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Locally Connected Spiking Neural Networks for Unsupervised Feature LearningApr 12 2019In recent years, Spiking Neural Networks (SNNs) have demonstrated great successes in completing various Machine Learning tasks. We introduce a method for learning image features by \textit{locally connected layers} in SNNs using spike-timing-dependent ... More

Improved robustness of reinforcement learning policies upon conversion to spiking neuronal network platforms applied to ATARI gamesMar 26 2019Various implementations of Deep Reinforcement Learning (RL) demonstrated excellent performance on tasks that can be solved by trained policy, but they are not without drawbacks. Deep RL suffers from high sensitivity to noisy and missing input and adversarial ... More

Determining Edge Expansion and Other Connectivity Measures of Graphs of Bounded GenusApr 26 2010In this paper, we show that for an $n$-vertex graph $G$ of genus $g$, the edge expansion of $G$ can be determined in time $n^{O(g^2)}$. We show that the same is true for various other similar measures of edge connectivity.

On the Residual Finiteness Growths of Particular Hyperbolic Manifold GroupsDec 21 2014Apr 26 2016We give a quantification of residual finiteness for the fundamental groups of hyperbolic manifolds that admit a totally geodesic immersion to a compact, right-angled Coxeter orbifold of dimension 3 or 4. Specifically, we give explicit upper bounds on ... More

Physics of Heavy Quarks from Lattice QCDNov 08 1996In the last few years, lattice QCD has made a dramatic progress in understanding the physics of hadrons containing heavy quarks, from the first principle. This review summarises the major achievements.

From Kondo Model and Strong Coupling Lattice QCD to the Isgur-Wise FunctionMay 03 1994Isgur-Wise functions parametrise the leading behaviour of weak decay form factors of mesons and baryons containing a single heavy quark. The form factors for the quark mass operator are calculated in strong coupling lattice QCD, and Isgur-Wise functions ... More

Mathematical Physics and LifeFeb 04 2002Apr 03 2003It is a fascinating subject to explore how well we can understand the processes of life on the basis of fundamental laws of physics. It is emphasised that viewing biological processes as manipulation of information extracts their essential features. This ... More

Weak Lensing with Radio Continuum SurveysFeb 24 2016Weak gravitational lensing is a powerful probe of cosmology and has emerged as a key probe for the Dark Universe. Up till now this science has been conducted mainly at optical wavelengths. Current upgraded and future radio facilities will provide greatly ... More

Semicontinuity of Persistence DiagramsJan 13 2016May 27 2016We generalize the persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer to the setting of constructible persistence modules valued in any symmetric monoidal category. This persistence diagram is stable to small perturbations of the module. If ... More

Special codimension one loci in Hurwitz spacesAug 25 2015We investigate two families of divisors which we expect to play a distinguished role in the global geometry of Hurwitz space. In particular, we show that they are extremal and rigid in the small degree regime $d \leq 5$. We further show their significance ... More

Survival of the Fittest and Zero Sum GamesJun 03 2002Jan 09 2003Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The dynamics of this selection is studied using a simple linear model. It has similarities to features of quantum ... More

Testing Quantum Dynamics in Genetic Information ProcessingFeb 06 2001Jul 26 2001Does quantum dynamics play a role in DNA replication? What type of tests would reveal that? Some statistical checks that distinguish classical and quantum dynamics in DNA replication are proposed.

