Miracle-dz/UniFAR-FTUs huggingface dataset:
Morse actions of discrete groups on symmetric space

We study the geometry and dynamics of discrete infinite covolume subgroups of higher rank semisimple Lie groups. We introduce and prove the equivalence of several conditions, capturing "rank one behavior'' of discrete subgroups of higher rank Lie groups. They are direct generalizations of rank one equivalents to convex cocompactness. We also prove that our notions are equivalent to the notion of Anosov subgroup, for which we provide a closely related, but simplified and more accessible reformulation, avoiding the geodesic flow of the group. We show moreover that the Anosov condition can be relaxed further by requiring only non-uniform unbounded expansion along the (quasi)geodesics in the group. A substantial part of the paper is devoted to the coarse geometry of these discrete subgroups. A key concept which emerges from our analysis is that of Morse quasigeodesics in higher rank symmetric spaces, generalizing the Morse property for quasigeodesics in Gromov hyperbolic spaces. It leads to the notion of Morse actions of word hyperbolic groups on symmetric spaces,i.e. actions for which the orbit maps are Morse quasiisometric embeddings, and thus provides a coarse geometric characterization for the class of subgroups considered in this paper. A basic result is a local-to-global principle for Morse quasigeodesics and actions. As an application of our techniques we show algorithmic recognizability of Morse actions and construct Morse "Schottky subgroups'' of higher rank semisimple Lie groups via arguments not based on Tits' ping-pong. Our argument is purely geometric and proceeds by constructing equivariant Morse quasiisometric embeddings of trees into higher rank symmetric spaces.
Accelerated Distributed Nesterov Gradient Descent

This paper considers the distributed optimization problem over a network, where the objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. We develop an accelerated distributed Nesterov gradient descent method. When the objective function is convex and <inline-formula><tex-math notation="LaTeX">$L$</tex-math></inline-formula>-smooth, we show that it achieves a <inline-formula><tex-math notation="LaTeX">$O(\frac{1}{t^{1.4-\epsilon }})$</tex-math></inline-formula> convergence rate for all <inline-formula><tex-math notation="LaTeX">$\epsilon \in (0,1.4)$</tex-math></inline-formula>. We also show the convergence rate can be improved to <inline-formula><tex-math notation="LaTeX">$O(\frac{1}{t^2})$</tex-math></inline-formula> if the objective function is a composition of a linear map and a strongly convex and smooth function. When the objective function is <inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>-strongly convex and <inline-formula><tex-math notation="LaTeX">$L$</tex-math></inline-formula>-smooth, we show that it achieves a linear convergence rate of <inline-formula><tex-math notation="LaTeX">$O([ 1 - C (\frac{\mu }{L})^{5/7} ]^t)$</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">$\frac{L}{\mu }$</tex-math></inline-formula> is the condition number of the objective, and <inline-formula><tex-math notation="LaTeX">$C>0$</tex-math></inline-formula> is some constant that does not depend on <inline-formula><tex-math notation="LaTeX">$\frac{L}{\mu }$</tex-math></inline-formula>.
A note on set-valued Henstock-McShane integral in Banach (lattice) space setting

We study Henstock-type integrals for functions defined in a Radon measure space and taking values in a Banach lattice $X$. Both the single-valued case and the multivalued one are considered (in the last case mainly $cwk(X)$-valued mappings are discussed). The main tool to handle the multivalued case is a R{\aa}dstr\"{o}m-type embedding theorem established in [50]: in this way we reduce the norm-integral to that of a single-valued function taking values in an $M$-space and we easily obtain new proofs for some decomposition results recently stated in [33,36], based on the existence of integrable selections. Also the order-type integral has been studied: for the single-valued case some basic results from [21] have been recalled, enlightning the differences with the norm-type integral, specially in the case of $L$-space-valued functions; as to multivalued mappings, a previous definition ([6]) is restated in an equivalent way, some selection theorems are obtained, a comparison with the Aumann integral is given, and decompositions of the previous type are deduced also in this setting. Finally, some existence results are also obtained, for functions defined in the real interval $[0,1]$.
Traumatic experiences and PTSD symptoms in substance use disorder: A comparison of recovered versus current users

