The fundamental fiber sequence in \'etale homotopy theory

Let $k$ be a field with separable closure $\bar{k}\supset k$, and let $X$ be a qcqs $k$-scheme. We use the theory of profinite Galois categories developed by Barwick-Glasman-Haine to provide a quick conceptual proof that the sequences \begin{equation*} \Pi_{<\infty}^{\mathrm{\acute{e}t}}(X_{\bar{k}}) \to \Pi_{<\infty}^{\mathrm{\acute{e}t}}(X) \to \mathrm{BGal}(\bar{k}/k) \qquad \text{and} \qquad \widehat{\Pi}{}_{\infty}^{\mathrm{\acute{e}t}}(X_{\bar{k}}) \to \widehat{\Pi}{}_{\infty}^{\mathrm{\acute{e}t}}(X) \to \mathrm{BGal}(\bar{k}/k) \end{equation*} of protruncated and profinite \'etale homotopy types are fiber sequences. This gives a common conceptual reason for the following two phenomena: first, the higher \'etale homotopy groups of $X$ and the geometric fiber $X_{\bar{k}}$ are isomorphic, and second, if $X_{\bar{k}}$ is connected, then the sequence of profinite \'etale fundamental groups $1\to\hat{\pi}{}_{1}^{\mathrm{\acute{e}t}}(X_{\bar{k}})\to\hat{\pi}{}_{1}^{\mathrm{\acute{e}t}}(X)\to\mathrm{Gal}(\bar{k}/k)\to 1$ is exact. It also proves the analogous results for the groupe fondamental \'elargi of SGA3.Comment: Comments very welcome! v2: 15 pages. Minor changes and added a reference. v1: 14 page

Score Matching via Differentiable Physics

Diffusion models based on stochastic differential equations (SDEs) gradually perturb a data distribution $p(\mathbf{x})$ over time by adding noise to it. A neural network is trained to approximate the score $\nabla_\mathbf{x} \log p_t(\mathbf{x})$ at time $t$, which can be used to reverse the corruption process. In this paper, we focus on learning the score field that is associated with the time evolution according to a physics operator in the presence of natural non-deterministic physical processes like diffusion. A decisive difference to previous methods is that the SDE underlying our approach transforms the state of a physical system to another state at a later time. For that purpose, we replace the drift of the underlying SDE formulation with a differentiable simulator or a neural network approximation of the physics. We propose different training strategies based on the so-called probability flow ODE to fit a training set of simulation trajectories and discuss their relation to the score matching objective. For inference, we sample plausible trajectories that evolve towards a given end state using the reverse-time SDE and demonstrate the competitiveness of our approach for different challenging inverse problems

A Measurement of Newton's Gravitational Constant

A precision measurement of the gravitational constant $G$ has been made using a beam balance. Special attention has been given to determining the calibration, the effect of a possible nonlinearity of the balance and the zero-point variation of the balance. The equipment, the measurements and the analysis are described in detail. The value obtained for G is 6.674252(109)(54) 10^{-11} m3 kg-1 s-2. The relative statistical and systematic uncertainties of this result are 16.3 10^{-6} and 8.1 10^{-6}, respectively.Comment: 26 pages, 20 figures, Accepted for publication by Phys. Rev.

Obtaining the equation of motion for a fermionic particle in a generalized Lorentz-violating system framework

Using a generalized procedure for obtaining the dispersion relation and the equation of motion for a propagating fermionic particle, we examine previous claims for a preferred axis at $n_{\mu}$($\equiv(1,0,0,1)$), $n^{2}=0$ embedded in the framework of very special relativity (VSR). We show that, in a relatively high energy scale, the corresponding equation of motion is reduced to a conserving lepton number chiral equation previously predicted in the literature. Otherwise, in a relatively low energy scale, the equation is reduced to the usual Dirac equation for a free propagating fermionic particle. It is accomplished by the suggestive analysis of some special cases where a nonlinear modification of the action of the Lorentz group is generated by the addition of a modified conformal transformation which, meanwhile, preserves the structure of the ordinary Lorentz algebra in a very peculiar way. Some feasible experiments, for which Lorentz violating effects here pointed out may be detectable, are suggested.Comment: 10 page

Co-infection of the four major Plasmodium species: effects on densities and gametocyte carriage

BACKGROUND: Co-infection of the four major species of human malaria parasite Plasmodium falciparum (Pf), P. vivax (Pv), P. malariae (Pm), and P. ovale sp. (Po) is regularly observed, but there is limited understanding of between-species interactions. In particular, little is known about the effects of multiple Plasmodium species co-infections on gametocyte production. METHODS: We developed molecular assays for detecting asexual and gametocyte stages of Pf, Pv, Pm, and Po. This is the first description of molecular diagnostics for Pm and Po gametocytes. These assays were implemented in a unique epidemiological setting in Papua New Guinea with sympatric transmission of all four Plasmodium species permitting a comprehensive investigation of species interactions. FINDINGS: The observed frequency of Pf-Pv co-infection for asexual parasites (14.7%) was higher than expected from individual prevalence rates (23.8%Pf x 47.4%Pv = 11.3%). The observed frequency of co-infection with Pf and Pv gametocytes (4.6%) was higher than expected from individual prevalence rates (13.1%Pf x 28.2%Pv = 3.7%). The excess risk of co-infection was 1.38 (95% confidence interval (CI): 1.09, 1.67) for all parasites and 1.37 (95% CI: 0.95, 1.79) for gametocytes. This excess co-infection risk was partially attributable to malaria infections clustering in some villages. Pf-Pv-Pm triple infections were four times more frequent than expected by chance alone, which could not be fully explained by infections clustering in highly exposed individuals. The effect of co-infection on parasite density was analyzed by systematic comparison of all pairwise interactions. This revealed a significant 6.57-fold increase of Pm density when co-infected with Pf. Pm gametocytemia also increased with Pf co-infection. CONCLUSIONS: Heterogeneity in exposure to mosquitoes is a key epidemiological driver of Plasmodium co-infection. Among the four co-circulating parasites, Pm benefitted most from co-infection with other species. Beyond this, no general prevailing pattern of suppression or facilitation was identified in pairwise analysis of gametocytemia and parasitemia of the four species. TRIAL REGISTRATION: This trial is registered with ClinicalTrials.gov, Trial ID: NCT02143934