What is Quantum Computation?Sep 27 1999Quantum computation is a rapidly progressing field today. What are its principles? In what sense is it distinct from conventional computation? What are its advantages and disadvantages? What type of problems can it address? How practical is it to make ... More

Generalized Persistence DiagramsJan 13 2016Jul 09 2017We generalize the persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer to the setting of constructible persistence modules valued in a symmetric monoidal category. We call this the type A persistence diagram of a persistence module. If the category ... More

Quantum Computation: Particle and Wave Aspects of AlgorithmsAug 08 2011Sep 14 2011The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen. Clever quantum ... More

The Triplet Genetic Code had a Doublet PredecessorMar 25 2004Oct 28 2004Information theoretic analysis of genetic languages indicates that the naturally occurring 20 amino acids and the triplet genetic code arose by duplication of 10 amino acids of class-II and a doublet genetic code having codons NNY and anticodons $\overleftarrow{\rm ... More

Another Look at Bell's Inequalities and Quantum MechanicsSep 14 1993Feynman's path integrals provide a hidden variable description of quantum mechanics (and quantum field theories). The expectation values defined through path integrals obey Bell's inequalities in Euclidean time, but not in Minkowski time. This observation ... More

Moduli of Linear Sections of a General HypersurfaceMay 05 2016We investigate the global variation of moduli of linear sections of a general hypersurface. We prove a "generic Torelli" result for a large proportion of cases, and we obtain a complete picture of the global variation of moduli of line slices of a general ... More

Towards a nonabelian cohomology of formsDec 23 2004Mar 07 2005We consider a simple and natural coboundary operator, on the Lie algebra valued differential forms on a manifold, which in the abelian case reduces to usual exterior derivative of such forms. Using the corresponding de Rham cohomology Lie superalgebra ... More

Three New Results on Continuation Criteria for the 3D Relativistic Vlasov-Maxwell SystemJul 25 2016In this paper, we consider sufficient conditions, called continuation criteria, for global existence and uniqueness of classical solutions to the three-dimensional relativistic Vlasov-Maxwell system. In the compact momentum support setting, we prove that ... More

Why Genetic Information Processing could have a Quantum BasisMay 01 2001Jun 11 2001Living organisms are not just random collections of organic molecules. There is continuous information processing going on in the apparent bouncing around of molecules of life. Optimisation criteria in this information processing can be searched for using ... More

Quantum Algorithms and the Genetic CodeFeb 14 2000Feb 06 2001Replication of DNA and synthesis of proteins are studied from the view-point of quantum database search. Identification of a base-pairing with a quantum query gives a natural (and first ever) explanation of why living organisms have 4 nucleotide bases ... More

On how to Produce Entangled States Violating Bell's Inequalities in Quantum TheoryOct 23 1998Dec 24 1998Feynman's path integrals provide a hidden variable description of quantum mechanics (and quantum field theories). The time evolution kernel is unitary in Minkowski time, but generically it becomes real and non-negative in Euclidean time. It follows that ... More

Recent Developments in Lattice QCDFeb 01 1993I review the current status of lattice QCD results. I concentrate on new analytical developments and on numerical results relevant to phenomenology.

The Future of ComputationMar 07 2005``The purpose of life is to obtain knowledge, use it to live with as much satisfaction as possible, and pass it on with improvements and modifications to the next generation.'' This may sound philosophical, and the interpretation of words may be subjective, ... More

Scalar and axial matrix elements of the nucleon: sea quark contentApr 22 1992Sea quark contributions to the scalar density and the axial current matrix elements of the nucleon are studied in lattice qcd with two flavours of dynamical wilson fermions. the results are compared to trends in heavy quark mass expansions, and contrasted ... More

On a Theorem of Peter ScottApr 23 2012Apr 17 2014We quantify Peter Scott's Theorem that surface groups are locally extended residually finite (LERF) in terms of geometric data. In the process, we will quantify another result by Scott that any closed geodesic in a surface lifts to an embedded loop in ... More

On SGD's Failure in Practice: Characterizing and Overcoming StallingFeb 01 2017Feb 07 2017Stochastic Gradient Descent (SGD) is widely used in machine learning problems to efficiently perform empirical risk minimization, yet, in practice, SGD is known to stall before reaching the actual minimizer of the empirical risk. SGD stalling has often ... More

Kalman-based Stochastic Gradient Method with Stop Condition and Insensitivity to ConditioningDec 03 2015Jun 10 2016Modern proximal and stochastic gradient descent (SGD) methods are believed to efficiently minimize large composite objective functions, but such methods have two algorithmic challenges: (1) a lack of fast or justified stop conditions, and (2) sensitivity ... More

