Publications without Fulltext
Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/3
Browse
318 results
Filters
Advanced Search
Filter by
Settings
Search Results
Publication Metadata only Metric-bourbaki algebroids: cartan calculus for m-theory(Elsevier, 2024) Çatal-Özer, Aybike; Doğan, Keremcan; Department of Physics; Dereli, Tekin; Department of Physics; College of SciencesString and M theories seem to require generalizations of usual notions of differential geometry on smooth manifolds. Such generalizations usually involve extending the tangent bundle to larger vector bundles equipped with various algebroid structures such as Courant algebroids, higher Courant algebroids, metric algebroids, or G-algebroids. The most general geometric scheme is not well understood yet, and a unifying framework for such algebroid structures is needed. Our aim in this paper is to propose such a general framework. Our strategy is to follow the hierarchy of defining axioms for a Courant algebroid: almostCourant - metric - pre -Courant - Courant. In particular, we focus on the symmetric part of the bracket and the metric invariance property, and try to make sense of them in a manner as general as possible. These ideas lead us to define new algebroid structures which we dub Bourbaki and metric-Bourbaki algebroids, together with their almostand pre -versions. For a special case of metric-Bourbaki algebroids that we call exact, we construct a collection of maps which generalize the Cartan calculus of exterior derivative, Lie derivative and interior product. This is done by a kind of reverse -mathematical analysis of the Severa classification of exact Courant algebroids. By abstracting crucial properties of this collection of maps, we define the notion of Bourbaki calculus. Conversely, given an arbitrary Bourbaki calculus, we construct a metric-Bourbaki algebroid by building up a standard bracket that is analogous to the Dorfman bracket. Moreover, we prove that any exact metric-Bourbaki algebroid satisfying some further conditions has to have a bracket that is the twisted version of the standard bracket; a partly analogous result to Severa classification. We prove that many physically and mathematically motivated algebroids from the literature are examples of these new algebroids, and when possible we construct a Bourbaki calculus on them. In particular, we show that the Cartan calculus can be seen as the Bourbaki calculus corresponding to an exact higher Courant algebroid. We also point out examples of Bourbaki calculi including the generalization of the Cartan calculus on vector bundle valued forms. One straightforward generalization of our constructions might be done by replacing the tangent bundle with an arbitrary Lie algebroid A. This step allows us to define an extension of our results, A -version, and extend our main results for them while proving many other algebroids from the literature fit into this framework.Publication Metadata only On the past, present, and future of the Diebold-Yilmaz approach to dynamic network connectedness(Elsevier Science Sa, 2023) Diebold, Francis X.; Department of Economics; Yılmaz, Kamil; Department of Economics; College of Administrative Sciences and EconomicsWe offer retrospective and prospective assessments of the Diebold-Yilmaz connected-ness research program, combined with personal recollections of its development. Its centerpiece in many respects is Diebold and Yilmaz (2014), around which our discussion is organized.Publication Metadata only Temporal evolution of entropy and chaos in low amplitude seismic wave prior to an earthquake(Pergamon-Elsevier Science Ltd, 2023) Akilli, Mahmut; Ak, Mine; Department of Physics; Yılmaz, Nazmi; Department of Physics; College of SciencesThis study investigates the temporal changes of entropy and chaos in low-amplitude continuous seismic wave data prior to two moderate-level earthquakes. Specifically, we examine seismic signals before and during the Istanbul-Turkey earthquake of September 26, 2019 (M = 5.7), and the Duzce-Turkey earthquake of November 17, 2021 (M = 5.2), which occurred near the Marmara Sea region on the north-Anatolian fault line. We aim to identify changes in complexity and chaotic characteristics in the pre-earthquake seismic waves and explore the possibility of earthquake forecasting minutes before an earthquake. To accomplish this, we utilize windowed scalogram entropy and sample entropy methods and compared the results with Lyapunov exponents and windowed scale index. Our findings indicate that measuring the temporal change of entropy using windowed scalogram entropy is sensitive to the change in complexity due to the frequency shifts during the weak ground motion approaching an earthquake.On the other hand, Lyapunov exponents and sample entropy appear more effective in their response to the change in complexity and chaotic characteristics due to the change in the signal amplitude. Additionally, the windowed scale index can detect temporal fluctuations in the aperiodicity of the signal. Overall, our results suggest that all four methods can be valuable in characterizing complexity and chaos in short-time pre -earthquake seismic signals, differentiating earthquakes, and contributing to the development of earthquake forecasting techniques.Publication Metadata only On the network topology of variance decompositions: measuring the connectedness of financial firms (Reprinted from Journal of Econometrics, Vol 182, Issue 1, September 2014, Pages 119-134)(Elsevier Science Sa, 2023) Diebold, Francis X.; Department of Economics; Yılmaz, Kamil; Department of Economics; College of Administrative Sciences and EconomicsWe propose several connectedness measures built from pieces of variance decomposi-tions, and we argue that they provide natural and insightful measures of connectedness. We also show that variance decompositions define weighted, directed networks, so that our connectedness measures are intimately related to key measures of connectedness used in the network literature. Building on these insights, we track daily time-varying connectedness of major U.S. financial institutions' stock return volatilities in recent years, with emphasis on the financial crisis of 2007-2008.