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Towards Neural Knowledge DNAFeb 27 2016In this paper, we propose the Neural Knowledge DNA, a framework that tailors the ideas underlying the success of neural networks to the scope of knowledge representation. Knowledge representation is a fundamental field that dedicate to representing information ... More

Uniform Correlation Mixture of Bivariate Normal Distributions and Hypercubically-contoured Densities That Are Marginally NormalNov 19 2015The bivariate normal density with unit variance and correlation $\rho$ is well-known. We show that by integrating out $\rho$, the result is a function of the maximum norm. The Bayesian interpretation of this result is that if we put a uniform prior over ... More

Calibrating 100 Years of Polar Faculae Measurements: Implications for the Evolution of the Heliospheric Magnetic FieldMar 02 2013Although the Sun's polar magnetic fields are thought to provide important clues for understanding the 11-year sunspot cycle, including the observed variations of its amplitude and period, the current database of high-quality polar-field measurements spans ... More

Discrete Envy-free Division of Necklaces and MapsOct 07 2015We study the discrete variation of the classical cake-cutting problem where n players divide a 1-dimensional cake with exactly (n-1) cuts, replacing the continuous, infinitely divisible "cake" with a necklace of discrete, indivisible "beads." We focus ... More

Accelerated High-Resolution Photoacoustic Tomography via Compressed SensingApr 30 2016Sep 28 2016Current 3D photoacoustic tomography (PAT) systems offer either high image quality or high frame rates but are not able to deliver high spatial and temporal resolution simultaneously, which limits their ability to image dynamic processes in living tissue. ... More

Intermodulation in Nonlinear SQUID Metamaterials: Experiment and TheoryJun 29 2016The response of nonlinear metamaterials and superconducting electronics to two-tone excitation is critical for understanding their use as low-noise amplifiers and tunable filters. A new setting for such studies is that of metamaterials made of radio frequency ... More

Independent Emission and Absorption Abundances for Planetary NebulaeJan 14 2008Emission-line abundances have been uncertain for more than a decade due to unexplained discrepancies in the relative intensities of the forbidden lines and weak permitted recombination lines in planetary nebulae (PNe) and H II regions. The observed intensities ... More

Calibrated Percentile Double Bootstrap For Robust Linear Regression InferenceNov 01 2015Jun 16 2016We consider inference for the parameters of a linear model when the covariates are random and the relationship between response and covariates is possibly non-linear. Conventional inference methods such as z intervals perform poorly in these cases. We ... More

Enhancing Compressed Sensing Photoacoustic Tomography by Simultaneous Motion EstimationFeb 14 2018A crucial limitation of current high-resolution 3D photoacoustic tomography (PAT) devices that employ sequential scanning is their long acquisition time. In previous work, we demonstrated how to use compressed sensing techniques to improve upon this: ... More

Geometric Endoscopy and Mirror SymmetryOct 31 2007Apr 05 2008The geometric Langlands correspondence has been interpreted as the mirror symmetry of the Hitchin fibrations for two dual reductive groups. This mirror symmetry, in turn, reduces to T-duality on the generic Hitchin fibers, which are smooth tori. In this ... More

Acoustic Wave Field Reconstruction from Compressed Measurements with Application in Photoacoustic TomographySep 09 2016We present a method for the recovery of compressively sensed acoustic fields using patterned, instead of point-by-point, detection. From a limited number of such compressed measurements, we propose to reconstruct the field on the sensor plane in each ... More

Superstring Perturbation Theory RevisitedSep 25 2012Nov 01 2012Perturbative superstring theory is revisited, with the goal of giving a simpler and more direct demonstration that multi-loop amplitudes are gauge-invariant (apart from known anomalies), satisfy space-time supersymmetry when expected, and have the expected ... More

A Note On The Chern-Simons And Kodama WavefunctionsJun 18 2003Jun 19 2003Yang-Mills theory in four dimensions formally admits an exact Chern-Simons wavefunction. It is an eigenfunction of the quantum Hamiltonian with zero energy. It is known to be unphysical for a variety of reasons, but it is still interesting to understand ... More

New Perspectives on the Quest for UnificationDec 01 1998Synthesizing older ideas about the 1/N expansion in gauge theory, the quantum mechanics of black holes, and quantum field theory in Anti de Sitter space, a new correspondence between gauge theory and quantum gravity has illuminated both subjects.

