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A Categorification of the Vandermonde DeterminantNov 20 2018Nov 26 2018In the spirit of Bar Natan's construction of Khovanov homology, we give a categorification of the Vandermonde determinant. Given a sequence of positive integers $\vec{x}=(x_1,...,x_n)$, we construct a commutative diagram in the shape of the Bruhat order ... More

Torsion in thin regions of Khovanov homologyMar 13 2019In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links, that is links whose Khovanov homology is supported on two adjacent diagonals, are known to only contain $\mathbb{Z}_2$ torsion. In this paper, we ... More

Extending the Harper Identity to Iterated Belief ChangeApr 19 2016The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change ... More

The Smith and critical groups of Paley graphsJan 31 2014Sep 30 2014There is a Paley graph for each prime power $q$ such that $q\equiv 1\pmod 4$. The vertex set is the field $\mathbb Fq$ and two vertices $x$ and $y$ are joined by an edge if and only if $x-y$ is a nonzero square of $\mathbb Fq$. We compute the Smith normal ... More

Length scale for the onset of Fickian diffusion in supercooled liquidsSep 16 2004Jan 25 2005The interplay between self-diffusion and excitation lines in space-time was recently studied in kinetically constrained models to explain the breakdown of the Stokes-Einstein law in supercooled liquids. Here, we further examine this interplay and its ... More

Spectrum of a Feinberg-Zee Random Hopping MatrixOct 04 2011Dec 23 2011This paper provides a new proof of a theorem of Chandler-Wilde, Chonchaiya and Lindner that the spectra of a certain class of infinite, random, tridiagonal matrices contain the unit disc almost surely. It also obtains an analogous result for a more general ... More

On Symmetries of the Feinberg-Zee Random Hopping MatrixSep 02 2015Nov 27 2016In this paper we study the spectrum $\Sigma$ of the infinite Feinberg-Zee random hopping matrix, a tridiagonal matrix with zeros on the main diagonal and random $\pm 1$'s on the first sub- and super-diagonals; the study of this non-selfadjoint random ... More

On Measuring Social Biases in Sentence EncodersMar 25 2019The Word Embedding Association Test shows that GloVe and word2vec word embeddings exhibit human-like implicit biases based on gender, race, and other social constructs (Caliskan et al., 2017). Meanwhile, research on learning reusable text representations ... More

Calibration for Stratified Classification ModelsOct 31 2017In classification problems, sampling bias between training data and testing data is critical to the ranking performance of classification scores. Such bias can be both unintentionally introduced by data collection and intentionally introduced by the algorithm, ... More

Regularization Effect of Fast Gradient Sign Method and its GeneralizationOct 27 2018Oct 30 2018Fast Gradient Sign Method (FGSM) is a popular method to generate adversarial examples that make neural network models robust against perturbations. Despite its empirical success, its theoretical property is not well understood. This paper develops theory ... More

Keldysh technique and non-linear sigma-model: basic principles and applicationsJan 23 2009Apr 27 2009The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of underlying microscopic ... More

Coulomb drag at zero temperatureOct 08 2007We show that the Coulomb drag effect exhibits saturation at small temperatures, when calculated to the third order in the interlayer interactions. The zero-temperature transresistance is inversely proportional to the third power of the dimensionless sheet ... More

Keldysh Ginzburg-Landau action of fluctuating superconductorsJun 19 2007Sep 24 2007We derive Ginzburg-Landau action by systematically integrating out electronic degrees of freedom in the framework of the Keldysh nonlinear sigma-model of disordered superconductors. The resulting Ginzburg-Landau functional contains a nonlocal $\Delta$-dependent ... More

From fifty years ago, the birth of modern liquid-state scienceSep 15 2016The story told in this autobiographical perspective begins fifty years ago at the 1967 Gordon Research Conference on the Physics and Chemistry of Liquids. It traces developments in liquid-state science from that time, including contributions from the ... More

Interpolation of Hilbert and Sobolev Spaces: Quantitative Estimates and CounterexamplesApr 14 2014Aug 19 2014This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is ... More

