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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/3
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Publication Metadata only On maximal partial Latin hypercubes(Springer, 2023) Donovan, Diane M.; Grannell, Mike J.; Department of Mathematics; Yazıcı, Emine Şule; Department of Mathematics; College of SciencesA lower bound is presented for the minimal number of filled cells in a maximal partial Latin hypercube of dimension d and order n. The result generalises and extends previous results for d= 2 (Latin squares) and d= 3 (Latin cubes). Explicit constructions show that this bound is near-optimal for large n> d . For d> n , a connection with Hamming codes shows that this lower bound gives a related upper bound for the same quantity. The results can be interpreted in terms of independent dominating sets in certain graphs, and in terms of codes that have covering radius 1 and minimum distance at least 2.Publication Metadata only QC-LDPC codes from difference matrices and difference covering arrays(IEEE-Inst Electrical Electronics Engineers Inc, 2023) Donovan, Diane M.; Rao, Asha; Üsküplü, Elif; Department of Mathematics; Yazıcı, Emine Şule; Department of Mathematics; ; College of Sciences;We give a framework that generalizes LDPC code constructions using transversal designs or related structures such as mutually orthogonal Latin squares. Our constructions offer a broader range of code lengths and codes rates. Similar earlier constructions rely on the existence of finite fields of order a power of a prime, which significantly restricts the functionality of the resulting codes. In contrast, the LDPC codes constructed here are based on difference matrices and difference covering arrays, structures that are available for any order a, resulting in LDPC codes across a broader class of parameters, notably length a(a - 1), for all even a. Such values are not possible with earlier constructions, thus establishing the novelty of these new constructions. Specifically the codes constructed here satisfy the RC constraint and for a odd, have length a(2) and rate 1 - (4a - 3)/a(2), and for a even, length a(2) - a and rate at least 1 - (4a - 6)/(a(2 )- a). When 3 does not divide a, these LDPC codes have stopping distance at least 8. When a is odd and both 3 and 5 do not divide a, our construction delivers an infinite family of QC-LDPC codes with minimum distance at least 10. We also determine lower bounds for the stopping distance of the code. Further we include simulation results illustrating the performance of our codes. The BER and FER performance of our codes over AWGN (via simulation) is at least equivalent to codes constructed previously.Publication Metadata only Multicast transport protocol analysis: self-similar sources(Springer-Verlag Berlin, 2004) Department of Mathematics; Department of Computer Engineering; Çağlar, Mine; Özkasap, Öznur; Faculty Member; Faculty Member; Department of Mathematics; Department of Computer Engineering; College of Sciences; College of Engineering; 105131; 113507We study the traffic that scalable multicast protocols generate in terms of message delays over the network as well as traffic counts at the link level in the case of self-similar sources. In particular, we study Bimodal Multicast and Scalable Reliable Multicast protocols proposed for scalable reliable multicasting. These protocols are based on different mechanisms for recovering from message losses and providing scalability. We discuss the protocol mechanisms as the main underlying factor in our empirical results. Our results can be considered as a contribution to the general problem of integration of multicast communication to large scale.Publication Metadata only Square integer Heffter arrays with empty cells(Springer, 2015) Archdeacon, Dan S.; Dinitz, Jeffrey H.; Donovan, Diane M.; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432A Heffter array is an matrix with nonzero entries from such that (i) each row contains filled cells and each column contains filled cells, (ii) every row and column sum to 0, and (iii) no element from appears twice. Heffter arrays are useful in embedding the complete graph on an orientable surface where the embedding has the property that each edge borders exactly one s-cycle and one t-cycle. Archdeacon, Boothby and Dinitz proved that these arrays can be constructed in the case when , i.e every cell is filled. In this paper we concentrate on square arrays with empty cells where every row sum and every column sum is in . We solve most of the instances of this case.Publication Metadata only Overall and pairwise segregation tests based on nearest neighbor contingency tables(Elsevier, 2009) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AMultivariate interaction between two or more classes (or species) has important consequences in many fields and may cause multivariate clustering patterns such as spatial segregation or association. The spatial segregation occurs when members of a class tend to be found near members of the same class (i.e., near conspecifics) while spatial association occurs when members of a class tend to be found near members of the other class or classes. These patterns can be studied using a nearest neighbor contingency table (NNCT). The null hypothesis is randomness in the nearest neighbor (NN) structure, which may result from - among other patterns - random labeling (RL) or complete spatial randomness (CSR) of points from two or more classes (which is called the CSR independence, henceforth). New versions of overall and cell-specific tests based on NNCTs (i.e., NNCT-tests) are introduced and compared with Dixon's overall and cell-specific tests and various other spatial clustering methods. Overall segregation tests are used to detect any deviation from the null case, while the cell-specific tests are post hoc pairwise spatial interaction tests that are applied when the overall test yields a significant result. The distributional properties of these tests are analyzed and finite sample performance of the tests are assessed by an extensive Monte Carlo simulation study. Furthermore, it is shown that the new NNCT-tests have better performance in terms of Type I error and power estimates. The methods are also applied on two real life data sets for illustrative purposes. (c) 2008 Elsevier B.V. All rights reserved.Publication Metadata only Multiclass G/M/1 queueing system with self-similar input and non-preemptive priority(Elsevier, 2008) Iftikhar, Mohsin; Singh, Tejeshwar; Landfeldt, Bjorn; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131In order to deliver innovative and cost-effective IP multimedia applications over mobile devices, there is a need to develop a unified service platform for the future mobile Internet referred as the Next Generation (NG) all-IP network. It is convincingly demonstrated by numerous recent studies that modern multimedia network traffic exhibits long-range dependence (LRD) and self-similarity. These characteristics pose many novel and challenging problems in traffic engineering and network planning. One of the major concerns is how to allocate network resources efficiently to diverse traffic classes with heterogeneous QoS constraints. However, much of the current understanding of wireless traffic modeling is based on classical Poisson distributed traffic, which can yield misleading results and hence poor network planning. Unlike most existing studies that primarily focus on the analysis of single-queue systems based on the simplest First-Come-First-Serve (FCFS) scheduling policy, in this paper we introduce the first of its kind analytical performance model for multiple-queue systems with self-similar traffic scheduled by priority queueing to support differentiated QoS classes. The proposed model is based on a G/M/1 queueing system that takes into account multiple classes of traffic that exhibit long-range dependence and self-similarity. We analyze the model on the basis of non-preemptive priority and find exact packet delay and packet loss rate of the corresponding classes. We develop a finite queue Markov chain for non-preemptive priority scheduling, extending the previous work on infinite capacity systems. We extract a numerical solution for the proposed analytical framework by formulating and solving the corresponding Markov chain. We further present a comparison of the numerical analysis with comprehensive simulation studies of the same system. We also implement a Cisco-router based test bed, which serves to validate the mathematical, numerical, and simulation results as well as to support in understanding the QoS behaviour of realistic traffic input.Publication Metadata only Traffic characterization of transport level reliable multicasting: comparison of epidemic and feedback controlled loss recovery(Elsevier, 2006) N/A; Department of Computer Engineering; Department of Mathematics; Özkasap, Öznur; Çağlar, Mine; Faculty Member; Faculty Member; Department of Computer Engineering; Department of Mathematics; College of Engineering; College of Sciences; 113507; 105131Transport level multicast protocols providing reliability and scalability properties are certainly essential building blocks for several distributed group applications. We consider the effect of reliable multicast transport mechanisms oil traffic characteristics and hence network performance. Although self-similarity property of unicast traffic, ill particular TCP. has been analyzed extensively. multicast traffic has not been incorporated from this perspective. In this Study. we focus oil traffic characterization of transport level reliable multicasting. In particular, we concentrate oil two scalable and reliable multicast protocols as case studies, namely Bimodal Multicast and Scalable Reliable Multicast (SRM). and analyze the traffic generated by them. Our study consists of a complete simulation analysis supported by theoretical work. which shows that self-similarity is protocol dependent. We demonstrate that the Markovian character of Bimodal Multicast's epidemic loss recovery distinguishes ail inherently superior