Anti De Sitter Space And HolographyFeb 20 1998Apr 06 1998Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. ... More

On S-Duality in Abelian Gauge TheoryMay 31 1995U(1) gauge theory on ${\bf R}^4$ is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action of $SL(2,{\bf Z})$. In this paper, the duality is studied on a general four-manifold and it is shown ... More

On the Landau-Ginzburg Description of $N=2$ Minimal ModelsApr 07 1993Jul 09 1993The conjecture that $N=2$ minimal models in two dimensions are critical points of a super-renormalizable Landau-Ginzburg model can be tested by computing the path integral of the Landau-Ginzburg model with certain twisted boundary conditions. This leads ... More

On Black Holes In String TheoryNov 25 1991In these lecture notes from Strings `91, I briefly sketch the analogy between two dimensional black holes and the s-wave sector of four dimensional black holes, and the physical interest of the latter, particularly in the magnetically charged case.

Multi-Trace Operators, Boundary Conditions, And AdS/CFT CorrespondenceDec 31 2001Jan 04 2002We argue that multi-trace interactions in quantum field theory on the boundary of AdS space can be incorporated in the AdS/CFT correspondence by using a more general boundary condition for the bulk fields than has been considered hitherto. We illustrate ... More

The Cosmological Constant From The Viewpoint Of String TheoryFeb 29 2000Mar 01 2000The mystery of the cosmological constant is probably the most pressing obstacle to significantly improving the models of elementary particle physics derived from string theory. The problem arises because in the standard framework of low energy physics, ... More

Duality Relations Among Topological Effects In String TheoryDec 10 1999Dec 30 1999We explore two different problems in string theory in which duality relates an ordinary p-form in one theory to a self-dual (p+1)-form in another theory. One problem involves comparing D4-branes to M5-branes, and the other involves comparing the Ramond-Ramond ... More

Heterotic String Conformal Field Theory And A-D-E SingularitiesSep 30 1999Dec 10 1999We analyze the behavior of the heterotic string near an A-D-E singularity without small instantons. This problem is governed by a strongly coupled worldsheet conformal field theory, which, by a combination of O(alpha') corrections and worldsheet instantons, ... More

Small Instantons in String TheoryNov 04 1995A long-standing puzzle about the heterotic string has been what happens when an instanton shrinks to zero size. It is argued here that the answer at the quantum level is that an extra $SU(2)$ gauge symmetry appears that is supported in the core of the ... More

Geometric Langlands From Six DimensionsMay 17 2009Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally understood as ... More

Branes, Instantons, And Taub-NUT SpacesFeb 05 2009Jun 06 2009ALE and Taub-NUT (or ALF) hyper-Kahler four-manifolds can be naturally constructed as hyper-Kahler quotients. In the ALE case, this construction has long been understood in terms of D-branes; here we give a D-brane derivation in the Taub-NUT case. Likewise, ... More

Two-Dimensional Models With (0,2) Supersymmetry: Perturbative AspectsApr 08 2005Nov 02 2006Certain perturbative aspects of two-dimensional sigma models with (0,2) supersymmetry are investigated. The main goal is to understand in physical terms how the mathematical theory of ``chiral differential operators'' is related to sigma models. In the ... More

Shor's Factoring Algorithm and Modern Cryptography. An Illustration of the Capabilities Inherent in Quantum ComputersNov 25 2004The security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (i.e., conventional) computers. In 1994, however, Peter ... More

Process-Oriented Parallel Programming with an Application to Data-Intensive ComputingJul 21 2014We introduce process-oriented programming as a natural extension of object-oriented programming for parallel computing. It is based on the observation that every class of an object-oriented language can be instantiated as a process, accessible via a remote ... More

Update on Modular Non-Rigid Calabi-Yau ThreefoldsFeb 29 2008We review some recent results on the modularity of non-rigid Calabi-Yau threefolds.

