3,408 research outputs found
Tableaux Modulo Theories Using Superdeduction
We propose a method that allows us to develop tableaux modulo theories using
the principles of superdeduction, among which the theory is used to enrich the
deduction system with new deduction rules. This method is presented in the
framework of the Zenon automated theorem prover, and is applied to the set
theory of the B method. This allows us to provide another prover to Atelier B,
which can be used to verify B proof rules in particular. We also propose some
benchmarks, in which this prover is able to automatically verify a part of the
rules coming from the database maintained by Siemens IC-MOL. Finally, we
describe another extension of Zenon with superdeduction, which is able to deal
with any first order theory, and provide a benchmark coming from the TPTP
library, which contains a large set of first order problems.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0117
Accurate and efficient evaluation of the a posteriori error estimator in the reduced basis method
The reduced basis method is a model reduction technique yielding substantial
savings of computational time when a solution to a parametrized equation has to
be computed for many values of the parameter. Certification of the
approximation is possible by means of an a posteriori error bound. Under
appropriate assumptions, this error bound is computed with an algorithm of
complexity independent of the size of the full problem. In practice, the
evaluation of the error bound can become very sensitive to round-off errors. We
propose herein an explanation of this fact. A first remedy has been proposed in
[F. Casenave, Accurate \textit{a posteriori} error evaluation in the reduced
basis method. \textit{C. R. Math. Acad. Sci. Paris} \textbf{350} (2012)
539--542.]. Herein, we improve this remedy by proposing a new approximation of
the error bound using the Empirical Interpolation Method (EIM). This method
achieves higher levels of accuracy and requires potentially less
precomputations than the usual formula. A version of the EIM stabilized with
respect to round-off errors is also derived. The method is illustrated on a
simple one-dimensional diffusion problem and a three-dimensional acoustic
scattering problem solved by a boundary element method.Comment: 26 pages, 10 figures. ESAIM: Mathematical Modelling and Numerical
Analysis, 201
Anatomically-based skeleton kinetics and pose estimation in freely-moving rodents
Forming a complete picture of the relationship between neural activity and body kinetics requires quantification of skeletal joint biomechanics during behavior. However, without detailed knowledge of the underlying skeletal motion, inferring joint kinetics from surface tracking approaches is difficult, especially for animals where the relationship between surface anatomy and skeleton changes during motion. Here we developed a videography-based method enabling detailed three-dimensional kinetic quantification of an anatomically defined skeleton in untethered freely-behaving animals. This skeleton-based model has been constrained by anatomical principles and joint motion limits and provided skeletal pose estimates for a range of rodent sizes, even when limbs were occluded. Model-inferred joint kinetics for both gait and gap-crossing behaviors were verified by direct measurement of limb placement, showing that complex decision-making behaviors can be accurately reconstructed at the level of skeletal kinetics using our anatomically constrained model
There is entanglement in the primes
Large series of prime numbers can be superposed on a single quantum register
and then analyzed in full parallelism. The construction of this Prime state is
efficient, as it hinges on the use of a quantum version of any efficient
primality test. We show that the Prime state turns out to be very entangled as
shown by the scaling properties of purity, Renyi entropy and von Neumann
entropy. An analytical approximation to these measures of entanglement can be
obtained from the detailed analysis of the entanglement spectrum of the Prime
state, which in turn produces new insights in the Hardy-Littlewood conjecture
for the pairwise distribution of primes. The extension of these ideas to a Twin
Prime state shows that this new state is even more entangled than the Prime
state, obeying majorization relations. We further discuss the construction of
quantum states that encompass relevant series of numbers and opens the
possibility of applying quantum computation to Arithmetics in novel ways.Comment: 30 pages, 11 Figs. Addition of two references and correction of typo
Representation of conscious percept without report in the macaque face patch network
A powerful paradigm to identify the neural correlates of consciousness is binocular rivalry, wherein a constant visual stimulus evokes a varying conscious percept. It has recently been suggested that activity modulations observed during rivalry could represent the act of report rather than the conscious percept itself. Here, we performed single-unit recordings from face patches in macaque inferotemporal (IT) cortex using a no-report paradigm in which the animal's conscious percept was inferred from eye movements. We found high proportions of IT neurons represented the conscious percept even without active report. Population activity in single trials, measured using a new 128-site Neuropixels-like electrode, was more weakly modulated by rivalry than by physical stimulus transitions, but nevertheless allowed decoding of the changing conscious percept. These findings suggest that macaque face patches encode both the physical stimulus and the animal's conscious visual percept, and the latter encoding does not require active report
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