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Concurrent Spatial and Channel Squeeze & Excitation in Fully Convolutional NetworksMar 07 2018Jun 08 2018Fully convolutional neural networks (F-CNNs) have set the state-of-the-art in image segmentation for a plethora of applications. Architectural innovations within F-CNNs have mainly focused on improving spatial encoding or network connectivity to aid gradient ... More

Data Augmentation with Manifold Exploring Geometric Transformations for Increased Performance and RobustnessJan 14 2019In this paper we propose a novel augmentation technique that improves not only the performance of deep neural networks on clean test data, but also significantly increases their robustness to random transformations, both affine and projective. Inspired ... More

'Squeeze & Excite' Guided Few-Shot Segmentation of Volumetric ImagesFeb 04 2019Deep neural networks enable highly accurate image segmentation, but require large amounts of manually annotated data for supervised training. Few-shot learning aims to address this shortcoming by learning a new class from a few annotated support examples. ... More

`Project & Excite' Modules for Segmentation of Volumetric Medical ScansJun 11 2019Jun 12 2019Fully Convolutional Neural Networks (F-CNNs) achieve state-of-the-art performance for image segmentation in medical imaging. Recently, squeeze and excitation (SE) modules and variations thereof have been introduced to recalibrate feature maps channel- ... More

Learning Optimal Deep Projection of $^{18}$F-FDG PET Imaging for Early Differential Diagnosis of Parkinsonian SyndromesOct 11 2018Several diseases of parkinsonian syndromes present similar symptoms at early stage and no objective widely used diagnostic methods have been approved until now. Positron emission tomography (PET) with $^{18}$F-FDG was shown to be able to assess early ... More

DASA: Domain Adaptation in Stacked Autoencoders using Systematic DropoutMar 19 2016Domain adaptation deals with adapting behaviour of machine learning based systems trained using samples in source domain to their deployment in target domain where the statistics of samples in both domains are dissimilar. The task of directly training ... More

Recalibrating Fully Convolutional Networks with Spatial and Channel 'Squeeze & Excitation' BlocksAug 23 2018In a wide range of semantic segmentation tasks, fully convolutional neural networks (F-CNNs) have been successfully leveraged to achieve state-of-the-art performance. Architectural innovations of F-CNNs have mainly been on improving spatial encoding or ... More

Deep Residual HashingDec 16 2016Hashing aims at generating highly compact similarity preserving code words which are well suited for large-scale image retrieval tasks. Most existing hashing methods first encode the images as a vector of hand-crafted features followed by a separate binarization ... More

Inherent Brain Segmentation Quality Control from Fully ConvNet Monte Carlo SamplingApr 19 2018Jun 08 2018We introduce inherent measures for effective quality control of brain segmentation based on a Bayesian fully convolutional neural network, using model uncertainty. Monte Carlo samples from the posterior distribution are efficiently generated using dropout ... More

Deep Neural Ensemble for Retinal Vessel Segmentation in Fundus Images towards Achieving Label-free AngiographySep 19 2016Automated segmentation of retinal blood vessels in label-free fundus images entails a pivotal role in computed aided diagnosis of ophthalmic pathologies, viz., diabetic retinopathy, hypertensive disorders and cardiovascular diseases. The challenge remains ... More

Bayesian QuickNAT: Model Uncertainty in Deep Whole-Brain Segmentation for Structure-wise Quality ControlNov 24 2018We introduce Bayesian QuickNAT for the automated quality control of whole-brain segmentation on MRI T1 scans. Next to the Bayesian fully convolutional neural network, we also present inherent measures of segmentation uncertainty that allow for quality ... More

Structure of Physical Theory from Information SymmetryMay 23 2019We propose a profound consequence of symmetry towards the axiomatic derivation of Hilbert space quantum theory. Specifically, we show that the symmetry of information gain in minimal error state discrimination induces a non-trivial proviso on the state ... More

