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Optimal Surface Segmentation with Convex Priors in Irregularly Sampled SpaceNov 09 2016Feb 14 2019Optimal surface segmentation is a state-of-the-art method used for segmentation of multiple globally optimal surfaces in volumetric datasets. The method is widely used in numerous medical image segmentation applications. However, nodes in the graph based ... More

Gravitational-wave flux for a particle orbiting a Kerr black hole to 20th post-Newtonian order: a numerical approachMar 11 2014May 24 2014In this article we present the post-Newtonian (pN) coefficients of the energy flux (and angular momentum flux) at infinity and event horizon for a particle in circular, equatorial orbits about a Kerr black hole (of mass $M$ and spin-parameter $a$) up ... More

iResum: a new paradigm for resumming gravitational wave amplitudesJun 01 2016Sep 28 2016We introduce a new, resummed, analytical form of the post-Newtonian (PN), factorized, multipolar amplitude corrections $f_{\ell m}$ of the effective-one-body (EOB) gravitational waveform of spinning, nonprecessing, circularized, coalescing black hole ... More

Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian orderMar 09 2015Apr 02 2015Using black hole perturbation theory and arbitrary-precision computer algebra, we obtain the post-Newtonian (pN) expansions of the linear-in-mass-ratio corrections to the spin-precession angle and tidal invariants for a particle in circular orbit around ... More

Self-force from reconstructed metric perturbations: numerical implementation in Schwarzschild spacetimeOct 11 2014Aug 07 2015We present a first numerical implementation of a new scheme by Pound et al. that enables the calculation of the gravitational self-force in Kerr spacetime from a reconstructed metric-perturbation in a radiation gauge. The numerical task of the metric ... More

Time in Fundamental PhysicsDec 21 2013The first three sections of this article contain a broad brush summary of the profound changes in the notion of time in fundamental physics that were brought about by three revolutions: the foundations of mechanics distilled by Newton in his Principia, ... More

Vote Aggregation as a Clustering ProblemNov 16 2016An important way to make large training sets is to gather noisy labels from crowds of non experts. We propose a method to aggregate noisy labels collected from a crowd of workers or annotators. Eliciting labels is important in tasks such as judging web ... More

Approximating Wisdom of Crowds using K-RBMsNov 16 2016Nov 17 2016An important way to make large training sets is to gather noisy labels from crowds of non experts. We propose a method to aggregate noisy labels collected from a crowd of workers or annotators. Eliciting labels is important in tasks such as judging web ... More

Metric perturbations produced by eccentric equatorial orbits around a Kerr black holeJun 15 2015Aug 17 2016We present the first numerical calculation of the (local) metric perturbation produced by a small compact object moving on an eccentric equatorial geodesic around a Kerr black hole, accurate to first order in the mass ratio. The procedure starts by first ... More

Dynamical Black Holes: Approach to the Final StateJun 24 2013Sep 27 2013Since black holes can be formed through widely varying processes, the horizon structure is highly complicated in the dynamical phase. Nonetheless, as numerical simulations show, the final state appears to be universal, well described by the Kerr geometry. ... More

Observables of a test-mass along an inclined orbit in a post-Newtonian approximated Kerr spacetime to leading-order-quadratic-in-spinMar 27 2013Jun 17 2013The orbital motion is derived for a non-spinning test-mass in the relativistic, gravitational field of a rotationally deformed body not restricted to the equatorial plane or spherical orbit. The gravitational field of the central body is represented by ... More

Raising and Lowering operators of spin-weighted spheroidal harmonicsMar 09 2015Jun 03 2016In this paper we generalize the spin-raising and lowering operators of spin-weighted spherical harmonics to linear-in-$\gamma$ spin-weighted spheroidal harmonics where $\gamma$ is an additional parameter present in the second order ordinary differential ... More

Simultaneous Multiple Surface Segmentation Using Deep LearningMay 19 2017The task of automatically segmenting 3-D surfaces representing boundaries of objects is important for quantitative analysis of volumetric images, and plays a vital role in biomedical image analysis. Recently, graph-based methods with a global optimization ... More

