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1,038
Probabilistic independence networks for hidden Markov probability models
, 1996
"... Graphical techniques for modeling the dependencies of random variables have been explored in a variety of different areas including statistics, statistical physics, artificial intelligence, speech recognition, image processing, and genetics. Formalisms for manipulating these models have been develop ..."
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Cited by 173 (12 self)
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Graphical techniques for modeling the dependencies of random variables have been explored in a variety of different areas including statistics, statistical physics, artificial intelligence, speech recognition, image processing, and genetics. Formalisms for manipulating these models have been developed relatively independently in these research communities. In this paper we explore hidden Markov models (HMMs) and related structures within the general framework of probabilistic independence networks (PINs). The paper contains a selfcontained review of the basic principles of PINs. It is shown that the wellknown forwardbackward (FB) and Viterbi algorithms for HMMs are special cases of more general inference algorithms for arbitrary PINs. Furthermore, the existence of inference and estimation algorithms for more general graphical models provides a set of analysis tools for HMM practitioners who wish to explore a richer class of HMM structures. Examples of relatively complex models to handle sensor fusion and coarticulation in speech recognition are introduced and treated within the graphical model framework to illustrate the advantages of the general approach.
Mean Field Theory for Sigmoid Belief Networks
 Journal of Artificial Intelligence Research
, 1996
"... We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. ..."
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Cited by 126 (12 self)
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We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics.
Microlocal analysis and interacting quantum field theory: Renormalizability on Physical Backgrounds
, 1999
"... We present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic (curved) spacetimes. We develop a purely local version of the StückelbergBogoliubovEpsteinGlaser method of renormalization by using techniques from microlocal analysis. Relying on recent r ..."
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Cited by 99 (15 self)
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We present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic (curved) spacetimes. We develop a purely local version of the StückelbergBogoliubovEpsteinGlaser method of renormalization by using techniques from microlocal analysis. Relying on recent results of Radzikowski, Köhler and the authors about a formulation of a local spectrum condition in terms of wave front sets of correlation functions of quantum fields on curved spacetimes, we construct timeordered operatorvalued products of Wick polynomials of free fields. They serve as building blocks for a local (perturbative) definition of interacting fields. Renormalization in this framework amounts to extensions of expectation values of timeordered products to all points of spacetime. The extensions are classified according to a microlocal generalization of Steinmann scaling degree corresponding to the degree of divergence in other renormalization schemes. As a result, we prove that the usual perturbative classification of interacting quantum
Enumeration of Rational Curves via Torus Actions
 in The Moduli Space of Curves, Dijkgraaf et al eds., Progress in Mathematics 129, Birkhäuser
, 1995
"... This paper contains an attempt to formulate rigorously and to check predictions in enumerative geometry of curves following from Mirror Symmetry. In a sense, we almost solved both problems. There are still certain gaps in the foundations. Nevertheless, we obtain “closed ” formulas for generating fun ..."
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Cited by 59 (0 self)
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This paper contains an attempt to formulate rigorously and to check predictions in enumerative geometry of curves following from Mirror Symmetry. In a sense, we almost solved both problems. There are still certain gaps in the foundations. Nevertheless, we obtain “closed ” formulas for generating functions in
Statistical Inference, Occam’s Razor, and Statistical Mechanics on the Space of Probability Distributions
, 1997
"... The task of parametric model selection is cast in terms of a statistical mechanics on the space of probability distributions. Using the techniques of lowtemperature expansions, I arrive at a systematic series for the Bayesian posterior probability of a model family that significantly extends known ..."
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Cited by 58 (3 self)
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The task of parametric model selection is cast in terms of a statistical mechanics on the space of probability distributions. Using the techniques of lowtemperature expansions, I arrive at a systematic series for the Bayesian posterior probability of a model family that significantly extends known results in the literature. In particular, I arrive at a precise understanding of how Occam’s razor, the principle that simpler models should be preferred until the data justify more complex models, is automatically embodied by probability theory. These results require a measure on the space of model parameters and I derive and discuss an interpretation of Jeffreys ’ prior distribution as a uniform prior over the distributions indexed by a family. Finally, I derive a theoretical index of the complexity of a parametric family relative to some true distribution that I call the razor of the model. The form of the razor immediately suggests several interesting questions in the theory of learning that can be studied using the techniques of statistical mechanics.
