentum transitions in atoms and molecules, for which conventional optical pumping would lead to significant population loss. Instead of applying circularly polarized cw ... More

Cosmic Axion Spin Precession Experiment (CASPEr)Jun 25 2013May 29 2014We propose an experiment to search for QCD axion and axion-like-particle (ALP) dark matter. Nuclei that are interacting with the background axion dark matter acquire time-varying CP-odd nuclear moments such as an electric dipole moment. In analogy with ... More

Bulk Nuclear Polarization Enhanced at Room-Temperature by Optical PumpingNov 25 2012Jun 05 2013Bulk 13C polarization can be strongly enhanced in diamond at room-temperature based on the optical pumping of nitrogen-vacancy color centers. This effect was confirmed by irradiating suitably aligned single-crystals at a ~50 mT field promoting anti-crossings ... More

Magneto-Optical Cooling of AtomsSep 23 2013We propose an alternative method to laser cooling. Our approach utilizes the extreme brightness of a supersonic atomic beam, and the adiabatic atomic coilgun to slow atoms in the beam or to bring them to rest. We show how internal-state optical pumping ... More

Sidebands in Optically Detected Magnetic Resonance Signals of Nitrogen Vacancy Centers in DiamondDec 23 2012Jun 06 2013We study features in the optically detected magnetic resonance (ODMR) signals associated with negatively charged nitrogen-vacancy (NV) centers coupled to other paramagnetic impurities in diamond. Our results are important for understanding ODMR line shapes ... More

Detection of a single cobalt microparticle with a microfabricated atomic magnetometerJul 11 2011Jul 12 2011We present magnetic detection of a single, 2 {\mu}m diameter cobalt microparticle using an atomic magnetometer based on a microfabricated vapor cell. These results represent an improvement by a factor of 105 in terms of the detected magnetic moment over ... More

Electromagnetically-induced transparency in a diamond spin ensemble enables all-optical electromagnetic field sensingMar 27 2013May 24 2013We use electromagnetically-induced transparency (EIT) to probe the narrow electron-spin resonance of nitrogen-vacancy centers in diamond. Working with a multi-pass diamond chip at temperatures 6-30 K, the zero-phonon absorption line (637 nm) exhibits ... More

Constraints on exotic spin-dependent interactions between electrons from helium fine-structure spectroscopyAug 20 2016Agreement between theoretical calculations of atomic structure and spectroscopic measurements is used to constrain possible contribution of exotic spin-dependent interactions between electrons to the energy differences between states in helium-4. In particular, ... More

Parahydrogen enhanced zero-field nuclear magnetic resonanceFeb 26 2011Nuclear magnetic resonance (NMR), conventionally detected in multi-tesla magnetic fields, is a powerful analytical tool for the determination of molecular identity, structure, and function. With the advent of prepolarization methods and alternative detection ... More

Liquid-state nuclear spin comagnetometersJan 21 2012Jan 24 2012We discuss nuclear spin comagnetometers based on ultra-low-field nuclear magnetic resonance in mixtures of miscible solvents, each rich in a different nuclear spin. In one version thereof, Larmor precession of protons and ${\rm ^{19}F}$ nuclei in a mixture ... More

Electron Spin Resonance Shift and Linewidth Broadening of Nitrogen-Vacancy Centers in Diamond as a Function of Electron Irradiation DoseDec 29 2009Aug 09 2012A high-nitrogen-concentration diamond sample was subject to 200-keV electron irradiation using a transmission electron microscope. The optical and spin-resonance properties of the nitrogen-vacancy (NV) color centers were investigated as a function of ... More

Controllable steep dispersion with gain in a four-level N-scheme with four-wave mixingMay 11 2012We present a theoretical analysis of the propagation of light pulses through a medium of four-level atoms, with two strong pump fields and a weak signal field in an N-scheme arrangement. We show that the generation of four-wave mixing has a profound effect ... More

