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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/3

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    An analytical model based on G/M/1 with self-similar input to provide end-to-end QoS in 3G networks
    (Association for Computing Machinery (ACM), 2006) Iftikhar, M.; Landfeldt, B.; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131
    The dramatic increase in demand for wireless Internet access has lead to the introduction of new wireless architectures and systems including 3G, Wi-Fi and WiMAX. 3G systems such as UMTS and CDMA2000 are leaning towards an all-IP architecture for transporting IP multimedia services, mainly due to its scalability and promising capability of inter-working heterogeneous wireless access networks. During the last ten years, substantial work has been done to understand the nature of wired IP traffic and it has been proven that IP traffic exhibits self-similar properties and burstiness over a large range of time scales. Recently, because of the large deployment of new wireless architectures, researchers have focused their attention towards understanding the nature of traffic carried by different wireless architecture and early studies have shown that wireless data traffic also exhibits strong long-range dependency. Thus, the classical tele-traffic theory based on a simple Markovian process cannot be used to evaluate the performance of wireless networks. Unfortunately, the area of understanding and modeling of different kinds of wireless traffic is still immature which constitutes a problem since it is crucial to guarantee tight bound QoS parameters to heterogeneous end users of the mobile Internet. In this paper, we make several contributions to the accurate modeling of wireless IP traffic by presenting a novel analytical model that takes into account four different classes of self-similar traffic. The model consists of four queues and is based on a G/M/1 queueing system. We analyze it on the basis of priority with no preemption and find exact packet delays. To date, no closed form expressions have been presented for G/M/1 with priority.
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    Chapter 6 stochastic representations for nonlinear parabolic pdes
    (Elsevier, 2007) Department of Mathematics; Soner, Halil Mete; Faculty Member; Department of Mathematics; College of Sciences; N/A
    We discuss several different representations of nonlinear parabolic partial differential equations in terms of Markov processes. After a brief introduction of the linear case, different representations for nonlinear equations are discussed. One class of representations is in terms of stochastic control and differential games. An extension to geometric equations is also discussed. All of these representations are through the appropriate expected values of the data. Different type of representations are also available through backward stochastic differential equations. A recent extension to second-order backward stochastic differential equations allow us to represent all fully nonlinear scalar parabolic equations.
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    Physics of spectral singularities
    (Trends in Mathematics, 2015) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In particular, we give a simple definition of spectral singularities, provide a general introduction to spectral consequences of ��-symmetry (clarifying some of the controversies surrounding this subject), outline the main ideas and constructions used in the pseudo-Hermitian representation of quantum mechanics, and discuss how spectral singularities entered in the physics literature as obstructions to these constructions. We then review the transfer matrix formulation of scattering theory and the application of complex scattering potentials in optics. These allow us to elucidate the physical content of spectral singularities and describe their optical realizations. Finally, we survey some of the most important results obtained in the subject, drawing special attention to the remarkable fact that the condition of the existence of linear and nonlinear optical spectral singularities yield simple mathematical derivations of some of the basic results of laser physics, namely the laser threshold condition and the linear dependence of the laser output intensity on the gain coefficient.
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    Stepwise probabilistic buffering for epidemic information dissemination
    (Institute of Electrical and Electronics Engineers (IEEE), 2006) 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; 113507
    For large-scale peer-to-peer applications, bioinspired epidemic protocols have considerable advantages as they are robust against network failures, scalable and provide probabilistic reliability guarantees. While providing reliability, a key issue to consider is the usage of system wide buffer space. In this context, we introduce a novel scheme called stepwise probabilistic buffering that reduces the amount of buffering and distributes the load of buffering to the entire system where every peer does not have the complete view of the system. We compute the performance measures through simulations of large-scale application scenarios.
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    An alternating service model with self-similar input to provide guaranteed QoS in wireless internet
    (IEEE, 2006) Iftikhar, Mohsin; Landfeldt, Bjorn; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131
    Over the past few years, we have witnessed a growing popularity of new wireless architectures such as 3G, WiFi and Wi-Max due to the increase in demand for wireless Internet access. The all-IP based future mobile and wireless network model is expected to be the most dominant architecture for QoS provisioning in next-generation wireless networks, mainly due to its scalability and capability of inter-working heterogeneous wireless access networks. Recently, the rapid growth of various wireless infrastructures and the interesting mixture of wireless traffic generated by large number of devices (PDAs, Laptops and cell-phones) have diverted the attention of wireless research community towards understanding the nature of traffic carried by different wireless architectures. A series of recent studies on GPRS aggregated traffic, WAP and Web traffic has proven that wireless traffic exhibits strong long-range dependency. However, much of the current understanding of wireless traffic modeling builds on classical Poisson distributed traffic, which can yield misleading results and hence poor wireless network planning. In this paper, we contribute to the accurate modeling of wireless IP traffic by considering two different types of traffic that exhibit long-range dependency and self-similarity. We consider a model of two queues based on G/M/1 queueing system and analyze it on the basis of 1-limited polling service and find exact bounds on packet delay.
