Mathematics / Matematik

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  • Article
    Citation - WoS: 30
    Citation - Scopus: 28
    Bianchi I Model: an Alternative Way To Model the Present-Day Universe
    (Oxford University Press, 2014) Russell, Esra; Kılınç, Can Battal; Pashaev, Oktay
    Although the new era of high-precision cosmology of the cosmic microwave background (CMB) radiation improves our knowledge to understand the infant as well as the presentday Universe, it also leads us to question the main assumption of the exact isotropy of the CMB. There are two pieces of observational evidence that hint towards there being no exact isotropy. These are: first, the existence of small anisotropy deviations from isotropy of theCMB radiation and secondly, the presence of large angle anomalies, although the existence of these anomalies is currently a huge matter of debate. These hints are particularly important since isotropy is one of the two main postulates of the Copernican principle on which the Friedmann Robertson Walker (FRW) models are built. This almost-isotropic CMB radiation implies that the universe is almost an FRW universe, as is proved by previous studies. Assuming that the matter component forms the deviations from isotropy in the CMB density fluctuations when matter and radiation decouples, we here attempt to find possible constraints on the FRW-type scale and Hubble parameter by using the Bianchi type I (BI) anisotropic model which is asymptotically equivalent to the standard FRW. To obtain constraints on such an anisotropic model, we derive average and late-time shear values that come from the anisotropy upper limits of the recent Planck data based on a model independent shear parameter of Maartens, Ellis & Stoeger and from the theoretical consistency relation. These constraints lead us to obtain a BI model which becomes an almost-FRWmodel in time, and which is consistent with the latest observational data of the CMB.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Extended Void Merging Tree Algorithm for Self-Similar Models
    (Oxford University Press, 2014) Russell, Esra
    In hierarchical evolution, voids exhibit two different behaviours related with their surroundings and environments, they can merge or collapse. These two different types of void processes can be described by the two-barrier excursion set formalism based on Brownian random walks. In this study, the analytical approximate description of the growing void merging algorithm is extended by taking into account the contributions of voids that are embedded into overdense region(s) which are destined to vanish due to gravitational collapse. Following this, to construct a realistic void merging model that consists of both collapse and merging processes, the twobarrier excursion set formalism of the void population is used. Assuming spherical voids in the Einstein-de Sitter Universe, the void merging algorithm which allows us to consider the two main processes of void hierarchy in one formalism is constructed. In addition to this, the merger rates, void survival probabilities, void size distributions in terms of the collapse barrier and finally, the void merging tree algorithm in the self-similar models are defined and derived.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 19
    Campways: Constrained Alignment Framework for the Comparative Analysis of a Pair of Metabolic Pathways
    (Oxford University Press, 2013) Abaka, Gamze; Bıyıkoğlu, Türker; Erten, Cesim
    Motivation: Given a pair of metabolic pathways, an alignment of the pathways corresponds to a mapping between similar substructures of the pair. Successful alignments may provide useful applications in phylogenetic tree reconstruction, drug design and overall may enhance our understanding of cellular metabolism.Results: We consider the problem of providing one-to-many alignments of reactions in a pair of metabolic pathways. We first provide a constrained alignment framework applicable to the problem. We show that the constrained alignment problem even in a primitive setting is computationally intractable, which justifies efforts for designing efficient heuristics. We present our Constrained Alignment of Metabolic Pathways (CAMPways) algorithm designed for this purpose. Through extensive experiments involving a large pathway database, we demonstrate that when compared with a state-of-the-art alternative, the CAMPways algorithm provides better alignment results on metabolic networks as far as measures based on same-pathway inclusion and biochemical significance are concerned. The execution speed of our algorithm constitutes yet another important improvement over alternative algorithms. © The Author 2013.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    Merging Tree Algorithm of Growing Voids in Self-Similar and Cdm Models
    (Oxford University Press, 2013) Russell, Esra
    Observational studies show that voids are prominent features of the large-scale structure of the present-day Universe. Even though their emerging from the primordial density perturbations and evolutionary patterns differ from dark matter haloes, N-body simulations and theoretical models have shown that voids also merge together to form large void structures. In this study, following Sheth & van de Weygaert, we formulate an analytical approximate description of the hierarchical void evolution of growing voids by adopting the halo merging algorithm given by Lacey & Cole in the Einstein de Sitter (EdS) Universe. To do this, we take into account the general volume distribution of voids which consists of two main void processes: merging and collapsing.We show that the volume distribution function can be reduced to a simple form, by neglecting the collapsing void contribution since the collapse process is negligible for largesize voids. Therefore, the void volume fraction has a contribution only from growing voids. This algorithm becomes the analogue of the halo merging algorithm. Based on this growing void distribution, we obtain the void merging algorithm in which we define and formulate void merging and absorption rates, as well as void size and redshift survival probabilities and also failure rates in terms of the self-similar and currently favoured dark-energy-dominated cold dark matter models in the EdS Universe.