QuickNAT: A Fully Convolutional Network for Quick and Accurate Segmentation of NeuroanatomyJan 12 2018Nov 24 2018Whole brain segmentation from structural magnetic resonance imaging (MRI) is a prerequisite for most morphological analyses, but is computationally intense and can therefore delay the availability of image markers after scan acquisition. We introduce ... More

Evidence of a Sub-Saturn around EPIC~211945201May 09 2018We report here strong evidence for a sub-Saturn around EPIC~211945201 and confirm its planetary nature. EPIC~211945201b was found to be a planetary candidate from {\it K2} photometry in Campaigns 5 \& 16, transiting a bright star ($V_{\rm mag}=10.15$, ... More

SynNet: Structure-Preserving Fully Convolutional Networks for Medical Image SynthesisJun 29 2018Cross modal image syntheses is gaining significant interests for its ability to estimate target images of a different modality from a given set of source images,like estimating MR to MR, MR to CT, CT to PET etc, without the need for an actual acquisition.Though ... More

3DQ: Compact Quantized Neural Networks for Volumetric Whole Brain SegmentationApr 05 2019Apr 16 2019Model architectures have been dramatically increasing in size, improving performance at the cost of resource requirements. In this paper we propose 3DQ, a ternary quantization method, applied for the first time to 3D Fully Convolutional Neural Networks ... More

`Project & Excite' Modules for Segmentation of Volumetric Medical ScansJun 11 2019Fully Convolutional Neural Networks (F-CNNs) achieve state-of-the-art performance for image segmentation in medical imaging. Recently, squeeze and excitation (SE) modules and variations thereof have been introduced to recalibrate feature maps channel- ... More

3DQ: Compact Quantized Neural Networks for Volumetric Whole Brain SegmentationApr 05 2019Model architectures have been dramatically increasing in size, improving performance at the cost of resource requirements. In this paper we propose 3DQ, a ternary quantization method, applied for the first time to 3D Fully Convolutional Neural Networks ... More

InfiNet: Fully Convolutional Networks for Infant Brain MRI SegmentationOct 11 2018We present a novel, parameter-efficient and practical fully convolutional neural network architecture, termed InfiNet, aimed at voxel-wise semantic segmentation of infant brain MRI images at iso-intense stage, which can be easily extended for other segmentation ... More

Error Corrective Boosting for Learning Fully Convolutional Networks with Limited DataMay 02 2017Jul 02 2017Training deep fully convolutional neural networks (F-CNNs) for semantic image segmentation requires access to abundant labeled data. While large datasets of unlabeled image data are available in medical applications, access to manually labeled data is ... More

BrainTorrent: A Peer-to-Peer Environment for Decentralized Federated LearningMay 16 2019Access to sufficient annotated data is a common challenge in training deep neural networks on medical images. As annotating data is expensive and time-consuming, it is difficult for an individual medical center to reach large enough sample sizes to build ... More

Hard collinear gluon radiation and multiple scattering in a mediumDec 15 2009Jan 07 2010The energy loss of hard jets produced in the Deep-Inelastic scattering (DIS) off a large nucleus is considered in the collinear limit. In particular, the single gluon emission cross section due to multiple scattering in the medium is calculated. Calculations ... More

Estimating $\hat{q}$ in Quenched Lattice SU(2) Gauge TheoryMar 01 2013The propagation of a virtual quark in a thermal medium is considered. The non-perturbative jet transport coefficient $\hat{q}$ is estimated in quark less SU(2) lattice gauge theory. The light like correlator which defines $\hat{q}$, defined in the regime ... More

Height in Splitting of Relatively Hyperbolic GroupsAug 21 2015Oct 28 2015Given a finite graph of relatively hyperbolic groups with its fundamental group relatively hyperbolic and edge groups embed quasi-isometrically in vertex groups. We prove that a vertex group is relatively quasiconvex if and only if all the vertex groups ... More