Illusions of phase coexistence: Comments on "Metastable liquid-liquid transition ..." by J. C. Palmer et al., Nature 510, 385 (2014)Jul 25 2014Aug 20 2014The recent paper cited above claims that a molecular simulation of one specific model of supercooled water establishes a stable interface separating two metastable liquid phases, which would imply the existence of metastable two-liquid criticality for ... More

Causes and Consequences of genetic background effects illuminated by integrative genomic analysisSep 02 2013Feb 01 2014The phenotypic consequences of individual mutations are modulated by the wild type genetic background in which they occur.Although such background dependence is widely observed, we do not know whether general patterns across species and traits exist, ... More

Long-time existence for Yang-Mills flowOct 11 2016We establish that finite-time singularities do not occur in four-dimensional Yang-Mills flow, confirming the conjecture of Schlatter, Struwe, and Tahvildar-Zadeh. The proof relies on a weighted energy identity and sharp decay estimates in the neck region. ... More

Characteristic Formulas 50 Years Later (An Algebraic Account)Jul 22 2014The Jankov (characteristic) formulas were introduced by V.Jankov fifty tears ago in 1963. Nowadays the Jankov (or frame) formulas are used in virtually every branch of propositional logic: intermediate, modal, fuzzy, relevant, many-valued, etc. All these ... More

New Algorithms for Solving Tropical Linear SystemsSep 20 2013The problem of solving tropical linear systems, a natural problem of tropical mathematics, has already proven to be very interesting from the algorithmic point of view: it is known to be in $NP\cap coNP$ but no polynomial time algorithm is known, although ... More

Shear viscosity of CFT plasma at finite couplingApr 19 2008May 29 2008We present evidence for the universality of the shear viscosity of conformal gauge theory plasmas beyond infinite coupling. We comment of subtleties of computing the shear viscosity in effective models of gauge/gravity correspondence rather than in string ... More

The Dirichlet Series for the Exterior Square $L$-function on GL(n)Sep 26 2009We present an elementary derivation of the Jacquet-Shalika construction for the exterior square L-function on GL(n), as a classical Dirichlet series in the Fourier coefficients $A(m_1,...,m_{n-1})$.

Black hole spectra in holography: consequences for equilibration of dual gauge theoriesJan 19 2015May 07 2015For a closed system to equilibrate from a given initial condition there must exist an equilibrium state with the energy equal to the initial one. Equilibrium states of a strongly coupled gauge theory with a gravitational holographic dual are represented ... More

Higgs PhysicsDec 14 2014With the discovery of the Higgs, we have access to a plethora of new physical processes that allow us to further test the SM and beyond. We show a convenient way to parametrize these physics using an effective theory for Higgs couplings, discussing the ... More

Boson Sampling is Robust to Small Errors in the Network MatrixDec 08 2014We demonstrate the robustness of BosonSampling to imperfections in the linear optical network that cause a small deviation in the matrix it implements. We show that applying a noisy matrix $\tilde{U}$ that is within $\epsilon$ of the desired matrix $U$ ... More

1D accretion discs around eccentric planets: observable near-infrared variabilityNov 04 2014Dec 29 2014I present the results of 1D models of circumplanetary discs around planets on eccentric orbits. I use a classical viscous heating model to calculate emission fluxes at the wavelengths targeted by the NIRCam instrument on JWST, and compare the variability ... More

AdS boson stars in string theoryOct 28 2015Boson stars are stationary soliton-like gravitational configurations supported by a complex scalar field charged under the global $U(1)$ symmetry. We discuss properties of boson stars in type IIB supergravity approximation to string theory. A notable ... More

Classical Liouville Theory and the Microscopic Interpretation of Black Hole EntropyMar 18 2004In this paper we will give a general introduction to the role of conformal symmetry in the microscopic interpretation of black hole entropy and then compute the entropy of a Schwarzschild black hole by finding a classical central charge of the Virasoro ... More

On Factoring an Operator Using Elements of its KernelNov 25 2015A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to other types of operators. In place of the derivation $\partial$ ... More

