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Negative spectrum in Harmonic oscillator under simultaneous Non-hermitian transformation of co-ordinate and momentum with Real wave functionFeb 27 2015Apr 14 2016We notice that PT symmetric non-Hermitian one dimensional simple Harmonic Oscillator under simultaneous transformation of co-ordinate and momentum with proper choice of positive oscillating frequency can reflect negative spectrum with well behaved wave ... More

A moment-generating formula for Erdős-Rényi component sizesJul 17 2017Mar 21 2018We derive a simple formula characterizing the distribution of the size of the connected component of a fixed vertex in the Erd\H{o}s-R\'enyi random graph which allows us to give elementary proofs of some results of Federico, van der Hofstad, den Hollander ... More

New approach on Supersymmetric Quantum Systems: Real and Complex HamiltoniansMay 01 2015Feb 28 2017We propose a new method for generating new Hamiltonians for the development of supersymmetric Quantum Mechanics for real as well as complex systems.interestingly Hamiltonians which can be realised in this method, can hardly be derieved using all previous ... More

Air Taxi Skyport Location Problem for Airport AccessApr 01 2019Air taxis are poised to be an additional mode of transportation in major cities suffering from ground transportation congestion. Among several potential applications of air taxis, we focus on their use within a city to transport passengers to nearby airports. ... More

Air Taxi Skyport Location Problem for Airport AccessApr 01 2019Apr 03 2019Air taxis are poised to be an additional mode of transportation in major cities suffering from ground transportation congestion. Among several potential applications of air taxis, we focus on their use within a city to transport passengers to nearby airports. ... More

Percolation on the stationary distributions of the voter modelFeb 04 2015Feb 18 2016The voter model on $\mathbb{Z}^d$ is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological species occupying space. When $d \geq 3$, the set of (extremal) stationary ... More

Comment on "PT Symmetry as a Generalization of Hermiticity" [arXiv:1002.2676]May 22 2019We notice that the general PT-symmetric Hamiltonian matrix(N=2) having 6-real parameters fails to reproduce one parameter PT-symmetric matrix.

Holographic Renyi Entropy from Quantum Error CorrectionNov 13 2018Feb 04 2019We study Renyi entropies $S_n$ in quantum error correcting codes and compare the answer to the cosmic brane prescription for computing $\widetilde{S}_n \equiv n^2 \partial_n (\frac{n-1}{n} S_n)$. We find that general operator algebra codes have a similar, ... More

Integrating GPS, GSM and Cellular Phone for Location Tracking and MonitoringJul 11 2013Jul 08 2014The wide spread of mobiles as handheld devices leads to various innovative applications that makes use of their ever increasing presence in our daily life. One such application is location tracking and monitoring. This paper proposes a prototype model ... More

Complex Energy of Harmonic Oscillator under Non-Hermitian transformation of momentum with real wave functionMay 19 2015For the first time in the literature of Quantum Physics, we present complex energy eigenvalues of non-Hermitian Harmonic Oscillator $H=\frac{(p+iLx)}^{2}}{2} + W^{2} \frac{x^{2}}{2}$ with real wave function having positive frequency of vibration $(w)$ ... More

Feller property of the multiplicative coalescent with linear deletionSep 30 2016We modify the definition of Aldous' multiplicative coalescent process and introduce the multiplicative coalescent with linear deletion (MCLD). A state of this process is a square-summable decreasing sequence of cluster sizes. Pairs of clusters merge with ... More

Time evolution of dense multigraph limits under edge-conservative preferential attachment dynamicsDec 19 2009Apr 26 2012We define the edge reconnecting model, a random multigraph evolving in time. At each time step we change one endpoint of a uniformly chosen edge: the new endpoint is chosen by linear preferential attachment. We consider a sequence of edge reconnecting ... More

A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests have been used to both assess the patient condition and to monitor the patient progress. This ... More

An understanding of some properties of wave functions in PT-symmetry using (2x2) matrix modelFeb 19 2019We propose a new CCS(complex-conjugate-space) to understand the behaviour of wave functions in non-hermitian PT-symmetry model in quantum mechanics.As an example of this ,we consider previous Bender,Brody and Jones model PT-symmetry operaor . In non-conventional ... More

