Miracle-dz/UniFAR-FTUs huggingface dataset:
The motivic anabelian geometry of local heights on abelian varieties

We study the problem of describing local components of height functions on abelian varieties over characteristic $0$ local fields as functions on spaces of torsors under various realisations of a $2$-step unipotent motivic fundamental group naturally associated to the defining line bundle. To this end, we present three main theorems giving such a description in terms of the $\mathbb Q_\ell$- and $\mathbb Q_p$-pro-unipotent etale realisations when the base field is $p$-adic, and in terms of the $\mathbb R$-pro-unipotent Betti--de Rham realisation when the base field is archimedean. In the course of proving the $p$-adic instance of these theorems, we develop a new technique for studying local non-abelian Bloch--Kato Selmer sets, working with certain explicit cosimplicial group models for these sets and using methods from homotopical algebra. Among other uses, these models enable us to construct a non-abelian generalisation of the Bloch--Kato exponential sequence under minimal conditions. On the geometric side, we also prove a number of foundational results on local constancy or analyticity of various non-abelian Kummer maps for pro-unipotent etale or Betti--de Rham fundamental groups of arbitrary smooth varieties.
Task Allocation Under Geo-Indistinguishability via Group-Based Noise Addition

Locations are usually necessary for task allocation in spatial crowdsourcing, which may put individual privacy in jeopardy without proper protection. Although existing studies have well explored the problem of location privacy protection in task allocation under geo-indistinguishability, they potentially assume the workers could perform any tasks, which might not be practical in reality. Moreover, they usually adopt planar laplacian mechanism to achieve geo-indistinguishability, which will introduce excessive noise due to its randomness and boundlessness. To this end, we propose a task alloCAtioN approach via grOup-based noisE addition under Geo-I, referred to as CANOE. Its main idea is that each worker uploads the noisy distances between his true location and the obfuscated locations of his preferred tasks instead of uploading his obfuscated location. In particular, to alleviate the total noise when conducting grouping, we put forward an optimized global grouping with adaptive local adjustment method OGAL with convergence guarantee. To collect the noisy distances which are required for subsequent task allocation, we develop a utility-aware obfuscated distance collection method UODC with solid privacy and utility guarantees. We further theoretically analyze the privacy, utility and complexity guarantees of CANOE. Extensive analyses and experiments over two real-world datasets confirm the effectiveness of CANOE.
Heavy-Traffic Analysis Through Uniform Acceleration of Queues with Diminishing Populations

We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic behavior by using uniform acceleration, which simultaneously lets $n$ and the service rate grow large, while the initial resource utilization approaches one. A key feature of the model is that, as time progresses, more customers have joined the queue, and fewer customers can potentially join. This diminishing population gives rise to a class of reflected stochastic processes that vanish over time, and hence do not have a stationary distribution. We establish that, when the arrival times are exponentially distributed, by suitably rescaling space and time, the queue length process converges to a Brownian motion with parabolic drift, a stochastic-process limit that captures the effect of a diminishing population by a negative quadratic drift. When the arrival times are generally distributed, our techniques provide information on the typical queue length and the first busy period.
Edge statistics of Dyson Brownian motion

We consider the edge statistics of Dyson Brownian motion with deterministic initial data. Our main result states that if the initial data has a spectral edge with rough square root behavior down to a scale $\eta_* \geq N^{-2/3}$ and no outliers, then after times $t \gg \sqrt{ \eta_*}$, the statistics at the spectral edge agree with the GOE/GUE. In particular we obtain the optimal time to equilibrium at the edge $t = N^{\varepsilon} / N^{1/3}$ for sufficiently regular initial data. Our methods rely on eigenvalue rigidity results similar to those appearing in [Lee-Schnelli], the coupling idea of [Bourgade-Erd\H{o}s-Yau-Yin] and the energy estimate of [Bourgade-Erd\H{o}s-Yau].
Knots with small lattice stick numbers