From rational billiards to dynamics on moduli spacesApr 30 2015Jul 26 2015This short expository note gives an elementary introduction to the study of dynamics on certain moduli spaces, and in particular the recent breakthrough result of Eskin, Mirzakhani, and Mohammadi. We also discuss the context and applications of this result, ... More

Schwarz triangle mappings and Teichmüller curves: the Veech-Ward-Bouw-Möller curvesMar 13 2012Jan 24 2013We study a family of Teichm\"uller curves T(n,m) constructed by Bouw and M\"oller, and previously by Veech and Ward in the cases n=2,3. We simplify the proof that T(n,m) is a Teichm\"uller curve, avoiding the use M\"oller's characterization of Teichm\"uller ... More

Gromov's measure equivalence and rigidity of higher rank latticesNov 01 1999In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are Measure Equivalent; this is one of the ... More

On (Non)Supermodularity of Average Control EnergySep 27 2016Oct 05 2016Given a linear system, we consider the expected energy to move from the origin to a uniformly random point on the unit sphere as a function of the set of actuated variables. We show this function is not necessarily supermodular, correcting some claims ... More

Stochastic selection processesNov 17 2015We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been studied on a case-by-case ... More

The Reasonable Effectiveness of Mathematics in the Physical SciencesDec 24 2012Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is discovered; Logicism ... More

Weak measurements of trajectories in quantum systems: classical, Bohmian and sum over pathsNov 14 2014Jun 11 2015Weak values, obtained from weak measurements, attempt to describe the properties of a quantum system as it evolves from an initial to a final state, without practically altering this evolution. Trajectories can be defined from weak measurements of the ... More

Interpolation and embeddings of weighted tent spacesSep 18 2015Feb 09 2016Given a metric measure space $X$, we consider a scale of function spaces $T^{p,q}_s(X)$, called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on $X$ we identify ... More

Super-Replication of the Best Pairs Trade in HindsightOct 04 2018Oct 17 2018For a market with $m$ assets and $T$ discrete trading sessions, Ordentlich and Cover (1998) found that the `Cost of Achieving the Best Rebalancing Rule in Hindsight' is $p(T,m)=\sum\limits_{n_1+\cdot\cdot\cdot+n_m=T}\binom{T}{n_1,...,n_m}(n_1/T)^{n_1}\cdot\cdot\cdot(n_m/T)^{n_m}$. ... More

Discriminants and Quasi-symmetryNov 24 2017This paper gives a geometric interpretation of the notion of quasi-symmetric representation and uses this to show that the discriminant locus associated to such a representation is a hyperplane arrangement. Moreover, we identify this hyperplane arrangement, ... More

Mean Curvature Motion of Graphs with Constant Contact Angle and Moving BoundariesMay 29 2008We consider the motion by mean curvature of an $n$-dimensional graph over a time-dependent domain in $\mathbb{R}^n$, intersecting $\mathbb{R}^n$ at a constant angle. In the general case, we prove local existence for the corresponding quasilinear parabolic ... More

Information Rates and post-FEC BER Prediction in Optical Fiber CommunicationsNov 28 2016Information-theoretic metrics to analyze optical fiber communications systems with binary and nonbinary soft-decision FEC are reviewed. The numerical evaluation of these metrics in both simulations and experiments is also discussed. Ready-to-use closed-form ... More

Compact groups and absolute extensorsAug 15 1999We discuss compact Hausdorff groups from the point of view of the general theory of absolute extensors. In particular, we characterize the class of simple, connected and simply connected compact Lie groups as AE(2)-groups the third homotopy group of which ... More

Quantum tasks in holographyFeb 19 2019Mar 05 2019We consider an operational restatement of the holographic principle, which we call the principle of asymptotic quantum tasks. Asymptotic quantum tasks are quantum information processing tasks with inputs given and outputs required on points at the boundary ... More

A volume-based approach to the multiplicative ergodic theorem on Banach spacesFeb 23 2015Dec 07 2015A volume growth-based proof of the Multiplicative Ergodic Theorem for Banach spaces is presented, following the approach of Ruelle for cocycles acting on a Hilbert space. As a consequence, we obtain a volume growth interpretation for the Lyapunov exponents ... More

