In this article we consider a piston modelled by a potential in the presence of extra dimensions. We analyze the functional determinant and the Casimir effect for this configuration.In order to compute the determinant and Casimir force we employ the zeta function scheme.Essentially, the computation reduces to the analysis of the zeta function associated with a scalar field living on an interval [0, L] in a background potential. Although, as a model for a piston, it seems reasonable to assume a potential having compact support within [0, L], we provide a formalism that can be applied to any sufficiently smooth potential.
A compressed full-text self-index for a text T is a data structure requiring reduced space and able to search for patterns P in T . It can also reproduce any substring of T , thus actually replacing T . Despite the recent explosion of interest on compressed indexes, there has not been much progress on functionalities beyond the basic exact search. In this paper we focus on indexed approximate string matching (ASM), which is of great interest, say, in bioinformatics. We study ASM algorithms for Lempel-Ziv compressed indexes and for compressed suffix trees/arrays. Most compressed self-indexes belong to one of these classes. We start by adapting the classical method of partitioning into exact search to self-indexes, and optimize it over a representative of either class of self-index. Then, we show that a LempelZiv index can be seen as an extension of the classical q-samples index. We give new insights on this type of index, which can be of independent interest, and then apply them to a LempelZiv index. Finally, we improve hierarchical verification, a successful technique for sequential searching, so as to extend the matches of pattern pieces to the left or right. Most compressed suffix trees/arrays support the required bidirectionality, thus enabling the implementation of the improved technique. In turn, the improved verification largely reduces the accesses to the text, which are expensive in self-indexes. We show experimentally that our algorithms are competitive and provide useful space-time tradeoffs compared to classical indexes.
In this work the Casimir effect is studied for scalar fields in the presence of boundaries and under the influence of arbitrary smooth potentials of compact support. In this setting, piston configurations are analyzed in which the piston is modeled by a potential. For these configurations, analytic results for the Casimir energy and force are obtained by employing the zeta function regularization method. Also, explicit numerical results for the Casimir force are provided for pistons modeled by a class of compactly supported potentials that are realizable as delta-sequences. These results are then generalized to higher dimensional pistons by considering additional Kaluza-Klein dimensions.
In female Wistar rats (n = 316) under pentobarbital sodium anesthesia, the soleus muscle was autografted with its nerve reimplanted. One purpose was to characterize the chronological development of graft innervation and recruitment during locomotion. Furthermore, we tested hypotheses regarding the efficacy of run conditioning of different intensities, durations, and postgrafting initiation times to alter mass and pyruvate-malate oxidation capacity of grafts. Choline acetyltransferase activity of grafts increased from 10% of control value at 7 days postgrafting to 55 and 100% at days 28 and 56, respectively. Running-induced glycogen depletion occurred in grafts; this is consistent with graft recruitment during locomotion. There was a threshold of conditioning intensity below which no improvements occurred and above which there were improvements. Spring (50 m/min) and endurance (30 m/min) conditioning of a duration of at least 28 days that was initiated at 28 or 56 days postgrafting increased mass of grafts by 30% compared with grafts from nonconditioned rats. Easy conditioning (15 m/min) had no effect on graft mass. Changes in graft total protein content paralleled those of mass. Oxidation capacity of grafts increased significantly with some conditioning protocols, but not to the same extent as mass. The exercise-induced adaptations should improve graft function in the host organism.
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