Miracle-dz/UniFAR-FTUs huggingface dataset:
Stability of closed characteristics on compact convex hypersurfaces in R^{2n}

Let $\Sigma\subset \R^{2n}$ with $n\geq2$ be any $C^2$ compact convex hypersurface and only has finitely geometrically distinct closed characteristics. Based on Y.Long and C.Zhu 's index jump methods \cite{LoZ1}, we prove that there are at least two geometrically distinct elliptic closed characteristics, and moreover, there exist at least $\varrho_{n} (\Sigma)$ ($\varrho_{n}(\Sigma)\geq[\frac{n}{2}]+1$) geometrically distinct closed characteristics such that for any two elements among them, the ratio of their mean indices is irrational number.
Reduced, tame and exotic fusion systems

We define here two new classes of saturated fusion systems: reduced fusion systems and tame fusion systems. These are motivated by our attempts to better understand and search for exotic fusion systems: fusion systems which are not the fusion systems of any finite group. Our main theorems say that every saturated fusion system reduces to a reduced fusion system which is tame only if the original one is realizable and that every reduced fusion system which is not tame is the reduction of some exotic (nonrealizable) fusion system.
A discrete districting plan

The outcome of elections is strongly dependent on the districting choices, making thus possible (and frequent) the gerrymandering phenomenon, i.e. politicians suitably changing the shape of electoral districts in order to win the forthcoming elections. While so far the problem has been treated using continuous analysis tools, it has been recently pointed out that a more reality-adherent model would use the discrete geometry of graphs or network. Here we propose a parameter-dependent discrete model for choosing an "optimal" districting plan. We analyze several properties of the model and lay foundations for further analysis on the subject.
Overview of Nanomaterials and Cellular Interactions

In the last three decades, there has been wide progress in nanomaterials development, and several studies are being performed to show its biological effects and cellular interaction for biomedical applications. Due to the exponential increase in nanomaterial diversity, production, and possibilities of applications in different areas, there is an important concern about its toxicity for humans, animals, and ecosystems. There is a great effort to minimize experimental assays in animals, and this is a commendable initiative. Several alternatives in vitro assays are available; however, several new protocols have been introduced to elucidate the mechanisms of cell-nanomaterial interaction. Wide and fast progress in nanotechnology has been observed. Nonetheless, the nanomaterial interaction with cells or biological systems is still not totally described. In this aspect, this paper is a brief overview of nanomaterials and cellular interactions (nano-bio interaction).
Government’s support for adoption of digital technologies and firms’ innovation during the COVID-19 pandemic

ABSTRACT The purpose of this study is to examine the relationship between government support, through technical assistance or subsidies, for adoption of digital technologies and the introduction of new or improved products or services by firms. By applying Probit regression to data provided in World Bank Enterprise Surveys covering the period in late 2020 to early 2021 for three lower-middle-income and high-income economies, we find that governmental support for adoption of digital technologies raised the probability of an enterprise’s innovation in those economies.
Series expansion for L^p Hardy inequalities

We consider a general class of sharp $L^p$ Hardy inequalities in $\R^N$ involving distance from a surface of general codimension $1\leq k\leq N$. We show that we can succesively improve them by adding to the right hand side a lower order term with optimal weight and best constant. This leads to an infinite series improvement of $L^p$ Hardy inequalities.
The Picard Group of the Universal Abelian Variety and the Franchetta Conjecture for Abelian Varieties

We compute the Picard group of the universal abelian variety over the moduli stack $\mathscr A_{g,n}$ of principally polarized abelian varieties over $\mathbb{C}$ with a symplectic principal level $n$-structure. We then prove that over $\mathbb{C}$ the statement of the Franchetta conjecture holds in a suitable form for $\mathscr A_{g,n}$.
SPECTROSCOPIC AND RADIATIVE PROPERTIES OF SM3+ DOPED SODIUM-LEAD-ZINC-LITHIUM-BORATE GLASSES