An apparent paradox concerning the field of an ideal dipoleApr 05 2016Sep 08 2016The electric or magnetic field of an ideal dipole is known to have a Dirac delta function at the origin. The usual textbook derivation of this delta function is rather ad hoc and cannot be used to calculate the delta-function structure for higher multipole ... More

Inconsistency of Primitive Recursive ArithmeticSep 30 2015The aim of this work is to show that contemporary mathematics, including Peano arithmetic, is inconsistent, to construct firm foundations for mathematics, and to begin building on these foundations.

Relativistic hydrodynamic accretion onto a spherical black holeOct 27 1997Oct 16 2001This paper has been withdrawn by the author. A revised and expanded version is gr-qc/9907028 (Phys.Rev. D60 (1999) 104043).

Surface Tension Supported Floating of Heavy Objects: Why Elongated Bodies Float Better?Nov 04 2015Floating of bodies heavier than the supporting liquid is discussed. Floating of cylindrical, ellipsoidal bodies and rectangular plates possessing lateral dimensions smaller than the capillary length is treated. It is demonstrated that more elongated bodies ... More

Surface Instabilities and Patterning in Liquids: Exemplifications of the "Hairy Ball Theorem"Mar 24 2015Application of the "hairy ball theorem" to the analysis of the surface instabilities inherent for liquid/vapor interfaces is reported. When a continuous tangential velocity field exists on the surface of the liquid sample which is homeomorphic to a ball, ... More

Topological representations of matroidsAug 22 2002Sep 18 2002There is a one-to-one correspondence between geometric lattices and the intersection lattices of arrangements of homotopy spheres. When the arrangements are essential and fully partitioned, Zaslavsky's enumeration of the cells of the arrangement still ... More

A characterization of bipartite Leonard pairs using the notion of a tailAug 18 2013Let $V$ denote a vector space with finite positive dimension. We consider an ordered pair of linear transformations $A: V\rightarrow V$ and $A^*: V\rightarrow V$ that satisfy (i) and (ii) below. (i) There exists a basis for $V$ with respect to which the ... More

On Types of Observables in Constrained TheoriesApr 19 2016The Kuchar observables notion is shown to apply only to a limited range of theories. Relational mechanics, slightly inhomogeneous cosmology and supergravity are used as examples that require further notions of observables. A suitably general notion of ... More

Problem of Time and Background Independence: the Individual FacetsSep 14 2014I lay out the problem of time facets as arising piecemeal from a number of aspects of background independence. Almost all of these already have simpler classical counterparts. This approach can be viewed as a facet by facet completion of the observation ... More

Beables/Observables in Classical and Quantum GravityDec 20 2013Aug 29 2014Observables 'are observed' whereas beables just 'are'. This gives beables more scope in the cosmological and quantum domains. Both observables and beables are entities that form 'brackets' with 'the constraints' that are 'equal to' zero. We explain how ... More

Classical dynamics on trianglelandFeb 15 2007Nov 02 2007In Euclidean relational particle mechanics (ERPM) only relative times, relative angles and relative separations are meaningful, while in similarity relational particle mechanics (SRPM) only relative times, relative angles and ratios of relative separations ... More

Emergent Semiclassical Time in Quantum Gravity. Full Geometrodynamics and Minisuperspace ExamplesNov 01 2006Nov 04 2007I apply the preceding paper's semiclassical treatment to geometrodynamics. The analogy between the two papers is quite useful at the level of the quadratic constraints, while I document the differences between the two due to the underlying differences ... More

Six New Mechanics corresponding to further Shape TheoriesMay 03 2015Apr 04 2016A suite of relational notions of shape are presented at the level of configuration space geometry, with corresponding new theories of shape mechanics and shape statistics. These further generalize two quite well known examples: --1) Kendall's (metric) ... More

Problem of Time in Slightly Inhomogeneous CosmologyMar 29 2014Apr 04 2016The Problem of Time (PoT) is a multi-faceted conceptual incompatibility between various areas of Theoretical Physics. Whilst usually stated as between GR and QM, in fact 8/9ths of it is already present at the classical level. Thus we adopt a `top-down' ... More

Kerr-Newman Black Hole Thermodynamical State Space: Blockwise CoordinatesJun 18 2012Oct 28 2013A coordinate system that blockwise-simplifies the Kerr-Newman black hole's thermodynamical state space Ruppeiner metric geometry is constructed, with discussion of the limiting cases corresponding to simpler black holes. It is deduced that one of the ... More