An Optimal Test for the Additive Model with Discrete or Categorical PredictorsJun 17 2019In multivariate nonparametric regression the additive models are very useful when a suitable parametric model is difficult to find. The backfitting algorithm is a powerful tool to estimate the additive components. However, due to complexity of the estimators, ... More

Relative Hyperbolic Extensions of Groups and Cannon-Thurston MapsJan 07 2008Jul 22 2008Let $1\to (K,K_1)\to (G,N_G(K_1))\to(Q,Q_1)\to 1$ be a short exact sequence of pairs of finitely generated groups with $K$ strongly hyperbolic relative to proper subgroup $K_1$. Assuming that for all $g\in G$ there exists $k\in K$ such that $gK_1g^{-1}=kK_1k^{-1}$, ... More

Incorporating Space-Time Within Medium-Modified Jet Event GeneratorsJan 22 2013Feb 05 2013We outline a novel approach to develop an in-medium shower Monte-Carlo event generator based on the higher-twist formalism of jet modification. By undoing one of the light-cone integrals which sets the corresponding light-cone momentum to be equal in ... More

Calculating the Jet Transport Coefficient $\hat{q}$ in Lattice Gauge TheoryOct 11 2012The formalism of jet modification in the higher twist approach is modified to describe a hard parton propagating through a hot thermalized medium. The leading order contribution to the transverse momentum broadening of a high energy (near on-shell) quark ... More

ReLayNet: Retinal Layer and Fluid Segmentation of Macular Optical Coherence Tomography using Fully Convolutional NetworkApr 07 2017Jul 07 2017Optical coherence tomography (OCT) is used for non-invasive diagnosis of diabetic macular edema assessing the retinal layers. In this paper, we propose a new fully convolutional deep architecture, termed ReLayNet, for end-to-end segmentation of retinal ... More

On the quest for generalized Hamiltonian descriptions of $3D$-flows generated by curl of a vector potentialJun 11 2019We study Hamiltonian analysis of three-dimensional advection flow $\mathbf{\dot{x}}=\mathbf{v}({\bf x})$ of incompressible nature $\nabla \cdot {\bf v} ={\bf 0}$ assuming that dynamics is generated by the curl of a vector potential $\mathbf{v} = \nabla ... More

Quasi-Integrability in Supersymmetric Sine-Gordon ModelsJul 25 2016The deformed supersymmetric sine-Gordon model, obtained through known deformation of the corresponding potential, is found to be quasi-integrable, like its non-supersymmetric counterpart, which was observed earlier. The system expectedly posses finite ... More

Spanning trees and Khovanov homologyJul 20 2006Jan 31 2008The Jones polynomial can be expressed in terms of spanning trees of the graph obtained by checkerboard coloring a knot diagram. We show there exists a complex generated by these spanning trees whose homology is the reduced Khovanov homology. The spanning ... More

On mutation and Khovanov homologyJan 31 2008Aug 12 2008It is conjectured that the Khovanov homology of a knot is invariant under mutation. In this paper, we review the spanning tree complex for Khovanov homology, and reformulate this conjecture using a matroid obtained from the Tait graph (checkerboard graph) ... More

A survey on the Turaev genus of knotsJun 08 2014The Turaev genus of a knot is a topological measure of how far a given knot is from being alternating. Recent work by several authors has focused attention on this interesting invariant. We discuss how the Turaev genus is related to other knot invariants, ... More

Determinant density and biperiodic alternating linksApr 13 2016Jul 29 2016Let L be any infinite biperiodic alternating link. We show that for any sequence of finite links that Folner converges almost everywhere to L, their determinant densities converge to the Mahler measure of the 2-variable characteristic polynomial of the ... More