Comment on: Measuring non-Hermitian operators via weak values [A.K.Pati, U Singh and U. Sinha, Phys.Rev.A92,052120 (2015), arXiv:1406.3007]Apr 22 2019We notice that the 5-parameter (2x2) matrix and the corresponding wave functions fail to satisfy the eigenvaue condition or relation reported earlier in this journal by A.K.Pati, U.Singh and U.Sinha (PSS), Phys.Rev. A 92, 052120 (2015) [arXiv:1406.3007]. ... More

A short proof of the phase transition for the vacant set of random interlacementsJul 31 2014Jan 22 2015The vacant set of random interlacements at level $u>0$, introduced in arXiv:0704.2560, is a percolation model on $\mathbb{Z}^d$, $d \geq 3$ which arises as the set of sites avoided by a Poissonian cloud of doubly infinite trajectories, where $u$ is a ... More

Identifying Mild Traumatic Brain Injury Patients From MR Images Using Bag of Visual WordsOct 18 2017Feb 14 2018Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests are used to both assess the patient condition and to monitor the patient progress. This work aims ... More

Integrated optomechanics and single-photon detection in diamond photonic integrated circuitsJan 06 2017The development of quantum computers and quantum simulators promises to provide solutions to problems, which can currently not be solved on classical computers. Finding the best physical implementation for such technologies is an important research topic ... More

A Machine Learning Approach For Identifying Patients with Mild Traumatic Brain Injury Using Diffusion MRI ModelingAug 27 2017While diffusion MRI has been extremely promising in the study of MTBI, identifying patients with recent MTBI remains a challenge. The literature is mixed with regard to localizing injury in these patients, however, gray matter such as the thalamus and ... More

MTBI Identification From Diffusion MR Images Using Bag of Adversarial Visual FeaturesJun 27 2018In this work, we propose bag of adversarial features (BAF) for identifying mild traumatic brain injury (MTBI) patients from their diffusion magnetic resonance images (MRI) (obtained within one month of injury) by incorporating unsupervised feature learning ... More

A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Apr 11 2018Mild traumatic brain injury is a growing public health problem with an estimated incidence of over 1.7 million people annually in US. Diagnosis is based on clinical history and symptoms, and accurate, concrete measures of injury are lacking. This work ... More

On decoupling inequalities and percolation of excursion sets of the Gaussian free fieldJul 10 2013Feb 04 2015We prove decoupling inequalities for the Gaussian free field on $\mathbb{Z}^d$, $d\geq 3$. As an application, we obtain exponential decay (with logarithmic correction for $d=3$) of the connectivity function of excursion sets for large values of the threshold. ... More

Prominent interference peaks in the dephasing Anderson modelOct 24 2018The Anderson model with decoherence features a temporal evolution from localized eigenstates to a uniform spatial distribution bar any interference features. We discuss the growth and decay of pronounced interference peaks on transient time-scales and ... More

Finsler space-time can explain both parity asymmetry and power deficit seen in CMB temperature anisotropiesJun 29 2018We propose a framework of Finsler space-time to explain the observed parity asymmetry and the power deficit in the low-$\ell$ ($2\leqslant \ell \leqslant 29$) multipole range of cosmic microwave background (CMB) temperature anisotropies. In the $3+1$ ... More

Uncertainties and shortcomings of ground surface temperature histories derived from inversion of temperature logsJun 14 2008Analysing borehole temperature data in terms of ground surface history can add useful information to reconstructions of past climates. Therefore, a rigorous assessment of uncertainties and error sources is a necessary prerequisite for the meaningful interpretation ... More

On two problems of Hardy and MahlerApr 01 2019It is a classical result of Mahler that for any rational number $\alpha$ > 1 which is not an integer and any real 0 < c < 1, the set of positive integers n such that $\alpha$ n < c n is necessarily finite. Here for any real x, x denotes the distance from ... More

Multigraph limits and exchangeabilityOct 03 2009Jun 11 2010The theory of limits of dense graph sequences was initiated by Lovasz and Szegedy. We give a possible generalization of this theory to multigraphs. Our proofs are based on the correspondence between dense graph limits and countable, exchangeable arrays ... More