RelationalismMay 06 2012Jul 15 2014This article contributes to the debate of the meaning of relationalism and background independence, which has remained of interest in theoretical physics from Newton versus Leibniz through to foundational issues for today's leading candidate theories ... More

Approaching the Problem of Time with a Combined Semiclassical-Records-Histories SchemeApr 13 2012Aug 31 2012I approach the Problem of Time and other foundations of Quantum Cosmology using a combined histories, timeless and semiclassical approach. This approach is along the lines pursued by Halliwell. It involves the timeless probabilities for dynamical trajectories ... More

Strong-coupled Relativity without RelativityMay 28 2002Nov 03 2003GR can be interpreted as a theory of evolving 3-geometries. A recent such formulation, the 3-space approach of Barbour, Foster and \'{O} Murchadha, also permits the construction of a limited number of other theories of evolving 3-geometries, including ... More

On the resonances of the Laplacian on waveguidesSep 21 2001The resonances for the Dirichlet and Neumann Laplacian are studied on compactly perturbed waveguides. An upper bound on the number of resonances near the physical plane is proven. In the absence of resonances, an upper bound is proven for the localised ... More

How much of the outgoing radiation can be intercepted by Schwarzschildean black holes?Sep 11 2000The Schwarzschild spacetime is for electromagnetic waves like a nonuniform medium with a varying refraction index. A fraction of an outgoing radiation scatters off the curvature of the geometry and can be intercepted by a gravitational center. The amount ... More

Global solutions of a free boundary problem for selfgravitating scalar fieldsJun 01 1995Apr 12 1996The weak cosmic censorship hypothesis can be understood as a statement that there exists a global Cauchy evolution of a selfgravitating system outside an event horizon. The resulting Cauchy problem has a free null-like inner boundary. We study a selfgravitating ... More

Singularities in string theoryDec 01 2002String theory is a quantum theory that reproduces the results of General Relativity at long distances but is completely different at short distances. Mathematically, string theory is based on a very new -- and little understood -- framework for geometry ... More

g-elements of matroid complexesOct 24 2002Let K be the face ring of the independence complex of a matroid. We show that if T is a generic linear system of parameters, then K/T satisfies a weak form of the Hard Lefschetz Theorem. As a result, the first half of the h-vector of the complex satisfies ... More

ElementsSep 30 2015The aim of this work is to show that contemporary mathematics, including Peano arithmetic, is inconsistent, to construct firm foundations for mathematics, and to begin building on these foundations.

A Scoring System for Continuous Glucose Monitor DataMay 12 2013As continuous glucose monitors (CGMs) are used increasingly by diabetic patients, new and intuitive tools are needed to help patients and their physicians use these streams of data to improve blood glucose management. In this paper, we propose a daily ... More

Problem of Time: Facets and Machian StrategyJun 25 2013Jul 15 2014The Problem of Time is that `time' in each of ordinary quantum theory and general relativity are mutually incompatible notions. This causes difficulties in trying to put these two theories together to form a theory of Quantum Gravity. The Problem of Time ... More

Relational mechanics of shape and scaleJan 07 2010Feb 15 2010Relational particle mechanics models (RPM's) are useful models for the problem of time in quantum gravity and other foundational issues in quantum cosmology. Some concrete examples of scalefree RPM's have already been studied, but it is the case with ... More

Machian Classical and Semiclassical Emergent TimeMay 21 2013Nov 25 2013Classical and semiclassical schemes are presented that are timeless at the primary level and recover time from Mach's `time is to be abstracted from change' principle at the emergent secondary level. The semiclassical scheme is a Machian variant of the ... More

On the Semiclassical Approach to Quantum CosmologyJan 25 2011The emergent semiclassical time approach to resolving the problem of time in quantum gravity involves heavy slow degrees of freedom providing via an approximately Hamilton-Jacobi equation an approximate timestandard with respect to which the quantum mechanics ... More

Smallest Relational Mechanics Model of Quantum CosmologyAug 13 2009Relational particle mechanics are models in which there is, overall, no time, position, orientation (nor, sometimes, scale). They are useful for whole-universe modelling - the setting for quantum cosmology. This note concerns 3 particles in 1d in shape-scale ... More

