A transformation monoid on a set Ω is called synchronizing if it contains an element of rank 1 (that is, mapping the whole of Ω to a single point). In this paper, I tackle the question: given n and k, what is the probability that the submonoid of the full transformation monoid Tn generated by k random transformations is synchronizing? The question has some similarities with a similar question a...

Example (1.1). We will start with some examples of dynamical systems: • S with Lebesgue σ-algebra and normalised measure, and rotation as the transformation; • multidimensional tori with the product σ-algebra, product measure and transformation given by an algebraic automorphism. (Lebesgue measure is preserved by unicity of the Haar measure). • for dynamical systems, the Hamiltonian flow ( ∂p =...

SMOOTHING A PROBABILISTIC LEXICON VIA SYNTACTIC TRANSFORMATIONS Jason Michael Eisner Supervisor: Professor Mitch Marcus Probabilistic parsing requires a lexicon that specifies each word’s syntactic preferences in terms of probabilities. To estimate these probabilities for words that were poorly observed during training, this thesis assumes the existence of arbitrarily powerful transformations (...

We consider a probability measure m on a Hilbert space X and a bounded linear transformation on X that preserves the measure. We characterize the linear dynamical systems (X, m, T) for the cases where either X is finite dimensional or T is unitary and we give an example where T is a weighted shift operator. We apply the results to the limit identification problem for a vector-valued ergodic the...

In this paper we make a novel use of the Johnson-Lindenstrauss Lemma. The Lemma has an existential form saying that there exists a JL transformation f of the data points into lower dimensional space such that all of them fall into predefined error range δ. We formulate in this paper a theorem stating that we can choose the target dimensionality in a random projection type JL linear transformati...

In this work we present an algorithmic transformation, that given two algorithms implementing respectively, sorting and searching, provides a randomized sorting algorithm that with high probability requires less time than the original sorting algorithm. This claim is true for a wide range of the parameters that describe the running time of the procedures for sorting and searching.

We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.

In this paper, we introduce a generalized minimum meansquare error short-time spectral amplitude estimator with a new prior estimation of the speech probability density function based on momentcumulant transformation. From the objective and subjective evaluation experiments, we show the improved noise reduction performance of the proposed method. key words: generalized MMSE STSA estimator, spee...

It is shown that for any given multi-dimensional probability distribution, there exists a unique coordinate-wise transformation such that the transformed distribution satisfies a Stein-type identity. The proof is based on an energy minimization problem over a subset of the Wasserstein space. The result is interpreted as a generalization of the diagonal scaling theorem established by Marshall an...