Optimal Multi-Object Segmentation with Novel Gradient Vector Flow Based Shape PriorsMay 22 2017Shape priors have been widely utilized in medical image segmentation to improve segmentation accuracy and robustness. A major way to encode such a prior shape model is to use a mesh representation, which is prone to causing self-intersection or mesh folding. ... More

Loop quantum cosmology and slow roll inflationDec 21 2009Oct 02 2010In loop quantum cosmology (LQC) the big bang is replaced by a quantum bounce which is followed by a robust phase of super-inflation. Rather than growing unboundedly in the past, the Hubble parameter \emph{vanishes} at the bounce and attains a \emph{finite ... More

Action and Hamiltonians in higher dimensional general relativity: First order frameworkAug 14 2008We consider $d>4$-dimensional space-times which are asymptotically flat at spatial infinity and show that, in the first order framework, the action principle is well-defined \emph{without the need of infinite counter terms.} It naturally leads to a covariant ... More

Gauss Linking Number and Electro-magnetic Uncertainty PrincipleJan 24 1997It is shown that there is a precise sense in which the Heisenberg uncertainty between fluxes of electric and magnetic fields through finite surfaces is given by (one-half $\hbar$ times) the Gauss linking number of the loops that bound these surfaces. ... More

Photon inner product and the Gauss linking numberAug 06 1996It is shown that there is an interesting interplay between self-duality, loop representation and knots invariants in the quantum theory of Maxwell fields in Minkowski space-time. Specifically, in the loop representation based on self-dual connections, ... More

Rate Constrained Random Access over a Fading ChannelAug 22 2009In this paper, we consider uplink transmissions involving multiple users communicating with a base station over a fading channel. We assume that the base station does not coordinate the transmissions of the users and hence the users employ random access ... More

Asymptotic Capacity of Wireless Ad Hoc Networks with Realistic Links under a Honey Comb TopologyNov 10 2007Oct 05 2010We consider the effects of Rayleigh fading and lognormal shadowing in the physical interference model for all the successful transmissions of traffic across the network. New bounds are derived for the capacity of a given random ad hoc wireless network ... More

Quantum Gravity in the Sky: Interplay between fundamental theory and observationsAug 15 2016Nov 12 2016Observational missions have provided us with a reliable model of the evolution of the universe starting from the last scattering surface all the way to future infinity. Furthermore given a specific model of inflation, using quantum field theory on curved ... More

Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculationDec 06 2013Mar 11 2014We present a novel analytic extraction of high-order post-Newtonian (pN) parameters that govern quasi-circular binary systems. Coefficients in the pN expansion of the energy of a binary system can be found from corresponding coefficients in an extreme-mass-ratio ... More

A Truth Serum for Large-Scale EvaluationsJul 25 2015Feb 16 2018A major challenge in obtaining large-scale evaluations, e.g., product or service reviews on online platforms, labeling images, grading in online courses, etc., is that of eliciting honest responses from agents in the absence of verifiability. We propose ... More

Experimental mathematics meets gravitational self-forceMar 09 2015Jul 27 2015It is now possible to compute linear in mass-ratio terms in the post-Newtonian (PN) expansion for compact binaries to very high orders using black hole perturbation theory applied to various invariants. For instance, a computation of the redshift invariant ... More

Quantum Gravity in the Sky: Interplay between fundamental theory and observationsAug 15 2016Observational missions have provided us with a reliable model of the evolution of the universe starting from the last scattering surface all the way to future infinity. Furthermore given a specific model of inflation, using quantum field theory on curved ... More

Generalized effective description of loop quantum cosmologySep 29 2015Oct 15 2015The effective description of loop quantum cosmology (LQC) has proved to be a convenient platform to study phenomenological implications of the quantum bounce that resolves the classical big-bang singularity. Originally, this description was derived using ... More

Quantum Theory of Gravity I: Area OperatorsFeb 23 1996Aug 23 1996A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces are introduced ... More

