This paper describes the Duluth systems that participated in the Sentiment Analysis track of the i2b2/VA/Cincinnati Children's 2011 Challenge. The top Duluth system was a rule-based approach derived through manual corpus analysis and the use of measures of association to identify significant ngrams. This performed in the median range of systems, attaining an F-measure of 0.45. The second system...

This gives us a new probability measure on (Ω,F), so we may define expectations with respect to this conditioned probability measure. Thus for F measurable Y : Ω → R we define the conditional expectation E[Y | X = x] by taking the expectation of Y with respect to the measure (1.1). Consider now how to generalize the idea of conditional probability to the case when P (X = x) = 0. We wish to do t...

This paper describes our study on identifying semantic relations that exist between diseases and treatments in biomedical sentences. We focus on three semantic relations: Cure, Prevent, and Side Effect. The contributions of this paper consists in the fact that better results are obtained compared to previous studies and the fact that our research settings allow the integration of biomedical and...

Kaimanovich and Masur [14] showed that a random walk on the mapping class group for an initial distribution whose support generates a non-elementary subgroup, when projected into Teichmüller space converges almost surely to a point in the space P M F of projective measured foliations on the surface. This defines a harmonic measure on P M F . Here, we show that when the initial distribution has ...

Statistical Models " Y is a random variable with density function f (y; θ) or f (y) ". This is the starting point for most of the material to be covered. Typically Y will be a scalar random variable or a vector random variable of length n, and f (y; θ) will be a density function with respect to counting measure or Lebesgue measure. The problem is to reason from observed data y back to θ or f (·...

We call a dynamical system on a measurable metric space measureexpansive if the probability of two orbits remain close each other for all time is negligible (i.e. zero). We extend results of expansive systems on compact metric spaces to the measure-expansive context. For instance, the measureexpansive homeomorphisms are characterized as those homeomorphisms f for which the diagonal is almost in...

A two-argument function is computed privately by two parties if after the computation, no party should know anything about the other inputs except for what he is able to deduce from his own input and the function value. In [1] Bar-Yehuda, Chor, Kushilevitz, and Orlitsky give a complete characterisation of two-argument functions which can be computed privately (in the information-theoretical sen...

It turns out that H1 is a measure, now called one-dimensional Hausdorff measure because it was generalized by Hausdorff [10] to the whole family of measures Hα, where α is any positive number (integer or noninteger). The modern theory of “fractals” is largely based on the notion of the Hausdorff dimension dimH (F) of a set F , defined by dimH (F) = inf{α > 0 : Hα(F) = 0}. We recommend the book ...

We relate the decomposition over a; b] of a measure dd (on R) into absolutely continuous, pure point, and singular continuous pieces to the behavior of integrals b R a (Im F(x + ii)) p dx as # 0. Here F is the Borel transform of dd, that is, F(z) = R (x ? z) ?1 dd(x). x1. Introduction Given any positive measure on R with Z dd(x) 1 + jxj < 1; (1.1) one can deene its Borel transform by F(z) = Z d...

where Entμ(f ) is the entropy of f with respect to μ (see below). It is well-known that the product measure μ of μ on R then satisfies the preceding inequalities (with the Euclidean length of the gradient of the function f on R) with the same constant C, in particular independent of the dimension n. Let now H be a smooth function on R such that ∫ edμ < ∞. Define Q the probability measure on R w...