Some Approximation Properties of New Families of Positive Linear OperatorsApr 18 2019In the present article, we propose the new class positive linear operators, which discrete type depending on a real parameters. These operators are similar to Jain operators but its approximation properties are different then Jain operators. Theorems ... More

Fairness for Whom? Critically reframing fairness with Nash Welfare ProductOct 19 2018Recent studies on disparate impact in machine learning applications have sparked a debate around the concept of fairness along with attempts to formalize its different criteria. Many of these approaches focus on reducing prediction errors while maximizing ... More

A Continuous Theory of Persistence for Mappings Between ManifoldsFeb 16 2011Oct 08 2013Using sheaf theory, I introduce a continuous theory of persistence for mappings between compact manifolds. In the case both manifolds are orientable, the theory holds for integer coefficients. The sheaf introduced here is stable to homotopic perturbations ... More

Quantum Algorithms: Database Search and its VariationsFeb 10 2011The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen. Clever quantum ... More

Optimal Database Search: Waves and CatalysisJan 25 2004Jun 04 2007Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any system that allows superposition of states. A physical realization of this algorithm is described using coupled simple harmonic ... More

Carbon--The First Frontier of Information ProcessingMar 05 2001Jun 10 2002Information is often encoded as an aperiodic chain of building blocks. Modern digital computers use bits as the building blocks, but in general the choice of building blocks depends on the nature of the information to be encoded. What are the optimal ... More

Constraints on $m_s$ and $ε'/ε$ from Lattice QCDMar 20 2000Results for light quark masses obtained from lattice QCD simulations are compared and contrasted with other determinations. Relevance of these results to estimates of $\epsilon'/\epsilon$ is discussed.

Form Factors for Semileptonic Decays of Heavy-Light HadronsDec 06 1994Dec 15 1994The strong coupling lattice QCD solution \cite{APtifr} for the Isgur-Wise functions, parametrising the semileptonic decay form factors of hadrons containing a single heavy quark, is reviewed. Several useful features connected with the result are pointed ... More

The Impact of Local Geometry and Batch Size on Stochastic Gradient Descent for Nonconvex ProblemsSep 14 2017May 05 2018In several experimental reports on nonconvex optimization problems in machine learning, stochastic gradient descent (SGD) was observed to prefer minimizers with flat basins in comparison to more deterministic methods, yet there is very little rigorous ... More

Optimisation of Quantum Evolution AlgorithmsMar 04 2015Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these trajectories can then ... More

Baryon Number Correlations in Heavy Ion CollisionsOct 22 2012Nov 19 2012The cross-over region of the quark-gluon plasma (QGP) created in heavy ion collisions is influenced by the nearby deconfinement, chiral and baryon condensation phase transitions. A characteristic signature of the deconfinement transition in this region ... More

Mesons in Transverse Lattice QCD at Strong Coupling and Large-NNov 23 2001Mesons in large-N QCD are analysed in light-front coordinates with a transverse lattice at strong coupling. In this limit, their properties can be expressed as simple renormalisations of the 't Hooft model results. The integral eigenvalue equation for ... More

Quantum Database Search can do without SortingDec 29 2000Jun 08 2001Sorting is a fundamental computational process, which facilitates subsequent searching of a database. It can be thought of as factorisation of the search process. The location of a desired item in a sorted database can be found by classical queries that ... More

Flux Tube Model Signals for Baryon Correlations in Heavy Ion CollisionsNov 01 2011Jun 13 2012The flux tube model offers a pictorial description of what happens during the deconfinement phase transition in QCD. The 3-point vertices of a flux tube network lead to formation of baryons upon hadronisation. Therefore, correlations in the baryon number ... More