Introduction: The aim of this study was to investigate the prevalence of traumatic experiences and symptoms of posttraumatic stress disorder (PTSD) in treatment-seeking individuals with ongoing substance use disorder (SUD) compared to individuals who have recovered from SUD. Methods: Patients with SUD recruited from the STAYER study (N = 114) underwent an examination of alcohol and drug use, childhood trauma, negative life events and PTSD symptomatology. In this study, only participants with 12-month concurrent polysubstance use was included. Using historical data from the STAYER study, alcohol and drug trajectories were dichotomised as (1) current SUD (current SUD) or (2) recovered from substance use disorder (recovered SUD). Crosstabs and chi-tests were used to measure differences between groups. Results: Childhood maltreatment, traumatic experiences later in life and symptoms of concurrent PTSD were highly prevalent in the study population. We found no significant difference between the current and recovered SUD groups. Recovered women reported a lower prevalence of physical neglect (p = 0.031), but a higher prevalence of multiple lifetime traumas (p = 0.019) compared to women with current SUD. Both women with current SUD and recovered women reported a significantly higher prevalence of sexual aggression than men (p < 0.001 and p < 0.001, respectively). In addition, men who have recovered from SUD reported a lower prevalence of PTSD symptoms over cut-off 38 (p = 0.017), of re-experiencing (p = 0.036) and of avoidance (p = 0.015), compared to recovered women. Conclusion: Reported trauma did not differ between persons with current SUD and those who had recovered from SUD. Gender differences discovered in this study indicate the importance of developing individualised and gender-specific treatment models for comorbid PTSD/SUD.
Nonstandard second-order formulation of the LWR model

ABSTRACT In this study, we present an equivalent second-order formulation of the LWR model based on Phillips’ model, in which the acceleration rate equals a relaxation term with an infinitesimal relaxation time. We convert the model into a continuum car-following model and demonstrate its equivalence to that of the LWR model. We demonstrate that the nonstandard second-order model is stable, but the original Phillips model is not. We derive conditions for the nonstandard model to be forward-traveling and collision-free, prove that the collision-free condition is consistent with but more general than the CFL condition, and demonstrate that only anisotropic and symplectic Euler discretization methods lead to physically meaningful solutions. Numerically, the nonstandard second-order model has the same shock and rarefaction wave solutions as the LWR model for both Greenshields and triangular fundamental diagrams; for a non-concave fundamental diagram, the collision-free condition, but not the CFL condition, yields physically meaningful results.
Wilf’s conjecture and Macaulay’s theorem

Let S $\subseteq$ N be a numerical semigroup with multiplicity m = min(S \ {0}), conductor c = max(N \ S) + 1 and minimally generated by e elements. Let L be the set of elements of S which are smaller than c. Wilf conjectured in 1978 that |L| is bounded below by c/e. We show here that if c $\le$ 3m, then S satisfies Wilf's conjecture. Combined with a recent result of Zhai, this implies that the conjecture is asymptotically true as the genus g(S) = |N \ S| goes to infinity. One main tool in this paper is a classical theorem of Macaulay on the growth of Hilbert functions of standard graded algebras.
A note on Products of Nilpotent Matrices

Let $\mathscr{F}$ be a field. A matrix $A$ of order $n \times n$ over $\mathscr{F}$ is a product of two nilpotent matrices if and only if it is singular, except if $A$ is a nonzero nilpotent matrix of order $2 \times 2$. This result was proved independently by Sourour and Laffey. While these results remain true and the general strategies and principles of the proofs correct, there are certain problematic details in the original proofs which are resolved in this article. A detailed and rigorous proof of the result based on Laffey's original proof is provided, and a problematic detail in the Proposition which is the main device underpinning the proof by Sourour is resolved.
Federated Onboard-Ground Station Computing With Weakly Supervised Cascading Pyramid Attention Network for Satellite Image Analysis

