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Interpreting Deep Learning: The Machine Learning Rorschach Test?Jun 01 2018Theoretical understanding of deep learning is one of the most important tasks facing the statistics and machine learning communities. While deep neural networks (DNNs) originated as engineering methods and models of biological networks in neuroscience ... More

Learning spatially-correlated temporal dictionaries for calcium imagingFeb 08 2019Calcium imaging has become a fundamental neural imaging technique, aiming to recover the individual activity of hundreds of neurons in a cortical region. Current methods (mostly matrix factorization) are aimed at detecting neurons in the field-of-view ... More

Nonlinear quantum optics mediated by Rydberg interactionsFeb 19 2016Jul 07 2016By mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons via electromagnetically induced transparency, it is now possible to realize a nonlinear optical medium which exhibits a strong optical nonlinearity ... More

Optical preparation and measurement of atomic coherence at gigahertz bandwidthNov 18 2011We detail a method for the preparation of atomic coherence in a high density atomic medium, utilising a coherent preparation scheme of gigahertz bandwidth pulses. A numerical simulation of the preparation scheme is developed, and its efficiency in preparing ... More

Graph State Preparation and Cluster Computation with Global Addressing of Optical LatticesJan 28 2005We present a novel way to manipulate ultra-cold atoms where four atomic levels are trapped by appropriately tuned optical lattices. When employed to perform quantum computation via global control, this unique structure dramatically reduces the number ... More

Lensing Probabilities for Spectroscopically Selected Galaxy-Galaxy Strong LensesMar 17 2008Spectroscopic galaxy-galaxy lens searches are presently the most prolific method of identifying strong lens systems in large data sets. We study the probabilities associated with these lens searches, namely the probability of identifying a candidate with ... More

Practical designs for permutation symmetric problem Hamiltonians on hypercubesDec 19 2018We present a method to experimentally realize large-scale permutation-symmetric Hamiltonians for continuous-time quantum protocols such as quantum walk and adiabatic quantum computation. In particular, the method can be used to perform an encoded continuous-time ... More

Off-resonance absorption and dispersion in a Doppler-broadened mediumMay 08 2009We study the absorptive and dispersive properties of Doppler-broadened atomic media as a function of detuning. Beginning from the exact lineshape calculated for a two-level atom, a series of approximations to the electric susceptibility are made. These ... More

Short Term Memory Capacity in Networks via the Restricted Isometry PropertyJul 01 2013Mar 03 2015Cortical networks are hypothesized to rely on transient network activity to support short term memory (STM). In this paper we study the capacity of randomly connected recurrent linear networks for performing STM when the input signals are approximately ... More

Automatic Response Category Combination in Multinomial Logistic RegressionMay 10 2017We propose a penalized likelihood method that simultaneously fits the multinomial logistic regression model and combines subsets of the response categories. The penalty is non differentiable when pairs of columns in the optimization variable are equal. ... More

Ridge Fusion in Statistical LearningOct 15 2013May 05 2014We propose a penalized likelihood method to jointly estimate multiple precision matrices for use in quadratic discriminant analysis and model based clustering. A ridge penalty and a ridge fusion penalty are used to introduce shrinkage and promote similarity ... More

Cooperative Ordering in Lattices of Interacting Two-Level DipolesOct 17 2014Dec 09 2015We investigate the cooperative behavior of regular monolayers of driven two-level dipoles, using classical electrodynamics simulations. The dipolar response results from the interference of many cooperative eigenmodes, each frequency-shifted from the ... More

Polarization spectroscopy of an excited state transitionJul 13 2011Jul 26 2011We demonstrate polarization spectroscopy of an excited state transition in room temperature cesium vapor. An anisotropy induced by a circularly polarized pump beam on the D2 transition is observed using a weak probe on the 6P3/2 to 7S1/2 transition. When ... More

Absolute absorption on the rubidium D lines: comparison between theory and experimentMay 08 2008We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric ... More