Light shift averaging in paraffin-coated alkali vapor cellsNov 17 2015Light shifts are an important source of noise and systematics in optically pumped magnetometers. We demonstrate that the long spin coherence time in paraffin-coated cells leads to spatial averaging of the light shifts over the entire cell volume. This ... More

Solid-state electronic spin coherence time approaching one secondNov 29 2012Dec 06 2012Solid-state electronic spin systems such as nitrogen-vacancy (NV) color centers in diamond are promising for applications of quantum information, sensing, and metrology. However, a key challenge for such solid-state systems is to realize a spin coherence ... More

Four-wave mixing in a ring cavityApr 17 2014We investigate a four-wave mixing process in an N interaction scheme in Rb vapor placed inside a low-finesse ring cavity. We observe strong amplification and generation of a probe signal, circulating in the cavity, in the presence of two strong optical ... More

Linewidth of collimated wavelength-converted emission in Rb vapoursJan 30 2013Oct 09 2013We present a study of the spectral linewidth of collimated blue light (CBL) that results from wave mixing of low-power cw laser radiation at 780 nm and 776 nm and an internally-generated mid-IR field at 5.23 um in Rb vapour. Using a high-finesse Fabry-Perot ... More

A Remotely Interrogated All-Optical $^{87}$Rb MagnetometerAug 06 2012Atomic magnetometry was performed at Earth's magnetic field over a free-space distance of ten meters. Two laser beams aimed at a distant alkali-vapor cell excited and detected the $^{87}$Rb magnetic resonance, allowing the magnetic field within the cell ... More

Characterization of high-temperature performance of cesium vapor cells with anti-relaxation coatingSep 15 2016Vapor cells with antirelaxation coating are widely used in modern atomic physics experiments due to the coating's ability to maintain the atoms' spin polarization during wall collisions. We characterize the performance of vapor cells with different coating ... More

Efficient polarization of high-angular-momentum systemsAug 31 2016Oct 21 2016We propose methods of optical pumping that are applicable to open, high-angular-momentum transitions in atoms and molecules, for which conventional optical pumping would lead to significant population loss. Instead of applying circularly polarized cw ... More

Metastable states and macroscopic quantum tunneling in a cold atom Josephson ringSep 18 2009We study macroscopic properties of a system of weakly interacting neutral bosons confined in a ring-shaped potential with a Josephson junction. We derive an effective low energy action for this system and evaluate its properties. In particular we find ... More

On Small Gaps in the Length SpectrumFeb 15 2016We discuss upper and lower bounds for the size of gaps in the length spectrum of negatively curved manifolds. For manifolds with algebraic generators for the fundamental group, we establish the existence of exponential lower bounds for the gaps. On the ... More

Coherent phase slips in superconducting nanoringsJul 15 2011We study quantum fluctuations of persistent current in a small superconducting ring. Based on a microscopic model of the ring we argue that under certain conditions such ring will exhibit coherent quantum phase slips, similar to those in a flux qubit. ... More

Kinetics of the Phase Separation Transition in Cold-Atom Boson-Fermion MixturesDec 04 2007Apr 16 2008We study the kinetics of the first order phase separation transition in boson-fermion cold-atom mixtures. At sufficiently low temperatures such a transition is driven by quantum fluctuations responsible for the formation of critical nuclei of a stable ... More

Cold Atom QubitsMay 29 2010Dec 20 2010We discuss a laser-trapped cold-atom superfluid qubit system. Each qubit is proposed as a macroscopic two-state system based on a set of Bose-Einstein condensate (BEC) currents circulating in a ring, cut with a Josephson barrier. We review the effective ... More

Investigation of two-frequency Paul traps for antihydrogen productionMar 31 2016Oct 13 2016Radio-frequency (rf) Paul traps operated with multifrequency rf trapping potentials provide the ability to independently confine charged particle species with widely different charge-to-mass ratios. In particular, these traps may find use in the field ... More