With advances in NanoSat (CubeSat) and high-resolution sensors, the amount of raw data to be analyzed by human supervisors has been explosively increasing for satellite image analysis. To reduce the raw data, the satellite onboard AI processing with low-power COTS (Commercial, Off-The-Shelf) HW has emerged from a real satellite mission. It filters the useless data (e.g. cloudy images) that is worthless to supervisors, achieving efficient satellite-ground station communication. In the application for complex object recognition, however, additional explanation is required for the reliability of the AI prediction due to its low performance. Although various explainable AI (XAI) methods for providing human-interpretable explanation have been studied, the pyramid architecture in a deep network leads to the background bias problem which visual explanation only focuses on the background context around the object. Missing the small objects in a tiny region leads to poor explainability although the AI model corrects the object class. To resolve the problems, we propose a novel federated onboard-ground station (FOGS) computing with Cascading Pyramid Attention Network (CPANet) for reliable onboard XAI in object recognition. We present an XAI architecture with a cascading attention mechanism for mitigating the background bias for the onboard processing. By exploiting the localization ability in pyramid feature blocks, we can extract high-quality visual explanation covering the both semantic and small contexts of an object. For enhancing visual explainability of complex satellite images, we also describe a novel computing federation with the ground station and supervisors. In the ground station, active learning-based sample selection and attention refinement scheme with a simple feedback method are conducted to achieve the robustness of explanation and efficient supervisor’s annotation cost, simultaneously. Experiments on various datasets show that the proposed system improves task accuracy in object recognition and accurate visual explanation detecting small contexts of objects even in a peripheral region. Then, our attention refinement mechanism demonstrates that the inconsistent explanation can be efficiently resolved only with very simple selection-based feedback.
Expansion of fractional derivatives in terms of an integer derivative series: physical and numerical applications

We use the displacement operator to derive an infinite series of integer order derivatives for the Gr\"{u}nwald-Letnikov fractional derivative and show its correspondence to the Riemann-Liouville and Caputo fractional derivatives. We demonstrate that all three definitions of a fractional derivative lead to the same infinite series of integer order derivatives. We find that functions normally represented by Taylor series with a finite radius of convergence have a corresponding integer derivative expansion with an infinite radius of convergence. Specifically, we demonstrate robust convergence of the integer derivative series for the hyperbolic secant (tangent) function, characterized by a finite radius of convergence of the Taylor series $R=\pi/2$, which describes bright (dark) soliton propagation in non-linear media. We also show that for a plane wave, which has a Taylor series with an infinite radius of convergence, as the number of terms in the integer derivative expansion increases, the truncation error decreases. Finally, we illustrate the utility of the truncated integer derivative series by solving two linear fractional differential equations, where the fractional derivative is replaced by an integer derivative series up to the second order derivative. We find that our numerical results closely approximate the exact solutions given by the Mittag-Leffler and Fox-Wright functions. Thus, we demonstrate that the truncated expansion is a powerful method for solving linear fractional differential equations, such as the fractional Schr\"{o}dinger equation.
On function field Mordell–Lang: the semiabelian case and the socle theorem

In this paper we complete our ‘second‐generation’ model‐theoretic account of the function field Mordell–Lang conjecture, where we avoid appeals to dichotomy theorems for (generalized) Zariski geometries. In the current paper we reduce the semiabelian case to the abelian case using model‐theoretic tools. We also use our results from Benoist, Bouscaren and Pillay [J. Math. Log. 16 (2016)] to prove modularity of the ‘Manin kernels’ (over Fp(t)sep in positive characteristic and over C(t)alg in characteristic 0).
A Longitudinal Velocity CF-MPC Model for Connected and Automated Vehicle Platooning

To optimize a vehicle platoon system in terms of car-following behavior, a decentralized model predictive control (MPC) strategy for longitudinal velocity control was established (namely, CF-MPC). Firstly, considering the influence of car-following behavior on vehicle states, a longitudinal velocity control model for platoons of connected and automated vehicles (CAV) was designed. Based on that model, an upper-level MPC controller was built to obtain the desired acceleration of the vehicles. Secondly, a lower-level controller received the desired acceleration signal and converted it into the expected throttle opening/braking pressure, to control acceleration/deceleration. Then, the Lyapunov stability method was used to detect the stability conditions that the model should satisfy. Finally, three simulation procedures—constant speed, acceleration, and deceleration were tested, and the validity of the CF-MPC method was verified from the perspectives of a model strategy and a control strategy. The simulation results show that with the proposed CF-MPC method, CAV platoons quickly completed velocity tracking and maintained a safe distance, thereby improving traffic efficiency, fuel economy, driving safety, and transportation capacity.
Responses of sedimentary proxy indicators to lake-level fluctuations on the central Tibetan Plateau since the last deglaciation

