Miracle-dz/UniFAR-FTUs huggingface dataset:
Equivariant rho-invariants and instanton homology of torus knots

The equivariant rho-invariants studied in this paper are a version of the classical rho-invariants of Atiyah, Patodi, and Singer in the presence of an isometric involution. We compute these rho-invariants for all involutions on the 3-dimensional lens spaces with 1-dimensional fixed point sets, as well as for some involutions on Brieskorn homology spheres. As an application, we compute the generators and Floer gradings in the singular instanton chain complex of (p,q)-torus knots with odd p and q.
Contextual Measures for Iris Recognition

The iris patterns of the human contain a large amount of randomly distributed and irregularly shaped microstructures. These microstructures make the human iris informative biometric traits. To learn identity representation from them, this paper regards each iris region as a potential microstructure and proposes contextual measures (CM) to model the correlations between them. CM adopts two parallel branches to learn global and local contexts in iris image. The first one is the globally contextual measure branch. It measures the global context involving the relationships between all regions for feature aggregation and is robust to local occlusions. Besides, we improve its spatial perception considering the positional randomness of the microstructures. The other one is the locally contextual measure branch. This branch considers the role of local details in the phenotypic distinctiveness of iris patterns and learns a series of relationship atoms to capture contextual information from a local perspective. In addition, we develop the perturbation bottleneck to make sure that the two branches learn divergent contexts. It introduces perturbation to limit the information flow from input images to identity features, forcing CM to learn discriminative contextual information for iris recognition. Experimental results suggest that global and local contexts are two different clues critical for accurate iris recognition. The superior performance on four benchmark iris datasets demonstrates the effectiveness of the proposed approach in within-database and cross-database scenarios.
Convergence of Heisenberg modules over quantum 2-tori for the modular Gromov-Hausdorff propinquity

The modular Gromov-Hausdorff propinquity is a distance on clas\-ses of modules endowed with quantum metric information, in the form of a metric form of a connection and a left Hilbert module structure. This paper proves that the family of Heisenberg modules over quantum two tori, when endowed with their canonical connections, form a continuous family for the modular propinquity.
Effective bounds in E.Hopf rigidity for billiards and geodesic flows

In this paper we show that in some cases the E.Hopf rigidity phenomenon admits quantitative interpretation. More precisely we estimate from above the measure of the set $\mathcal{M}$ swept by minimal orbits. These estimates are sharp, i.e. if $\mathcal{M}$ occupies the whole phase space we recover the E.Hopf rigidity. We give these estimates in two cases: the first is the case of convex billiards in the plane, sphere or hyperbolic plane. The second is the case of conformally flat Riemannian metrics on a torus. It seems to be a challenging question to understand such a quantitative bounds for Burago-Ivanov theorem.
The Neumann numerical boundary condition for transport equations

In this article, we show that prescribing homogeneous Neumann type numerical boundary conditions at an outflow boundary yields a convergent discretization in $\ell^\infty$ for transport equations. We show in particular that the Neumann numerical boundary condition is a stable, local, and absorbing numerical boundary condition for discretized transport equations. Our main result is proved for explicit two time level numerical approximations of transport operators with arbitrarily wide stencils. The proof is based on the energy method and bypasses any normal mode analysis.
Cone avoiding closed sets

We prove that for an arbitrary subtree $T$ of $2^{<\omega}$ with each element extendable to a path, a given countable class $\mathcal{M}$ closed under disjoint union, and any set $A$, if none of the members of $\mathcal{M}$ strongly $k$-enumerate $T$ for any $k$, then there exists an infinite set contained in either $A$ or $\bar{A}$ such that for every $C\in\mathcal{M}$, $C\oplus G$ also does not strongly $k$-enumerate $T$. We give applications of this result, which include: (1) $\mathsf{RT_2^2}$ doesn't imply $\mathsf{WWKL_0}$; (2) (Ambos-Spies et al.2004) $\mathsf{DNR}$ is strictly weaker than $\mathsf{WWKL_0}$; (3) (Kjos-Hanssen 2009) for any Martin-L\"{o}f random set $A$ either $A$ or $\bar{A}$ contains an infinite subset that does not compute any Martin-L\"{o}f random set; etc. We also discuss further generalizations of this result.
Stack-sorting for words

