Miracle-dz/UniFAR-FTUs huggingface dataset:
Profinite invariants of arithmetic groups

Abstract We prove that the sign of the Euler characteristic of arithmetic groups with the congruence subgroup property is determined by the profinite completion. In contrast, we construct examples showing that this is not true for the Euler characteristic itself and that the sign of the Euler characteristic is not profinite among general residually finite groups of type F. Our methods imply similar results for $\ell^2$ -torsion as well as a strong profiniteness statement for Novikov–Shubin invariants.
FINITE, FIBER- AND ORIENTATION-PRESERVING ACTIONS ON ORIENTABLE SEIFERT MANIFOLDS WITH NON-ORIENTABLE BASE SPACE

This paper extends the results from the author’s previous paper to consider ﬁnite, ﬁber- and orientation-preserving group actions on closed, orientable Seifert manifolds M that ﬁber over a non-orientable base space. An orientable base space double cover ˜ M of M is constructed and then an isomorphism between the ﬁber- and orientation-preserving diffeomorphisms of M and the ﬁber- and orientation-preserving actions on ˜ M that preserve the orientation on the ﬁbers and commute with the covering translation is shown. This result and previous results lead to a construction of all actions that satisfy a condition on the obstruction class and the structure of the ﬁnite groups that can act on M .
Enhanced CUSUM control charts for monitoring Coeﬃcient of Variation: A case study in Textile industry (cid:63)

: The recent blooming developments of Artiﬁcial Intelligence (AI), Internet of Things (IoT), and Data Science (DS) have put Smart Manufacturing (SM) into a new context. This leads to more attractions on control charts as one of the useful tools that contribute to the success in SM by anomaly detection (AD) approach. Coeﬃcient of variation (CV) is a recent popular statistic that is used in the quality control of SM. In this paper, we propose investigating the performance of Cumulative sum (CUSUM) control charts monitoring CV with a fast initial response (FIR) strategy. The chart parameters are also optimized according to the random shift size in a given interval with the proposed Nelder-Mead optimization algorithm. The numerical results show that the performance of FIR CUSUM- γ 2 charts are greater than the initial CUSUM- γ 2 ones. An example in monitoring yarn quality at the spinning mill with the design of FIR CUSUM- γ 2 charts is also proposed. These ﬁndings are useful for practitioners as well as managers and researchers. The proposed design of FIR CUSUM- γ 2 charts could be applied in other processes of various domains such as ﬁnance,
The observed spatial distribution of matter on scales ranging from 100kpc to 1Gpc is inconsistent with the standard dark-matter-based cosmological models

The spatial arrangement of galaxies (of satellites on a scale of 100kpc) as well as their three-dimensional distribution in galaxy groups such as the Local Group (on a scale of 1Mpc), the distribution of galaxies in the nearby volume of galaxies (on a scale of 8Mpc) and in the nearby Universe (on a scale of 1Gpc) is considered. There is further evidence that the CMB shows irregularities and for anisotropic cosmic expansion. The overall impression one obtains, given the best data we have, is matter to be arranged as not expected in the dark-matter based standard model of cosmology (SMoC). There appears to be too much structure, regularity and organisation. Dynamical friction on the dark matter halos is a strong direct test for the presence of dark matter particles, but this process does not appear to be operative in the real Universe. This evidence suggests strongly that dynamically relevant dark matter does not exist and therefore cosmology remains largely not understood theoretically. More-accepted awareness of this case would by itself constitute a major advance in research providing fabulous opportunities for bright minds, and the observational data strongly suggest that gravitation must be effectively Milgromian, corresponding to a generalized Poisson equation in the classical limit. Thus, physical cosmology offers a significant historically relevant opportunity for ground-breaking work, at least for those daring to do so.
Revisiting the Birkhoff theorem from a dual null point of view