Search for plant biomagnetism with a sensitive atomic magnetometerJun 17 2010Aug 16 2011We report what we believe is the first experimental limit placed on plant biomagnetism. Measurements with a sensitive atomic magnetometer were performed on the Titan arum (Amorphophallus titanum) inflorescence, known for its fast bio-chemical processes ... More

Sensitive Magnetic Control of Ensemble Nuclear Spin Hyperpolarisation in DiamondNov 30 2012Dynamic nuclear polarisation, which transfers the spin polarisation of electrons to nuclei, is routinely applied to enhance the sensitivity of nuclear magnetic resonance; it is also critical in spintronics, particularly when spin hyperpolarisation can ... More

Microwave-free magnetometry with nitrogen-vacancy centers in diamondJun 09 2016We use magnetic-field-dependent features in the photoluminescence of negatively charged nitrogen-vacancy centers to measure magnetic fields without the use of microwaves. In particular, we present a magnetometer based on the level anti-crossing in the ... More

Optical quenching and recovery of photoconductivity in single-crystal diamondJul 28 2016Oct 11 2016We study the photocurrent induced by pulsed-light illumination (pulse duration is several nanoseconds) of single-crystal diamond containing nitrogen impurities. Application of additional continuous-wave light of the same wavelength quenches pulsed photocurrent. ... More

Near-zero-field nuclear magnetic resonanceJul 08 2011We investigate nuclear magnetic resonance (NMR) in near-zero-field, where the Zeeman interaction can be treated as a perturbation to the electron mediated scalar interaction (J-coupling). This is in stark contrast to the high field case, where heteronuclear ... More

Accurate solution of near-colliding Prony systems via decimation and homotopy continuationDec 31 2014Oct 21 2016We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the system is a-priori ... More

Faster Lightweight Lempel-Ziv ParsingApr 25 2015Jun 08 2015We present an algorithm that computes the Lempel-Ziv decomposition in $O(n(\log\sigma + \log\log n))$ time and $n\log\sigma + \epsilon n$ bits of space, where $\epsilon$ is a constant rational parameter, $n$ is the length of the input string, and $\sigma$ ... More

QCD measurements at the TevatronNov 30 2011Dec 30 2011Selected quantum chromodynamics (QCD) measurements performed at the Fermilab Run II Tevatron ppbar collider running at sqrt{s} = 1.96 TeV by CDF and D0 Collaborations are presented. The inclusive jet, dijet production and three-jet cross section measurements ... More

Sums with convolution of Dirichlet charactersApr 02 2011We improve a recent result by Shparlinski and Banks related to sums with convolution of Dirichlet characters.

Elimination of generalised imaginaries and Galois cohomologyDec 08 2013Nov 12 2014The objective of this article is to characterise elimination of finite generalised imaginaries (as defined by Hrushovski) in terms of group cohomology. As an application, I consider series of Zariski geometries constructed by Hrushovski and Zilber, and ... More

Quantum Predictive Learning and Communication Complexity with Single InputDec 17 2008Mar 15 2012We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate a relational ... More

On the Role of Shared EntanglementApr 08 2006Aug 22 2006Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement analogue" for ... More

A question about Parisi functionalDec 22 2004We conjecture that the Parisi functional in the SK model is convex in the functional order parameter and prove a partial result that shows the convexity along one-sided directions. A consequence of this result is log-convexity of L_1 norm for a class ... More

A central limit theorem for weighted averages of spins in the high temperature region of the Sherrington-Kirkpatrick modelMay 18 2004In this paper we prove that in the high temperature region of the Sherrington-Kirkpatrick model for a typical realization of the disorder the weighted average of spins $\sum_{i\leq N} t_i \sigma_i$ will be approximately Gaussian provided that $\max_{i\leq ... More

