Miracle-dz/UniFAR-FTUs huggingface dataset:
A General Fractional Porous Medium Equation

We develop a theory of existence and uniqueness for the following porous medium equation with fractional diffusion: \input amssym $$\left\{ {\matrix{ {{{\partial u} \over {\partial t}} + \left( { ‐ \Delta } \right)^{\sigma /2} \left( {\left| u \right|^{m ‐ 1} u} \right) = 0,} \hfill & {x \in {\Bbb R} ^N ,\,\,t > 0,} \hfill \cr {u\left( {x,0} \right) = f\left( x \right),} \hfill & {x \in {\Bbb R} ^N . } \hfill \cr } } \right. $$ We consider data \input amssym $f\in L^1(\Bbb{R}^N)$ and all exponents $0<\sigma<2\;and\;m>0$. Existence and uniqueness of a strong solution is established for $ m > {m_\ast}={(N-\sigma)_+}/N$, giving rise to an L1‐contraction semigroup. In addition, we obtain the main qualitative properties of these solutions. In the lower range ${0 < m} \le {m_\ast}$ existence and uniqueness happen under some restrictions, and the properties of the solutions are different from the ones for the case above m*. We also study the dependence of solutions on f, m, and σ. Moreover, we consider the above questions for the problem posed in a bounded domain. © 2012 Wiley Periodicals, Inc.
Severe Covid‐19 and acute pulmonary hypertension: 24‐month follow‐up regarding mortality and relationship to initial echocardiographic findings and biomarkers

Critically ill Covid‐19 patients are likely to develop the sequence of acute pulmonary hypertension (aPH), right ventricular strain, and eventually right ventricular failure due to currently known pathophysiology (endothelial inflammation plus thrombo‐embolism) that promotes increased pulmonary vascular resistance and pulmonary artery pressure. Furthermore, an in‐hospital trans‐thoracic echocardiography (TTE) diagnosis of aPH is associated with a substantially increased risk of early mortality. The aim of this retrospective observational follow‐up study was to explore the mortality during the 1–24‐month period following the TTE diagnosis of aPH in the intensive care unit (ICU).
Control efficacy and joint toxicity of metaflumizone mixed with chlorantraniliprole or indoxacarb against the fall armyworm, Spodoptera frugiperda.

BACKGROUND The fall armyworm (FAW), Spodoptera frugiperda is the main destructive pest of grain crops, and has led to substantial economic losses worldwide. Chemical pesticides are the most effective way to manage FAW. Here, a lab test using an artificial diet-incorporated assay was conducted to determine the toxicity of five insecticides and the joint effect of the binary combination insecticides to FAW larvae. The field plot test using foliar spray was carried out to assess the control efficacy of metaflumizone mixed with chlorantraniliprole or indoxacarb against FAW. RESULTS The bioassay results showed that metaflumizone had a stronger insecticidal effect than indoxacarb toward FAW larvae. Furthermore, the mixture of metaflumizone and chlorantraniliprole in a volume ratio of 3:7 had the strongest synergistic effect against FAW, with a co-toxicity coefficient (CTC) of 317.18. While the best synergistic effect for mixtures of metaflumizone and indoxacarb was observed at a 1:9 volume ratio, with a CTC of 185.98. However, there was an antagonistic effect of metaflumizone mixed with emamectin benzoate or lufenuron, since the co-toxic factor was less than -20 at volume ratios of 8:2 and 9:1, respectively. According to the results of the field trial, metaflumizone mixed with chlorantraniliprole or indoxacarb at a 50% reduction of the application rate can effectively control FAW with efficacy ranging from 77.73 to 94.65% during 1-7 days after application. CONCLUSION Overall, our findings suggest that metaflumizone and its binary combination insecticides can be utilized in the FAW integrated management program. This article is protected by copyright. All rights reserved.
A generalised multicomponent system of Camassa-Holm-Novikov equations

In this paper we introduce a two-component system, depending on a parameter $b$, which generalises the Camassa-Holm ($b=1$) and Novikov equations ($b=2$). By investigating its Lie algebra of classical and higher symmetries up to order $3$, we found that for $b\neq 2$ the system admits a $3$-dimensional algebra of point symmetries and apparently no higher symmetries, whereas for $b=2$ it has a $6$-dimensional algebra of point symmetries and also higher order symmetries. Also we provide all conservation laws, with first order characteristics, which are admitted by the system for $b=1,2$. In addition, for $b=2$, we show that the system is a particular instance of a more general system which admits an $\mathfrak{sl}(3,\mathbb{R})$-valued zero-curvature representation. Finally, we found that the system admits peakon solutions and, in particular, for $b=2$ there exist 1-peakon solutions with non-constant amplitude.
$L^0$-regularized Variational Methods for Sparse Phase Retrieval