Extremal Numbers for 2 to 1 Directed Hypergraphs with Two Edges Part II: The Degenerate CasesJul 18 2016Let a 2 to 1 directed hypergraph be a 3-uniform hypergraph where every edge has two tail vertices and one head vertex. For any such directed hypergraph F let the nth extremal number of F be the maximum number of edges that any directed hypergraph on n ... More

Extremal Numbers for 2 to 1 Directed Hypergraphs with Two Edges Part I: The Nondegenerate CasesJul 18 2016Let a 2 to 1 directed hypergraph be a 3-uniform hypergraph where every edge has two tail vertices and one head vertex. For any such directed hypergraph F let the nth extremal number of F be the maximum number of edges that any directed hypergraph on n ... More

Regression adjustments for estimating the global treatment effect in experiments with interferenceAug 27 2018Mar 05 2019Standard estimators of the global average treatment effect can be biased in the presence of interference. This paper proposes regression adjustment estimators for removing bias due to interference in Bernoulli randomized experiments. We use a fitted model ... More

Multilinear Superhedging of Lookback OptionsOct 04 2018In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $\theta(\cdot)$) and "nature," who picks the matrix $X$ of gross-returns of all stocks in all periods. Their ... More

Reflection identities of harmonic sums of weight fourSep 12 2018We consider the reflection identities for harmonic sums at weight four. We decompose a product of two harmonic sums with mixed pole structure into a linear combination of terms each having a pole at either negative or positive values of the argument. ... More

Generators for Coulomb branches of quiver gauge theoriesMar 18 2019We study the Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories, focusing on the generators for their quantized coordinate rings. We show that there is a surjective map from a shifted Yangian onto the quantized Coulomb branch, once the deformation ... More

Genus From Sandpile Torsor AlgorithmApr 20 2018Previous work by Chan-Church-Grochow and Baker-Wang showed that the structure of the output of the rotor routing or Bernardi process can be used to distinguish a planar ribbon graph from a nonplanar ribbon graph. Here, we show that the structure of the ... More

Linear Flows on $κ$-SolenoidsJun 24 1999Linear flows on inverse limits of tori are defined and it is shown that two linear flows on an inverse limit of tori are equivalent if and only if there is an automorphism of the inverse limit generating the equivalence.

On the Inapproximability of the Discrete Witsenhausen ProblemApr 11 2019We consider a discrete version of the Witsenhausen problem where all random variables are bounded and take on integer values. Our main goal is to understand the complexity of computing good strategies given the distributions for the initial state and ... More

${\cal N}=2^*$ de Sitter vacuum from localization?Apr 22 2019Holographic correspondence is used to study properties of $dS_4$ vacuum of mass deformed ${\cal N}=4$ supersymmetric Yang-Mills theory - the ${\cal N}=2^*$ gauge theory. Upon analytical continuation $dS_4\to S^4$ the model (with appropriate background ... More

Pseudocompact paratopological groups that are topologicalJun 08 2014We obtain necessary and sufficient conditions when a pseudocompact paratopological group is topological. (2-)pseudocompact and countably compact paratopological groups that are not topological are constructed. It is proved that each 2-pseudocompact paratopological ... More

Factorization of a Matrix Differential Operator Using Functions in its KernelSep 17 2015Just as knowing some roots of a polynomial allows one to factor it, a well-known result provides a factorization of any scalar differential operator given a set of linearly independent functions in its kernel. This note provides a straight-forward generalization ... More

Uhlenbeck compactness for Yang-Mills flow in higher dimensionsDec 28 2018Feb 08 2019This paper proves a general Uhlenbeck compactness theorem for sequences of solutions of Yang-Mills flow on Riemannian manifolds of dimension $n \geq 4,$ including rectifiability of the singular set.

