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Graph Convolutional Transformer: Learning the Graphical Structure of Electronic Health RecordsJun 11 2019Jun 28 2019Effective modeling of electronic health records (EHR) is rapidly becoming an important topic in both academia and industry. A recent study showed that utilizing the graphical structure underlying EHR data (e.g. relationship between diagnoses and treatments) ... More

The Intrinsically X-ray Weak Quasar PHL 1811. I. X-ray Observations and Spectral Energy DistributionNov 10 2006This is the first of two papers reporting observations and analysis of the unusually bright (m_b=14.4), luminous (M_B=-25.5), nearby (z=0.192) narrow-line quasar PHL 1811, focusing on the X-ray properties and the spectral energy distribution. Two Chandra ... More

Causal RegularizationFeb 08 2017Feb 23 2017In application domains such as healthcare, we want accurate predictive models that are also causally interpretable. In pursuit of such models, we propose a causal regularizer to steer predictive models towards causally-interpretable solutions and theoretically ... More

Compositional Obverter Communication Learning From Raw Visual InputApr 06 2018One of the distinguishing aspects of human language is its compositionality, which allows us to describe complex environments with limited vocabulary. Previously, it has been shown that neural network agents can learn to communicate in a highly structured, ... More

Implementation and evaluation of various demons deformable image registration algorithms on GPUSep 04 2009Online adaptive radiation therapy (ART) promises the ability to deliver an optimal treatment in response to daily patient anatomic variation. A major technical barrier for the clinical implementation of online ART is the requirement of rapid image segmentation. ... 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

The definability criterions for convex projective polyhedral reflection groupsJun 11 2012Oct 14 2013Following Vinberg, we find the criterions for a subgroup generated by reflections $\Gamma \subset \SL^{\pm}(n+1,\mathbb{R})$ and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in ... More

Congruences in fractional partition functionsAug 11 2019Aug 14 2019The coefficients of the generating function $(q;q)^\alpha_\infty$ produce $p_\alpha(n)$ for $\alpha \in \mathbb{Q}$. In particular, when $\alpha = -1$, the partition function is obtained. Recently, Chan and Wang identified and proved congruences of the ... 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

On quotients of Banach spaces having shrinking unconditional basesNov 16 1990It is proved that if a Banach space $Y$ is a quotient of a Banach space having a shrinking unconditional basis, then every normalized weakly null sequence in $Y$ has an unconditional subsequence. The proof yields the corollary that every quotient of Schreier's ... More

Recent Advances in the Langlands ProgramMar 06 2003Sep 30 2003These are the notes for the lecture given by the author at the "Current Events" Special Session of the AMS meeting in Baltimore on January 17, 2003. Topics reviewed include the Langlands correspondence for GL(n) in the function field case and its proof ... More

Vertex Algebras and Algebraic CurvesJul 10 2000Sep 07 2001This is the text of the Bourbaki seminar that I gave on June 24, 2000.

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

Nambu variant of Local Resolution of Problem of Time and Background IndependenceAug 08 2019A Local Resolution of the Problem of Time has recently been given, alongside reformulation as A Local Theory of Background Independence. The classical part of this can be viewed as requiring just Lie's Mathematics, albeit entrenched in subsequent topological ... More

A Local Resolution of the Problem of Time. II. Configurational Relationalism via a generalization of Group AveragingMay 15 2019Jul 08 2019In this article, we consider a second Problem of Time Facet. This started life as Wheeler's Thin Sandwich Problem, within the narrow context of 1) GR-as-Geometrodynamics, in particular its momentum constraint. 2) A Lagrangian variables level treatment. ... More

Spaces of SpacesNov 30 2014May 13 2015Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I consider furthmore ... More

Where to Apply RelationalismNov 16 2014May 17 2015Relationalism -- along the lines developed by Barbour and collaborators in the past 3 decades -- can be considered an advance with 1/4 of the facets of the canonical approach's Problem of Time as identified by Isham and Kuchar. Indeed, almost all of the ... More

On Background IndependenceOct 05 2013This paper concerns what Background Independence itself is (as opposed to some particular physical theory that is background independent). The notions presented mostly arose from a layer-by-layer analysis of the facets of the Problem of Time in Quantum ... More

