Regularizing effect and local existence for non-cutoff Boltzmann equation

The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section. However, even though so far this has been justified satisfactorily for the spatially homogeneous Boltzmann equation, it is still basically unsolved for the spatially inhomogeneous Boltzmann equation. In this paper, by sharpening the coercivity and upper bound estimates for the collision operator, establishing the hypo-ellipticity of the Boltzmann operator based on a generalized version of the uncertainty principle, and analyzing the commutators between the collision operator and some weighted pseudo differential operators, we prove the regularizing effect in all (time, space and velocity) variables on solutions when some mild regularity is imposed on these solutions. For completeness, we also show that when the initial data has this mild regularity and Maxwellian type decay in velocity variable, there exists a unique local solution with the same regularity, so that this solution enjoys the $C^\infty$ regularity for positive time

Global existence and full regularity of the Boltzmann equation without angular cutoff

We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the solutions thus obtained are shown to be non-negative and $C^\infty$ in all variables for any positive time. In this paper, we study the Maxwellian molecule type collision operator with mild singularity. One of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator. This norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated H-theorem

Effect of Gravitational Lensing on Measurements of the Sunyaev-Zel'dovich Effect

The Sunyaev-Zel'dovich (SZ) effect of a cluster of galaxies is usually measured after background radio sources are removed from the cluster field. Gravitational lensing by the cluster potential leads to a systematic deficit in the residual intensity of unresolved sources behind the cluster core relative to a control field far from the cluster center. As a result, the measured decrement in the Rayleigh-Jeans temperature of the cosmic microwave background is overestimated. We calculate the associated systematic bias which is inevitably introduced into measurements of the Hubble constant using the SZ effect. For the cluster A2218, we find that observations at 15 GHz with a beam radius of 0'.4 and a source removal threshold of 100 microJy underestimate the Hubble constant by 6-10%. If the profile of the gas pressure declines more steeply with radius than that of the dark matter density, then the ratio of lensing to SZ decrements increases towards the outer part of the cluster.Comment: 11 pages, 3 figures, submitted to ApJ

Rapid and MR-Independent IK1 activation by aldosterone during ischemia-reperfusion

In ST elevation myocardial infarction (STEMI) context, clinical studies have shown the deleterious effect of high aldosterone levels on ventricular arrhythmia occurrence and cardiac mortality. Previous in vitro reports showed that during ischemia-reperfusion, aldosterone modulates K+ currents involved in the holding of the resting membrane potential (RMP). The aim of this study was to assess the electrophysiological impact of aldosterone on IK1 current during myocardial ischemia-reperfusion. We used an in vitro model of “border zone” using right rabbit ventricle and standard microelectrode technique followed by cell-attached recordings from freshly isolated rabbit ventricular cardiomyocytes. In microelectrode experiments, aldosterone (10 and 100 nmol/L, n=7 respectively) increased the action potential duration (APD) dispersion at 90% between ischemic and normoxic zones (from 95±4ms to 116±6 ms and 127±5 ms respectively, P<0.05) and reperfusion-induced sustained premature ventricular contractions occurrence (from 2/12 to 5/7 preparations, P<0.05). Conversely, potassium canrenoate 100 nmol/L and RU 28318 1 μmol/l alone did not affect AP parameters and premature ventricular contractions occurrence (except Vmax which was decreased by potassium canrenoate during simulated-ischemia). Furthermore, aldosterone induced a RMP hyperpolarization, evoking an implication of a K+ current involved in the holding of the RMP. Cell-attached recordings showed that aldosterone 10 nmol/L quickly activated (within 6.2±0.4 min) a 30 pS K+-selective current, inward rectifier, with pharmacological and biophysical properties consistent with the IK1 current (NPo =1.9±0.4 in control vs NPo=3.0±0.4, n=10, P<0.05). These deleterious effects persisted in presence of RU 28318, a specific MR antagonist, and were successfully prevented by potassium canrenoate, a non specific MR antagonist, in both microelectrode and patch-clamp recordings, thus indicating a MR-independent IK1 activation. In this ischemia-reperfusion context, aldosterone induced rapid and MR-independent deleterious effects including an arrhythmia substrate (increased APD90 dispersion) and triggered activities (increased premature ventricular contractions occurrence on reperfusion) possibly related to direct IK1 activation

