Computer complexes

Despite all the effort to reduce both the frequency of Coulomb solves (periodic or not) and the computational complexity of each call when required, the long-range force evaluation remains the dominant computational cost of MD simulations. 

The depth-first search algorithm the backtracking algorithm, respectively) has an exponential order of computational complexity CC [11] CC = 0(b ). The ex-... 

Henrici, P. Applied and Computational Complex Analysis, Wiley, New York (1974). 

Before we can analyze the electronic structure of a nanotube in terms of its helical symmetry, we need to find an appropriate helical operator S>(h,ip), representing a screw operation with a translation h units along the cylinder axis in conjunction with a rotation if radians about this axis. We also wish to find the operator S that requires the minimum unit cell size (i.e., the smallest set of carbon atoms needed to generate the entire nanotube using S) to minimize the computational complexity of calculating the electronic structure. We can find this helical operator by first... 

Integral equations provide a satisfactory formalism for the study of homogeneous and inhomogeneous fluids. If the usual OZ equation is used, the best results are obtained from semiempirical closures such as the MV and DHH closures. However, this empirical element can be avoided by using integral equations that involve higher-order distribution functions, but at the cost of some computational complexity. 

Mitchell, M., P.T.IIrabor and J.P.Crutchfield, Revisiting the edge of chaos evolving cellular automata to perform computations, Complex Systems, Volume 7, 1993, 89-130. 

Algorithmic Complexity Dynamic Measures complexity of given string vice ensemble Hard to compute complexity equated with randomness... 

Computational complexity measures the time and memory resources that a computer requires in order to solve a problem. For example, given the problem of... 

Let represent the final state solution of the computation. Then the computational complexity, is defined to be the time it takes for the fastest... 

We have only given a cursory look at computational complexity. More detailed discussions appear in the texts by Garey and. Johnson [garcy79], Hoperoft and Ullman [hopc.79) and Davis and Weynker [davisni83]. 

In this burner configuration, fuel is injected directly into the combustion chamber and hence, one would initially categorize it as a nonpremixed burner. However, the overall combustion process is quite complex and involves features of nonpremixed, partially premixed, and stratified combustion, as well as the possibility that the autoignition of hot mixtures of fuel, air, and recirculated combushon products may play a role in stabilizing the flame. Thus, while one may start from simple concepts of nonpremixed turbulent flames, the inclusion of local exhnchon or flame lift-off quickly increases the physical and computational complexity of flames that begin with nonpremixed streams of fuel and oxidizer. 

The ontology that underlies the information extraction and annotation process is solely based on taxonomic relationships. We intend to enrich our ontology with typed relationships. We are currently evaluating how typed relationships can extend the functionality of the UltraLink and how the expressivity for our ontology impacts the computational complexity of formal reasoning [9]. 

The computational complexity of the lower bound is presented in Lagweg et al. (1978). 

While there are plenty of methods to predict 1-octanol-water partition coefficients, logP (see Chapters 14 and 15), the number of approaches to predict 1-octanol-water distribution coefficients is rather limited. This is due to a lower availability of log D data and, in general, higher computational complexity of this property compared to that of log P. The approaches to predict log D can be roughly classified into two major categories (i) calculation of log D at an arbitrary pH and (ii) calculation of log D at a fixed pH. 

The twin facts that heavy-atom compounds like BaF, T1F, and YbF contain many electrons and that the behavior of these electrons must be treated relati-vistically introduce severe impediments to theoretical treatments, that is, to the inclusion of sufficient electron correlation in this kind of molecule. Due to this computational complexity, calculations of P,T-odd interaction constants have been carried out with relativistic matching of nonrelativistic wavefunctions (approximate relativistic spinors) [42], relativistic effective core potentials (RECP) [43, 34], or at the all-electron Dirac-Fock (DF) level [35, 44]. For example, the first calculation of P,T-odd interactions in T1F was carried out in 1980 by Hinds and Sandars [42] using approximate relativistic wavefunctions generated from nonrelativistic single particle orbitals. 

The opposite approach has also been considered to make accuracy paramount, independent of computational cost. For example, these cases typically employ the most accurate methods and complex sampling methods, both of which contribute to the computational complexity of the calculation. Clearly, just because a calculation is computationally demanding does not in itself demonstrate that it will be more accurate. However, elements which contribute to the accuracy of a calculation in terms of more accurate models — e.g., all-atom models, explicit solvation — or enhancing the degree of sampling would clearly be more computationally demanding. 

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