Communications in Number Theory and Physics | Year: 2013
Motivated by applications of log-sine integrals to a wide range of mathematical and physical problems, it is shown that real numbers and certain types of log-sine integrals can be strongly approximated by linear combinations of special values of the harmonic zeta function with the property that the coefficients belonging to these combinations turn out to be universal in the sense of being independent of special values. The approximation of real numbers by combinations of special values is reminiscent of the classical Diophantine approximation of Liouville numbers by rationals. Moreover, explicit representations of some specific log-sine integrals are obtained in terms of special values of the harmonic zeta function and the Riemann zeta function through a study of Fourier series involving harmonic numbers. In particular, special values of the harmonic zeta function and the less studied odd harmonic zeta function are expressed in terms of log-sine integrals over [0, 2π] and [0, π].
Jonas A.,Technical University of Istanbul |
Aas M.,KocUniversity |
Karadag Y.,KocUniversity |
Bayraktar H.,Istanbul University |
And 3 more authors.
Optics InfoBase Conference Papers | Year: 2014
We demonstrate lasing in water/glycerol microdroplets which stand on a superhydrophobic surface and contain purified Venus variant of the yellow fluorescent protein or dilute suspensions of E. Coli bacterial cells expressing stably the Venus protein. © 2014 OSA.
Sahillioglu Y.,KocUniversity |
IEEE Transactions on Pattern Analysis and Machine Intelligence | Year: 2012
We present a purely isometric method that establishes 3D correspondence between two (nearly) isometric shapes. Our method evenly samples high-curvature vertices from the given mesh representations, and then seeks an injective mapping from one vertex set to the other that minimizes the isometric distortion. We formulate the problem of shape correspondence as combinatorial optimization over the domain of all possible mappings, which then reduces in a probabilistic setting to a log-likelihood maximization problem that we solve via the Expectation-Maximization (EM) algorithm. The EM algorithm is initialized in the spectral domain by transforming the sampled vertices via classical Multidimensional Scaling (MDS). Minimization of the isometric distortion, and hence maximization of the log-likelihood function, is then achieved in the original 3D euclidean space, for each iteration of the EM algorithm, in two steps: by first using bipartite perfect matching, and then a greedy optimization algorithm. The optimal mapping obtained at convergence can be one-to-one or many-to-one upon choice. We demonstrate the performance of our method on various isometric (or nearly isometric) pairs of shapes for some of which the ground-truth correspondence is available. © 2012 IEEE.
Miko A.,KocUniversity |
Demirel A.L.,KocUniversity |
Journal of Materials Chemistry | Year: 2012
We report the synthesis of vertically oriented, long-range ordered hexagonal mesoporous zirconia thin films. The orientation of hexagonally ordered cylindrical mesopores in thin films was effectively controlled by taking advantage of the temperature dependent hydrophobicity of the templating block copolymer PEO-PPO-PEO. Vertical orientation was obtained when temperature was 30°C or above throughout the process. Dehydration and enhanced chemical incompatibility between the PEO and PPO blocks at slightly elevated temperatures are proposed to play a key role in the vertical orientation of the mesopores. The temperature changes act on the entire film rather than just at the interfaces and the process can be applied to any mesoporous inorganic film. © 2012 The Royal Society of Chemistry.
Ucar S.,KocUniversity |
Ergen S.C.,KocUniversity |
IEEE Transactions on Vehicular Technology | Year: 2016
Several vehicular ad hoc network (VANET) studies have focused on communication methods based on IEEE 802.11p, which forms the standard for wireless access for vehicular environments. In networks employing IEEE 802.11p only, the broadcast storm and disconnected network problems at high and low vehicle densities, respectively, degrade the delay and delivery ratio of safety message dissemination. Recently, as an alternative to the IEEE 802.11p-based VANET, the usage of cellular technologies has been investigated due to their low latency and wide-range communication. However, a pure cellular-based VANET communication is not feasible due to the high cost of communication between the vehicles and the base stations and the high number of handoff occurrences at the base station, considering the high mobility of the vehicles. This paper proposes a hybrid architecture, namely, VMaSC-LTE, combining IEEE 802.11p-based multihop clustering and the fourth-generation (4G) cellular system, i.e., Long-Term Evolution (LTE), with the goal of achieving a high data packet delivery ratio (DPDR) and low delay while keeping the usage of the cellular architecture at a minimum level. In VMaSC-LTE, vehicles are clustered based on a novel approach named Vehicular Multihop algorithm for Stable Clustering (VMaSC). The features of VMaSC are cluster head (CH) selection using the relative mobility metric calculated as the average relative speed with respect to the neighboring vehicles, cluster connection with minimum overhead by introducing a direct connection to the neighbor that is already a head or a member of a cluster instead of connecting to the CH in multiple hops, disseminating cluster member information within periodic hello packets, reactive clustering to maintain the cluster structure without excessive consumption of network resources, and efficient size- and hop-limited cluster merging mechanism based on the exchange of cluster information among CHs. These features decrease the number of CHs while increasing their stability, therefore minimizing the usage of the cellular architecture. From the clustered topology, elected CHs operate as dual-interface nodes with the functionality of the IEEE 802.11p and LTE interface to link the VANET to the LTE network. Using various key metrics of interest, including DPDR, delay, control overhead, and clustering stability, we demonstrate the superior performance of the proposed architecture compared with both previously proposed hybrid architectures and alternative routing mechanisms, including flooding and cluster-based routing via extensive simulations in ns-3 with the vehicle mobility input from the Simulation of Urban Mobility. The proposed architecture also allows achieving higher required reliability of the application quantified by the DPDR at the cost of higher LTE usage measured by the number of CHs in the network. © 1967-2012 IEEE.