On diagonal lower bound of Markov kernel from $L^2$ analyticityAug 10 2015Let $\Gamma$ be a graph and $P$ be a reversible random walk on $\Gamma$. From the $L^2$ analyticity of the Markov operator $P$, we deduce an on-diagonal lower bound of an iterate of odd number of $P$. The proof does not require the doubling property on ... More

Cosmic ConundrumsApr 10 2014What do we do when cosmology raises questions it cannot answer? These include the existence of a multiverse and the universality of the laws of physics. We cannot settle any of these issues by experiment, and this is where philosophers enter the debate. ... More

Feedback in Galaxy FormationFeb 01 2011I review the outstanding problems in galaxy formation theory, and the role of feedback in resolving them. I address the efficiency of star formation, the galactic star formation rate, and the roles of supernovae and supermassive black holes.

Self-Organized Criticality on Quasiperiodic GraphsApr 16 1999Jul 26 1999Self-organized critical models are used to describe the 1/f-spectra of rather different physical situations like snow avalanches, noise of electric currents, luminosities of stars or topologies of landscapes. The prototype of the SOC-models is the sandpile ... More

On the Existence of an Orthogonal Factorization System on 1-Cob and 2-CobJun 09 2015We define the category 2-Cob combinatorially and use this definition to prove the existence of an orthogonal factorization system. In the second half of the paper, we define oriented 1-Cob similarly and define a functor from oriented 1-Cob to 2-Cob. After ... More

Chaos in the black hole S-matrixMay 29 2015Jun 01 2015Recent work by Shenker, Stanford, and Kitaev has related the black hole horizon geometry to chaotic behavior. We extend this from eternal black holes to black holes that form and then evaporate. This leads to an identity for the change in the black hole ... More

The Cosmological Constant and the String LandscapeMar 31 2006Apr 21 2006Theories of the cosmological constant fall into two classes, those in which the vacuum energy is fixed by the fundamental theory and those in which it is adjustable in some way. For each class we discuss key challenges. The string theory landscape is ... More

S-Matrices from AdS SpacetimeJan 18 1999In the large-N limit of d=4, N=4 gauge theory, the dual AdS spacetime becomes flat. We identify a gauge theory correlator whose large-N limit is the flat spacetime S-matrix.

Recent Results in String DualityNov 22 1995Nov 22 1995This is a talk given at YKIS '95, primarily to non-string theorists. I review the evidence for string duality, the principle that any string theory at strong coupling looks like another string theory at weak coupling. A postscript summarizes developments ... More

Low Energy Dynamics of the Spinon-Gauge SystemMar 21 1993The normal phase of the high-$T_c$ cuprates is apparently not described by Fermi liquid theory. It has been proposed that a dynamically generated gauge field must appear in the effective field theory. Even a simple spinon-gauge system is complicated, ... More

General bound of overfitting for MLP regression modelsJan 03 2012Multilayer perceptrons (MLP) with one hidden layer have been used for a long time to deal with non-linear regression. However, in some task, MLP's are too powerful models and a small mean square error (MSE) may be more due to overfitting than to actual ... More

Testing the number of parameters with multidimensional MLPFeb 21 2008This work concerns testing the number of parameters in one hidden layer multilayer perceptron (MLP). For this purpose we assume that we have identifiable models, up to a finite group of transformations on the weights, this is for example the case when ... More

Authentication Based Solutions to Counterfeiting of Manufactured GoodsNov 27 2015May 21 2016Counterfeiting of manufactured goods is presented as the theft of intellectual property, patents, copyright etc. accompanied by identity theft. The purpose of the identity theft is to facilitate the intellectual property theft. Without it the intellectual ... More

The Game of PhishingNov 12 2015Aug 04 2016Phishing attacks occur because of a failure of computer users to authenticate Bob. The computer user's role, her job, is to authenticate Bob. Nobody else can carry out this task. I researched the ability of browsers to counterfeit the behaviour of installed ... More

Cover times and generic chainingJul 04 2012Jul 10 2012A recent result of Ding, Lee and Peres expresses the cover time of the random walk on a graph in terms of generic chaining for the commute distance. Their proof is very involved and the purpose of this article is to present a simpler approach to this ... More