Lake sediments are valuable archives to investigate past changes in climate and environment on various timescales. Closed-basin lakes can be regarded as precipitation gauges, which are ideal for studying past climate changes. However, the climatic implications of various sedimentary proxy indicators from closed-basin lakes are often confounded by lake-level fluctuations, which are affected by lake watershed processes, besides climate change. Here, we present records of multi-proxy indicators since the last deglaciation at Lake Cuoe, on the central Tibetan Plateau, which was once connected with Selin Co and became separated during the middle Holocene, as evidenced by a series of paleo-shorelines. The sedimentary proxies are categorized into three groups based on their origins, with differences in their environmental significance. The proxy indicators derived from within-lake processes effectively revealed past lake-level fluctuations, including the Ca/(Al, Ti, Fe) ratio, Fe/Mn ratio, carbonate minerals, stable carbon and oxygen isotopes of authigenic carbonate, and the percentage of aquatic inputs (Paq) derived from n-alkanoic acids. These proxy indicators showed obvious changes at ∼7–6 ka, when Lake Cuoe became hydrologically separated from Selin Co. The stable oxygen isotope record of Lake Cuoe, apparently modulated by lake-level changes, differs significantly from that from Selin Co. The proxy indicators reflecting watershed processes, including terrigenous elements, Rb/Sr ratio, grain size, and the chain length proxy based on n-alkanoic acids, directly reflected changes in the regional climate and environment. The proxy indicators derived from both allochthonous and authigenic sources, including total organic carbon (TOC) and total nitrogen (TN), reflected the effects of climate change as well as lake-level fluctuations. Overall, our results suggest that great caution should be applied in interpreting proxy records of climatic and environmental changes from closed-basin lakes on the Tibetan Plateau. They also highlight the potential of using sedimentary proxies to reconstruct continuous records of lake-level fluctuations.
Tightness for the Cover Time of compact two dimensional manifolds

Let $\mathcal{C}^*_{\epsilon,M}$ denote the cover time of a two dimensional compact manifold $M$ by a Wiener sausage of radius $\epsilon$. We prove that $\sqrt{\mathcal{C}^*_{\epsilon,M} } -\sqrt{\frac{2A_{M}}{\pi}}(\log \epsilon^{-1}-\frac14\log\log \epsilon^{-1})$ is tight, where $A_M$ denotes the area of $M$.
Extracellular Vesicles Released after Doxorubicin Treatment in Rats Protect Cardiomyocytes from Oxidative Damage and Induce Pro-Inflammatory Gene Expression in Macrophages

Doxorubicin (DOXO)-induced cardiomyopathy (DIC) is a lethal complication in cancer patients. Major mechanisms of DIC involve oxidative stress in cardiomyocytes and hyperactivated immune response. Extracellular vesicles (EVs) mediate cell–cell communication during oxidative stress. However, functions of circulating EVs released after chronic DOXO exposure on cardiomyocytes and immune cells are still obscured. Herein, we developed a DIC in vivo model using male Wistar rats injected with 3 mg/kg DOXO for 6 doses within 30 days (18 mg/kg cumulative dose). One month after the last injection, the rats developed cardiotoxicity evidenced by increased BCL2-associated X protein and cleaved caspase-3 in heart tissues, along with N-terminal pro B-type natriuretic peptide in sera. Serum EVs were isolated by size exclusion chromatography. EV functions on H9c2 cardiomyocytes and NR8383 macrophages were evaluated. EVs from DOXO-treated rats (DOXO_EVs) attenuated ROS production via increased glutathione peroxidase-1 and catalase gene expression, and reduced hydrogen peroxide-induced cell death in cardiomyocytes. In contrast, DOXO_EVs induced ROS production, interleukin-6, and tumor necrosis factor-alpha, while suppressing arginase-1 gene expression in macrophages. These results suggested the pleiotropic roles of EVs against DIC, which highlight the potential role of EV-based therapy for DIC with a concern of its adverse effect on immune response.
Effects of Carbonated Beverage Consumption on Oral pH and Bacterial Proliferation in Adolescents: A Randomized Crossover Clinical Trial