Enhanced optical cross section via collective coupling of atomic dipoles in a 2D arrayOct 27 2015Mar 10 2016Enhancing the optical cross section is an enticing goal in light-matter interactions, due to its fundamental role in quantum and non-linear optics. Here, we show how dipolar interactions can suppress off-axis scattering in a two-dimensional atomic array, ... More

Optical control of Faraday rotation in hot Rb vaporDec 09 2009We demonstrate controlled polarization rotation of an optical field conditional on the presence of a second field. Induced rotations of greater than pi/2 rad are seen with a transmission of 95%, corresponding to a ratio of phase shift to absorption of ... More

Sagnac Interferometry in a Slow-Light MediumDec 14 2005We use a Sagnac interferometer to measure the dispersive and absorptive properties of room temperature Rubidium vapor on the D_2 line at 780.2 nm. We apply a pump beam such that the resulting Lambda system exhibits Electromagnetically Induced Transparency. ... More

The Cosmic Microwave Background and the Stellar Initial Mass FunctionSep 10 2018Sep 24 2018We argue that an increased temperature in star-forming clouds alters the stellar initial mass function to be more bottom-light than in the Milky Way. At redshifts $z \gtrsim 6$, heating from the cosmic microwave background radiation produces this effect ... More

Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen-Back regimeAug 09 2012Here we report on measurements of the absolute absorption and dispersion properties of an isotopically pure 87Rb vapour for magnetic fields up to and including 0.6 T. We discuss the various regimes that arise when the hyperfine and Zeeman interactions ... More

Dressed-state electromagnetically induced transparency for light storage in uniform phase spin-wavesJul 27 2016We present, experimentally and theoretically, a scheme for dressed-state electromagnetically induced transparency (EIT) in a three-step cascade system where a four-level system is mapped into an effective three-level system. Theoretical analysis reveals ... More

Slow-light Faraday effect: an atomic probe with gigahertz bandwidthNov 14 2008The ability to control the speed and polarisation of light pulses will allow for faster data flow in optical networks of the future. Optical delay and switching have been achieved using slow-light techniques in various media, including atomic vapour. ... More

Faraday filtering of Raman light in an isotopically pure alkali metal vaporApr 27 2009We present an application of the Faraday effect to produce a narrow band atomic filter in an alkali metal vapor. In our experiment two Raman beams separated in frequency by the ground state hyperfine splitting in 87Rb are produced using an EOM and then ... More

ElecSus: A program to calculate the electric susceptibility of an atomic ensembleSep 05 2014Feb 09 2015We present a computer program and underlying model to calculate the electric susceptibility of a gas, which is essential to predict its absorptive and dispersive properties. Our program focusses on alkali-metal vapours where we use a matrix representation ... More

Driven-dissipative many-body systems with mixed power-law interactions: Bistabilities and temperature-driven non-equilibrium phase transitionsDec 07 2015Feb 26 2016We investigate the non-equilibrium dynamics of a driven-dissipative spin ensemble with competing power-law interactions. We demonstrate that dynamical phase transitions as well as bistabilities can emerge for asymptotic van der Waals interactions, but ... More

Cooperative non-equilibrium phase transition in a dilute Rydberg ensembleFeb 26 2013Aug 27 2013We demonstrate a non-equilibrium phase transition in a dilute thermal atomic gas. The phase transition, between states of low and high Rydberg occupancy, is induced by resonant dipole-dipole interactions between Rydberg atoms. The gas can be considered ... More

Phase diagram of non-equilibrium phase transition in a strongly-interacting Rydberg atom vapourJun 28 2016Feb 14 2019Far-from equilibrium dynamics that lead to self-organization are highly relevant to complex dynamical systems not only in physics, but also in life-, earth-, and social sciences. It is challenging however to find systems with sufficiently controlled interactions ... More