We study the problem of recovering the underlining sparse signals from clean or noisy phaseless measurements. Due to the sparse prior of signals, we adopt an L0regularized variational model to ensure only a small number of nonzero elements being recovered in the signal and two different formulations are established in the modeling based on the choices of data fidelity, i.e., L2and L1norms. We also propose efficient algorithms based on the Alternating Direction Method of Multipliers (ADMM) with convergence guarantee and nearly optimal computational complexity. Thanks to the existence of closed-form solutions to all subproblems, the proposed algorithm is very efficient with low computational cost in each iteration. Numerous experiments show that our proposed methods can recover sparse signals from phaseless measurements with higher successful recovery rates and lower computation cost compared with the state-of-art methods.
Sticky couplings of multidimensional diffusions with different drifts

We present a novel approach of coupling two multidimensional and non-degenerate It\^o processes $(X_t)$ and $(Y_t)$ which follow dynamics with different drifts. Our coupling is sticky in the sense that there is a stochastic process $(r_t)$, which solves a one-dimensional stochastic differential equation with a sticky boundary behavior at zero, such that almost surely $|X_t-Y_t|\leq r_t$ for all $t\geq 0$. The coupling is constructed as a weak limit of Markovian couplings. We provide explicit, non-asymptotic and long-time stable bounds for the probability of the event $\{X_t=Y_t\}$.
A Finite-Element Coarse-Grid Projection Method: A Dual Acceleration/Mesh Refinement Tool for Incompressible Flows

Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic Poisson equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping operators execute data transfer between the grids. The CGP framework is constructed upon spatial and temporal discretization schemes. This framework has been established for finite volume/difference discretizations as well as explicit time integration methods. In this article we present for the first time a version of CGP for finite element discretizations, which uses a semi-implicit time integration scheme. The mapping functions correspond to the finite-element shape functions. With the novel data structure introduced, the mapping computational cost becomes insignificant. We apply CGP to pressure-correction schemes used for the incompressible Navier-Stokes flow computations. This version is validated on standard test cases with realistic boundary conditions using unstructured triangular meshes. We also pioneer investigations of the effects of CGP on the accuracy of the pressure field. It is found that although CGP reduces the pressure field accuracy, it preserves the accuracy of the pressure gradient and thus the velocity field, while achieving speedup factors ranging from approximately 2 to 30. Exploring the influence of boundary conditions on CGP, the minimum speedup occurs for velocity Dirichlet boundary conditions, while the maximum speedup occurs for open boundary conditions. We discuss the CGP method as a guide for partial mesh refinement of incompressible flow computations and show its application for simulations of flow over a backward-facing step and flow past a cylinder.
Weights, raising and lowering operators, and K-types for automorphic forms on SL(3,R)

We give a fully explicit description of Lie algebra derivatives (generalizing raising and lowering operators) for representations of SL(3,R) in terms of a basis of Wigner functions. This basis is natural from the point of view of principal series representations, as well as computations in the analytic theory of automorphic forms (e.g., with Whittaker functions). The method is based on the Clebsch-Gordan multiplication rule for Wigner functions, and applies to other Lie groups whose maximal compact subgroup is isogenous to a product of SU(2) and U(1) factors. As an application, we give a complete and explicit description of the K-type structure of certain cohomological representations.
Airway Phenotypes and Nocturnal Wearing of Dentures in Elders with Sleep Apnea

