Miracle-dz/UniFAR-FTUs huggingface dataset:
OTFS—A Mathematical Foundation for Communication and Radar Sensing in the Delay-Doppler Domain

Orthogonal time frequency space (OTFS) is a framework for communication and active sensing that processes signals in the delay-Doppler (DD) domain. This article explores three key features of the OTFS framework, and explains their value to applications. The first feature is a compact and sparse DD domain parameterization of the wireless channel, where the parameters map directly to physical attributes of the reflectors that comprise the scattering environment, and as a consequence these parameters evolve predictably. The second feature is a novel waveform/modulation technique, matched to the DD channel model, that embeds information symbols in the DD domain. The relation between channel inputs and outputs is localized, non-fading, and predictable, even in the presence of significant delay and Doppler spread, and as a consequence the channel can be efficiently acquired and equalized. By avoiding fading, the post equalization signal to noise ratio remains constant across all information symbols in a packet, so that bit error performance is superior to contemporary multicarrier waveforms. Further, the OTFS carrier waveform is a localized pulse in the DD domain, making it possible to separate reflectors along both delay and Doppler simultaneously, and to achieve a high-resolution DD radar image of the environment. In other words, the DD parameterization provides a common mathematical framework for communication and radar. This is the third feature of the OTFS framework, and it is ideally suited to intelligent transportation systems involving self-driving cars and unmanned ground/aerial vehicles, which are self/network controlled. The OTFS waveform is able to support stable and superior performance over a wide range of user speeds. In the emerging 6G systems and standards, it is ideally suited to support mobility-on-demand envisaged in next generation cellular and WiFi systems, as well as high-mobility use cases. Finally, the compactness and predictability of the OTFS input–output relation makes it a natural fit for machine learning and AI algorithms designed for the intelligent nonmyopic management of control plane resources in future mobile networks.
The dual group of a spherical variety

Let $X$ be a spherical variety for a connected reductive group $G$. Work of Gaitsgory-Nadler strongly suggests that the Langlands dual group $G^\vee$ of $G$ has a subgroup whose Weyl group is the little Weyl group of $X$. Sakellaridis-Venkatesh defined a refined dual group $G^\vee_X$ and verified in many cases that there exists an isogeny $\phi$ from $G^\vee_X$ to $G^\vee$. In this paper, we establish the existence of $\phi$ in full generality. Our approach is purely combinatorial and works (despite the title) for arbitrary $G$-varieties.
PLANTING FERTILIZATION AND NITROGEN DOSES IN TOPDRESSING IN SECOND-CROP CORN

The present study aimed to evaluate the influence of fertilization formulated at planting and doses of nitrogen in topdressing on the yield components of second-crop corn. The experiment was conducted between March and June 2018 on the farm of the State University of Goiás, University Unit of Ipameri-GO. The randomized block design, arranged in a 3 x 5 factorial scheme with four replications, was used. Three fertilizer formulations at planting (06-22-12; 08-20-15 and 06-22-12 + 2% organic carbon) and five doses of N (0, 50, 100, 150 and 200 kg ha-1) in topdressing were evaluated. Leaf nitrogen content, fresh and dry mass of leaves, plant height, stem diameter, first ear insertion height, length and diameter of ears, 1000-grain weight, the mass of plants per hectare, extraction of nitrogen, and grain yield were assessed. Given the results, NPK formulated fertilizers can be used indifferently to grow second-crop corn. Nitrogen doses in topdressing have satisfactory results up to the estimated rate of 135 kg ha-1 for the cultivation of second-crop corn.
Foreground Fusion-Based Liquefied Natural Gas Leak Detection Framework From Surveillance Thermal Imaging