The glasses with a composition of (65 - x) B2O3 – 5ZnO – 5Li2O – 15 Na2O – 10PbO – x Sm2O3 (x = 0.0; 0.05; 0.1; 0.5; 1.0; 2.0 and 4.0 mol.%) which has been prepared using the melt quenching technique (1100oC for 3 hour). The spectroscopic properties can be determined by investigating the absorption, excitation, and emission spectra of a glass sample. There are 14 centered absorption bands starting from 6H5/2. The excitation spectrum of the Sm3+ doped borate glasses was measured at the wavelength of 300-550 nm which is the strongest intensity (4F7/2 at 403 nm) used as the excitation wavelength to measure the glass emission spectrum. The emission peaks transition starts from 4G5/2. The Judd-Ofelt theory has been applied to the absorption spectrum of Sm3+ doped borate glass to estimate the intensity parameters (Ωλ, λ = 2, 4 and 6) which are then used to calculate the radiative properties. The energy of the optical bandgap is in the range 3.85-3.77 eV for direct transitions and 3.42 - 4.22 eV for indirect transitions. The decay times obtained were 3.42, 3.99, 3.98, 2.96, 1.67, 1.48 ms for 0.05 - 4.00 mol%. Using the CIE chromaticity diagram for borate glass it can be determined that the glass from this work has a high performance for use as an orange emitting material application.
Effective medium theory for elastic metamaterials in thin elastic plates

An effective medium theory for resonant and nonresonant metamaterials for flexural waves in thin plates is presented. The theory provides closed-form expressions for the effective mass density, rigidity, and Poisson's ratio of arrangements of isotropic scatterers in thin plates, valid for low frequencies and moderate filling fractions. It is found that the effective Young's modulus and Poisson's ratio are induced by a combination of the monopolar and quadrupolar scattering coefficient, as it happens for bulk elastic waves, while the effective mass density is induced by the monopolar coefficient, contrarily as it happens for bulk elastic waves, where the effective mass density is induced by the dipolar coefficient. It is shown that resonant positive or negative effective elastic parameters are possible, being therefore the monopolar resonance responsible for creating an effective medium with negative mass density. Several examples are given for both nonresonant and resonant effective parameters and the results are numerically verified by multiple scattering theory and finite element analysis.
Cramér’s estimate for a reflected Lévy process

The natural analogue for a Levy process of Cramer's estimate for a reflected random walk is a statement about the exponential rate of decay of the tail of the characteristic measure of the height of an excursion above the minimum. We establish this estimate for any Levy process with finite negative mean which satisfies Cramer's condition, and give an explicit formula for the limiting constant. Just as in the random walk case, this leads to a Poisson limit theorem for the number of ``high excursions. ''
A covariance formula for topological events of smooth Gaussian fields

We derive a covariance formula for the class of `topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example (i) crossing events for level or excursion sets, (ii) events measurable with respect to the number of connected components of level or excursion sets of a given diffeomorphism class, and (iii) persistence events. As an application of the covariance formula, we derive strong mixing bounds for topological events, as well as lower concentration inequalities for additive topological functionals (e.g. the number of connected components) of the level sets that satisfy a law of large numbers. The covariance formula also gives an alternate justification of the Harris criterion, which conjecturally describes the boundary of the percolation university class for level sets of stationary Gaussian fields. Our work is inspired by a recent paper by Rivera and Vanneuville, in which a correlation inequality was derived for certain topological events on the plane, as well as by an old result of Piterbarg, in which a similar covariance formula was established for finite-dimensional Gaussian vectors.
Dynamics of tectonic plates

We suggest a model that describes a mutual dynamics of tectonic plates. It is a sort of stick-slip dynamics modeled by a Markov random process. The process defines the dynamics on a micro-level. A macro-level is obtained by a scaling limit which leads to a system of integrodifferential equations which determines a kind of mean field systems. The conditions when the Gutenberg-Richter empirical law holds are presented at the mean field level. Those conditions are rather universal and independent of the features of the resistant forces.
Flow Decomposition Reveals Dynamical Structure of Markov Process