The objective of this study was to examine to what extent the anatomic characteristics of the upper airway can influence the effect of nocturnal wearing of dentures on the sleep of edentulous elders with untreated sleep apnea. This study used the data from a randomized crossover clinical trial and an exploratory approach to address its objectives. Cone beam computed tomography scans of 65 edentulous individuals (female, n = 37; male, n = 28; mean ± SD age, 74.54 ± 6.42 y) with untreated obstructive sleep apnea (OSA) were used to identify anatomic variables. Polysomnography data were collected by means of one portable overnight recording. The respiratory variable values, including apnea–hypopnea index (AHI), with and without denture worn during sleep were used to calculate the change. Statistical analyses included multiple linear regressions, cluster analysis, and binary logistic regressions. A receiver operator characteristic curve was used to illustrate the accuracy of the statistical model. The regression model explained 15.8% (R2) of AHI change. An increase in the lateral dimension of the minimum cross-sectional area was associated with a decrease in AHI, oxygen desaturation index, and respiratory arousal index changes (P ≤ 0.041). Furthermore, an increase in the length of the hypopharynx was associated with an increase in AHI and oxygen desaturation index changes (P ≤ 0.027). An increase in the lateral dimension of the minimum cross-sectional area of the upper airway was associated with a decreased likelihood of being in the group having a worsened AHI (odds ratio = 0.85; 95% CI, 0.76 to 0.95; P = 0.006). An increase in the length of the oropharynx was associated with an increased likelihood of having increased AHI (odds ratio = 1.10; 95% CI, 1.01 to 1.20; P = 0.026). The nocturnal aggravation of respiratory variables in edentulous individuals with OSA who wear dentures at night can be linked to certain anatomic characteristics of the upper airway. Replication of these findings may open novel avenues for personalized advice regarding nocturnal wearing of dentures in edentulous individuals with OSA (ClinicalTrials.gov: NCT01868295).
A Lift of the Schur and Hall–Littlewood Bases to Non-commutative Symmetric Functions

Abstract We introduce a new basis of the algebra of non-commutative symmetric functions whose images under the forgetful map are Schur functions when indexed by a partition. Dually, we build a basis of the quasi-symmetric functions that expand positively in the fundamental quasi-symmetric functions. We then use the basis to construct a non-commutative lift of the Hall–Littlewood symmetric functions with similar properties to their commutative counterparts.
Meander knots and links

We introduced concept of meander knots, 2-component meander links and multi-component meander links and derived different families of meander knots and links from open meanders with $n\le 16$ crossings. We also defined semi-meander knots (or knots with ordered Gauss code) and their product.
Smooth invariant densities for random switching on the torus

We consider a random dynamical system obtained by switching between the flows generated by two smooth vector fields on the 2d-torus, with the random switchings happening according to a Poisson process. Assuming that the driving vector fields are transversal to each other at all points of the torus and that each of them allows for a smooth invariant density and no periodic orbits, we prove that the switched system also has a smooth invariant density, for every switching rate. Our approach is based on an integration by parts formula inspired by techniques from Malliavin calculus.
Necessary and sufficient conditions for a nonnegative matrix to be strongly R-positive

Using the Perron-Frobenius eigenfunction and eigenvalue, each finite irreducible nonnegative matrix $A$ can be transformed into a probability kernel $P$. This was generalized by David Vere-Jones who gave necessary and sufficient conditions for a countably infinite irreducible nonnegative matrix $A$ to be transformable into a recurrent probability kernel $P$, and showed uniqueness of $P$. Such $A$ are called R-recurrent. Let us say that $A$ is strongly R-positive if the return times of the Markov chain with kernel $P$ have exponential moments of some positive order. Then we prove that strong R-positivity is equivalent to the property that lowering the value of finitely many entries of $A$ lowers the spectral radius. This condition is more robust than the condition of Vere-Jones and can often be checked even in cases where the spectral radius is not known explicitly. We also prove a complementary characterization of R-transience.
A generalization of Wigner’s unitary–antiunitary theorem to Hilbert modules

Let H be a Hilbert C*-module over a matrix algebra A. It is proved that any function T:H→H which preserves the absolute value of the (generalized) inner product is of the form Tf=φ(f )Uf (f∈H), where φ is a phase-function and U is an A-linear isometry. The result gives a natural extension of Wigner’s classical unitary–antiunitary theorem for Hilbert modules.
Inequalities for Zero-Balanced Gaussian hypergeometric function

In this paper, we consider the monotonicity of certain combinations of the Gaussian hypergeometric functions $F(a-1,b;a+b;1-x^c)$ and $F(a-1-\delta,b+\delta;a+b;1-x^d)$ on $(0,1)$ for $\delta\in(a-1,0)$, and study the problem of comparing these two functions, thus get the largest value $\delta_1=\delta_1(a,c,d)$ such that the inequality $F(a-1,b;a+b;1-x^c)<F(a-1-\delta,b+\delta;a+b;1-x^d)$ holds for all $x\in (0,1)$.
An explicit Baker-type lower bound of exponential values

