1,728 research outputs found
Producing power-law distributions and damping word frequencies with two-stage language models
Standard statistical models of language fail to capture one of the most striking properties of natural languages: the power-law distribution in the frequencies of word tokens. We present a framework for developing statisticalmodels that can generically produce power laws, breaking generativemodels into two stages. The first stage, the generator, can be any standard probabilistic model, while the second stage, the adaptor, transforms the word frequencies of this model to provide a closer match to natural language. We show that two commonly used Bayesian models, the Dirichlet-multinomial model and the Dirichlet process, can be viewed as special cases of our framework. We discuss two stochastic processes-the Chinese restaurant process and its two-parameter generalization based on the Pitman-Yor process-that can be used as adaptors in our framework to produce power-law distributions over word frequencies. We show that these adaptors justify common estimation procedures based on logarithmic or inverse-power transformations of empirical frequencies. In addition, taking the Pitman-Yor Chinese restaurant process as an adaptor justifies the appearance of type frequencies in formal analyses of natural language and improves the performance of a model for unsupervised learning of morphology.48 page(s
The twisted open string partition function and Yukawa couplings
We use the operator formalism to derive the bosonic contribution to the
twisted open string partition function in toroidal compactifications. This
amplitude describes, for instance, the planar interaction between g+1
magnetized or intersecting D-branes. We write the result both in the closed and
in the open string channel in terms of Prym differentials on the appropriate
Riemann surface. Then we focus on the g=2 case for a 2-torus. By factorizing
the twisted partition function in the open string channel we obtain an explicit
expression for the 3-twist field correlator, which is the main ingredient in
the computation of Yukawa couplings in D-brane phenomenological models. This
provides an alternative method for computing these couplings that does not rely
on the stress-energy tensor technique.Comment: 32 pages, 5 figures, Latex; v2: typos correcte
Markov chains, -trivial monoids and representation theory
We develop a general theory of Markov chains realizable as random walks on
-trivial monoids. It provides explicit and simple formulas for the
eigenvalues of the transition matrix, for multiplicities of the eigenvalues via
M\"obius inversion along a lattice, a condition for diagonalizability of the
transition matrix and some techniques for bounding the mixing time. In
addition, we discuss several examples, such as Toom-Tsetlin models, an exchange
walk for finite Coxeter groups, as well as examples previously studied by the
authors, such as nonabelian sandpile models and the promotion Markov chain on
posets. Many of these examples can be viewed as random walks on quotients of
free tree monoids, a new class of monoids whose combinatorics we develop.Comment: Dedicated to Stuart Margolis on the occasion of his sixtieth
birthday; 71 pages; final version to appear in IJA
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