Brute force techniques

Search for the overall optimum within the available parameter space Factorial, simplex, regression, and brute-force techniques. The classical, the brute-force, and the factorial methods are applicable to the optimization of the experiment. The simplex and various regression methods can be used to optimize both the experiment and fit models to data. 

Microarray data cannot be analyzed by purely brute force techniques to generate a causal model of a set of biological processes because the data represents gene expression patterns that are only correlated with temporal processes of interest in the organism. Lander (1999) comments on this problem as follows ... 

The variables are updated and the step is repeated until convergence is achieved. Errors can be propagated either linearly in a matrix form by computing the derivatives of the unknowns with respect to the observations or by Monte-Carlo (brute force) techniques (e.g., Albarede 1995). 

The intent of this was to start with a useful calculation, which could not be done using brute force techniques, and demonstrate the importance of optimizing the numerical implementation of a reactive flow model to run on a vector computer. As similar problems in combustion become more extensive and intricate, it behooves us to utilize computers in the most efficient manner possible. It is no longer feasible to continue to "ask the computer to do more and more work, without thought as to how a particular problem is to be implemented. The number of problems for which one would like to use a computer, as well as the complexity of these problems, is increasing at an astronomical rate. The other side of the coin, of course is that computers, and especially central processors (CPU s) are becoming cheaper. 

The class of problem which we are presenting here can not be done with a reasonable amount of computer time, using brute force techniques. It is necessary, for example, to solve a two-dimensional problem rather than a three dimensional problem. Another example is the problem of molecular diffusion (4,5,6). The usual binary diffusion approximation is inadequate. At the very least total mass is transported in this approximation. The primary difficulty in a general treatment is that of inverting a large (N. x N ) matrix at each time step and for each grid... 

Using the techniques discussed in section III and IV we have been able to study the effect of acceleration on ignition of a homogeneous fuel oxydizer mixture. The ability to study multidimensional effects (buoyancy, turbulence etc.) hinges on the use of numerical methods (slow-flow, asymptotic chemistry etc.) which circumvent the time constraints encountered in brute force techniques. These methods go hand in hand with modem fast computers, especially vector machines where judicious programming allows us to attain the actual memory or CPU cycle time. 

Two routes have been followed in reaction stereodynamics. One is to orient a molecular reactant in space and see how the reaction cross-section varies with the molecular orientation. This direction has been pioneered in molecular beam experiments using focusing of an electric hexapole field to control the molecular orientation [221-223a]. Numerous studies have applied this technique to electron-transfer reactions of alkaline-earth atoms [223b]. This technique is now complemented by the so-called brute force technique, where polar molecules are oriented in extremely strong electric fields [83]. 

Anyone reading this chapter has, undoubtedly, solved an inverse-type problem in one form or another. The key to efficient solution lies in the restriction of the solution space. If constraints are composed such that the solution space is limited, a brute-force technique (try all candidates) can guarantee a solution. In the field of molecular design, however, the solution space comes from all compounds that can be reasonably made from the various atoms in the Periodic Table. Hence, we need a way to limit this solution space to arrive at candidate solutions efficiently. We will describe some of these techniques. 

In the brute-force technique, for each chosen orientation (0,(p) of B, one diagonalizes the spin-Hamiltonian matrix for a large munber of values of B to find the resonant magnetic-field value. It requires exorbitant computer time, especially... 

Loesch H J and Remscheid A 1990 Brute force in molecular reaction dynamics a novel technique for measuring steric effects J. Chem. Phys. 93 4779-90... 

Molecular dynamics consists of the brute-force solution of Newton s equations of motion. It is necessary to encode in the program the potential energy and force law of interaction between molecules the equations of motion are solved numerically, by finite difference techniques. The system evolution corresponds closely to what happens in real life and allows us to calculate dynamical properties, as well as thennodynamic and structural fiinctions. For a range of molecular models, packaged routines are available, either connnercially or tlirough the academic conmuinity. 

If it is known that a drug must bind to a particular spot on a particular protein or nucleotide, then a drug can be tailor-made to bind at that site. This is often modeled computationally using any of several different techniques. Traditionally, the primary way of determining what compounds would be tested computationally was provided by the researcher s understanding of molecular interactions. A second method is the brute force testing of large numbers of compounds from a database of available structures. 

Solvent cleaning is a much more delicate technique than the brute force of abrasion. In reality, there will almost always be some abrasive action involved. The idea is to dissolve the deposit in a solvent. The solution must... 

The method of optimization is a brute-force search technique. All the possible laminates that can be obtained by changing the individual laminae orientations by 5° increments are candidates for the optimization process. We consider RC7 because this program is widely used and because it is representative of the brute-force search technique. The basic question is because we must carry a certain load, what laminate do we need We have no idea how many layers are required, much less their orientation, but we must start someplace. 

The algebraic/iterative and the brute force methods are numerical respectively computational techniques that operate on the chosen mathematical model. Raw residuals r are weighted to reflect the relative reliabilities of the measurements. 

To calculate the inverse of a matrix by this procedure is equally tedious and probably more work than solving a set of equations by the brute-force high-school technique. However, the procedure is readily converted into computer code and this is now the only way recommended for matrix inversions. 

There are two possible solutions to this problem. We may either modify our ansatz for the wavefunction, including terms that depend explicitly on the interelectronic coordinates [26-30], or we may take advantage of the smooth convergence of the correlation-consistent basis sets to extrapolate to the basis-set limit [6, 31-39], In our work, we have considered both approaches as we shall see, they are fully consistent with each other and with the available experimental data. With these techniques, the accurate calculation of AEs is achieved at a much lower cost than with the brute-force approach described in the present section. 

The effect of the problem-solving mindset was clear students made few connections with the conceptual aspects of the material. The evidence for this was found in how these students studied for their exams. They tended to perceive that there were many equations they had to learn, and, as the following extracts from tutoring sessions illustrates, they adopted the technique of brute force memorization. 

It was soon realised that at least unequal intervals, crowded closely around the UMDE edge, might help with accuracy, and Heinze was the first to use these in 1986 [300], as well as Bard and coworkers [71] in the same year. Taylor followed in 1990 [545]. Real Crank-Nicolson was used in 1996 [138], in a brute force manner, meaning that the linear system was simply solved by LU decomposition, ignoring the sparse nature of the system. More on this below. The ultimate unequal intervals technique is adaptive FEM, and this too has been tried, beginning with Nann [407] and Nann and Heinze [408,409], and followed more recently by a series of papers by Harriman et al. [287,288,289, 290,291,292,293], some of which studies concern microband electrodes and recessed UMDEs. One might think that FEM would make possible the use of very few sample points in the simulation space however, as an example, Harriman et al. [292] used up to about 2000 nodes in their work. This is similar to the number of points one needs to use with conformal mapping and multi-point approximations in finite difference methods, for similar accuracy. 

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