Particle phenomenology on noncommutative spacetimeNov 24 2008May 12 2009We introduce particle phenomenology on the noncommutative spacetime called the Groenewold-Moyal plane. The length scale of spcetime noncommutativity is constrained from the CPT violation measurements in $K^{0}-\bar{K}^{0}$ system and $g-2$ difference ... More

Blackbody Friction: Analytic expressions for velocity and positionNov 08 2012The equations of motion are solved analytically for speed and position for the case of blackbody friction on objects traveling at relativistic speeds with respect to observers fixed in the frame of the blackbody radiation. Two model cases are considered, ... More

The $R_{\mathrm{h}}=ct$ universe and quintessenceJan 20 2016Over the last few years the $R_{\mathrm{h}}=ct$ universe has received a lot of attention, particularly when observational evidence seems to favor this over the standard $\Lambda$ cold dark matter ($\Lambda CDM$) universe. Like the $\Lambda CDM$, the $R_{\mathrm{h}}=ct$ ... More

Dileptons and Photons from Coarse-Grained Microscopic Dynamics and Hydrodynamics Compared to Experimental DataOct 09 2002We compute the radiation of dileptons and photons using relativistic hydrodynamics and a coarse-grained version of the microscopic event generator UrQMD, both of which provide a good description of the hadron spectra. The currently most accurate dilepton ... More

Wave approach for the resonances of rectangular and triangular membranesJun 09 2011This study develops a ray technique for determining the resonance frequencies of triangular membranes. The technique is demonstrated for homogenous rectangular and triangular membranes with fixed boundaries. Where possible, the results are compared with ... More

Optimal bounds for the growth of Sobolev norms of solutions of a quadratic Szegő equationOct 04 2017In this paper, we study a quadratic equation on the one-dimensional torus : $$i \partial_t u = 2J\Pi(|u|^2)+\bar{J}u^2, \quad u(0, \cdot)=u_0,$$ where $J=\int_\mathbb{T}|u|^2u \in\mathbb{C}$ has constant modulus, and $\Pi$ is the Szeg\H{o} projector onto ... More

Intersections via resolutionsApr 08 2014We investigate the viability of defining an intersection product on algebraic cycles on a singular algebraic variety by pushing forward intersection products formed on a resolution of singularities. For varieties with resolutions having a certain structure ... More

Stacks in Representation Theory. What is a continuous representation of an algebraic group ?Oct 02 2014May 12 2016In this note I introduce a new approach to (or rather a new language for) representation theory of groups. Namely, I propose to consider a (complex) representation of a group $G$ as a sheaf on some geometric object (a stack). This point of view necessarily ... More

Relativity and Aether Theory, a Crucial DistinctionOct 10 2006Dec 14 2008We study the case of two rockets which meet at a point O of an inertial co-ordinate system S, and are scheduled to move at constant speed, in opposite directions, toward two targets placed at equal distances from point O. At the instant they meet, the ... More

On Multiplicative Functions with Bounded Partial SumsAug 06 2011Consider a multiplicative function f(n) taking values on the unit circle. Is it possible that the partial sums of this function are bounded? We show that if we weaken the notion of multiplicativity so that f(pn)=f(p)f(n) for all primes p in some finite ... More

A preparation theorem for the kashiwara $b(\infty)$ crystalOct 21 2015The Kashiwara $B(\infty)$ crystal pertains to a Verma module for a Kac- Moody Lie algebra. Ostensibly it provides only a parametrisation of the global/canonical basis for the latter. Yet it is much more having a rich combinatorial structure from which ... More

Trails, $S$-graphs and Identities in Demazure ModulesFeb 01 2017The Kashiwara crystal $B(\infty)$ parametrizes a basis for the Verma module of a Kac-Moody algebra. It has a deep combinatorial structure which one seeks to understand. For each sequence $J$ of reduced decompositions of elements of the Weyl group $W$, ... More

Smart city analysis using spatial data and predicting the sustainabilityJun 19 2014Smart city [1] planning is crucial as it should balance among resources and the needs of the city .It allows to achieve good eco-friendly industries, there by supporting both the nature and the stake holders. Setting up an industry is a difficult problem, ... More