Machian Time Is To Be Abstracted From What Change?Sep 06 2012Apr 18 2013"It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction at which we arrive through the changes of things." Ernst Mach [1]. What change? Three answers to this are `any change' (Rovelli), 'all ... More

The Problem of Time in Quantum GravitySep 11 2010Jul 20 2012The problem of time in quantum gravity occurs because `time' is taken to have a different meaning in each of general relativity and ordinary quantum theory. This incompatibility creates serious problems with trying to replace these two branches of physics ... More

A Local Resolution of the Problem of Time. VI. Combining Temporal and Configurational Relationalism for Field Theories and GRJun 09 2019We next combine Temporal and Configurational Relationalism's resolution for Field Theory, including in particular for GR. The current Article also provides the finite-and-field theory portmanteau notation, by which the rest of this series' reworking of ... More

Shape Theories. I. Their Diversity is Killing-Based and thus NongenericNov 15 2018Mar 12 2019Kendall's Shape Theory covers shapes formed by $N$ points in $\mathbb{R}^d$ upon quotienting out the similarity transformations. This theory is based on the geometry and topology of the corresponding configuration space: shape space. Kendall studied this ... More

Specific PDEs for Preserved Quantities in Geometry. II. Affine Transformations and SubgroupsSep 06 2018Sep 24 2018We extend finding geometrically-significant preserved quantities by solving specific PDEs to the affine transformations and subgroups. This can be viewed not only as a purely geometrical problem but also as a subcase of finding physical observables, and ... More

$N$-Body Problem: Minimal $N$'s for Qualitative NontrivialitiesJul 23 2018We review the $N$-Body Problem in arbitrary dimension $d$ at the kinematical level, with modelling Background Independence in mind. In particular, we give a structural analysis of its reduced configuration spaces, decomposing this subject matter into ... 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

Triangleland. I. Classical dynamics with exchange of relative angular momentumSep 06 2008Sep 23 2009In Euclidean relational particle mechanics, only relative times, relative angles and relative separations are meaningful. Barbour--Bertotti (1982) theory is of this form and can be viewed as a recovery of (a portion of) Newtonian mechanics from relational ... More

Leibniz--Mach foundations for GR and fundamental physicsMay 05 2004May 17 2004Consider the configuration space Q for some physical system, and a continuous group of transformations G whose action on the configurations is declared to be physically irrelevant. Implement G indirectly by adjoining 1 auxiliary g per independent generator ... More

A modular quintic Calabi-Yau threefold of level 55Mar 06 2009In this note we search the parameter space of Horrocks-Mumford quintic threefolds and locate a Calabi-Yau threefold which is modular, in the sense that the L-function of its middle-dimensional cohomology is associated to a classical modular form of weight ... More

Clinical Concept Extraction for Document-Level CodingJun 08 2019The text of clinical notes can be a valuable source of patient information and clinical assessments. Historically, the primary approach for exploiting clinical notes has been information extraction: linking spans of text to concepts in a detailed domain ... More

MiME: Multilevel Medical Embedding of Electronic Health Records for Predictive HealthcareOct 22 2018Deep learning models exhibit state-of-the-art performance for many predictive healthcare tasks using electronic health records (EHR) data, but these models typically require training data volume that exceeds the capacity of most healthcare systems. External ... More

Fivebranes and KnotsJan 17 2011Aug 11 2011We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approches involved other descriptions of the relevant spaces of BPS states). The starting point is a system of D3-branes ending on an NS5-brane with a nonzero ... More

On Schreier unconditional sequencesMar 22 1991Let $(x_n)$ be a normalized weakly null sequence in a Banach space and let $\varep>0$. We show that there exists a subsequence $(y_n)$ with the following property: $$\hbox{ if }\ (a_i)\subseteq \IR\ \hbox{ and }\ F\subseteq \nat$$ satisfies $\min F\le ... More

The Synergy between Numerical and Perturbative Approaches to Black HolesJun 23 1998I describe approaches to the study of black hole spacetimes via numerical relativity. After a brief review of the basic formalisms and techniques used in numerical black hole simulations, I discuss a series of calculations from axisymmetry to full 3D ... More

An SYK-Like Model Without DisorderOct 31 2016Nov 03 2016Making use of known facts about "tensor models," it is possible to construct a quantum system without quenched disorder that has the same large $n$ limit for its correlation functions and thermodynamics as the SYK model. This might be useful in further ... More

