Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+\beta\log(1+t^\alpha)},00$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.Comment: 12 pages, LaTe

Integrated mRNA and microRNA transcriptome sequencing characterizes sequence variants and mRNA – microRNA regulatory network in nasopharyngeal carcinoma model systems

Nasopharyngeal carcinoma (NPC) is a prevalent malignancy in Southeast Asia among the Chinese population. Aberrant regulation of transcripts has been implicated in many types of cancers including NPC. Herein, we characterized mRNA and miRNA transcriptomes by RNA sequencing (RNASeq) of NPC model systems. Matched total mRNA and small RNA of undifferentiated Epstein-Barr virus (EBV)-positive NPC xenograft X666 and its derived cell line C666, well-differentiated NPC cell line HK1, and the immortalized nasopharyngeal epithelial cell line NP460 were sequenced by Solexa technology. We found 2812 genes and 149 miRNAs (human and EBV) to be differentially expressed in NP460, HK1, C666 and X666 with RNASeq; 533 miRNA-mRNA target pairs were inversely regulated in the three NPC cell lines compared to NP460. Integrated mRNA/miRNA expression profiling and pathway analysis show extracellular matrix organization, Beta-1 integrin cell surface interactions, and the PI3K/AKT, EGFR, ErbB, and Wnt pathways were potentially deregulated in NPC. Real-time quantitative PCR was performed on selected mRNA/miRNAs in order to validate their expression. Transcript sequence variants such as short insertions and deletions (INDEL), single nucleotide variant (SNV), and isomiRs were characterized in the NPC model systems. A novel TP53 transcript variant was identified in NP460, HK1, and C666. Detection of three previously reported novel EBV-encoded BART miRNAs and their isomiRs were also observed. Meta-analysis of a model system to a clinical system aids the choice of different cell lines in NPC studies. This comprehensive characterization of mRNA and miRNA transcriptomes in NPC cell lines and the xenograft provides insights on miRNA regulation of mRNA and valuable resources on transcript variation and regulation in NPC, which are potentially useful for mechanistic and preclinical studies. © 2014 The Authors.published_or_final_versio

Cross-polarized photon-pair generation and bi-chromatically pumped optical parametric oscillation on a chip

Nonlinear optical processes are one of the most important tools in modern optics with a broad spectrum of applications in, for example, frequency conversion, spectroscopy, signal processing and quantum optics. For practical and ultimately widespread implementation, on-chip devices compatible with electronic integrated circuit technology offer great advantages in terms of low cost, small footprint, high performance and low energy consumption. While many on-chip key components have been realized, to date polarization has not been fully exploited as a degree of freedom for integrated nonlinear devices. In particular, frequency conversion based on orthogonally polarized beams has not yet been demonstrated on chip. Here we show frequency mixing between orthogonal polarization modes in a compact integrated microring resonator and demonstrate a bi-chromatically pumped optical parametric oscillator. Operating the device above and below threshold, we directly generate orthogonally polarized beams, as well as photon pairs, respectively, that can find applications, for example, in optical communication and quantum optics

The Berkeley Contact Lens Extended Wear Study. Part II : Clinical results.

ObjectiveTo describe the principal clinical outcomes associated with 12 months use of rigid gas-permeable (RGP) extended wear contact lenses and address two primary study questions: (1) does extended wear (EW) of high oxygen transmissibility (Dk/t) RGP lenses reduce the incidence of ocular complications, and (2) does the wearing of high-Dk/t lenses reduce the rate of failure to maintain 6-night RGPEW over 12 months?DesignA randomized, concurrently controlled clinical trial.InterventionSubjects who adapted to EW with high Dk (oxygen permeability) RGP lenses were randomized to either high Dk or medium-Dk RGP lenses for 12 months of 6-night EW.Main outcome measuresContact lens-associated keratopathies (CLAK), changes in refractive error and corneal curvature, and survival in EW.ResultsTwo hundred one subjects were randomized to medium or high-Dk lenses for 12 months of EW. Sixty-two percent of the subjects in each group completed 12 months of EW; however, the probability of failure was significantly greater for the medium-Dk group. Although the risk of complications was similar for the two groups, the number of CLAK events that led to termination were 16 versus 5 for the medium-Dk and high-Dk groups, respectively. This suggests that the type of adverse response or the inability to reverse an adverse event was different for the group being exposed to the lower oxygen dose.ConclusionsThe level of oxygen available to the cornea has a significant impact on maintaining successful RGP extended contact lens wear, but not on the initial onset of CLAK. The number of clinical events leading to termination was substantially higher for the medium Dk group, which suggests that corneal hypoxia is an important factor in the development of CLAK. Although overnight contact lens wear should be recommended with caution and carefully monitored for early detection of ocular complications, it appears that high-Dk RGP lenses can be a safe and effective treatment for correction of refractive error for most individuals who can adapt to EW

The Berkeley Contact Lens Extended Wear Study. Part I : Study design and conduct.

