Miracle-dz/UniFAR-FTUs huggingface dataset:
Tight small Seifert fibered manifolds with
e0= −2

In this paper we provide the classification of tight contact structures on some small Seifert fibered manifolds. As an application of this classification, combined with work of Lekili in \cite{L2010}, we obtain infinitely many counterexamples to a question of Honda-Kazez-Mati\'{c} that asks whether a right-veering, non-destabilizable open book necessarily supports a tight contact structure.
Julia and escaping set spiders' webs of positive area

We study the dynamics of a collection of families of transcendental entire functions which generalises the well-known exponential and cosine families. We show that for functions in many of these families the Julia set, the escaping set and the fast escaping set are all spiders' webs of positive area. This result is unusual in that most of these functions lie outside the Eremenko-Lyubich class Β. This is also the first result on the area of a spider's web.
Bipartite fluctuations as a probe of many-body entanglement

We investigate in detail the behavior of the bipartite fluctuations of particle number $\hat{N}$ and spin $\hat{S}^z$ in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the R\'{e}nyi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the R\'{e}nyi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.
SOLUTIONS TO POLYNOMIAL CONGRUENCES IN WELL-SHAPED SETS

Abstract We use a generalisation of Vinogradov’s mean value theorem of Parsell et al. [‘Near-optimal mean value estimates for multidimensional Weyl sums’, arXiv:1205.6331] and ideas of Schmidt [‘Irregularities of distribution. IX’, Acta Arith. 27 (1975), 385–396] to give nontrivial bounds for the number of solutions to polynomial congruences, when the solutions lie in a very general class of sets, including all convex sets.
Cluster algebras and symmetric matrices

In this paper, we show that, for skew-symmetric cluster algebras, the c-vectors of any seed with respect to an acyclic initial seed define a quasi-Cartan companion of the corresponding exchange matrix. As an application, we show that any cluster tilted quiver has an admissible cut of edges.
Generalized oscillatory integrals and Fourier integral operators

Abstract In this paper, a theory is developed of generalized oscillatory integrals (OIs) whose phase functions and amplitudes may be generalized functions of Colombeau type. Based on this, generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is motivated by the need for a general framework for partial differential operators with non-smooth coefficients and distribution dataffi The mapping properties of these FIOs are studied, as is microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wavefront sets.
Normal forms of Hopf-zero singularity

The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative–nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov–Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov–Takens singularities. Despite this, the normal form computations of Bogdanov–Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative–nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto–Sivashinsky equations to demonstrate the applicability of our results.
Low-mass neutron stars: universal relations, the nuclear symmetry energy and gravitational radiation

The lowest neutron star masses currently measured are in the range $1.0-1.1~M_\odot$, but these measurement have either large uncertainties or refer to isolated neutron stars. The recent claim of a precisely measured mass $M/M_{\odot} = 1.174 \pm 0.004$ by Martinez et al [Astrophys. J. 812, 143 (2015)] in a double neutron star system suggests that low-mass neutron stars may be an interesting target for gravitational-wave detectors. Furthermore, Sotani et al [PTEP 2014, 051E01 (2014)] recently found empirical formulas relating the mass and surface redshift of nonrotating neutron stars to the star's central density and to the parameter $\eta\equiv (K_0 L^2)^{1/3}$, where $K_0$ is the incompressibility of symmetric nuclear matter and $L$ is the slope of the symmetry energy at saturation density. Motivated by these considerations, we extend the work by Sotani et al to slowly rotating and tidally deformed neutron stars. We compute the moment of inertia, quadrupole moment, quadrupole ellipticity, tidal and rotational Love number and apsidal constant of slowly rotating neutron stars by integrating the Hartle-Thorne equations at second order in rotation, and we fit all of these quantities as functions of $\eta$ and of the central density. These fits may be used to constrain $\eta$, either via observations of binary pulsars in the electromagnetic spectrum, or via near-future observations of inspiralling compact binaries in the gravitational-wave spectrum.
Continuous Breuer–Major theorem: Tightness and nonstationarity

