Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as in its successor, the DLMF, but their proofs were lost. We use generating functions and symbolic summation techniques to produce new proofs for them.Comment: Final version, some typos were corrected. 21 pages, uses svmult.cl

A review of the Sentusidinium complex of dinoflagellate cysts

The Jurassic to Neogene (Miocene) dinoflagellate cyst genus Sentusidinium has a relatively simple overall morphology. This genus, together with Batiacasphaera, Kallosphaeridium and Pentafidia, comprises the Sentusidinium complex. This is distinct from the superficially similar laterally asymmetrical and subspheroidal/lenticular Cyclonephelium complex. The genus Sentusidinium is an acavate, subcircular, proximate to proximochorate, sexiform gonyaulacacean genus with an apical archaeopyle and typically low relief ornamentation. Since the erection of Sentusidinium in 1978, three similar genera have been established, which we consider to be taxonomic junior synonyms of that genus: Barbatacysta, Escharisphaeridia and Pilosidinium. However, we deem the Early Cretaceous to Miocene genera Batiacasphaera, Kallosphaeridium and Pentafidia are deemed to be separate from Sentusidinium. We refine the definition of the Early Cretaceous to Miocene genus Batiacasphaera to circumscribe cysts with a reticulate to rugulate autophragm and an apical archaeopyle with a free operculum. By contrast, Kallosphaeridium has a ventrally attached apical archaeopyle with five plates that can be interpreted as type (4A1I)@ or type (5A)@; it also has a small operculum relative to the overall cyst diameter. The six accepted Kallosphaeridium species are confined to the Palaeogene. The Australian genus Pentafidia is unusual in appearing to only have five precingular plates; this comprises two species from the Jurassic–Cretaceous transition of Western Australia. Therefore, we emend Sentusidinium to restrict it to acavate, proximate or proximochorate dinoflagellate cysts with an autophragm devoid of, or covered with, highly variable, non-linear ornamentation and a type (tA) apical archaeopyle. Occasionally the elements of ornamentation may be connected, but rarely is a cingulum indicated, and the tabulation is never clearly evident. A kalyptra may be occasionally present. The operculum is free. Following a comprehensive literature review, we accept 17 species in Batiacasphaera. In Kallosphaeridium we accept six species confidently and consider six species to be problematical. We list 38 (34 accepted and four problematical) species of Sentusidinium. Kallosphaeridium? helbyi is here transferred to Cyclonephelium without question. The species Batiacasphaera angularis is occasionally tabulate and hence we transfer it, with question, to Meiourgonyaulax. The Sentusidinium complex is clearly polyphyletic, and all genera considered herein belong to the order Gonyaulacales. Batiacasphaera, Kallosphaeridium and Pentafidia cannot be confidently assigned to a family, whereas Sentusidinium belongs to the Gonyaulacaceae. The number of species within the complex has been reduced from 137 to 68; furthermore, all infraspecific taxa have been eliminated

Assessing threats to shallow groundwater quality from soil pollutants in Glasgow, UK: development of a new screening tool

A new GIS-based screening tool to assess threats to shallow groundwater quality has been trialled in Glasgow, UK. The GRoundwater And Soil Pollutants (GRASP) tool is based on a British Standard method for assessing the threat from potential leaching of metal pollutants in unsaturated soil/superficial materials to shallow groundwater, using data on soil and Quaternary deposit properties, climate and depth to groundwater. GRASP breaks new ground by also incorporating a new Glasgow-wide soil chemistry dataset. GRASP considers eight metals, including chromium, lead and nickel at 1622 soil sample locations. The final output is a map to aid urban management, which highlights areas where shallow groundwater quality may be at risk from current and future surface pollutants. The tool indicated that 13% of soil sample sites in Glasgow present a very high potential threat to groundwater quality, due largely to shallow groundwater depths and high soil metal concentrations. Initial attempts to validate GRASP revealed partial spatial coincidence between the GRASP threat ranks (low, moderate, high and very high) and groundwater chemistry, with statistical correlation between areas of high soil and groundwater metal concentrations for both Cr and Cu (r2>0.152; P<0.05). Validation was hampered by a lack of, and inconsistency in, existing groundwater chemistry data. To address this, standardised subsurface data collection networks have been trialled recently in Glasgow. It is recommended that, once available, new groundwater depth and chemistry information from these networks is used to validate the GRASP model further

Management recommendations for the northern goshawk in the southwestern United States