Information Processing beyond Quantum ComputationJun 23 2003Dec 13 2004Recent developments in quantum computation have made it clear that there is a lot more to computation than the conventional Boolean algebra. Is quantum computation the most general framework for processing information? Having gathered the courage to go ... More

An SO(10)XS4 Model of Quark-Lepton ComplementarityAug 30 2010The present observations of Cabbibo angle and solar mixing angle satisfy the empirical relation called Quark-Lepton Complementarity(QLC), namely $\theta_{12}^l\sim \pi/4-\theta_C$. It suggests the existence of correlation between quarks and leptons which ... More

Solving Graph Isomorphism Problem for a Special caseNov 22 2017Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The base algorithm for the general case works in quasi-polynomial time. The solutions in polynomial time for some special ... More

Bottleneck Stability for Generalized Persistence DiagramsJun 01 2018In this paper, we extend bottleneck stability to the setting of one dimensional constructible persistences module valued in any small abelian category.

Experimental Study on Low Power Wide Area Networks (LPWAN) for Mobile Internet of ThingsMay 19 2017In the past decade, we have witnessed explosive growth in the number of low-power embedded and Internet-connected devices, reinforcing the new paradigm, Internet of Things (IoT). The low power wide area network (LPWAN), due to its long-range, low-power ... More

Single image super resolution in spatial and wavelet domainSep 09 2013Recently single image super resolution is very important research area to generate high resolution image from given low resolution image. Algorithms of single image resolution are mainly based on wavelet domain and spatial domain. Filters support to model ... More

Evaluating ECG Capturing Using Sound-Card of PC/LaptopFeb 15 2014The purpose of the Evaluating ECG capturing using sound-card of PC/Laptop is provided portable and low cost ECG monitoring system using laptop and mobile phones. There is no need to interface micro controller or any other device to transmit ECG data. ... More

A theorem of Mœglin-Waldspurger for covering groupsMar 19 2014Apr 22 2014Let $E$ be a non-Archimedian local field of characteristic zero and residue characteristic $p$. Let ${\bf G}$ be a connected reductive group defined over $E$ and $\pi$ an irreducible admissible representation of $G={\bf G}(E)$. A result of C. M{\oe}glin ... More

Invariants of a general branched cover of ${\bf P}^{1}$Apr 15 2015We investigate the resolution of a general branched cover $\alpha : C \to {\bf P}^1$ in its relative canonical embedding $C \subset {\bf P} E$. We conjecture that the syzygy bundles appearing in the resolution are balanced for a general cover, provided ... More

Self similar flow under the action of monochromatic radiation behind a cylindrical shock wave in a self-gravitating, rotating axisymmetric dusty gasJul 18 2018The propagation of a cylindrical shock wave in a self-gravitating, rotating axisymmetric dusty gas under the action of monochromatic radiation with a constant intensity per unit area, which has variable azimuthal and axial components of fluid velocity, ... More

Spatial Search on Graphs with Multiple Targets using Flip-flop Quantum WalkJan 04 2018Oct 30 2018We analyse the eigenvalue and eigenvector structure of the flip-flop quantum walk on regular graphs, explicitly demonstrating how it is quadratically faster than the classical random walk. Then we use it in a controlled spatial search algorithm with multiple ... More

Role of Horizons in Semiclassical Gravity: Entropy and the Area SpectrumSep 09 2003In any space-time, it is possible to have a family of observers who have access to only part of the space-time manifold, because of the existence of a horizon. We demand that \emph{physical theories in a given coordinate system must be formulated entirely ... More

An Evolutionary Formalism for Weak Quantum MeasurementsDec 03 2014Jun 23 2015Unitary evolution and projective measurement are fundamental axioms of quantum mechanics. Even though projective measurement yields one of the eigenstates of the measured operator as the outcome, there is no theory that predicts which eigenstate will ... More

Efficient Energy Transport in Photosynthesis: Roles of Coherence and EntanglementApr 07 2011Recently it has been discovered---contrary to expectations of physicists as well as biologists---that the energy transport during photosynthesis, from the chlorophyll pigment that captures the photon to the reaction centre where glucose is synthesised ... More