Three-photon electromagnetically induced transparency using Rydberg statesMay 11 2012Aug 01 2012We demonstrate electromagnetically induced transparency (EIT) in a four-level cascade system where the upper level is a Rydberg state. The observed spectral features are sub-Doppler and can be enhanced due to the compensation of Doppler shifts with AC ... More

Active narrowband filtering, line narrowing and gain using ladder electromagnetically induced transparency in an optically thick atomic vapourNov 28 2013Jan 24 2014Electromagnetically induced transparency (EIT) resonances using the $5\rm{S}_{1/2}\rightarrow5\rm{P}_{3/2}\rightarrow5\rm{D}_{5/2}$ ladder-system in optically thick Rb atomic vapour are studied. We observe a strong line narrowing effect and gain at the ... More

A single-mode external cavity diode laser using an intra-cavity atomic Faraday filter with short-term linewidth $<400$ kHz and long-term stability of $<1$ MHzJul 07 2016We report on the development of a diode laser system - the `Faraday laser' - using an atomic Faraday filter as the frequency-selective element. In contrast to typical external-cavity diode laser systems which offer tunable output frequency but require ... More

Atomic Faraday filter with equivalent noise bandwidth less than 1 GHzFeb 25 2015We demonstrate an atomic bandpass optical filter with an equivalent noise bandwidth less than 1 GHz using the D$_1$ line in a cesium vapor. We use the ElecSus computer program to find optimal experimental parameters, and find that for important quantities ... More

Single-photon interference due to motion in an atomic collective excitationDec 16 2016May 23 2017We experimentally demonstrate the generation of heralded bi-chromatic single photons from an atomic collective spin excitation (CSE). The photon arrival times display collective quantum beats, a novel interference effect resulting from the relative motion ... More

Probing an excited-state atomic transition using hyperfine quantum beat spectroscopyAug 15 2014Oct 06 2014We describe a method to observe the dynamics of an excited-state transition in a room temperature atomic vapor using hyperfine quantum beats. Our experiment using cesium atoms consists of a pulsed excitation of the D2 transition, and continuous-wave driving ... More

Network Modeling of Short Over-Dispersed Spike-Counts: A Hierarchical Parametric Empirical Bayes FrameworkMay 10 2016May 28 2018Accurate statistical models of neural spike responses can characterize the information carried by neural populations. Yet, challenges in recording at the level of individual neurons commonly results in relatively limited samples of spike counts, which ... More

Efficient Tracking of Sparse Signals via an Earth Mover's Distance Dynamics RegularizerJun 12 2018Feb 20 2019Sparse signal models have enjoyed great success, achieving state-of-the-art performance in many applications. Some algorithms further improve performance by taking advantage of temporal dynamics for streaming observations. However, the tracking regularizers ... More

The cooperative Lamb shift in an atomic nanolayerJan 25 2012We present an experimental measurement of the cooperative Lamb shift and the Lorentz shift using an atomic nanolayer with tunable thickness and atomic density. The cooperative Lamb shift arises due to the exchange of virtual photons between identical ... More

Absolute absorption on rubidium D1 line: including resonant dipole-dipole interactionsJul 15 2011Jul 18 2011Here we report on measurements of the absolute absorption spectra of dense rubidium vapour on the D1 line in the weak-probe regime for temperatures up to 170 C and number densities up to 3 \times 10^14 cm^-3. In such vapours, modifications to the homogeneous ... More

Topological properties of a dense atomic lattice gasMar 09 2017We investigate the existence of topological phases in a dense two-dimensional atomic lattice gas. The coupling of the atoms to the radiation field gives rise to dissipation and a non-trivial coherent long-range exchange interaction whose form goes beyond ... More

Electromagnetically induced absorption in a non-degenerate three-level ladder systemMay 14 2015We investigate, theoretically and experimentally, the transmission of light through a thermal vapour of three-level ladder-type atoms, in the presence of 2 counter-propagating control fields. A simple theoretical model predicts the presence of electromagnetically ... More

Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regimeFeb 29 2016May 03 2016Applying large magnetic fields to gain access to the hyperfine Paschen-Back regime can isolate three-level systems in a hot alkali metal vapors, thereby simplifying usually complex atom-light interactions. We use this method to make the first direct measurement ... More

Optical transmission through a dipolar layerSep 16 2011Sep 20 2011The interaction between light and matter is fundamental to developments in quantum optics and information. Over recent years enormous progress has been made in controlling the interface between light and single emitters including ions, atoms, molecules, ... More

The hyperfine Paschen-Back Faraday effectJan 08 2014Mar 26 2014We investigate experimentally and theoretically the Faraday effect in an atomic medium in the hyperfine Paschen-Back regime, where the Zeeman interaction is larger than the hyperfine splitting. We use a small permanent magnet and a micro-fabricated vapour ... More

Measuring the Stokes parameters for light transmitted by a high-density rubidium vapour in large magnetic fieldsDec 16 2011Here we report on measurements of the absolute absorption and dispersion of light in a dense rubidium vapour on the D2 line in the weak-probe regime with an applied magnetic field. A model for the electric susceptibility of the vapour is presented which ... More

Coherent Excitation Transfer in a Spin Chain of Three Rydberg AtomsAug 05 2014Mar 21 2015We study coherent excitation hopping in a spin chain realized using highly excited individually addressable Rydberg atoms. The dynamics are fully described in terms of an XY spin Hamiltonian with a long range resonant dipole-dipole coupling that scales ... More

Reliable operations on oscillatory functionsMay 14 1999Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the discretization errors ... More

Finiteness of the Hopping Induced Energy Corrections in CupratesMar 09 2009The paper continues the rigorous investigations of the mean field Green function solution of the effective two-dimensional two-band Hubbard model [N. M. Plakida et al., Phys. Rev. B, Vol.51, 16599 (1995)] of the superconducting phase transitions in cuprates, ... More

Rigorous derivation of the mean field Green functions of the two-band Hubbard model of superconductivityApr 05 2007The Green function (GF) equation of motion technique for solving the effective two-band Hubbard model of high-T_c superconductivity in cuprates [N.M. Plakida et al., Phys. Rev. B, v. 51, 16599 (1995); JETP, v. 97, 331 (2003)] rests on the Hubbard operator ... More

The boundary layer problem in Bayesian adaptive quadratureSep 25 2006The boundary layer of a finite domain [a, b] covers mesoscopic lateral neighbourhoods, inside [a, b], of the endpoints a and b. The correct diagnostic of the integrand behaviour at a and b, based on its sampling inside the boundary layer, is the first ... More

Mean field solutions to singlet hopping and superconducting pairing within a two-band Hubbard modelSep 25 2006The mean field Green function solution of the two-band singlet-hole Hubbard model for high-$T\sb{c}$ superconductivity in cuprates (Plakida, N.M. et al., Phys. Rev. B51, 16599 (1995), JETP 97, 331 (2003)) involves expressions of higher order correlation ... More

Signature of Fermi surface jumps in positron spectroscopy dataAug 05 1999A subtractionless method for solving Fermi surface sheets ({\tt FSS}), from measured $n$-axis-projected momentum distribution histograms by two-dimensional angular correlation of the positron-electron annihilation radiation ({\tt 2D-ACAR}) technique, ... More

Effect of line broadening on the performance of Faraday filtersApr 14 2015We show that homogeneous line broadening drastically affects the performance of atomic Faraday filters. We use a computerized optimization algorithm to find the best magnetic field and temperature for Faraday filters with a range of cell lengths. The ... More

Dynamic Filtering of Time-Varying Sparse Signals via l1 MinimizationJul 22 2015Feb 22 2016Despite the importance of sparsity signal models and the increasing prevalence of high-dimensional streaming data, there are relatively few algorithms for dynamic filtering of time-varying sparse signals. Of the existing algorithms, fewer still provide ... More