On motives associated to graph polynomials
 Commun. Math. Phys
"... Abstract. The appearance of multiple zeta values in anomalous dimensions and βfunctions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions. In this paper we start to hunt the motive, restricting our attention to a su ..."
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Cited by 51 (12 self)
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Abstract. The appearance of multiple zeta values in anomalous dimensions and βfunctions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions. In this paper we start to hunt the motive, restricting our attention to a subclass of graphs in four dimensional scalar field theory which give scheme independent contributions to the above functions. Calculations of Feynman integrals arising in perturbative quantum field theory [4, 5] reveal interesting patterns of zeta and multiple zeta values. Clearly, these are motivic in origin, arising from the existence of Tate mixed Hodge structures with periods given by Feynman integrals.
The electronic properties of graphene
 Rev. Mod. Phys. 2009
"... This article reviews the basic theoretical aspects of graphene, a oneatomthick allotrope of carbon, with unusual twodimensional Diraclike electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or t ..."
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Cited by 41 (0 self)
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This article reviews the basic theoretical aspects of graphene, a oneatomthick allotrope of carbon, with unusual twodimensional Diraclike electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge �surface � states in graphene depend on the edge termination �zigzag or armchair � and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electronelectron and electronphonon interactions in single layer and multilayer graphene are also
Topological gravity as large N topological gauge theory
 Adv. Theor. Math. Phys
, 1998
"... We consider topological closed string theories on CalabiYau manifolds which compute superpotential terms in the corresponding compactified type II effective action. In particular, near certain singularities we compare the partition function of this topological theory (the KodairaSpencer theory) to ..."
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Cited by 38 (4 self)
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We consider topological closed string theories on CalabiYau manifolds which compute superpotential terms in the corresponding compactified type II effective action. In particular, near certain singularities we compare the partition function of this topological theory (the KodairaSpencer theory) to SU(∞) ChernSimons theory on the vanishing 3cycle. We find agreement between these theories, which we check explicitly for the case of shrinking S3 and Lens spaces, at the perturbative level. Moreover, the gauge theory has nonperturbative contributions which have a natural interpretation in the Type IIB picture. We provide a heuristic explanation for this agreement as well as suggest further equivalences in other topological gravity/gauge systems. February
Quantum chromodynamics and other field theories on the light cone
, 1997
"... In recent years lightcone quantization of quantum field theory has emerged as a promising method for solving problems in the strong coupling regime. The approach has a number of unique features that make it particularly appealing, most notably, the ground state of the free theory is also a ground s ..."
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Cited by 37 (10 self)
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In recent years lightcone quantization of quantum field theory has emerged as a promising method for solving problems in the strong coupling regime. The approach has a number of unique features that make it particularly appealing, most notably, the ground state of the free theory is also a ground state of the full theory. We discuss the lightcone quantization of gauge theories from two perspectives: as a calculational tool for representing hadrons as QCD boundstates of relativistic quarks and gluons, and also as a novel method for simulating quantum field theory on a computer. The lightcone Fock state expansion of wavefunctions provides a precise definition of the parton model and a general calculus for hadronic matrix elements. We present several new applications of lightcone Fock methods, including calculations of exclusive weak decays of heavy hadrons, and intrinsic heavyquark contributions to structure functions. A general nonperturbative method for numerically solving quantum field theories, “discretized lightcone quantization”, is outlined and applied to several gauge theories. This method is invariant under the
Worldsheet formulations of gauge theories and gravity. talk given at the 7th Marcel Grossmann Meeting Stanford
, 1994
"... The evolution operator for states of gauge theories in the graph representation (closely related to the loop representation) is formulated as a weighted sum over worldsheets interpolating between initial and final graphs. As examples, lattice SU(2) BF and YangMills theories are expressed as worldsh ..."
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Cited by 37 (7 self)
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The evolution operator for states of gauge theories in the graph representation (closely related to the loop representation) is formulated as a weighted sum over worldsheets interpolating between initial and final graphs. As examples, lattice SU(2) BF and YangMills theories are expressed as worldsheet theories, and (formal) worldsheet forms of several continuum U(1) theories are given. It is argued that the world sheet framework should be ideal for representing GR, at least euclidean GR, in 4 dimensions, because it is adapted to both the 4diffeomorphism invariance of GR, and the discreteness of 3geometry found in the loop representation quantization of the theory. However, the weighting of worldsheets in GR has not yet been found. 1