Present forest conditions--loss of a herbaceous and shrubby understory, reductions in the amount of older forests, and increased areas of dense tree regeneration--reflect the extent of human influence on these forests. These changes may also be affecting goshawk populations. Information on goshawk nesting habitat and foraging behavior, and the food and habitats of selected goshawk prey, was therefore synthesized to develop a set of management objectives, desired forest conditions, and management recommendations. Key objectives of the guidelines are to provide (1) nesting, post-fledging, and foraging areas for goshawks, and (2) habitat to support abundant populations of 14 primary goshawk prey. Thinning trees in the understory, creating small openings in the forest, and prescribed fires should help produce and maintain the desired forest conditions. Other habitat elements critical for maintaining both goshawk and prey populations include abundant snags and large downed logs, woody debris, interspersion of different tree sizes across the landscape, and the majority of a goshawk's home range in older-aged forests. These guidelines should also benefit forest health, soil productivity, and the habitats of other old-growth dependent plants and animals

Infections in Dupilumab Clinical Trials in Atopic Dermatitis : A Comprehensive Pooled Analysis

Background: Patients with moderate-to-severe atopic dermatitis (AD) have increased infection risk, including skin infections and systemic infections. Immunomodulators (e.g., anti-tumor necrosis factors, anti-interleukin [anti-IL]-23, anti-IL-17, Janus kinase inhibitors) increase risk of infections. Dupilumab (a monoclonal antibody blocking the shared receptor component for IL-4 and IL-13) is approved for inadequately controlled moderate-to-severe AD and for moderate-to-severe eosinophilic or oral corticosteroid-dependent asthma. Objective: The aim was to determine the impact of dupilumab on infection rates in patients with moderate-to-severe AD. Methods: This analysis pooled data from seven randomized, placebo-controlled dupilumab trials in adults with moderate-to-severe AD. Exposure-adjusted analyses assessed infection rates. Results: Of 2932 patients, 1091 received placebo, 1095 dupilumab 300 mg weekly, and 746 dupilumab 300 mg every 2 weeks. Treatment groups had similar infection rates overall per 100 patient-years (placebo, 155; dupilumab weekly, 150; dupilumab every 2 weeks, 156; dupilumab combined, 152), and similar non-skin infection rates. Serious/severe infections were reduced with dupilumab (risk ratio 0.43; p < 0.05), as were bacterial and other non-herpetic skin infections (risk ratio 0.44; p < 0.001). Although herpesviral infection rates overall were slightly higher with dupilumab than placebo, clinically important herpesviral infections (eczema herpeticum, herpes zoster) were less common with dupilumab (risk ratio 0.31; p < 0.01). Systemic anti-infective medication use was lower with dupilumab. Conclusions: Dupilumab is associated with reduced risk of serious/severe infections and non-herpetic skin infections and does not increase overall infection rates versus placebo in patients with moderate-to-severe AD. ClinicalTrials.gov Identifiers: NCT01548404, NCT02210780, NCT01859988, NCT02277743, NCT02277769, NCT02260986, and NCT02755649

Chaos assisted tunnelling with cold atoms

In the context of quantum chaos, both theory and numerical analysis predict large fluctuations of the tunnelling transition probabilities when irregular dynamics is present at the classical level. We consider here the non-dissipative quantum evolution of cold atoms trapped in a time-dependent modulated periodic potential generated by two laser beams. We give some precise guidelines for the observation of chaos assisted tunnelling between invariant phase space structures paired by time-reversal symmetry.Comment: submitted to Phys. Rev. E ; 16 pages, 13 figures; figures of better quality can be found at http://www.phys.univ-tours.fr/~mouchet

Molecular velocity auto-correlation of simple liquids observed by NMR MGSE method

The velocity auto-correlation spectra of simple liquids obtained by the NMR method of modulated gradient spin echo show features in the low frequency range up to a few kHz, which can be explained reasonably well by a $t^{-3/2}$ long time tail decay only for non-polar liquid toluene, while the spectra of polar liquids, such as ethanol, water and glycerol, are more congruent with the model of diffusion of particles temporarily trapped in potential wells created by their neighbors. As the method provides the spectrum averaged over ensemble of particle trajectories, the initial non-exponential decay of spin echoes is attributed to a spatial heterogeneity of molecular motion in a bulk of liquid, reflected in distribution of the echo decays for short trajectories. While at longer time intervals, and thus with longer trajectories, heterogeneity is averaged out, giving rise to a spectrum which is explained as a combination of molecular self-diffusion and eddy diffusion within the vortexes of hydrodynamic fluctuations.Comment: 8 pages, 6 figur

Two Phase 3 Trials of Dupilumab versus Placebo in Atopic Dermatitis.

