Search results for "Logarithm"
showing 10 items of 182 documents
Fisher Renormalization for Logarithmic Corrections
2008
For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogs. The scheme is tested in lattice animals and the Yang-Lee problem at t…
Dynamics of the Number of Trades of Financial Securities
1999
We perform a parallel analysis of the spectral density of (i) the logarithm of price and (ii) the daily number of trades of a set of stocks traded in the New York Stock Exchange. The stocks are selected to be representative of a wide range of stock capitalization. The observed spectral densities show a different power-law behavior. We confirm the $1/f^2$ behavior for the spectral density of the logarithm of stock price whereas we detect a $1/f$-like behavior for the spectral density of the daily number of trades.
ORDERING KINETICS IN QUASI-ONE-DIMENSIONAL ISING-LIKE SYSTEMS
1993
We present results of a Monte Carlo simulation of the kinetics of ordering in the two-dimensional nearest-neighbor Ising model in anL xM geometry with two free boundaries of length M≫L. This model can be viewed as representing an adsorbant on a stepped surface with mean terrace widthL. We follow the ordering kinetics after quenches to temperatures 0.25 ⩽ T/Tc ⩽ 1 starting from a random initial configuration at a coverage ofΘ=0.5 in the corresponding lattice gas picture. The systems evolve in time according to a Glauber kinetics with nonconserved order parameter. The equilibrium structure is given by a one-dimensional sequence of ordered domains. The ordering process evolves from a short ini…
GEPOL: An improved description of molecular surfaces II. Computing the molecular area and volume
1991
The algorithm used by the program GEPOL for a finer description of molecular surface (for a fast calculation of molecular area and volume and for an efficient selection of sampling points) is presented in detail. Different types of surfaces such as van der Waals and Richard's molecular surfaces can be computed. As we described in the first article (J.L. Pascual-Ahuir and E. Silla, J. Comp. Chem., 11, 1047(1990)), GEPOL begins by building a set of spherical surfaces which fill the space which is not solvent accessible. In this second article, a triangular tessellation approach to select the parts of these spherical surfaces which form the molecular surface is described. By using a data coded…
Upper bounds on multiparty communication complexity of shifts
1996
We consider some communication complexity problems which arise when proving lower bounds on the complexity of Boolean functions. In particular, we prove an \(O(\frac{n}{{2\sqrt {\log n} }}\log ^{1/4} n)\)upper bound on 3-party communication complexity of shifts, an O(n e ) upper bound on the multiparty communication complexity of shifts for a polylogarithmic number of parties. These bounds are all significant improvements over ones recently considered “unexpected” by Pudlak [5].
The Average State Complexity of the Star of a Finite Set of Words Is Linear
2008
We prove that, for the uniform distribution over all sets Xof m(that is a fixed integer) non-empty words whose sum of lengths is n, $\mathcal{D}_X$, one of the usual deterministic automata recognizing X*, has on average $\mathcal{O}(n)$ states and that the average state complexity of X*is i¾?(n). We also show that the average time complexity of the computation of the automaton $\mathcal{D}_X$ is $\mathcal{O}(n\log n)$, when the alphabet is of size at least three.
Ageing of isotactic polypropylene due to morphology evolution, experimental limitations of realtime density measurements with a gradient column
2006
Abstract Ageing in crystalline polymers is responsible for the deterioration of physical properties leading, for example, to a decrease in toughness and to dimensional changes that are to some extent responsible for warpage and scrap production in injection molding. Since, it depends on the mutual transformation of stable and metastable phases, being always related to changes in morphological organization, it is here preferred to call it ‘Morphological ageing’. Although, one would expect the ageing regime to be determined by the complex morphology with amorphous phases of different mobility and eventually multiple crystalline phases, transformed into each other at an associated transition, …
Multi-dimensional pattern matching with dimensional wildcards
1995
We introduce a new multi-dimensional pattern matching problem, which is a natural generalization of the on-line search in string matching. We are given a text matrix A[1: n1, ..., 1:n d ] of size N= n1×n2×...×n d , which we may preprocess. Then, we are given, online, an r-dimensional pattern matrix B[1:m1,...,1:m r ] of size M= m1×m2×...×m r , with 1≤r≤d. We would like to know whether B*=B*[*, 1:m1,*, ...,1: mr, *] occurs in A, where * is a dimensional wildcard such that B* is any d-dimensional matrix having size 1 × ... × m1×...1×m r ×...1 and containing the same elements as B. Notice that there might be (d/r)≤2d occurrences of B* for each position of A. We give CRCW-PRAM algorithms for pr…
Modeling long-range memory with stationary Markovian processes
2009
In this paper we give explicit examples of power-law correlated stationary Markovian processes y(t) where the stationary pdf shows tails which are gaussian or exponential. These processes are obtained by simply performing a coordinate transformation of a specific power-law correlated additive process x(t), already known in the literature, whose pdf shows power-law tails 1/x^a. We give analytical and numerical evidence that although the new processes (i) are Markovian and (ii) have gaussian or exponential tails their autocorrelation function still shows a power-law decay =1/T^b where b grows with a with a law which is compatible with b=a/2-c, where c is a numerical constant. When a<2(1+c) th…
Species–area relationships in continuous vegetation: Evidence from Palaearctic grasslands
2019
Aim Species-area relationships (SARs) are fundamental scaling laws in ecology although their shape is still disputed. At larger areas, power laws best represent SARs. Yet, it remains unclear whether SARs follow other shapes at finer spatial grains in continuous vegetation. We asked which function describes SARs best at small grains and explored how sampling methodology or the environment influence SAR shape. Location Palaearctic grasslands and other non-forested habitats. Taxa Vascular plants, bryophytes and lichens. Methods We used the GrassPlot database, containing standardized vegetation-plot data from vascular plants, bryophytes and lichens spanning a wide range of grassland types throu…