The free energy in a multi-species Sherrington-Kirkpatrick modelOct 24 2013Dec 22 2015The authors of [Ann. Henri Poincar\'{e} 16 (2015) 691-708] introduced a multi-species version of the Sherrington-Kirkpatrick model and suggested the analogue of the Parisi formula for the free energy. Using a variant of Guerra's replica symmetry breaking ... More

Parametric Estimation of the Ultimate Size of HypercomputersNov 18 2011The performance of the emerging petaflops-scale supercomputers of the nearest future (hypercomputers) will be governed not only by the clock frequency of the processing nodes or by the width of the system bus, but also by such factors as the overall power ... More

On solutions of the reduced model for the dynamical evolution of contact linesFeb 05 2013We solve the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a hydrodynamic flow at a 180 contact ... More

Survey on global existence in the nonlinear Dirac equations in one dimensionNov 26 2010We consider the nonlinear Dirac equations in one dimension and review various results on global existence of solutions in H1. Depending on the character of the nonlinear terms, existence of the large-norm solutions can be extended for all times. Global ... More

The Baum-Connes conjecture and proper group actions on affine buildingsMar 30 2007We study the possibility of applying a finite-dimensionality argument in order to address parts of the Baum-Connes conjecture for finitely generated linear groups. This gives an alternative approach to the results of Guentner, Higson, and Weinberger concerning ... More

Enumeration of uni-singular algebraic hypersurfacesMay 18 2005Apr 21 2009We enumerate complex algebraic hypersurfaces in $P^n$, of a given (high) degree with one singular point of a given singularity type. Our approach is to compute the (co)homology classes of the corresponding equi-singular strata in the parameter space of ... More

The Delsarte Method in the Problem of the Antipodal Contact Numbers of Euclidean Spaces of High DimensionsJun 28 2003We study the Delsarte problem for even functions continuous on [-1,1], nonpositive on [-1/2,1/2], and representable as series with respect to the ultraspherical polynomials. The value of the Delsarte problem gives an upper bound for the largest power ... More

On the norm of inverses of confluent Vandermonde matricesDec 02 2012Dec 04 2012In this note we present a simple upper bound for the row-wise norm of the inverses of general confluent Vandermonde matrices.

Embedding punctured n-manifolds in Euclidean (2n-1)-spaceOct 20 2010Let $N$ be a closed orientable connected $n$-manifold, $n\ge 4$. We classify embeddings of the punctured manifold $N_0$ into $\R^{2n-1}$ up to isotopy. Our result in some sense extends results of J.C. Becker -- H.H. Glover (1971) and O. Saeki (1999).

Sequential Covariance Calculation for Exoplanet Image ProcessingJan 05 2015Direct imaging of exoplanets involves the extraction of very faint signals from highly noisy data sets, with noise that often exhibits significant spatial, spectral and temporal correlations. As a results, a large number of post-processing algorithms ... More

Application of the quadratures method to the NLS with saturationJan 19 2009The solution of nonlinear Schroedinger equation with saturation was found by means the quadratures method in terms of degeneracy theory. It was shown the existence conditions for soliton solutions.

The transversality conditions in infinite horizon problems and the stability of adjoint variableAug 12 2011This paper investigates the necessary conditions of optimality for uni- formly overtaking optimal control on infinite horizon with free right endpoint. Clarke's form of the Pontryagin Maximum Principle is proved without the as- sumption on boundedness ... More

A discrete analogue of the modified Novikov-Veselov hierarchyApr 23 2009Jun 15 2012We construct a discrete analogue of the integrable two-dimensional Dirac operator and describe the spectral properties of its eigenfunctions. We construct an integrable discrete analogue of the modified Novikov-Veselov hierarchy. We derive the first two ... More

Tauberian theorem for value functionsJul 20 2016Jul 22 2016For two-person dynamic zero-sum games (both discrete and continuous settings), we investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity and the limit of value functions of $\lambda$-discounted ... More

Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation ProcedureNov 01 2016Nov 10 2016We study the consistency conditions for interactions of massless fields of any spin in four-dimensional flat space using the light-cone approach. We show that they can be equivalently rewritten as the Ward identities for the off-shell light-cone amplitudes ... More

On $c_2$ invariants of 4-regular Feynman graphsOct 03 2016The obstruction for application of effective techniques like denominator reduction for the computation of the $c_2$ invariant of Feynman graphs in general is the absence of a 3-valent vertex for the initial steps. In this paper such a formula for a 4-valent ... More

Exponential energy growth due to slow parameter oscillations in quantum mechanical systemsJan 09 2016It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantum mechanical system subjected to a slow periodic variation of parameters. The main example is given by systems (e.g., ... More

Spectral components analysis of diffuse emission processesFeb 06 2012We develop a novel method to separate the components of a diffuse emission process based on an association with the energy spectra. Most of the existing methods use some information about the spatial distribution of components, e.g., closeness to an external ... More

Cayley Automatic Groups and Numerical Characteristics of Turing TransducersJun 27 2016This paper is devoted to the problem of finding characterizations for Cayley automatic groups. The concept of Cayley automatic groups was recently introduced by Kharlampovich, Khoussainov and Miasnikov. We address this problem by introducing three numerical ... More

Dual Graph Polynomials and a 4-face FormulaAug 14 2015We study the dual graph polynomials and the case when a Feynman graph has no triangles but has a 4-face. This leads to the proof of the duality-admissibility of all graphs up to 18 loops. As a consequence, the $c_2$ invariant is the same for all 4 Feynman ... More

Reduction of a problem of finiteness of Tate-Shafarevich group to a result of Zagier typeNov 15 2004Aug 11 2005Kolyvagin proved that the Tate-Shafarevich group of an elliptic curve over Q of analytic rank 0 or 1 is finite, and that its algebraic rank is equal to its analytic rank. A program of generalisation of this result to the case of some motives which are ... More

Lipschitz inverse shadowing for nonsingular flowsFeb 27 2013We prove that Lipschitz inverse shadowing for nonsingular flows is equivalent to structural stability.

Generalizations of analogs of theorems of Maizel and Pliss and their application in Shadowing TheoryFeb 20 2012Nov 28 2012We generalize two classical results of Maizel and Pliss that describe relations between hyperbolicity properties of linear system of difference equations and its ability to have a bounded solution for every bounded inhomogeneity. We also apply one of ... More

On subexponential tails for the maxima of negatively driven compound renewal and Lévy processesAug 31 2016Nov 20 2016We study subexponential tail asymptotics for the distribution of the maximum $M_t:=\sup_{u\in[0,t]}X_u$ of a process $X_t$ with negative drift for the entire range of $t>0$. We consider compound renewal processes with linear drift and L\'evy processes. ... More

A connection between the Ghirlanda--Guerra identities and ultrametricityOct 04 2008Jan 27 2010We consider a symmetric positive definite weakly exchangeable infinite random matrix and show that, under the technical condition that its elements take a finite number of values, the Ghirlanda--Guerra identities imply ultrametricity.

Exponential control of overlap in the replica method for p-spin Sherrington-Kirkpatrick modelJan 30 2007Recently, Michel Talagrand computed the large deviations limit $\lim_{N\to\infty}(Na)^{-1}\log \e Z_N^a$ for the moments of the partition function $Z_N$ in the Sherrington-Kirkpatrick model for all real $a\geq 0.$ For $a\geq 1$ the limit is given by Guerra's ... More

Global generalized solutions for Maxwell-alpha and Euler-alpha equationsDec 21 2010Nov 15 2011We study initial-boundary value problems for the Lagrangian averaged alpha models for the equations of motion for the corotational Maxwell and inviscid fluids in 2D and 3D. We show existence of (global in time) dissipative solutions to these problems. ... More