The lattice stick number of a knot type is defined to be the minimal number of straight line segments required to construct a polygon presentation of the knot type in the cubic lattice. In this paper, we mathematically prove that the trefoil knot 31 and in figure 8 knot 41 are the only knot types of lattice stick number less than 15, which verifies the result from previous numerical estimations on this quantity.
The Hyperview Challenge: Estimating Soil Parameters from Hyperspectral Images

Improving agricultural practices through exploiting the recent imaging and machine learning advancements plays a key role nowadays to ensure sustainable food security, and to help us deal with the climate change. Quantifying soil parameters can lead to optimizing the fertilization process but it is cumbersome, time-consuming and difficult to scale, as it requires performing in-situ soil measurements that are later analyzed in the laboratory settings. In the HYPER-VIEW challenge, we aim at automating the soil analysis thanks to the utilization of hyperspectral images that capture very detailed information about the scanned objects in hundreds of contiguous hyperspectral bands. Such imagery can be effectively analyzed using an array of classical and deep machine learning approaches. Also, the AI techniques can be deployed on-board the imaging satellites— it opens new doors related to the scalability of the solution. The winners of the challenge will be offered a unique opportunity to run their proposed solution in orbit, on-board the Intuition-1 satellite, equipped with a hyperspectral imager and on-board AI capabilities.
Increased Material Density within a New Biomechanism

A new mechanism, applied in this study as a biomechanical device, known as a Bioactive Kinetic Screw (BKS) for bone implants is described. The BKS was designed as a bone implant, in which the bone particles, blood, cells, and protein molecules removed during bone drilling are used as a homogeneous autogenous transplant at the same implant site, aiming to optimize the healing process and simplify the surgical procedure. In this work, the amount of bone that will be compacted inside and around the new biomechanism was studied, based on the density of the bone applied. This study allows us to analyze the average bone density in humans (1.85 mg/mm3 or 1850 µg/mm³) with four different synthetic bone densities (Sawbones PCF 10, 20, 30 and 40). The results show that across all four different synthetic bones densities, the bone within the new model is 3.45 times denser. After a pilot drill (with 10 mm length and 1.8 mm diameter), in cases where a guide hole is required, the increase in ratio is equal to 2.7 times inside and around the new biomechanism. The in vitro test validated the mathematical results, describing that in two different materials, the same compact factor of 3.45 was determined with the new biomechanical device. It was possible to describe that BKS can become a powerful tool in the diagnosis and treatment of natural bone conditions and any type of disease.
Asymptotic bounds on renewal process stopping times

Suppose that i.i. d. random variables $X_{1}, X_{2}, \ldots$ are chosen uniformly from $[0,1]$, and let $f: [0,1] \rightarrow [0,1]$ be an increasing bijection. Define $\mu_{f}$ to be the expected value of $f(X_{i})$ for each $i$. Define the random variable $K_{f}$ be to be minimal so that $\sum_{i = 1}^{K_{f}} f(X_{i}) > t$ and let $N_{f}(t)$ be the expected value of $K_{f}$. We prove that if $c_{f} = \frac{\int_{0}^{1} \int_{f^{-1}(u)}^{1} (f(x)-u) dx du}{\mu_{f}}$, then $N_{f}(t) = \frac{t+c_{f}}{\mu_{f}}+o(1)$. This generalizes a result of Curgus and Jewett (2007) on the case $f(x) = x$.
A Birman-series type result for geodesics with infinitely many self-intersections

Given a hyperbolic surface $\S$, a classic result of Birman and Series states that for each $K$, all complete geodesics with at most $K$ self-intersections can only pass through a certain nowhere dense, Hausdorff dimension 1 subset of $\S$. We define a self-intersection function for each complete geodesic, which bounds the number of self-intersections in finite length subarcs. We then extend the Birman-Series result to sets of complete geodesics with certain bounds on their self-intersection functions. In fact, we get the same conclusion as the Birman-Series result for sets of complete geodesics whose self-intersection functions are in $o(l^2)$, where $l$ measures arclength.
Fleet Management and Charging Scheduling for Shared Mobility-on-Demand System: A Systematic Review