Unveiling Su Aurigae in the near Infrared: New high spatial resolution results using Adaptive OpticsFeb 16 2004We present here new results on circumstellar nebulosity around SU Aurigae, a T-Tauri star of about 2 solar mass and 5 Myrs old at 152 pc in the J, H and K bands using high resolution adaptive optics imaging (0$\farcs$30) with the Penn state IR Imaging ... More

Data Driven Prognosis: A multi-physics approach verified via balloon burst experimentOct 31 2014A multi-physics formulation for Data Driven Prognosis (DDP) is developed. Unlike traditional predictive strategies that require controlled off-line measurements or training for determination of constitutive parameters to derive the transitional statistics, ... More

Thermodynamics of black holes and the symmetric generalized uncertainty principleAug 18 2014Aug 23 2014In this paper, we have investigated the thermodynamics of Schwarzschild black holes using the symmetric generalized uncertainty principle which contains correction terms involving momentum and position uncertainty. We obtain the mass-temperature relation ... More

Vibrational properties of phonons in random binary alloys: An augmented space recursive technique in the k-representationJul 29 2003Dec 04 2003We present here an augmented space recursive technique in the k-representation which include diagonal, off-diagonal and the environmental disorder explicitly : an analytic, translationally invariant, multiple scattering theory for phonons in random binary ... More

Twisting quasi-alternating linksDec 16 2007Jan 13 2009Quasi-alternating links are homologically thin for both Khovanov homology and knot Floer homology. We show that every quasi-alternating link gives rise to an infinite family of quasi-alternating links obtained by replacing a crossing with an alternating ... More

On the tail of Jones polynomials of closed braids with a full twistApr 15 2010For a closed n-braid L with a full positive twist and with k negative crossings, 0\leq k \leq n, we determine the first n-k+1 terms of the Jones polynomial V_L(t). We show that V_L(t) satisfies a braid index constraint, which is a gap of length at least ... More

Image Similarity Using Sparse Representation and Compression DistanceJun 12 2012May 07 2013A new line of research uses compression methods to measure the similarity between signals. Two signals are considered similar if one can be compressed significantly when the information of the other is known. The existing compression-based similarity ... More

A general theory of wave interactions in layered flowsApr 03 2016Using kinematics, we propose a theory of non-modal interactions between the interfaces of a 2D, inviscid, multi-layered fluid system. Specifically, a $3$-interface problem with kinematic and geometric symmetry is explored. Repetitive, extremely short ... More

Stochastic Variational formulas for solutions to linear diffusion equationsDec 01 2009This paper is concerned with solutions to a one dimensional linear diffusion equation and their relation to some problems in stochastic control theory. A stochastic variational formula is obtained for the logarithm of the solution to the diffusion equation, ... More

Towards Open World RecognitionDec 18 2014With the of advent rich classification models and high computational power visual recognition systems have found many operational applications. Recognition in the real world poses multiple challenges that are not apparent in controlled lab environments. ... More

Augmented space recursion for partially disordered systemsJul 12 2001Off-stoichiometric alloys exhibit partial disorder, in the sense that only some of the sublattices of the stoichiometric ordered alloy become disordered. This paper puts forward a generalization of the augmented space recursion (ASR) (introduced earlier ... More

Teleportation and Multipartite Quantum State Sharing using a Seven Qubit Genuinely Entangled StateDec 14 2014Jan 08 2015We have tried to gauge the utility of a recently introduced seven-qubit state by Xin-Wei Zha et al for quantum teleportation and quantum state sharing. It is shown that this state can be used for the teleportation of an arbitrary single, double and triple ... More

Effect of average number of reference speckles on the SNR of object retrieved using off-axis holographic techniqueSep 04 2017The propagation of coherent light through a random scattering medium generates speckle pattern. Although the speckle is random in nature, the object information is scrambled into it. The scrambled object information can be retrieved using off-axis holographic ... More

Growth and engineering of perovskite SrIrO3 thin filmsAug 01 2016Feb 15 20175d transition-metal-based oxides display emergent phenomena due to the competition between the relevant energy scales of the correlation, bandwidth, and most importantly, the strong spin-orbit coupling (SOC). Starting from the prediction of novel oxide ... More