A leak detection and repair survey (LDAR) is essential to ensure a reliable and safe liquefied natural gas (LNG) supply. Modern LDAR systems deploy numerous fixed thermal imaging devices to automatically monitor the risk of potential leaks empowered by computational intelligence frameworks. Existing frameworks employ either background subtraction-based (BGS-based) or deep neural network-based (DNN-based) frameworks for LNG leak detection from thermal images. However, the BGS-based frameworks feature high sensitivity to perceive LNG emissions with low precision. On the contrary, the DNN-based frameworks can precisely classify the LNG leak after training while the sensitivity is low. Additionally, conventional DNN-based frameworks are difficult in modeling non-rigid objects such as LNG gas due to limited perceptive fields. Therefore, this study proposes a hybrid framework, namely foreground fusion-based gas detection (FFBGD), combining the advantages of BGS-based and DNN-based detectors for improved detection robustness through newly introduced concept of information fusion to LNG industries. Specifically, a foreground fusion network (FFN) is designed to fuse information of original thermal and foreground images after BGS based on the visual attention mechanism. Meanwhile, several advanced modules, i.e. deformable convolution, feature pyramid network, and cascade region-of-interest (ROI) head are adopted to enhance leak detection by offering better perceptive fields. Extensive experiments are carried out in this study to demonstrate the significant improvement brought by the proposed FFBGD over leak detection accuracy and robustness. Hence, the proposed solution can be deployed in energy facilities and enable reliable visual surveillance of LNG leaks.
Cooperative Ecological Adaptive Cruise Control for Plug-In Hybrid Electric Vehicle Based on Approximate Dynamic Programming

Eco-driving control generates significant energy-saving potential in car-following scenarios. However, the influence of preceding vehicle may impose unnecessary velocity waves and deteriorate fuel economy. In this research, a learning-based method is exploited to achieve satisfied fuel economy for connected plug-in hybrid electric vehicles (PHEVs) with the advantage of vehicle-to-vehicle communication system. A data-driven energy consumption model is leveraged to generate reinforcement signals for approximate dynamic programming (ADP) with the consideration of nonlinear efficiency characteristics of hybrid powertrain system. An advanced ADP scheme is designed for connected PHEVs driving in car-following scenarios. In addition, the cooperative information is incorporated to further improve the fuel economy of the vehicle under the premise of driving safety. The proposed method is mode-free and showcases acceptable computational efficiency as well as adaptability. The simulation results demonstrate that the fuel economy during car-following processes is remarkably improved through cooperative driving information, thereby partially paving the theoretical basis for energy-saving transportation.
Assessing the Suitability of Boosting Machine-Learning Algorithms for Classifying Arsenic-Contaminated Waters: A Novel Model-Explainable Approach Using SHapley Additive exPlanations

There is growing tension between high-performance machine-learning (ML) models and explainability within the scientific community. In arsenic modelling, understanding why ML models make certain predictions, for instance, “high arsenic” instead of “low arsenic”, is as important as the prediction accuracy. In response, this study aims to explain model predictions by assessing the relationship between influencing input variables, i.e., pH, turbidity (Turb), total dissolved solids (TDS), and electrical conductivity (Cond), on arsenic mobility. The two main objectives of this study are to: (i) classify arsenic concentrations in multiple water sources using novel boosting algorithms such as natural gradient boosting (NGB), categorical boosting (CATB), and adaptive boosting (ADAB) and compare them with other existing representative boosting algorithms, and (ii) introduce a novel SHapley Additive exPlanation (SHAP) approach for interpreting the performance of ML models. The outcome of this study indicates that the newly introduced boosting algorithms produced efficient performances, which are comparable to the state-of-the-art boosting algorithms and a benchmark random forest model. Interestingly, the extreme gradient boosting (XGB) proved superior over the remaining models in terms of overall and single-class performance metrics measures. Global and local interpretation (using SHAP with XGB) revealed that high pH water is highly correlated with high arsenic water and vice versa. In general, high pH, high Cond, and high TDS were found to be the potential indicators of high arsenic water sources. Conversely, low pH, low Cond, and low TDS were the main indicators of low arsenic water sources. This study provides new insights into the use of ML and explainable methods for arsenic modelling.
On cubes of Frobenius extensions

Given a hypercube of Frobenius extensions between commutative algebras, we provide a diagrammatic description of some natural transformations between compositions of induction and restriction functors, in terms of colored transversely-intersecting planar 1-manifolds. The relations arise in the first and third authors' work on (singular) Soergel bimodules.
Local space and time scaling exponents for diffusion on compact metric spaces