The set of maps F_{a,b}: x -> x+a+{b/{2 pi}} sin(2 pi x) with any given rotation interval is contractibleMay 14 1994Consider the two-parameter family of real analytic maps $F_{a,b}:x \mapsto x+ a+{b\over 2\pi} \sin(2\pi x)$ which are lifts of degree one endomorphisms of the circle. The purpose of this paper is to provide a proof that for any closed interval $I$, the ... More

Distributed Sequence Memory of Multidimensional Inputs in Recurrent NetworksMay 26 2016Nov 04 2016Recurrent neural networks (RNNs) have drawn interest from machine learning researchers because of their effectiveness at preserving past inputs for time-varying data processing tasks. To understand the success and limitations of RNNs, it is critical that ... More

Manipulating ultracold atoms with a reconfigurable nanomagnetic system of domain wallsDec 02 2011Dec 05 2011The divide between the realms of atomic-scale quantum particles and lithographically-defined nanostructures is rapidly being bridged. Hybrid quantum systems comprising ultracold gas-phase atoms and substrate-bound devices already offer exciting prospects ... More

Distributed Sequence Memory of Multidimensional Inputs in Recurrent NetworksMay 26 2016Recurrent neural networks (RNNs) have drawn interest from machine learning researchers because of their effectiveness at preserving past inputs for time-varying data processing tasks. To understand the success and limitations of RNNs, it is critical that ... More

Ultra-high-speed Terahertz Imaging Using Atomic VapourMar 04 2019Mar 15 2019Terahertz (THz) technologies, generally defined as operating in the 0.1-10THz range, bridge the gap between electronic and photonic devices. Because THz radiation passes readily through materials such as plastics, paper and cloth it can be employed in ... More

Intrinsic Optical Bistability in a Strongly-Driven Rydberg EnsembleMar 04 2016We observe and characterize intrinsic optical bistability in a dilute Rydberg vapor. The bistability is characterized by sharp jumps between states of low and high Rydberg occupancy with jump up and down positions displaying hysteresis depending on the ... More

Faster than superradiant light emission due to collective mode interferenceAug 25 2018Sep 07 2018The optical properties of an ensemble of light scatterers can be dramatically modified when the scatterers behave collectively rather than independently. Certain collective effects such as superradiance and subradiance are well known and have been observed ... More

Observation of interference effects via four photon excitation of highly excited Rydberg states in thermal cesium vaporOct 06 2015Nov 22 2015We report on the observation of electromagnetically induced transparency (EIT) and absorption (EIA) of highly excited Rydberg states in thermal Cs vapor using a four-step excitation scheme. The advantage of this four-step scheme is that the final transition ... More

Ultra-high-speed Terahertz Imaging Using Atomic VapourMar 04 2019Terahertz (THz) technologies, generally defined as operating in the 0.1-10THz range, bridge the gap between electronic and photonic devices. Because THz radiation passes readily through materials such as plastics, paper and cloth it can be employed in ... More

Terahertz-driven phase transition applied as a room-temperature terahertz detectorSep 01 2017There are few demonstrated examples of phase transitions that may be driven directly by terahertz-frequency electric fields, and those that are known require field strengths exceeding 1 MVcm$^{-1}$. Here we report a room-temperature phase transition driven ... More

Real-Time Near-Field Terahertz Imaging with Atomic Optical FluorescenceMar 23 2016Oct 12 2016Terahertz (THz) near-field imaging is a flourishing discipline [1], with applications from fundamental studies of beam propagation [2,3] to the characterisation of metameterials [4,5] and waveguides [6,7]. Beating the diffraction limit typically involves ... More