The normality of digits in almost constant additive functionsJun 06 2012We consider numbers formed by concatenating some of the base b digits from additive functions f(n) that closely resemble the prime counting function \Omega(n). If we concatenate the last \lceil y \frac{\log \log \log n}{\log b} \rceil digits of each f(n) ... More

On multiplicativity of Fourier coefficients at cusps other than infinityFeb 11 2011This paper treats the problem of determining conditions for the Fourier coefficients of a Maass-Hecke newform at cusps other than infinity to be multiplicative. To be precise, the Fourier coefficients are defined using a choice of matrix in SL(2, Z) which ... More

On On_pAug 03 2011Feb 17 2015Generalizing John Conway's construction of the Field On_2, we give the "minimal" definitions of addition and multiplication that turn the ordinals into a Field of characteristic p, for any prime p. We then analyze the structure of the resulting Field, ... More

Diophantine properties of continued fractions on the Heisenberg groupSep 20 2013Aug 11 2014We provide several results on the diophantine properties of continued fractions on the Heisenberg group, many of which are analogous to classical results for real continued fractions. In particular, we show an analog of Khinchin's theorem and that convergents ... More

Random Heegaard splittingsSep 29 2008Nov 16 2010A random Heegaard splitting is a 3-manifold obtained by using a random walk of length n on the mapping class group as the gluing map between two handlebodies. We show that the joint distribution of random walks of length n and their inverses is asymptotically ... More

On the Yao-Yao partition theoremNov 09 2010The Yao-Yao partition theorem states that given a probability measure on an affine space of dimension n having a density which is continuous and bounded away from 0, it is possible to partition the space into 2^n regions of equal measure in such a way ... More

Derived autoequivalences from periodic algebrasJun 14 2011Feb 18 2013We present a construction of autoequivalences of derived categories of symmetric algebras based on projective modules with periodic endomorphism algebras. This construction generalises autoequivalences previously constructed by Rouquier-Zimmermann and ... More

Eigenvector convergence for minors of unitarily invariant infinite random matricesOct 06 2018Pickrell has fully characterized the unitarily invariant probability measures on infinite Hermitian matrices, and an alternative proof of this classification has been found by Olshanski and Vershik. Borodin and Olshanski deduced from this proof that under ... More

Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian KrigingMar 21 2017Dec 17 2018Models are often defined through conditional rather than joint distributions, but it can be difficult to check whether the conditional distributions are compatible, i.e. whether there exists a joint probability distribution which generates them. When ... More

Midy's Theorem for Periodic DecimalsMay 07 2006The decimal expansion of 1/7 is 0.142857142857..., the block 142857 repeating forever. We call 142857 the period and its length is 6 = 2x3. If the period is broken into 2 pieces each of length 3 which are then added, the result is 142 + 857 = 999; similarly ... More

Regularization in $L_1$ for the Ornstein--Uhlenbeck semigroupMay 15 2015Let $\gamma_n$ be the standard Gaussian measure on $\mathbb R^n$ and let $(Q_t)$ be the Ornstein--Ulhenbeck semigroup. Eldan and Lee recently established that for every non--negative function $f$ of integral $1$ and any time $t$ the following tail inequality ... More

Pénalisations of Walsh's Brownian motionJun 16 2005In this paper, we construct a family of probability measures, by penalizations of a Walsh's Brownian motion with a weight dependent on its value and its local time at a time t. We prove that this family converges to a probability measure as t tends to ... More

Symplectomorphism groups and isotropic skeletonsApr 27 2004Jun 17 2005The symplectomorphism group of a 2-dimensional surface is homotopy equivalent to the orbit of a filling system of curves. We give a generalization of this statement to dimension 4. The filling system of curves is replaced by a decomposition of the symplectic ... More

Prequantization of logsymplectic structuresJan 12 2010In this paper, we study quatization condition of logsymplectic struc- ture using integrality of such structue on the complement of associated divisor D.

