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Yayın On computing the multivariate poisson probability distribution(Springer, 2023-06-20) Çekyay, Bora; Frenk, Johannes Bartholomeus Gerardus; Javadi, SonyaWithin the theory of non-negative integer valued multivariate infinitely divisible distributions, the multivariate Poisson distribution plays a key role. As in the univariate case, any non-negative integer valued infinitely divisible multivariate distribution can be approximated by a multivariate distribution belonging to the compound Poisson family. The multivariate Poisson distribution is an important member of this family. In recent years, the multivariate Poisson distributions also has gained practical importance, since they serve as models to describe counting data having a positive covariance structure. However, due to the computational complexity of computing the multivariate Poisson probability mass function (pmf) and its corresponding cumulative distribution function (cdf), their use within these counting models is limited. Since most of the theoretical properties of the multivariate Poisson probability distribution seem already to be known, the main focus of this paper is on proposing more efficient algorithms to compute this pmf. Using a well known property of a Poisson multivariate distributed random vector, we propose in this paper a direct approach to calculate this pmf based on finding all solutions of a system of linear Diophantine equations. This new approach complements an already existing procedure depending on the use of recurrence relations existing for the pmf. We compare our new approach with this already existing approach applied to a slightly different set of recurrence relations which are easier to evaluate. A proof of this new set of recurrence relations is also given. As a result, several algorithms are proposed where some of them are based on the new approach and some use the recurrence relations. To test these algorithms, we provide an extensive analysis in the computational section. Based on the experiments in this section, we conclude that the approach finding all solutions of a set of linear Diophantine equations is computationally more efficient than the approach using the recurrence relations to evaluate the pmf of a multivariate Poisson distributed random vector.Yayın VC-dimension of univariate decision trees(IEEE-INST Electrical Electronics Engineers Inc, 2015-02-25) Yıldız, Olcay TanerIn this paper, we give and prove the lower bounds of the Vapnik-Chervonenkis (VC)-dimension of the univariate decision tree hypothesis class. The VC-dimension of the univariate decision tree depends on the VC-dimension values of its subtrees and the number of inputs. Via a search algorithm that calculates the VC-dimension of univariate decision trees exhaustively, we show that our VC-dimension bounds are tight for simple trees. To verify that the VC-dimension bounds are useful, we also use them to get VC-generalization bounds for complexity control using structural risk minimization in decision trees, i.e., pruning. Our simulation results show that structural risk minimization pruning using the VC-dimension bounds finds trees that are more accurate as those pruned using cross validation.Yayın Predictive modelling of surface roughness and residual stress induced by milling of hot forged and heat treated AA7075(Springer Nature, 2025-11-03) Tok, Görkem; Dinçer, Ammar Tarık; Kuzu, Ali Taner; Bakkal, MustafaThis study investigates the influence of cutting parameters on residual stress and surface roughness during the milling of hot-forged and T6 heat-treated AA7075 components. Using Taguchi L9 and full-factorial experimental designs and regression modelling, the research highlights important relationships between cutting parameters (cutting speed, feed rate, and depth of cut), residual stress and surface roughness. Higher cutting speeds (350 m/min) and lower feed rates (0.1 mm/tooth) significantly minimized residual stresses, with hoop stress values decreasing from 108.7 MPa at lower speeds (150 m/min) to approximately 73.4 MPa at higher speeds, and axial stress values ranging from 45.9 MPa to 88.5 MPa. Surface roughness (Ra) was most influenced by feed rate, with measurement values varying between 0.25 mu m and 0.92 mu m. Support Vector Regression (SVR) demonstrated better accuracy for predicting residual stress (MAPE: 11.5%) and surface roughness (MAPE: 7%), outperforming Lasso and Ridge regression models. These findings provide a consistent framework for optimizing cutting parameters and enhancing residual stress and surface roughness in AA7075 machining processes, offering practical implications for improving component performance and manufacturing efficiency.