Completeness of Wilson loop functionals on the moduli space of $SL(2,C)$ and $SU(1,1)$-connectionsApr 30 1993The structure of the moduli spaces $\M := \A/\G$ of (all, not just flat) $SL(2,C)$ and $SU(1,1)$ connections on a n-manifold is analysed. For any topology on the corresponding spaces $\A$ of all connections which satisfies the weak requirement of compatibility ... More

Optimal Multiple Surface Segmentation with Convex Priors in Irregularly Sampled SpaceNov 09 2016Optimal surface segmentation is widely used in numerous medical image segmentation applications. However, nodes in the graph based optimal surface segmentation method typically encode uniformly distributed orthogonal voxels of the volume. Thus the segmentation ... More

Truth Serums for Massively Crowdsourced Evaluation TasksJul 25 2015Nov 08 2016A major challenge in crowdsourcing evaluation tasks like labeling objects, grading assignments in online courses, etc., is that of eliciting truthful responses from agents in the absence of verifiability. In this paper, we propose new reward mechanisms ... More

Stabilizing Adversarial Nets With Prediction MethodsMay 20 2017Feb 08 2018Adversarial neural networks solve many important problems in data science, but are notoriously difficult to train. These difficulties come from the fact that optimal weights for adversarial nets correspond to saddle points, and not minimizers, of the ... More

Truth Serums for Massively Crowdsourced Evaluation TasksJul 25 2015Sep 06 2016A major challenge in crowdsourcing evaluation tasks like labeling objects, grading assignments in online courses, etc., is that of eliciting truthful responses from agents in the absence of verifiability. In this paper, we propose new reward mechanisms ... More

EMRI corrections to the angular velocity and redshift factor of a mass in circular orbit about a Kerr black holeJul 24 2012Sep 26 2012This is the first of two papers on computing the self-force in a radiation gauge for a particle moving in circular, equatorial orbit about a Kerr black hole. In the EMRI (extreme-mass-ratio inspiral) framework, with mode-sum renormalization, we compute ... More

3-D Surface Segmentation Meets Conditional Random FieldsJun 11 2019Automated surface segmentation is important and challenging in many medical image analysis applications. Recent deep learning based methods have been developed for various object segmentation tasks. Most of them are a classification based approach, e.g. ... More

DAiSEE: Towards User Engagement Recognition in the WildSep 07 2016Nov 16 2016Recognizing user engagement plays an important role in several contemporary vision applications including advertising, healthcare, and e-learning. However, the lack of any publicly available dataset to address this problem severely limits the development ... More

Asymptotically Anti-de Sitter Space-times: Conserved QuantitiesNov 29 1999Asymptotically anti-de Sitter space-times are considered in a general dimension $d\ge 4$. As one might expect, the boundary conditions at infinity ensure that the asymptotic symmetry group is the anti-de Sitter group (although there is an interesting ... More

On the ambiguity in the notion of transverse traceless modes of gravitational wavesJul 31 2017Sep 21 2017Somewhat surprisingly, in many of the widely used monographs and review articles the term Transverse-Traceless modes of linearized gravitational waves is used to denote two entirely different notions. These treatments generally begin with a decomposition ... More

A Loop Representation for the Quantum Maxwell FieldFeb 19 1992Quantization of the free Maxwell field in Minkowski space is carried out using a loop representation and shown to be equivalent to the standard Fock quantization. Because it is based on coherent state methods, this framework may be useful in quantum optics. ... More

Background Independent Quantum Gravity: A Status ReportApr 05 2004Sep 03 2004The goal of this article is to present an introduction to loop quantum gravity -a background independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation ... More

Quantum Theory of Geometry II: Volume operatorsNov 10 1997A functional calculus on the space of (generalized) connections was recently introduced without any reference to a background metric. It is used to continue the exploration of the quantum Riemannian geometry. Operators corresponding to volume of three-dimensional ... More

Representation Theory of Analytic Holonomy C* AlgebrasNov 07 1993Nov 07 1993Integral calculus on the space of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well--suited for quantization of diffeomorphism invariant theories of connections. The ... More

Essentially Critically Compressible ModulesMar 14 2012The main purpose of this paper is to introduce the concept of essentially critically compressible modules. We call an R-module M essentially critically compressible module if it is essentially compressible and additionally it cannot be imbedded in any ... More