We introduce operators $\mathsf{hare}$ and $\mathsf{tortoise}$, which act on words as natural generalizations of West's stack-sorting map. We show that the heuristically slower algorithm $\mathsf{tortoise}$ can sort words arbitrarily faster than its counterpart $\mathsf{hare}$. We then generalize the combinatorial objects known as valid hook configurations in order to find a method for computing the number of preimages of any word under these two operators. We relate the question of determining which words are sortable by $\mathsf{hare}$ and $\mathsf{tortoise}$ to more classical problems in pattern avoidance, and we derive a recurrence for the number of words with a fixed number of copies of each letter (permutations of a multiset) that are sortable by each map. We conclude with several open problems and conjectures. In particular, our investigation of $\mathsf{tortoise}$-sortable words leads us to conjecture that there are $\frac{1}{\ell n+1}{(\ell+1)n\choose n}$ $\ell$-uniform (normalized) words of length $\ell n$ that avoid the patterns $231$ and $221$; we prove this conjecture in the case $\ell=2$.
TOPOLOGICAL ENTROPY AND IRREGULAR RECURRENCE

This paper is devoted to problems stated by Z. Zhou and F. Li in 2009. They concern relations between almost periodic, weakly almost periodic, and quasi-weakly almost periodic points of a continuous map f and its topological entropy. The negative answer follows by our recent paper. But for continuous maps of the interval and other more general one-dimensional spaces we give more results; in some cases, the answer is positive.
Coordinates adapted to vector fields III: Real analyticity

Given a finite collection of $C^1$ vector fields on a $C^2$ manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector fields are real analytic. We give necessary and sufficient, coordinate-free conditions for the existence of such a coordinate system. Moreover, we present a quantitative study of these coordinate charts. This is the third part in a three-part series of papers. The first part, joint with Stovall, lay the groundwork for the coordinate system we use in this paper and showed how such coordinate charts can be viewed as scaling maps for sub-Riemannian geometry. The second part dealt with the analogous questions with real analytic replaced by $C^\infty$ and Zygmund spaces.
Inequalities for the quantum privacy

In this work we investigate the asymptotic behavior related to the quantum privacy for multipartite systems. In this context, an inequality for quantum privacy was obtained by exploiting of quantum entropy properties. Subsequently, we derive a lower limit for the quantum privacy through the entanglement fidelity. In particular, we show that there is an interval where an increase in entanglement fidelity implies a decrease in quantum privacy.
Thickness Dependence of Interface‐Generated Spin Currents in Ferromagnet/Ti/CoFeB Trilayers

Interface‐generated spin currents in ferromagnet (FM)/nonmagnet (NM) structures provide both in‐plane and out‐of‐plane spin–orbit torques (SOTs), enabling the field‐free switching of perpendicular magnetization of the other FM layer in magnetic trilayers. In this study, the NM thickness dependence of interface‐generated spin currents and associated SOTs in FM/Ti/CoFeB trilayers is investigated. In such magnetic trilayers, it is known that the in‐plane SOT results from the spin–orbit filtering of the interface‐generated spin current, while the out‐of‐plane SOT is due to the spin–orbit precession. These results show that the polarity of current‐induced magnetization switching under an in‐plane magnetic field reverses with increasing Ti thickness. This indicates that the sign of the in‐plane SOT depends on the current distribution between the bottom FM and Ti layers. On the other hand, field‐free switching occurs only for a Ti thickness of up to ≈4 nm, and the same polarity is retained, demonstrating that out‐of‐plane SOT is governed by the charge current flowing near the interface. These results suggest that field‐free switching efficiency can be enhanced by engineering the relative conductance of the FM/NM bilayers to constructively combine in‐plane and out‐of‐plane SOTs caused by interface‐generated spin currents.
Continuous breakdown of Purcell's scallop theorem with inertia

Purcell’s scallop theorem defines the type of motions of a solid body—reciprocal motions—which cannot propel the body in a viscous fluid with zero Reynolds number. For example, the flapping of a wing is reciprocal and, as was recently shown, can lead to directed motion only if its frequency Reynolds number, Ref, is above a critical value of order one. Using elementary examples, we show the existence of oscillatory reciprocal motions which are effective for all arbitrarily small values of the frequency Reynolds number and induce net velocities scaling as Refα (α>0). This demonstrates a continuous breakdown of the scallop theorem with inertia.
Structure and bases of modular space sequences $(M_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$ and $(S_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$. Part III: Cuspidal spaces