Markov process is widely applied in almost all aspects of literature, especially important for understanding non-equilibrium processes. We introduce a decomposition to general Markov process in this paper. This decomposition decomposes the process into 3 independent parts: stationary distribution, symmetric detailed-balance part and anti-symmetric breaking detailed-balance part. This complete decomposition captures the steady state as well as the dynamics of the process, providing an elegant perspective for construction or analyzing problems. In light of the decomposition, a unique definition of relative entropy is found to formally separate the effect of detailed-balance part and breaking detailed-balance part. We find that the relative Gini entropy production introduced in the paper is not affected by the non-detailed balance part of the process. This property do not holds for other entropy definition in general discrete case.
Duality between S^2 P^4 and the Double Quintic Symmetroid

We obtain homological properties of the second symmetric product of P^4 and the double cover of the symmetric determinantal quintic hypersurface in P^{14} (the double quintic symmetroids), which indicate the homological projective duality between (suitable noncommutative resolutions of) them. Among other things, we construct their good desingularizations and also (dual) Lefschetz collections in the derived categories of the desingularizations. These are expected to give (dual) Lefschetz decompositions of suitable noncommutative resolutions. The desingularization of the double quintic symmetroids also contains its interesting birational geometries.
Background independent quantum gravity: A Status report

The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the review should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the review is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well-established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the review to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.
Learning-Based Control Policy and Regret Analysis for Online Quadratic Optimization With Asymmetric Information Structure

In this article, we propose a learning approach to analyze dynamic systems with an asymmetric information structure. Instead of adopting a game-theoretic setting, we investigate an online quadratic optimization problem driven by system noises with unknown statistics. Due to information asymmetry, it is infeasible to use the classic Kalman filter nor optimal control strategies for such systems. It is necessary and beneficial to develop an admissible approach that learns the probability statistics as time goes forward. Motivated by the online convex optimization (OCO) theory, we introduce the notion of regret, which is defined as the cumulative performance loss difference between the optimal offline-known statistics cost and the optimal online-unknown statistics cost. By utilizing dynamic programming and linear minimum mean square biased estimate (LMMSUE), we propose a new type of online state-feedback control policy and characterize the behavior of regret in a finite-time regime. The regret is shown to be sublinear and bounded by $O(\ln T)$ . Moreover, we address an online optimization problem with output-feedback control policy and propose a heuristic online control policy.
The Hermitian curvature flow on manifolds with non-negative Griffiths curvature

Abstract:In this paper we study a particular version of the {\it Hermitian curvature flow} (HCF) over a compact complex Hermitian manifold $(M,g,J)$. We prove that if the initial metric has Griffiths positive (non-negative) Chern curvature $\Omega$, then this property is preserved along the flow. On a manifold with Griffiths non-negative Chern curvature the HCF has nice regularization properties, in particular, for any $t>0$ the zero set of $\Omega(\xi,\bar\xi,\eta,\bar\eta)$ becomes invariant under certain {\it torsion-twisted} parallel transport.
ournal of C osmology and A stroparticle hysics J A coarse grained perturbation theory for the Large Scale Structure, with cosmology and time independence in the UV