Admissibility in Positive LogicsOct 27 2016The paper studies admissibility of multiple-conclusion rules in the positive logics. Using modification of a method used by M.~Wajsberg in the proof of the separation theorem, it is shown that the problem of admissibility in positive logics is equivalent ... More

Factor equivalence of Galois modules and regulator constantsSep 17 2012Jun 21 2013We compare two approaches to the study of Galois module structures: on the one hand factor equivalence, a technique that has been used by Fr\"ohlich and others to investigate the Galois module structure of rings of integers of number fields and of their ... More

Asymptotic cohomological functions on projective varietiesJan 27 2005In this paper we define certain analogues of the volume of a divisor - called asymptotic cohomological functions - and investigate their behaviour on the Neron--Severi space. We establish that asymptotic cohomological functions are invariant with respect ... More

On the Picard group of a Delsarte surfaceJul 01 2013We suggest an algorithm computing, in some cases, an explicit generating set for the N\'eron--Severi lattice of a Delsarte surface.

Plane sextics with a type $\mathbf{E}_6$ singular pointJul 27 2009Jan 25 2010We give a classification up to equisingular deformation and compute the fundamental groups of maximizing plane sextics with a type $\mathbf{E}_6$ singular point.

Fundamental groups of symmetric sextics. IIMay 15 2008We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with the set of inner singularities $2\bold{A}_8$ or $\bold{A}_{17}$. We also compute the fundamental groups of a number of other sextics, both of and not of ... More

Zariski $k$-plets via dessins d'enfantsOct 01 2007Apr 17 2008We construct exponentially large collections of pairwise distinct equisingular deformation families of irreducible plane curves sharing the same sets of singularities. The fundamental groups of all curves constructed are abelian.

Tent spaces over metric measure spaces under doubling and related assumptionsMay 10 2013Sep 25 2013In this article, we define the Coifman-Meyer-Stein tent spaces $T^{p,q,\alpha}(X)$ associated with an arbitrary metric measure space $(X,d,\mu)$ under minimal geometric assumptions. While gradually strengthening our geometric assumptions, we prove duality, ... More

On the unit distance problemSep 23 2017The Erd\H os unit distance conjecture in the plane says that the number of pairs of points from a point set of size $n$ separated by a fixed (Euclidean) distance is $\leq C_{\epsilon} n^{1+\epsilon}$ for any $\epsilon>0$. The best known bound is $Cn^{\frac{4}{3}}$. ... More

The Alexander module of a trigonal curve. IIFeb 17 2012Sep 19 2012We complete the enumeration of the possible roots of the Alexander polynomial (both conventional and over finite fields) of a trigonal curve. The curves are not assumed proper or irreducible.

Poisson--Dirichlet distribution for random Belyi surfacesJan 19 2005Nov 21 2006Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a ``typical'' compact Riemann surface of large genus based on compactifying ... More

On Setting of Heat-and-Mass Transfer Problems under Directed CrystallizationAug 11 2011So far the problem of interface behavior upon phase transition has not yet acquired a satisfactory mathematical formulation due to a variety of the physical phenomena involved. Analytical solutions exist only for elementary problems describing the free ... More

Numerical homotopy continuation for control and online identification of nonlinear systems: the survey of selected resultsJan 26 2013The article gives an overview of the parameter numerical continuation methodology applied to setpoint control and parameter identification of nonlinear systems. The control problems for affine systems as well as general (nonaffine) nonlinear systems are ... More

How Einstein Discovered Dark EnergyNov 22 2012In 1917 Einstein published his Cosmological Considerations Concerning the General Theory of Relativity. In it was the first use of the cosmological constant. Shortly thereafter Schr\"odinger presented a note providing a solution to these same equations ... More

The Negative Cycle Vectors of Signed Complete GraphsDec 30 2015A signed graph is a graph where the edges are assigned labels of either "$+$" or "$-$". The sign of a cycle in the graph is the product of the signs of its edges. We equip each signed complete graph with a vector whose entries are the number of negative ... More

The Local-Global Principle for Integral Soddy Sphere PackingsAug 27 2012Fix an integral Soddy sphere packing P. Let K be the set of all curvatures in P. A number n is called represented if n is in K, that is, if there is a sphere in P with curvature equal to n. A number n is called admissible if it is everywhere locally represented, ... More

