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Publication Metadata only ‘Anti-commutable’ local pre-Leibniz algebroids and admissible connections(Elsevier, 2023) Department of Physics; N/A; Dereli, Tekin; Doğan, Keremcan; Faculty Member; PhD Student; Department of Physics; College of Sciences; Graduate School of Sciences and Engineering; 201358; N/AThe concept of algebroid is convenient as a basis for constructions of geometrical frameworks. For example, metric-affine and generalized geometries can be written on Lie and Courant algebroids, respectively. Furthermore, string theories might make use of many other algebroids such as metric algebroids, higher Courant algebroids, or conformal Courant algebroids. Working on the possibly most general algebroid structure, which generalizes many of the algebroids used in the literature, is fruitful as it creates a chance to study all of them at once. Local pre-Leibniz algebroids are such general ones in which metric-connection geometries are possible to construct. On the other hand, the existence of the 'locality operator', which is present for the left-Leibniz rule for the bracket, necessitates the modification of torsion and curvature operators in order to achieve tensorial quantities. In this paper, this modification of torsion and curvature is explained from the point of view that the modification is applied to the bracket instead. This leads one to consider 'anti-commutable' local pre-Leibniz algebroids which satisfy an anti-commutativity-like property defined with respect to a choice of an equivalence class of connections. These 'admissible' connections are claimed to be the necessary ones while working on a geometry of algebroids. This claim is due to the fact that one can prove many desirable properties and relations if one uses only admissible connections. For instance, for admissible connections, we prove the first and second Bianchi identities, Cartan structure equations, Cartan magic formula, the construction of Levi-Civita connections, the decomposition of connection in terms of torsion and non-metricity. These all are possible because the modified bracket becomes anti-symmetric for an admissible connection so that one can apply the machinery of almost-or pre-Lie algebroids. We investigate various algebroid structures from the literature and show that they admit admissible connections which are metric-compatible in some generalized sense. Moreover, we prove that local pre-Leibniz algebroids that are not anti-commutable cannot be equipped with a torsion-free, and in particular Levi-Civita, connection.Publication Metadata only 3D shape correspondence by isometry-driven greedy optimization(IEEE Computer Soc, 2010) N/A; Department of Computer Engineering; Sahillioğlu, Yusuf; Yemez, Yücel; PhD Student; Faculty Member; Department of Computer Engineering; Graduate School of Sciences and Engineering; College of Engineering; 215195; 107907We present an automatic method that establishes 3D correspondence between isometric shapes. Our goal is to find an optimal correspondence between two given (nearly) isometric shapes, that minimizes the amount of deviation from isometry. We cast the problem as a complete surface correspondence problem. Our method first divides the given shapes to be matched into surface patches of equal area and then seeks for a mapping between the patch centers which we refer to as base vertices. Hence the correspondence is established in a fast and robust manner at a relatively coarse level as imposed by the patch radius. We optimize the isometry cost in two steps. in the first step, the base vertices are transformed into spectral domain based on geodesic affinity, where the isometry errors are minimized in polynomial time by complete bipartite graph matching. the resulting correspondence serves as a good initialization for the second step of optimization in which we explicitly minimize the isometry cost via an iterative greedy algorithm in the original 3D Euclidean space. We demonstrate the performance of our method on various isometric (or nearly isometric) pairs of shapes for some of which the ground-truth correspondence is available.Publication Metadata only A constant-factor approximation algorithm for multi-vehicle collection for processing problem(Springer Heidelberg, 2013) Gel, Esma S.; N/A; Department of Industrial Engineering; Department of Industrial Engineering; Yücel, Eda; Salman, Fatma Sibel; Örmeci, Lerzan; PhD Student; Faculty Member; Faculty Member; Department of Industrial Engineering; Graduate School of Sciences and Engineering; College of Engineering; College of Engineering; 235501; 178838; 32863We define the multiple-vehicle collection for processing problem (mCfPP) as a vehicle routing and scheduling problem in which items that accumulate at customer sites over time should be transferred by a series of tours to a processing facility. We show that this problem with the makespan objective (mCfPP()) is NP-hard using an approximation preserving reduction from a two-stage, hybrid flowshop scheduling problem. We develop a polynomial-time, constant-factor approximation algorithm to solve mCfPP(). The problem with a single site is analyzed as a special case with two purposes. First, we identify the minimum number of vehicles required to achieve a lower bound on the makespan, and second, we characterize the optimal makespan when a single vehicle is utilized.Publication Metadata only A LES/PDF simulator on block-structured meshes(Taylor & Francis Ltd, 2019) Pope, Stephen B.; N/A; Department of