Perturbative Corrections for Staggered Fermion BilinearsOct 30 1992We calculate the perturbative corrections to fermion bilinears that are used in numerical simulations when extracting weak matrix elements using staggered fermions. This extends previous calculations of Golterman and Smit, and Daniel and Sheard. In particular, ... More

Vector bundles and finite coversAug 04 2016Jan 06 2019Motivated by the problem of finding algebraic constructions of finite coverings in commutative algebra, the Steinitz realization problem in number theory, and the study of Hurwitz spaces in algebraic geometry, we investigate the vector bundles underlying ... More

Total Magnification and Magnification Centroid Due to Strongly Naked Singularity LensingJun 16 2015Aug 16 2015A strongly naked singularity (SNS) was modelled at the center of the Galaxy. This specific type of naked singularity was characterized in 2008 by Virbhadra and Keeton. The lens is described using the Janis-Newman-Winicour metric, which has an ordinary ... More

Comparison of Advance Tree Data StructuresSep 28 2012Btree and Rtree are two basic index structures; many different variants of them are proposed after them. Different variants are used in specific application for the performance optimization. In this paper different variants of Btree and Rtree are discussed ... More

Interpolation Problems: Del Pezzo SurfacesJan 21 2016We consider the problem of interpolating projective varieties through points and linear spaces. After proving general facts about interpolation, we show that del Pezzo surfaces satisfy weak interpolation.

Approaches for Sentiment Analysis on Twitter: A State-of-Art studyDec 03 2015Microbloging is an extremely prevalent broadcast medium amidst the Internet fraternity these days. People share their opinions and sentiments about variety of subjects like products, news, institutions, etc., every day on microbloging websites. Sentiment ... More

Techniques for Deep Query UnderstandingMay 19 2015Query Understanding concerns about inferring the precise intent of search by the user with his formulated query, which is challenging because the queries are often very short and ambiguous. The report discusses the various kind of queries that can be ... More

Improving the query complexity of quantum spatial search in two dimensionsOct 30 2018The question of whether quantum spatial search in two dimensions can be made optimal has long been an open problem. We report progress towards its resolution by showing that the oracle complexity for target location can be made optimal, by increasing ... More

Syzygy divisors on Hurwitz spacesMay 02 2018We describe a sequence of effective divisors on the Hurwitz space $H_{d,g}$ for $d$ dividing $g-1$ and compute their cycle classes on a partial compactification. These divisors arise from vector bundles of syzygies canonically associated to a branched ... More

A Transverse Lattice QCD Model for MesonsSep 14 2003QCD is analysed with two light-front continuum dimensions and two transverse lattice dimensions. In the limit of large number of colours and strong transverse gauge coupling, the contributions of light-front and transverse directions factorise in the ... More

Perturbative Corrections for Staggered Four-Fermion OperatorsOct 05 1993Oct 05 1993We present results for one-loop matching coefficients between continuum four-fermion operators, defined in the Naive Dimensional Regularization scheme, and staggered fermion operators of various types. We calculate diagrams involving gluon exchange between ... More

Semiclassical quantization of gravity I: Entropy of horizons and the area spectrumMay 19 2003The principle of equivalence provides a description of gravity in terms of the metric tensor and determines how gravity affects the light cone structure of the space-time. This, in turn, leads to the existence of observers (in any space-time) who do not ... More

On perfect powers that are sums of two Fibonacci numbersJun 30 2017We study the equation $F_n + F_m = y^p$, where $F_n$ and $F_m$ are respectively the $n$-th and $m$-th Fibonacci numbers and $p \ge 2$. We find all solutions under the assumption $n \equiv m \pmod{2}$.