BACKGROUND Dupilumab, a human monoclonal antibody against interleukin-4 receptor alpha, inhibits signaling of interleukin-4 and interleukin-13, type 2 cytokines that may be important drivers of atopic or allergic diseases such as atopic dermatitis. METHODS In two randomized, placebo-controlled, phase 3 trials of identical design (SOLO 1 and SOLO 2), we enrolled adults with moderate-to-severe atopic dermatitis whose disease was inadequately controlled by topical treatment. Patients were randomly assigned in a 1:1:1 ratio to receive, for 16 weeks, subcutaneous dupilumab (300 mg) or placebo weekly or the same dose of dupilumab every other week alternating with placebo. The primary outcome was the proportion of patients who had both a score of 0 or 1 (clear or almost clear) on the Investigator’s Global Assessment and a reduction of 2 points or more in that score from baseline at week 16. RESULTS We enrolled 671 patients in SOLO 1 and 708 in SOLO 2. In SOLO 1, the primary outcome occurred in 85 patients (38%) who received dupilumab every other week and in 83 (37%) who received dupilumab weekly, as compared with 23 (10%) who received placebo (P<0.001 for both comparisons with placebo). The results were similar in SOLO 2, with the primary outcome occurring in 84 patients (36%) who received dupilumab every other week and in 87 (36%) who received dupilumab weekly, as compared with 20 (8%) who received placebo (P<0.001 for both comparisons). In addition, in the two trials, an improvement from baseline to week 16 of at least 75% on the Eczema Area and Severity Index was reported in significantly more patients who received each regimen of dupilumab than in patients who received placebo (P<0.001 for all comparisons). Dupilumab was also associated with improvement in other clinical end points, including reduction in pruritus and symptoms of anxiety or depression and improvement in quality of life. Injection-site reactions and conjunctivitis were more frequent in the dupilumab groups than in the placebo groups. CONCLUSIONS In two phase 3 trials of identical design involving patients with atopic dermatitis, dupilumab improved the signs and symptoms of atopic dermatitis, including pruritus, symptoms of anxiety and depression, and quality of life, as compared with placebo. Trials of longer duration are needed to assess the long-term effectiveness and safety of dupilumab. (Funded by Sanofi and Regeneron Pharmaceuticals; SOLO 1 ClinicalTrials.gov number, NCT02277743; SOLO 2 ClinicalTrials .gov number, NCT02277769.

Coherent Photoproduction of pi^+ from 3^He

We have measured the differential cross section for the $\gamma$$^3$He$\rightarrow \pi^+ t$ reaction. This reaction was studied using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. Real photons produced with the Hall-B bremsstrahlung tagging system in the energy range from 0.50 to 1.55 GeV were incident on a cryogenic liquid $^3$He target. The differential cross sections for the $\gamma$$^3$He$\rightarrow \pi^+ t$ reaction were measured as a function of photon-beam energy and pion-scattering angle. Theoretical predictions to date cannot explain the large cross sections except at backward angles, showing that additional components must be added to the model.Comment: 11 pages, 16 figure

Non--power law behavior of the radial profile of phase--space density of halos

We study the pseudo phase-space density, $\rho(r)/\sigma^3(r)$, of $\Lambda$CDM dark matter halos with and without baryons (baryons+DM, and pure DM), by using the model introduced in Del Popolo (2009), which takes into account the effect of dynamical friction, ordered and random angular momentum, baryons adiabatic contraction and dark matter baryons interplay. We examine the radial dependence of $\rho(r)/\sigma^3(r)$ over 9 orders of magnitude in radius for structures on galactic and cluster of galaxies scales. We find that $\rho(r)/\sigma^3(r)$ is approximately a power-law only in the range of halo radius resolved by current simulations (down to 0.1% of the virial radius) while it has a non-power law behavior below the quoted scale, with inner profiles changing with mass. The non-power-law behavior is more evident for halos constituted both of dark matter and baryons while halos constituted just of dark matter and with angular momentum chosen to reproduce a Navarro-Frenk-White (NFW) density profile, are characterized by an approximately power-law behavior. The results of the present paper lead to conclude that density profiles of the NFW type are compatible with a power-law behavior of $\rho(r)/\sigma^3(r)$, while those flattening to the halo center, like those found in Del Popolo (2009) or the Einasto profile, or the Burkert profile, cannot produce radial profile of the pseudo-phase-space density that are power-laws at all radii. The results argue against universality of the pseudo phase-space density and as a consequence argue against universality of density profiles constituted by dark matter and baryons as also discussed in Del Popolo (2009).Comment: 20 pages; 7 figs. arXiv admin note: substantial text overlap with arXiv:0906.4447 and arXiv:1012.432