Mechanical Engineering; Türkeri, Hasret; Muradoğlu, Metin; PhD Student; Faculty Member; Department of Mechanical Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; 46561A block-structured mesh large-eddy simulation (LES)/probability density function (PDF) simulator is developed within the OpenFOAM framework for computational modelling of complex turbulent reacting flows. The LES/PDF solver is a hybrid solution methodology consisting of (i) a finite-volume (FV) method for solving the filtered mass and momentum equations (LES solver), and (ii) a Lagrangian particle-based Monte Carlo algorithm (PDF solver) for solving the modelled transport equation of the filtered joint PDF of compositions. Both the LES and the PDF methods are developed and combined to form a hybrid LES/PDF simulator entirely within the OpenFOAM framework. The in situ adaptive tabulation method [S.B. Pope, Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation, Combust. Theory Model. 1 (1997), pp. 41-63; L. Lu, S.R. Lantz, Z. Ren, and B.S. Pope, Computationally efficient implementation of combustion chemistry in parallel PDF calculations, J. Comput. Phys. 228 (2009), pp. 5490-5525] is incorporated into the new LES/PDF solver for efficient computations of combustion chemistry with detailed reaction kinetics. The method is designed to utilise a block-structured mesh and can readily be extended to unstructured grids. The three-stage velocity interpolation method of Zhang and Haworth [A general mass consistency algorithm for hybrid particle/finite-volume PDF methods, J. Comput. Phys. 194 (2004), pp. 156-193] is adapted to interpolate the LES velocity field onto particle locations accurately and to enforce the consistency between LES and PDF fields at the numerical solution level. The hybrid algorithm is fully parallelised using the conventional domain decomposition approach. A detailed examination of the effects of each stage and the overall performance of the velocity interpolation algorithm is performed. Accurate coupling of the LES and PDF solvers is demonstrated using the one-way coupling methodology. Then the fully two-way coupled LES/PDF solver is successfully applied to simulate the Sandia Flame-D, and a turbulent non-swirling premixed flame and a turbulent swirling stratified flame from the Cambridge turbulent stratified flame series [M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames I: Non-swirling flows, Combust. Flame 159 (2012), pp. 2896-2911; M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames II: Swirling flows, Combust. Flame 159 (2012), pp. 2912-2929]. It is found that the LES/PDF method is very robust and the results are in good agreement with the experimental data for both flames.Publication Metadata only A new gravity model with variable distance decay(Vilnius Gediminas Technical Univ Press, Technika, 2008) N/A; Department of Business Administration; Department of Business Administration; Sandıkçıoğlu, Müge; Ali, Özden Gür; Sayın, Serpil; Master Student; Faculty Member; Faculty Member; Department of Business Administration; Graduate School of Sciences and Engineering; College of Administrative Sciences and Economics; College of Administrative Sciences and Economics; N/A; 57780; 6755Our main goal is to understand the customers' store choice behavior in a grocery retail setting. We see this as a first vital step in order to make store location, format and product promotion decisions in the retail organization Proposed models in the literature generate consumer utility functions for different stores which are used in store sales estimation. For example, in one of its basic forms, Huff model proposes that, utility of a store for an individual is equal to the sales area of the store divided by a power of the individual's distance to the store. Parallel to this stream of research Multiplicative Competitor Interaction model estimates log-transformed utility functions by ordinary least squares regression. It is less specific in terms of variable selection compared to the Huff model. This paper proposes a new market share model which is a variant of the Huff model and evaluates most established market share models such as Huff and Multiplicative Competitor Interaction Model as well as a data mining method in a one-brand heterogonous size retail store setting. We observe that the Huff model performs well in its basic form. By representing distance decay value as a function of the sales area of the retail store we are able to improve the performance of the Huff model. We propose using optimization for estimating the model parameters in certain cases and observe that this improves the generalization ability of the model.Publication Metadata only Almost all hyperharmonic numbers are not integers(Elsevier, 2017) Sertbaş, Doğa Can; N/A; Göral, Haydar; Master Student; Graduate School of Sciences and Engineering; 252019It is an open question asked by Mezo that there is no hyperharmonic integer except 1. So far it has been proved that all hyperharmonic numbers are not integers up to order r = 25. In this paper, we extend the current results for large orders. Our method will be based on three different approaches, namely analytic, combinatorial and algebraic. From analytic point of view, by exploiting primes in short intervals we prove that almost all hyperharmonic numbers are not integers. Then using combinatorial techniques, we show that if n is even or a prime power, or r is odd then the corresponding hyperharmonic number is not integer. Finally as algebraic methods, we relate the integerness