We provide a new definition of a local walk dimension $\beta$ that depends only on the metric and not on the existence of a particular regular Dirichlet form or heat kernel asymptotics. Moreover, we study the local Hausdorff dimension $\alpha$ and prove that any variable Ahlfors regular measure of variable dimension $Q$ is strongly equivalent to the local Haudorff measure with $Q=\alpha,$ generalizing the constant dimensional case. Additionally, we provide constructions of several variable dimensional spaces, including a new example of a variable dimensional Sierpinski carpet. We show also that there exist natural examples where $\alpha$ and $\beta$ both vary continuously. We prove $\beta\geq 2$ provided the space is doubling. We use the local exponent $\beta$ in time-scale renormalization of discrete time random walks, that are approximate at a given scale in the sense that the expected jump size is the order of the space scale. In analogy with the variable Ahlfors regularity space scaling condition involving $\alpha$, we consider the condition that the expected time to leave a ball scales like the radius of the ball to the power $\beta$ of the center. Under this local time scaling condition along with the local space scaling condition of Ahlfors regularity, we then study the $\Gamma$ and Mosco convergence of the resulting continuous time approximate walks as the space scale goes to zero. We prove that a non-trivial Dirichlet form with Dirichlet boundary conditions on a ball exists as a Mosco limit of approximate forms. One of the novel ideas in this construction is the use of exit time functions, analogous to the torsion functions of Riemannian geometry, as test functions to ensure the resulting domain contains enough functions. We also prove tightness of the associated continuous time processes.
Molecular Detection and Phylogenetic Analyses of Diverse Bartonella Species in Bat Ectoparasites Collected from Yunnan Province, China

Bartonella species has been validated as blood-borne bacteria in mammals and has a substantial opportunity to be harbored by a variety of hematophagous arthropod vectors. Bats, along with their ectoparasites, are recognized worldwide as one of the natural reservoir hosts for these bacteria. However, there have been few investigations of Bartonella bacteria toward a broad range of obligated bat ectoparasites in China. Here, molecular detection of Bartonella species was performed to survey the infection among bat ectoparasites and follow-up phylogenetic analyses to further characterize the evolutionary relationships of the genus. A total of 434 bat ectoparasites involving four types of arthropods, namely, bat mites, bat tick, bat fleas, and bat flies (further divided into traditionally fly-like bat flies and wingless bat flies) were collected in 10 trapping sites in Yunnan Province, southwestern China. Bartonella was detected by PCR amplification and sequencing through four gene target fragments (gltA, ftsZ, rpoB, and ITS). Accordingly, diverse Bartonella species were discovered, including both the validated species and the novel genotypes, which were characterized into several geographical regions with high prevalence. Phylogenetic analyses based on gltA and multi-locus concatenated sequences both demonstrated strong phylogeny–trait associations of Bartonella species from bats and their parasitic arthropods, suggesting the occurrence of host switches and emphasizing the potential connecting vector role of these ectoparasites. Nevertheless, the maintenance and transmission of Bartonella in both bat and hemoparasite populations have not been fully understood, as well as the risk of spillage to humans, which warrants in-depth experimental studies focusing on these mammals and their ectoparasites.
Magnetic susceptibility of the quark condensate and polarization from chiral models

We compute the magnetic susceptibility of the quark condensate and the polarization of quarks at zero temperature and in a uniform magnetic background. Our theoretical framework consists of two chiral models that allow to treat self-consistently the spontaneous breaking of chiral symmetry: the linear $\sigma-$model coupled to quarks, dubbed quark-meson model, and the Nambu-Jona-Lasinio model. We also perform analytic estimates of the same quantities within the renormalized quark-meson model, both in the regimes of weak and strong fields. Our numerical results are in agreement with the recent literature; moreover, we confirm previous Lattice findings, related to the saturation of the polarization at large fields.
Nonexistence of Bigeodesics in Integrable Models of Last Passage Percolation