Search for SUSY in (Leptons +) Jets + E_T^miss final statesNov 19 1998We study the observability of the squarks and gluinos in CMS at LHC. Classical E_T^miss + jets final state as well as a number of additional multilepton signatures (0 leptons, 1 lepton, 2 leptons of the same sign, 2 leptons of the opposite sign and 3 ... More

Study of leptoquark pair production at the LHC with the CMS detectorMay 19 1999May 27 1999We study the discovery potential of the CMS detector for the scalar leptoquark pair production at the LHC. Present and future exclusion limits are considered. We find that the maximal leptoquark mass reach is about 1.47 TeV for the branching ratio of ... More

Comparative Analysis of the Main Nasal Cavity and the Paranasal Sinuses in Chronic Rhinosinusitis: An Anatomic Study of Maximal Medical TherapyNov 01 2018Objective: Minimal literature exists investigating changes in inflammation with respect to the main nasal cavity (MNC) and paranasal sinuses (PS) before and after maximal medical therapy (MMT) for chronic rhinosinusitis (CRS). We hypothesized that MMT ... More

Habitable worlds with no signs of lifeSep 03 2013Sep 04 2013'Most habitable worlds in the cosmos will have no remotely detectable signs of life' is proposed as a biological hypothesis to be tested in studies of exoplanets. Habitable planets could be discovered elsewhere in the Universe, yet there are many hypothetical ... More

A High-z Correction to the Hubble LineApr 10 2005Apr 11 2005This paper was withdrawn as it may have appeared elsewhere, although in a different form.

Comparative Study of Simulated Nebulized and Spray Particle Deposition in Chronic Rhinosinusitis PatientsNov 01 2018Introduction: Topical intranasal drugs are widely prescribed for Chronic Rhinosinusitis (CRS), although delivery can vary with device type and droplet size. The study objective was to compare nebulized and sprayed droplet deposition in the paranasal sinuses ... More

Non-local charges, Zm gradings and coset space actionsMar 01 2005Aug 22 2005The construction of flat currents, and hence conserved non-local charges, for the superstring on AdS_5 x S^5 is generalised. It is shown that such currents exist for sigma-model type actions on all coset (super-)spaces G/H in which, at the level of the ... More

The Impact of Speed and Bias on the Cognitive Processes of Experts and Novices in Medical Image Decision-makingSep 19 2017May 18 2018Training individuals to make accurate decisions from medical images is a critical component of education in diagnostic pathology. We describe a joint experimental and computational modeling approach to examine the similarities and differences in the cognitive ... More

Knowing what you know in brain segmentation using deep neural networksDec 03 2018Dec 18 2018In this paper, we describe a deep neural network trained to predict FreeSurfer segmentations of structural MRI volumes, in seconds rather than hours. The network was trained and evaluated on an extremely large dataset (n = 11,148), obtained by combining ... More

Identification of the Red Supergiant Progenitor of Supernova 2005cs: Do the Progenitors of Type II-P Supernovae Have Low Mass?Jul 18 2005The stars that end their lives as supernovae (SNe) have been directly observed in only a handful of cases, due mainly to the extreme difficulty in identifying them in images obtained prior to the SN explosions. Here we report the identification of the ... More

A Modest Proposal for Open Market Risk Assessment to Solve the Cyber-Security ProblemApr 29 2016We introduce a model for a market based economic system of cyber-risk valuation to correct fundamental problems of incentives within the information technology and information processing industries. We assess the makeup of the current day marketplace, ... More

Charged Schrodinger Black HolesJul 13 2009We construct charged and rotating asymptotically Schrodinger black hole solutions of IIB supergravity. We begin by obtaining a closed-form expression for the null Melvin twist of a broad class of type IIB backgrounds, including solutions of minimal five-dimensional ... More

Clustering with a Reject Option: Interactive Clustering as Bayesian Prior ElicitationJun 19 2016A good clustering can help a data analyst to explore and understand a data set, but what constitutes a good clustering may depend on domain-specific and application-specific criteria. These criteria can be difficult to formalize, even when it is easy ... More

$\mathrm{CAT}(0)$ Extensions of Right-angled Coxeter GroupsAug 21 2015We show that any split extension of a right-angled Coxeter group $W_{\Gamma}$ by a generating automorphism of finite order acts faithfully and geometrically on a $\mathrm{CAT}(0)$ metric space.