Standard cosmological perturbation theory (SPT) for the Large Scale Structure (LSS) of the Universe fails at small scales (UV) due to strong nonlinearities and to multi-streaming eﬀects. In ref. [1] a new framework was proposed in which the large scales (IR) are treated perturbatively while the information on the UV, mainly small scale velocity dispersion, is obtained by nonlinear methods like N-body simulations. Here we develop this approach, showing that it is possible to reproduce the fully nonlinear power spectrum (PS) by combining a simple (and fast) 1-loop computation for the IR scales and the measurement of a single, dominant, correlator from N-body simulations for the UV ones. We measure this correlator for a suite of seven diﬀerent cosmologies, and we show that its inclusion in our perturbation scheme reproduces the fully non-linear PS with percent level accuracy, for wave numbers up to k ∼ 0 . 4 h Mpc − 1 down to z = 0. We then show that, once this correlator has been measured in a given cosmology, there is no need to run a new simulation for a diﬀerent cosmology in the suite. Indeed, by rescaling this correlator by a proper function computable in SPT, the reconstruction procedure works also for the other cosmologies and for all redshifts, with comparable accuracy. Finally, we clarify the relation of this approach to the Eﬀective Field Theory methods recently proposed in the LSS context.
A normal form for 1-infinite type hypersurfaces in $\mathbb C^2$. I. Formal Theory

In this paper, we study the real hypersurfaces $M$ in $\mathbb C^2$ at points $p\in M$ of infinite type. The degeneracy of $M$ at $p$ is assumed to be the least possible, namely such that the Levi form vanishes to first order in the CR transversal direction. A new phenomenon, compared to known normal forms in other cases, is the presence of resonances as roots of an universal polynomial in the $7$-jet of the defining function of $M$. The main result is a complete (formal) normal form at points $p$ with no resonances. Remarkably, our normal form at such infinite type points resembles closely the Chern-Moser normal form at Levi-nondegenerate points. For a fixed hypersurface, its normal forms are parametrized by $S^1\times \mathbb R^*$, and as a corollary we find that the automorphisms in the stability group of $M$ at $p$ without resonances are determined by their $1$-jets at $p$. In the last section, as a contrast, we also give examples of hypersurfaces with arbitrarily high resonances that possess families of distinct automorphisms whose jets agree up to the resonant order.
Diverse structural evolution at z > 1 in cosmologically simulated galaxies

From mock Hubble Space Telescope images, we quantify non-parametric statistics of galaxy morphology, thereby predicting the emergence of relationships among stellar mass, star formation, and observed rest-frame optical structure at 1 10^10 M_sun contain relatively more disc-dominated light profiles than those with lower mass, reflecting significant disc brightening in some haloes at 1 10^10 M_sun. We analyze a cosmological major merger at z ~ 1.5 and find that the newly proposed MID morphology diagnostics trace later merger stages while G-M20 trace earlier ones. MID is sensitive also to clumpy star-forming discs. The observability time of typical MID-enhanced events in our simulation sample is less than 100 Myr. A larger sample of cosmological assembly histories may be required to calibrate such diagnostics in the face of their sensitivity to viewing angle, segmentation algorithm, and various phenomena such as clumpy star formation and minor mergers.
Mask-Induced Facial Dermatoses in the Saudi Arabian Population During the COVID-19 Pandemic: A Cross-Sectional Study

Background The severe acute respiratory syndrome coronavirus 2 (SARS-COV-2) emerged in 2019 and was responsible for noteworthy morbidity and death throughout the world. Due to preventive measures, various adverse reactions to the skin occurred which were associated with prolonged use of wearing a face mask. Objectives The study aimed to determine the incidence and assess the clinical features of mask-induced dermatoses. Methods A cross-sectional study was conducted involving both healthcare and non-healthcare individuals in Saudi Arabia. A questionnaire was designed that included mask-related problems, preexisting skin conditions, frequency and duration of use of face masks, type of face mask, and demographic information. Further information on their clinical symptoms was collected. Results This study included 2326 participants. Participants who refused to participate in the study and did not wear masks (232) were excluded from the study. Redness, itchiness, and acne were the most reported symptoms. 37.8% of the total wore the mask daily with 58.2% using their face mask for more than two hours per day. 44.4% of the participants had mask-induced dermatosis. Almost half of the participants (46.8%) had the cheek as the most affected area. Contact dermatitis was significantly less in non-healthcare workers as compared to healthcare workers (p<0.001). Similarly, conditions like nonspecific erythema (p=0.004) and rosacea (p=0.027) were also significantly less in non-healthcare workers as compared to healthcare workers. Conclusion There was a strong relationship between the frequency of mask use and facial dermatosis during the pandemic. The prevalence or pattern of mask-induced facial dermatoses was not significantly different between healthcare workers and non-healthcare workers. However, contact dermatitis and nonspecific erythema were significantly more common in healthcare workers.
Dynamical systems of eternal inflation: a possible solution to the problems of entropy, measure, observables and initial conditions

