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We study the prime number race for elliptic curves over the function field of a proper, smooth and geometrically connected curve over a finite field. This constitutes a function field analogue of prior work by Mazur, Sarnak and the second author. In this geometric setting we can prove unconditional results whose counterparts in the number field case are conditional on a Riemann Hypothesis and a linear independence hypothesis on the zeros of the implied L-functions. Notably we show that in certain natural families of elliptic curves, the bias generically dissipates as the conductor grows. This is achieved by proving a central limit theorem and combining it with generic linear independence results that will appear in a separate paper. Also we study in detail a particular family of elliptic curves that have been considered by Ulmer. In contrast to the generic case we show that the race exhibits very diverse outcomes, some of which are believed to be impossible in the number field setting. Such behaviors are possible in the function field case because the zeros of Hasse-Weil L-functions for those elliptic curves can be proven to be highly dependent among themselves, which is a very non generic situation.

AbstractIn this paper, we study the expressive power and the complexity of first-order logic with arithmetic, as a query language over relational and constraint databases. We consider constraints over various domains (N, Z, Q, and R), and with various arithmetical operations (⩽, +, ×, etc.).We first consider the data complexity of first-order queries. We prove in particular that linear queries can be evaluated in AC0 over finite integer databases, and in NC1 over linear constraint databases. This improves previously known bounds. We also show that over all domains, enough arithmetic lead to arithmetical queries, therefore, showing the frontiers of constraints for database purposes.We then tackle the problem of the expressive power, with the definability of the parity and the connectivity, which are the most classical examples of queries not expressible in first-order logic over finite structures. We prove that these two queries are first-order definable in the presence of (enough) arithmetic. Nevertheless, we show that they are not definable with constraints of interest for constraint databases such as linear constraints for instance. Finally, we developed reduction techniques for queries over constraint databases, that allow us to draw conclusions with respect to their undefinability in various constraint query languages.

This study presents a multiparameter analysis of aerosol trends over the last 2 decades at regional and global scales. Regional time series have been computed for a set of nine optical, chemical-composition and mass aerosol properties by using the observations from several ground-based networks. From these regional time series the aerosol trends have been derived for the different regions of the world. Most of the properties related to aerosol loading exhibit negative trends, both at the surface and in the total atmospheric column. Significant decreases in aerosol optical depth (AOD) are found in Europe, North America, South America, North Africa and Asia, ranging from −1.2 % yr−1 to −3.1 % yr−1. An error and representativity analysis of the spatially and temporally limited observational data has been performed using model data subsets in order to investigate how much the observed trends represent the actual trends happening in the regions over the full study period from 2000 to 2014. This analysis reveals that significant uncertainty is associated with some of the regional trends due to time and space sampling deficiencies. The set of observed regional trends has then been used for the evaluation of 10 models (6 AeroCom phase III models and 4 CMIP6 models) and the CAMS reanalysis dataset and of their skills in reproducing the aerosol trends. Model performance is found to vary depending on the parameters and the regions of the world. The models tend to capture trends in AOD, the column Ångström exponent, sulfate and particulate matter well (except in North Africa), but they show larger discrepancies for coarse-mode AOD. The rather good agreement of the trends, across different aerosol parameters between models and observations, when co-locating them in time and space, implies that global model trends, including those in poorly monitored regions, are likely correct. The models can help to provide a global picture of the aerosol trends by filling the gaps in regions not covered by observations. The calculation of aerosol trends at a global scale reveals a different picture from that depicted by solely relying on ground-based observations. Using a model with complete diagnostics (NorESM2), we find a global increase in AOD of about 0.2 % yr−1 between 2000 and 2014, primarily caused by an increase in the loads of organic aerosols, sulfate and black carbon.

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the "half-way" point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis. Comment: 18 pages, 2 figures. (v2): discussion of decoding complexity clarified

We study specific star formation rate (sSFR) and gas profiles of star forming and green valley galaxies in the Simba cosmological hydrodynamic simulation. Star-forming galaxy half-light radii ($R_{\rm half}$) at $z=0$ and their evolution ($\propto(1+z)^{-0.78}$) agree with observations. Passive galaxy $R_{\rm half}$ agree with observations at high redshift, but by $z=0$ are too large, owing to numerical heating. We compare Simba $z=0$ sSFR radial profiles for star forming and green valley galaxies to observations. Simba shows strong central depressions in star formation rate (SFR), sSFR, and gas fraction in green valley galaxies and massive star-forming systems, qualitatively as observed, owing to black hole X-ray feedback, which pushes central gas outwards. Turning off X-ray feedback leads to centrally peaked sSFR profiles as in other simulations. In conflict with observations, Simba yields green valley galaxies with strongly dropping sSFR profiles beyond $\gtrsim R_{\rm half}$, regardless of AGN feedback. The central depression owes to lowering molecular gas content; the drop in the outskirts owes to reduced star formation efficiency. Simba's satellites have higher central sSFR and lower outskirts sSFR than centrals, in qualitative agreement with observations. At $z=2$ Simba does not show central depressions in massive star-forming galaxies, suggesting Simba's X-ray feedback should be more active at high-$z$. High resolution tests indicate central sSFR suppression is not sensitive to numerical resolution. Reproducing the central sSFR depression in $z=0$ green valley galaxies represents a unique success of Simba. The remaining discrepancies highlight the importance of SFR and gas profiles in constraining quenching mechanisms. 21 pages, 11 figures, accepted by MNRAS