Let $Y=(Y(t))_{t\geq0}$ be a zero-mean Gaussian stationary process with covariance function $\rho:\mathbb{R}\to\mathbb{R}$ satisfying $\rho(0)=1$. Let $f:\mathbb{R}\to\mathbb{R}$ be a square-integrable function with respect to the standard Gaussian measure, and suppose the Hermite rank of $f$ is $d\geq 1$. If $\int_\mathbb{R} |\rho(s)|^dds<\infty$, then the celebrated Breuer-Major theorem (in its continuous version) asserts that the finite-dimensional distributions of $Z_\varepsilon:=\sqrt{\varepsilon}\int_0^{\cdot/\varepsilon}f(Y(s))ds$ converge to those of $\sigma W$ as $\varepsilon\to 0$, where $W$ is a standard Brownian motion and $\sigma$ is some explicit constant. Since its first appearance in 1983, this theorem has become a crucial probabilistic tool in different areas, for instance in signal processing or in statistical inference for fractional Gaussian processes. The goal of this paper is twofold. Firstly, we investigate the tightness in the Breuer-Major theorem. Surprisingly, this problem did not receive a lot of attention until now, and the best available condition due to Ben Hariz [1] is neither arguably very natural, nor easy-to-check in practice. In contrast, our condition very simple, as it only requires that $|f|^p$ must be integrable with respect to the standard Gaussian measure for some $p$ strictly bigger than 2. It is obtained by means of the Malliavin calculus, in particular Meyer inequalities. Secondly, and motivated by a problem of geometrical nature, we extend the continuous Breuer-Major theorem to the notoriously difficult case of self-similar Gaussian processes which are not necessarily stationary. An application to the fluctuations associated with the length process of a regularized version of the bifractional Browninan motion concludes the paper.
Brackets in the Pontryagin algebras of manifolds

Given a smooth oriented manifold $M$ with non-empty boundary, we study the Pontryagin algebra $A=H_\ast(\Omega )$ where $ \Omega $ is the space of loops in $M$ based at a distinguished point of $ \partial M$. Using the ideas of string topology of Chas-Sullivan, we define a linear map $\{\{-,-\}\}: A \otimes A \to A\otimes A$ which is a double bracket in the sense of Van den Bergh satisfying a version of the Jacobi identity. For $\dim(M)\geq 3$, the double bracket $\{\{-,-\}\}$ induces Gerstenhaber brackets in the representation algebras associated with $A$. This extends our previous work on the case $\dim(M)=2$ where $A= H_0(\Omega )$ is the group algebra of the fundamental group $\pi_1(M)$ and the double bracket $\{\{-,-\}\}$ induces the standard Poisson brackets on the moduli spaces of representations of $\pi_1(M)$.
Diamond-Shaped Regions as Microcosmoi

We give a geometrically intrinsic construction of a global time function for relatively compact diamond-shaped regions in arbitrary spacetimes. In the case of Minkowski spacetime, the flow of diffeomorphisms associated to a suitably normalized gradient of this time function becomes the conformal isotropy subgroup of the diamond. In full generality, this time function is elegantly expressed in terms of the Lorentzian distance function, and it has an asymptotic behavior at large absolute times similar to the one in Minkowski spacetime.
THE H i PROBABILITY DISTRIBUTION FUNCTION AND THE ATOMIC-TO-MOLECULAR TRANSITION IN MOLECULAR CLOUDS

We characterize the column-density probability distribution functions (PDFs) of the atomic hydrogen gas, H i, associated with seven Galactic molecular clouds (MCs). We use 21 cm observations from the Leiden/Argentine/Bonn Galactic H i Survey to derive column-density maps and PDFs. We find that the peaks of the H i PDFs occur at column densities in the range ∼1–2 × 1021 (equivalently, ∼0.5–1 mag). The PDFs are uniformly narrow, with a mean dispersion of (∼0.1 mag). We also investigate the H i-to-H2 transition toward the cloud complexes and estimate H i surface densities ranging from 7 to 16 at the transition. We propose that the H i PDF is a fitting tool for identifying the H i-to-H2 transition column in Galactic MCs.
Superconnections and A Finslerian Gauss-Bonnet-Chern Formula

In this paper, we obtain a Finslerian Gauss-Bonnet-Chern formula for an even dimensional closed Finsler manifold $(M,F)$ by using a Mathai-Quillen type formula of Feng and Zhang in \cite{FZ} on the Euler characteristic. As an application, we will deduce a simple Finslerian Gauss-Bonnet-Chern formula for closed Berwald spaces. Moreover, by using the geometric localization procedure, we also obtain a Bao-Chern type Gauss-Bonnet-Chern formula for closed Berwald spaces.
Zero-shot Cross-Lingual Counterfactual Detection via Automatic Extraction and Prediction of Clue Phrases

Counterfactual statements describe events that did not or cannot take place unless some conditions are satisfied. Existing counterfactual detection (CFD) methods assume the availability of manually labelled statements for each language they consider, limiting the broad applicability of CFD. In this paper, we consider the problem of zero-shot cross-lingual transfer learning for CFD. Specifically, we propose a novel loss function based on the clue phrase prediction for generalising a CFD model trained on a source language to multiple target languages, without requiring any human-labelled data. We obtain clue phrases that express various language-specific lexical indicators of counterfactuality in the target language in an unsupervised manner using a neural alignment model. We evaluate our method on the Amazon Multilingual Counterfactual Dataset (AMCD) for English, German, and Japanese languages in the zero-shot cross-lingual transfer setup where no manual annotations are used for the target language during training. The best CFD model fine-tuned on XLM-R improves the macro F1 score by 25% for German and 20% for Japanese target languages compared to a model that is trained only using English source language data.
Neural responses to naturalistic audiovisual speech are related to listening demand in cochlear implant users

