59,100 research outputs found
On the complexity of computing Gr\"obner bases for weighted homogeneous systems
Solving polynomial systems arising from applications is frequently made
easier by the structure of the systems. Weighted homogeneity (or
quasi-homogeneity) is one example of such a structure: given a system of
weights , -homogeneous polynomials are polynomials
which are homogeneous w.r.t the weighted degree
. Gr\"obner bases for weighted homogeneous systems can be
computed by adapting existing algorithms for homogeneous systems to the
weighted homogeneous case. We show that in this case, the complexity estimate
for Algorithm~\F5 \left(\binom{n+\dmax-1}{\dmax}^{\omega}\right) can be
divided by a factor . For zero-dimensional
systems, the complexity of Algorithm~\FGLM (where is the
number of solutions of the system) can be divided by the same factor
. Under genericity assumptions, for
zero-dimensional weighted homogeneous systems of -degree
, these complexity estimates are polynomial in the
weighted B\'ezout bound .
Furthermore, the maximum degree reached in a run of Algorithm \F5 is bounded by
the weighted Macaulay bound , and this bound is
sharp if we can order the weights so that . For overdetermined
semi-regular systems, estimates from the homogeneous case can be adapted to the
weighted case. We provide some experimental results based on systems arising
from a cryptography problem and from polynomial inversion problems. They show
that taking advantage of the weighted homogeneous structure yields substantial
speed-ups, and allows us to solve systems which were otherwise out of reach
Free and regular mixed-model sequences by a linear program-assisted hybrid algorithm GRASP-LP
A linear program-assisted hybrid algorithm (GRASP-LP) is presented to solve a mixed-model sequencing problem in an assembly line. The issue of the problem is to obtain manufacturing sequences of product models with the minimum work overload, allowing the free interruption of operations at workstations and preserving the production mix. The implemented GRASP-LP is compared with other procedures through a case study linked with the Nissan’ Engine Plant from Barcelona.Peer ReviewedPostprint (author's final draft
Combining Insertion and Deletion in RNA-editing Preserves Regularity
Inspired by RNA-editing as occurs in transcriptional processes in the living
cell, we introduce an abstract notion of string adjustment, called guided
rewriting. This formalism allows simultaneously inserting and deleting
elements. We prove that guided rewriting preserves regularity: for every
regular language its closure under guided rewriting is regular too. This
contrasts an earlier abstraction of RNA-editing separating insertion and
deletion for which it was proved that regularity is not preserved. The
particular automaton construction here relies on an auxiliary notion of slice
sequence which enables to sweep from left to right through a completed rewrite
sequence.Comment: In Proceedings MeCBIC 2012, arXiv:1211.347
Musical rhythm effects on visual attention are non-rhythmical: Evidence against metrical entrainment
The idea that external rhythms synchronize attention cross-modally has attracted much interest and scientific inquiry. Yet, whether associated attentional modulations are indeed rhythmical in that they spring from and map onto an underlying meter has not been clearly established. Here we tested this idea while addressing the shortcomings of previous work associated with confounding (i) metricality and regularity, (ii) rhythmic and temporal expectations or (iii) global and local temporal effects. We designed sound sequences that varied orthogonally (high/low) in metricality and regularity and presented them as task-irrelevant auditory background in four separate blocks. The participants' task was to detect rare visual targets occurring at a silent metrically aligned or misaligned temporal position. We found that target timing was irrelevant for reaction times and visual event-related potentials. High background regularity and to a lesser extent metricality facilitated target processing across metrically aligned and misaligned positions. Additionally, high regularity modulated auditory background frequencies in the EEG recorded over occipital cortex. We conclude that external rhythms, rather than synchronizing attention cross-modally, confer general, nontemporal benefits. Their predictability conserves processing resources that then benefit stimulus representations in other modalities
Decision Problems for Deterministic Pushdown Automata on Infinite Words
The article surveys some decidability results for DPDAs on infinite words
(omega-DPDA). We summarize some recent results on the decidability of the
regularity and the equivalence problem for the class of weak omega-DPDAs.
Furthermore, we present some new results on the parity index problem for
omega-DPDAs. For the specification of a parity condition, the states of the
omega-DPDA are assigned priorities (natural numbers), and a run is accepting if
the highest priority that appears infinitely often during a run is even. The
basic simplification question asks whether one can determine the minimal number
of priorities that are needed to accept the language of a given omega-DPDA. We
provide some decidability results on variations of this question for some
classes of omega-DPDAs.Comment: In Proceedings AFL 2014, arXiv:1405.527
Order regularity for Birkhoff interpolation with lacunary polynomials
In this short paper we present sufficient conditions for the order
regularity problem in Birkhoff interpolation with lacunary polynomials.
These conditions are a generalization of the Atkinson-Sharma theorem.Peer ReviewedPostprint (published version
Anosov subgroups: Dynamical and geometric characterizations
We study infinite covolume discrete subgroups of higher rank semisimple Lie
groups, motivated by understanding basic properties of Anosov subgroups from
various viewpoints (geometric, coarse geometric and dynamical). The class of
Anosov subgroups constitutes a natural generalization of convex cocompact
subgroups of rank one Lie groups to higher rank. Our main goal is to give
several new equivalent characterizations for this important class of discrete
subgroups. Our characterizations capture "rank one behavior" of Anosov
subgroups and are direct generalizations of rank one equivalents to convex
cocompactness. Along the way, we considerably simplify the original definition,
avoiding the geodesic flow. We also show that the Anosov condition can be
relaxed further by requiring only non-uniform unbounded expansion along the
(quasi)geodesics in the group.Comment: 88 page
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