protocol. It discretely feeds well-behaved traffic and copes with the existing self-similarity. Oil the other hand. the feedback controlled loss recovery mechanism of SRM triggers self-similarity. Drawing upon both theoretical and Simulation analysis, our results Substantiate that transport level can induce long-range dependence even in the absence of application/user level causes.Publication Metadata only Type-speciric analysis of morphometry of dendrite spines of mice(Institute of Electrical and Electronics Engineers (IEEE), 2007) Fong, L.; Tasky, T. N.; Hurdal, M. K.; Beg, M. F.; Martone, M. E.; Ratnanather, J. T.; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AIn this article, we analyze the morphometric measures of dendrite spines of mice derived from electron tomography images for different spine types based on pre-assigned categories. The morphometric measures we consider include the metric distance, volume, surface area, and length of dendrite spines of mice. The question of interest is how these morphometric measures differ by condition of mice; and how the metric distance relates to volume, surface area, length, and condition of mice. The Large Deformation Diffeomorphic Metric Mapping algorithm is the tool we use to obtain the metric distances that quantize the morphometry of binary images of dendrite spines with respect to a template spine. We demonstrate that for the values not adjusted for scale metric distances and other morphometric measures are significantly different between the conditions. The morphometric measures (rather than the mice condition) explain almost all the variation in metric distances. Since size (or scale) dominates the other variables in variation, we adjust metric distances and other morphometric measures for scale. We demonstrate that the scaled metric distances and other scaled morphometric variables still differ for condition, and scaled metric distances depend most significantly on scaled morphometric measures. The methodology used is also valid for morphometric measures of other organs or tissues and metric distances other than LDDMM.Publication Metadata only Traffic behavior of scalable multicast: self-similarity and protocol dependence(Elsevier Science Bv, 2003) N/A; Department of Computer Engineering; Department of Mathematics; Özkasap, Öznur; Çağlar, Mine; Faculty Member; Faculty Member; Department of Computer Engineering; Department of Mathematics; College of Engineering; College of Sciences; 113507; 105131The development of high-speed networks and the expansion of the Internet have increased both geographical extent and participant population of applications such as videoconferencing, multimedia dissemination, electronic stock exchange, and distributed cooperative work. The key property of this type of applications is the need to distribute data among multiple participants together with application specific quality of service needs which fact makes multicast protocols an essential underlying communication structure. In this paper, we analyze traffic characteristics of two scalable multicast protocols, namely Bimodal Multicast (Pbcast) and Scalable Reliable Multicast (SRM), each having different approaches for loss recovery and providing reliability. Particularly, our simulation studies demonstrate that epidemic approach of Bimodal Multicast generates a more desirable traffic than SRM with lower overhead traffic and transport delays. SRM delays show long-range dependence and self-similarity whereas Bimodal Multicast delays are shortrange dependent. Self-similarity and long-range dependence are ubiquitous in wide area networks, which lead to adverse consequences in network performance. We elaborate on the protocol mechanisms as the underlying factor in our empirical results. The intrinsic relation of these mechanisms to traffic characteristics is explored.Publication Metadata only Stepwise fair-share buffering underneath bio-inspired P2P data dissemination(IEEE Computer Soc, 2007) N/A; Department of Mathematics; Department of Computer Engineering; Ahi, Emrah; Çağlar, Mine; Özkasap, Öznur; Master Student; Faculty Member; Faculty Member; Department of Mathematics; Department of Computer Engineering; Graduate School of Sciences and Engineering; College of Sciences; College of Engineering; N/A; 105131; 113507We consider buffer management problem in support of large-scale bio-inspired peer-to-peer data dissemination services. Bio-inspired epidemic protocols have considerable benefits as they are robust against network failures, scalable and provide probabilistic reliability guarantees. Coupled with an efficient buffering mechanism, system wide buffer usage can be optimized while providing reliability and scalability in such protocols. We propose a novel algorithm, Stepwise Fair-share Buffering, that provides uniform load distribution in comparison to earlier approaches and reduces the overall buffer usage where every peer has the partial view of the system. We report and discuss the comparative performance results and provide an analytical evaluation of our approach.