Miracle-dz/UniFAR-FTUs huggingface dataset:
Characteristic Boundary Layers for Mixed Hyperbolic‐Parabolic Systems in One Space Dimension and Applications to the Navier‐Stokes and MHD Equations

We provide a detailed analysis of the boundary layers for mixed hyperbolic‐parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so‐called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so‐called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic‐parabolic system and for the hyperbolic system obtained by neglecting the second‐order terms. Our analysis applies in particular to the compressible Navier‐Stokes and MHD equations in Eulerian coordinates, with both positive and null electrical resistivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to nonconservative systems. © 2020 Wiley Periodicals, Inc.
Exponential stability of Euler integral in the three--body problem

The first integral characteristic of the two--centres problem is proven to be an approximate integral (in the sense of N.N.Nekhorossev) to the three--body problem, at least if the masses are very different and the particles are constrained on the same plane. The proof uses a new normal form result, carefully designed around the degeneracies of the problem, and a new study of the phase portrait of the unperturbed problem. Applications to the prediction of collisions between the two minor bodies are shown.
Biomedical Application of Photoacoustics: A Plethora of Opportunities

The photoacoustic (PA) technique is a non-invasive, non-ionizing hybrid technique that exploits laser irradiation for sample excitation and acquires an ultrasound signal generated due to thermoelastic expansion of the sample. Being a hybrid technique, PA possesses the inherent advantages of conventional optical (high resolution) and ultrasonic (high depth of penetration in biological tissue) techniques and eliminates some of the major limitations of these conventional techniques. Hence, PA has been employed for different biomedical applications. In this review, we first discuss the basic physics of PA. Then, we discuss different aspects of PA techniques, which includes PA imaging and also PA frequency spectral analysis. The theory of PA signal generation, detection and analysis is also detailed in this work. Later, we also discuss the major biomedical application area of PA technique.
The many polarizations of powers of maximal ideals

In this paper, we study different polarizations of powers of the maximal ideal m^d, and polarizations of its related square-free version I_d. For n = 3, we show that every minimal free cellular resolution of m^d comes from a certain polarization of the ideal m^d. When I is a square-free ideal, we show that the Alexander dual of any polarization of I is a polarization of the Alexander dual ideal of I. We apply this theorem and study different polarizations of I_d and its Alexander dual I_{n-d+1} simultaneously. We do this by giving a combinatorial description of the polarizations, which has a natural duality. We study the case of d = 2 and d = n-1 in more detail. Here, we show that there is a one- to-one correspondence between spanning trees of the complete graph K_n and the maximal polarizations of these ideals.
Tumor-Associated Lymphatics Upregulate MHC-II to Suppress Tumor-Infiltrating Lymphocytes

Steady-state lymphatic endothelial cells (LECs) can induce peripheral tolerance by presenting endogenous antigens on MHC class I (MHC-I) molecules. Recent evidence suggests that lymph node LECs can cross-present tumor antigens on MHC-I to suppress tumor-specific CD8+ T cells. Whether LECs can act as immunosuppressive cells in an MHC-II dependent manner in the local tumor microenvironment (TME) is not well characterized. Using murine heterotopic and spontaneous tumor models, we show that LECs in the TME increase MHC-II expression in the context of increased co-inhibitory signals. We provide evidence that tumor lymphatics in human melanoma and breast cancer also upregulate MHC-II compared to normal tissue lymphatics. In transgenic mice that lack LEC-specific MHC-II expression, heterotopic tumor growth is attenuated, which is associated with increased numbers of tumor-specific CD8+ and effector CD4+ T cells, as well as decreased numbers of T regulatory CD4+ cells in the TME. Mechanistically, we show that murine and human dermal LECs can take up tumor antigens in vitro. Antigen-loaded LECs in vitro can induce antigen-specific proliferation of CD8+ T cells but not CD4+ T cells; however, these proliferated CD8+ T cells have reduced effector function in the presence of antigen-loaded LECs. Taken together, our study suggests LECs can act as immunosuppressive cells in the TME in an MHC-II dependent manner. Whether this is a result of direct tumor antigen presentation on MHC-II requires additional investigation.
Multi-ASV Collision Avoidance for Point-to-Point Transitions Based on Heading-Constrained Control Barrier Functions with Experiment