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    Topology dependent information dissemination in P2P networks for anti-entropy algorithms
    (IEEE, 2008) N/A; Department of Computer Engineering; Department of Mathematics; Özkasap, Öznur; Çağlar, Mine; İskender, Emre; Faculty Member; Faculty Member; Master Student; Department of Computer Engineering; Department of Mathematics; College of Engineering; College of Sciences; Graduate School of Sciences and Engineering; 113507; 105131; N/A
    Analyzing the behavior of epidemic spreading in a network is a good way of modeling several network phenomena. There are several studies analyzing the spreading of email viruses. Spreading of epidemics is also a good model for several types of information dissemination in distributed systems. In this study, we examine spreading of epidemics for anti-entropy algorithms in a peer-to-peer network with any given topology. We derive nodes' exact probability distributions of being infected in each epidemic cycle.
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    Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results
    (Charles University Faculty of Mathematics and Physics, 2020) Donovan, Diane M.; Grannell, Mike; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432
    We review results for the embedding of orthogonal partial Latin squares in orthogonal Latin squares, comparing and contrasting these with results for embedding partial Latin squares in Latin squares. We also present a new construction that uses the existence of a set of t mutually orthogonal Latin squares of order n to construct a set of 2t mutually orthogonal Latin squares of order n(t).
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    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/A
    In 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.
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    Statistical analysis of morphometric measures based on labeled cortical distance maps
    (IEEE, 2007) Hosakere M.; Nishino T.; Alexopoulos J.; Todd R.D.; Botteron K.N.; Miller M.I.; Ratnanather J.T.; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Shape differences in cortical structures in the brain can be associated with various neuropsychiatric and neuro-developmental diseases or disorders. Labeled Cortical Distance Map (LCDM) can be a powerful tool to quantize such differences in shapes derived from magnetic resonance images (MRI). This article investigates some aspects of LCDM distances in relation to morphometry. Simple morphometric measures based on LCDM indicate some aspect of the shape or size of the tissue in question. The length of the LCDM distance vector provides the number of voxels and thus volume of the tissue. The median, mode, range, and variance of LCDM distances and volume of the tissue are all suggestive of size, thickness, and shape differences. Statistical tests are employed to detect left-right asymmetry, group differences, and stochastic ordering (cdf differences) of these LCDM-based variables. We perform LCDM analysis of gray matter in ventral medial prefrontal cortices (VMPFCs) obtained from a neuro-imaging study of major depressive disorder (MDD), high risk, and control twin subjects. We find significant evidence that VMPFCs with MDD exhibit significant morphometric left-right asymmetry compared to those in high risk and control subjects. The method is also valid for analysis of morphometric measures of other organs or tissues and distances similar to LCDM distances.
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    The full metamorphosis of λ-fold block designs with block size four into λ-fold triple systems
    (Charles Babbage Research Centre, 2012) Lindner, Curt; Department of Mathematics; Department of Mathematics; Yazıcı, Emine Şule; Küçükçifçi, Selda; Faculty Member; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; 27432; 105252
    Let (X, B) be a λ-fold block design with block size 4. If a star is removed from each block of B the resulting collection of triangles T is a partial λ-fold triple system (X, T). If the edges belonging to the deleted stars can be arranged into a collection of triangles S, then (X,T ∪ S) is a λ-fold triple system, called a metamorphosis of the A-fold block design (X, B) into a λ-fold triple system. Label the elements of each block b with b 1,b 2,b 3, and b 4 (in any manner). For each i = 1,2,3,4 define a set of triangles T iand a set of stars S i as follows: for each block b = [b 1,b 2,b 3,b 4] belonging to B, partition b into a triangle and a star centered at b i, and place the triangle in T i and the star in S i. Then (X, T i) is a partial λ-fold triple system. Now if the edges belonging to the stars in S i can be arranged into a collection of triangles S i, then (X, T i ∪ S i) is a λ-fold triple system and we say that M i = (X, T i∪S i) is the ith metamorphosis of (X, B). The full metamorphosis of (X, B) is the set of four metamorphoses {M 1, M 2, M 3, M 4}. The purpose of this work is to give a complete solution of the following problem: For which n and λ does there exist a λ-fold block design with block size 4 having a full metamorphosis into λ-fold triple systems? Copyright © 2012, Charles Babbage Research Centre All rights reserved.