Birkhoff theorem is a well-known result in General Relativity and it is used in many applications. However, its most general version, due to Bona, is almost unknown and presented in a form less accessible to the relativists and cosmologists community. Moreover, many wield it mistakenly as a simple transposition of Newton's iron spheres theorem. In the present work, we propose a modern, dual null, presentation -- useful in many explorations, including black holes -- of the theorem that renders accessible most of the results of Bona's version. In addition, we discuss the fluid contents admissible for the application of the theorem, beyond vacuum, and we demonstrate how the formalism greatly simplifies solving the dynamical equations and allows to express the solution as a power expansion in $r$. We present a family of solutions that share the properties predicted by the Birkhoff theorem and discuss the existence of trapped/antitrapped regions. The formalism manifestly shows how the type of region -- trapped or untrapped -- determines the character of the Killing vector.
Willmore type inequality using monotonicity formulas

Simon type monotonicity formulas for the Willmore functional $\int | \mathbf{H} |^2$ in the hyperbolic space $\mathbb{H}^n$ and $\mathbb{S}^n$ are obtained. The formula gives a lower bound of $\int_{\Sigma} | \mathbf{H} |^2$ where $\Sigma^2$ is any closed surface in $\mathbb{H}^n$.
Average optimality for continuous-time Markov decision processes in polish spaces

This paper is devoted to studying the average optimality in continuous-time Markov decision processes with fairly general state and action spaces. The criterion to be maximized is expected average rewards. The transition rates of underlying continuous-time jump Markov processes are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. We first provide two optimality inequalities with opposed directions, and also give suitable conditions under which the existence of solutions to the two optimality inequalities is ensured. Then, from the two optimality inequalities we prove the existence of optimal (deterministic) stationary policies by using the Dynkin formula. Moreover, we present a ``semimartingale characterization'' of an optimal stationary policy. Finally, we use a generalized Potlach process with control to illustrate the difference between our conditions and those in the previous literature, and then further apply our results to average optimal control problems of generalized birth--death systems, upwardly skip-free processes and two queueing systems. The approach developed in this paper is slightly different from the ``optimality inequality approach'' widely used in the previous literature.
q-Levy processes

We continue the investigation of the Levy processes on a q-deformed full Fock space started in a previous paper. First, we show that the vacuum vector is cyclic and separating for the algebra generated by such a process. Next, we describe a chaotic representation property in terms of multiple integrals with respect to diagonal measures, in the style of Nualart and Schoutens. We define stochastic integration with respect to these processes, and calculate their combinatorial stochastic measures. Finally, we show that they generate infinite von Neumann algebras.
Numerical Approximations for the Variable Coefficient Fractional Diffusion Equations with Non-smooth Data

Abstract In this article, we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient fractional diffusion equation of the same order. The transformed equation retains the desirable stability property of being an elliptic equation. A spectral approximation scheme is proposed and analyzed for the transformed equation, with error estimates for the approximated solution derived. An approximation to the unknown of the variable coefficient fractional diffusion equation is then obtained by post-processing the computed approximation to the transformed equation. Error estimates are also presented for the approximation to the unknown of the variable coefficient equation with both smooth and non-smooth diffusivity coefficient and right-hand side. Numerical experiments are presented to test the performance of the proposed method.
$\Sigma_1(\kappa)$-definable subsets of $\mathrm{H}(\kappa^+)$