Asymmetry gap in the electronic band structure of bilayer grapheneAug 09 2006Nov 02 2006A tight binding model is used to calculate the band structure of bilayer graphene in the presence of a potential difference between the layers that opens a gap $\Delta$ between the conduction and valence bands. In particular, a self consistent Hartree ... More

Gauge Theory and Langlands DualityJun 15 2009The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed which leads to a mysterious duality between certain categories of sheaves ... More

Free field realizations in representation theory and conformal field theoryAug 18 1994Invited lecture at the International Congress of Mathematicians, Zuerich, August 3-11, 1994 (extended version), reviews free field realizations of affine Kac-Moody and W-algebras and their applications.

Lectures on the Langlands Program and Conformal Field TheoryDec 15 2005These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric reformulation, ... More

Five Lectures on Soliton EquationsNov 30 1997This is a self-contained review of a new approach to soliton equations of KdV type developed by the author together with B. Feigin and B. Enriquez.

A Local Resolution of the Problem of Time. II. Configurational Relationalism via a generalization of Group AveragingMay 15 2019Jun 09 2019In this article, we consider a second Problem of Time Facet. This started life as Wheeler's Thin Sandwich Problem, within the narrow context of 1) GR-as-Geometrodynamics, in particular its momentum constraint. 2) A Lagrangian variables level treatment. ... More

Nijenhuis-type variants of Local Theory of Background IndependenceAug 01 2019A local resolution of the Problem of Time has recently been given, alongside reformulation as a local theory of Background Independence. The classical part of this can be viewed as requiring just Lie's Mathematics, albeit entrenched in subsequent Topology ... More

Specific PDEs for Preserved Quantities in Geometry. III. 1-d Projective Transformations and SubgroupsSep 06 2018Sep 24 2018We extend finding geometrically-significant preserved quantities by solving specific PDEs to 1-$d$ projective transformations and subgroups. This can be viewed not only as a purely geometrical problem but also as a subcase of finding physical observables, ... More

A Local Resolution of the Problem of TimeSep 06 2018Sep 24 2018We here announce and outline a solution of this major and longstanding foundational problem, dealing with all seven of its heavily-interrelated local facets.

Absolute versus Relational Debate: a Modern Global VersionMay 24 2018Suppose one seeks to free oneself from a symmetric absolute space by quotienting out its symmetry group. This in general however fails to erase all memory of this absolute space's symmetry properties. Stratification is one major reason for this, which ... More

Shape (In)dependent Inequalities for Triangleland's Jacobi and Democratic-Linear Ellipticity QuantititiesDec 12 2017Sides and medians are both Jacobi coordinate magnitudes, moreover then equably entering the spherical coordinates on Kendall's shape sphere and the Hopf coordinates. This motivates treating medians on the same footing as sides in triangle geometry and ... More

Alice in Triangleland: Lewis Carroll's Pillow Problem and Variants Solved on Shape Space of TrianglesNov 30 2017We provide a natural answer to Lewis Carroll's pillow problem of what is the probability that a triangle is obtuse, Prob(Obtuse). This arises by straightforward combination of a) Kendall's Theorem - that the space of all triangles is a sphere - and b) ... 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

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

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

A Local Resolution of the Problem of Time. IV. Quantum outline and piecemeal ConclusionMay 15 2019Jun 09 2019In this final preliminary piecemeal treatment of local Problem of Time facets, and underlying Background Independence aspects, we first reconsider the nine local facets and aspects considered so far at the quantum level. This is essential both to appreciate ... More

Geometry from Brackets ConsistencyNov 01 2018We argue for Brackets Consistency to be a `Pillar of Geometry', i.e.\ a foundational approach, other Pillars being 1) Euclid's constructive approach, 2) the algebraic approach, 3) the projective approach, and 4) the geometrical automorphism groups `Erlangen' ... More

Specific PDEs for Preserved Quantities in Geometry. I. Similarities and SubgroupsSep 06 2018Sep 24 2018We provide specific PDEs for preserved quantities $Q$ in Geometry, as well as a bridge between this and specific PDEs for observables $O$ in Physics. We furthermore prove versions of four other theorems either side of this bridge: the below enumerated ... 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