Nanoplasmonic Tweezers Visualize Protein p53 Suppressing Unzipping of Single DNA-HairpinsMar 16 2014Here we report on the use of double-nanohole (DNH) optical tweezers as a label-free and free-solution single-molecule probe for protein-DNA interactions. Using this approach, we demonstrate the unzipping of individual 10 base pair DNA-hairpins, and quantify ... More

Initial conditions for cosmological perturbationsOct 28 2016Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms ... More

Positive cosmological constant in loop quantum cosmologyDec 01 2011The k=0 Friedmann Lemaitre Robertson Walker model with a positive cosmological constant and a massless scalar field is analyzed in detail. If one uses the scalar field as relational time, new features arise already in the Hamiltonian framework of classical ... More

Laws Governing Isolated Horizons: Inclusion of Dilaton CouplingsOct 20 1999Dec 24 1999Mechanics of non-rotating black holes was recently generalized by replacing the static event horizons used in standard treatments with `isolated horizons.' This framework is extended to incorporate dilaton couplings. Since there can be gravitational and ... More

Symmetry reduced Einstein gravity and generalized sigma and chiral modelsDec 11 1997Feb 12 1998Certain features associated with the symmetry reduction of the vacuum Einstein equations by two commuting, space-like Killing vector fields are studied. In particular, the discussion encompasses the equations for the Gowdy $T^3$ cosmology and cylindrical ... More

Projective Techniques and Functional IntegrationNov 17 1994A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out integration over the ... More

A Security Analysis of Browser ExtensionsMar 13 2014Browser Extensions (often called plugins or addons) are small pieces of code that let developers add additional functionality to the browser. However, with extensions comes a security price: the user must trust the developer. We look at ways in which ... More

Local entropy of a nonequilibrium fermion systemNov 22 2016The local entropy of a nonequilibrium system of independent fermions is investigated, and analyzed in the context of the laws of thermodynamics. It is shown that the local temperature and chemical potential can only be expressed in terms of derivatives ... More

Computationally Tractable Algorithms for Finding a Subset of Non-defective Items from a Large PopulationFeb 14 2015Feb 28 2016In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the "complete defective set" given the outcomes of different group tests. In contrast, the main goal of a "non-defective ... More

Construction of cyclic DNA codes over the Ring $\Z_4[u]/\langle u^2-1 \rangle $ Based on the deletion distanceMar 13 2016In this paper, we develop the theory for constructing DNA cyclic codes of odd length over $R=\Z_4[u]/\langle u^2-1 \rangle$ based on the deletion distance. Firstly, we relate DNA pairs with a special 16 elements of ring $R$. Cyclic codes of odd length ... More

Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation GaugeSep 24 2010Mar 07 2011This is the second of two companion papers on computing the self-force in a radiation gauge; more precisely, the method uses a radiation gauge for the radiative part of the metric perturbation, together with an arbitrarily chosen gauge for the parts of ... More

Self-force as a cosmic censor in the Kerr overspinning problemAug 17 2015It is known that a near-extremal Kerr black hole can be spun up beyond its extremal limit by capturing a test particle. Here we show that overspinning is always averted once back-reaction from the particle's own gravity is properly taken into account. ... More

Gravitational Self-force in a Radiation GaugeApr 13 2010Oct 22 2014In this, the first of two companion papers, we present a method for finding the gravitational self-force in a modified radiation gauge for a particle moving on a geodesic in a Schwarzschild or Kerr spacetime. An extension of an earlier result by Wald ... More

Biconvex Relaxation for Semidefinite Programming in Computer VisionMay 31 2016Aug 08 2016Semidefinite programming is an indispensable tool in computer vision, but general-purpose solvers for semidefinite programs are often too slow and memory intensive for large-scale problems. We propose a general framework to approximately solve large-scale ... More

When is it Better to Compare than to Score?Jun 25 2014When eliciting judgements from humans for an unknown quantity, one often has the choice of making direct-scoring (cardinal) or comparative (ordinal) measurements. In this paper we study the relative merits of either choice, providing empirical and theoretical ... More

Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology DependenceMay 06 2015Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a latent vector ... More

Gauge-invariant perturbations of Schwarzschild spacetimeNov 24 2016We study perturbations of Schwarzschild spacetime in a coordinate-free, covariant form. The GHP formulation, having the advantage of not only being covariant but also tetrad-rotation invariant, is used to write down the previously known odd- and even-parity ... More

Approximative $K$-Atomic Decompositions and frames in Banach SpacesJan 17 2019[L. Gavruta, Frames for Operators, Appl. comput. Harmon. Anal. 32(2012), 139-144] introduced a special kind of frames, named $K$-frames, where $K$ is an operator, in Hilbert spaces, is significant in frame theory and has many applications. In this paper, ... More

Expansive Automorphisms on Locally Compact GroupsDec 04 2018We show that any connected locally compact group which admits an expansive automorphism is nilpotent. We also show that for any locally compact group $G$, $\alpha\in {\rm Aut}(G)$ is expansive if and only if for any $\alpha$-invariant closed subgroup ... More

Kinematics and Dynamics of Young Star Clusters with TMTSep 26 2018Oct 12 2018Star clusters are evolving n-body systems. We discuss the early dynamics of star clusters, the process of primordial mass segregation and clustering observed in certain young clusters. We discuss how the dynamics coupled with stellar evolution of a cluster ... More

Smooth phase transition of energy equilibration in a springy Sinai billiardSep 17 2018Statistical equilibration of energies in a slow-fast system is a fundamental open problem in physics. In a recent paper, it was shown that the equilibration rate in a springy billiard can remain strictly positive in the limit of vanishing mass ratio (of ... More

On 3-dimensional asymptotically harmonic manifolds with minimal horospheresAug 22 2011May 21 2013Let $(M,g)$ be a complete, simply connected Riemannian manifold of dimension 3 without conjugate points. We show that $M$ is a flat manifold, provided $M$ is asymptotically harmonic of constant $h = 0$.

Hölder continuity of bounded, weak solutions of a variational system in the critical caseSep 14 2016Let $\Omega\subset\mathbb{R}^{2}$ be a bounded, Lipschitz domain. We consider bounded, weak solutions ($u\in W^{1, 2}\cap L^{\infty}(\Omega;\mathbb{R}^N)$) of the vector-valued, Euler-Lagrange system: \text{div } \big( A(x, u)Du\big)=g(x, u, Du)\quad\text{in ... More

Study of hyperon-hyperon correlations and search for $H$-dibaryon using STAR detector at RHICDec 02 2011High yield of strange particle production per central collision in nucleus-nucleus collisions at RHIC and high statistics data set from STAR experiment allow us to measure \Lambda\Lambda correlations. The \Lambda\Lambda correlation measurement is also ... More

Orbits of Distal Actions on Locally Compact GroupsOct 27 2010We discuss properties of orbits of (semi)group actions on locally compact groups G. In particular, we show that if a compactly generated locally compact abelian group acts distally on G then the closure of each of its orbits is a minimal closed invariant ... More

Standardization in the UV with Astrosat and its issues related to star cluster studiesOct 07 2018The Ultra-Violet Imaging Telescope (UVIT) is one of the payloads in Astrosat, the first Indian Space Observatory. The UVIT instrument has two 375 mm telescopes: one for the far-ultraviolet (FUV) channel (1300-1800 A), and the other for the near-ultraviolet ... More

Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categoriesSep 28 2018Jun 23 2019We generalise some of the theory developed for abelian categories in papers of Auslander and Reiten to semi-abelian and quasi-abelian categories. In addition, we generalise some Auslander-Reiten theory results of S. Liu for Krull-Schmidt categories by ... More

Approximative Atomic Systems for operators in Banach spacesSep 11 2019$K$-frames and atomic systems for an operator $K$ in Hilbert spaces were introduced by Gavruta \cite{12} and further studied by Xio, Zhu and Gavruta \cite{21}. In this paper, we have introduced the notion of an approximative atomic system for an operator ... More

