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Publication Metadata only A Bayesian generalized linear model for Crimean–Congo hemorrhagic fever incidents(Springer, 2018) Ryu, Duchwan; Bilgili, Devrim; Liang, Faming; Ebrahimi, Nader; Ergönül, Önder; Faculty Member; School of Medicine; 110398Global spread of the Crimean-Congo hemorrhagic fever (CCHF) is a fatal viral infection disease found in parts of Africa, Asia, Eastern Europe and Middle East, with a fatality rate of up to 30%. A timely prediction of the prevalence of CCHF incidents is highly desirable, while CCHF incidents often exhibit nonlinearity in both temporal and spatial features. However, the modeling of discrete incidents is not trivial. Moreover, the CCHF incidents are monthly observed in a long period and take a nonlinear pattern over a region at each time point. Hence, the estimation and the data assimilation for incidents require extensive computations. In this paper, using the data augmentation with latent variables, we propose to utilize a dynamically weighted particle filter to take advantage of its population controlling feature in data assimilation. We apply our approach in an analysis of monthly CCHF incidents data collected in Turkey between 2004 and 2012. The results indicate that CCHF incidents are higher at Northern Central Turkey during summer and that some beforehand interventions to stop the propagation are recommendable. Supplementary materials accompanying this paper appear on-line.Publication Metadata only A comparison of analysis of covariate-adjusted residuals and analysis of covariance(Taylor & Francis Inc, 2009) Goad, Carla L.; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AVarious methods to control the influence of a covariate on a response variable are compared. These methods are ANOVA with or without homogeneity of variances (HOV) of errors and Kruskal-Wallis (K-W) tests on (covariate-adjusted) residuals and analysis of covariance (ANCOVA). Covariate-adjusted residuals are obtained from the overall regression line fit to the entire data set ignoring the treatment levels or factors. It is demonstrated that the methods on covariate-adjusted residuals are only appropriate when the regression lines are parallel and covariate means are equal for all treatments. Empirical size and power performance of the methods are compared by extensive Monte Carlo simulations. We manipulated the conditions such as assumptions of normality and HOV, sample size, and clustering of the covariates. The parametric methods on residuals and ANCOVA exhibited similar size and power when error terms have symmetric distributions with variances having the same functional form for each treatment, and covariates have uniform distributions within the same interval for each treatment. In such cases, parametric tests have higher power compared to the K-W test on residuals. When error terms have asymmetric distributions or have variances that are heterogeneous with different functional forms for each treatment, the tests are liberal with K-W test having higher power than others. The methods on covariate-adjusted residuals are severely affected by the clustering of the covariates relative to the treatment factors when covariate means are very different for treatments. For data clusters, ANCOVA method exhibits the appropriate level. However, such a clustering might suggest dependence between the covariates and the treatment factors, so makes ANCOVA less reliable as well.Publication Metadata only A multitask multiple kernel learning formulation for discriminating early- and late-stage cancers(Oxford University Press (OUP), 2020) N/A; N/A; Department of Industrial Engineering; Rahimi, Arezou; Gönen, Mehmet; PhD Student; Faculty Member; Department of Industrial Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; 237468Motivation: Genomic information is increasingly being used in diagnosis, prognosis and treatment of cancer. The severity of the disease is usually measured by the tumor stage. Therefore, identifying pathways playing an important role in progression of the disease stage is of great interest. Given that there are similarities in the underlying mechanisms of different cancers, in addition to the considerable correlation in the genomic data, there is a need for machine learning methods that can take these aspects of genomic data into account. Furthermore, using machine learning for studying multiple cancer cohorts together with a collection of molecular pathways creates an opportunity for knowledge extraction. Results: We studied the problem of discriminating early- and late-stage tumors of several cancers using genomic information while enforcing interpretability on the solutions. To this end, we developed a multitask multiple kernel learning (MTMKL) method with a co-clustering step based on a cutting-plane algorithm to identify the relationships between the input tasks and kernels. We tested our algorithm on 15 cancer cohorts and observed that, in most cases, MTMKL outperforms other algorithms (including random forests, support vector machine and single-task multiple kernel learning) in terms of predictive power. Using the aggregate results from multiple replications, we also derived similarity matrices between cancer cohorts, which are, in many cases, in agreement with available relationships reported in the relevant literature.Publication Metadata only A new family of random graphs for testing spatial segregation(Wiley, 2007) Priebe, Carey E.; Marchette, David J.; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AThe authors discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. The authors address specifically the problem of testing. complete spatial randomness against spatial patterns of segregation or association between two or more classes of points on the plane. To this end, they use a particular type of parameterized random digraph called a proximity catch digraph (PCD) which is based on relative positions of the data points from various classes. The statistic employed is the relative density of the PCD, which is a U-statistic when scaled properly. The authors derive the limiting distribution of the relative, density, using the standard asymptotic theory of U-statistics. They evaluate the finite-sample performance of their test