There is a weak relationship between clinical and self-reported speech perception outcomes in cochlear implant (CI) listeners. Such poor correspondence may be due to differences in clinical and “real-world” listening environments and stimuli. Speech in the real world is often accompanied by visual cues, background environmental noise, and is generally in a conversational context, all factors that could affect listening demand. Thus, our objectives were to determine if brain responses to naturalistic speech could index speech perception and listening demand in CI users. Accordingly, we recorded high-density electroencephalogram (EEG) while CI users listened/watched a naturalistic stimulus (i.e., the television show, “The Office”). We used continuous EEG to quantify “speech neural tracking” (i.e., TRFs, temporal response functions) to the show’s soundtrack and 8–12 Hz (alpha) brain rhythms commonly related to listening effort. Background noise at three different signal-to-noise ratios (SNRs), +5, +10, and +15 dB were presented to vary the difficulty of following the television show, mimicking a natural noisy environment. The task also included an audio-only (no video) condition. After each condition, participants subjectively rated listening demand and the degree of words and conversations they felt they understood. Fifteen CI users reported progressively higher degrees of listening demand and less words and conversation with increasing background noise. Listening demand and conversation understanding in the audio-only condition was comparable to that of the highest noise condition (+5 dB). Increasing background noise affected speech neural tracking at a group level, in addition to eliciting strong individual differences. Mixed effect modeling showed that listening demand and conversation understanding were correlated to early cortical speech tracking, such that high demand and low conversation understanding occurred with lower amplitude TRFs. In the high noise condition, greater listening demand was negatively correlated to parietal alpha power, where higher demand was related to lower alpha power. No significant correlations were observed between TRF/alpha and clinical speech perception scores. These results are similar to previous findings showing little relationship between clinical speech perception and quality-of-life in CI users. However, physiological responses to complex natural speech may provide an objective measure of aspects of quality-of-life measures like self-perceived listening demand.
Kinetic Modeling of Multiple Scattering of Acoustic Waves in Randomly Heterogeneous Flows

We study the propagation of sound waves in a three-dimensional, infinite ambient flow with weak random fluctuations of the mean particle velocity and speed of sound. We more particularly address the regime where the acoustic wavelengths are comparable to the correlation lengths of the weak inhomogeneities--the so-called weak coupling limit. The analysis is carried on starting from the linearized Euler equations and the convected wave equation with variable density and speed of sound, which can be derived from the nonlinear Euler equations. We use a multi-scale expansion of the Wigner distribution of a velocity potential associated to the waves to derive a radiative transfer equation describing the evolution of the angularly resolved wave action in space/time phase space. The latter experiences convection, refraction and scattering when it propagates through the heterogeneous ambient flow, although the overall wave action is conserved. The convection and refraction phenomena are accounted for by the convective part of the transport equation and depend on the smooth variations of the ambient quantities. The scattering phenomenon is accounted for by the collisional part of the transport equation and depends on the cross-power spectral densities of the fluctuations of the ambient quantities at the wavelength scales. The refraction, phase shift, spectral broadening, and multiple scattering effects of the high-frequency regimes described in various previous publications are thus encompassed by the proposed model. The overall derivation is based on the interpretation of spatial-temporal Wigner transforms in terms of semiclassical operators, along the same lines as Bal [Wave Motion 43, 132-157 (2005)] and Baydoun et al. [Wave Motion 51, 1325-1348 (2014)].
Homotypic cell-in-cell structures as an adverse prognostic predictor of hepatocellular carcinoma

Hepatocellular carcinoma (HCC) is one of the most common malignant liver tumors. A homotypic cell-in-cell structure (hoCIC) refers to one or more cells internalized into the same type as their neighbors, which predominantly occurs in multiple tumors. The objective of this study was to investigate the prognostic value of hoCICs in HCC and its relationship with other clinicopathological features. By immunostaining analysis of a panel of HCC tissues, we found that hoCICs were prevalent in tumor tissues (54/90) but not in para-tumor tissues (17/90). The presence of hoCICs in tumor tissues was closely associated with E-cadherin expression. The presence of CICs was identified as significantly associated with poor survival rates of patients with HCC, comparable to traditional clinicopathological parameters, such as histological grade [hazard ratio (HR) = 0.734, p = 0.320]. Multivariate Cox regression analysis further confirmed that CICs were an independent risk factor for poor survival (HR = 1.902, p = 0.047). In addition, hoCICs were the predominant contributor in a nomogram model constructed for survival prediction at 1, 3, and 5 years [the areas under the curve (AUCs) were 0.760, 0.733, and 0.794, respectively]. Stratification analysis indicated that hoCICs tend to selectively affect patients with high-grade disease (HR = 2.477, p = 0.009) and at the early TNM stage (HR = 2.351, p = 0.05). Thus, hoCICs predict poor survival of patients with HCC, particularly those with higher grades and at an early stage.
Taxonomy and multi-gene phylogeny of Micropsalliota (Agaricales, Agaricaceae) with description of six new species from China

