Miracle-dz/UniFAR-FTUs huggingface dataset:
On sign-changing solutions for (p,q)-Laplace equations with two parameters

Abstract We investigate the existence of nodal (sign-changing) solutions to the Dirichlet problem for a two-parametric family of partially homogeneous ( p , q ) {(p,q)} -Laplace equations - Δ p ⁢ u - Δ q ⁢ u = α ⁢ | u | p - 2 ⁢ u + β ⁢ | u | q - 2 ⁢ u {-\Delta_{p}u-\Delta_{q}u=\alpha\lvert u\rvert^{p-2}u+\beta\lvert u\rvert^{q-2% }u} where p ≠ q {p\neq q} . By virtue of the Nehari manifolds, the linking theorem, and descending flow, we explicitly characterize subsets of the ( α , β ) {(\alpha,\beta)} -plane which correspond to the existence of nodal solutions. In each subset the obtained solutions have prescribed signs of energy and, in some cases, exactly two nodal domains. The nonexistence of nodal solutions is also studied. Additionally, we explore several relations between eigenvalues and eigenfunctions of the p- and q-Laplacians in one dimension.
Polynomial bases: Positivity and Schur multiplication

We establish a poset structure on combinatorial bases of multivariate polynomials defined by positive expansions and study properties common to bases in this poset. Included are the well-studied bases of Schubert polynomials, Demazure characters, and Demazure atoms; the quasi-key, fundamental, and monomial slide bases introduced in 2017 by Assaf and the author; and a new basis we introduce completing this poset structure. We show the product of a Schur polynomial and that an element of a basis in this poset expands positively in that basis; in particular, we give the first Littlewood-Richardson rule for the product of a Schur polynomial and a quasi-key polynomial. This rule simultaneously extends Haglund, Luoto, Mason, and van Willigenburg’s (2011) Littlewood-Richardson rule for quasi-Schur polynomials and refines their Littlewood-Richardson rule for Demazure characters. We also establish bijections connecting combinatorial models for these polynomials including semi-skyline fillings and quasi-key tableaux.
A tighter S-type singular value inclusion set for rectangular tensors

A new S-type singular value inclusion set for rectangular tensors is given and proved to be tighter than that in [Sang C.L. , An S-type singular value inclusion set for rectangular tensors, J. Inequal. Appl. 2017: 141, 2017]. Based on this set, new bounds for the largest singular value of nonnegative rectangular tensors are obtained and proved to be better than some existing results. Compared with the results in the paper mentioned above, the advantage of the new results is that, under the same computations, we can obtain a tighter singular value inclusion set for rectangular tensors and sharper bounds for the largest singular value of nonnegative rectangular tensors. Finally, a numerical example is given to verify the theoretical results.
Self‐compassion and fear of cancer recurrence in Chinese breast cancer patients: The mediating role of maladaptive cognitive styles

Previous studies have examined the benefits of self‐compassion for psychological symptoms in breast cancer patients; however, little is known about the role of self‐compassion for patients' fear of cancer recurrence (FCR) as well as the underlying mediating mechanisms. This study aimed to examine the effect of self‐compassion on FCR, and whether maladaptive cognitive styles mediate this relationship.
Arrival times of Cox process with independent increment with application to prediction problems

Properties of arrival times are studied for a Cox process with independent (and stationary) increments. Under a reasonable setting the directing random measure is shown to take over independent (and stationary) increments of the process, from which the sets of arrival times and their numbers in disjoint intervals are proved to be independent (and stationary). Moreover, we derive the exact joint distribution of these quantities with Gamma random measure, whereas for a general random measure the method of calculation is presented. Based on the derived properties we consider prediction problems for the shot noise process with Cox process arrival times which trigger additive processes off. We obtain a numerically tractable expression for the predictor which works reasonably in view of numerical experiments.
The shape of low energy configurations of a thin elastic sheet with a single disclination

