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Simetrik olmayan matrisler için spektral bölümlemeyi yeniden değerlendirme
Parallel solutions to scientific problems having graph representation require efficient tasks and partitioning data. In this thesis, various parallel graph partitioning algorithms are studied. While these algorithms are applicable to both directed and undirected graphs, we focus on the directed case whose matrix representations are sparse and unsymmetric arising in linear system of equations representing various application domains such as computational fluid dynamics and thermal problems. Strategies inspected in this study are ParMETIS with the Multilevel Kernighan-Lin algorithm and the spectral partitioning algorithm with k-means clustering (SPEC) as well as the recursive spectral partitioning algorithm in CHACO. We have implemented SPEC in C programming language using PETSc and SLEPc libraries, whereas CHACO and ParMETIS are called from PETSc. Weighted partitioning is done under the consideration of the edge weights of the graph. SPEC is compared with the libraries only when the unweighted partitioning is made due to the limitations of the libraries for weighted partitioning. Hence, for weighted partitioning, only various eigensolver tolerances in SLEPc are studied in terms of the edge-cut and partitioning time. Another study is performed for the spectral partitioning algorithm based on eigensolver tolerance used with the k-means algorithm in MATLAB. The comparison is based on the quality of the partitioning (edge-cut and partition imbalance) and the number of iterations. The quality of partitioning is determined by the edge-cut and the load imbalance, which could be based on the edge and vertex imbalance ratios of partitions depending on the application. Since the adjacency matrix of a graph is structurally symmetric, the eigenvalue problem can only be solved approximately when the matrix is unsymmetric. Thus, only approximate results are provided in this study. It is deduced that using SPEC performs better than the existing software libraries when the number of cut edges is compared in unweighted partitioning of unsymmetric matrices.
Biyolojik ağlardaki yaklaşık stokastik simülasyon algoritmalarında sıçrama koşulunun genişletilmesi
The approximate stochastic simulation (ASS) algorithms are the alternative approaches to generate the complex biological systems with a loss in accuracy by gaining from computational demand. There are a number of approximate methods which can successfully simulate the systems, such as poisson tau-leap and approximate Gillespie algorithms. The common property of these approaches is that they are based on the leap conditon which controls the change in hazard functions under a time interval. By means of this interval we can find an interval for the number of simultaneous reactions k in the time interval generated from the leap condition. In this study, we propose alternative intervals for k that are dependent on the sufficient statistics and also, we derive confidence intervals for k whose parameters are obtained via maximum likelihood estimator, moment estimators and bayesian estimators. Furthermore, we extend the leap condition by using higher order Taylor expansion whose original estimators are found under the first order. In our derivations, we use the poisson tau-leap approach since it is the fundamental approximate stochastic simulation method. Moreover, we apply the approximate Gillespie algorithm since it is one of the recent approaches that is derived from the idea of the poisson tau-leap method. We consider that although the proposal approaches to these two algortihms, they can be also adapted to other algorithms whose derivation are based on the parametric assumption.
Pekiştiırmeli öğrenme yöntemleriyle kısmi gözlenebilirortamda çift bacaklı robotun yürütülmesi
Deep Reinforcement Learning methods on mechanical control have been successfully applied in many environments and used instead of traditional optimal and adaptive control methods for some complex problems. However, Deep Reinforcement Learning algorithms do still have some challenges. One is to control on partially observable environments. When an agent is not informed well of the environment, it must recover information from the past observations. In this thesis, walking of Bipedal Walker Hardcore (OpenAI GYM) environment, which is partially observable, is studied by two continuous actor-critic reinforcement learning algorithms; Twin Delayed Deep Determinstic Policy Gradient and Soft Actor-Critic. Several neural architectures are implemented. The first one is Residual Feed Forward Neural Network under the observable environment assumption, while the second and the third ones are Long Short Term Memory and Transformer using observation history as input to recover the hidden information due to the partially observable environment.
COVID-19 dinamikleriıni analiz ve tahmin etmek için veriyedayalı epidemik modeli
Due to recent evolution of the COVID-19 outbreak, accurate mathematical modelling to capture the dynamics of disease transmission is of vital importance. Since the availability and quality of data differs from region to region, it is very difficult to develop an accurate model from the global perspective. Nevertheless, local predictive models can be developed by collecting data from certain regions. In this thesis, we propose a modified version of Susceptible-Exposed-Infected-Recovered-Dead (SEIRD) differential model for the analysis and forecast of COVID-19 spread. Parameter estimation of the model is the first step of analysis which is carried out by fitting the model to available data in the least square sense. In second step of analysis, simulations are performed by using the optimal values of parameters. Through numerical simulations, we observe the effects of public measures, such as isolation, social distancing on the dynamics of COVID-19 outbreak. The model is applied for the COVID-19 outbreak in Turkey, Italy, and Spain. Time to reach the peak, total infected, recovered and dead cases are compared with real data and found to be in good agreement for all the countries.