Duality symmetry of BFKL equation: reggeized gluons vs color dipolesNov 27 2009We show that the duality symmetry of the BFKL equation can be interpreted as a symmetry under rotation of the BFKL Kernel in the transverse space from s-channel (color dipole model) to t-channel (reggeized gluon formulation). We argue that the duality ... More

Integer Lattice Gases at EquilibriumDec 14 2005Jan 24 2006Integer lattice gas automata can be utilized as building blocks in statistical mechanics. The presented deterministic and reversible automaton generates semiclassical statistical distributions. A possible approach to Bose-Einstein statistics from cellular ... More

Smooth models of singular $K3$-surfacesAug 24 2016Sep 05 2016We show that the classical Fermat quartic has exactly three smooth spatial models. As a generalization, we give a classification of smooth spatial (as well as some other) models of singular $K3$-surfaces of small discriminant. As a by-product, we observe ... More

On (Non)Supermodularity of Average Control EnergySep 27 2016Given a linear system, we consider the expected energy to move from the origin to a uniformly random point on the unit sphere as a function of the set of actuated variables. We show this function is not necessarily supermodular, correcting some claims ... More

A model-insensitive determination of First-hitting-time densities with Application to Equity default-swapsFeb 12 2010Mar 29 2010Equity default-swaps pay the holder a fixed amount of money when the underlying spot level touches a (far-down) barrier during the life of the instrument. While most pricing models give reasonable results when the barrier lies within the range of liquidly ... More

Critical phenomena in N=4 SYM plasmaMay 05 2010Strongly coupled N=4 supersymmetric Yang-Mills plasma at finite temperature and chemical potential for an R-symmetry charge undergoes a second order phase transition. We demonstrate that this phase transition is of the mean field theory type. We explicitly ... More

Gauge theories on hyperbolic spaces and dual wormhole instabilitiesFeb 21 2004Jul 26 2004We study supergravity duals of strongly coupled four dimensional gauge theories formulated on compact quotients of hyperbolic spaces. The resulting background geometries are represented by Euclidean wormholes, which complicates establishing the precise ... More

Compactifications of the N=2^* flowFeb 14 2003In hep-th/0004063 Pilch and Warner (PW) constructed N=2 supersymmetric RG flow corresponding to the mass deformation of the N=4 SU(N) Yang-Mills theory. In this paper we present exact deformations of PW flow when the gauge theory 3-space is compactified ... More

Finite temperature resolution of the Klebanov-Tseytlin singularityNov 16 2000Feb 19 2001Naked singularities in the gravitational backgrounds dual to gauge theories can be hidden behind the black hole horizon. We present an exact black hole solution in the Klebanov-Tseytlin geometry [hep-th/0002159]. Our solution realizes Maldacena dual of ... More

Violation of the holographic bulk viscosity boundOct 01 2011Motivated by gauge theory/string theory correspondence, a lower bound on the bulk viscosity of strongly coupled gauge theory plasma was proposed in arXiv:0708.3459. We consider strongly coupled N=4 supersymmetric Yang-Mills plasma compactified on a two-manifold ... More

Chiral symmetry breaking in cascading gauge theory plasmaDec 10 2010Nov 12 2013N=1 supersymmetric SU(K+P)xSU(K) cascading gauge theory of Klebanov et.al [1,2] undergoes a first-order finite temperature confinement/deconfinement phase transition at T_c=0.6141111(3) Lambda, where Lambda is the strong coupling scale of the theory. ... More

On universality of stress-energy tensor correlation functions in supergravityAug 11 2004Jan 21 2005Using the Minkowski space AdS/CFT prescription we explicitly compute in the low-energy limit the two-point correlation function of the boundary stress-energy tensor in a large class of type IIB supergravity backgrounds with a regular translationally invariant ... More

Gauge/string correspondence in curved spaceNov 15 2002Jan 08 2003We discuss Gubser-Klebanov-Polyakov proposal for the gauge/string theory correspondence for gauge theories in curved space. Specifically, we consider Klebanov-Tseytlin cascading gauge theory compactified on S^3. We explain regime when this gauge theory ... More