Sharma-Mittal Quantum DiscordNov 22 2018May 15 2019We demonstrate a generalization of quantum discord using a generalized definition of von-Neumann entropy, which is Sharma-Mittal entropy; and the new definition of discord is called Sharma-Mittal quantum discord. Its analytic expressions are worked out ... More

Realizable receivers for discriminating arbitrary coherent-state waveforms and multi-copy quantum states near the quantum limitDec 10 2012Feb 13 2013Coherent states of light, and methods for distinguishing between them, are central to all applications of laser light. We obtain the ultimate quantum limit on the error probability exponent for discriminating among any M multimode coherent-state waveforms ... More

How to make a cylinder roll uphillOct 16 2015Slithering, crawling, slipping, gliding are various modes of limbless locomotion that have been mimicked for micro-manipulation of soft, slender and sessile objects. A lesser known mode is rolling which involves periodic, asymmetric and lateral muscular ... More

Thermal states minimize the output entropy of single-mode phase-insensitive Gaussian channels with an input entropy constraintJul 18 2016Shannon's entropy power inequality (EPI), $e^{2h(X+Y)} \ge e^{2h(X)} + e^{2h(Y)}$ for independent continuous random variables $X$ and $Y$, with $h(X)$ the differential entropy of $X$, has found many applications in Gaussian channel coding theorems. Equality ... More

Study Of A Planar Lattice Model With $P_4$ InteractionAug 18 1997A planar square lattice model with 3-d spins interacting with nearest neighbours through a potential -$\epsilon P_4 (cos \theta_{ij})$ is studied by Monte Carlo technique. Lattice sizes from 10$\times$10 to 30$\times$30 are considered for calculating ... More

Quasi-Exact Solvability and Deformations of Sl(2) AlgebraApr 08 2013Algebraic structure of a class of differential equations including Heun is shown to be related with the deformations of sl(2) algebra. These include both quadratic and cubic ones. The finite dimensional representation of cubic algebra is explicitly shown ... More

Stability against $α$ decay of some recently observed superheavy elementsJan 06 2011The probability of $\alpha$ particle emission for some recently observed superheavy nuclei (SHN) are investigated. The $\alpha$-decay half lives of SHN are calculated in a quantum tunneling model with density dependent M3Y (DDM3Y) effective nuclear interaction ... More

Electric Charge Separation in Strong Transient Magnetic FieldsMar 11 2010Jun 10 2010We discuss various mechanisms for the creation of an asymmetric charge fluctuation with respect to the reaction plane among hadrons emitted in relativistic heavy-ion collisions. We show that such mechanisms exist in both, the hadronic gas and the partonic ... More

DNA Elasticity : Topology of Self-AvoidanceApr 08 2005Apr 25 2006We present a theoretical treatment of DNA stretching and twisting experiments, in which we discuss global topological subtleties of self avoiding ribbons and provide an underlying justification for the worm like rod chain (WLRC) model proposed by Bouchiat ... More

Deviations from universality in the fluctuation behavior of a heterogeneous complex system reveal intrinsic properties of components: The case of the international currency marketJun 20 2016Jun 21 2018Identifying behavior that is relatively invariant under different conditions is a challenging task in far-from-equilibrium complex systems. As an example of how the existence of a semi-invariant signature can be masked by the heterogeneity in the properties ... More

Generalized uncertainty principle and black hole thermodynamicsJul 26 2013Jan 08 2014We study the Schwarzschild and Reissner-Nordstr\"{o}m black hole thermodynamics using the simplest form of the generalized uncertainty principle (GUP) proposed in the literature. The expressions for the mass-temperature relation, heat capacity and entropy ... More