We consider a geometrically fully nonlinear variational model for thin elastic sheets that contain a single disclination. The free elastic energy contains the thickness $h$ as a small parameter. We give an improvement of a recently proved energy scaling law, removing the next-to leading order terms in the lower bound. Then we prove the convergence of (almost-)minimizers of the free elastic energy towards the shape of a radially symmetric cone, up to Euclidean motions, weakly in the spaces $W^{2,2}(B_1\setminus B_\rho;\mathbb{R}^3)$ for every $0<\rho<1$, as the thickness $h$ is sent to 0.
Support varieties: an ideal approach

We define support varieties in an axiomatic setting using the prime spectrum of a lattice of ideals. A key observation is the functoriality of the spectrum and that this functor admits an adjoint. We assign to each ideal its support and can classify ideals in terms of their support. Applications arise from studying abelian or triangulated tensor categories. Specific examples from algebraic geometry and modular representation theory are discussed, illustrating the power of this approach which is inspired by recent work of Balmer.
On the normal bundle of submanifolds of $\mathbb P^n$

Let X be a submanifold of dimension d > 2 of the complex projective space P". We prove results of the following type.i) If X is irregular and n = 2d, then the normal bundle N X|P n is indecomposable. ii) If X is irregular, d > 3 and n = 2d +1, then N X|P n is not the direct sum of two vector bundles of rank > 2. iii) If d > 3, n = 2d- 1 and N X|P n is decomposable, then the natural restriction map Pic(P n ) → Pic(X) is an isomorphism (and, in particular, if X = P d-1 x P 1 is embedded Segre in P 2d-1 , then N X|p 2d-1 is indecomposable). iv) Let n ≤ 2d and d > 3, and assume that N X|P n is a direct sum of line bundles; if n = 2d assume furthermore that X is simply connected and O x (1) is not divisible in Pic(X). Then X is a complete intersection. These results follow from Theorem 2.1 below together with Le Potier's vanishing theorem. The last statement also uses a criterion of Faltings for complete intersection. In the case when n < 2d this fact was proved by M. Schneider in 1990 in a completely different way.
Unraveling the role of relative telomere length and CAG expansion on initial symptoms of juvenile Huntington disease

Juvenile‐onset Huntington disease (JHD) is defined when symptoms initiate before 20 years of age. Mechanisms explaining differences between juvenile and adult onset are not fully understood. Our aim was to analyze the distribution of initial symptoms in a cohort of JHD patients and to explore its relationship with CAG expansion and relative telomere length (RTL).
Statistical theory on optical directional couplers with random parameters

Statistical coupling characteristics of optical directional couplers subject to random irregularities are studied theoretically by means of coupled mode theory. A new method is used for solving coupled mode equations in which random components of coupling coefficients and phase constants are assumed to be Gaussian random processes with an arbitrary correlation length. Mean values, variances, and probability distributions of coupled powers in 0-dB and 3-dB directional couplers are presented. The influence of random parameters is made clear. It is seen that tolerance requirements can be relaxed by a proper choice of the average parameters. Discussions about the film waveguide couplers for integrated optics applications are presented.
Elimination of the weak inversion hump in Si3N4/InGaAs (001) gate stacks using an in situ NH3 pre-treatment

Silicon nitride thin films were deposited by plasma enhanced chemical vapor deposition on In0.53Ga0. 47As (001) surfaces with and without NH3 pre-deposition treatments. The influence of the NH3 pre-deposition treatments on the electrical properties of the Si3N4/In0.53Ga0. 47As interface was investigated by frequency dependent capacitance-voltage and conductance-voltage measurements. A fully unpinned C-V behavior was obtained for all samples. Samples that underwent NH3 pre-deposition treatment exhibited electrical characteristics with no evidence of the midgap interface states (Dit) effects in weak inversion, which are reported in the literature on In0.53Ga0. 47As capacitors.
Implementing convection into Lorenz’s global cycle. Part II. A new estimate of the conversion rate into kinetic energy

