Mellin Transforms of the Generalized Fractional Integrals and Derivatives

We obtain the Mellin transforms of the generalized fractional integrals and derivatives that generalize the Riemann-Liouville and the Hadamard fractional integrals and derivatives. We also obtain interesting results, which combine generalized $\delta_{r,m}$ operators with generalized Stirling numbers and Lah numbers. For example, we show that $\delta_{1,1}$ corresponds to the Stirling numbers of the $2^{nd}$ kind and $\delta_{2,1}$ corresponds to the unsigned Lah numbers. Further, we show that the two operators $\delta_{r,m}$ and $\delta_{m,r}$, $r,m\in\mathbb{N}$, generate the same sequence given by the recurrence relation $$S(n,k)=\sum_{i=0}^r \big(m+(m-r)(n-2)+k-i-1\big)_{r-i}\binom{r}{i} S(n-1,k-i), \;\; 0< k\leq n,$$ with $S(0,0)=1$ and $S(n,0)=S(n,k)=0$ for $n>0$ and $1+min\{r,m\}(n-1) < k$ or $k\leq 0$. Finally, we define a new class of sequences for $r \in \{\frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}, ...\}$ and in turn show that $\delta_{\frac{1}{2},1}$ corresponds to the generalized Laguerre polynomials.Comment: 17 pages, 1 figure, 9 tables, Accepted for publication in Applied Mathematics and Computatio

Conduction through the Inward Rectifier Potassium Channel, Kir2.1, Is Increased by Negatively Charged Extracellular Residues

Ion channel conductance can be influenced by electrostatic effects originating from fixed “surface” charges that are remote from the selectivity filter. To explore whether surface charges contribute to the conductance properties of Kir2.1 channels, unitary conductance was measured in cell-attached recordings of Chinese hamster ovary (CHO) cells transfected with Kir2.1 channels over a range of K+ activities (4.6–293.5 mM) using single-channel measurements as well as nonstationary fluctuation analysis for low K+ activities. K+ ion concentrations were shown to equilibrate across the cell membrane in our studies using the voltage-sensitive dye DiBAC4(5). The dependence of γ on the K+ activity (aK) was fit well by a modified Langmuir binding isotherm, with a nonzero intercept as aK approaches 0 mM, suggesting electrostatic surface charge effects. Following the addition of 100 mM N-methyl-d-glucamine (NMG+), a nonpermeant, nonblocking cation or following pretreatment with 50 mM trimethyloxonium (TMO), a carboxylic acid esterifying agent, the γ–aK relationship did not show nonzero intercepts, suggesting the presence of surface charges formed by glutamate or aspartate residues. Consistent with surface charges in Kir2.1 channels, the rates of current decay induced by Ba2+ block were slowed with the addition of NMG or TMO. Using a molecular model of Kir2.1 channels, three candidate negatively charged residues were identified near the extracellular mouth of the pore and mutated to cysteine (E125C, D152C, and E153C). E153C channels, but not E125C or D152C channels, showed hyperbolic γ–aK relationships going through the origin. Moreover, the addition of MTSES to restore the negative charges in E53C channels reestablished wild-type conductance properties. Our results demonstrate that E153 contributes to the conductance properties of Kir2.1 channels by acting as a surface charge

Towards psi-extension of Rota`s Finite Operator Calculus

A class of extended umbral calculi in operator form is presented. Extensions of all basic theorems of classical Finite Operator Calculus are shown to hold. The impossibility of straightforward extending of quantum q-plane formulation of the q-umbral caculus to the general psi-calculus case is demonstrated.Comment: 38 page

Application of Developed APCVD Transparent Conducting Oxides and Undercoat Technologies for Economical OLED Lighting