ObjectiveThe primary aim of the Berkeley Contact Lens Extended Wear Study (CLEWS) was to test the hypotheses that extended wear of rigid gas-permeable (RGP) contact lenses with greater oxygen permeability (Dk) reduces the incidence of contact lens-associated keratopathy (CLAK) and increases the survival rate in RGP extended wear (EW). In this article we describe the clinical trial design in detail, present the results of subject recruitment and retention, and provide the baseline demographic and ocular characteristics of the CLEWS subjects, whose data will be analyzed to address the study aims in a companion article.DesignA randomized, concurrently controlled clinical trial.InterventionSubjects were fitted with day wear (DW) high-Dk RGP lenses and then adapted to EW. Subjects who adapted to EW were then randomly assigned to either high- or medium-Dk RGP lenses for 12 months of 6-nights/week EW.Main outcome measuresSlit-lamp assessment and grading of 17 possible keratopathies, measurement of refractive error and corneal curvature, and symptoms. Follow-up data were collected every 3 months.ResultsFrom 545 subjects entering the DW adaptation phase, 201 adapted to EW and were randomly assigned to medium- or high-Dk lenses for 12 months of EW. The baseline characteristics of the two study groups were similar and did not differ from the 344 DW subjects who failed to adapt to EW. The distributions of oxygen transmissibility for the two study groups were disjoint, indicating that each group received distinctly different levels of hypoxia.ConclusionsWe show that CLEWS was appropriately designed to address the study hypotheses, was conducted with regard for the safety of the subjects, and adhered to rigorous protocols designed to control for bias and ensure the integrity of study data. We establish the internal validity of between-group statistical comparisons and characterize our study population to permit informed evaluation of the applicability of our results to the contact lens-wearing population in general

Assessing the Health of Richibucto Estuary with the Latent Health Factor Index

The ability to quantitatively assess the health of an ecosystem is often of great interest to those tasked with monitoring and conserving ecosystems. For decades, research in this area has relied upon multimetric indices of various forms. Although indices may be numbers, many are constructed based on procedures that are highly qualitative in nature, thus limiting the quantitative rigour of the practical interpretations made from these indices. The statistical modelling approach to construct the latent health factor index (LHFI) was recently developed to express ecological data, collected to construct conventional multimetric health indices, in a rigorous quantitative model that integrates qualitative features of ecosystem health and preconceived ecological relationships among such features. This hierarchical modelling approach allows (a) statistical inference of health for observed sites and (b) prediction of health for unobserved sites, all accompanied by formal uncertainty statements. Thus far, the LHFI approach has been demonstrated and validated on freshwater ecosystems. The goal of this paper is to adapt this approach to modelling estuarine ecosystem health, particularly that of the previously unassessed system in Richibucto in New Brunswick, Canada. Field data correspond to biotic health metrics that constitute the AZTI marine biotic index (AMBI) and abiotic predictors preconceived to influence biota. We also briefly discuss related LHFI research involving additional metrics that form the infaunal trophic index (ITI). Our paper is the first to construct a scientifically sensible model to rigorously identify the collective explanatory capacity of salinity, distance downstream, channel depth, and silt-clay content --- all regarded a priori as qualitatively important abiotic drivers --- towards site health in the Richibucto ecosystem.Comment: On 2013-05-01, a revised version of this article was accepted for publication in PLoS One. See Journal reference and DOI belo

Most vital segment barriers

We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of "most vital arcs" for flows/paths to geometric environments. We give hardness results and efficient algorithms for various versions of the problem, (almost) completely separating hard and polynomially-solvable cases

The dynamics of apparent horizons in Robinson-Trautman spacetimes

We present an alternative scheme of finding apparent horizons based on spectral methods applied to Robinson-Trautman spacetimes. We have considered distinct initial data such as representing the spheroids of matter and the head-on collision of two non-rotating black holes. The evolution of the apparent horizon is presented. We have obtained in some cases a mass gap between the final Bondi and apparent horizon masses, whose implications were briefly commented in the light of the thermodynamics of black holes.Comment: 9 pages, 7 figure

Statistical modeling of ground motion relations for seismic hazard analysis

We introduce a new approach for ground motion relations (GMR) in the probabilistic seismic hazard analysis (PSHA), being influenced by the extreme value theory of mathematical statistics. Therein, we understand a GMR as a random function. We derive mathematically the principle of area-equivalence; wherein two alternative GMRs have an equivalent influence on the hazard if these GMRs have equivalent area functions. This includes local biases. An interpretation of the difference between these GMRs (an actual and a modeled one) as a random component leads to a general overestimation of residual variance and hazard. Beside this, we discuss important aspects of classical approaches and discover discrepancies with the state of the art of stochastics and statistics (model selection and significance, test of distribution assumptions, extreme value statistics). We criticize especially the assumption of logarithmic normally distributed residuals of maxima like the peak ground acceleration (PGA). The natural distribution of its individual random component (equivalent to exp(epsilon_0) of Joyner and Boore 1993) is the generalized extreme value. We show by numerical researches that the actual distribution can be hidden and a wrong distribution assumption can influence the PSHA negatively as the negligence of area equivalence does. Finally, we suggest an estimation concept for GMRs of PSHA with a regression-free variance estimation of the individual random component. We demonstrate the advantages of event-specific GMRs by analyzing data sets from the PEER strong motion database and estimate event-specific GMRs. Therein, the majority of the best models base on an anisotropic point source approach. The residual variance of logarithmized PGA is significantly smaller than in previous models. We validate the estimations for the event with the largest sample by empirical area functions. etc

Introduction to Khovanov Homologies. I. Unreduced Jones superpolynomial

An elementary introduction to Khovanov construction of superpolynomials. Despite its technical complexity, this method remains the only source of a definition of superpolynomials from the first principles and therefore is important for development and testing of alternative approaches. In this first part of the review series we concentrate on the most transparent and unambiguous part of the story: the unreduced Jones superpolynomials in the fundamental representation and consider the 2-strand braids as the main example. Already for the 5_1 knot the unreduced superpolynomial contains more items than the ordinary Jones.Comment: 33 page