Fixed points of multivalued contractions via generalized class of simulation functionsJan 15 2018In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in $\alpha$-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well-known fixed point ... More

Extremal effective divisors of Brill-Noether and Gieseker-Petri type in $\overline{\mathcal M}_{1,n}$Jul 18 2014We show that certain divisors of Brill-Noether and Gieseker-Petri type span extremal rays of the effective cone in the moduli space of stable genus one curves with $n$ ordered marked points. In particular, they are different from the infinitely many extremal ... More

Inflectionary Invariants for Isolated Complete Intersection Curve SingularitiesMay 24 2017Feb 19 2019We investigate the role played by curve singularity germs in the enumeration of inflection points in families of curves acquiring singular members. Let $N \geq 2$, and consider an isolated complete intersection curve singularity germ $f \colon (\mathbb{C}^N,0) ... More

Interpolation Problems: Del Pezzo SurfacesJan 21 2016Dec 09 2016We consider the problem of interpolating projective varieties through points and linear spaces. We show that del Pezzo surfaces satisfy weak interpolation.

Precipitation Nowcasting: Leveraging bidirectional LSTM and 1D CNNOct 24 2018Short-term rainfall forecasting, also known as precipitation nowcasting has become a potentially fundamental technology impacting significant real-world applications ranging from flight safety, rainstorm alerts to farm irrigation timings. Since weather ... More

Fuzzy Inference Systems OptimizationOct 15 2011This paper compares various optimization methods for fuzzy inference system optimization. The optimization methods compared are genetic algorithm, particle swarm optimization and simulated annealing. When these techniques were implemented it was observed ... More

A question on splitting of metaplectic coversJun 16 2014Let $E/F$ be a quadratic extension of a non-Archimedian local field. Splitting of the 2-fold metaplectic cover of ${\rm Sp}_{2n}(F)$ when restricted to various subgroups of ${\rm Sp}_{2n}(F)$ plays an important role in application of the Weil representation ... More

QOS based user driven scheduler for grid environmentFeb 02 2011As grids are in essence heterogeneous, dynamic, shared and distributed environments, managing these kinds of platforms efficiently is extremely complex. A promising scalable approach to deal with these intricacies is the design of self-managing of autonomic ... More

Hamilton cycles in sparse robustly expanding digraphsJul 16 2015The notion of robust expansion has played a central role in the solution of several conjectures involving the packing of Hamilton cycles in graphs and directed graphs. These and other results usually rely on the fact that every robustly expanding (di)graph ... More

Deterministic polynomial-time approximation algorithms for partition functions and graph polynomialsJul 05 2016Oct 27 2016In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In particular, our approach works for the Tutte ... More

Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integralsNov 30 2016This arXiv post announces the public release of Package-X 2.0, a Mathematica package for the analytic calculation of one-loop integrals. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals ... More

Inflectionary Invariants for Isolated Complete Intersection Curve SingularitiesMay 24 2017Jan 09 2019In this article, we investigate the role played by germs of curve singularities in the enumeration of inflection points in families of curves acquiring singular members. More precisely, let $k$ be an algebraically closed field of characteristic $0$, let ... More

Vector bundles and finite coversAug 04 2016We prove that, up to twist, every vector bundle on a smooth projective curve arises from the direct image of the structure sheaf of a smooth, connected branched cover.

Optimisation of Quantum Hamiltonian Evolution: From Two Projection Operators to Local HamiltoniansMar 05 2015Apr 14 2016Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series expansions. A choice ... More

Noncommmutative theorems: Gelfand Duality, Spectral, Invariant Subspace, and Pontryagin DualityMar 07 2005We extend the Gelfand-Naimark duality of commutative C*-algebras, "A COMMUTATIVE C*-ALGEBRA -- A LOCALLY COMPACT HAUSDORFF SPACE" to "A C*-ALGEBRA--A QUOTIENT OF A LOCALLY COMPACT HAUSDORFF SPACE". Thus, a C*-algebra is isomorphic to the convolution algebra ... More

Canonical stratifications along bisheavesDec 13 2018A theory of bisheaves has been recently introduced to measure the homological stability of fibers of maps to manifolds. A bisheaf over a topological space is a triple consisting of a sheaf, a cosheaf, and compatible maps from the stalks of the sheaf to ... More