Based on the notion of strong modular form developed in Part I, we propose to structure the family of cuspidal modular form spaces $(S_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$ and to determine bases for each of these spaces, once known bases for the first values of $k$. We then apply these theoretical results to explicitly determine bases for space families $(S_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$ when $1\leq N \leq 10$.
Monte Carlo evaluation of multijunction solar systems in tandem and 4-terminal configurations

Multijunction systems are a promising alternative to overcome the efficiency limit of single-junction cells. A comparison between the two connection schemes, tandem and 4-terminal, is necessary for the development of the applications of this technology. To this purpose, we employed a Monte Carlo simulation algorithm, validated on experimental data, to evaluate the power conversion efficiency of a multijunction system in both configurations by obtaining the absorption spectrum of each layer and calculating the current-voltage characteristics for different thicknesses of each layer in the top cell.
Steepest entropy ascent paths towards the Max-Ent distribution

With reference to two general probabilistic description frameworks, Information Theory and Classical Statistical Mechanics, we discuss the geometrical reasoning and mathematical formalism leading to the differential equation that defines in probability space the smooth path of Steepest Entropy Ascent (SEA) connecting an arbitrary initial probability distribution to the unique Maximum Entropy (MaxEnt) distribution with the same mean values of a set of constraints. The SEA path is relative to a metric chosen to measure distances in square-root probability distribution space. Along the resulting SAE path, the metric turns out to be proportional to the concept of Onsager resistivity generalized to the far non-equilibrium domain. The length of the SEA path to MaxEnt provides a novel global measure of degree of disequilibrium (DoD) of the initial probability distribution, whereas a local measure of DoD is given by the norm of a novel generalized concept of non-equilibrium affinity.
Stapledon Decompositions and Inequalities for Coefficients of Chromatic Polynomials

We use a polynomial decomposition result by Stapledon to show that the numerator polynomial of the Ehrhart series of an open polytope is the difference of two symmetric polynomials with nonnegative integer coefficients. We obtain a related decomposition for order polytopes and for the numerator polynomial of the corresponding series for chromatic polynomials. The nonnegativity of the coefficients in such decompositions provide inequalities satisfied by the coefficients of chromatic polynomials for any simple graph.
From KAM Tori to Isospectral Invariants and Spectral Rigidity of Billiard Tables

This article is a part of a project investigating the relationship between the dynamics of completely integrable or "close" to completely integrable billiard tables, the integral geometry on them, and the spectrum of the corresponding Laplace-Beltrami operators. It is concerned with new isospectral invariants and with the spectral rigidity problem for the Laplace-Beltrami operators ∆ t , t ∈ [0, 1], with Dirichlet, Neumann or Robin boundary conditions , associated with C 1 families of billiard tables (X, g t). We introduce a notion of weak isospectrality for such deformations. The main dynamical assumption on (X, g 0) is that the corresponding billiard ball map B 0 or an iterate P 0 = B m 0 of it posses a Kronecker invariant torus with a Diophantine frequency ω 0 and that the corresponding Birkhoff Normal Form is nondegenerate in Kolmogorov sense. Then we prove that there exists δ 0 > 0 and a set Ξ of Diophantine frequencies containing ω 0 and of full Lebesgue measure around ω 0 such that for each ω ∈ Ξ and 0 < δ < δ 0 there exists a C 1 family of Kronecker tori Λ t (ω) of P t for t ∈ [0, δ]. If the family ∆ t , t ∈ [0, 1], satisfies the weak isospectral condition we prove that the average action β t (ω) on Λ t (ω) and the Birkhoff Normal Form of P t at Λ t (ω) are independent of t ∈ [0, δ] for each ω ∈ Ξ. As an application we obtain infinitesimal spectral rigidity for Liouville billiard tables in dimensions 2 and 3. In particular infinitesimal spectral rigidity for the ellipse and the ellipsoid is obtained under the weak isospectral condition. Applications are obtained also for strictly convex billiard tables in R 2 as well as in the case when (X, g 0) admits an elliptic periodic billiard trajectory with no resonances of order ≤ 4. In particular we obtain spectral rigidity (under the weak isospectral condition) of elliptical billiard tables in the class of analytic and Z 2 × Z 2 symmetric billiard tables in R 2. We prove also that billiard tables with boundaries close to ellipses are spectrally rigid in this class. The results are based on a construction of C 1 families of quasi-modes associated with the Kronecker tori Λ t (ω) and on suitable KAM theorems for C 1 families of Hamiltonians. We propose a new iteration schema (a modified iterative lemma) in the proof of the KAM theorem with parameters, which avoids the Whitney extension theorem for C ∞ jets and allows one to obtain global estimates of the corresponding canonical transformations and Hamiltonians in the scale of all Holder norms. The classical and quantum Birkhoff Normal Forms for C 1 or analytic families of symplectic mappings (Hamiltonians) obtained here can be used as well in order to investigate problems related to the quantum non-ergodicity of C ∞-smooth KAM systems.
5-HT1A Receptor Agonist Treatment Partially Ameliorates Rett Syndrome Phenotypes in mecp2-Null Mice by Rescuing Impairment of Neuron Transmission and the CREB/BDNF Signaling Pathway

