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

Monetary reward and punishment to response inhibition modulate activation and synchronization within the inhibitory brain network

© 2018 Chikara, Chang, Lu, Lin, Lin and Ko. A reward or punishment can modulate motivation and emotions, which in turn affect cognitive processing. The present simultaneous functional magnetic resonance imaging-electroencephalography study examines neural mechanisms of response inhibition under the influence of a monetary reward or punishment by implementing a modified stop-signal task in a virtual battlefield scenario. The participants were instructed to play as snipers who open fire at a terrorist target but withhold shooting in the presence of a hostage. The participants performed the task under three different feedback conditions in counterbalanced order: a reward condition where each successfully withheld response added a bonus (i.e., positive feedback) to the startup credit, a punishment condition where each failure in stopping deduced a penalty (i.e., negative feedback), and a no-feedback condition where response outcome had no consequences and served as a control setting. Behaviorally both reward and punishment conditions led to significantly down-regulated inhibitory function in terms of the critical stop-signal delay. As for the neuroimaging results, increased activities were found for the no-feedback condition in regions previously reported to be associated with response inhibition, including the right inferior frontal gyrus and the pre-supplementary motor area. Moreover, higher activation of the lingual gyrus, posterior cingulate gyrus (PCG) and inferior parietal lobule were found in the reward condition, while stronger activation of the precuneus gyrus was found in the punishment condition. The positive feedback was also associated with stronger changes of delta, theta, and alpha synchronization in the PCG than were the negative or no-feedback conditions. These findings depicted the intertwining relationship between response inhibition and motivation networks

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

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

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

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

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

Differential activation of JNK1 isoforms by TRAIL receptors modulate apoptosis of colon cancer cell lines

Tumour necrosis factor-related apoptosis-inducing ligand (TRAIL) induces apoptosis on binding to its receptors, death receptor 4 and 5 (DR4, DR5). TRAIL can also activate c-Jun N-terminal kinase (JNK) through the adaptor molecules, TNF receptor-associated factor 2 (TRAF2) and receptor-interacting protein (RIP). The role of JNK in TRAIL-induced tumour cell apoptosis is unclear. In this study, we demonstrate that JNK is activated by TRAIL in colon cancer cells. Inhibition of JNK with L-JNKI reduced rhTRAIL-induced cell death but enhanced cell death induced by selective activation of DR4 or DR5. This difference was unrelated to receptor internalisation or differential activation of c-Jun, but activation of different JNK isoforms. Our data demonstrate that JNK1, but not JNK2 is activated by rhTRAIL in the examined colon cancer cell lines. Although rhTRAIL activated both the long and short isoforms of JNK1, selective activation of DR4 or DR5 led to predominant activation of the short JNK1 isoforms (JNK1α1 and/or JNK1β1). Knockdown of JNK1α1 by shRNA enhanced apoptosis induced by TRAIL, agonistic DR4 or DR5 antibodies. On the other hand, knockdown of the long JNK1 isoforms (JNK1α2 and JNK1β2) had the opposite effect; it reduced TRAIL-induced cell death. These data indicate that the short JNK1 isoforms transmit an antiapoptotic signal, whereas the long isoforms (JNK1α2 or JNK1β2) act in a proapoptotic manner