Non-normality Can Facilitate Pulsing in Biomolecular CircuitsOct 21 2017Jun 02 2018Non-normality can underlie pulse dynamics in many engineering contexts. However, its role in pulses generated in biomolecular contexts is generally unclear. Here, we address this issue using the mathematical tools of linear algebra and systems theory ... More

Efficient Quantum Algorithms for State Measurement and Linear Algebra ApplicationsOct 05 2017Oct 15 2018We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the quantum state, and ... More

Quantum error correction using weak measurementsJul 27 2017The standard quantum error correction protocols use projective measurements to extract the error syndromes from the encoded states. We consider the more general scenario of weak measurements, where only partial information about the error syndrome can ... More

Weak Measurements, Quantum State Collapse and the Born RuleSep 28 2015Aug 08 2017Projective measurement is used as a fundamental axiom in quantum mechanics, even though it is discontinuous and cannot predict which measured operator eigenstate will be observed in which experimental run. The probabilistic Born rule gives it an ensemble ... More

A derivation of Regge trajectories in large-N transverse lattice QCDDec 05 2000Large-N QCD is analysed in light-front coordinates with a transverse lattice at strong coupling. The general formalism can be looked up on as a d+n expansion with a stack of d-dimensional hyperplanes uniformly spaced in n transverse dimensions. It can ... More

Reinforcement Learning approach for Real Time Strategy Games Battle city and S3Feb 16 2016In this paper we proposed reinforcement learning algorithms with the generalized reward function. In our proposed method we use Q-learning and SARSA algorithms with generalised reward function to train the reinforcement learning agent. We evaluated the ... More

Package-X: A Mathematica package for the analytic calculation of one-loop integralsMar 04 2015Sep 04 2015Package-X, a Mathematica package for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described. Package-X computes arbitrarily high rank tensor integrals with up to three propagators, and gives compact ... More

Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integralsNov 30 2016May 17 2017This article summarizes new features and enhancements of the first major update of Package-X. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals with up to four distinct propagators, ... More

Periodic points and tail lengths of split polynomial maps modulo primesOct 21 2017Explicit formulas are obtained for the number of periodic points and maximum tail length of split polynomial maps over finite fields for affine and projective space. This work includes a detailed analysis of the structure of the directed graph for Chebyshev ... More

VC density of definable families over valued fieldsApr 17 2018May 07 2018In this article, we give tight bounds on the Vapnik-Chervonenkis density (VC-density) for definable families over any algebraically closed valued field $K$ (of any characteristic pair) in the language $\mathcal{L}_{\mathrm{div}}$ with signature $(0,1,+,\times,|)$ ... More

Bottleneck Stability for Generalized Persistence DiagramsJun 01 2018Apr 06 2019In this paper, we extend bottleneck stability to the setting of one dimensional constructible persistences module valued in any small abelian category.

Noncommutative Gelfand Duality and Applications I: The Existence of invariant subspacesNov 12 2008Gelfand duality between unital commutative C*-algebras and Compact Hausdorff spaces is extended to all unital C*-algebras, where the dual objects are what we call compact Hausdorff quantum spaces. We apply this result to obtain, a characterization of ... More

Branching laws on the metaplectic cover of ${\rm GL}_{2}$Jun 20 2014Representation theory of $p$-adic groups naturally comes in the study of automorphic forms and one way to understand representations of a group is by restricting to its nice subgroups. D. Prasad studied the restriction for pairs $({\rm GL}_{2}(E), {\rm ... More

Finitely generated ideals in Frechet algebras and a famous problem of Gleason in the theory of SCVOct 07 2014Oct 31 2014We establish the Gleason result for finitely generated ideals in the context of Frechet algebras, and, in particular, provide an affirmative answer to the question about the Gleason result in (uniform) commutative Frechet algebras (posed by Carpenter ... More