Sugary soft drinks modify salivary pH and favor bacterial proliferation and are associated with the development of caries. Information on the effects of consuming carbonated drinks without sucrose is limited. Methods: In this crossover clinical trial, salivary and dental biofilm pH were determined at 0, 5, 10, 15, 30, 45, and 60 min after the participants (n = 18) ingested a soft drink with sucrose, a soft drink with aspartame/acesulfame K, carbonated water, and plain water on different days. Dental biofilm cultures were conducted at 0- and 120-min. Results: Salivary pH decreased significantly after ingestion of the sucrose-containing soft drink when compared with the other types of beverages (median difference, −0.3–−0.4, p ≤ 0.05), and the greatest difference was found with mineral water. A greater bacterial proliferation (Colony Forming Units [CFU]) was observed after ingestion of the drink with sucrose (↑310 × 103 CFU, p ≤ 0.01), followed by the drink with aspartame/acesulfame K (↑160 × 103 CFU, p ≤ 0.01) and carbonated water (↑60 × 103 CFU, p ≤ 0.05). No significant changes in bacterial proliferation were observed after the consumption of natural water. Conclusions: Ingestion of sucrose-containing soft drinks favors the acidification of salivary pH and the bacterial proliferation of dental biofilm. Although to a lesser extent, soft drinks containing aspartame/acesulfame K also favor bacterial proliferation.
Smooth skew morphisms of the dihedral groups

A skew morphism φ of a finite group A is a permutation on A fixing the identity element of A and for which there exists an integer-valued function π on A such that φ ( a b ) = φ ( a ) φ π ( a ) ( b ) for all a , b ∈ A . In the case where π ( φ ( a )) = π ( a ) , for all a ∈ A , the skew morphism is smooth. The concept of smooth skew morphism is a generalization of that of t -balanced skew morphism. The aim of this paper is to develop a general theory of smooth skew morphisms. As an application we classify smooth skew morphisms of dihedral groups.
Electromagnetic Fields Exposure Assessment in Europe Utilizing Publicly Available Data

The ever-increasing use of wireless communication systems during the last few decades has raised concerns about the potential health effects of electromagnetic fields (EMFs) on humans. Safety limits and exposure assessment methods were developed and are regularly updated to mitigate health risks. Continuous radiofrequency EMF monitoring networks and in situ measurement campaigns provide useful information about environmental EMF levels and their variations over time and in different microenvironments. In this study, published data from the five largest monitoring networks and from two extensive in situ measurement campaigns in different European countries were gathered and processed. Median electric field values for monitoring networks across different countries lay in the interval of 0.67–1.51 V/m. The median electric field value across different microenvironments, as evaluated from in situ measurements, varied from 0.10 V/m to 1.42 V/m. The differences between networks were identified and mainly attributed to variations in population density. No significant trends in the temporal evolution of EMF levels were observed. The influences of parameters such as population density, type of microenvironment, and height of measurement on EMF levels were investigated.
No Cauchy datum needed for the unique solution in $\mathcal{S}^\prime(\mathbb{R}^{1+2d})$ of the linearized Vlasov-Maxwell system with the limiting absorption principle

For the linearized Vlasov equation, we establish a mathematically rigorous characterization of the specific (unique) solution which physically describes the response of a hot plasma to an external small-amplitude electromagnetic disturbance. This allows us to define the plasma conductivity operator $\sigma$ which gives the current density $J = \sigma E$ induced in the plasma by the electric field $E$ of the disturbance. With this aim we study first a simple model problem with damping and explain the relationship between the general solutions of the Cauchy problem with given data and the tempered solution which is unique. We apply them to the specific case of a hot uniform non-magnetized non-relativistic plasma (linear Landau damping).