Challenged by urbanization and increasing travel needs, existing transportation systems call for new mobility paradigms. In this article, we present the fleet management and charging scheduling of a shared mobility-on-demand system, whereby electric vehicle fleets are operated by a centralized platform to provide customers with mobility service. We provide a comprehensive review of system operation based on the operational objectives. The fleet scheduling strategies are categorized into four types: i) order dispatching, ii) order-dispatching and rebalancing, iii) order-dispatching, rebalancing and charging, and iv) extended. Specifically, we first identify mathematical modeling techniques implemented in the transportation network, then analyze and summarize the solution approaches including mathematical programming, reinforcement learning, and hybrid methods. The advantages and disadvantages of different models and solution approaches are compared. Finally, we present research outlook in various directions.
Approximation properties for locally compact quantum groups

This is a survey of some aspects of the subject of approximation properties for locally compact quantum groups, based on lectures given at the {\it Topological Quantum Groups} Graduate School, 28 June - 11 July, 2015 in Bed\l{}ewo, Poland. We begin with a study of the dual notions of amenability and co-amenability, and then consider weakenings of these properties in the form of the Haagerup property and weak amenability. For discrete quantum groups, the interaction between these properties and various operator algebra approximation properties are investigated. We also study the connection between central approximation properties for discrete quantum groups and monoidal equivalence for their compact duals. We finish by discussing the central weak amenability and central Haagerup property for free quantum groups.
Refined global Gross–Prasad conjecture on special Bessel periods and Böcherer’s conjecture

In this paper we pursue the refined global Gross-Prasad conjecture for Bessel periods formulated by Yifeng Liu in the case of special Bessel periods for $\mathrm{SO}\left(2n+1\right)\times\mathrm{SO}\left(2\right)$. Recall that a Bessel period for $\mathrm{SO}\left(2n+1\right)\times\mathrm{SO}\left(2\right)$ is called special when the representation of $\mathrm{SO}\left(2\right)$ is trivial. Let $\pi$ be an irreducible cuspidal tempered automorphic representation of a special orthogonal group of an odd dimensional quadratic space over a totally real number field $F$ whose local component $\pi_v$ at any archimedean place $v$ of $F$ is a discrete series representation. Let $E$ be a quadratic extension of $F$ and suppose that the special Bessel period corresponding to $E$ does not vanish identically on $\pi$. Then we prove the Ichino-Ikeda type explicit formula conjectured by Liu for the central value $L\left(1/2,\pi\right)L\left(1/2,\pi\times\chi_E\right)$, where $\chi_E$ denotes the quadratic character corresponding to $E$. Our result yields a proof of Boecherer's conecture on holomorphic Siegel cusp forms of degree two which are Hecke eigenforms.
On the proper moduli spaces of smoothable Kähler–Einstein Fano varieties

In this paper, we investigate the geometry of the orbit space of the closure of the subscheme parametrizing smooth Fano K\"ahler-Einstein manifolds inside an appropriate Hilbert scheme. In particular, we prove that being K-semistable is a Zariski open condition and establish the uniqueness for the Gromov-Hausdorff limit for a punctured flat family of Fano K\"ahler-Einstein manifolds. Based on these, we construct a proper scheme parameterizing the S-equivalent classes of $\QQ$-Gorenstein smoothable, K-semistable Fano varieties, and verify various necessary properties to guarantee that it is a good moduli space.
Non-natural metrics on the tangent bundle

Natural metrics provide a way to induce a metric on the tangent bundle from the metric on its base manifold. The most studied type is the Sasaki metric, which applies the base metric separately to the vertical and horizontal components. We study a more general class of metrics which introduces interactions between the vertical and horizontal components, with scalar weights. Additionally, we explicitly clarify how to apply our and other induced metrics on the tangent bundle to vector fields where the vertical component is not constant along the fibers. We give application to the Special Orthogonal Group SO(3) as an example.
Effective and Infinite-Rank Superrigidity in the Context of Representation Stability