Let 𝕀 denote an imaginary quadratic field or the field ℚ of rational numbers and let ℤ𝕀 denote its ring of integers. We shall prove a new explicit Baker-type lower bound for a ℤ𝕀-linear form in the numbers 1, eα1 , . , eαm, m ⩾ 2, where α0 = 0, α1, . , αm are m + 1 different numbers from the field 𝕀. Our work gives substantial improvements on the existing explicit versions of Baker’s work about exponential values at rational points. In particular, dependencies on m are improved.
Nightmare distress is related to traumatic childhood experiences, critical life events and emotional appraisal of a dream rather than to its content

Nightmares are a substantial burden for sleep quality. Previous studies have shown that traumatic experiences can increase the probability of nightmares, and also waking‐life distress can enhance this effect. There is evidence that the intensity of negative dream emotions is more responsible for rating a dream as a nightmare than threatening dream contents. However, there is still a lack of research concerning effects on nightmare distress. We hypothesise that traumatic childhood experiences (such as emotional abuse, obtained by the Childhood Trauma Questionnaire), critical life events (obtained by the Social Readjustment Rating Scale) and threatening dream contents are associated with nightmare distress. A sample of N = 103 participants kept a dream diary over 28 consecutive days. About 60% of the sample were frequent nightmare dreamers. The participants recorded their violent dream contents and dream emotions in their diary. To predict nightmare distress, regression models were constructed; nightmare distress was measured with the Nightmare Distress Questionnaire. Results showed that emotional abuse in childhood and critical life events predicted nightmare distress. Moreover, violent dream contents were associated with nightmare distress but, after we controlled for nightmare frequency and the intensity of negative dream emotions, the significant impact of violent dream contents decreased. The results suggest that the emotional appraisal of a dream has a substantial influence on nightmares in addition to traumatic childhood experiences and critical life events.
Disease specific and nonspecific metabolic brain networks in behavioral variant of frontotemporal dementia

Behavioral variant of frontotemporal dementia (bvFTD) is common among young‐onset dementia patients. While bvFTD‐specific multivariate metabolic brain pattern (bFDRP) has been identified previously, little is known about its temporal evolution, internal structure, effect of atrophy, and its relationship with nonspecific resting‐state networks such as default mode network (DMN). In this multicenter study, we explored FDG‐PET brain scans of 111 bvFTD, 26 Alzheimer's disease, 16 Creutzfeldt‐Jakob's disease, 24 semantic variant primary progressive aphasia (PPA), 18 nonfluent variant PPA and 77 healthy control subjects (HC) from Slovenia, USA, and Germany. bFDRP was identified in a cohort of 20 bvFTD patients and age‐matched HC using scaled subprofile model/principle component analysis and validated in three independent cohorts. It was characterized by hypometabolism in frontal cortex, insula, anterior/middle cingulate, caudate, thalamus, and temporal poles. Its expression in bvFTD patients was significantly higher compared to HC and other dementia syndromes (p < .0004), correlated with cognitive decline (p = .0001), and increased over time in longitudinal cohort (p = .0007). Analysis of internal network organization by graph‐theory methods revealed prominent network disruption in bvFTD patients. We have further found a specific atrophy‐related pattern grossly corresponding to bFDRP; however, its contribution to the metabolic pattern was minimal. Finally, despite the overlap between bFDRP and FDG‐PET‐derived DMN, we demonstrated a predominant role of the specific bFDRP. Taken together, we validated the bFDRP network as a diagnostic/prognostic biomarker specific for bvFTD, provided a unique insight into its highly reproducible internal structure, and proved that bFDRP is unaffected by structural atrophy and independent of normal resting state networks loss.
GENERALIZED FRACTIONAL INTEGRALS AND THEIR COMMUTATORS OVER NON-HOMOGENEOUS METRIC MEASURE SPACES

Let $({\mathcal X},d,\mu)$ be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions. In this paper, the authors establish some equivalent characterizations for the boundedness of fractional integrals over $({\mathcal X},d,\mu)$. The authors also prove that multilinear commutators of fractional integrals with RBMO(μ) functions are bounded on Orlicz spaces over $({\mathcal X},d,\mu)$, which include Lebesgue spaces as special cases. The weak type endpoint estimates for multilinear commutators of fractional integrals with functions in the Orlicz-type space ${\mathrm{Osc}_{\exp L^r}(\mu)}$, where $r\in [1,\infty)$, are also presented. Finally, all these results are applied to a specific example of fractional integrals over non-homogeneous metric measure spaces.
The moduli space of complex Lagrangian submanifolds

