Publications with Fulltext
Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/6
Browse
12 results
Search Results
Publication Open Access Conditional law and occupation times of two-sided sticky Brownian motion(Elsevier, 2020) Department of Mathematics; Çağlar, Mine; Can, Buğra; Faculty Member; Department of Mathematics; College of Sciences; 105131; N/ASticky Brownian motion on the real line can be obtained as a weak solution of a system of stochastic differential equations. We find the conditional distribution of the process given the driving Brownian motion, both at an independent exponential time and at a fixed time t>0. As a classical problem, we find the distribution of the occupation times of a half-line, and at 0, which is the sticky point for the process.Publication Open Access Minimal number of singular fibers in a nonorientable Lefschetz fibration(Springer, 2022) Onaran, Sinem; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746We show that there exists an admissible nonorientable genus g Lefschetz fibration with only one singular fiber over a closed orientable surface of genus h if and only if g >= 4 and h >= 1.Publication Open Access Application of stochastic flows to the sticky Brownian motion equation(Multidisciplinary Digital Publishing Institute (MDPI), 2017) Hajri, Hatem; Arnaudon, Marc; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131We investigate the relationship between the levels of industry collaboration and entrepreneurial activities at universities and the employment choices of their science and engineering doctoral students. Using data from 176 U.S. universities over the period 1996-2005, we document that more interaction with industry at a university is typically associated with more of the university's doctoral students choosing industry employment. We also document a positive relationship between universities' licenses and startups and their graduates' post-doctoral study choices.Publication Open Access Maximum drawdown and drawdown duration of spectrally negative Lévy processes decomposed at extremes(Springer Nature, 2021) Vardar-Acar, Ceren; Avram, Florin; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131Path decomposition is performed to characterize the law of the pre-/post-supremum, post-infimum and the intermediate processes of a spectrally negative Lévy process taken up to an independent exponential time T. As a result, mainly the distributions of the supremum of the post-infimum process and the maximum drawdown of the pre-/post-supremum, post-infimum processes and the intermediate processes are obtained together with the law of drawdown durations.Publication Open Access Distribution of maximum loss of fractional Brownian motion with drift(Elsevier, 2013) Vardar-Acar, Ceren; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131In this paper, we find bounds on the distribution of the maximum loss of fractional Brownian motion with H >= 1/2 and derive estimates on its tail probability. Asymptotically, the tail of the distribution of maximum loss over [0, t] behaves like the tail of the marginal distribution at time t.Publication Open Access Defining sets of full designs with block size three II(Springer, 2012) Donovan, Diane; Lefevre, James; Waterhouse, Mary; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432A defining set of a t-(v, k, lambda) design is a subcollection of its blocks which is contained in a unique t-design with the given parameters. A minimal defining set is a defining set, none of whose proper subcollections is a defining set. The spectrum of minimal defining sets of a design D is the set {|M| | M is a minimal defining set of D}. The unique simple design with parameters is said to be the full design on v elements. This paper studies the minimal defining sets of full designs when t = 2 and k = 3. The largest known minimal defining set is given. The existence of a continuous section of the spectrum comprising asymptotically 9v (2)/50 values is shown. This gives a quadratic length section of continuous spectrum where only a linear section with respect to v was known before.Publication Open Access Metric distances between hippocampal shapes indicate different rates of change over time in nondemented and demented subjects(Bentham Science, 2013) Beg, M. F.; Ceritoglu, C.; Wang, L.; Morris, J. C.; Csernansky, J. G.; Miller, M. I.; Ratnanather, J. T.; Department of Mathematics; Ceyhan, Elvan; Undergraduate Student; Faculty Member; Department of Mathematics; College of SciencesIn this article, we use longitudinal morphometry (shape and size) measures of hippocampus in subjects with mild dementia of Alzheimer type (DAT) and nondemented controls in logistic discrimination. The morphometric measures we use are volume and metric distance measures at baseline and follow-up (two years apart from baseline). Morphometric differences with respect to a template hippocampus were measured by the metric distance obtained from the large deformation diffeomorphic metric mapping (LDDMM) algorithm. LDDMM assigns metric distances on the space of anatomical images, thereby allowing for the direct comparison and quantization of morphometric changes. We also apply principal component analysis (PCA) on volume and metric distance measures to obtain principal components that capture some salient aspect of morphometry. We construct classifiers based on logistic regression to distinguish diseased and healthy hippocampi (hence potentially diagnose the mild form of DAT). We consider logistic classifiers based on volume and metric distance change over time (from baseline to follow-up), on the raw volumes and metric distances, and on principal components from various types of PCA analysis. We provide a detailed comparison of the performance of these classifiers and guidelines for their practical use. Moreover, combining the information conveyed by volume and metric distance measures by PCA can provide a better biomarker for detection of dementia compared to volume, metric distance, or both.Publication Open Access The weak phillips property(Institute of Mathematics, Polish Academy of Sciences, 2001) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of SciencesLet X be a Banach space. If the natural projection p : X∗∗∗ → X∗ is sequentially weak∗ -weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.Publication Open Access Tail probability of avoiding Poisson traps for branching Brownian motion(Elsevier, 2013) Department of Mathematics; Öz, Mehmet; Çağlar, Mine; PhD. Student; Faculty Member; Department of Mathematics; College of Sciences; N/A; 105131We consider a branching Brownian motion Z with exponential branching times and general offspring distribution evolving in R-d, where Poisson traps are present. A Poisson trap configuration with radius a is defined to be the random subset K of R-d given by K = boolean OR(x)l(,is an element of supp)(M) (B) over bar (x(i), a), where M is a Poisson random measure on B(R-d) with constant trap intensity. Survival up to time t is defined to be the event {T > t) with T = inf{s >= 0 : Z(s)(K) > 0} being the first trapping time. Following the work of Englander (2000), Englander and den Hollander (2003), where strictly dyadic branching is considered, we consider here a general offspring distribution for Z and settle the problem of survival asymptotics for the system.Publication Open Access Structure of apéry-like series and monotonicity properties for binomial sums(The Korean Mathematical Society, 2017) Department of Mathematics; Alkan, Emre; Faculty Member; Department of Mathematics; College of Sciences; 32803A family of Apery-like series involving reciprocals of central binomial coefficients is studied and it is shown that they represent transcendental numbers. The structure of such series is further examined in terms of finite combinations of logarithms and arctangents with arguments and coefficients belonging to a suitable algebraic extension of rationals. Monotonicity of certain quotients of weighted binomial sums which arise in the study of competitive cheap talk models is established with the help of a continuous extension of the discrete model at hand. The monotonic behavior of such quotients turns out to have important applications in game theory.