Recognizing Right-Angled Coxeter Groups Using InvolutionsOct 16 2014Dec 03 2015We consider the question of determining whether a given group (especially one generated by involutions) is a right-angled Coxeter group. We describe a group invariant, the involution graph, and we characterize the involution graphs of right-angled Coxeter ... More

Effect of buffer gas on electromagnetically induced transparency in a ladder system using thermal rubidium vaporMay 24 2010We report on the first observation of electromagnetically induced transparency (EIT) in a ladder system in the presence of a buffer gas. In particular we study the 5S1/2 - 5P3/2 - 5D5/2 transition in thermal rubidium vapor with a neon buffer gas at a ... More

The Effects of Latency Penalties in Evaluating Push Notification SystemsJun 09 2016We examine the effects of different latency penalties in the evaluation of push notification systems, as operationalized in the TREC 2015 Microblog track evaluation. The purpose of this study is to inform the design of metrics for the TREC 2016 Real-Time ... More

Sl_n-character varieties as spaces of graphsJun 03 1998Feb 05 2001An SL_n-character of a group G is the trace of an SL_n-representation of G. We show that all algebraic relations between SL_n-characters of G can be visualized as relations between graphs (resembling Feynman diagrams) in any topological space X, with ... More

Experimental prospects for $V_{ud}$, $V_{us}$, $V_{cd}$, $V_{cs}$ and (semi-)leptonic decays at LHCbJan 15 2019We review the prospects of measurements of the CKM matrix elements corresponding to the first two generations of quarks, as well as measurements of leptonic and semileptonic charm meson decays at LHCb. We review the status of searches for Lepton Non-Universality ... More

G-Character varieties for G=SO(n,C) and other not simply connected groupsMar 28 2013Apr 01 2015We describe the relation between G-character varieties, $X_G(\Gamma)$, and $G/H$-character varieties, where $H$ is a finite, central subgroup of $G.$ In particular, we find finite generating sets of coordinate rings $C[X_{G/H}(\Gamma)]$ for classical ... More

Generating sets for coordinate rings of character varietiesJun 23 2011Apr 04 2013We find finite, reasonably small, generator sets of the coordinate rings of G-character varieties of finitely generated groups for all classical groups G. This result together with the method of Grobner basis gives an algorithm for describing character ... More

Torus and Z/p actions on manifoldsMay 01 2002Sep 30 2003Let G be either a finite cyclic group of prime order or S^1. We find new relations between cohomology of a manifold (or a Poincare duality space) M with a G-action on it and cohomology of the fixed point set, M^G. Our main tool is the notion of Poincare ... More

Cut numbers of 3-manifoldsDec 12 2001Sep 18 2003The cut number of a manifold M, c(M), is the largest number of disjoint two-sided hypersurfaces in M which do not separate M. Equivalently, it is the largest rank of a free group being an epimorphic image of pi_1(M). We investigate the relations between ... More

Quantizations of Character Varieties and Quantum Knot InvariantsJul 07 2008Jul 18 2008Let G be a simple complex algebraic group and g its Lie algebra. We show that the g-Witten-Reshetikhin-Turaev quantum invariants determine a deformation-quantization, C_q[X_G(torus)], of the coordinate ring of the G-character variety of the torus. We ... More

Topology on the spaces of orderings of groupsOct 31 2001Sep 30 2003A natural topology on the space of left orderings of an arbitrary semi-group is introduced. It is proved that this space is compact and that for free abelian groups it is homeomorphic to the Cantor set. An application of this result is a new proof of ... More