Dear Editor, Collision avoidance is critical for safe operations of multiple autonomous surface vehicles (ASVs). It is a challenging task to design collision-free control laws to ensure safety, especially in a crowded sea environment. This letter presents a collision-free point-to-point transition strategy for multiple ASVs subject to static obstacles, dynamic obstacles and neighboring ASVs based on control barrier functions (CBFs). Existing CBFs consider only the position and not the heading, which makes it difficult to apply them to under-actuated ASVs. To address it, a heading-constrained CBF is proposed to design a yaw rate control law for avoiding collision with static obstacles, dynamic obstacles and vehicle neighbors. A quadratic program (QP) problem is formulated to compute the optimal yaw rate for each ASV such that the reach-avoid task can be achieved with safety guarantees. Both hardware-in-loop (HIL) simulation and field experiment results are given to substantiate the efficacy of the proposed heading-constrained CBFs.
Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas

In this paper, we show how the Gordin martingale approximation method fits into the anisotropic Banach space framework. In particular, for the time-one map of a finite horizon planar periodic Lorentz gas, we prove that Hölder observables satisfy statistical limit laws such as the central limit theorem and associated invariance principles. Previously, these properties were known only for a restricted class of observables, excluding for instance velocity.
Haar null and Haar meager sets: a survey and new results

We survey results about Haar null subsets of (not necessarily locally compact) Polish groups. The aim of this paper is to collect the fundamental properties of the various possible definitions of Haar null sets, and also to review the techniques that may enable the reader to prove results in this area. We also present several recently introduced ideas, including the notion of Haar meager sets, which are closely analogous to Haar null sets. We prove some results in a more general setting than that of the papers where they were originally proved and prove some results for Haar meager sets which were already known for Haar null sets.
Working Together: Peer Interactions to Support Students with Disabilities in the Music Classroom

There are many models for structuring peer interactions in the music classroom. From peer mentoring to peer tutoring, to other structured interaction models that have emerged from other areas of education, music teachers have many options when considering how to include structured peer interaction activities. This article describes the various models of structured peer interaction activities that can be used in music classrooms and provides strategies for implementing these activities in ways that support students with disabilities.
Bacterial Wilt Resistance in Blueberry Species

ABSTRACT Blueberry production is expanding rapidly in the United States and globally. In 2016, bacterial wilt was discovered in Florida blueberry production. Because of the international movement of plants, this disease poses a significant risk to production. The purpose of this project was to evaluate the resistance of blueberry species and cultivars to the three genetically distinct populations of Ralstonia identified in Florida blueberry production. Nineteen cultivars/species of Vaccinium were used in this study. Plants were selected from wild, northern, southern, midbush, lowbush, and rabbiteye varieties. Plants were inoculated with three genetically distinct strains of the pathogen, and experiments were replicated three times. Varying levels of quantitative (multigenic) bacterial wilt resistance were observed among varieties tested, with rabbiteye cultivars being the most resistant. These results are similar to bacterial wilt resistance observed in other agronomic crops. We also observed a unique specific qualitative (vertical) resistance in the rabbiteye cultivar ´Ochlockonee’. The pathogen was unable to colonize plant tissue and cause disease on this cultivar. This is the first report of qualitative resistance to Ralstonia solanacearum in blueberry. Both the multigenic and vertical resistance can be incorporated into blueberry breeding programs to mitigate potential losses to bacterial wilt.
Nurse Leadership and Work Environment Association with Outcome Expectancy and Self-Efficacy in Evidence-Based Practice among Hospital Nurses in The Netherlands: A Cross-Sectional Study

