In the first four chapters, we will talk about the OpenMPI implementation of parallel computing on Linux. The small differences observed in the image are related to the quality of the random numbers used in our simulations.
Conclusions
We are able to obtain the exact values of the variational parameter α and local energy value EL required to designate the ground state of the three-dimensional quantum harmonic oscillator. For some problems, like ours, this quality is good enough or can be improved by further processing the raw data.
Acknowledgments
The insignificant difference in the calculated values of the local energy for different $\alpha$ values compared to a reference case can be attributed to the many factors not only related to the quality of the noise extraction, but to a thorough analysis of these noise sources in different channels. What is the difference between multiprocessing on the clusters and on the individual multicore CPUs.
HURST EXPONENT ESTIMATION, VERIFICATION, PORTABILITY AND PARALLELIZATION
Introduction
Our primary goal in this work is effective analysis of raw data, reliability of results from the Hurst exponent calculations, and cross-platform compatibility software.
3) and the rescaled range R
The value of H can then be calculated by fitting the table data into a polynomial (see Matlab's polyfit data on Fig.3), or calculating the slope of the straight line log(E)=log(C)+H *log(n) ) (see Matlab's lsqcurvefit model plotted on Fig.2). The results of the code adaptation to a C/C++ programming environment and parallel calculation code are listed on the last Fig.4.
Results and Discussion
The Hurst exponent estimates in our study agree with the majority of the previously obtained results for geomagnetic indices [8] where H value is above 0.5. To test the validity of the program, we reproduced the exact same time series Y(i) used by Higuchi in his derivations [3].
Conclusion
We can see this transition when we go from Higuchi time series to chaos in Gaussian noise. This may be due to the loss of differences between time series of different origins at small scales.
Acknowledgements
In addition to the straightforward workload distribution between the parallel processes, performed by partitioning the data on the channel or on the calculated scale basis, we also identified common features in the computations of two variables of interest and tracked them in a single common outer loop within a single thread, which provides further optimization of the code. Our data and algorithms have several applications such as fast data self-affinity test [12] and have great potentials for the future development. The code is compiled to run independently on different networked computers and can be used as a tool to study time series of different nature and origin.
Ecological studies of biotic data by Hurst exponent and the R/S analysis fitting to short time series. How long/short the data time series should be to provide a reliable information about the process under consideration. Describe and sketch a simple code that explains how to use Matlab's polyfit and lsqcurvefit functions for data analysis.
Estimate the data analysis performance when switching from Microsoft Excel to the serialized C++ code and on to the parallel multithreaded implementation of the algorithm.
QUICK AND EASY PARALLELIZATION TECHNIQUE FOR THE ISING 2D MODEL IN OPEN MPI
This fact severely degrades the efficiency of computations and reduces the naturally parallel tasks to the bottleneck of a single threaded application. We implemented Monte Carlo method with importance sampling in 2D spinning glasses for the Ising model [5] as an example of multithreading and performance optimization in scientific computing. Conventionally, performance can be obtained by compartmentalization and deployment of custom communicator between compartments for the transient phenomena.
Our choice is to enlarge the simulation grid by copying the right border column to the left and the left border column to the right, as well as the top row to the bottom and the bottom row to the top, (see the gray-shaded columns and rows in Fig. The upper bound for the first sum is determined by the extent of interaction and number of spins within this range.We must include only those configurations sampled according to the Boltzman factor, see algorithm below.
For a sequence of N such states, the magnetization for a given temperature will be given by the formula
4) The following steps should be taken repeatedly to achieve a
Repeat the previous steps to achieve an equilibrium magneti- zation value for a given simulation grid at the temperature selected
The red line with pentagram markers stands for the incomplete implementation of the boundary conditions and exhibits anomalous behavior at phase transition. For the formal performance evaluation and further optimization of the arbitrary code, the LogP model of Culler is available [15]. We have reported our studies on the implementation and efficiency of the fast and robust method of compartmentalization for the 2D Ising model.
The model and its evolution represent the computational basis for the whole generation of the quantum algorithms for approximation of partition. Why we give a name «toroidal» boundary condition to the special type of the boundary conditions in the Ising model. What are the factors that prevent the linear increase in algorithm performance with the increase of the number of parallel threads.
131 // reconstruct the extended array back to the original ones, 132 // removing boundaries.