Exceptional Points in an Specialty Microcavity: Interplay between State-Conversion and Cavity Control ParametersMar 14 2018Exploiting scattering-matrix in a gain-loss assisted optical-microcavity, interplay between asymmetric-state-conversion and cavity-control parameters around exceptional points is analyzed; where occupying a least area by coupled states during switching, ... More

A fractional calculus approach to Rosenzweig-MacArthur predator-prey model and its solutionJun 04 2019In this paper we present analytical solution of a fractional order predator-prey model, where prey grows logistically and predation occurs following type II response function, by homotopy perturbation method. Numerical solutions are presented to illustrate ... More

Black hole immunity theorem and dark matterJun 30 2004Oct 23 2005We prove that the primordial black holes in the early universe did not decay until the gravity decoupled from the other interactions. Rabinowitz' two objections to the formation of Holeums are shown to be inapplicable. We show that primordial black holes ... More

Analysis of a fractional order eco-epidemiological model with prey infection and type II functional responseJun 04 2019In this paper, we introduce fractional order into an ecoepidemiological model, where predator consumes disproportionately large number of infected preys following type II response function. We prove different mathematical results like existence, uniqueness, ... More

Cosmological magnetic fieldsJul 24 2000Magnetic fields are observed not only in stars, but in galaxies, clusters, and even high redshift Lyman-alpha systems. In principle, these fields could play an important role in structure formation and also affect the anisotropies in the cosmic microwave ... More

PHENIX Measurements of Higher-order Flow Harmonics in Au+Au collisions at Root_s = 200 GeVAug 02 2011Flow coefficients $v_n$ for $n$ = 2, 3, 4, characterizing the anisotropic collective flow in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV, are presented. They indicate the expected growth of viscous damping for sound propagation in the quark gluon plasma ... More

Information-Theoretic Methods for Planning and Learning in Partially Observable Markov Decision ProcessesSep 24 2016Bounded agents are limited by intrinsic constraints on their ability to process information that is available in their sensors and memory and choose actions and memory updates. In this dissertation, we model these constraints as information-rate constraints ... More

Lorentz gauge and Green's formula in classical electrodynamicsJul 27 1996We dicuss the resolution of initial value problems of electrodynamics in the Lorentz gauge.

The Pentagonal InequalityMay 30 2017Given a positive linear combination of five (respectively seven) cosines, where the angles are positive and sum to pi, the aim of this article is to express the sharp bound of the combination as a Positive Real Fraction in the coefficients (hence cosine-free). ... More

The Rational Distance Problem for Equilateral TrianglesMar 20 2017Mar 24 2017Let (P) denote the problem of existence of a point in the plane of a given triangle T, that is at rational distance from all the vertices of T. In this article, we provide a complete solution to (P) for all equilateral triangles.

Generalized Weinstein tubular neighbourhood & Space of Lagrangian submersionsMay 05 2009We present a generalized Weinstein Tubular Neighbourhood theorem for Lagrangian subbundles of Symplectic fibrations. This is then used to study the space of Lagrangian fibrations of symplectic manifolds.

On Integrable Systems & Rigidity for PDEs with SymmetryDec 03 2017This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We motivate the definition ... More

Ultra High Energy Cosmic Rays from decays of Holeums in Galactic HalosJun 03 2008Stable, quantized gravitational bound states of primordial black holes called Holeums could have been produced in the early universe and could be a component of the Super Heavy Dark Matter (SHDM) present in galactic halos. We show that Holeums of masses ... More

Holeum,enigmas of cosmology and gravitational wavesSep 08 2003Jun 24 2004The principle of nuclear democracy is invoked to prove the formation of stable quantized gravitational bound states of primordial black holes called Holeums. The latter come in four varieties: ordinary Holeums H, Black Holeums BH, Hyper Holeums HH and ... More

Dark matter and stable bound states of primordial black holesAug 17 2003We present three reasons for the formation of gravitational bound states of primordial black holes,called holeums,in the early universe.Using Newtonian gravity and nonrelativistic quantum mechanics we find a purely quantum mechanical mass-dependant exclusion ... More