Big Data and the Internet of ThingsMar 24 2015Advances in sensing and computing capabilities are making it possible to embed increasing computing power in small devices. This has enabled the sensing devices not just to passively capture data at very high resolution but also to take sophisticated ... More

The Open Universe and Data-driven AstronomyOct 08 2018Activities related to access to astronomical facilities and data could offer an effective, entry-level path for outreach and astronomy education. The Government of Italy proposed the Open Universe initiative that was adopted by the United Nations Office ... More

Geometry of Asymptotically harmonic manifolds with minimal horospheresMar 01 2017Feb 19 2018$(M^n,g)$ be a complete Riemannian manifold without conjugate points. In this paper, we show that if $M$ is also simply connected, then $M$ is flat, provided that $M$ is also asymptotically harmonic manifold with minimal horospheres (AHM). The (first ... More

The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observationsFeb 01 2013Apr 08 2013Using techniques from loop quantum gravity, the standard theory of cosmological perturbations was recently generalized to encompass the Planck era. We now apply this framework to explore pre-inflationary dynamics. The framework enables us to isolate and ... More

The Approximate Capacity of the Many-to-One and One-to-Many Gaussian Interference ChannelsSep 21 2008Recently, Etkin, Tse, and Wang found the capacity region of the two-user Gaussian interference channel to within one bit/s/Hz. A natural goal is to apply this approach to the Gaussian interference channel with an arbitrary number of users. We make progress ... More

A Hamiltonian Formulation of the BKL ConjectureFeb 17 2011Mar 12 2011The Belinskii, Khalatnikov and Lifshitz conjecture \cite{bkl1} posits that on approach to a space-like singularity in general relativity the dynamics are well approximated by `ignoring spatial derivatives in favor of time derivatives.' In \cite{ahs1} ... More

Scanning Tunneling ThermometryJan 26 2019Temperature imaging of nanoscale systems is a fundamental problem which has myriad potential technological applications. For example, nanoscopic cold spots can be used for spot cooling electronic components while hot spots could be used for precise activation ... More

Quantum Theory of Geometry III: Non-commutativity of Riemannian StructuresJun 09 1998Aug 12 1998The basic framework for a systematic construction of a quantum theory of Riemannian geometry was introduced recently. The quantum versions of Riemannian structures --such as triad and area operators-- exhibit a non-commutativity. At first sight, this ... More

An Energy-Aware WLAN Discovery Scheme for LTE HetNetOct 25 2017Recently, there has been significant interest in the integration and co-existence of Third Generation Partnership Project (3GPP) Long Term Evolution (LTE) with other Radio Access Technologies, like IEEE 802.11 Wireless Local Area Networks (WLANs). Although, ... More

Performance Evaluation of Optimal Radio Access Technology Selection Algorithms for LTE-WiFi NetworkMay 20 2017A Heterogeneous Network (HetNet) comprises of multiple Radio Access Technologies (RATs) allowing a user to associate with a specific RAT and steer to other RATs in a seamless manner. To cope up with the unprecedented growth of data traffic, mobile data ... More

Minisuperspaces: Observables and QuantizationFeb 21 1993A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit expressions of Dirac ... More

Behavior of Einstein-Rosen Waves at Null InfinityAug 16 1996The asymptotic behavior of Einstein-Rosen waves at null infinity in 4 dimensions is investigated in {\it all} directions by exploiting the relation between the 4-dimensional space-time and the 3-dimensional symmetry reduction thereof. Somewhat surprisingly, ... More

Quantum gravity, shadow states, and quantum mechanicsJul 26 2002Nov 20 2002A program was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and their solutions through a toy model: quantum mechanics of ... More

An Extension of the Quantum Theory of Cosmological Perturbations to the Planck EraNov 06 2012Jan 16 2013Cosmological perturbations are generally described by quantum fields on (curved but) classical space-times. While this strategy has a large domain of validity, it can not be justified in the quantum gravity era where curvature and matter densities are ... More

