3,448 research outputs found
Synchronous Boltzmann machines can be universal approximators
AbstractWe prove in this paper that the class of reversible synchronous Boltzmann machines is universal for the representation of arbitrary functions defined on finite sets. This completes a similar result from Sussmann in the sequential case
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Summary of challenges relevant to refugees’ education in Jordan
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Stochastic Development Regression on Non-Linear Manifolds
We introduce a regression model for data on non-linear manifolds. The model
describes the relation between a set of manifold valued observations, such as
shapes of anatomical objects, and Euclidean explanatory variables. The approach
is based on stochastic development of Euclidean diffusion processes to the
manifold. Defining the data distribution as the transition distribution of the
mapped stochastic process, parameters of the model, the non-linear analogue of
design matrix and intercept, are found via maximum likelihood. The model is
intrinsically related to the geometry encoded in the connection of the
manifold. We propose an estimation procedure which applies the Laplace
approximation of the likelihood function. A simulation study of the performance
of the model is performed and the model is applied to a real dataset of Corpus
Callosum shapes
On the Complexity of Temporal-Logic Path Checking
Given a formula in a temporal logic such as LTL or MTL, a fundamental problem
is the complexity of evaluating the formula on a given finite word. For LTL,
the complexity of this task was recently shown to be in NC. In this paper, we
present an NC algorithm for MTL, a quantitative (or metric) extension of LTL,
and give an NCC algorithm for UTL, the unary fragment of LTL. At the time of
writing, MTL is the most expressive logic with an NC path-checking algorithm,
and UTL is the most expressive fragment of LTL with a more efficient
path-checking algorithm than for full LTL (subject to standard
complexity-theoretic assumptions). We then establish a connection between LTL
path checking and planar circuits, which we exploit to show that any further
progress in determining the precise complexity of LTL path checking would
immediately entail more efficient evaluation algorithms than are known for a
certain class of planar circuits. The connection further implies that the
complexity of LTL path checking depends on the Boolean connectives allowed:
adding Boolean exclusive or yields a temporal logic with P-complete
path-checking problem
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