BUILDING THE DENSITY OF STATES FROM THE WANG-LANDAU PARALLEL ALGORITHM
We have reproduced a unique variation of the Monte Carlo method using significance sampling of the Metropolis algorithm type [2]. Convergence to the equilibrium values of the observed parameters with one revolution of rotation is slow. That is, if the left neighbor in the left corner of the interaction pattern is missing, assume its place is taken by a spin across the entire grid on the right boundary.
Some normalization constants can be used to adjust dimensionality of the equation to the common energy units. For our analysis, we need to keep track of the two values, which are H(E) – the number of times this particular configuration is observed and g(E) – calculated density of states. These steps, which are repeated several times in the order of the number of sites in the simulation grid represent a single Monte Carlo step.
Second, this overlap in the further development of the Wang-Landau sampling algorithm allows us to propagate the particular spin configuration between processes.
Results and Discussions
The first left column of the graphs in Figure 1 represents H(E) - the number of hits per energy value collected for each separate energy range for all three models immediately after the last change to g(E) before the data is transferred to hard disk. . In the case of the Ising model, the positive part is easily reconstructed by specular reflection. We can see that the difference between the number of visits can be significant for different parts of the same model, see subplots (a), (d) and (g), nevertheless the first derivative (a factor that determines the quality of sewing) for two pieces g(E ) at the connecting points, as can be understood from the procedure, mainly depends on the smoothness of H(E).
At this stage, depending on the number of artifacts in the data, the head of each successive piece of data is aligned with the tail of the previous one. The algorithm works well for all types of models and only requires the correct definition of the interaction Hamiltonian in C++. Parallelization of the two-dimensional Ising model on an IBM RISC system cluster / 6000 workstations // Parallel computing.
242% increase/decrease of the entire RIGHT subset of data according to the findings of the previous loop.
MICROSOFT VISUAL STUDIO IDE WITH OPENMP ADD-ON USED TO BUILD A RADIOLOGICAL
AND RECONSTRUCTED CROSS-SECTIONS
Originally defined for client/server type programming to run across a network, MPI therefore includes time and resource cost analysis for message queuing and selection, and requires the existence of completely separate memories. They must be explicitly placed by the user at the correct execution level, which will allow the program to run in parallel mode. The use of the special key "omp" directive indicates that the commands are related to OpenMP and to avoid accidental coincidence of the names of OpenMP directives with other names.
Our task is to create a numerical phantom with a size of up to 1024 by 1024 by 1024 voxels and provide information for each voxel about the type of material and the attenuation coefficients µ, so that this information can later be used to make a projection create in the light. - ting gamma ray field. When we talk about the attenuation of gamma rays by matter, we have to consider three basic mechanisms of the scattering of gamma rays, namely the photoelectric effect, Compton scattering and pair formation. Depending on the situation, one or two of these mechanisms may become more prominent than the rest, see Figure 1.
For the sake of numerical simulations, all three are usually combined into the single µ-value depending on the energy of gamma-ray quanta, see Figure 2.
![Figure 1. Gamma rays attenuation processes as a function of energy, see [1]](https://thumb-ap.123doks.com/thumbv2/azdokorg/8357054.79835/72.629.160.467.607.775/figure-gamma-rays-attenuation-processes-function-energy.webp)
The detector could also be moved in the ZY plane if required by the displaced image of the phantom's projection. Three projections are given with non-zero elevation of the X-ray source and the additional modulation coefficient proportional to the inverse square of the distance from the source to the detector cell, see Figure 4. The third differs from the original by addition. of the white noise. a) original projection (b) Gaussian noise added (c) white noise added Figure 4.
The names of the elements used for the phantom generation are taken from the input_file.txt text file, see the end of the chapter, and the mu data is extracted according to the steps of the energy bins used in the description of the spectrum of the X-ray source. In both cases, see the program code below, we parallelized the loop by scanning the voxels of the detectors from top to bottom. Artifacts, visible in the photos as the light rays shooting from the sharp corners of the phantom, are from the beam hardening.
126 // I use three elements of the phantom data to store information about the size of the matrix. 242 // we need to move the origin to the center of the phantom by adding w_idth/2 etc. 160 // we need to move the origin to the center of the phantom by adding w_idth/2 etc.
