Gibbs' theorem for open systems with incomplete statistics

Gibbs' theorem, which is originally intended for canonical ensembles with complete statistics has been generalized to open systems with incomplete statistics. As a result of this generalization, it is shown that the stationary equilibrium distribution of inverse power law form associated with the incomplete statistics has maximum entropy even for open systems with energy or matter influx. The renormalized entropy definition given in this paper can also serve as a measure of self-organization in open systems described by incomplete statistics.Comment: 6 pages, accepted to Chaos, Solitons and Fractal

Renormalized entropy for one dimensional discrete maps: periodic and quasi-periodic route to chaos and their robustness

We apply renormalized entropy as a complexity measure to the logistic and sine-circle maps. In the case of logistic map, renormalized entropy decreases (increases) until the accumulation point (after the accumulation point up to the most chaotic state) as a sign of increasing (decreasing) degree of order in all the investigated periodic windows, namely, period-2, 3, and 5, thereby proving the robustness of this complexity measure. This observed change in the renormalized entropy is adequate, since the bifurcations are exhibited before the accumulation point, after which the band-merging, in opposition to the bifurcations, is exhibited. In addition to the precise detection of the accumulation points in all these windows, it is shown that the renormalized entropy can detect the self-similar windows in the chaotic regime by exhibiting abrupt changes in its values. Regarding the sine-circle map, we observe that the renormalized entropy detects also the quasi-periodic regimes by showing oscillatory behavior particularly in these regimes. Moreover, the oscillatory regime of the renormalized entropy corresponds to a larger interval of the nonlinearity parameter of the sine-circle map as the value of the frequency ratio parameter reaches the critical value, at which the winding ratio attains the golden mean.Comment: 14 pages, 7 figure

Polarization Beam Splitter Based on Self-Collimation of a Hybrid Photonic Crystal

A photonic crystal polarization beam splitter based on photonic band gap and self-collimation effects is designed for optical communication wavelengths. The photonic crystal structure consists of a polarization-insensitive self-collimation region and a splitting region. TM- and TE-polarized waves propagate without diffraction in the self-collimation region, whereas they split by 90 degrees in the splitting region. Efficiency of more than 75% for TM- and TE-polarized light is obtained for a polarization beam splitter size of only 17 μm x 17 μm in a wavelength interval of 60 nm including 1.55 μm

Connectivity-Driven Coherence in Complex Networks

We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the coupling function. These findings predict that in random graphs, the enhancement of coherence is proportional to the mean degree. In locally connected networks, coherence is no longer controlled by the mean degree, but rather on how the mean degree scales with the network size. In these networks, even when the coherence is absent, adding a fraction s of random connections leads to an enhancement of coherence proportional to s. Our results provide a way to control the emergent properties by the manipulation of the dynamics of the elements and the network connectivity.Comment: 4 pages, 2 figure

Deep Multi-Modal Classification of Intraductal Papillary Mucinous Neoplasms (IPMN) with Canonical Correlation Analysis

Pancreatic cancer has the poorest prognosis among all cancer types. Intraductal Papillary Mucinous Neoplasms (IPMNs) are radiographically identifiable precursors to pancreatic cancer; hence, early detection and precise risk assessment of IPMN are vital. In this work, we propose a Convolutional Neural Network (CNN) based computer aided diagnosis (CAD) system to perform IPMN diagnosis and risk assessment by utilizing multi-modal MRI. In our proposed approach, we use minimum and maximum intensity projections to ease the annotation variations among different slices and type of MRIs. Then, we present a CNN to obtain deep feature representation corresponding to each MRI modality (T1-weighted and T2-weighted). At the final step, we employ canonical correlation analysis (CCA) to perform a fusion operation at the feature level, leading to discriminative canonical correlation features. Extracted features are used for classification. Our results indicate significant improvements over other potential approaches to solve this important problem. The proposed approach doesn't require explicit sample balancing in cases of imbalance between positive and negative examples. To the best of our knowledge, our study is the first to automatically diagnose IPMN using multi-modal MRI.Comment: Accepted for publication in IEEE International Symposium on Biomedical Imaging (ISBI) 201

Antibacterial activity and composition of the essential oils of two endemic Salvia sp. from Turkey

Water-distilled essential oils from dried aerial parts of Salvia cryptantha and Salvia heldreichiana (Lamiaceae), endemic in Turkey, were analysed using gas chromatography-mass spectrometry (GCMS). Camphor (19.1%), 1,8-cineole (16.4%), borneol (11.9%), viridiflorol (11.5%) and bornyl acetate (2.4%) were found to be the major constituents in the oil of S. cryptantha. The major constituents in the oil of S. heldreichiana were linalool (9.4%), a-pinene (5.6%), 1,8-cineole (5.6%), borneol (5.6%), cryptone (5.3%), linalyl acetate (4.9%), a-terpineol (4.4%), camphor (3.9%), terpinen-4-ol (3.3%), trans-linalool oxide (Furanoid) (2.9%), trans-verbenol (2.2%), geranyl acetate (2.2%) and cis-linalool oxide (Furanoid) (2.1%). Essential oil of S. heldreichiana exhibited antimicrobial activity using the disc diffusion method against Escherichia coli, Sarcinia lutea and Salmonella typhimurium. The oil of S. cryptantha inhibited the growth of S. lutea