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A Separation Logic for Concurrent Randomized ProgramsFeb 08 2018We present a concurrent separation logic with support for probabilistic reasoning. As part of our logic, we extend the idea of coupling, which underlies recent work on probabilistic relational logics, to the setting of programs with both probabilistic ... More

A Separation Logic for Concurrent Randomized ProgramsFeb 08 2018Nov 21 2018We present Polaris, a concurrent separation logic with support for probabilistic reasoning. As part of our logic, we extend the idea of coupling, which underlies recent work on probabilistic relational logics, to the setting of programs with both probabilistic ... More

A Higher-Order Logic for Concurrent Termination-Preserving RefinementJan 20 2017Compiler correctness proofs for higher-order concurrent languages are difficult: they involve establishing a termination-preserving refinement between a concurrent high-level source language and an implementation that uses low-level shared memory primitives. ... More

Sketching for Latent Dirichlet-Categorical ModelsOct 02 2018Recent work has explored transforming data sets into smaller, approximate summaries in order to scale Bayesian inference. We examine a related problem in which the parameters of a Bayesian model are very large and expensive to store in memory, and propose ... More

Augur: a Modeling Language for Data-Parallel Probabilistic InferenceDec 12 2013Jun 10 2014It is time-consuming and error-prone to implement inference procedures for each new probabilistic model. Probabilistic programming addresses this problem by allowing a user to specify the model and having a compiler automatically generate an inference ... 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

Generically large nongaussianity in small multifield inflationFeb 09 2015Jul 14 2015If forthcoming measurements of cosmic photon polarization restrict the primordial tensor-to-scalar ratio to $r < 0.01$, small field inflation will be a principal candidate for the origin of the universe. Here we show that small multifield inflation, without ... More

Littlewood-Paley functionals on graphsApr 04 2014Jun 09 2015Let $\Gamma$ be a graph equipped with a Markov operator $P$. We introduce discrete fractional Littlewood-Paley square functionals and prove their $L^p$-boundedness under various geometric assumptions on $\Gamma$.

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

Higher zigzag algebrasNov 02 2017Feb 26 2018Given any Koszul algebra of finite global dimension one can define a new algebra, which we call a higher zigzag algebra, as a twisted trivial extension of the Koszul dual of our original algebra. If our original algebra is the path algebra of a quiver ... 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

Containment in (s,t)-core PartitionsSep 12 2008We introduce the idea of (s,t)-closure and delta-sets and show that (s,t)-closed beta-sets which are contained set-wise in (s,t)-closed delta-sets are also contained partition-wise. This implies the maximal (s,t)-core partition theorem of Olsson and Stanton. ... 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

Holomorphy of adjoint $L$ functions for quasisplit A2Oct 31 2016Nov 29 2016We study the poles of the twisted adjoint L function of a generic cuspidal automorphic representation of GL(3) or a quasisplit unitary group using a method pioneered by Ginzburg and Jiang and based on the theory of integral representations.

Period three actions on lens spacesNov 02 2003Feb 04 2008We show that a free period three action on a lens space is standard, i.e. the quotient is homeomorphic to a lens space. This is an extension of the result for period three actions on the three-sphere, arXiv:math.GT/0204077, by the author and J. Hyam Rubinstein. ... 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

Determinants, Choices and CombinatoricsMar 26 2018Sep 19 2018We prove a formula which generalizes both Onn's colorful determinantal formula, related to Rota's basis conjecture, and Svrtan's $n!$ formula, related to the Atiyah-Sutcliffe problem. In some cases, our formula allows us to prove some results similar ... 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

Functional calculus and joint torsion of pairs of almost commuting operatorsSep 22 2014This paper investigates the transformation of determinants of pairs of Fredholm operators with trace class commutators. We study the extent to which the functional calculus commutes, modulo operator ideals, with projections in a finitely summable Fredholm ... 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

Failure of the parametric h-principle for maps with prescribed jacobianDec 06 2005Let M and N be closed n-dimensional manifolds, and equip N with a volume form \sigma. Let \mu be an exact n-form on M. Arnold then asked the question: When can one find a map f:;N such that f*\sigma=\mu. In 1973 Eliashberg and Gromov showed that this ... More

Shapley regressions: A framework for statistical inference on machine learning modelsMar 11 2019Machine learning models often excel in the accuracy of their predictions but are opaque due to their non-linear and non-parametric structure. This makes statistical inference challenging and disqualifies them from many applications where model interpretability ... 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

Cohomology theories with supportsJul 11 2012For $E$ a presheaf of spectra on the category of smooth $k$-schemes satisfying Nisnevich excision, we prove that the canonical map from the algebraic singular complex of the theory $E$ with quasi-finite supports to the theory $E$ with supports intersecting ... More

Towards a sharp converse of Wall's theorem on arithmetic progressionsNov 19 2017Wall's theorem on arithmetic progressions says that if $0.a_1a_2a_3\dots$ is normal, then for any $k,\ell\in \mathbb{N}$, $0.a_ka_{k+\ell}a_{k+2\ell}\dots$ is also normal. We examine a converse statement and show that if $0.a_{n_1}a_{n_2}a_{n_3}\dots$ ... More

Lattice Formulation of ${\cal N} = 2^*$ Yang-MillsOct 26 2017Jun 01 2018We formulate ${\cal N} = 2^*$ supersymmetric Yang-Mills theory on a Euclidean spacetime lattice using the method of topological twisting. The lattice formulation preserves one scalar supersymmetry charge at finite lattice spacing. The lattice theory is ... More

The weak null condition and global existence using the p-weighted energy methodAug 29 2018Sep 30 2018We prove global existence for solutions arising from small initial data for a large class of quasilinear wave equations satisfying the `weak null condition' of Lindblad and Rodnianski, significantly enlarging upon the class of equations for which global ... More

About the quadratic Szeg{ö} hierarchyApr 04 2018The purpose of this paper is to go further into the study of the quadratic Szeg{\"o} equation, which is the following Hamiltonian PDE : $i \partial\_t u = 2J\Pi(|u|^2)+\bar{J}u^2$, $u(0, \cdot)=u\_0$, where $\Pi$ is the Szeg{\"o} projector onto nonnegative ... More

Autonomous Systems -- An Architectural CharacterizationNov 26 2018The concept of autonomy is key to the IoT vision promising increasing integration of smart services and systems minimizing human intervention. This vision challenges our capability to build complex open trustworthy autonomous systems. We lack a rigorous ... 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

Small Scale Behavior of Cosmic String NetworksMar 04 2008The evolution of cosmic string networks is an interesting dynamical problem. The equations governing these networks are classical and fully specified, but the length scale at which cosmic string loops form has been uncertain to tens of orders of magnitude. ... More

Monopoles, Duality, and String TheoryApr 04 2003Dirac showed that the existence of magnetic monopoles would imply quantization of electric charge. I discuss the converse, and propose two `principles of completeness' which I illustrate with various examples.

Quantum Gravity at the Planck LengthDec 15 1998I describe our understanding of physics near the Planck length, in particular the great progress in the last four years in string theory. These are lectures presented at the 1998 SLAC Summer Institute.

Strings and QCD?Oct 08 1992Is large-$N$ QCD equivalent to a string theory? Maybe, maybe not. I review various attempts to answer the question.

Random Quantum Circuits and Pseudo-Random Operators: Theory and ApplicationsOct 12 2004Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and generated on ... More

Learning continuous Q-Functions using generalized Benders cutsFeb 20 2019Q-functions are widely used in discrete-time learning and control to model future costs arising from a given control policy, when the initial state and input are given. Although some of their properties are understood, Q-functions generating optimal policies ... More