New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM splitNov 02 2007I show how there is an ambiguity in how one treats auxiliary variables in gauge theories including general relativity cast as 3 + 1 geometrodynamics. Auxiliary variables may be treated pre-variationally as multiplier coordinates or as the velocities corresponding ... More

A characterization of Leonard pairs using the parameters $\{a_i\}_{i=0}^{d}$May 20 2012Let $V$ denote a vector space with finite positive dimension. We consider an ordered pair of linear transformations $A: V\to V$ and $A^*: V\to V$ that satisfy (i) and (ii) below. (i) There exists a basis for $V$ with respect to which the matrix representing ... More

A characterization of Leonard pairs using the notion of a tailOct 31 2009Let $V$ denote a vector space with finite positive dimension. We consider an ordered pair of linear transformations $A: V\to V$ and $A^*: V\to V$ that satisfy (i) and (ii) below: (i) There exists a basis for $V$ with respect to which the matrix representing ... More

Value Monoids of Zero-Dimensional Valuations of Rank OneApr 13 2005Classically, Groebner bases are computed by first prescribing a set monomial order. Moss Sweedler suggested an alternative and developed a framework to perform such computations by using valuation rings in place of monomial orders. We build on these ideas ... More

The arithmetic of solidsApr 06 2012The set of segments, each of the next is n times bigger than the first one is a simple geometric interpretation of the set $\mathbb{N}$ of natural numbers. In this paper we investigate the opposite situation. We construct an algebraic structure similar ... More

A scalar curvature bound along the conical Kähler-Ricci flowMay 08 2015Starting with a model conical K\"ahler metric, we prove a uniform scalar curvature bound for solutions to the conical K\"ahler-Ricci flow assuming a semi-ampleness type condition on the twisted canonical bundle. In the proof, we also establish uniform ... More

Lower bounds for h-vectors of k-CM, independence and broken circuit complexesAug 24 2004We present a number of lower bounds for the h-vectors of k-CM, broken circuit and independence complexes. These lead to bounds on the coefficients of the characteristic and reliability polynomials of matroids. The main techniques are the use of series ... More

Fixed Points of Maps on the Space of Rational FunctionsDec 17 2004Given integers s,t, define a function phi_{s,t} on the space of all formal series expansions by phi_{s,t} (sum a_n x^n) = sum a_{sn+t} x^n. For each function phi_{s,t}, we determine the collection of all rational functions whose Taylor expansions at zero ... More

Comments on the CMS discovery of the "Ridge" in High Multiplicity pp collisions at LHCSep 23 2010A very recent paper by the CMS collaboration \cite{cms_ridge} has created large discussion in the media, which call it important but did not explain why, in some places even calling it "unundestandable". While it is of course too soon to know what causes ... More

Quark-Gluon Plasma - New FrontiersApr 08 2008As implied by organizers, this talk is not a conference summary but rather an outline of progress/challenges/``frontiers'' of the theory. Some fundamental questions addressed are: Why is sQGP such a good liquid? Do we understand (de)confinement and what ... More

Emerging Theory of Strongly Coupled Quark-Gluon PlasmaMar 19 2007RHIC data have shown robust collective flows, including recent spectacular ``conical flow'' from quenched jets: that confirms that QGP above the critical line is in a strongly coupled regime. One way to study Non-Abelian classical strongly coupled plasmas ... More

Physics of Strongly coupled Quark-Gluon PlasmaJul 18 2008Sep 15 2008This review cover our current understanding of strongly coupled Quark-Gluon Plasma (sQGP), especially theoretical progress in (i) explaining the RHIC data by hydrodynamics, (ii) describing lattice data using electric-magnetic duality; (iii) understanding ... More

The conical flow from quenched jets in sQGPSep 05 2006Starting with a reminder of what is strongly coupled Quark-Gluon Plasma (sQGP), we proceed to recent advances in jet quenching and heavy quark diffusion, with a brief summary of various results based on AdS/CFT correspondence. The conical flow is a hydrodynamical ... More

A Cosmological Constant from Gauge Field Instantons?Jul 21 2004Although all interactions in the Standard Model generate nonzero shifts of the vacuum energy and pressure, gravity does not interact with them. Assuming (i) that the reason why it is so breaks down at some scale $M_g$ and that (ii) the instanton-induced ... More