Weak solutions for a bioconvection model related to Bacillus subtilisMar 21 2012We consider the initial-boundary value problem for the coupled Navier-Stokes-Keller-Segel-Fisher-Kolmogorov-Petrovskii-Piskunov system in two- and three-dimensional domains. The problem describes oxytaxis and growth of Bacillus subtilis in moving water. ... More

A look at perpetuities via asymptotically homogeneous in space Markov chainsMar 28 2016It is shown how a natural representation of perpetuities as asymptotically homogeneous in space Markov chains allows to prove various asymptotic tail results for stable perpetuities and limit theorems for unstable ones. Some of these results are new while ... More

On an example for the Uniform Tauberian theorem in abstract control systemsApr 25 2016The paper is devoted to the asymptotic behavior of value functions of abstract control problem with the long-time and discounted averages. The Uniform Tauberian Theorem for these problems states that the uniform convergence of value functions for long-time~averages ... More

Hierarchical exchangeability of pure states in mean field spin glass modelsJul 08 2013The main result in this paper is motivated by the M\'ezard-Parisi ansatz which predicts a very special structure for the distribution of spins in diluted mean field spin glass models, such as the random K-sat model. Using the fact that one can safely ... More

Multidimensional Random Polymers : A Renewal ApproachNov 30 2014In these lecture notes, which are based on the mini-course given at 2013 Prague School on Mathematical Statistical Physics, we discuss ballistic phase of quenched and annealed stretched polymers in random environment on ${\mathbb Z}^d$ with an emphasis ... More

On a property of random-oriented percolation in a quadrantMay 26 2012Jun 08 2012Grimmett's random-orientation percolation is formulated as follows. The square lattice is used to generate an oriented graph such that each edge is oriented rightwards (resp. upwards) with probability $p$ and leftwards (resp. downwards) otherwise. We ... More

The Sherrington-Kirkpatrick model: an overviewNov 06 2012The goal of this paper is to review some of the main ideas that emerged from the attempts to confirm mathematically the predictions of the celebrated Parisi ansatz in the Sherrington-Kirkpatrick model. We try to focus on the big picture while sketching ... More

A unified stability property in spin glassesJun 20 2011Nov 03 2011Gibbs' measures in the Sherrington-Kirkpatrick type models satisfy two asymptotic stability properties, the Aizenman-Contucci stochastic stability and the Ghirlanda-Guerra identities, which play a fundamental role in our current understanding of these ... More

Enumeration of singular algebraic curvesJul 21 2004Oct 04 2006We enumerate plane complex algebraic curves of a given degree with one singularity of any given topological type. Our approach is to compute the homology classes of the corresponding equisingular strata in the parameter spaces of plane curves. We suggest ... More

Microlocal condition for non-displaceablilitySep 09 2008We formulate a sufficient condition for non-displaceability (by Hamiltonian symplectomorphisms which are identity outside of a compact) of a pair of subsets in a cotangent bundle. This condition is based on micro-local analysis of sheaves on manifolds ... More

Contact integral geometry and the Heisenberg algebraDec 26 2017Jan 03 2018Generalizing Weyl's tube formula and building on Chern's work, Alesker reinterpreted the Lipschitz-Killing curvature integrals as a family of valuations (finitely-additive measures with good analytic properties), attached canonically to any Riemannian ... More

A remark on approximation of open sets with regular bounded onesDec 08 2010We show that any open set in $\R^n$ is a union of an ascending sequence of bounded open sets with analytic boundary. This is just a technical result, which is probably known. We believe, however, that it can be useful for studing BVPs on irregular open ... More

Topological Semantics and DecidabilityMar 05 2007Jun 01 2007It is well-known that the basic modal logic of all topological spaces is $S4$. However, the structure of basic modal and hybrid logics of classes of spaces satisfying various separation axioms was until present unclear. We prove that modal logics of $T_0$, ... More