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

A Local Resolution of the Problem of Time. XIV. Grounding on Lie's MathematicsJul 31 2019In a major advance and simplification of this field, we show that A Local Resolution of the Problem of Time - also viewable as A Local Theory of Background Independence - can at the classical level be described solely by of Lie's Mathematics. This comprises ... 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

The Chern-Ricci flow on primary Hopf surfacesMay 30 2019The Hopf surfaces provide a family of minimal non-K\"ahler surfaces of class VII on which little is known about the Chern-Ricci flow. We use a construction of Gauduchon-Ornea for locally conformally K\"ahler metrics on primary Hopf surfaces of class 1 ... 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

Steady state clusters and the Rath-Toth mean field forest fire modelSep 10 2018We introduce a random finite rooted tree $\mathcal{C}$, the steady state cluster, characterized by a recursive description: $\mathcal{C}$ is a singleton with probability $1/2$ and otherwise is obtained by joining by an edge the roots of two independent ... 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

Medical Concept Representation Learning from Electronic Health Records and its Application on Heart Failure PredictionFeb 11 2016Objective: To transform heterogeneous clinical data from electronic health records into clinically meaningful constructed features using data driven method that rely, in part, on temporal relations among data. Materials and Methods: The clinically meaningful ... More

Electronic properties of monolayer and bilayer grapheneMay 22 2012The tight-binding model of electrons in graphene is reviewed. We derive low-energy Hamiltonians supporting massless Dirac-like chiral fermions and massive chiral fermions in monolayer and bilayer graphene, respectively, and we describe how their chirality ... More

Mathematics, Love, and TattoosNov 14 2012Reflections on the film "Rites of Love and Math" (directed by Reine Graves and the author) and its "formula of love".

Langlands Program, Trace Formulas, and their GeometrizationFeb 09 2012Nov 06 2014The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After giving an introduction ... More

Affine Algebras, Langlands Duality and Bethe AnsatzJun 05 1995Sep 23 1999We review various aspects of representation theory of affine algebras at the critical level, geometric Langlands correspondence, and Bethe ansatz in the Gaudin models. Geometric Langlands correspondence relates D-modules on the moduli space of G-bundles ... More

Ramifications of the geometric Langlands ProgramNov 09 2006Nov 24 2006The global geometric Langlands correspondence relates Hecke eigensheaves on the moduli stack of G-bundles on a smooth projective algebraic curve X and holomorphic G'-bundles with connection on X, where G' is the Langlands dual group of G. This correspondence ... More

Lower Bound on Entanglement of Formation for the Qubit-Qudit SystemJan 06 2003Wootters [PRL 80, 2245 (1998)] has derived a closed formula for the entanglement of formation (EOF) of an arbitrary mixed state in a system of two qubits. There is no known closed form expression for the EOF of an arbitrary mixed state in any system more ... More

Perturbative Gauge Theory As A String Theory In Twistor SpaceDec 15 2003Oct 06 2004Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space ... More

Anomaly Cancellation On Manifolds Of G_2 HolonomyAug 22 2001Smooth manifolds of G_2 holonomy, used to compactify M-theory to four dimensions, give only abelian gauge groups without charged matter multiplets. But singular G_2-manifolds can give abelian or nonabelian gauge groups with chiral fermions. We describe ... More

Lepton Number And Neutrino MassesJun 28 2000I briefly review the arguments which in the 1970's convinced many theoretical physicists to anticipate lepton number violation, and to guess a range of neutrino masses.

Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge TheoriesMar 16 1998Apr 07 1998The correspondence between supergravity (and string theory) on $AdS$ space and boundary conformal field theory relates the thermodynamics of ${\cal N}=4$ super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in ... More

On The Conformal Field Theory Of The Higgs BranchJul 11 1997Jul 22 1997We study 1+1-dimensional theories of vector and hypermultiplets with (4,4) supersymmetry. Despite strong infrared fluctuations, these theories flow in general to distinct conformal field theories on the Coulomb and Higgs branches. In some cases there ... More

On Flux Quantization In M-Theory And The Effective ActionSep 16 1996Oct 18 1996The quantization law for the antisymmetric tensor field of $M$-theory contains a gravitational contribution not known previously. When it is included, the low energy effective action of $M$-theory, including one-loop and Chern-Simons contributions, is ... More