Browsing by Subject "Lattice"
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Item Open Access Bistable behavior of a two-mode Bose-Einstein condensate in an optical cavity(IOP Institute of Physics Publishing, 2013-01-11) Safaei, S.; Mustecaplioglu, Ö. E.; Tanatar, BilalWe consider a two-component Bose-Einstein condensate in a one-dimensional optical cavity. Specifically, the condensate atoms are taken to be in two degenerate modes due to their internal hyperfine spin degrees of freedom and they are coupled to the cavity field and an external transverse laser field in a Raman scheme. A parallel laser also excites the cavity mode. When the pump laser is far detuned from its resonance atomic transition frequency, an effective nonlinear optical model of the cavity-condensate system is developed under the discrete mode approximation (DMA), while matter-field coupling has been considered beyond the rotating wave approximation. By analytical and numerical solutions of the nonlinear dynamical equations, we examine the mean cavity field and population difference (magnetization) of the condensate modes. The stationary solutions of both the mean cavity field and normalized magnetization demonstrate bistable behavior under certain conditions for the laser pump intensity and matter-field coupling strength.Item Open Access Equitable stable matchings under modular assessment(ACM, 2023-07-09) Alkan, A.; Yıldız, KemalItem Open Access Parallel sequence mining on distributed- memory systems(2001) Karapınar, EmbiyaDiscovering all the frequent sequences in very large databases is a time consuming task. However, large databases forces to partition the original database into chunks of data to process in main-memory. Most current algorithms require as many database scans as the longest frequent sequences. Spade is a fast algorithm which reduces the number of database scans to three by using lattice-theoretic approach to decompose origional problem into small pieces(equivalence classes) which can be processed in main-memory independently. In this thesis work, we present dSpade, a parallel algorithm, based on Spade, for discov- ering the set of all frequent sequences, targeting distributed-memory systems. In dSpade, horizontal database partitioning method is used, where each processor stores equal number of customer transactions. dSpade is a synchronous algorithm for discovering frequent 1-sequences (F1) and frequent 2-sequences ( F2). Each processor performs the same computation on its local data to get local support counts and broadcasts the results to other processors to nd global frequent sequences during F1 and F2 computation. After discovering all F1 and F2, all frequent sequences are inserted into lattice to decompose the original problem into equivalence classes. Equivalence classes are mapped in a greedy heuristic to the least loaded processors in a roundrobin manner. Finally, each processor asynchronously begins to compute Fk on its mapped equivalence classes to nd all frequent sequences. We present results of performance experiments conducted on a 32-node Beowulf Cluster. Experiments show that dSpade delivers good speedup and scales linearly in the database size.Item Open Access Which algebraic K3 surfaces cover an enriques surface(2018-09) Sonel, SerkanWe partially determine the necessary and su cient conditions on the entries of the intersection matrix of the transcendental lattice of algebraic K3 surface with Picard number 18 (X) 19 for the surface to doubly cover an Enriques surface.Item Open Access Which algebraic K3 surfaces doubly cover an enriques surface: a computational approach(2019-02) Yörük, OğuzhanThe relationship between K3 Surfaces and Enriques Surfaces is known to mathematicians for the last 30 years. We examined this relationship from a lattice theoretical point of view by looking at transcendental lattice of a K3 surface in the case of Picard number 18 and 19. We established a better way of attacking this problem with the help of a computer assistance.