Search results for "Exponential growth"
showing 10 items of 52 documents
Involution Codimensions of Finite Dimensional Algebras and Exponential Growth
1999
Abstract Let F be a field of characteristic zero and let A be a finite dimensional algebra with involution ∗ over F . We study the asymptotic behavior of the sequence of ∗ -codimensions c n ( A , ∗ ) of A and we show that Exp(A, ∗ ) = lim n → ∞ c n ( A , ∗ ) exists and is an integer. We give an explicit way for computing Exp( A , ∗ ) and as a consequence we obtain the following characterization of ∗ -simple algebras: A is ∗ -simple if and only if Exp( A , ∗ ) = dim F A .
Star-polynomial identities: computing the exponential growth of the codimensions
2017
Abstract Can one compute the exponential rate of growth of the ⁎-codimensions of a PI-algebra with involution ⁎ over a field of characteristic zero? It was shown in [2] that any such algebra A has the same ⁎-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution B. Here, by exploiting this result we are able to provide an exact estimate of the exponential rate of growth e x p ⁎ ( A ) of any PI-algebra A with involution. It turns out that e x p ⁎ ( A ) is an integer and, in case the base field is algebraically closed, it coincides with the dimension of an admissible subalgebra of maximal dimension of B.
Finite-dimensional non-associative algebras and codimension growth
2011
AbstractLet A be a (non-necessarily associative) finite-dimensional algebra over a field of characteristic zero. A quantitative estimate of the polynomial identities satisfied by A is achieved through the study of the asymptotics of the sequence of codimensions of A. It is well known that for such an algebra this sequence is exponentially bounded.Here we capture the exponential rate of growth of the sequence of codimensions for several classes of algebras including simple algebras with a special non-degenerate form, finite-dimensional Jordan or alternative algebras and many more. In all cases such rate of growth is integer and is explicitly related to the dimension of a subalgebra of A. One…
An almost nilpotent variety of exponent 2
2013
We construct a non-associative algebra A over a field of characteristic zero with the following properties: if V is the variety generated by A, then V has exponential growth but any proper subvariety of V is nilpotent. Moreover, by studying the asymptotics of the sequence of codimensions of A we deduce that exp(V) = 2.
Dynamical scaling of surface growth in simple lattice models
2003
We present extensive simulations of the atomistic Edwards-Wilkinson (EW) and Restricted Edwards-Wilkinson (REW) models in 2+1 dimensions. Dynamic finite-size scaling analyses of the interfacial width and structure factor provide the estimates for the dynamic exponent z=1.65+/-0.05 for the EW model and z=2.0+/-0.1 for the REW model. The stochastic contribution to the interface velocity U due to the deposition and diffusion of particles is characterized for both the models using a blocking procedure. For the EW model the time-displaced temporal correlations in U show nonexponential decay, while the temporal correlations decay exponentially for the REW model. Dynamical scaling of the temporal …
Enhancerless Cytomegalovirus Is Capable of Establishing a Low-Level Maintenance Infection in Severely Immunodeficient Host Tissues but Fails in Expon…
2010
ABSTRACT Major immediate-early transcriptional enhancers are genetic control elements that act, through docking with host transcription factors, as a decisive regulatory unit for efficient initiation of the productive virus cycle. Animal models are required for studying the function of enhancers paradigmatically in host organs. Here, we have sought to quantitatively assess the establishment, maintenance, and level of in vivo growth of enhancerless mutants of murine cytomegalovirus in comparison with those of an enhancer-bearing counterpart in models of the immunocompromised or immunologically immature host. Evidence is presented showing that enhancerless viruses are capable of forming restr…
Motif patterns in 2D
2008
AbstractMotif patterns consisting of sequences of intermixed solid and don’t-care characters have been introduced and studied in connection with pattern discovery problems of computational biology and other domains. In order to alleviate the exponential growth of such motifs, notions of maximal saturation and irredundancy have been formulated, whereby more or less compact subsets of the set of all motifs can be extracted, that are capable of expressing all others by suitable combinations. In this paper, we introduce the notion of maximal irredundant motifs in a two-dimensional array and develop initial properties and a combinatorial argument that poses a linear bound on the total number of …
Anomalies on codimension growth of algebras
2015
Abstract This paper deals with the asymptotic behavior of the sequence of codimensions c n ( A ) ${c_{n}(A)}$ , n = 1 , 2 , … , ${n=1,2,\ldots,}$ of an algebra A over a field of characteristic zero. It is shown that when such sequence is polynomially bounded, then lim sup n → ∞ log n c n ( A ) ${\limsup_{n\to\infty}\log_{n}c_{n}(A)}$ and lim inf n → ∞ log n c n ( A ) ${\liminf_{n\to\infty}\log_{n}c_{n}(A)}$ can be arbitrarily distant. Also, in case the codimensions are exponentially bounded, we can construct an algebra A such that exp ( A ) = 2 ${\exp(A)=2}$ and, for any q ≥ 1 ${q\geq 1}$ , there are infinitely many integers n such that c n ( A ) > n q 2 n ${c_{n}(A)&…
Correlation at low temperature I. Exponential decay
2003
Abstract The present paper generalizes the analysis in (Ann. H. Poincare 1 (2000) 59, Math. J. (AMS) 8 (1997) 123) of the correlations for a lattice system of real-valued spins at low temperature. The Gibbs measure is assumed to be generated by a fairly general Hamiltonian function with pair interaction. The novelty, as compared to [2,20], is that the single-site (self-) energies of the spins are not required to have only a single local minimum and no other extrema. Our derivation of exponential decay of correlations goes through the spectral analysis of a deformed Laplacian closely related to the Witten Laplacian studied in [2,20]. We prove that this Laplacian has a spectral gap above zero…
Inverted and mirror repeats in model nucleotide sequences.
2007
We analytically and numerically study the probabilistic properties of inverted and mirror repeats in model sequences of nucleic acids. We consider both perfect and non-perfect repeats, i.e. repeats with mismatches and gaps. The considered sequence models are independent identically distributed (i.i.d.) sequences, Markov processes and long range sequences. We show that the number of repeats in correlated sequences is significantly larger than in i.i.d. sequences and that this discrepancy increases exponentially with the repeat length for long range sequences.