Rett syndrome (RTT) is an X-linked neurodevelopmental disorder caused by mutations in the gene that encodes methyl CpG-binding protein 2 (MECP2) and is characterized by the loss of acquired motor and language skills, stereotypic movements, respiratory abnormalities and autistic features. There has been no effective treatment for this disorder until now. In this study, we used a Mecp2-null (KO) mouse model of RTT to investigate whether repeated intraperitoneal treatment with the 5-HT1A receptor agonist tandospirone could improve the RTT phenotype. The results showed that administration of tandospirone significantly extended the lifespan of Mecp2-KO mice and obviously ameliorated RTT phenotypes, including general condition, hindlimb clasping, gait, tremor and breathing in Mecp2-KO mice. Tandospirone treatment significantly improved the impairment in GABAergic, glutaminergic, dopaminergic and serotoninergic neurotransmission in the brainstem of Mecp2-KO mice. Decreased dopaminergic neurotransmission in the cerebellum of Mecp2-KO mice was also significantly increased by tandospirone treatment. Moreover, RNA-sequencing analysis found that tandospirone modulates the RTT phenotype, partially through the CREB1/BDNF signaling pathway in Mecp2-KO mice. These findings provide a new option for clinical treatment.
Novel Gaussian Acceleration Profile for Smooth Jerk-Bounded Trajectories

Industrial machines regularly work at their limits causing excessive long-term vibrations that deteriorate their movement, stability, and precision. In this sense, reference profiles are able to reduce the detrimental vibration effects by manipulating the machine motion dynamics using predefined movement trajectories. Most of the approaches for lessening damages due to long-term machine vibrations are based on polynomial functions with high computational complexity and high resources demand. Hence, in this work, an innovative acceleration outline based on a Gaussian function is proposed for machine motion trajectories. The introduced strategy simplifies the position-profile estimation that works as reference for restraining the machine movements through the parameters that define its motion dynamics; thus, a smooth and continuous jerk contour is produced, which reduces vibrations and improves the machine stability. Exhaustive computer-based and real-time experimental comparisons of the introduced scheme produces a significantly lower maximum jerk value than any of the others. The assessment of the presented approach was performed utilizing the software Matlab (R2020a) on a PC with an Intel Core i7-6500U microprocessor at 2.5 GHz, with 16 GB in RAM and a 64-bit operating system.
Free fermions in classical and quantum integrable models

This thesis studies the role of free fermions in certain classical and quantum integrable models. The classical models studied are the KP and BKP hierarchies of partial differential equations. We review the presence of free fermions in the theory of these hierarchies, a topic which was established in the work of the Kyoto school. The quantum models studied are descendents and relatives of the XYZ model, or its lattice equivalent, the eight-vertex model. We give a number of new results in the context of these models, revealing the presence of fermions in typical quantities such as Bethe eigenvectors, partition functions and scalar products.
A direct proof of F. Riesz representation Theorem