A generalized Swanson Hamiltonian in a second-derivative pseudo-supersymmetric frameworkJan 16 2015We study a generalized scheme of Swanson Hamiltonian from a second-derivative pseudosupersymmetric approach. We discuss plausible choices of the underlying quasi-Hamiltonian and consider the viability of applications to systems like the isotonic oscillator ... More

Brane-world cosmological perturbationsFeb 20 2004Brane-world models provide a phenomenology that allows us to explore the cosmological consequences of some M theory ideas, and at the same time to use precision cosmology as a test of these ideas. In order to achieve this, we need to understand how brane-world ... More

Causal Thermodynamics in RelativitySep 18 1996I review the causal relativistic thermodynamics developed by Israel and Stewart, and discuss some applications in cosmology and astrophysics. The lectures begin with an overview of relativistic fluid dynamics (in a covariant formalism) and equilibrium ... More

Dark Energy from Brane-world GravityFeb 18 2006Recent observations provide strong evidence that the universe is accelerating. This confronts theory with a severe challenge. Explanations of the acceleration within the framework of general relativity are plagued by difficulties. General relativistic ... More

Geometry and dynamics of the brane-worldJan 16 2001Apr 17 2001Recent developments in string theory have led to 5-dimensional warped spacetime models in which standard-model fields are confined to a 3-brane (the observed universe), while gravity can propagate in the fifth dimension. Gravity is localized near the ... More

Cosmological dynamics on the braneApr 24 2000Aug 08 2000In Randall-Sundrum-type brane-world cosmologies, the dynamical equations on the three-brane differ from the general relativity equations by terms that carry the effects of imbedding and of the free gravitational field in the five-dimensional bulk. We ... More

Nonlinear Effects in the Cosmic Microwave BackgroundJul 21 1999Major advances in the observation and theory of cosmic microwave background anisotropies have opened up a new era in cosmology. This has encouraged the hope that the fundamental parameters of cosmology will be determined to high accuracy in the near future. ... More

Classification of massive and gapless phases in bilayer grapheneNov 08 2012Sep 16 2013We here classify of all the fully gapped \emph{massive} and \emph{gapless} phases in bilayer graphene. The effective low energy theory in bilayer graphene is constructed, and various discrete and continuous symmetries of the non-interacting system is ... More

On Jensen-type inequalities for unbounded radial scattering solutions of a loglog energy-supercritical Schrodinger equationSep 05 2017Sep 20 2017Given $n \in \{ 3,4 \} (resp. n=5) and k > 1$ (resp. $\frac{4}{3} > k > 1$), we prove scattering of the radial $\tilde{H}^{k}:= \dot{H}^{k}(\mathbb{R}^{n}) \cap \dot{H}^{1}(\mathbb{R}^{n})$ solutions of the loglog energy-supercritical Schrodinger equation ... More

Scattering above energy norm of a focusing size-dependent log energy-supercritical Schrodinger equation with radial data below ground stateJan 10 2017Sep 20 2017Given $n \in \{ 3,4,5 \}$ and $k > 1$ (resp. $\frac{4}{3} > k > 1$) if $n \in \{ 3,4 \}$ (resp. n=5), we prove scattering of the radial $\tilde{H}^{k}:= \dot{H}^{k}(\mathbb{R}^{n}) \cap \dot{H}^{1}(\mathbb{R}^{n})$ solutions of a focusing size-dependent ... More

Effect of dark matter halo substructures on galaxy rotation curvesSep 10 2010The effect of halo substructures on galaxy rotation curves is investigated in this paper using a simple model of dark matter clustering. A dark matter halo density profile is developed based only on the scale free nature of clustering that leads to a ... More

