On some problems involving Hardy's function

Some problems involving the classical Hardy function $$Z(t) := \zeta(1/2+it)\bigl(\chi(1/2+it)\bigr)^{-1/2}, \quad \zeta(s) = \chi(s)\zeta(1-s)$$ are discussed. In particular we discuss the odd moments of $Z(t)$, the distribution of its positive and negative values and the primitive of $Z(t)$. Some analogous problems for the mean square of $|\zeta(1/2+it)|$ are also discussed.Comment: 15 page

Парсическая роль интеллигенции в истории

In 1661, Borelli and Ecchellensis published a Latin translation of a text which they called the Ltmmas of Archimedes. The first fifteen propositions of this translation correspond to the contents of the Arabic Book of Assumptions, which the Arabic tradition attributes to Archimedes. The work is not found in Greek and the attribution is uncertain at best. Nevertheless, the Latin translation of the fifteen propositions was adopted as a work of Archimedes in the standard editions and translations by Heiberg, Heath, Ver Eecke and others. Our paper concerns the remaining two propositions, 16 and 17, in the Latin translation by Borelli and Ecchellensis, which are not found in the Arabic Book of Assumptions. Borelli and Ecchellensis believed that the Arabic Book of Assumptions is a mutilated version of a lost "old book" by Archimedes which is mentioned by Eutodus (ca. A.D. 500) in his commentary to Proposition 4 of Book 2 of Archimedes' On the Sphere and Cylinder. This proposition is about cutting a sphere by a plane in such a way that the volumes of the segments have a given ratio. Because the fifteen propositions in the Arabic Book of Assumptions have no connection whatsoever to this problem, Borelli and Ecchellensis "restored" two more propositions, their 16 and 17. Propositions 16 and 17 concern the problem of cutting a given line segment AG at a point X in such a way that the product AX· XG2 is equal to a given volume K. This problem is mentioned by Archimedes, and although he promised a solution, the solution is not found in On the Sphere and Cylinder. In his commentary, Eutodus presents a solution which he adapted from the "old book" of Archimedes which he had found. Proposition 17 is the synthesis of the problem by means of two conic sections, as adapted by Eutodus. Proposition 16 presents the diorismos: the problem can be solved only if K::::;;; AB · BG2, where point B is defined on AG such that AB = 1/zBG. We will show that Borelli and Ecchellensis adapted their Proposition 16 not from the commentary by Eutocius but from the Arabic text On Filling the Gaps in Archimedes' Sphere and Cylinder which was written by Abu Sahl al-Kuru in the tenth century, and which was published by Len Berggren. Borelli preferred al-Kiihi's diorismos (by elementary means) to the diorismos by means of conic sections in the commentary of Eutocius, even though Eutocius says that he had adapted it from the "old book." Just as some geometers in later Greek antiquity, Borelli and Ecchellensis bdieved that it is a "sin" to use conic sections in the solution of geometrical problems if elementary Euclidean means are possible. They (incorrectly) assumed that Archimedes also subscribed to this opinion, and thus they included their adaptation of al-Kuru's proposition in their restoration of the "old book" of Archimedes. Our paper includes the Latin text and an English translation of Propositions 16 and 17 of Borelli and Ecchellensis

Gaming motivation and problematic video gaming: The role of needs frustration

Motivation is often used as a predictor of a problematic style of video game engagement, implying that individuals' gaming undermines optimal functioning. Drawing from recent advances in Self-Determination Theory (SDT), the present study explores the links between gaming motivations, the daily frustration of basic psychological needs, and reports of problematic video gaming (PVG). A sample of 1029 participants (72.8% male; M = 22.96 years; SD = 4.13 years) completed items regarding their gaming engagement and gaming motivation as well as their experience of needs frustration and PVG symptoms. Results revealed positive associations between gaming motivations and PVG, and between daily needs frustration and PVG. Finally, after comparing several competing models, a mediational model whereby needs frustration explained the association between individuals' gaming motivation and PVG emerged as best fitting the data. The discussion addresses the theoretical and practical implications of these findings in the context of recent research

On the protection of extrasolar Earth-like planets around K/M stars against galactic cosmic rays

Previous studies have shown that extrasolar Earth-like planets in close-in habitable zones around M-stars are weakly protected against galactic cosmic rays (GCRs), leading to a strongly increased particle flux to the top of the planetary atmosphere. Two main effects were held responsible for the weak shielding of such an exoplanet: (a) For a close-in planet, the planetary magnetic moment is strongly reduced by tidal locking. Therefore, such a close-in extrasolar planet is not protected by an extended magnetosphere. (b) The small orbital distance of the planet exposes it to a much denser stellar wind than that prevailing at larger orbital distances. This dense stellar wind leads to additional compression of the magnetosphere, which can further reduce the shielding efficiency against GCRs. In this work, we analyse and compare the effect of (a) and (b), showing that the stellar wind variation with orbital distance has little influence on the cosmic ray shielding. Instead, the weak shielding of M star planets can be attributed to their small magnetic moment. We further analyse how the planetary mass and composition influence the planetary magnetic moment, and thus modify the cosmic ray shielding efficiency. We show that more massive planets are not necessarily better protected against galactic cosmic rays, but that the planetary bulk composition can play an important role.Comment: 7 figure