Mean ergodic multiplication operators on weighted spaces of continuous functions

[EN] Multiplication operators on weighted Banach spaces and locally convex spaces of continuous functions have been thoroughly studied. In this note, we characterize when continuous multiplication operators on a weighted Banach space and on a weighted inductive limit of Banach spaces of continuous functions are power bounded, mean ergodic or uniformly mean ergodic. The behaviour of the operator on weighted inductive limits depends on the properties of the defining sequence of weights and it differs from the Banach space case.The research of Bonet was partially supported by Project Prometeo/2017/102 of the Generalitat Valenciana. The authors authors were also partially supported by MINECO Project MTM2016-76647-P. Rodriguez also thanks the support of the Grant PAID-01-16 of the Universitat Politecnica de Valencia.Bonet Solves, JA.; Jorda Mora, E.; Rodríguez-Arenas, A. (2018). Mean ergodic multiplication operators on weighted spaces of continuous functions. Mediterranean Journal of Mathematics. 15(3):1:108-11:108. https://doi.org/10.1007/s00009-018-1150-8S1:10811:108153Bierstedt, K.D.: An introduction to locally convex inductive limits, Functional analysis and its applications (Nice, 1986), 35–133, ICPAM Lecture Notes. World Sci. Publishing, Singapore (1988)Bierstedt, K.D.: A survey of some results and open problems in weighted inductive limits and projective description for spaces of holomorphic functions. Bull. Soc. Roy. Sci. Liège 70(4–6), 167–182 (2001)Bierstedt, K.D., Bonet, J.: Some recent results on VC(X). In: Advances in the theory of Fréchet spaces (Istanbul, 1988), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 287, pp. 181–194. Kluwer Acad. Publ., Dordrecht (1989)Bierstedt, K.D., Bonet, J.: Completeness of the (LB)-spaces VC(X). Arch. Math. (Basel) 56(3), 281–285 (1991)Bierstedt, K.D., Bonet, J.: Some aspects of the modern theory of Fréchet spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat 97(2), 159–188 (2003)Bierstedt, K.D., Meise, R., Summers, W.H.: A projective description of weighted inductive limits. Trans. Am. Math. Soc. 272(1), 107–160 (1982)Bierstedt, K.D., Meise, R., Summers, W.H.: Köthe sets and Köthe sequence spaces. In: Functional analysis, holomorphy and approximation theory, Rio de Janeiro, pp. 27–91 (1980)Bonet, J., Ricker, W.J.: Mean ergodicity of multiplication operators in weighted spaces of holomorphic functions. Arch. Math. 92, 428–437 (2009)Klilou, M., Oubbi, L.: Multiplication operators on generalized weighted spaces of continuous functions. Mediterr. J. Math. 13(5), 3265–3280 (2016)Krengel, U.: Ergodic Theorems. de Gruyter, Berlin (1985)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 2 (1974)Lotz, H.P.: Uniform convergence of operators on $$L^\infty$$ L ∞ and similar spaces. Math. Z. 190, 207–220 (1985)Manhas, J.S.: Compact multiplication operators on weighted spaces of vector-valued continuous functions. Rocky Mt. J. Math. 34(3), 1047–1057 (2004)Manhas, J.S.: Compact and weakly compact multiplication operators on weighted spaces of vector-valued continuous functions. Acta Sci. Math. (Szeged) 70(1–2), 361–372 (2004)Manhas, J.S., Singh, R.K.: Compact and weakly compact weighted composition operators on weighted spaces of continuous functions. Integral Equ. Oper. Theory 29(1), 63–69 (1997)Meise, R., Vogt, D.: Introduction to Functional Analysis. The Clarendon Press, Oxford University Press, New York (1997)Oubbi, L.: Multiplication operators on weighted spaces of continuous functions. Port. Math. (N.S.) 59(1), 111–124 (2002)Oubbi, L.: Weighted composition operators on non-locally convex weighted spaces. Rocky Mt. J. Math. 35(6), 2065–2087 (2005)Singh, R.K., Manhas, J.S.: Multiplication operators on weighted spaces of vector-valued continuous functions. J. Austral. Math. Soc. Ser. A 50(1), 98–107 (1991)Singh, R.K., Manhas, J.S.: Composition operators on function spaces. North-Holland Publishing Co., Amsterdam (1993)Singh, R.K., Manhas, J.S.: Operators and dynamical systems on weighted function spaces. Math. Nachr. 169, 279–285 (1994)Wilanski, A.: Topology for Analysis. Ginn, Waltham (1970)Yosida, K.: Functional Analysis. Springer, Berlin (1980