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Yayın Modeling repair demand in existence of a nonstationary installed base(Elsevier B.V., 2023-09) Hekimoğlu, Mustafa; Karlı, DenizLife cycles of products consist of 3 phases, namely growth, maturity, and decline phases. Modeling repair demand is particularly difficult in the growth and decline stages due to nonstationarity. In this study, we suggest respective stochastic models that capture the dynamics of repair demand in these two phases. We apply our theory to two different operations management problems. First, using the moments of spare parts demand, we suggest an algorithm that selects a parametric distribution from the hypergeometric family (Ord, 1967) for each period in time. We utilize the algorithm in a single echelon inventory control problem. Second, we focus on investment decisions of Original Equipment Manufacturers (OEMs) to extend economic lifetimes of products with technology upgrades. Our results indicate that the second moment is sufficient for growing customer bases, whereas using the third moment doubles the approximation quality of theoretical distributions for a declining customer base. From a cost minimization perspective, using higher moments of demand leads to savings up to 13.6% compared to the single-moment approach. Also, we characterize the optimal investment policy for lifetime extension decisions from risk-neutral and risk-averse perspectives. We find that there exists a critical level of investment cost and installed base size for profitability of lifetime extension for OEMs. From a managerial point of view, we find that a risk-neutral decision maker finds the lifetime extension problem profitable. In contrast, even a slight risk aversion can make the lifetime extension decision economically undesirable.Yayın Some boundary Harnack principles with uniform constants(Springer Science and Business Media B.V., 2022-10) Barlow, Martin T.; Karlı, DenizWe prove two versions of a boundary Harnack principle in which the constants do not depend on the domain by using probabilistic methods.Yayın Optimization of wastewater treatment systems for growing industrial parks(Elsevier B.V., 2023-12-20) Savun Hekimoğlu, Başak; İşler, Zülal; Hekimoğlu, Mustafa; Burak, Selmin; Karlı, Deniz; Yücekaya, Ahmet; Akpınar, Ersin; Ediger, Volkan Ş.Wastewater treatment is one of the crucial functions of industrial parks as wastewater from industrial facilities usually contains toxic compounds that can cause damage to the environment. To control their environmental loads, industrial parks make investment decisions for wastewater treatment plants. For this, they need to consider technical and economic factors as well as future growth projections as substantial construction and operational costs of wastewater treatment plants have to be shared by all companies in an industrial park. In this paper, we consider the long-term capacity planning problem for wastewater treatment facilities of a stochastically growing industrial park. By explicitly modeling randomness in the arrival of new tenants and their random wastewater discharges, our model calculates the future mean and variance of wastewater flow in the industrial park. Mean and variance are used in a Mixed Integer Programming Model to optimize wastewater treatment plant selection over a long planning horizon (30 years). By fitting our first model to empirical data from an industrial park in Turkey, we find that considering the variance of wastewater load is critical for long-term planning. Also, we quantify the economic significance of lowering wastewater discharges which can be achieved by water recycling or interplant water exchange.Yayın A multiplier related to symmetric stable processes(Hacettepe University, 2017) Karlı, DenizIn two recent papers [5] and [6], we generalized some classical results of Harmonic Analysis using probabilistic approach by means of a d- dimensional rotationally symmetric stable process. These results allow one to discuss some boundedness conditions with weaker hypotheses. In this paper, we study a multiplier theorem using these more general results. We consider a product process consisting of a d-dimensional symmetric stable process and a 1-dimensional Brownian motion, and use properties of jump processes to obtain bounds on jump terms and the Lp(Rd)-norm of a new operator.Yayın Adaptive convolution kernel for artificial neural networks(Academic Press Inc., 2021-02) Tek, Faik Boray; Çam, İlker; Karlı, DenizMany deep neural networks are built by using stacked convolutional layers of fixed and single size (often 3 × 3) kernels. This paper describes a method for learning the size of convolutional kernels to provide varying size kernels in a single layer. The method utilizes a differentiable, and therefore backpropagation-trainable Gaussian envelope which can grow or shrink in a base grid. Our experiments compared the proposed adaptive layers to ordinary convolution layers in a simple two-layer network, a deeper residual network, and a U-Net architecture. The results in the popular image classification datasets such as MNIST, MNIST-CLUTTERED, CIFAR-10, Fashion, and ‘‘Faces in the Wild’’ showed that the adaptive kernels can provide statistically significant improvements on ordinary convolution kernels. A segmentation experiment in the Oxford-Pets dataset demonstrated that replacing ordinary convolution layers in a U-shaped network with 7 × 7 adaptive layers can improve its learning performance and ability to generalize.Yayın An extension of a boundedness result for singular integral operators(Polska Akademia Nauk, 2016-03-30) Karlı, DenizWe study some operators originating from classical Littlewood–Paley the- ory. We consider their modification with respect to our discontinuous setup, where the un- derlying process is the product of a one-dimensional Brownian motion and a d-dimensional symmetric stable process. Two operators in focus are the G? and area functionals. Using the results obtained in our previous paper, we show that these operators are bounded on Lp. Moreover, we generalize a classical multiplier theorem by weakening its conditions on the tail of the kernel of singular integrals.Yayın Extension of mikhlin multiplier theorem to fractional derivatives and stable processes(Walter De Gruyter GMBH, 2018-04-25) Karlı, DenizIn this paper, we prove a new generalized Mikhlin multiplier theorem whose conditions are given with respect to fractional derivatives in integral forms with two different integration intervals. We also discuss the connection between fractional derivatives and stable processes and prove a version of Mikhlin theorem under a condition given in terms of the infinitesimal generator of symmetric stable process. The classical Mikhlin theorem is shown to be a corollary of this new generalized version in this paper.Yayın Some remarks on uniform boundary Harnack principles(Cornell Univ, 2021-03-18) Barlow, Martin T.; Karlı, DenizWe prove two versions of a boundary Harnack principle in which the constants do not depend on the domain by using probabilistic methods.