Variable Selection in High Dimensions with Random Designs and Orthogonal Matching PursuitSep 04 2011The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the design matrix, ... More

A minimal counterexample to a strengthening of Perles' conjectureSep 03 2018Sep 06 2018In this paper, we present a minimal counterexample to a conjecture of Perles that answers a question of Haase and Ziegler. The example is a simple 4-polytope that has an induced 3-connected 3-regular subgraph, whose graph complement is connected. This ... More

Antichain toggling and rowmotionSep 27 2017Feb 23 2019In this paper, we analyze the toggle group on the set of antichains of a poset. Toggle groups, generated by simple involutions, were first introduced by Cameron and Fon-Der-Flaass for order ideals of posets. Recently Striker has motivated the study of ... More

Riesz transform on graphs under subgaussian estimatesMay 26 2015Jan 14 2016Let $\Gamma$ be a doubling graph satisfying some pointwise subgaussian estimates of the Markov kernel. We introduce a space $H^1(\Gamma)$ of functions and a space $H^1(T_\Gamma)$ of 1-forms and give various characterizations of them. We prove the $H^1$-boundedness ... More

Moments of the Gaussian ChaosNov 09 2010This paper deals with Lata{\l}a's estimation of the moments of Gaussian chaoses. It is shown that his argument can be simplified significantly using Talagrand's generic chaining.

Deformations of algebras defined by tilting bundlesMay 15 2015In this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles. We do this in two settings, first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal deformations ... More

A Center-Median Filtering Method for Detection of Temporal Variation in Coronal ImagesNov 13 2015Jan 29 2016Events in the solar corona are often widely separated in their timescales, which can allow them to be identified when they would otherwise be confused with emission from other sources in the corona. Methods for cleanly separating such events based on ... More

Sacler lecturesJan 31 1995The series of three lectures given at Tel-Aviv University in 1992: 1. Tensor categories. 2. Quantum groups. 3. Topological (quantum) field theories. Published as the preprint IAS 897-92 of Tel-Aviv University and The Mortimer and Raymond Sacler Institute ... More

A note on dark matter and dark energyOct 30 2013Since the geometry of our universe seems to depend very little on baryonic matter, we consider a variational principle involving only dark matter and dark energy which in addition make them depend on each other. There are no adjustable parameters or scalar ... More

Wick Rotation in the Tangent SpaceOct 26 2015Wick rotation is usually performed by rotating the time coordinate to imaginary values. In a general curved spacetime, the notion of a time coordinate is ambiguous. We note here, that within the tetrad formalism of general relativity, it is possible to ... More

Lattice formulations of supersymmetric gauge theories with matter fieldsSep 30 2014Certain classes of supersymmetric gauge theories, including the well known N=4 supersymmetric Yang-Mills theory, that takes part in the AdS/CFT correspondence, can be formulated on a Euclidean spacetime lattice using the techniques of exact lattice supersymmetry. ... More

Lattice formulation of three-dimensional ${\cal N}=4$ gauge theory with fundamental matter fieldsJul 11 2013Sep 15 2013We construct lattice action for three-dimensional ${\cal N}=4$ supersymmetric gauge theory with matter fields in the fundamental representation.

Supersymmetric Yang--Mills theories with exact supersymmetry on the latticeOct 27 2011Dec 24 2011Inspired by the ideas from topological field theory it is possible to rewrite the supersymmetric charges of certain classes of extended supersymmetric Yang--Mills (SYM) theories in such a way that they are compatible with the discretization on a Euclidean ... More

The integrality of an adapted pairFeb 19 2014Let $\mathfrak a$ be an algebraic Lie algebra. An adapted pair for $\mathfrak a$ is pair $(h,\eta)$ consisting of an ad-semisimple element of $h \in \mathfrak a$ and a regular element of $\eta \in \mathfrak a^*$ satisfying $(ad \ h)\eta=-\eta$. An adapted ... More

Supersymmetric quiver gauge theories on the latticeNov 20 2013Jan 21 2014In this paper we detail the lattice constructions of several classes of supersymmetric quiver gauge theories in two and three Euclidean spacetime dimensions possessing exact supersymmetry at finite lattice spacing. Such constructions are obtained through ... More

Analogue Zhelobenko Invariants and the Kostant Clifford Algebra ConjectureNov 15 2011Let g be a complex simple Lie algebra and h a Cartan subalgebra. The Clifford algebra C(g) of g admits a Harish-Chandra map. Kostant conjectured (as communicated to Bazlov in about 1997) that the value of this map on a (suitably chosen) fundamental invariant ... More