Analytic Continuation Of Chern-Simons TheoryJan 18 2010Aug 28 2010The title of this article refers to analytic continuation of three-dimensional Chern-Simons gauge theory away from integer values of the usual coupling parameter k, to explore questions such as the volume conjecture, or analytic continuation of three-dimensional ... More

Geometric Langlands And The Equations Of Nahm And BogomolnyMay 29 2009Nov 06 2009Geometric Langlands duality relates a representation of a simple Lie group $G^\vee$ to the cohomology of a certain moduli space associated with the dual group $G$. In this correspondence, a principal $SL_2$ subgroup of $G^\vee$ makes an unexpected appearance. ... More

Mirror Symmetry, Hitchin's Equations, And Langlands DualityFeb 07 2008Geometric Langlands duality can be understood from statements of mirror symmetry that can be formulated in purely topological terms for an oriented two-manifold $C$. But understanding these statements is extremely difficult without picking a complex structure ... More

Chiral Ring Of Sp(N) And SO(N) Supersymmetric Gauge Theory In Four DimensionsFeb 25 2003Jul 17 2003The chiral ring of classical supersymmetric Yang-Mills theory with gauge group $Sp(N)$ or SO(N) is computed, extending previous work (of Cachazo, Douglas, Seiberg, and the author) for SU(N). The result is that, as has been conjectured, the ring is generated ... More

Quest For UnificationJul 09 2002The GUT-based approach to physics has been attractive since it was first put forward close to thirty years ago; it has been enriched by new ideas, notably supersymmetry and strings; and there are real hints that it is on the right track, notably from ... More

Deconstruction, G_2 Holonomy, and Doublet-Triplet SplittingJan 04 2002Jan 15 2002We describe a mechanism for using discrete symmetries to solve the doublet-triplet splitting problem of four-dimensional supersymmetric GUT's. We present two versions of the mechanism, one via ``deconstruction,'' and one in terms of M-theory compactification ... More

World-Sheet Corrections Via D-InstantonsJul 07 1999We use a D-instanton or physical gauge approach to re-derive the heterotic string worldsheet instanton contribution to the superpotential in Calabi-Yau compactification. We derive an analogous formula for worldsheet instanton corrections to the moduli ... More

Theta Dependence In The Large N Limit Of Four-Dimensional Gauge TheoriesJul 15 1998The theta dependent of pure gauge theories in four dimensions can be studied using a duality of large N gauge theories with string theory on a certain spacetime. Via this duality, one can argue that for every theta, there are infinitely many vacua that ... More

New ``Gauge'' Theories In Six DimensionsOct 07 1997Dec 08 1997More general constructions are given of six-dimensional theories that look at low energy like six-dimensional super Yang-Mills theory. The constructions start with either parallel fivebranes in Type IIB, or M-theory on $(\C^2\times\S^1)/\Gamma$ for $\Gamma$ ... More

Branes And The Dynamics Of QCDJun 13 1997Jun 30 1997A brane configuration is described that is relevant to understanding the dynamics of N=1 supersymmetric Yang-Mills theory. Confinement and spontaneous breaking of a discrete chiral symmetry can be understood as consequences of the topology of the brane. ... More

Solutions Of Four-Dimensional Field Theories Via M TheoryMar 24 1997N=2 supersymmetric gauge theories in four dimensions are studied by formulating them as the quantum field theories derived from configurations of fourbranes, fivebranes, and sixbranes in Type IIA superstrings, and then reinterpreting those configurations ... More

Is Supersymmetry Really Broken?Sep 19 1994In 2 + 1 dimensions, in the presence of gravity, supersymmetry can ensure the vanishing of the cosmological constant without requiring the equality of bose and fermi masses.

Ground Ring Of Two Dimensional String TheoryAug 16 1991String theories with two dimensional space-time target spaces are characterized by the existence of a ``ground ring'' of operators of spin $(0,0)$. By understanding this ring, one can understand the symmetries of the theory and illuminate the relation ... More

Conformal Field Theory In Four And Six DimensionsDec 02 2007Feb 07 2008The goal of these notes is to give a brief explanation of how electric-magnetic duality in four dimensions is related to the existence of an unusual conformal field theory in six dimensions.