A direct proof of the Riesz representation theorem is provided. This theorem characterizes the linear functionals acting on the vector space $C(K)$ of continuous functions defined on a compact subset $K$ of the real numbers $\mathbb{R}$. This proof avoids complicated arguments commonly used in generalizations of Riesz original theorem.
Representation Formulae and Monotonicity of the Generalized k-Bessel Functions

This paper introduces and studies a generalization of the $\mathtt{k}$-Bessel function of order $\nu$ given by \[\mathtt{W}^{\mathtt{k}}_{\nu, c}(x):= \sum_{r=0}^\infty \frac{(-c)^r}{\Gamma_{\mathtt{k}}\left( r \mathtt{k} +\nu+\mathtt{k}\right) r! } \left(\frac{x}{2}\right)^{2r+\frac{\nu}{\mathtt{k}}}. \] Representation formulae are derived for $\mathtt{W}^{\mathtt{k}}_{\nu, c}. $ Further the function $\mathtt{W}^{\mathtt{k}}_{\nu, c}$ is shown to be a solution of a second order differential equation. Monotonicity and log-convexity properties for the generalized $\mathtt{k}$-Bessel function $\mathtt{W}^{\mathtt{k}}_{\nu, c}$ are investigated, particularly in the case $c=-1$. Several inequalities, including the Turan-type inequality are established.
Development and characterization of lanolin incorporated electrospun nanofibers for nursing pads

Abstract In this study, to combine the biological properties of lanolin and the advantages of electrospun nanofiber mats for developing a potent topical wound dressing/nursing pads that includes lanolin, lanolin incorporated electrospun cellulose acetate (CA), polyethylene oxide (PEO), polyethylene oxide/chitosan (PEO/chitosan) and thermoplastic polyurethane (TPU) nanofibers were developed and characterized. Surface tension, viscosity and conductivity measurements of each polymer solution were carried out in order to characterize the spinning solutions. Lanolin addition did not affect the conductivity values but increase the viscosity of each spinning solution. According to the SEM images, smooth nanofiber surfaces were produced which could be appropriate for a top layer of a nursing pad. Slightly attached, thicker nanofibers could be seen from the TPU/Lanolin images. Similar to TPU nanofibers, CA nanofibers were smoother and thinner than CA/Lanolin nanofibers. Lanolin effected the uniformity of the PEO nanofibers, but it could be said that homogeneous distribution of lanolin was achieved. Characterization of these nanofiber membranes were also carried out with FTIR, DSC, swelling and weight loss analysis. Since TPU nanofibers were hydrophobic and the addition of lanolin made the nanofiber more hydrophobic, they did not show high swelling ratios. CA nanofibers swelled 610% due to their relatively hydrophilic nature and bulky structure. PEO nanofibers were totally dissolved in the water, a very thin layer remained for PEO-Chitosan/lanolin nanofibers. So, using electrospun CA and TPU nanofiber membranes for a nursing pad upper layer could be suitable. CA/lanolin nanofibers showed better hydrophilicity and swelling when compared to TPU nanofibers. On the other hand, TPU nanofibers are more elastic and durable with lower swelling.
Sequentially embeddable graphs

We call a (not necessarily planar) embedding of a graph G in the plane sequential if its vertices lie in Z 2 and the line segments between adjacent vertices contain no interior integer points. In this note, we prove (a) a graph G has a sequential embedding if and only if G is 4‐colorable and (b) if G is planar, then G has a sequential planar embedding.
Cultural Tourism Management Platform Based on Personalized Recommendation Algorithm

Tourism is a way for people to relax in today's era. How to learn local cultures and satisfy users' leisure experience in tourism requires the development of a tourism platform that suits the needs of tourists. According to the needs of platform development, this paper designs a cultural tourism management based on a personalized recommendation algorithm, which can be used to analyze users' travel preferences and recommend scenic spots and surrounding information. The platform integrates cultural tourism resources from all over the world, provides online browsing of cultural tourism information, and applies personalized recommendation technology to the platform to achieve precise connection of tourism resources, thereby enhancing user experience and promoting tourism market revenue. In the research and analysis of the corresponding performance test of the platform and the satisfaction survey of the recommendation results, it is shown that the performance of the platform meets the operating requirements and the user's expectations.