A Conical Tear Drop as a Vacuum-Energy Drain for the Solution of the Cosmological Constant ProblemJun 02 2004Feb 01 2005We propose a partial solution to the cosmological constant problem by using the simple observation that a three-brane in a six-dimensional bulk is flat. A model is presented in which Standard Model vacuum energy is always absorbed by the transverse space. ... More

Relativistic Superluminal NeutrinosSep 28 2011Oct 13 2011We present a possible solution to the reported OPERA anomaly for the speed of neutrinos, based on the idea that it is a local effect caused by a scalar field sourced by the earth. The coupling of the scalar to neutrinos effectively changes the background ... More

Universality of small black hole instability in AdS/CFTSep 25 2015$AdS_5$ type IIb supergravity compactifications on five-dimensional Einstein manifolds ${\cal V}_5$ realize holographic duals to four-dimensional conformal field theories. Black holes in such geometries are dual to thermal states in these CFTs. When black ... More

Eigenvalue Clustering, Control Energy, and Logarithmic CapacityNov 01 2015Apr 23 2016We prove two bounds showing that if the eigenvalues of a matrix are clustered in a region of the complex plane then the corresponding discrete-time linear system requires significant energy to control. A curious feature of one of our bounds is that the ... More

The "Most informative boolean function" conjecture holds for high noiseOct 29 2015We prove the "Most informative boolean function" conjecture of Courtade and Kumar for high noise $\epsilon \ge 1/2 - \delta$, for some absolute constant $\delta > 0$. Namely, if $X$ is uniformly distributed in $\{0,1\}^n$ and $Y$ is obtained by flipping ... More

The Debris Disk Fraction for M-dwarfs in Nearby, Young, Moving GroupsJan 25 2016I present the first substantial work to measure the fraction of debris disks for M-dwarfs in nearby moving groups (MGs). Utilising the $AllWISE$ IR catalog, 17 out of 151 MG members are found with an IR photometric excess indicative of disk structure. ... More

A Meta-Logic of Inference Rules: SyntaxNov 27 2014This work was intended to be an attempt to introduce the meta-language for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and especially the ... More

Z(N) wall junctions: Monopole fossils in hot QCDFeb 27 2001We point out that the effective action of hot Yang--Mills theories has semi-classical solutions, which are naturally identified with monopole world lines, ``frozen'' into the short imaginary time dimension. The solutions look like wall junctions: lines ... More

n-Schur Functions and Determinants on an Infinite GrassmannianNov 11 1998A set of functions is defined which is indexed by a positive integer $n$ and partitions of integers. The case $n=1$ reproduces the standard Schur polynomials. These functions are seen to arise naturally as a determinant of an action on the frame bundle ... More

Description of Black Hole Microstates by Means of a Free Affine-Scalar FieldMay 13 2004In this article we will investigate the origin of central extensions in the Poisson algebra of charges, which arise in the dimensionally reduced theories describing black holes. We will see that the equations of motion and constraints arising from the ... More

All-orders wormhole vertex operators from the Wheeler-deWitt equationJan 29 1992Jan 30 1992We discuss the calculation of semi-classical wormhole vertex operators from wave functions which satisfy the Wheeler-deWitt equation and momentum constraints, together with certain `wormhole boundary conditions'. We consider a massless minimally coupled ... More

The field of definition of affine invariant submanifolds of the moduli space of abelian differentialsOct 17 2012Apr 03 2014The field of definition of an affine invariant submanifold M is the smallest subfield of the reals such that M can be defined in local period coordinates by linear equations with coefficients in this field. We show that the field of definition is equal ... More

Sums of Adjoint OrbitsOct 09 2009Mar 26 2011Let G be a real compact connected simple Lie group, and g its Lie algebra. We study the problem of determining, from root data, when a sum of adjoint orbits in g, or a product of conjugacy classes in G, contains an open set. Our general methods allow ... More

The Tits Alternative: An Elementary ExpositionOct 09 2009Nov 25 2009This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.