Micropsalliota is a relatively small genus containing only 62 previously identified species. Here, we describe six new taxa of Micropsalliota based on morphological and phylogenetic analyses: M. minor, M. ovalispora, M. pseudodelicatula, M. rufosquarrosa, M. tenuipes, and M. wuyishanensis and a new record taxon to China. The first Maximum likelihood and Bayesian analyses of a three-gene dataset (ITS, LSU, and rpb2) separated the genus into 18 weakly to strongly supported major clades and subclades, but only a few subclades were synapomorphies. According to phylogenetic analyses, M. cornuta does not belong in Micropsalliota. A key to 20 species of Micropsalliota in China is provided.
Research progress in the risk factors and screening assessment of dysphagia in the elderly

With the aging of the population, the incidence of dysphagia has gradually increased and become a major clinical and public health issue. Early screening of dysphagia in high-risk populations is crucial to identify the risk factors of dysphagia and carry out effective interventions and health management in advance. In this study, the current epidemiology, hazards, risk factors, preventive, and therapeutic measures of dysphagia were comprehensively reviewed, and a literature review of screening instruments commonly used globally was conducted, focusing on their intended populations, main indicators, descriptions, and characteristics. According to analysis and research in the current study, previous studies of dysphagia were predominantly conducted in inpatients, and there are few investigations and screenings on the incidence and influencing factors of dysphagia in the community-dwelling elderly and of dysphagia developing in the natural aging process. Moreover, there are no unified, simple, economical, practical, safe, and easy-to-administer screening tools and evaluation standards for dysphagia in the elderly. It is imperative to focus on dysphagia in the community-dwelling elderly, develop unified screening and assessment tools, and establish an early warning model of risks and a dietary structure model for dysphagia in the community-dwelling elderly.
Generalized St. Petersburg games revisited

The topic of the present paper is a generalized St.\ Petersburg game in which the distribution of the payoff $X$ is given by $P(X=sr^{k-1})=pq^{k-1}$, $k=1,2,\ldots$, where $p+q=1$, and $s,\,r>0$. As for main results, we first extend Feller's classical weak law and Martin-L\"of's 1985-theorem on convergence in distribution along the $2^n$-subsequence. In his 2008-paper Martin-L\"of considers a truncated version of the game and the problem "How much does one gain until 'game over'\,", and a variation where the player can borrow money but has to pay interest on the capital, also for the classical setting. We extend these problems to our more general setting. We close with some additional results and remarks.
Multi-instrument observations of the Pajala fireball: Origin, characteristics, and atmospheric implications

Meteor observations provide information about Solar System constituents and their influx onto Earth, their interaction processes in the atmosphere, as well as the neutral dynamics of the upper atmosphere. This study presents optical, radar, and infrasound measurements of a daytime fireball that occurred on 4 December 2020 at 13:30 UTC over Northeast Sweden. The fireball was recorded with two video cameras, allowing a trajectory determination to be made. The orbital parameters are compatible with the Northern Taurid meteor shower. The dynamic mass estimate based on the optical trajectory was found to be 0.6–1.7 kg, but this estimate can greatly vary from the true entry mass significantly due to the assumptions made. The meteor trail plasma was observed with an ionosonde as a sporadic E-like ionogram trace that lasted for 30 min. Infrasound emissions were detected at two sites, having propagation times consistent with a source location at an altitude of 80–90 km. Two VHF specular meteor radars observed a 6 minute long non-specular range spread trail echo as well as a faint head echo. Combined interferometric range-Doppler analysis of the meteor trail echoes at the two radars, allowed estimation of the mesospheric horizontal wind altitude profile, as well as tracking of the gradual deformation of the trail over time due to a prevailing neutral wind shear. This combined analysis indicates that the radar measurements of long-lived non-specular range-spread meteor trails produced by larger meteoroids can be used to measure the meteor radiant by observing the line traveled by the meteor. Furthermore, a multistatic meteor radar observation of these types of events can be used to estimate mesospheric neutral wind altitude profiles.