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 A characterization of heaviness in terms of relative symplectic cohomology(Wiley, 2024) Mak, Cheuk Yu; Sun, Yuhan; Department of Mathematics; Varolgüneş, Umut; Department of Mathematics; College of SciencesFor a compact subset K$K$ of a closed symplectic manifold (M,omega)$(M, \omega)$, we prove that K$K$ is heavy if and only if its relative symplectic cohomology over the Novikov field is nonzero. As an application, we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results is also included.Publication Metadata only Orthogonal cycle systems with cycle length less than 10(John Wiley and Sons Inc, 2024) Department of Mathematics; Küçükçifçi, Selda; Yazıcı, Emine Şule; Department of Mathematics; College of SciencesAn H-decomposition of a graph G is a partition of the edge set of G into subsets, where each subset induces a copy of the graph H. A k-orthogonal H-decomposition of G is a set of kH-decompositions of G such that any two copies of H in distinct H-decompositions intersect in at most one edge. When G = K-v, we call the H-decomposition an H-system of order v. In this paper, we consider the case H is an l-cycle and construct a pair of orthogonal l-cycle systems for all admissible orders when l is an element of {5, 6, 7, 8, 9}, except when l = v.Publication Metadata only Complex vs. convex Morse functions and geodesic open books(World Scientific, 2024) Dehornoy, Pierre; Department of Mathematics; Özbağcı, Burak; Department of Mathematics; College of SciencesSuppose that Sigma is a closed and oriented surface equipped with a Riemannian metric. In the literature, there are three seemingly distinct constructions of open books on the unit (co)tangent bundle of Sigma, having complex, contact and dynamical flavors, respectively. Each one of these constructions is based on either an admissible divide or an ordered Morse function on Sigma. We show that the resulting open books are pairwise isotopic provided that the ordered Morse function is adapted to the admissible divide on Sigma. Moreover, we observe that if Sigma has positive genus, then none of these open books are planar and furthermore, we determine the only cases when they have genus one pages.Publication Metadata only Uniform syndeticity in multiple recurrence(CAMBRIDGE UNIV PRESS, 2024) Pan, Minghao; Department of Mathematics; Jamneshan, Asgar; Department of Mathematics; College of SciencesThe main theorem of this paper establishes a uniform syndeticity result concerning the multiple recurrence of measure-preserving actions on probability spaces. More precisely, for any integers d, l >= 1 and any epsilon > 0, we prove the existence of delta > 0 and K >= 1 (dependent only on d, l, and epsilon) such that the following holds: Consider a solvable group Gamma of derived length l, a probability space (X, mu), and d pairwise commuting measure-preserving Gamma-actions T-1, & mldr;, T-d on (X, mu). Let E be a measurable set in X with mu(E) >= epsilon. Then, K many (left) translates of {gamma is an element of Gamma: mu (T-1(gamma-1 )(E)boolean AND T-2(gamma-1)degrees T-1(gamma-1 )(E) boolean AND center dot center dot center dot boolean AND T-d(gamma-1 )degrees T-d-1(gamma-1 )degrees center dot center dot center dot degrees T-1(gamma-1 )(E)) >= delta} cover Gamma. This result extends and refines uniformity results by Furstenberg and Katznelson. As a combinatorial application, we obtain the following uniformity result. For any integers d, l >= 1 and any epsilon>0, there are delta>0 and K >= 1 (dependent only on d, l, and epsilon) such that for all finite solvable groups G of derived length l and any subset E subset of G(d) with m(circle times d)(E) >= epsilon (where m is the uniform measure on G), we have that K-many (left) translates of {g is an element of G:m(circle times d)({(a(1), & mldr;, a(n)) is an element of G(d): (a(1), & mldr;, a(n)), (ga(1), a(2), & mldr;, a(n)), & mldr;, (ga(1), ga(2), & mldr;, ga(n)) is an element of E}) >= delta} cover G. The proof of our main result is a consequence of an ultralimit version of Austin's amenable ergodic Szemeredi theorem.Publication Metadata only Stopping levels for a spectrally negative Markov additive process(Springer Science and Business Media Deutschland GmbH, 2024) Vardar-Acar, C.; Department of Mathematics; Çağlar, Mine; Department of Mathematics; College of SciencesThe optimal stopping problem for pricing Russian options in finance requires taking the supremum of the discounted reward function over all finite stopping times. We assume the logarithm of the asset price is a spectrally negative Markov additive process with finitely many regimes. The reward function is given by the exponential of the running supremum of the price process. Previous work on Russian optimal stopping problem suggests that the optimal stopping time would be an upcrossing time of the drawdown at a certain level for each regime. We derive explicit formulas for identifying the stopping levels and computing the corresponding value functions through a recursive algorithm. A numerical is provided for finding these stopping levels and their value functions.