Dynamical Systems Analysis of Various Dark Energy ModelsNov 25 2015In this thesis, we used dynamical systems analysis to find the qualitative behaviour of some dark energy models. Specifically, dynamical systems analysis of quintessence scalar field models, chameleon scalar field models and holographic models of dark ... More

Intersections of Lagrangian submanifolds and the Mel'nikov 1-formMay 25 2005Mar 16 2006We make explicit the geometric content of Mel'nikov's method for detecting heteroclinic points between transversally hyperbolic periodic orbits. After developing the general theory of intersections for pairs of family of Lagrangian submanifolds constrained ... More

A semi-classical K.A.M. theoremMar 25 2004May 24 2005We consider a semi-classical completely integrable system defined by a $\hbar$-pseudodifferential operator $\hat{H}$ on the torus $\mathbb{T}^{d}$. In order to study perturbed operators of the form $\hat{H}+\hbar^{\kappa}\hat{K}$, where $\hat{K}$ is an ... More

Decomposition of symplectic vector fields with respect to a fibration in lagrangian toriMar 24 2004Given a fibration of a symplectic manifold by lagrangian tori, we show that each symplectic vector field splits into two parts : the first is Hamiltonian and the second is symplectic and preserves the fibration. We then show an application of this result ... More

Band geometry of fractional topological insulatorsAug 09 2012Recent numerical simulations of flat band models with interactions which show clear evidence of fractionalized topological phases in the absence of a net magnetic field have generated a great deal of interest. We provide an explanation for these observations ... More

Topological Majorana and Dirac zero modes in superconducting vortex coresJan 14 2010We provide an argument based on flux insertion to show that certain superconductors with a non-trivial topological invariant have protected zero modes in their vortex cores. This argument has the flavor of a two dimensional index theorem and applies to ... More

On the $Z_2$ classification of Quantum Spin Hall ModelsApr 07 2006Sep 18 2006We propose an alternative formulation of the $Z_2$ topological index for quantum spin Hall systems and band insulators when time reversal invariance is not broken. The index is expressed in terms of the Chern numbers of the bands of the model, and a connection ... More

Measuring the deviation from maximal mixing of atmospheric muon neutrinos at INOJan 02 2006Neutrino factfile and $D \equiv 1/2 - sin^2 \theta_{23}$ $\nu_mu$, $\bar\nu_mu$ survival probabilities and binned up-down asymmetries Error analysis and sensitivity to $D$

A measure of transcendence for singular points on conicsSep 11 2018A singular point on a plane conic defined over $\mathbb{Q}$ is a transcendental point of the curve which admits very good rational approximations, uniformly in terms of the height. Extremal numbers and Sturmian continued fractions are abscissa of such ... More

Markoff-Lagrange spectrum and extremal numbersJun 02 2009Let gamma denote the golden ratio. H. Davenport and W. M.Schmidt showed in 1969 that, for each non-quadratic irrational real number xi, there exists a constant c>0 with the property that, for arbitrarily large values of X, the inequalities |x_0| \le X, ... More

Small value estimates for the multiplicative groupJan 04 2013We generalize Gel'fond's transcendence criterion to the context of a sequence of polynomials whose first derivatives take small values on large subsets of a fixed subgroup of the multiplicative group C* of the field of complex numbers.

Bounds for codes and designs in complex subspacesJun 13 2008We introduce the concepts of complex Grassmannian codes and designs. Let G(m,n) denote the set of m-dimensional subspaces of C^n: then a code is a finite subset of G(m,n) in which few distances occur, while a design is a finite subset of G(m,n) that polynomially ... More

Maharam extension and stationary stable processesJan 05 2010May 28 2012We give a second look at stationary stable processes by interpreting the self-similar property at the level of the L\'evy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences.

Brane-world gravityDec 10 2003Apr 29 2004The observable universe could be a 1+3-surface (the "brane") embedded in a 1+3+d-dimensional spacetime (the "bulk"), with standard-model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the d extra spatial ... More