A family of graded epistemic logics

Multi-Agent Epistemic Logic has been investigated in Computer Science [Fagin, R., J. Halpern, Y. Moses and M. Vardi, “Reasoning about Knowledge,” MIT Press, USA, 1995] to represent and reason about agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge and probabilities [Fagin, R. and J. Halpern, Reasoning about knowledge and probability, Journal of the ACM 41 (1994), pp. 340–367] and also with a fuzzy semantics have been proposed [Fitting, M., Many-valued modal logics, Fundam. Inform. 15 (1991), pp. 235–254; Maruyama, Y., Reasoning about fuzzy belief and common belief: With emphasis on incomparable beliefs, in: IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16–22, 2011, 2011, pp. 1008–1013]. This paper introduces a parametric method to build graded epistemic logics inspired in the systematic method to build Multi-valued Dynamic Logics introduced in [Madeira, A., R. Neves and M. A. Martins, An exercise on the generation of many-valued dynamic logics, J. Log. Algebr. Meth. Program. 85 (2016), pp. 1011–1037. URL http://dx.doi.org/10.1016/j.jlamp.2016.03.004; Madeira, A., R. Neves, M. A. Martins and L. S. Barbosa, A dynamic logic for every season, in: C. Braga and N. Martí-Oliet, editors, Formal Methods: Foundations and Applications – 17th Brazilian Symposium, SBMF 2014, Maceió, AL, Brazil, September 29-October 1, 2014. Proceedings, Lecture Notes in Computer Science 8941 (2014), pp. 130–145. URL http://dx.doi.org/10.1007/978-3-319-15075-8_9]. The parameter in both methods is the same: an action lattice [Kozen, D., On action algebras, Logic and Information Flow (1994), pp. 78–88]. This algebraic structure supports a generic space of agent knowledge operators, as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non bivalent interpretation of the assertions (as a residuated lattice).publishe

Radial Age and Metal Abundance Gradients in the Stellar Content of M32

We present long-slit spectroscopy of the elliptical galaxy M32, obtained with the 8-m Subaru telescope at Mauna Kea, the 1.5-m Tillinghast telescope at the F. L. Whipple Observatory, and the 4-m Mayall telescope at the Kitt Peak National Observatory. The spectra cover the Lick index red spectral region as well as higher order Balmer lines in the blue. Spectra have been taken with the slit off-set from the nucleus to avoid scattered light contamination from the bright nucleus of M32. An analysis of numerous absorption features, particularly involving the H$\gamma$ and H$\beta$ Balmer lines, reveals that systematic radial trends are evident in the integrated spectrum of M32. Population synthesis models indicate a radial change in both the age and chemical composition of the light-weighted mean stellar population in M32, from the nucleus out to 33", i.e., approximately 1.0 effective radius, R_e. Specifically, the light-weighted mean stellar population at 1 R_e is older, by \~3 Gyr, and more metal-poor, by ~-0.25 dex in [Fe/H], t han the central value of ~4 Gyr and [Fe/H]~0.0. We show that this apparent population trend cannot be attributed to a varying contribution from either hot stars or emission line contamination. The increase in age and decrease in metal-abundance with radius are sufficiently well-matched to explain the flat radial color profiles previously observed in M32. In addition, the ratio of Mg to Fe abundance, [Mg/Fe], increases from ~-0.25 in the nucleus to ~-0.08 at 1 R_e. Finally, we find spuriously pronounced line strength gradients in the Mayall data that are an artifact of scattered light from the bright nucleus. Scattered light issues may explain the lack of consistency among previously published studies of radial line strength gradients in M32.Comment: 25 pages, 14 figures, 3 tables, accepted for publication in the Astronomical Journa

Modeling the ecology and evolution of biodiversity: Biogeographical cradles, museums, and graves