The global conversion rates into available potential and kinetic energy (Lorenz’s quantities Gand C) have been traditionally evaluated on the gridscale (Ggrid, Cgrid≈+2.5±0.4 W/m2). Convective phenomena acting on the sub-gridscale ( like, e.g., thunderstorms) have been treatedas molecular. In Part I of this study it has been outlined how Lorenz’s energy cycle may beextended to include sub-gridscale processes. For this purpose new fluxes, particularly the globalmean conversion rate into kinetic energy on the sub-gridscale (Csub), have been defined.Evaluating them is the purpose of the present Part II. Csub is closely related to the buoyancyproduction term of turbulence kinetic energy which can be expressed through the vertical subgridscalefluxes of moisture and heat. A thermodynamic diagnostic model (DIAMOD) thatestimates these fluxes indirectly from gridscale analyses is applied. In this way the conversionrate has been calculated for three months using global reanalysis data from ECMWF and from NCEP/NCAR. The errors of our results are caused by the analysis data used, by the specificationof the ratio between moisture and heat fluxes (the main closure assumption in DIAMOD)and by uncertainties in the radiative heating field; they are given here at the 95% level.We find Csub=+2.2±1.7W/m2. The new complete conversion rate C=Cgrid+Csub is+4.7±2.0W/m2. This figure is the main result of this study, presented here for the first time:Lorenz’s energy cycle, if extended to the sub-gridscale, is about twice as intense as in thetraditional approximations. In contrast to Csub the sub-gridscale generation rate Gsub and therefore the complete G cannot be evaluated. All one can do is to improve the estimate of Ggrid by improving the estimates of the net heating. For Ggrid we find the new value of +3.1±0.5W/m2.
The hybrid spectral test

The starting point of this paper is the interplay between the construction principle of a sequence and the characters of the compact abelian group that underlies the construction. In case of the Halton sequence in base $\mathbf b=(b_1, \ldots, b_s)$ in the $s$-dimensional unit cube $[0,1)^s$, which is an important type of a digital sequence, this kind of duality principle leads to the so-called $\mathbf b$-adic function system and provides the basis for the $\mathbf b$-adic method, which we present in connection with hybrid sequences. This method employs structural properties of the compact group of $\mathbf b$-adic integers as well as $\mathbf b$-adic arithmetic to derive tools for the analysis of the uniform distribution of sequences in $[0,1)^s$. We first clarify the point which function systems are needed to analyze digital sequences. Then, we present the hybrid spectral test in terms of trigonometric-, Walsh-, and $\mathbf b$-adic functions. Various notions of diaphony as well as many figures of merit for rank-1 quadrature rules in Quasi-Monte Carlo integration and for certain linear types of pseudo-random number generators are included in this measure of uniform distribution. Further, discrepancy may be approximated arbitrarily close by suitable versions of the spectral test.
A moment-generating formula for Erdős-Rényi component sizes

We derive a simple formula characterizing the distribution of the size of the connected component of a fixed vertex in the Erdős-Renyi random graph which allows us to give elementary proofs of some results of Federico, van der Hofstad, den Hollander and Hulshof as well as Janson and Luczak about the susceptibility in the subcritical graph and the central limit theorem of Pittel for the size of the giant component in the supercritical graph.
Online Advance Admission Scheduling for Services with Customer Preferences.

We study web and mobile applications that are used to schedule advance service, from medical appointments to restaurant reservations. We model them as online weighted bipartite matching problems with non-stationary arrivals. We propose new algorithms with performance guarantees for this class of problems. Specifically, we show that the expected performance of our algorithms is bounded below by $1-\sqrt{\frac{2}{\pi}}\frac{1}{\sqrt{k}}+O(\frac{1}{k})$ times that of an optimal offline algorithm, which knows all future information upfront, where $k$ is the minimum capacity of a resource. This is the tightest known lower bound. This performance analysis holds for any Poisson arrival process. Our algorithms can also be applied to a number of related problems, including display ad allocation problems and revenue management problems for opaque products. We test the empirical performance of our algorithms against several well-known heuristics by using appointment scheduling data from a major academic hospital system in New York City. The results show that the algorithms exhibit the best performance among all the tested policies. In particular, our algorithms are $21\%$ more effective than the actual scheduling strategy used in the hospital system according to our performance metric.
Change in coronary heart disease hospitalization after chronic disease management: a programme policy in China