property of hyperharmonic numbers with solutions of some polynomials in finite fields. (C) 2016 Elsevier Inc. All rights reserved.Publication Metadata only Anomalies in the transcriptional regulatory network of the Yeast Saccharomyces cerevisiae(Elsevier, 2010) N/A; Department of Physics; Tuğrul, Murat; Kabakçıoğlu, Alkan; N/A; Faculty Member; Department of Physics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 49854We investigate the structural and dynamical properties of the transcriptional regulatory network of the Yeast Saccharomyces cerevisiae and compare it with two "unbiased" ensembles: one obtained by reshuffling the edges and the other generated by mimicking the transcriptional regulation mechanism within the cell. Both ensembles reproduce the degree distributions (the first-by construction-exactly and the second approximately), degree-degree correlations and the k-core structure observed in Yeast. An exceptionally large dynamically relevant core network found in Yeast in comparison with the second ensemble points to a strong bias towards a collective organization which is achieved by subtle modifications in the network's degree distributions. We use a Boolean model of regulatory dynamics with various classes of update functions to represent in vivo regulatory interactions. We find that the Yeast's core network has a qualitatively different behavior, accommodating on average multiple attractors unlike typical members of both reference ensembles which converge to a single dominant attractor. Finally, we investigate the robustness of the networks and find that the stability depends strongly on the used function class. The robustness measure is squeezed into a narrower band around the order-chaos boundary when Boolean inputs are required to be nonredundant on each node. However, the difference between the reference models and the Yeast's core is marginal, suggesting that the dynamically stable network elements are located mostly on the peripherals of the regulatory network. Consistently, the statistically significant three-node motifs in the dynamical core of Yeast turn out to be different from and less stable than those found in the full transcriptional regulatory network.Publication Metadata only Blow up of solutions to the initial boundary value problem for quasilinear strongly damped wave equations(Academic Press Inc Elsevier Science, 2013) N/A; Department of Mathematics; Bilgin, Bilgesu Arif; Kalantarov, Varga; PhD Student; Faculty Member; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 117655We obtain sufficient conditions on initial functions for which the initial boundary value problem for second order quasilinear strongly damped wave equations blow up in a finite time. (C) 2013 Elsevier Inc. All rights reserved.Publication Metadata only Clustering grocery shopping paths of customers by using optimization-based models(Vilnius Gediminas Technical Univ Press, Technika, 2008) N/A; Department of Business Administration; Department of Industrial Engineering; Yaman, Tuğba; Karabatı, Selçuk; Karaesmen, Fikri; Master Student; Faculty Member; Faculty Member; Department of Business Administration; Department of Industrial Engineering; Graduate School of Sciences and Engineering; College of Administrative Sciences and Economics; College of Engineering; N/A; 38819; 3579This study presents a preliminary investigation of shopping behavior of customers in a grocery store. Using each customer's in-store shopping path information, gathered by a wireless video camera that is affixed to the shopping cart, we classify customers into a predetermined number of clusters, and create a shopping path-based segmentation of customers. For this purpose a number of optimization models are developed. The results are presented in this paper. The next step is to analyze this collected data from different perspectives and developing different optimization models to achieve a better solution to the above clustering problem.Publication Metadata only Code notes: designing a low-cost tangible coding tool for/with children(Association for Computing Machinery (ACM), 2018) N/A; Department of Psychology; N/A; Department of Psychology; Sabuncuoğlu, Alpay; Erkaya, Merve; Buruk, Oğuz Turan; Göksun, Tilbe; PhD Student; Undergraduate Student; PhD Student; Faculty Member; Department of Psychology; KU Arçelik Research Center for Creative Industries (KUAR) / KU Arçelik Yaratıcı Endüstriler Uygulama ve Araştırma Merkezi (KUAR); Graduate School of Sciences and Engineering; College of Social Sciences and Humanities; Graduate School of Social Sciences and Humanities; College of Social Sciences and Humanities; N/A; N/A; N/A; 47278Programming has become an essential subject for today's education curriculum and as a result, the importance of creating the right environments to teach is increasing. For such environments, featuring tangible tools enhances creativity and collaboration. However, due to their high prices, current tangible tools are not reachable by most of the students. We developed Code Notes as a low-cost, attainable and tangible tool aimed to motivate children to support programming education. Code Notes is comprised of an Android app and code-cardboards to teach the basic concepts in programming. We continue to develop the platform with insights gained from children. This paper shares the design phases of Code Notes and observations from our two-month programming project. We also presented some future concepts of Code Notes that offer an active and embodied interaction with the teaching material.