The Last Eight Minutes of a Primordial Black HoleNov 16 1999About eight minutes before a black hole expires it has a decreasing mass of 10^{10} g, an increasing temperature of 1 TeV, and an increasing luminosity of 7x10^{27} erg/s. I show that such a black hole is surrounded by a quasi-stationary shell of matter ... More

Formation and evolution of disk galaxiesSep 02 2008Global star formation is the key to understanding galaxy disk formation. This in turn depends on gravitational instability of disks and continuing gas accretion as well as minor merging. A key component is feedback from supernovae. Primary observational ... More

Ultraluminous Starbursts from SMBH-induced outflowsSep 06 2005Dec 06 2005I argue that there are two modes of global star formation. Disks and smaller spheroids form stars relatively inefficiently as a consequence of supernova-triggered negative feedback via a sequence of ministarbursts (S mode), whereas massive spheroids formed ... More

The Cosmic Microwave BackgroundDec 12 2002I review the discovery of the temperature fluctuations in the cosmic microwave background radiation. The underlying theory and the implications for cosmology are reviewed, and I describe the prospects for future progress.

Challenges in Cosmology from the Big Bang to Dark Energy, Dark Matter and Galaxy FormationNov 29 2016I review the current status of Big Bang Cosmology, with emphasis on current issues in dark matter, dark energy, and galaxy formation. These topics motivate many of the current goals of experimental cosmology which range from targeting the nature of dark ... More

Formation and Evolution of Disk GalaxiesOct 16 2002I review several of the current issues in the theory of disk galaxy formation. There is sti ll much to be done, observationally and theoretically, before we can expect to approach an understanding of disk galaxies that is reliable enough to make robust ... More

The Formation of Galaxy DisksOct 31 2000Galaxy disk formation must incorporate the multiphase nature of the interstellar medium. The resulting two-phase structure is generated and maintained by gravitational instability and supernova energy input, which yield a source of turbulent viscosity ... More

Baryonic Dark MatterJul 07 1994In the first two of these lectures, I present the evidence for baryonic dark matter and describe possible forms that it may take. The final lecture discusses formation of baryonic dark matter, and sets the cosmological context.

Aspects of Galaxy FormationDec 13 2001I describe some of the current challenges in galaxy formation theory with applications to formation of disks and of spheroids. Forthcoming deep surveys of galaxies with Keck and VLT will provide high quality spectra of $\sim 10^5$ galaxies that will probe ... More

Seven Paradigms in Structure FormationMar 25 1999Have we converged on the definitive model of cosmology? I present a critical assessment of the current paradigms for the evolution of large-scale structure.

Feedback, Disk Self-regulation and Galaxy FormationDec 11 1996Dec 12 1996Self-regulation of star formation in disks is controlled by two dimensionless parameters: the Toomre parameter for gravitational instability and the porosity of the interstellar medium to supernova remnant-heated gas. An interplay between these leads ... More

Self Organizing Map algorithm and distortion measureFeb 21 2008We study the statistical meaning of the minimization of distortion measure and the relation between the equilibrium points of the SOM algorithm and the minima of distortion measure. If we assume that the observations and the map lie in an compact Euclidean ... More

Estimation of linear autoregressive models with Markov-switching, the E.M. algorithm revisitedFeb 21 2008This work concerns estimation of linear autoregressive models with Markov-switching using expectation maximisation (E.M.) algorithm. Our method generalise the method introduced by Elliot for general hidden Markov models and avoid to use backward recursion. ... More

Consistent estimation of the architecture of multilayer perceptronsFeb 22 2008We consider regression models involving multilayer perceptrons (MLP) with one hidden layer and a Gaussian noise. The estimation of the parameters of the MLP can be done by maximizing the likelihood of the model. In this framework, it is difficult to determine ... More

Dualities of Fields and StringsDec 18 2014Jul 27 2015Duality, the equivalence between seemingly distinct quantum systems, is a curious property that has been known for at least three quarters of a century. In the past two decades it has played a central role in mapping out the structure of theoretical physics. ... More