Individual processes shaping geographical patterns of biodiversity are increasingly understood, but their complex interactions on broad spatial and temporal scales remain beyond the reach of analytical models and traditional experiments. To meet this challenge, we built a spatially explicit, mechanistic simulation model implementing adaptation, range shifts, fragmentation, speciation, dispersal, competition, and extinction, driven by modeled climates of the past 800,000 years in South America. Experimental topographic smoothing confirmed the impact of climate heterogeneity on diversification. The simulations identified regions and episodes of speciation (cradles), persistence (museums), and extinction (graves). Although the simulations had no target pattern and were not parameterized with empirical data, emerging richness maps closely resembled contemporary maps for major taxa, confirming powerful roles for evolution and diversification driven by topography and climate

Topological Line Defects around Graphene Nanopores for DNA Sequencing

Topological line defects in graphene represent an ideal way to produce highly controlled structures with reduced dimensionality that can be used in electronic devices. In this work we propose using extended line defects in graphene to improve nucleobase selectivity in nanopore-based DNA sequencing devices. We use a combination of QM/MM and non-equilibrium Green's functions methods to investigate the conductance modulation, fully accounting for solvent effects. By sampling over a large number of different orientations generated from molecular dynamics simulations, we theoretically demonstrate that distinguishing between the four nucleobases using line defects in a graphene-based electronic device appears possible. The changes in conductance are associated with transport across specific molecular states near the Fermi level and their coupling to the pore. Through the application of a specifically tuned gate voltage, such a device would be able to discriminate the four types of nucleobases more reliably than that of graphene sensors without topological line defects.Comment: 6 figures and 6 page

Period-doubling bifurcations and islets of stability in two-degree-of-freedom Hamiltonian systems

In this paper, we show that the destruction of the main KAM islands in two-degree-of-freedom Hamiltonian systems occurs through a cascade of period-doubling bifurcations. We calculate the corresponding Feigenbaum constant and the accumulation point of the period-doubling sequence. By means of a systematic grid search on exit basin diagrams, we find the existence of numerous very small KAM islands ('islets') for values below and above the aforementioned accumulation point. We study the bifurcations involving the formation of islets and we classify them in three different types. Finally, we show that the same types of islets appear in generic two-degree-of-freedom Hamiltonian systems and in area-preserving maps

First-in-Human Phase I Study to Evaluate the Brain-Penetrant PI3K/mTOR Inhibitor GDC-0084 in Patients with Progressive or Recurrent High-Grade Glioma.

PurposeGDC-0084 is an oral, brain-penetrant small-molecule inhibitor of PI3K and mTOR. A first-in-human, phase I study was conducted in patients with recurrent high-grade glioma.Patients and methodsGDC-0084 was administered orally, once daily, to evaluate safety, pharmacokinetics (PK), and activity. Fluorodeoxyglucose-PET (FDG-PET) was performed to measure metabolic responses.ResultsForty-seven heavily pretreated patients enrolled in eight cohorts (2-65 mg). Dose-limiting toxicities included 1 case of grade 2 bradycardia and grade 3 myocardial ischemia (15 mg), grade 3 stomatitis (45 mg), and 2 cases of grade 3 mucosal inflammation (65 mg); the MTD was 45 mg/day. GDC-0084 demonstrated linear and dose-proportional PK, with a half-life (∼19 hours) supportive of once-daily dosing. At 45 mg/day, steady-state concentrations exceeded preclinical target concentrations producing antitumor activity in xenograft models. FDG-PET in 7 of 27 patients (26%) showed metabolic partial response. At doses ≥45 mg/day, a trend toward decreased median standardized uptake value in normal brain was observed, suggesting central nervous system penetration of drug. In two resection specimens, GDC-0084 was detected at similar levels in tumor and brain tissue, with a brain tissue/tumor-to-plasma ratio of &gt;1 and &gt;0.5 for total and free drug, respectively. Best overall response was stable disease in 19 patients (40%) and progressive disease in 26 patients (55%); 2 patients (4%) were nonevaluable.ConclusionsGDC-0084 demonstrated classic PI3K/mTOR-inhibitor related toxicities. FDG-PET and concentration data from brain tumor tissue suggest that GDC-0084 crossed the blood-brain barrier