The discovery of GW170817 with gravitational waves (GWs) and electromagnetic (EM) radiation is prompting new questions in strong-gravity astrophysics. Importantly, it remains unknown whether the progenitor of the merger comprised two neutron stars (NSs), or a NS and a black hole (BH). Using new numerical-relativity simulations and incorporating modeling uncertainties we produce novel GW and EM observables for NS-BH mergers with similar masses. A joint analysis of GW and EM measurements reveals that if GW170817 is a NS-BH merger, <40% of the binary parameters consistent with the GW data are compatible with EM observations. Comment: 8 pages

The use of past experiences to accelerate temporal difference (TD) learning of value functions, or experience replay, is a key component in deep reinforcement learning. Prioritization or reweighting of important experiences has shown to improve performance of TD learning algorithms.In this work, we propose to reweight experiences based on their likelihood under the stationary distribution of the current policy. Using the corresponding reweighted TD objective, we implicitly encourage small approximation errors on the value function over frequently encountered states. We use a likelihood-free density ratio estimator over the replay buffer to assign the prioritization weights. We apply the proposed approach empirically on two competitive methods, Soft Actor Critic (SAC) and Twin Delayed Deep Deterministic policy gradient (TD3) -- over a suite of OpenAI gym tasks and achieve superior sample complexity compared to other baseline approaches.

AbstractBackgroundSequencing technology and assembly algorithms have matured to the point that high-quality de novo assembly is possible for large, repetitive genomes. Current assemblies traverse transposable elements (TEs) and provide an opportunity for comprehensive annotation of TEs. Numerous methods exist for annotation of each class of TEs, but their relative performances have not been systematically compared. Moreover, a comprehensive pipeline is needed to produce a non-redundant library of TEs for species lacking this resource to generate whole-genome TE annotations.ResultsWe benchmark existing programs based on a carefully curated library of rice TEs. We evaluate the performance of methods annotating long terminal repeat (LTR) retrotransposons, terminal inverted repeat (TIR) transposons, short TIR transposons known as miniature inverted transposable elements (MITEs), and Helitrons. Performance metrics include sensitivity, specificity, accuracy, precision, FDR, andF1. Using the most robust programs, we create a comprehensive pipeline called Extensivede-novoTE Annotator (EDTA) that produces a filtered non-redundant TE library for annotation of structurally intact and fragmented elements. EDTA also deconvolutes nested TE insertions frequently found in highly repetitive genomic regions. Using other model species with curated TE libraries (maize and Drosophila), EDTA is shown to be robust across both plant and animal species.ConclusionsThe benchmarking results and pipeline developed here will greatly facilitate TE annotation in eukaryotic genomes. These annotations will promote a much more in-depth understanding of the diversity and evolution of TEs at both intra- and inter-species levels. EDTA is open-source and freely available:https://github.com/oushujun/EDTA.

Despite the need for a strong Science, Technology, Engineering, and Math (STEM) workforce, there is a high attrition rate for students who intend to complete undergraduate majors in these disciplines. Students who leave STEM degree programs often cite uninspiring instruction in introductory courses, including traditional lecturing, as a reason. While undergraduate courses play a critical role in STEM retention, little is understood about the instructional transitions students encounter upon moving from secondary to post-secondary STEM courses. This study compares classroom observation data collected using the Classroom Observation Protocol for Undergraduate STEM (COPUS) from over 450 middle school, high school, introductory-level university, and advanced-level university classes across STEM disciplines. We find similarities between middle school and high school classroom instruction, which are characterized by a large proportion of time spent on active-learning instructional strategies, such as small-group activities and peer discussion. In contrast, introductory and advanced university instructors devote more time to instructor-centered teaching strategies, such as lecturing. These instructor-centered teaching strategies are present in classes regardless of class enrollment size, class period length, or whether or not the class includes a separate laboratory section. Middle school, high school, and university instructors were also surveyed about their views of what STEM instructional practices are most common at each educational level and asked to provide an explanation of those perceptions. Instructors from all levels struggled to predict the level of lecturing practices and often expressed uncertainty about what instruction looks like at levels other than their own. These findings suggest that more opportunities need to be created for instructors across multiple levels of the education system to share their active learning teaching practices and discuss the transitions students are making between different educational levels.

Despite the central importance of noncoding DNA to gene regulation and evolution, understanding of the extent of selection on plant noncoding DNA remains limited compared to that of other organisms. Here we report sequencing of genomes from three Brassicaceae species (Leavenworthia alabamica, Sisymbrium irio and Aethionema arabicum) and their joint analysis with six previously sequenced crucifer genomes. Conservation across orthologous bases suggests that at least 17% of the Arabidopsis thaliana genome is under selection, with nearly one-quarter of the sequence under selection lying outside of coding regions. Much of this sequence can be localized to approximately 90,000 conserved noncoding sequences (CNSs) that show evidence of transcriptional and post-transcriptional regulation. Population genomics analyses of two crucifer species, A. thaliana and Capsella grandiflora, confirm that most of the identified CNSs are evolving under medium to strong purifying selection. Overall, these CNSs highlight both similarities and several key differences between the regulatory DNA of plants and other species.