There are two main approaches to non-equlibrium statistical mechanics: one using stochastic processes and the other using dynamical systems. To model the dynamics during inflation one usually adopts a stochastic description, which is known to suffer from serious conceptual problems. To overcome the problems and/or to gain more insight, we develop a dynamical systems approach. A key assumption that goes into analysis is the chaotic hypothesis, which is a natural generalization of the ergodic hypothesis to non-Hamiltonian systems. The unfamiliar feature for gravitational systems is that the local phase space trajectories can either reproduce or escape due to the presence of cosmological and black hole horizons. We argue that the effect of horizons can be studied using dynamical systems and apply the so-called thermodynamic formalism to derive the equilibrium (or Sinai-Ruelle-Bowen) measure given by a variational principle. We show that the only physical measure is not the Liouville measure (i.e. no entropy problem), but the equilibrium measure (i.e. no measure problem) defined over local trajectories (i.e. no problem of observables) and supported on only infinite trajectories (i.e. no problem of initial conditions). Phenomenological aspects of the fluctuation theorem are discussed.
Universality at an Endpoint for Orthogonal Polynomials with Geronimus-Type Weights

We provide a new closed form expression for the Geronimus polynomials on the unit circle and use it to obtain new results and formulas. Among our results is a universality result at an endpoint of an arc for polynomials orthogonal with respect to a Geronimus type weight on an arc of the unit circle. The key tool is a formula of McLaughlin for powers of a two-by-two matrix, which we use to derive convenient formulas for Geronimus polynomials.
Topology and \epsilon-regularity Theorems on Collapsed Manifolds with Ricci Curvature Bounds

In this paper we discuss and prove $\epsilon$-regularity theorems for Einstein manifolds $(M^n,g)$, and more generally manifolds with just bounded Ricci curvature, in the collapsed setting. A key tool in the regularity theory of noncollapsed Einstein manifolds is the following: If $x\in M^n$ is such that $Vol(B_1(x))>v>0$ and that $B_2(x)$ is sufficiently Gromov-Hausdorff close to a cone space $B_2(0^{n-\ell},y^*)\subset \mathbb{R}^{n-\ell}\times C(Y^{\ell-1})$ for $\ell\leq 3$, then in fact $|Rm|\leq 1$ on $B_1(x)$. No such results are known in the collapsed setting, and in fact it is easy to see without more such results are false. It turns out that the failure of such an estimate is related to topology. Our main theorem is that for the above setting in the collapsed context, either the curvature is bounded, or there are topological constraints on $B_1(x)$. More precisely, using established techniques one can see there exists $\epsilon(n)$ such that if $(M^n,g)$ is an Einstein manifold and $B_2(x)$ is $\epsilon$-Gromov-Hausdorff close to ball in $B_2(0^{k-\ell},z^*)\subset\mathbb{R}^{k-\ell}\times Z^\ell$, then the fibered fundamental group $\Gamma_\epsilon(x)\equiv Image[\pi_1(B_\epsilon(x))\to\pi_1(B_2(x))]$ is almost nilpotent with $rank(\Gamma_{\epsilon}(x))\leq n-k$. The main result of the this paper states that if $rank(\Gamma_{\epsilon}(x))= n-k$ is maximal, then $|Rm|\leq C$ on $B_1(x)$. In the case when the ball is close to Euclidean, this is both a necessary and sufficient condition. There are generalizations of this result to bounded Ricci curvature and even just lower Ricci curvature.