Blind Normalization of Speech From Different Channels

We show how to construct a channel-independent representation of speech that has propagated through a noisy reverberant channel. This is done by blindly rescaling the cepstral time series by a non-linear function, with the form of this scale function being determined by previously encountered cepstra from that channel. The rescaled form of the time series is an invariant property of it in the following sense: it is unaffected if the time series is transformed by any time-independent invertible distortion. Because a linear channel with stationary noise and impulse response transforms cepstra in this way, the new technique can be used to remove the channel dependence of a cepstral time series. In experiments, the method achieved greater channel-independence than cepstral mean normalization, and it was comparable to the combination of cepstral mean normalization and spectral subtraction, despite the fact that no measurements of channel noise or reverberations were required (unlike spectral subtraction).Comment: 25 pages, 7 figure

First-order limits, an analytical perspective

In this paper we present a novel approach to graph (and structural) limits based on model theory and analysis. The role of Stone and Gelfand dualities is displayed prominently and leads to a general theory, which we believe is naturally emerging. This approach covers all the particular examples of structural convergence and it put the whole in new context. As an application, it leads to new intermediate examples of structural convergence and to a "grand conjecture" dealing with sparse graphs. We survey the recent developments

Characterizing Quantifier Extensions of Dependence Logic

We characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quantifiers in terms of quantifier extensions of existential second-order logic.Comment: 9 page

On theories of random variables

We study theories of spaces of random variables: first, we consider random variables with values in the interval $[0,1]$, then with values in an arbitrary metric structure, generalising Keisler's randomisation of classical structures. We prove preservation and non-preservation results for model theoretic properties under this construction: i) The randomisation of a stable structure is stable. ii) The randomisation of a simple unstable structure is not simple. We also prove that in the randomised structure, every type is a Lascar type

On Spatial Point Processes with Uniform Births and Deaths by Random Connection

This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current configuration for some response function $f$. An equivalent view point is that each pair of points of the configuration establishes a random connection at an exponential time determined by $f$, which results in the death of one of the two points. We concentrate on space-motion invariant processes of this type. Under some natural conditions on $f$, we construct the unique time-stationary regime of this class of point processes by a coupling argument. We then use the birth and death structure to establish a hierarchy of balance integral relations between the factorial moment measures. Finally, we show that the time-stationary point process exhibits a certain kind of repulsion between its points that we call $f$-repulsion

Ignorance and indifference

The epistemic state of complete ignorance is not a probability distribution. In it, we assign the same, unique, ignorance degree of belief to any contingent outcome and each of its contingent, disjunctive parts. That this is the appropriate way to represent complete ignorance is established by two instruments, each individually strong enough to identify this state. They are the principle of indifference (PI) and the notion that ignorance is invariant under certain redescriptions of the outcome space, here developed into the 'principle of invariance of ignorance' (PII). Both instruments are so innocuous as almost to be platitudes. Yet the literature in probabilistic epistemology has misdiagnosed them as paradoxical or defective since they generate inconsistencies when conjoined with the assumption that an epistemic state must be a probability distribution. To underscore the need to drop this assumption, I express PII in its most defensible form as relating symmetric descriptions and show that paradoxes still arise if we assume the ignorance state to be a probability distribution. Copyright 2008 by the Philosophy of Science Association. All rights reserved