Browsing by Subject "Applied mathematics"

Now showing 1 - 4 of 4

Open Access
Bifurcation analysis of the dynamics of interacting subnetworks of a spiking network
(Nature Publishing Group, 2019-08) Lagzi, F.; Atay, Fatihcan M.; Rotter, S.
We analyze the collective dynamics of hierarchically structured networks of densely connected spiking neurons. These networks of sub-networks may represent interactions between cell assemblies or diferent nuclei in the brain. The dynamical activity pattern that results from these interactions depends on the strength of synaptic coupling between them. Importantly, the overall dynamics of a brain region in the absence of external input, so called ongoing brain activity, has been attributed to the dynamics of such interactions. In our study, two diferent network scenarios are considered: a system with one inhibitory and two excitatory subnetworks, and a network representation with three inhibitory subnetworks. To study the efect of synaptic strength on the global dynamics of the network, two parameters for relative couplings between these subnetworks are considered. For each case, a bifurcation analysis is performed and the results have been compared to large-scale network simulations. Our analysis shows that Generalized Lotka-Volterra (GLV) equations, well-known in predator-prey studies, yield a meaningful population-level description for the collective behavior of spiking neuronal interaction, which have a hierarchical structure. In particular, we observed a striking equivalence between the bifurcation diagrams of spiking neuronal networks and their corresponding GLV equations. This study gives new insight on the behavior of neuronal assemblies, and can potentially suggest new mechanisms for altering the dynamical patterns of spiking networks based on changing the synaptic strength between some groups of neurons.
Open Access
The parallel surrogate constraint approach to the linear feasibility problem
(Springer, 1996) Özaktaş, Hakan; Akgül, Mustafa; Pınar, Mustafa Ç.
The linear feasibility problem arises in several areas of applied mathematics and medical science, in several forms of image reconstruction problems. The surrogate constraint algorithm of Yang and Murty for the linear feasibility problem is implemented and analyzed. The sequential approach considers projections one at a time. In the parallel approach, several projections are made simultaneously and their convex combination is taken to be used at the next iteration. The sequential method is compared with the parallel method for varied numbers of processors. Two improvement schemes for the parallel method are proposed and tested.
Open Access
Partitioning sparse matrices for parallel preconditioned iterative methods
(Society for Industrial and Applied Mathematics, 2007) Uçar, B.; Aykanat, Cevdet
This paper addresses the parallelization of the preconditioned iterative methods that use explicit preconditioners such as approximate inverses. Parallelizing a full step of these methods requires the coefficient and preconditioner matrices to be well partitioned. We first show that different methods impose different partitioning requirements for the matrices. Then we develop hypergraph models to meet those requirements. In particular, we develop models that enable us to obtain partitionings on the coefficient and preconditioner matrices simultaneously. Experiments on a set of unsymmetric sparse matrices show that the proposed models yield effective partitioning results. A parallel implementation of the right preconditioned BiCGStab method on a PC cluster verifies that the theoretical gains obtained by the models hold in practice. © 2007 Society for Industrial and Applied Mathematics.
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Rassal matematiğin Türkiye'deki öncü ismi: Ahmet Hayri Körezlioğlu
(Bilkent University, 2020) Aydın, Uğur; İleri, Ahmet; Keleş, Ahmet Abdullah; Dağlı, Oğuzhan; Yalvaç, Bahadır
Matematik dalında Avrupa'nın en iyi üniversitelerinde, olasılık teorisinde döneminin en önde gelen isimlerinin talebesi olarak lisans ve lisansüstü eğitimini tamamladıktan sonra bir akademisyen olarak hayatına devam eden Hayri Körezlioğlu, uluslararası düzeyde saygın bir akademik kariyere sahip olmanın yanı sıra, rassal analize dair çalışmaların Türkiye'de sistemli bir hâl almasına da önayak olması dolayısıyla son yarım asrın en önemli Türk matematikçileri arasında yer almaktadır. Bu makalede, Körezlioğlu'nun eğitim ve çalışma hayatı ile birlikte Türkiye'deki birtakım girişimleri incelenerek kendisinin Türk matematiğine katkıları ele alınacaktır.