Plant-pollinator networks in semi-natural grasslands are resistant to the loss of pollinators during blooming of mass-flowering crops

Mass-flowering crops lead to spatial redistributions of pollinators and to transient shortages within nearby semi-natural grasslands, but the impacts on plant–pollinator interactions remain largely unexplored. Here, we characterised which pollinator species are attracted by oilseed rape and how this affected the structure of plant–pollinator networks in nearby grasslands. We surveyed 177 networks from three countries (Germany, Sweden and United Kingdom) in 24 landscapes with high crop cover, and compared them to 24 landscapes with low or no oilseed rape during and after crop blooming. On average 55% of grassland pollinator species were found on the crop, which attracted 8–35% of individuals away from grasslands. However, networks in the grasslands were resistant to these reductions, since mainly abundant and highly mobile species were attracted. Nonetheless, simulations indicated that network structural changes could be triggered if > 50% of individuals were attracted to the crop (a value well-above that found in our study system), which could affect community stability and resilience to further disturbance

A scheme with two large extra dimensions confronted with neutrino physics

We investigate a particle physics model in a six-dimensional spacetime, where two extra dimensions form a torus. Particles with Standard Model charges are confined by interactions with a scalar field to four four-dimensional branes, two vortices accommodating ordinary type fermions and two antivortices accommodating mirror fermions. We investigate the phenomenological implications of this multibrane structure by confronting the model with neutrino physics data.Comment: LATEX, 24 pages, 9 figures, minor changes in the tex

Observation of two time scales in the ferromagnetic manganite La(1-x)Ca(x)MnO(3), x = 0.3

We report new zero-field muon spin relaxation and neutron spin echo measurements in ferromagnetic (FM) (La,Ca)MnO3 which taken together suggest two spatially separated regions in close proximity possessing very different Mn-ion spin dynamics. One region corresponds to an extended cluster which displays 'critical slowing down' near Tc and an increasing volume fraction below Tc. The second region possesses more slowly fluctuating spins and a decreasing volume fraction below Tc. These data are discussed in terms of the growth of small polarons into overlapping regions of correlated spins below Tc, resulting in a microscopically inhomogeneous FM transition.Comment: 10 pages, 3 figure

An efficient two-polymer binder for high-performance silicon nanoparticle-based lithium-ion batteries: A systematic case study with commercial polyacrylic acid and polyvinyl butyral polymers

Silicon is one of the most promising anode materials for high energy density lithium ion batteries (LIBs) due to its high theoretical capacity and natural abundance. Unfortunately, significant challenges arise due to the large volume change of silicon upon lithiation/delithiation which inhibit its broad commercialization. An advanced binder can, in principle, reversibly buffer the volume change, and maintain strong adhesion toward various components as well as the current collector. In this work, we present the first report on the applicability of polyvinyl butyral (PVB) polymer as a binder component for silicon nanoparticles-based LIBs. Characteristic binder properties of commercial PVB and polyacrylic acid (PAA) polymers are compared. The work focuses on polymer mixtures of PVB polymers with PAA, for an improved binder composition which incorporates their individual advantages. Different ratios of polymers are systematically studied to understand the effect of particular polymer chains, functional groups and mass fractions, on the electrochemical performance. We demonstrate a high-performance polymer mixture which exhibits good binder-particle interaction and strong adhesion to Cu-foil. PAA/PVB-based electrode with a Si loading of ∼1 mg/cm2 tested between 0.01 and 1.2 V vs. Li/Li+ demonstrate specific capacities as high as 2170 mAh/g after the first hundred cycles. © The Author(s) 2019

Muon Spin Relaxation Study of (La, Ca)MnO3

We report predominantly zero field muon spin relaxation measurements in a series of Ca-doped LaMnO_3 compounds which includes the colossal magnetoresistive manganites. Our principal result is a systematic study of the spin-lattice relaxation rates 1/T_1 and magnetic order parameters in the series La_{1-x}Ca_xMnO_3, x = 0.0, 0.06, 0.18, 0.33, 0.67 and 1.0. In LaMnO_3 and CaMnO_3 we find very narrow critical regions near the Neel temperatures T_N and temperature independent 1/T_1 values above T_N. From the 1/T_1 in LaMnO_3 we derive an exchange integral J = 0.83 meV which is consistent with the mean field expression for T_N. All of the doped manganites except CaMnO_3 display anomalously slow, spatially inhomogeneous spin-lattice relaxation below their ordering temperatures. In the ferromagnetic (FM) insulating La_{0.82}Ca_{0.18}MnO_3 and ferromagnetic conducting La_{0.67}Ca_{0.33}MnO_3 systems we show that there exists a bi-modal distribution of \muSR rates \lambda_f and \lambda_s associated with relatively 'fast' and 'slow' Mn fluctuation rates, respectively. A physical picture is hypothesized for these FM phases in which the fast Mn rates are due to overdamped spin waves characteristic of a disordered FM, and the slower Mn relaxation rates derive from distinct, relatively insulating regions in the sample. Finally, likely muon sites are identified, and evidence for muon diffusion in these materials is discussed.Comment: 21 pages, 17 figure