1,144 research outputs found
Sampling algebraic sets in local intrinsic coordinates
Numerical data structures for positive dimensional solution sets of
polynomial systems are sets of generic points cut out by random planes of
complimentary dimension. We may represent the linear spaces defined by those
planes either by explicit linear equations or in parametric form. These
descriptions are respectively called extrinsic and intrinsic representations.
While intrinsic representations lower the cost of the linear algebra
operations, we observe worse condition numbers. In this paper we describe the
local adaptation of intrinsic coordinates to improve the numerical conditioning
of sampling algebraic sets. Local intrinsic coordinates also lead to a better
stepsize control. We illustrate our results with Maple experiments and
computations with PHCpack on some benchmark polynomial systems.Comment: 13 pages, 2 figures, 2 algorithms, 2 table
Powerful nonparametric checks for quantile regression
We address the issue of lack-of-fit testing for a parametric quantile
regression. We propose a simple test that involves one-dimensional kernel
smoothing, so that the rate at which it detects local alternatives is
independent of the number of covariates. The test has asymptotically gaussian
critical values, and wild bootstrap can be applied to obtain more accurate ones
in small samples. Our procedure appears to be competitive with existing ones in
simulations. We illustrate the usefulness of our test on birthweight data.Comment: 32 pages, 2 figure
A dynamical systems approach to the discrimination of the modes of operation of cryptographic systems
Evidence of signatures associated with cryptographic modes of operation is
established. Motivated by some analogies between cryptographic and dynamical
systems, in particular with chaos theory, we propose an algorithm based on
Lyapunov exponents of discrete dynamical systems to estimate the divergence
among ciphertexts as the encryption algorithm is applied iteratively. The
results allow to distinguish among six modes of operation, namely ECB, CBC,
OFB, CFB, CTR and PCBC using DES, IDEA, TEA and XTEA block ciphers of 64 bits,
as well as AES, RC6, Twofish, Seed, Serpent and Camellia block ciphers of 128
bits. Furthermore, the proposed methodology enables a classification of modes
of operation of cryptographic systems according to their strength.Comment: 14 pages, 10 figure
Counterexample Generation in Probabilistic Model Checking
Providing evidence for the refutation of a property is an essential, if not the most important, feature of model checking. This paper considers algorithms for counterexample generation for probabilistic CTL formulae in discrete-time Markov chains. Finding the strongest evidence (i.e., the most probable path) violating a (bounded) until-formula is shown to be reducible to a single-source (hop-constrained) shortest path problem. Counterexamples of smallest size that deviate most from the required probability bound can be obtained by applying (small amendments to) k-shortest (hop-constrained) paths algorithms. These results can be extended to Markov chains with rewards, to LTL model checking, and are useful for Markov decision processes. Experimental results show that typically the size of a counterexample is excessive. To obtain much more compact representations, we present a simple algorithm to generate (minimal) regular expressions that can act as counterexamples. The feasibility of our approach is illustrated by means of two communication protocols: leader election in an anonymous ring network and the Crowds protocol
Reparametrizing Swung Surfaces over the Reals
Let K⊆R be a computable subfield of the real numbers (for instance, Q). We present an algorithm to decide whether a given parametrization of a rational swung surface, with coefficients in K(i), can be reparametrized over a real (i.e., embedded in R) finite field extension of K. Swung surfaces include, in particular, surfaces of revolution
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