Bi-infinite geodesics are fundamental objects of interest in planar first passage percolation. A longstanding conjecture states that under mild conditions there are almost surely no bigeodesics, however the result has not been proved in any case. For the exactly solvable model of directed last passage percolation on $\mathbb{Z}^2$ with i.i. d. exponential passage times, we study the corresponding question and show that almost surely the only bigeodesics are the trivial ones, i.e., the horizontal and vertical lines. The proof makes use of estimates for last passage time available from the integrable probability literature to study coalescence structure of finite geodesics, thereby making rigorous a heuristic argument due to Newman.
On the Monodromies and the Limit Mixed Hodge Structures of Families of Algebraic Varieties

We study the monodromies and the limit mixed Hodge structures of families of complete intersection varieties over a punctured disk in the complex plane. For this purpose, we express their motivic nearby fibers in terms of the geometric data of some Newton polyhedra. In particular, the limit mixed Hodge numbers and some part of the Jordan normal forms of the monodromies of such a family will be described very explicitly.
Laurent phenomenon and simple modules of quiver Hecke algebras

In this paper we study consequences of the results of Kang et al. [Monoidal categorification of cluster algebras, J. Amer. Math. Soc. 31 (2018), 349–426] on a monoidal categorification of the unipotent quantum coordinate ring $A_{q}(\mathfrak{n}(w))$ together with the Laurent phenomenon of cluster algebras. We show that if a simple module $S$ in the category ${\mathcal{C}}_{w}$ strongly commutes with all the cluster variables in a cluster $[\mathscr{C}]$ , then $[S]$ is a cluster monomial in $[\mathscr{C}]$ . If $S$ strongly commutes with cluster variables except for exactly one cluster variable $[M_{k}]$ , then $[S]$ is either a cluster monomial in $[\mathscr{C}]$ or a cluster monomial in $\unicode[STIX]{x1D707}_{k}([\mathscr{C}])$ . We give a new proof of the fact that the upper global basis is a common triangular basis (in the sense of Qin [Triangular bases in quantum cluster algebras and monoidal categorification conjectures, Duke Math. 166 (2017), 2337–2442]) of the localization $\widetilde{A}_{q}(\mathfrak{n}(w))$ of $A_{q}(\mathfrak{n}(w))$ at the frozen variables. A characterization on the commutativity of a simple module $S$ with cluster variables in a cluster $[\mathscr{C}]$ is given in terms of the denominator vector of $[S]$ with respect to the cluster $[\mathscr{C}]$ .
The CMV bispectral problem

A classical result due to Bochner classifies the orthogonal polynomials on the real line which are common eigenfunctions of a second order linear differential operator. We settle a natural version of the Bochner problem on the unit circle which answers a similar question concerning orthogonal Laurent polynomials and can be formulated as a bispectral problem involving CMV matrices. We solve this CMV bispectral problem in great generality proving that, except the Lebesgue measure, no other one on the unit circle yields a sequence of orthogonal Laurent polynomials which are eigenfunctions of a linear differential operator of arbitrary order. Actually, we prove that this is the case even if such an eigenfunction condition is imposed up to finitely many orthogonal Laurent polynomials.
A Comparative Study on Mechanic and Structural Properties of Recycled Pet (R-Pet) and Viscose Blended Yarns

: Environmental pollution caused by plastic bottles is shown as one of the biggest environmental disasters of recent years. Not only in the form of plastic bottles, but the microplastics formed from these bottles threaten many areas of life such as soil and ocean pollution. Converting plastic bottle wastes into textile products is one of the effective methods that not only prevents environmental pollution caused by these materials but also ensures the reuse of raw materials. In this study, the properties of blended yarns produced using viscose fibers and recycled polyethylene terephthalate fibers (r-PET) obtained from recycling plastic bottles were investigated. Within the scope of the study, blended yarns at the ratios of 33-67%, 50-50%, 67%-33% r-PET/viscose fibers, and also 100% r-PET yarns were produced. The physical, mechanical, and structural properties and also cross-sectional images of the yarns examined. The results show that the blending ratio is statistically significant on the yarn properties in general. Among the measured properties, yarns containing 33% and 50% r-PET fibers generally show similar physical, structural and mechanical properties. It is revealed that blended yarns consisting of 67% r-PET have generally better properties in comparison with other types of blended yarns. Therefore, it is possible that higher r-Pet fiber fraction in yarn can create more positive effects on yarn properties and the results are comparable with 100% r-PET yarns.
Prevalence of Mucosal Lesions in People Consuming Chewable Tobacco in Hormozgan Province, Iran