Abstract This study aims at examining changes in coronary heart disease (CHD) hospitalization associated with a novel county-scale chronic disease management (CDM) programme policy implemented in March 2019 in China during the 13th Five-Year period (2016–2020). The CDM programme was designed to improve the health of populations with chronic diseases by means of an integrated way involving both county-level public hospitals and primary care institutes. Data originated from the medical files of CHD inpatients discharged from a secondary hospital from January 2017 to December 2020. A total of 6111 CHD patient records were collected. Univariate and multivariate regression analyses were performed to assess changes in hospitalization direct medical costs and length of stay of CHD patients. The mean direct medical cost of CHD hospitalization was 8419.73 Yuan, and the mean length of stay was 7.57 days. Results suggested that the implementation of CDM reduced hospitalization direct medical cost and bed days by about 23% (1956.12 Yuan at means) and 11.5% (almost 1 day at means), respectively. In addition, a further decreasing trend in medical costs over time was associated with chronic disease management. It is implied that chronic disease management is an effective way of relieving the medical and financial burden of hospitalization.
Effects of ischemic postconditioning and long non-coding RNAs in ischemic stroke

ABSTRACT Stroke is a main cause of disability and death among adults in China, and acute ischemic stroke accounts for 80% of cases. The key to ischemic stroke treatment is to recanalize the blocked blood vessels. However, more than 90% of patients cannot receive effective treatment within an appropriate time, and delayed recanalization of blood vessels causes reperfusion injury. Recent research has revealed that ischemic postconditioning has a neuroprotective effect on the brain, but the mechanism has not been fully clarified. Long non-coding RNAs (lncRNAs) have previously been associated with ischemic reperfusion injury in ischemic stroke. LncRNAs regulate important cellular and molecular events through a variety of mechanisms, but a comprehensive analysis of potential lncRNAs involved in the brain protection produced by ischemic postconditioning has not been conducted. In this review, we summarize the common mechanisms of cerebral injury in ischemic stroke and the effect of ischemic postconditioning, and we describe the potential mechanisms of some lncRNAs associated with ischemic stroke. Graphical abstract
Magnetic transport in a straight parabolic channel

We study a charged two-dimensional particle conﬁned to a straight parabolic-potential channel and exposed to a homogeneous magnetic ﬁeld under inﬂuence of a potential perturbation W . If W is bounded and periodic along the channel, a perturbative argument yields the absolute continuity of the bottom of the spectrum. We show it can have any ﬁnite number of open gaps provided the conﬁning potential is suf-ﬁciently strong. However, if W depends on the periodic variable only, we prove by Thomas argument that the whole spectrum is absolutely continuous, irrespectively of the size of the perturbation. On the other hand, if W is small and satisﬁes a weak localization condition in the the longitudinal direction, we prove by Mourre method that a part of the absolutely continuous spectrum persists.
The nodal line of the second eigenfunction of the Robin Laplacian in $\mathbb{R}^2$ can be closed

We construct a multiply connected domain in $\mathbb{R}^2$ for which the second eigenfunction of the Laplacian with Robin boundary conditions has an interior nodal line. In the process, we adapt a bound of Donnelly-Fefferman type to obtain a uniform estimate on the size of the nodal sets of a sequence of solutions to a certain class of elliptic equations in the interior of a sequence of domains, which does not depend directly on any boundary behaviour. This also gives a new proof of the nodal line property of the example in the Dirichlet case.
Sentiment Analysis of Insomnia-Related Tweets via a Combination of Transformers Using Dempster-Shafer Theory: Pre– and Peri–COVID-19 Pandemic Retrospective Study