Supersymmetric Index Of Three-Dimensional Gauge TheoryFeb 27 1999Apr 11 1999In N=1 super Yang-Mills theory in three spacetime dimensions, with a simple gauge group $G$ and a Chern-Simons interaction of level $k$, the supersymmetric index $\Tr (-1)^F$ can be computed by making a relation to a pure Chern-Simons theory or microscopically ... More

Physical Interpretation Of Certain Strong Coupling SingularitiesSep 18 1996We interpret certain strong coupling singularities of the $E_8\times E_8$ heterotic string on K3 in terms of exotic six-dimensional theories in which $E_8$ is a gauge symmetry. These theories are closely related to theories obtained at small instanton ... More

Non-Perturbative Superpotentials In String TheoryApr 05 1996May 07 1996The non-perturbative superpotential can be effectively calculated in $M$-theory compactification to three dimensions on a Calabi-Yau four-fold $X$. For certain $X$, the superpotential is identically zero, while for other $X$, a non-perturbative superpotential ... More

Five-branes And $M$-Theory On An OrbifoldDec 29 1995Feb 08 1996We relate Type IIB superstrings compactified to six dimensions on K3 to an eleven-dimensional theory compactified on $({\bf S}^1)^5/{\bf Z}_2$. Eleven-dimensional five-branes enter the story in an interesting way.

Sigma Models And The ADHM Construction Of InstantonsOct 07 1994This paper is devoted to the construction of a family of linear sigma models with $(0,4)$ supersymmetry which should flow in the infrared to the stringy version of Yang-Mills instantons on ${\bf R}^4$. The family depends on the full set of expected parameters ... More

More On Gauge Theory And Geometric LanglandsJun 13 2015The geometric Langlands correspondence was described some years ago in terms of $S$-duality of $\N=4$ super Yang-Mills theory. Some additional matters relevant to this story are described here. The main goal is to explain directly why an $A$-brane of ... More

Billiards with BombsJun 01 2015In this paper, we define a variant of billiards in which the ball bounces around a square grid erasing walls as it goes. We prove that there exist periodic tunnels with arbitrarily large period from any possible starting point, that there exist non-periodic ... More

The "Parity" Anomaly On An Unorientable ManifoldMay 08 2016Sep 06 2016The "parity" anomaly -- more accurately described as an anomaly in time-reversal or reflection symmetry -- arises in certain theories of fermions coupled to gauge fields and/or gravity in a spacetime of odd dimension. This anomaly has traditionally been ... More

A Dynamical Mechanism for the Big Bang and Non-Regularizability for $w=1$Nov 14 2014We consider a contracting universe and its transition to expansion through the big bang singularity with a time varying equation of state $w$, where $w$ approaches $1$ as the universe contracts to the big bang. We show that this singularity is non-regularizable. ... More

Network Models in Epidemiology: Considering Discrete and Continuous DynamicsOct 19 2015Discrete and Continuous Dynamics is the first in a series of articles on Network Models for Epidemiology. This project began in the Fall quarter of 2014 in my continuous modeling course. Since then, it has taken off and turned into a series of articles, ... More

Notes On Holomorphic String And Superstring Theory Measures Of Low GenusJun 16 2013Dec 03 2013It has long been known that in principle, the genus g vacuum amplitude for bosonic strings or superstrings in 26 or 10 dimensions can be entirely determined from conditions of holomorphy. Moreover, this has been done in practice for bosonic strings of ... More

The Problem of Time and Quantum Cosmology in the Relational Particle Mechanics ArenaNov 07 2011Feb 12 2013This article contains a local solution to the notorious Problem of Time in Quantum Gravity at the conceptual level and which is actually realizable for the relational triangle. The Problem of Time is that `time' in GR and `time' in ordinary quantum theory ... More

Relational Quadrilateralland Interpretation of CP^2 and QuotientsFeb 14 2011Aug 07 2013I investigate qualitatively significant regions of the configuration space for the classical and quantum mechanics of the relational quadrilateral in 2-d. This is relational in the sense that only relative ratios of separations, relative angles and relative ... More