We discuss certain effective improvements on superrigidity for $SL_n(\mathbb{Z})$ for finite $n>2$. Using these ideas we then use superrigidity to prove a representation stability theorem about pointwise finite dimensional $VIC(\mathbb{Z})$-modules, which itself can be viewed as a superrigidity theorem for $VIC(\mathbb{Z})$ and $GL_\infty(\mathbb{Z})$
An optimal Berry–Esseen type theorem
for integrals of smooth functions

We prove a Berry-Esseen type inequality for approximating expectations of sufficiently smooth functions $f$, like $f=|\cdot|^3$, with respect to standardized convolutions of laws $P_1,\ldots, P_n$ on the real line by corresponding expectations based on symmetric two-point laws $Q_1,\ldots,Q_n$ isoscedastic to the $P_i$. Equality is attained for every possible constellation of the Lipschitz constant $\|f"\|^{}_{\mathrm{L}}$ and the variances and the third centred absolute moments of the $P_i$. The error bound is strictly smaller than $\frac 16$ times the Lyapunov ratio times $\|f"\|^{}_{\mathrm{L}}$, and tends to zero also if $n$ is fixed and the third standardized absolute moments of the $P_i$ tend to one. In the homoscedastic case of equal variances of the $P_i$, and hence in particular in the i.i. d. case, the approximating law is a standardized symmetric binomial one. The inequality is strong enough to yield for some constellations, in particular in the i.i. d. case with $n$ large enough given the standardized third absolute moment of $P_1$, an improvement of a more classical and already optimal Berry-Esseen type inequality of Tyurin (2009). Auxiliary results presented include some inequalities either purely analytical or concerning Zolotarev's $\zeta$-metrics, and some binomial moment calculations.
A study of the urban heat island effect in Guangzhou

As the world economy continues to grow and energy consumption increases, the global climate is gradually warming. Among them, the economic activities in metropolitan areas are more intense compared to other areas, forming an urban heat island effect where the temperature in the urban area is higher than that in the surrounding areas. This article selects Guangzhou, a rapidly developing city in southern China over the past two decades, as a case study. Surface temperature data for five time periods, namely 2000, 2005, 2010, 2015 and 2020, are collected to analyse how Guangzhou is affected by the urban heat island effect and its relationship with land use status and population density. The results of the article found that the urban heat island effect in Guangzhou is very obvious, mainly in the central and southern parts of the city, where the spatial distribution and evolution of land use type and population density are significantly related to the intensity of the heat island effect. In the future, Guangzhou can alleviate the impact of climate change and urban heat island effect by rationally planning urban layout, optimizing urban ecological environment, improving the material of urban underlying surface and actively developing renewable energy.
On global-in-time weak solutions to the magnetohydrodynamic system of compressible inviscid fluids

We consider the motion of an inviscid compressible fluid under the mutual interactions with magnetic field. We show that the initial value problem is ill-posed in the class of weak solutions for a large class of physically admissible data. We also consider the same problem for inviscid heat-conductive fluid and show the same result under certain restrictions imposed on the magnetic field. The main tool is the method of convex integration adapted from the Euler system with ‘variable coefficients’.
On the Law of Large Numbers for Nonmeasurable Identically Distributed Random Variables

Let $\Omega$ be a countable infinite product $\Omega^\N$ of copies of the same probability space $\Omega_1$, and let ${\Xi_n}$ be the sequence of the coordinate projection functions from $\Omega$ to $\Omega_1$. Let $\Psi$ be a possibly nonmeasurable function from $\Omega_1$ to $\R$, and let $X_n(\omega) = \Psi(\Xi_n(\omega))$. Then we can think of ${X_n}$ as a sequence of independent but possibly nonmeasurable random variables on $\Omega$. Let $S_n = X_1+. +X_n$. By the ordinary Strong Law of Large Numbers, we almost surely have $E_*[X_1] \le \liminf S_n/n \le \limsup S_n/n \le E^*[X_1]$, where $E_*$ and $E^*$ are the lower and upper expectations. We ask if anything more precise can be said about the limit points of $S_n/n$ in the non-trivial case where $E_*[X_1] < E^*[X_1]$, and obtain several negative answers. For instance, the set of points of $\Omega$ where $S_n/n$ converges is maximally nonmeasurable: it has inner measure zero and outer measure one.
Lp-Caffarelli–Kohn–Nirenberg type inequalities on homogeneous groups