Alpha-synuclein mRNA expression in oligodendrocytes in MSA

Multiple system atrophy (MSA) is a progressive neurodegenerative disease presenting clinically with parkinsonian, cerebellar, and autonomic features. α‐Synuclein (αsyn), encoded by the gene SNCA, is the main constituent of glial cytoplasmic inclusion (GCI) found in oligodendrocytes in MSA, but the methods of its accumulation have not been established. The aim of this study is to investigate alterations in regional and cellular SNCA mRNA expression in MSA as a possible substrate for GCI formation. Quantitative reverse transcription polymerase chain reaction (qPCR) was performed on postmortem brain samples from 15 MSA, 5 IPD, and 5 control cases to investigate regional expression in the frontal and occipital regions, dorsal putamen, pontine base, and cerebellum. For cellular expression analysis, neurons and oligodendrocytes were isolated by laser‐capture microdissection from five MSA and five control cases. SNCA mRNA expression was not significantly different between the MSA, IPD and control cases in all regions (multilevel model, P = 0.14). After adjusting for group effect, the highest expression was found in the occipital cortex while the lowest was in the putamen (multilevel model, P < 0.0001). At the cellular level, MSA oligodendrocytes expressed more SNCA than control oligodendrocytes and expression in MSA neurons was slightly lower than that in controls, however, these results did not reach statistical significance. We have demonstrated regional variations in SNCA expression, which is higher in cortical than subcortical regions. This study is the first to demonstrate SNCA mRNA expression by oligodendrocytes in human postmortem tissue using qPCR and, although not statistically significant, could suggest that this may be increased in MSA compared to controls. GLIA 2014;62:964–97

A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems

This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker-Planck equation for the stochastic fluctuations. The McKendrick--von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation and the McKendrick--von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.Comment: 27 pages, 4 figures. Final version as published. Only minor change

A general framework for combining ecosystem models

When making predictions about ecosystems, we often have available a number of different ecosystem models that attempt to represent their dynamics in a detailed mechanistic way. Each of these can be used as a simulator of large-scale experiments and make projections about the fate of ecosystems under different scenarios to support the development of appropriate management strategies. However, structural differences, systematic discrepancies and uncertainties lead to different models giving different predictions. This is further complicated by the fact that the models may not be run with the same functional groups, spatial structure or time scale. Rather than simply trying to select a “best” model, or taking some weighted average, it is important to exploit the strengths of each of the models, while learning from the differences between them. To achieve this, we construct a flexible statistical model of the relationships between a collection of mechanistic models and their biases, allowing for structural and parameter uncertainty and for different ways of representing reality. Using this statistical meta-model, we can combine prior beliefs, model estimates and direct observations using Bayesian methods and make coherent predictions of future outcomes under different scenarios with robust measures of uncertainty. In this study, we take a diverse ensemble of existing North Sea ecosystem models and demonstrate the utility of our framework by applying it to answer the question what would have happened to demersal fish if fishing was to stop

A novel length back-calculation approach accounting for ontogenetic changes in the fish length – otolith size relationship during the early life of sprat (Sprattus sprattus)

(Sprattus sprattus), accounting for ontogenetic changes in the relationship between fish length and otolith length. In sprat, metamorphosis from larvae to juveniles is characterized by the coincidence of low length growth, strong growth in body height, and maximal otolith growth. Consequently, the method identifies a point of metamorphosis for an individual as the otolith radius at maximum increment widths. By incorporating this information in our back-calculation method, estimated length growth for the early larval stage was more than 60% higher compared with the result of the biological intercept model. After minimal length growth during metamorphosis, we found the highest increase in length during the early juvenile stage. We thus located the strongest growth potential in the early juvenile stage, which is supposed to be critical in determining recruitment strength in Baltic sprat

Recurrent mutations in the U2AF1 splicing factor in myelodysplastic syndromes

Myelodysplastic syndromes (MDS) are hematopoietic stem cell disorders that often progress to chemotherapy-resistant secondary acute myeloid leukemia (sAML). We used whole-genome sequencing to perform an unbiased comprehensive screen to discover the somatic mutations in a sample from an individual with sAML and genotyped the loci containing these mutations in the matched MDS sample. Here we show that a missense mutation affecting the serine at codon 34 (Ser34) in U2AF1 was recurrently present in 13 out of 150 (8.7%) subjects with de novo MDS, and we found suggestive evidence of an increased risk of progression to sAML associated with this mutation. U2AF1 is a U2 auxiliary factor protein that recognizes the AG splice acceptor dinucleotide at the 3' end of introns, and the alterations in U2AF1 are located in highly conserved zinc fingers of this protein. Mutant U2AF1 promotes enhanced splicing and exon skipping in reporter assays in vitro. This previously unidentified, recurrent mutation in U2AF1 implicates altered pre-mRNA splicing as a potential mechanism for MDS pathogenesis

Adsorption of mono- and multivalent cat- and anions on DNA molecules

Adsorption of monovalent and multivalent cat- and anions on a deoxyribose nucleic acid (DNA) molecule from a salt solution is investigated by computer simulation. The ions are modelled as charged hard spheres, the DNA molecule as a point charge pattern following the double-helical phosphate strands. The geometrical shape of the DNA molecules is modelled on different levels ranging from a simple cylindrical shape to structured models which include the major and minor grooves between the phosphate strands. The densities of the ions adsorbed on the phosphate strands, in the major and in the minor grooves are calculated. First, we find that the adsorption pattern on the DNA surface depends strongly on its geometrical shape: counterions adsorb preferentially along the phosphate strands for a cylindrical model shape, but in the minor groove for a geometrically structured model. Second, we find that an addition of monovalent salt ions results in an increase of the charge density in the minor groove while the total charge density of ions adsorbed in the major groove stays unchanged. The adsorbed ion densities are highly structured along the minor groove while they are almost smeared along the major groove. Furthermore, for a fixed amount of added salt, the major groove cationic charge is independent on the counterion valency. For increasing salt concentration the major groove is neutralized while the total charge adsorbed in the minor groove is constant. DNA overcharging is detected for multivalent salt. Simulations for a larger ion radii, which mimic the effect of the ion hydration, indicate an increased adsorbtion of cations in the major groove.Comment: 34 pages with 14 figure