The active participation of nurses in evidence-based practice (EBP) is challenging and topical, as shown by the worldwide calls for appropriate, accessible, affordable care and the de-implementation of unnecessary care. Nurses’ perceived support from their managers and work environments may affect their self-efficacy and outcome expectancy in EBP, as well as hinder them in EBP. Associations between these issues have not yet been explored. This study examines the association of self-efficacy and outcome expectancy levels in EBP, as well as the perceived support for EBP from nurse leaders and in the working environment, among Dutch hospital nurses. Methods. Questionnaires measuring nurses’ self-efficacy, outcome expectancy, and perceived support for EBP from nurse leaders and their work environment were completed by 306 nurses in eight hospitals between March 2021 and June 2021. We used multilevel regression analyses to determine the associations and covariates. Results. This study shows that EBP-supportive leaders and work environments positively contribute to nurses’ self-efficacy and outcome expectancy in EBP, along with the covariates undertaking EBP activities and educational level. Conclusions. To improve nurses’ active participation in EBP, nurses need to increase their self-efficacy and outcome expectancy in EBP. Supportive leaders and a supportive work environment do have an impact. Hence, these factors need attention when implementing EBP among nurses.
Energy-Aware AI-Driven Framework for Edge-Computing-Based IoT Applications

The significant growth in the number of Internet of Things (IoT) devices has given impetus to the idea of edge computing for several applications. In addition, energy harvestable or wireless-powered wearable devices are envisioned to empower the edge intelligence in IoT applications. However, the intermittent energy supply and network connectivity of such devices in scenarios including remote areas and hard-to-reach regions such as in-body applications can limit the performance of edge computing-based IoT applications. Hence, deploying state-of-the-art convolutional neural networks (CNNs) on such energy-constrained devices is not feasible due to their computational cost. Existing model compression methods, such as network pruning and quantization can reduce complexity, but these methods only work for fixed computational or energy requirements, which is not the case for edge devices with an intermittent energy source. In this work, we propose a pruning scheme based on deep reinforcement learning (DRL), which can compress the CNN model adaptively according to the energy dictated by the energy management policy and accuracy requirements for IoT applications. The proposed energy policy uses predictions of energy to be harvested and dictates the amount of energy that can be used by the edge device for deep learning inference. We compare the performance of our proposed approach with existing state-of-the-art CNNs and data sets using different filter-ranking criteria and pruning ratios. We observe that by using DRL-driven pruning, the convolutional layers that consume relatively higher energy are pruned more as compared to their counterparts. Thereby, our approach outperforms existing approaches by reducing energy consumption and maintaining accuracy.
On the structure of the $C^*$-algebra generated by the field operators

We study the $C^*$-algebra generated by the field operators associated to representations of a symplectic space and the operators affiliated to it. We show that the algebra is graded by the semilattice of all finite dimensional subspaces of the symplectic space and in the finite dimensional case we give an intrinsic description of the components of the grading.
Conditions Implying Commutativity of Unbounded Self-adjoint Operators and Related Topics

Let $B$ be a bounded self-adjoint operator and let $A$ be a nonnegative self-adjoint unbounded operator. It is shown that if $BA$ is normal, it must be self-adjoint and so must be $AB$. Commutativity is necessary and sufficient for this result. If $AB$ is normal, it must be self-adjoint and $BA$ is essentially self-adjoint. Although the two problems seem to be alike, two different and quite interesting approaches are used to tackle each one of them.
Machine learning based estimation of field-scale daily, high resolution, multi-depth soil moisture for the Western and Midwestern United States