Background The COVID-19 pandemic has imposed additional stress on population health that may result in a change of sleeping behavior. Objective In this study, we hypothesized that using natural language processing to explore social media would help with assessing the mental health conditions of people experiencing insomnia after the outbreak of COVID-19. Methods We designed a retrospective study that used public social media content from Twitter. We categorized insomnia-related tweets based on time, using the following two intervals: the prepandemic (January 1, 2019, to January 1, 2020) and peripandemic (January 1, 2020, to January 1, 2021) intervals. We performed a sentiment analysis by using pretrained transformers in conjunction with Dempster-Shafer theory (DST) to classify the polarity of emotions as positive, negative, and neutral. We validated the proposed pipeline on 300 annotated tweets. Additionally, we performed a temporal analysis to examine the effect of time on Twitter users’ insomnia experiences, using logistic regression. Results We extracted 305,321 tweets containing the word insomnia (prepandemic tweets: n=139,561; peripandemic tweets: n=165,760). The best combination of pretrained transformers (combined via DST) yielded 84% accuracy. By using this pipeline, we found that the odds of posting negative tweets (odds ratio [OR] 1.39, 95% CI 1.37-1.41; P<.001) were higher in the peripandemic interval compared to those in the prepandemic interval. The likelihood of posting negative tweets after midnight was 21% higher than that before midnight (OR 1.21, 95% CI 1.19-1.23; P<.001). In the prepandemic interval, while the odds of posting negative tweets were 2% higher after midnight compared to those before midnight (OR 1.02, 95% CI 1.00-1.07; P=.008), they were 43% higher (OR 1.43, 95% CI 1.40-1.46; P<.001) in the peripandemic interval. Conclusions The proposed novel sentiment analysis pipeline, which combines pretrained transformers via DST, is capable of classifying the emotions and sentiments of insomnia-related tweets. Twitter users shared more negative tweets about insomnia in the peripandemic interval than in the prepandemic interval. Future studies using a natural language processing framework could assess tweets about other types of psychological distress, habit changes, weight gain resulting from inactivity, and the effect of viral infection on sleep.
Changes in microvascular perfusion of heart and skeletal muscle in sheep around the time of birth

What is the central question of this study? How does the microvascular perfusion of striated muscle change during the dynamic developmental period between the late gestation fetus and early neonate? What is the main finding and its importance? In both myocardium and skeletal muscle, perfusion of striated muscle is significantly reduced in the neonate compared to the late term fetus, but flow reserve is unchanged. The results suggest striated muscle capillary networks grow more slowly relative to the myofibres they nourish during the perinatal period.
A multivalent nucleoside-modified mRNA vaccine against all known influenza virus subtypes

Seasonal influenza vaccines offer little protection against pandemic influenza virus strains. It is difficult to create effective prepandemic vaccines because it is uncertain which influenza virus subtype will cause the next pandemic. In this work, we developed a nucleoside-modified messenger RNA (mRNA)–lipid nanoparticle vaccine encoding hemagglutinin antigens from all 20 known influenza A virus subtypes and influenza B virus lineages. This multivalent vaccine elicited high levels of cross-reactive and subtype-specific antibodies in mice and ferrets that reacted to all 20 encoded antigens. Vaccination protected mice and ferrets challenged with matched and mismatched viral strains, and this protection was at least partially dependent on antibodies. Our studies indicate that mRNA vaccines can provide protection against antigenically variable viruses by simultaneously inducing antibodies against multiple antigens. Description A cornucopia of antigens Vaccines serve as an indispensable tool for the control and prevention of influenza, but several challenges remain. Some populations, for example, the elderly, respond poorly to vaccination. Furthermore, the highly variable nature of influenza viruses can make targeting optimal antigens difficult. Broadly neutralizing antibodies have been proposed as a solution to such disadvantages, but they present their own pitfalls, including limited cross-reactivity to both influenza A and B strains and the need for repeated injections during flu season. Arevalo et al. developed a nucleoside-modified messenger RNA-lipid nanoparticle vaccine encoding hemagglutinin antigens from all 20 known influenza A and B virus subtypes (see the Perspective by Kelvin and Falzarano). Such vaccines may provide protection against antigenically variable viruses by simultaneously inducing antibodies against multiple antigens. —STS mRNA vaccines expressing antigens from all known influenza subtypes elicit protective responses in mice and ferrets.
Critical Percolation Probabilities for the Next-Nearest-Neighbouring Site Problems on Sierpinski Carpets

In this paper, we compute the next-nearest-neighbouring site percolation (Connections exist not only between nearest-neighbouring sites, but also between next-nearest-neighbouring sites.) probabilities on the two-dimensional Sierpinski carpets, using the translational-dilation method and Monte Carlo technique. We obtain a relation among , fractal dimensionality and connectivity . For the family of carpets with central cutouts, , where , the critical percolation probability for the next-nearest-neighbouring site problem on square lattice. As reaches , which is in agreement with the critical percolation probability on square lattices with next-nearest-neighbouring interactions.