Background: Tobacco has a high level of carcinogenic components. The maximum effect of the component is on the oral cavity and the location of tobacco. Quantitative studies were conducted according to the oral effect of tobacco usage by people of the south of Iran, specifically in Hormozgan province. In this experiment, the prevalence of oral lesions was studied in people who use tobacco in Hormozgan province in 2018. Materials and Methods: In this descriptive cross-sectional study, 395 patients were examined on oral lesions in Hormozgan province. Data were collected and described by a mean frequency table and then analyzed by an inferential statistical test such as the 2-dimensional chi-square test by SPSS, version 23 (P<0.05). Results: Experiments showed that 75.5% (299 from 395) of patients had mucosal lesions. The most lesions were tobacco pouch, wound, white plaque, and erythematic lesions. In addition, a significant correlation was found among parameters, including all mucosal lesions with time, all mucosal lesions with age (except wound), white plaque and erythematic mucosal lesions with smoking, tobacco pouch, and white plaque with alcohol use. However, no significant correlation was observed between oral mucosal lesions with a history of family oral lesions, tobacco pouch and wound with cigarette usage, and wound and erythematic lesions with alcohol use. Conclusion: Compared with other studies, oral mucosal lesions were highly prevalent in Hormozgan province. The possibility of oral mucosal lesions increases as one gets older; in addition, the duration of tobacco usage is a primary factor for the lesions.
A mixed-element two-grid discretization for Helmholtz transmission eigenvalues

The Helmholtz transmission eigenvalue problem has received much concern in materials science, so it's significant to explore the efficient calculational method of the problem to mathematics and mechanics community. In this paper, based on a variational formulation proposed by Cakon, Monk and Sun, we introduce a mixed-element two-grid discretization and prove error estimates for this method theoretically. Some numerical results are presented to confirm the theoretical analysis and show that the method here is efficient.
A-priori bounds for quasilinear problems in critical dimension

Abstract We establish uniform a-priori bounds for solutions of the quasilinear problems −ΔNu=f(u)in Ω,u=0on ∂Ω, $$\begin{array}{} \displaystyle \begin{cases} -{\it\Delta}_Nu=f(u)\quad&\mbox{in }{\it\Omega},\\ u=0\quad&\mbox{on }{\partial{\it\Omega}}, \end{cases} \end{array}$$ where Ω ⊂ ℝN is a bounded smooth convex domain and f is positive, superlinear and subcritical in the sense of the Trudinger-Moser inequality. The typical growth of f is thus exponential. Finally, a generalisation of the result for nonhomogeneous nonlinearities is given. Using a blow-up approach, this paper completes the results in [1, 2], extending the class of nonlinearities for which the uniform a-priori bound applies.
Pathwise convergence of the hard spheres Kac process

Using the stability properties of the Boltzmann equation, we prove two estimates with better long-time properties than previously know, for the hard-spheres kernel Kac Process. We compare the empirical distribution of velocities to the flow of the mean-field Boltzmann equation and find that, for large $N$, the processes agree with tolerance $N^{-\alpha}$ in $L^p$- Wasserstein distance, for some positive exponent $\alpha>0$
Schur partition theorems via perfect crystal

We propose a generalization of Schur regular partitions for each odd integer $p\geq 3$. Applying Kashiwara crystal theory, we prove that the number of partitions of $n$ with this condition is equinumerous to the number of strict $p$-class regular partitions of $n$. At $p=3$, it is Schur's 1926 partition theorem found as a mod 6 analog of the Rogers-Ramanujan partition theorem (RRPT). The statement for $p=5$ was conjectured by Andrews in 1970s in a course of his 3 parameter generalization of RRPT and proved in 1994 by Andrews-Bessenrodt-Olsson with an aid of computer.