Background High-resolution soil moisture estimates are critical for planning water management and assessing environmental quality. In-situ measurements alone are too costly to support the spatial and temporal resolutions needed for water management. Recent efforts have combined calibration data with machine learning algorithms to fill the gap where high resolution moisture estimates are lacking at the field scale. This study aimed to provide calibrated soil moisture models and methodology for generating gridded estimates of soil moisture at multiple depths, according to user-defined temporal periods, spatial resolution and extent. Methods We applied nearly one million national library soil moisture records from over 100 sites, spanning the U.S. Midwest and West, to build Quantile Random Forest (QRF) calibration models. The QRF models were built on covariates including soil moisture estimates from North American Land Data Assimilation System (NLDAS), soil properties, climate variables, digital elevation models, and remote sensing-derived indices. We also explored an alternative approach that adopted a regionalized calibration dataset for the Western U.S. The broad-scale QRF models were independently validated according to sampling depths, land cover type, and observation period. We then explored the model performance improved with local samples used for spiking. Finally, the QRF models were applied to estimate soil moisture at the field scale where evaluation was carried out to check estimated temporal and spatial patterns. Results The broad-scale QRF model showed moderate performance (R2 = 0.53, RMSE = 0.078 m3/m3) when data points from all depth layers (up to 100 cm) were considered for an independent validation. Elevation, NLDAS-derived moisture, soil properties, and sampling depth were ranked as the most important covariates. The best model performance was observed for forest and pasture sites (R2 > 0.5; RMSE < 0.09 m3/m3), followed by grassland and cropland (R2 > 0.4; RMSE < 0.11 m3/m3). Model performance decreased with sampling depths and was slightly lower during the winter months. Spiking the national QRF model with local samples improved model performance by reducing the RMSE to less than 0.05 m3/m3 for grassland sites. At the field scale, model estimates illustrated more accurate temporal trends for surface than subsurface soil layers. Model estimated spatial patterns need to be further improved and validated with management data. Conclusions The model accuracy for top 0–20 cm soil depth (R2 > 0.5, RMSE < 0.08 m3/m3) showed promise for adopting the methodology for soil moisture monitoring. The success of spiking the national model with local samples showed the need to collect multi-year high frequency (e.g., hourly) sensor-based field measurements to improve estimates of soil moisture for a longer time period. Future work should improve model performance for deeper depths with additional hydraulic properties and use of locally-selected calibration datasets.
On the blow-up results for a class of strongly perturbed semilinear heat equations

We consider in this work some class of strongly perturbed for the semilinear heat equation with Sobolev sub-critical power nonlinearity. We first derive a Lyapunov functional in similarity variables and then use it to derive the blow-up rate. We also classify all possible asymptotic behaviors of the solution when it approaches to singularity. Finally, we describe precisely the blow-up profiles corresponding to these behaviors.
Continuous mappings with null support

Let $X$ be a (topological) space and let ${\mathscr I}$ be an ideal in $X$, that is, a collection of subsets of $X$ which contains all subsets of its elements and is closed under finite unions. The elements of ${\mathscr I}$ are called null. The space $X$ is locally null if each $x$ in $X$ has a null neighborhood in $X$. Let $C_b(X)$ denote the normed algebra of all continuous bounded real-valued mappings on $X$ equipped with the supremum norm, $C_0(X)$ denote the subalgebra of $C_b(X)$ consisting of elements vanishing at infinity and $C_{00}(X)$ the subalgebra of $C_b(X)$ consisting of elements with compact support. We study the normed subalgebra $C^{\mathscr I}_{00}(X)$ of $C_b(X)$ consisting of all $f$ in $C_b(X)$ whose support has a null neighborhood in $X$, and the Banach subalgebra $C^{\mathscr I}_0(X)$ of $C_b(X)$ consisting of all $f$ in $C_b(X)$ such that $|f|^{-1}([1/n,\infty))$ has a null neighborhood in $X$ for all positive integer $n$. We prove that if $X$ is a normal locally null space then $C^{\mathscr I}_{00}(X)$ and $C^{\mathscr I}_0(X)$ are respectively isometrically isomorphic to $C_{00}(Y)$ and $C_0(Y)$ for a unique locally compact Hausdorff space $Y$; furthermore, $C^{\mathscr I}_{00}(X)$ is dense in $C^{\mathscr I}_0(X)$. We construct $Y$ explicitly as a subspace of the Stone--\v{C}ech compactification $\beta X$ of $X$. The space $Y$ is locally compact (and countably compact, in certain cases), contains $X$ densely, and in specific cases turns out to be familiar subspaces of $\beta X$. The known topological structure of $Y$ enables us to establish several commutative Gelfand--Naimark type theorems and derive results not generally expected to be deducible from the standard Gelfand theory.
A good universal weight for nonconventional ergodic averages in norm