We prove $L^{p}$-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups, which is one of most general subclasses of nilpotent Lie groups, all with sharp constants. We also discuss some of their consequences. Already in the abelian case of $\mathbb{R}^{n}$ our results provide new insights in view of the arbitrariness of the choice of the not necessarily Euclidean quasi-norm.
Waiting time in the premilking holding pen and subsequent lying and walking behaviors of Holstein cows

Graphical Abstract Summary: The objective of this study was to assess the effect of waiting time (WT) in the premilking holding pen on the subsequent lying and locomotion behaviors of Holstein cows. We analyzed the effect of WT on lying time, number of lying bouts, and number of steps using a commercial 3-dimensional accelerometer affixed to the hind leg. Mean values for each behavior between consecutive milkings were compared among 3 WT categories (short, intermediate, and long). No significant effects were detected for overall WT on any of the behaviors. However, analysis by milking shift indicated that, during the period following the night milking, cows subjected to short WT had the lowest lying time, whereas cows in the long WT category had the greatest number of lying bouts. No effect of WT category was observed for number of steps after any of the milking shifts. Variables such as parity, temperature-humidity index, and time of day affected cow behavior and should be considered when evaluating the effect of routine management of milking on commercial farms.
Diffuse interface methods for multiple phase materials: an energetic variational approach

In this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydro- dynamical system is derived through an energetic variational approach. The total energy of the system includes the kinetic energy and the mixing (interfacial) ener- gies. The least action principle (or the principle of virtual work) is applied to derive the conservative part of the dynamics, with a focus on the reversible part of the stress tensor arising from the mixing energies. The dissipative part of the dynam- ics is then introduced through a dissipation function in the energy law, in line with Onsager's principle of maximum dissipation. The final system, formed by a set of coupled time-dependent partial differential equations, reflects a balance among var- ious conservative and dissipative forces and governs the evolution of velocity and phase fields. To demonstrate the applicability of the proposed model, a few two- dimensional simulations have been carried out, including (1) the force balance at the three-phase contact line in equilibrium, (2) a rising bubble penetrating a fluid- fluid interface, and (3) a solid particle falling in a binary fluid. The effects of slip at solid surface have been examined in connection with contact line motion and a pinch-off phenomenon.
Challenges and Insights From Treating Psychotic Disorders During COVID-19 Pandemic in Brazil

Abstract The COVID-19 pandemic mainly affected the most vulnerable individuals. Among those, patients with schizophrenia especially suffered from unexpected changes in their routines, barriers to treatment, and distress-related events. We conducted a narrative review using all available sources of information to describe the challenges faced by schizophrenia patients and their families in Brazil, including the strategies that have been adopted to tackle them. In addition, we analyzed public data on antipsychotic prescriptions and hospitalizations. It was found that digital prescriptions with extended expiration dates implemented during the pandemic in Brazil allowed patients to maintain their access to antipsychotics. Hospitalizations among patients with schizophrenia, schizotypal, and schizoaffective disorders decreased at the beginning of the pandemic. Nevertheless, in the following months, the admissions returned to a trend similar to the prepandemic period. The systematization of online resources will be one of the main legacies to mental health care, including schizophrenia. We believe one of the main limitations of the policies adopted was the decision to not prioritize COVID-19 vaccination in patients with severe psychiatric disorders, despite preliminary evidence of a higher risk of complications in this group. The coronavirus pandemic is still ongoing and a longer time will be required to have a better perspective of its effects, but we expect this record of challenges and insights about the lessons learned during the pandemic can help healthcare professionals to face similar situations in the future.