Following an earlier paper on the differential-geometric structure of the moduli space of special Lagrangian submanifolds in a Calabi-Yau manifold, we follow an analogous approach for compact complex Lagrangian submanifolds of a (K\"ahlerian) complex symplectic manifold. The natural geometric structure on the moduli space is a special K\"ahler metric, but we offer a different point of view on the local differential geometry of these, based on the structure of a submanifold of $V\times V$ (where $V$ is a symplectic vector space) which is Lagrangian with respect to two constant symplectic forms. As an application, we show using this point of view how the hyperk\"ahler metric of Cecotti, Ferrara and Girardello associated to a special K\"ahler structure fits into the Legendre transform construction of Lindstr\"om and Ro\v cek.
Parents' knowledge, attitude and practice towards seasonal influenza vaccination in Riyadh region, Saudi Arabia.

INTRODUCTION Parents' knowledge and attitudes regarding influenza vaccine significantly determine whether or not their children will receive the vaccine. The objective of the present study was to evaluate the knowledge, attitude and practice among Saudi parents towards vaccinating their children against influenza. METHODOLOGY A descriptive cross-sectional study was conducted in multiple regions of Riyadh. We used a convenience sampling technique to enroll study subjects. Individuals who were Saudi nationals, with at least one child between 6 months and 14 years of age were included. RESULTS Over half of the Saudi parents (53.8%) scored well on influenza and vaccine knowledge, while most of them (92.0%) showed positive attitude towards vaccination. Most of the children (87.9%) were immunized with national vaccination program and 63.6% of the parents were aware of the availability of seasonal influenza vaccines in primary healthcare centres (PHCs) and hospitals. However, only 28% of the parents and 18% of their children received the seasonal influenza vaccine between 2019 and 2020. High education level, high monthly household income and being part of a medical profession were statistically significant (p < 0.05) determinants of good knowledge. Similarly, male gender, younger parent, low monthly income, working in a medical profession and parents with one child aged between 6 months and 14 years were significant predictors (p < 0.05) of positive attitude. CONCLUSIONS Compliance of Saudi parents towards influenza vaccination is fairly poor despite positive attitude. Stringent efforts are needed to encourage the parents to actively ensure annual influenza immunization of their children.
Nica-Toeplitz algebras associated with right tensor $C^*$-precategories over right LCM semigroups: Part I Uniqueness results

We introduce and analyze the full $\mathcal{NT}_{\mathcal{L}}(\mathcal{K})$ and the reduced $\mathcal{NT}_{\mathcal{L}}^r(\mathcal{K})$ Nica-Toeplitz algebra associated to an ideal $\mathcal{K}$ in a right tensor $C^*$-precategory $\mathcal{L}$ over a right LCM semigroup $P$. Our main results are uniqueness theorems in the spirit of classical Coburn's theorem, generalizing uniqueness results for Toeplitz-type $C^*$-algebras associated to single $C^*$-correspondences, quasi-lattice ordered semigroups, and crossed products twisted by product systems of $C^*$-correspondences obtained by Fowler, Laca and Raeburn. We formulate geometric conditions on a representation $\Phi$ of $\mathcal{K}$ so that the $C^*$-algebra it generates, $C^*(\Phi(\mathcal{K}))$, naturally lies between $\mathcal{NT}_{\mathcal{L}}^r(\mathcal{K})$ and $\mathcal{NT}_{\mathcal{L}}(\mathcal{K})$. Under suitable amenability hypotheses, $C^*(\Phi(\mathcal{K}))$ and $\mathcal{NT}_{\mathcal{L}}(\mathcal{K})$ are isomorphic. The geometric conditions are necessary for our uniqueness result when the right tensoring preserves $\mathcal{K}$ and in general they capture uniqueness of the $C^*$-algebra generated by a natural extension of $\Phi$ to $\mathcal{L}$. In particular, the latter algebra could be viewed as a Doplicher-Roberts version of $\mathcal{NT}_{\mathcal{L}}(\mathcal{K})$.