We will show that the sequence appearing in the double recurrence theorem is a good universal weight for the Furstenberg averages. That is, given a system $(X,{\mathcal{F}},\unicode[STIX]{x1D707},T)$ and bounded functions $f_{1},f_{2}\in L^{\infty }(\unicode[STIX]{x1D707})$ , there exists a set of full-measure $X_{f_{1},f_{2}}$ in $X$ that is independent of integers $a$ and $b$ and a positive integer $k$ such that, for all $x\in X_{f_{1},f_{2}}$ , for every other measure-preserving system $(Y,{\mathcal{G}},\unicode[STIX]{x1D708},S)$ and for each bounded and measurable function $g_{1},\ldots ,g_{k}\in L^{\infty }(\unicode[STIX]{x1D708})$ , the averages $$\begin{eqnarray}\frac{1}{N}\mathop{\sum }_{n=1}^{N}f_{1}(T^{an}x)f_{2}(T^{bn}x)g_{1}\circ S^{n}g_{2}\circ S^{2n}\cdots g_{k}\circ S^{kn}\end{eqnarray}$$ converge in $L^{2}(\unicode[STIX]{x1D708})$ .
Determination of electromagnetic Bloch modes in a medium with frequency-dependent coefficients

We provide a functional framework and a numerical algorithm to compute the Bloch variety for Maxwell's equations when the electric permittivity is frequency dependent. We incorporate the idea of a mixed formulation for Maxwell's equations to obtain a quadratic eigenvalue for the wave-vector in terms of the frequency. We reformulate this problem as a larger linear eigenvalue problem and prove that this results in the need to compute eigenvalues of a compact operator. Using finite elements, we provide preliminary numerical examples of the scheme for both frequency independent and frequency dependent permittivity.
A Nonlinear Transform for the Diagonalization of the Bernoulli-Laplace Diffusion Model and Orthogonal Polynomials.

The Bernoulli-Laplace model describes a diffusion process of two types of particles between two urns. To analyze the finite-size dynamics of this process, and for other constructive results we diagonalize the corresponding transition matrix and calculate explicitly closed-form expressions for all eigenvalues and eigenvectors of the Markov transition matrix $T_{BL}$. This is done by a new method based on mapping the eigenproblem for $T_{BL}$ to the associated problem for a linear partial differential operator $L_{BL}$ acting on the vector space of homogeneous polynomials in three indeterminates. The method is applicable to other Two Urns models and is relatively easy to use compared to previous methods based on orthogonal polynomials or group representations.
Gallai-Ramsey numbers of C10 and C12

A Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles, and a Gallai k-coloring is a Gallai coloring that uses k colors. Given an integer k ≥ 1 and graphs H1, . , Hk, the Gallai-Ramsey number GR(H1, . . . , Hk) is the least integer n such that every Gallai k-coloring of the complete graph Kn contains a monochromatic copy of Hi in color i for some i ∈ {1, . , k}. When H = H1 = · · · = Hk, we simply write GRk(H). We continue to study Gallai-Ramsey numbers of even cycles and paths. For all n ≥ 3 and k ≥ 1, let Gi = P2i+3 be a path on 2i + 3 vertices for all i ∈ {0, 1, . , n − 2} and Gn−1 ∈ {C2n, P2n+1}. Let ij ∈ {0, 1, . , n−1} for all j ∈ {1, . , k} with i1 ≥ i2 ≥ · · · ≥ ik. Song recently conjectured that GR(Gi1 , . . . , Gik) = 3 + min{i1, n ∗ − 2} + ∑k j=1 ij , where n ∗ = n when Gi1 6= P2n+1 and n∗ = n + 1 when Gi1 = P2n+1. This conjecture has been verified to be true for n ∈ {3, 4} and all k ≥ 1. In this paper, we prove that the aforementioned conjecture holds for n ∈ {5, 6} and all k ≥ 1. Our result implies that for all k ≥ 1, GRk(C2n) = GRk(P2n) = (n− 1)k + n+ 1 for n ∈ {5, 6} and GRk(P2n+1) = (n− 1)k + n+ 2 for 1 ≤ n ≤ 6.
Stability for a magnetic Schr\"odinger operator on a Riemann surface with boundary

We consider a magnetic Schr\"odinger operator $(\nabla^X)^*\nabla^X+q$ on a compact Riemann surface with boundary and prove a $\log\log$-type stability estimate in terms of Cauchy data for the electric potential and magnetic field under the assumption that they satisfy appropriate a priori bounds. We also give a similar stability result for the holonomy of the connection 1-form $X$.