Economics is a key factor for application of organic light emitting diodes (OLED) in general lighting relative to OLED flat panel displays that can handle high cost materials such as indium tin oxide (ITO) or Indium zinc oxide (IZO) as the transparent conducting oxide (TCO) on display glass. However, for OLED lighting to penetrate into general illumination, economics and sustainable materials are critical. The issues with ITO have been documented at the DOE SSL R&amp;D and Manufacturing workshops for the last 5 years and the issue is being exacerbated by export controls from China (one of the major sources of elemental indium). Therefore, ITO is not sustainable because of the fluctuating costs and the United States (US) dependency on other nations such as China. Numerous alternatives to ITO/IZO are being evaluated such as Ag nanoparticles/nanowires, carbon nanotubes, graphene, and other metal oxides. Of these other metal oxides, doped zinc oxide has attracted a lot of attention over the last 10 years. The volume of zinc mined is a factor of 80,000 greater than indium and the US has significant volumes of zinc mined domestically, resulting in the ability for the US to be self-sufficient for this element that can be used in optoelectronic applications. The costs of elemental zinc is over 2 orders of magnitude less than indium, reflecting the relative abundance and availability of the elements. Arkema Inc. and an international primary glass manufacturing company, which is located in the United States, have developed doped zinc oxide technology for solar control windows. The genesis of this DOE SSL project was to determine if doped zinc oxide technology can be taken from the commodity based window market and translate the technology to OLED lighting. Thus, Arkema Inc. sought out experts, Philips Lighting, Pacific Northwest National Laboratories (PNNL) and National Renewable Research Laboratories (NREL), in OLED devices and brought them into the project. This project had a clear focus on economics and the work plan focused both on doped ZnO process and OLED device structure that would be consistent with the new TCO. The team successfully made 6 inch OLEDs with a serial construction. More process development is required to optimize commercial OLED structures. Feasibility was demonstrated on two different light extraction technologies: 1/4 lambda refractive index matching and high-low-high band pass filter. Process development was also completed on the key precursors for the TCO, which are ready for pilot-plant scale-up. Subsequently, Arkema has developed a cost of ownership model that is consistent with DOE SSL R&amp;D Manufacturing targets as outlined in the DOE SSL R&amp;D Manufacturing 2010 report. The overall outcome of this project was the demonstration that doped zinc oxide can be used for OLED devices without a drop-off in performance while gaining the economic and sustainable benefits of a more readily available TCO. The broad impact of this project, is the facilitation of OLED lighting market penetration into general illumination, resulting in significant energy savings, decreased greenhouse emissions, with no environmental impact issues such as mercury found in Fluorescent technology. The primary objective of this project was to develop a commercially viable process for 'Substrates' (Substrate/ undercoat/ TCO topcoat) to be used in production of OLED devices (lamps/luminaries/modules). This project focused on using Arkema's recently developed doped ZnO technology for the Fenestration industry and applying the technology to the OLED lighting industry. The secondary objective was the use of undercoat technology to improve light extraction from the OLED device. In optical fields and window applications, technology has been developed to mitigate reflection losses by selecting appropriate thicknesses and refractive indices of coatings applied either below or above the functional layer of interest. This technology has been proven and implemented in the fenestration industry for more than 15 years. Successful completion of this project would provide doped ZnO coated on inexpensive soda lime glass resulting in a significantly lower cost relative to the current ITO coated Flat Panel Display Glass substrates. Additional benefits will be a more consistent TCO that does not need an activation step with better optical performance. Clearly, this will serve to enhance penetration of OLED technologies into the lighting market

The Period Changes of the Cepheid RT Aurigae

Observations of the light curve for the 3.7-day Cepheid RT Aur both before and since 1980 indicate that the variable is undergoing an overall period increase, amounting to +0.082 +-0.012 s/yr, rather than a period decrease, as implied by all observations prior to 1980. Superposed on the star's O-C variations is a sinusoidal trend that cannot be attributed to random fluctuations in pulsation period. Rather, it appears to arise from light travel time effects in a binary system. The derived orbital period for the system is P = 26,429 +-89 days (72.36 +-0.24 years). The inferred orbital parameters from the O-C residuals differ from those indicated by existing radial velocity data. The latter imply the most reasonable results, namely a1 sin i = 9.09 (+-1.81) x 10^8 km and a minimum secondary mass of M2 = 1.15 +-0.25 Msun. Continued monitoring of the brightness and radial velocity changes in the Cepheid are necessary to confirm the long-term trend and to provide data for a proper spectroscopic solution to the orbit.Comment: Accepted for publication in PASP (November 2007

Causal hierarchy within the thalamo-cortical network in spike and wave discharges