Perturbations in loop quantum cosmologyApr 05 2012The era of precision cosmology has allowed us to accurately determine many important cosmological parameters, in particular via the CMB. Confronting Loop Quantum Cosmology with these observations provides us with a powerful test of the theory. For this ... More

On Coretractable ModuleMay 31 2015The main aim of this paper is to discuss the structure of coretractble and mono-coretractble modules. We have provided the characterizations of coretractable modules in terms of Kasch ring, CS modules, mono-coretractble modules, projective modules, epi ... More

Mathematical structure of loop quantum cosmologyApr 21 2003Dec 24 2003Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big bang singularity. However, the precise mathematical ... More

Mechanics of Rotating Isolated HorizonsMar 09 2001Apr 11 2001Black hole mechanics was recently extended by replacing the more commonly used event horizons in stationary space-times with isolated horizons in more general space-times (which may admit radiation arbitrarily close to black holes). However, so far the ... More

Quantum Extension of the Kruskal Space-timeJun 06 2018Feb 14 2019A new description of macroscopic Kruskal black holes that incorporates the quantum geometry corrections of loop quantum gravity is presented. It encompasses both the `interior' region that contains classical singularities and the `exterior' asymptotic ... More

Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categoriesSep 28 2018Jun 10 2019We generalise some of the theory developed for abelian categories in papers of Auslander and Reiten to semi-abelian and quasi-abelian categories. In addition, we generalise some Auslander-Reiten theory results of S. Liu for Krull-Schmidt categories by ... More

Transactional Partitioning: A New Abstraction for Main-Memory DatabasesJan 16 2017The growth in variety and volume of OLTP (Online Transaction Processing) applications poses a challenge to OLTP systems to meet performance and cost demands in the existing hardware landscape. These applications are highly interactive (latency sensitive) ... More

Dispersion relation of an electromagnetic wave in unmagnetized cold plasmaSep 12 2008The dispersion relation of an electromagnetic wave in an unmagnetized neutral plasma is well known to be w^2=wp^2+(ck)^2. A modified dispersion relation is presented taking into account the ion restoring force in the transverse direction.

Interpolating PeriodsMay 13 2013We study the interpolation of Hodge-Tate and de Rham periods in families of Galois representations. Given a Galois representation on a coherent locally free sheaf over a reduced rigid space and a bounded range of weights, we obtain a stratification of ... More

Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categoriesSep 28 2018We generalise some of the theory developed for abelian categories in papers of Auslander and Reiten to semi-abelian and quasi-abelian categories. In addition, we generalise some Auslander-Reiten theory results of S. Liu for Krull-Schmidt categories by ... More

Security Landscape for RoboticsApr 05 2019In this paper, the current state of security in robotics is described to be in need of review. When we consider safety mechanisms implemented in an Internet-connected robot, the requirement of safety becomes a crucial security requirement. Upon review ... More

Parametrized higher category theory and higher algebra: Exposé II - Indexed homotopy limits and colimitsSep 16 2018We develop foundations for the category theory of $\infty$-categories parametrized by a base $\infty$-category. Our main contribution is a theory of indexed homotopy limits and colimits, which specializes to a theory of $G$-colimits for $G$ a finite group ... More

Expansive Automorphisms on Locally Compact GroupsDec 04 2018Feb 20 2019We show that any connected locally compact group which admits an expansive automorphism is nilpotent. We also show that for any locally compact group $G$, $\alpha\in {\rm Aut}(G)$ is expansive if and only if for any $\alpha$-invariant closed subgroup ... More

Weaving a classical geometry with quantum threadsMar 30 1992Results that illuminate the physical interpretation of states of nonperturbative quantum gravity are obtained using the recently introduced loop variables. It is shown that: i) While local operators such as the metric at a point may not be well-defined, ... More

From General Relativity to Quantum GravityAug 19 2014In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature of GR is at ... More

Hairy Black Holes, Horizon Mass and SolitonsNov 22 2000Feb 05 2001Properties of the horizon mass of hairy black holes are discussed with emphasis on certain subtle and initially unexpected features. A key property suggests that hairy black holes may be regarded as `bound states' of ordinary black holes without hair ... More