1,929 research outputs found
From coinductive proofs to exact real arithmetic: theory and applications
Based on a new coinductive characterization of continuous functions we
extract certified programs for exact real number computation from constructive
proofs. The extracted programs construct and combine exact real number
algorithms with respect to the binary signed digit representation of real
numbers. The data type corresponding to the coinductive definition of
continuous functions consists of finitely branching non-wellfounded trees
describing when the algorithm writes and reads digits. We discuss several
examples including the extraction of programs for polynomials up to degree two
and the definite integral of continuous maps
Maximizing Protein Translation Rate in the Ribosome Flow Model: the Homogeneous Case
Gene translation is the process in which intracellular macro-molecules,
called ribosomes, decode genetic information in the mRNA chain into the
corresponding proteins. Gene translation includes several steps. During the
elongation step, ribosomes move along the mRNA in a sequential manner and link
amino-acids together in the corresponding order to produce the proteins.
The homogeneous ribosome flow model(HRFM) is a deterministic computational
model for translation-elongation under the assumption of constant elongation
rates along the mRNA chain. The HRFM is described by a set of n first-order
nonlinear ordinary differential equations, where n represents the number of
sites along the mRNA chain. The HRFM also includes two positive parameters:
ribosomal initiation rate and the (constant) elongation rate. In this paper, we
show that the steady-state translation rate in the HRFM is a concave function
of its parameters. This means that the problem of determining the parameter
values that maximize the translation rate is relatively simple. Our results may
contribute to a better understanding of the mechanisms and evolution of
translation-elongation. We demonstrate this by using the theoretical results to
estimate the initiation rate in M. musculus embryonic stem cell. The underlying
assumption is that evolution optimized the translation mechanism.
For the infinite-dimensional HRFM, we derive a closed-form solution to the
problem of determining the initiation and transition rates that maximize the
protein translation rate. We show that these expressions provide good
approximations for the optimal values in the n-dimensional HRFM already for
relatively small values of n. These results may have applications for synthetic
biology where an important problem is to re-engineer genomic systems in order
to maximize the protein production rate
Faster Query Answering in Probabilistic Databases using Read-Once Functions
A boolean expression is in read-once form if each of its variables appears
exactly once. When the variables denote independent events in a probability
space, the probability of the event denoted by the whole expression in
read-once form can be computed in polynomial time (whereas the general problem
for arbitrary expressions is #P-complete). Known approaches to checking
read-once property seem to require putting these expressions in disjunctive
normal form. In this paper, we tell a better story for a large subclass of
boolean event expressions: those that are generated by conjunctive queries
without self-joins and on tuple-independent probabilistic databases. We first
show that given a tuple-independent representation and the provenance graph of
an SPJ query plan without self-joins, we can, without using the DNF of a result
event expression, efficiently compute its co-occurrence graph. From this, the
read-once form can already, if it exists, be computed efficiently using
existing techniques. Our second and key contribution is a complete, efficient,
and simple to implement algorithm for computing the read-once forms (whenever
they exist) directly, using a new concept, that of co-table graph, which can be
significantly smaller than the co-occurrence graph.Comment: Accepted in ICDT 201
Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data
Constraint Programming (CP) has proved an effective paradigm to model and
solve difficult combinatorial satisfaction and optimisation problems from
disparate domains. Many such problems arising from the commercial world are
permeated by data uncertainty. Existing CP approaches that accommodate
uncertainty are less suited to uncertainty arising due to incomplete and
erroneous data, because they do not build reliable models and solutions
guaranteed to address the user's genuine problem as she perceives it. Other
fields such as reliable computation offer combinations of models and associated
methods to handle these types of uncertain data, but lack an expressive
framework characterising the resolution methodology independently of the model.
We present a unifying framework that extends the CP formalism in both model
and solutions, to tackle ill-defined combinatorial problems with incomplete or
erroneous data. The certainty closure framework brings together modelling and
solving methodologies from different fields into the CP paradigm to provide
reliable and efficient approches for uncertain constraint problems. We
demonstrate the applicability of the framework on a case study in network
diagnosis. We define resolution forms that give generic templates, and their
associated operational semantics, to derive practical solution methods for
reliable solutions.Comment: Revised versio
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