Background: Generalised spike wave (GSW) discharges are the electroencephalographic (EEG) hallmark of absence seizures, clinically characterised by a transitory interruption of ongoing activities and impaired consciousness, occurring during states of reduced awareness. Several theories have been proposed to explain the pathophysiology of GSW discharges and the role of thalamus and cortex as generators. In this work we extend the existing theories by hypothesizing a role for the precuneus, a brain region neglected in previous works on GSW generation but already known to be linked to consciousness and awareness. We analysed fMRI data using dynamic causal modelling (DCM) to investigate the effective connectivity between precuneus, thalamus and prefrontal cortex in patients with GSW discharges. Methodology and Principal Findings: We analysed fMRI data from seven patients affected by Idiopathic Generalized Epilepsy (IGE) with frequent GSW discharges and significant GSW-correlated haemodynamic signal changes in the thalamus, the prefrontal cortex and the precuneus. Using DCM we assessed their effective connectivity, i.e. which region drives another region. Three dynamic causal models were constructed: GSW was modelled as autonomous input to the thalamus (model A), ventromedial prefrontal cortex (model B), and precuneus (model C). Bayesian model comparison revealed Model C (GSW as autonomous input to precuneus), to be the best in 5 patients while model A prevailed in two cases. At the group level model C dominated and at the population-level the p value of model C was ∼1. Conclusion: Our results provide strong evidence that activity in the precuneus gates GSW discharges in the thalamo-(fronto) cortical network. This study is the first demonstration of a causal link between haemodynamic changes in the precuneus - an index of awareness - and the occurrence of pathological discharges in epilepsy. © 2009 Vaudano et al

High-throughput sequence-based epigenomic analysis of Alu repeats in human cerebellum

DNA methylation, the only known covalent modification of mammalian DNA, occurs primarily in CpG dinucleotides. 51% of CpGs in the human genome reside within repeats, and 25% within Alu elements. Despite that, no method has been reported for large-scale ascertainment of CpG methylation in repeats. Here we describe a sequencing-based strategy for parallel determination of the CpG-methylation status of thousands of Alu repeats, and a computation algorithm to design primers that enable their specific amplification from bisulfite converted genomic DNA. Using a single primer pair, we generated amplicons of high sequence complexity, and derived CpG-methylation data from 31 178 Alu elements and their 5′ flanking sequences, altogether representing over 4 Mb of a human cerebellum epigenome. The analysis of the Alu methylome revealed that the methylation level of Alu elements is high in the intronic and intergenic regions, but low in the regions close to transcription start sites. Several hypomethylated Alu elements were identified and their hypomethylated status verified by pyrosequencing. Interestingly, some Alu elements exhibited a strikingly tissue-specific pattern of methylation. We anticipate the amplicons herein described to prove invaluable as epigenome representations, to monitor epigenomic alterations during normal development, in aging and in diseases such as cancer

The Outcome of Phagocytic Cell Division with Infectious Cargo Depends on Single Phagosome Formation

Given that macrophages can proliferate and that certain microbes survive inside phagocytic cells, the question arises as to the post-mitotic distribution of microbial cargo. Using macrophage-like cells we evaluated the post-mitotic distribution of intracellular Cryptococcus yeasts and polystyrene beads by comparing experimental data to a stochastic model. For beads, the post-mitotic distribution was that expected from chance alone. However, for yeast cells the post-mitotic distribution was unequal, implying preferential sorting to one daughter cell. This mechanism for unequal distribution was phagosomal fusion, which effectively reduced the intracellular particle number. Hence, post-mitotic intracellular particle distribution is stochastic, unless microbial and/or host factors promote unequal distribution into daughter cells. In our system unequal cargo distribution appeared to benefit the microbe by promoting host cell exocytosis. Post-mitotic infectious cargo distribution is a new parameter to consider in the study of intracellular pathogens since it could potentially define the outcome of phagocytic-microbial interactions

Perioperative risk stratification in non cardiac surgery: role of pharmacological stress echocardiography

Perioperative ischemia is a frequent event in patients undergoing major non-cardiac vascular or general surgery. This is in agreement with clinical, pathophysiological, and epidemiological evidence and constitutes an additional diagnostic therapeutic factor in the assessment of these patients. Form a clinical standpoint, it is well known that multidistrict disease, especially at the coronary level, is a severe aggravation of the operative risk. From a pathophysiological point of view, however, surgery creates conditions able to unmask coronary artery disease. Prolonged hypotension, hemorrhages, and haemodynamic stresses caused by aortic clamping and unclamping during major vascular surgery are the most relevant factors endangering the coronary circulation with critical stenoses. From the epidemiological standpoint, coronary disease is known to be the leading cause of perioperative mortality and morbidity following vascular and general surgery: The diagnostic therapeutic corollary of these considerations is that coronary artery disease – and therefore the perioperative risk – in these patients has to be identified in an effective way preoperatively