ℓ\ell-adic local systems and Higgs bundles: the generic case

Let $X$ be a projective smooth geometrically connected curve defined over a finite field $\mathbb{F}_q$ of cardinality $q$. Let $S$ be a finite set of closed points of $X$. Let $\bar{X}$ and $\bar{S}$ be the base change of $X$, $S$ to an algebraic closure. We consider the set of $\ell$-adic ($\ell\nmid q$) local systems of rank $n$ over $\bar{X}-\bar{S}$ with prescribed tame regular semisimple and generic ramifications in $\bar{S}$. The genericity ensures that such an $\ell$-adic local system is automatically irreducible. We show that the number of these $\ell$-adic local systems fixed by Frobenius endomorphism equals the number of stable logarithmic Higgs bundles of rank $n$ and degree $e$ coprime to $n$, with a fixed residue, up to a power of $q$. In the split case, this number is equal to the number of stable parabolic Higgs bundles (with full flag structures) fixed by $\mathbb{G}_m$-action with generic parabolic weights.Comment: 40 pages. This is a part of my article arXiv:2110.13858, which has been divided into two separate articles. The current one focuses on the GL(n) cas

Backscatter laser depolarization studies of simulated stratospheric aerosols: Crystallized sulfuric acid droplets

The optical depolarizing properties of simulated stratospheric aerosols were studied in laboratory laser (0.633 micrometer) backscattering experiments for application to polarization lidar observations. Clouds composed of sulfuric acid solution droplets, some treated with ammonia gas, were observed during evaporation. The results indicate that the formation of minute ammonium sulfate particles from the evaporation of acid droplets produces linear depolarization ratios of beta equivalent to 0.02, but beta equivalent to 0.10 to 0.15 are generated from aged acid cloud aerosols and acid droplet crystallization effects following the introduction of ammonia gas into the chamber. It is concluded that partially crystallized sulfuric acid droplets are a likely candidate for explaining the lidar beta equivalent to 0.10 values that have been observed in the lower stratosphere in the absence of the relatively strong backscattering from homogeneous sulfuric acid droplet (beta equivalent to 0) or ice crystal (beta equivalent to 0.5) clouds

A simplified excavation chamber pressure model for EPBM tunneling

This paper presents a simplified excavation chamber pressure model for earth pressure balance shield tunnel boring machine (EPBM) tunneling in granular soils, capable of predicting chamber pressure response during both excavation and standstill periods. Two physical processes, (1) compressible material flow, and (2) chamber fluid seepage, are modeled. The chamber pressure model is physics-based and is built upon chamber muck mass conservation. The model assumes muck behavior to be pressure-dependent and quasi-static. Given recorded EPBM operations, including advance rate, chamber additive injection rates and screw conveyor rotation speed, the model can predict the chamber pressure fluctuation with good accuracy, both during excavation and standstill periods. A case study using tunneling project data is included, where the model’s capability to simulate chamber pressure evolution during excavation of a single ring and multiple consecutive rings is demonstrated

LTR retrotransposons reveal recent extensive inter-subspecies nonreciprocal recombination in Asian cultivated rice

<p>Abstract</p> <p>Background</p> <p>Long Terminal Repeats retrotransposons (LTR elements) are ubiquitous Eukaryotic transposable elements (TEs). They are considered to be one of the major forces underlying plant genome evolution. Because of relatively high evolutionary speed, active transposition of LTR elements in the host genomes provides rich information on their short-term history. As more and more genomes, especially those of closely related organisms, have been sequenced, it is possible to perform global comparative study of their LTR retrotransposons to reveal events in the history.</p> <p>Results</p> <p>The present research is designed to investigate important evolutionary events in the origin of Asian cultivated rice through the comparison of LTR elements. We have developed LTR_INSERT, a new method for LTR elements discovery in two closely related genomes. Our method has a distinctive feature that it is capable of judging whether an insertion occurs prior or posterior to the divergence of genomes. LTR_INSERT identifies 993 full-length LTR elements, annotates 15916 copies related with them, and discovers at least 16 novel LTR families in the whole-genome comparative map of two cultivated rice subspecies. From the full-length LTR elements, we estimate that a significant proportion of the rice genome has experienced inter-subspecies nonreciprocal recombination (ISNR) in as recent as 53,000 years. Large-scale samplings further support that more than 15% of the rice genome has been involved in such recombination. In addition, LTR elements confirm that the genome of <it>O. sativa ssp. indica </it>and that of <it>japonica </it>diverged about 600,000 years ago.</p> <p>Conclusion</p> <p>A new LTR retrotransposon identification method integrating both comparative genomics and <it>ab initio </it>algorithm is introduced and applied to Asian cultivated rice genomes. At whole-genome level, this work confirms that recent ISNR is an important factor that molds modern cultivated rice genome.</p

Comptage des syst\`emes locaux ℓ\ell-adiques sur une courbe

Let $X_{1}$ be a projective, smooth and geometrically connected curve over $\mathbb{F}_{q}$ with $q=p^{n}$ elements where $p$ is a prime number, and let $X$ be its base change to an algebraic closure of $\mathbb{F}_{q}$. We give a formula for the number of irreducible $\ell$-adic local systems ($\ell\neq p$) with a fixed rank over $X$ fixed by the Frobenius endomorphism. We prove that this number behaves like a Lefschetz fixed point formula for a variety over $\mathbb{F}_q$, which generalises a result of Drinfeld in rank $2$ and proves a conjecture of Deligne. To do this, we pass to the automorphic side by Langlands correspondence, then use Arthur's non-invariant trace formula and link this number to the number of $\mathbb{F}_q$-points of the moduli space of stable Higgs bundles.Comment: In French; improved a littl

Crime Prediction with Historical Crime and Movement Data of Potential Offenders Using a Spatio-Temporal Cokriging Method

Crime prediction using machine learning and data fusion assimilation has become a hot topic. Most of the models rely on historical crime data and related environment variables. The activity of potential offenders affects the crime patterns, but the data with fine resolution have not been applied in the crime prediction. The goal of this study is to test the effect of the activity of potential offenders in the crime prediction by combining this data in the prediction models and assessing the prediction accuracies. This study uses the movement data of past offenders collected in routine police stop-and-question operations to infer the movement of future offenders. The offender movement data compensates historical crime data in a Spatio-Temporal Cokriging (ST-Cokriging) model for crime prediction. The models are implemented for weekly, biweekly, and quad-weekly prediction in the XT police district of ZG city, China. Results with the incorporation of the offender movement data are consistently better than those without it. The improvement is most pronounced for the weekly model, followed by the biweekly model, and the quad-weekly model. In sum, the addition of offender movement data enhances crime prediction, especially for short periods

Local Binary Fitting Segmentation by Cooperative Quantum Particle Optimization

Recently, sophisticated segmentation techniques, such as level set method, which using valid numerical calculation methods to process the evolution of the curve by solving linear or nonlinear elliptic equations to divide the image availably, has become being more popular and effective. In Local Binary Fitting (LBF) algorithm, a simple contour is initialized in an image and then the steepest-descent algorithm is employed to constrain it to minimize the fitting energy functional. Hence, the initial position of the contour is difficult or impossible to be well chosen for the final performance. To overcoming this drawback, this work treats the energy fitting problem as a meta-heuristic optimization algorithm and imports a varietal particle swarm optimization (PSO) method into the inner optimization process. The experimental results of segmentations on medical images show that the proposed method is not only effective to both simple and complex medical images with adequate stochastic effects, but also shows the accuracy and high efficiency