Search results for "General Computer Science"
showing 10 items of 895 documents
Periodicity, morphisms, and matrices
2003
In 1965, Fine and Wilf proved the following theorem: if (fn)n≥0 and (gn)n≥0 are periodic sequences of real numbers, of period lengths h and k, respectively, and fn = gn for 0 ≤ n > h + k - gcd(h,k), then fn = gn for all n ≥ 0. Furthermore, the constant h + k - gcd(h,k) is best possible. In this paper, we consider some variations on this theorem. In particular, we study the case where fn ≤ gn, instead of fn = gn. We also obtain generalizations to more than two periods.We apply our methods to a previously unsolved conjecture on iterated morphisms, the decreasing length conjecture: if h : Σ* → Σ* is a morphism with |Σ|= n, and w is a word with |w| < |h(w)| < |h2(w)| < ... < |hk(w)|, then k ≤ n.
A multidimensional critical factorization theorem
2005
AbstractThe Critical Factorization Theorem is one of the principal results in combinatorics on words. It relates local periodicities of a word to its global periodicity. In this paper we give a multidimensional extension of it. More precisely, we give a new proof of the Critical Factorization Theorem, but in a weak form, where the weakness is due to the fact that we loose the tightness of the local repetition order. In exchange, we gain the possibility of extending our proof to the multidimensional case. Indeed, this new proof makes use of the Theorem of Fine and Wilf, that has several classical generalizations to the multidimensional case.
Quantitative prediction of effective material properties of heterogeneous media
1999
Effective electrical conductivity and electrical permittivity of water-saturated natural sandstones are evaluated on the basis of local porosity theory (LPT). In contrast to earlier methods, which characterize the underlying microstructure only through the volume fraction, LPT incorporates geometric information about the stochastic microstructure in terms of local porosity distribution and local percolation probabilities. We compare the prediction of LPT and of traditional effective medium theory with the exact results. The exact results for the conductivity and permittivity are obtained by solving the microscopic mixed boundary value problem for the Maxwell equations in the quasistatic app…
Effect of electron correlation corrections on phase competition in Ag film on MgO substrate
2002
Abstract The effect of electron correlation corrections in the novel theory predicting the growth mode of a thin metallic film on an insulating substrate has been studied. We discuss the influence of the substrate slab thickness on the energies of formation for several two-dimensional phases, which, in principle, may form in Ag layer on (0 0 1) MgO substrate. We analyze also the sensitivity of the key energy parameter––Fourier transform of the mixing potential V (0) to the choice of correlation functionals.
Molecular dynamics study of high-pressure alumina polymorphs with a tight-binding variable-charge model
2016
Abstract A tight-binding variable-charge model aimed at performing large-scale realistic simulations of bulk, surfaces and interfaces of aluminum oxides have been developed. This model is based on the charge equilibration (QEq) method and explicitly takes into account the mixed iono–covalent character of the metal–oxygen bond by means of a tight-binding analytical approach in the second-moment approximation of the electronic structure. The parameters of the model were optimized to reproduce structural and energetic properties of the α-Al2O3 corundum structure at room temperature and pressure. The model exhibits a good transferability between five alumina polymorphs: corundum, Rh2O3(II)-type…
The smectic phase in semiflexible polymer materials: A large scale Molecular Dynamics study
2019
Abstract Semiflexible polymers in concentrated lyotropic solution are studied within a bead-spring model by molecular dynamics simulations, focusing on the emergence of a smectic A phase and its properties. We systematically vary the density of the monomeric units for several contour lengths that are taken smaller than the chain persistence length. The difficulties concerning the equilibration of such systems and the choice of appropriate ensemble (constant volume versus constant pressure, where all three linear dimensions of the simulation box can fluctuate independently) are carefully discussed. Using HOOMD-blue on graphics processing units, systems containing more than a million monomeri…
Sur les Codes ZigZag et Leur Décidabilité
1990
AbstractThis paper deals with zigzag factorizations and zigzag codes. The language of “zigzag” over a regular language is represented by constructing a special family of two-way automata. Decidability of zigzag codes, previously shown for the finite languages, is proved here for all regular languages by the analysis of the set of “crossing sequences” produced by a two-way automation in the family. We also obtain that it is decidable whether or not a two-way automation of a certain type is non-ambiguous.RésuméDans ce papier on reprend les notions de factorisation zigzag et de code zigzag. On construit pour tout langage rationnel, une famille d'automates bilatéres lesquels reconnaissent les m…
Mathematical description of the stimuli to the lateral line system of fish derived from a three-dimensional flow field analysis
1992
The spatial distributions of the stimuli to the lateral line system of a fish moving alongside or above a plane surface are derived mathematically. The derivation was done from the analysis of the three-dimensional potential flow field on the surface of fish with bodies of circular cross-section with different shapes.
A minimal Gō-model for rebuilding whole genome structures from haploid single-cell Hi-C data
2020
Abstract We present a minimal computational model, which allows very fast, on-the-fly construction of three dimensional haploid interphase genomes from single-cell Hi-C contact maps using the HOOMD-blue molecular dynamics package on graphics processing units. Chromosomes are represented by a string of connected beads, each of which corresponds to 100,000 base pairs, and contacts are mediated via a structure-based harmonic potential. We suggest and test two minimization protocols which consistently fold into conformationally similar low energy states. The latter are similar to previously published structures but are calculated in a fraction of the time. We find evidence that mere fulfillment…
Small-signal analysis of the encoder mechanism in the lobster stretch receptor and the frog and cat muscle spindle.
1975
Ausgehend von der Leitwert-Potential-Beziehung als Bedingung fur die Impulsauslosung an erregbaren Membranen (Chaplain, 1974) wird eine Kleinsignal-Analyse des Kodierungsvorganges in Mechanorezeptoren beschrieben. Hierbei wird die Theorie der Systeme mit zeitvariablen Parametern angewendet. Das beschriebene mathematische Modell erlaubt quantitative Aussagen fur den Frequenzgang unabhangig davon ob die Momentafrequenz oder die Impulsdichte als Ausgangssignal betrachtet wird. Die Approximation experimenteller Daten gelingt sowohl fur die Ansteuerung des Kodierers bei intrazellularer Stromstimulierung im Fall des Dehnungsrezeptors wie auch durch Leitwertanderungen als Folge des mechano-elektri…