Analogies between group actions on 3-manifolds and number fieldsJul 29 2001Jun 07 2003Mazur, Kapranov, Reznikov, and others developed ``Arithmetic Topology,'' a theory describing some surprising analogies between 3-dimensional topology and number theory, which can be summarized by saying that knots are like prime numbers. We extend their ... More

Reliability Conditions in Quadrature AlgorithmsMar 06 2003The detection of insufficiently resolved or ill-conditioned integrand structures is critical for the reliability assessment of the quadrature rule outputs. We discuss a method of analysis of the profile of the integrand at the quadrature knots which allows ... More

Skein theory for SU(n)-quantum invariantsJul 16 2004Oct 23 2005For any n>1 we define an isotopy invariant, <Gamma>_n, for a certain set of n-valent ribbon graphs Gamma in R^3, including all framed oriented links. We show that our bracket coincides with the Kauffman bracket for n=2 and with the Kuperberg's bracket ... More

An implicit wetting and drying approach for non-hydrostatic baroclinic flows in high aspect ratio domainsDec 22 2013Mar 24 2017A new approach to modelling free surface flows is developed that enables, for the first time, 3D consistent non-hydrostatic baroclinic physics that wets and dries in the large aspect ratio spatial domains that characterise geophysical systems. This is ... More

Character VarietiesFeb 16 2009Aug 25 2010We study properties of irreducible and completely reducible representations of finitely generated groups Gamma into reductive algebraic groups G in in the context of the geometric invariant theory of the G-action on Hom(Gamma,G) by conjugation. In particular, ... More

Skein modules at the 4th roots of unityNov 20 2000Aug 30 2001The Kauffman bracket skein modules, S(M,A), have been calculated for A=+1,-1, for all 3-manifolds M by relating them to the SL(2,C)-character varieties. We extend this description to the case when A is a 4-th root of 1 and M is either a surface x [0,1] ... More

A consistent approach to unstructured mesh generation for geophysical modelsMar 24 2017Geophysical model domains typically contain irregular, complex fractal-like boundaries and physical processes that act over a wide range of scales. Constructing geographically constrained boundary-conforming spatial discretizations of these domains with ... More

Character Varieties of Abelian GroupsJul 23 2012Oct 28 2013We prove that for every reductive group G with a maximal torus T and the Weyl group W there is a natural normalization map chi from T^N/W to an irreducible component of the G-character variety of Z^N. We prove that chi is an isomorphism for all classical ... More

SO(2n,C)-character varieties are not varieties of charactersMar 28 2015May 26 2015We prove that the coordinate rings of SO(2n,C)-character varieties are not generated by trace functions nor generalized trace functions for $n\geq 2$ and all groups Gamma of corank $\geq 2.$ Furthermore, we give examples of non-conjugate completely reducible ... More

Quantification pour les paires symetriques et diagrammes de KontsevichSep 25 2006Mar 25 2008In this article we use the expansion for biquantization described in Cattaneo-Felder [math.QA/0309180] for the case of symmetric spaces. We introduce a function of two variables $E(X,Y)$ for any symmetric pairs. This function has an expansion in terms ... More

Weak measurement of the Dirac distributionOct 04 2011Dec 22 2011Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. `strong') measurement of the complementary variable. We generalize this method to mixed states by considering ... More

Observing Dirac's classical phase space analog to the quantum stateSep 05 2013Nov 29 2013In 1945, Dirac attempted to develop a "formal probability" distribution to describe quantum operators in terms of two non-commuting variables, such as position x and momentum p [Rev. Mod. Phys. 17, 195 (1945)]. The resulting quasi-probability distribution ... More

What Do We Really Know About Cosmic Acceleration?Dec 23 2005Essentially all of our knowledge of the acceleration history of the Universe - including the acceleration itself - is predicated upon the validity of general relativity. Without recourse to this assumption, we use SNeIa to analyze the expansion history ... More