statistic by Monte Carlo simulations and assess its asymptotic performance via Pitman's asymptotic efficiency, thereby yielding the optimal parameters for testing. They further stress that their methodology remains valid for data in higher dimensions.Publication Metadata only A note on the geometric ergodicity of a nonlinear AR-ARCH model(Elsevier Science Bv, 2010) Saikkonen, Pentti; Department of Economics; Meitz, Mika; Faculty Member; Department of Economics; College of Administrative Sciences and Economics; N/AThis note studies the geometric ergodicity of nonlinear autoregressive models with conditionally heteroskedastic errors. A nonlinear autoregression of order p (AR(p)) with the conditional variance specified as the conventional linear autoregressive conditional heteroskedasticity model of order q (ARCH(q)) is considered. Conditions under which the Markov chain representation of this nonlinear AR-ARCH model is geometrically ergodic and has moments of known order are provided. The obtained results complement those of Liebscher [Liebscher, E., 2005. Towards a unified approach for proving geometric ergodicity and mixing properties of nonlinear autoregressive processes, journal of Time Series Analysis, 26,669-689] by showing how his approach based on the concept of the joint spectral radius of a set of matrices can be extended to establish geometric ergodicity in nonlinear autoregressions with conventional ARCH(q) errors.Publication Metadata only A solution method for linear and geometrically nonlinear MDOF systems with random properties subject to random excitation(Elsevier, 1998) Micaletti, RC; Çakmak, Ahmet Ş.; Nielsen, Søren R.K.; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/AA method for computing the lower-order moments of response of randomly excited multi-degree-of-freedom (MDOF) systems with random structural properties is proposed. The method is grounded in the techniques of stochastic calculus, utilizing a Markov diffusion process to model the structural system with random structural properties. The resulting state-space formulation is a system of ordinary stochastic differential equations with random coefficients and deterministic initial conditions which are subsequently transformed into ordinary stochastic differential equations with deterministic coefficients and random initial conditions, This transformation facilitates the derivation of differential equations which govern the evolution of the unconditional statistical moments of response. Primary consideration is given to linear systems and systems with odd polynomial nonlinearities, for in these cases there is a significant reduction in the number of equations to be solved. The method is illustrated for a five-story shear-frame structure with nonlinear interstory restoring forces and random damping and stiffness properties. The results of the proposed method are compared to those estimated by extensive Monte-Carlo simulation.Publication Metadata only Admission and termination control of a two class loss system(Taylor & Francis Inc, 2011) Ulukuş, Mehmet Yasin; Güllü, Refik; Department of Industrial Engineering; Örmeci, Lerzan; Faculty Member; Department of Industrial Engineering; College of Engineering; 32863We consider dynamic admission and termination control policies in a Markovian loss system with two classes, each with a fixed reward, a termination cost, an arrival and service rate. The system may admit or reject an arriving job or admit it by terminating a job in the system to maximize its total expected discounted reward. We prove that (1) when there is an idle server, it is never optimal to terminate a job, (2) there exists an optimal threshold policy for both admission and termination decisions. Furthermore, we identify the conditions which ensure that a class is "preferred" or "strongly preferred."Publication Metadata only Admission policies for a two class loss system with general interarrival times(Taylor & Francis Inc, 2006) van der Wal, J.; Department of Industrial Engineering; Örmeci, Lerzan; Faculty Member; Department of Industrial Engineering; College of Engineering; 32863This paper considers the problem of dynamic admission control in a loss queueing system with two classes of jobs. The jobs require an exponential amount of service time with different means and bring different revenues, whereas the arrivals occur according to a general distribution. We establish the existence of optimal acceptance thresholds for both job classes and show that under certain conditions there exists a preferred class. We also provide an example to demonstrate that for a Markov modulated Poisson arrival process there may be states in which both classes are rejected.Publication Metadata only An investigation of new graph invariants related to the domination number of random proximity catch digraphs(Springer, 2012) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AProximity catch digraphs (PCDs) are a special type of proximity graphs based on proximity maps which yield proximity regions. PCDs are defined using the relative allocation of points from two or more classes in a region of interest and have applications in various fields. We introduce some auxiliary tools for PCDs and graph invariants related to the domination number of the PCDs and investigate their probabilistic properties. We consider the cases in which the vertices of the PCDs come from uniform and non-uniform distributions in the region of interest. We also provide some of the newly defined proximity maps as illustrative examples.Publication Metadata only Balanced and strongly balanced 4-kite designs(Utilitas Mathematica Publishing, 2013) Gionfriddo, Mario; Milazzo, Lorenzo; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252A G-design is called balanced if the degree of each vertex x is a constant. A G-design is called strongly balanced if for every i = 1, 2, ⋯, h, there exists a constant Ci such that dAi(x)= Ci for every vertex x, where AiS are the orbits of the automorphism group of G on its vertex-set and dAi(x) of a vertex is the number of blocks of containing x as an element of Ai. We say that a G-design is simply balanced if it is balanced, but not strongly balanced. In this paper we determine the spectrum of simply balanced and strongly balanced 4-kite designs.