15,168 research outputs found
Perspectives for proof unwinding by programming languages techniques
In this chapter, we propose some future directions of work, potentially
beneficial to Mathematics and its foundations, based on the recent import of
methodology from the theory of programming languages into proof theory. This
scientific essay, written for the audience of proof theorists as well as the
working mathematician, is not a survey of the field, but rather a personal view
of the author who hopes that it may inspire future and fellow researchers
On the enumeration of closures and environments with an application to random generation
Environments and closures are two of the main ingredients of evaluation in
lambda-calculus. A closure is a pair consisting of a lambda-term and an
environment, whereas an environment is a list of lambda-terms assigned to free
variables. In this paper we investigate some dynamic aspects of evaluation in
lambda-calculus considering the quantitative, combinatorial properties of
environments and closures. Focusing on two classes of environments and
closures, namely the so-called plain and closed ones, we consider the problem
of their asymptotic counting and effective random generation. We provide an
asymptotic approximation of the number of both plain environments and closures
of size . Using the associated generating functions, we construct effective
samplers for both classes of combinatorial structures. Finally, we discuss the
related problem of asymptotic counting and random generation of closed
environemnts and closures
Predicting Genetic Regulatory Response Using Classification
We present a novel classification-based method for learning to predict gene
regulatory response. Our approach is motivated by the hypothesis that in simple
organisms such as Saccharomyces cerevisiae, we can learn a decision rule for
predicting whether a gene is up- or down-regulated in a particular experiment
based on (1) the presence of binding site subsequences (``motifs'') in the
gene's regulatory region and (2) the expression levels of regulators such as
transcription factors in the experiment (``parents''). Thus our learning task
integrates two qualitatively different data sources: genome-wide cDNA
microarray data across multiple perturbation and mutant experiments along with
motif profile data from regulatory sequences. We convert the regression task of
predicting real-valued gene expression measurement to a classification task of
predicting +1 and -1 labels, corresponding to up- and down-regulation beyond
the levels of biological and measurement noise in microarray measurements. The
learning algorithm employed is boosting with a margin-based generalization of
decision trees, alternating decision trees. This large-margin classifier is
sufficiently flexible to allow complex logical functions, yet sufficiently
simple to give insight into the combinatorial mechanisms of gene regulation. We
observe encouraging prediction accuracy on experiments based on the Gasch S.
cerevisiae dataset, and we show that we can accurately predict up- and
down-regulation on held-out experiments. Our method thus provides predictive
hypotheses, suggests biological experiments, and provides interpretable insight
into the structure of genetic regulatory networks.Comment: 8 pages, 4 figures, presented at Twelfth International Conference on
Intelligent Systems for Molecular Biology (ISMB 2004), supplemental website:
http://www.cs.columbia.edu/compbio/geneclas
Symmetry-breaking Answer Set Solving
In the context of Answer Set Programming, this paper investigates
symmetry-breaking to eliminate symmetric parts of the search space and,
thereby, simplify the solution process. We propose a reduction of disjunctive
logic programs to a coloured digraph such that permutational symmetries can be
constructed from graph automorphisms. Symmetries are then broken by introducing
symmetry-breaking constraints. For this purpose, we formulate a preprocessor
that integrates a graph automorphism system. Experiments demonstrate its
computational impact.Comment: Proceedings of ICLP'10 Workshop on Answer Set Programming and Other
Computing Paradig
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Automatic Generation of Cognitive Theories using Genetic Programming
Cognitive neuroscience is the branch of neuroscience that studies the neural mechanisms underpinning cognition and develops theories explaining them. Within cognitive neuroscience, computational neuroscience focuses on modeling behavior, using theories expressed as computer programs. Up to now, computational theories have been formulated by neuroscientists. In this paper, we present a new approach to theory development in neuroscience: the automatic generation and testing of cognitive theories using genetic programming. Our approach evolves from experimental data cognitive theories that explain âthe mental programâ that subjects use to solve a specific task. As an example, we have focused on a typical neuroscience experiment, the delayed-match-to-sample (DMTS) task. The main goal of our approach is to develop a tool that neuroscientists can use to develop better cognitive theories
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