We study $\Sigma_1(\omega_1)$-definable sets (i.e. sets that are equal to the collection of all sets satisfying a certain $\Sigma_1$-formula with parameter $\omega_1$) in the presence of large cardinals. Our results show that the existence of a Woodin cardinal and a measurable cardinal above it imply that no well-ordering of the reals is $\Sigma_1(\omega_1)$-definable, the set of all stationary subsets of $\omega_1$ is not $\Sigma_1(\omega_1)$-definable and the complement of every $\Sigma_1(\omega_1)$-definable Bernstein subset of ${}^{\omega_1}\omega_1$ is not $\Sigma_1(\omega_1)$-definable. In contrast, we show that the existence of a Woodin cardinal is compatible with the existence of a $\Sigma_1(\omega_1)$-definable well-ordering of $\mathrm{H}({\omega_2})$ and the existence of a $\Delta_1(\omega_1)$-definable Bernstein subset of ${}^{\omega_1}\omega_1$. We also show that, if there are infinitely many Woodin cardinals and a measurable cardinal above them, then there is no $\Sigma_1(\omega_1)$-definable uniformization of the club filter on $\omega_1$. Moreover, we prove a perfect set theorem for $\Sigma_1(\omega_1)$-definable subsets of ${}^{\omega_1}\omega_1$, assuming that there is a measurable cardinal and the non-stationary ideal on $\omega_1$ is saturated. The proofs of these results use iterated generic ultrapowers and Woodin's $\mathbb{P}_{\mathrm{max}}$-forcing. Finally, we also prove variants of some of these results for $\Sigma_1(\kappa)$-definable subsets of ${}^{\kappa}\kappa$, in the case where $\kappa$ itself has certain large cardinal properties.
Spin-isospin nuclear response using the existing microscopic Skyrme functionals

Our paper aims at providing an answer to the question of whether one can reliably describe the properties of the most important spin-isospin nuclear excitations by using the available nonrelativistic Skyrme energy functionals. Our method, which has been introduced in a previous publication devoted to the isobaric analog states, is the self-consistent quasiparticle random-phase approximation (QRPA). The inclusion of pairing is instrumental for describing a number of experimentally measured spherical systems which are characterized by open shells. We discuss the effect of isoscalar and isovector pairing correlations. Based on the results for the Gamow-Teller resonance in $^{90}\mathrm{Zr}$, $^{208}\mathrm{Pb}$, and a few Sn isotopes, we draw definite conclusions on the performance of different Skyrme parametrizations, and we suggest improvements for future fits. We also use the spin-dipole resonance as a benchmark of our statements.
Reflected BSDEs when the obstacle is not right-continuous in a general filtration.

We prove existence and uniqueness of the reflected backward stochastic differential equation's (RBSDE) solution with a lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous in a filtration that supports a Brownian motion $W$ and an independent Poisson random measure $\pi$. The result is established by using some tools from the general theory of processes such as Mertens decomposition of optional strong (but not necessarily right continuous) supermartingales and some tools from optimal stopping theory, as well as an appropriate generalization of It\^{o}'s formula due to Gal'chouk and Lenglart. Two applications on dynamic risk measure and on optimal stopping will be given.
Hamiltonian consistency of the gravitational constraint algebra under deformations

The importance of the first-class constraint algebra of general relativity is not limited just by its self-contained description of the gauge nature of spacetime, but it also provides conditions to properly evolve the geometry by selecting a gauge only once throughout the whole evolution of a gravitational system. This must be a property of all background independent theories. In this paper we consider gravitational theories which arise from deformations of the fundamental canonical variables of general relativity where the proposed deformations are inspired by modifications of gravity. These variable deformations result in new theories when the deformation is not a canonical transformation. The new theory must preserve the first-class structure of the algebra, which is a non-trivial restriction for generic deformations. In this vein we present a general deformation scheme along with consistency conditions, so that the algebra of constraints is still satisfied in the resulting theory. This is illustrated both in metric theory as well as in tetrad theory.
Non-i.i.d. random holomorphic dynamical systems and the probability of tending to infinity

We consider random holomorphic dynamical systems on the Riemann sphere whose choices of maps are related to Markov chains. Our motivation is to generalize the facts which hold in i.i. d. random holomorphic dynamical systems. In particular, we focus on the function which represents the probability of tending to infinity. We show some sufficient conditions which make continuous on the whole space and we characterize the Julia sets in terms of the function under certain assumptions.
The Cauchy integral, bounded and compact commutators

We study the commutator of the well-known Cauchy integral operator with a locally integrable function $b$ on $\mathbb R$, and establish the characterisation of the BMO space on $\mathbb R$ via the $L^p$ boundedness of this commutator. Moreover, we also establish the characterisation of the VMO space on $\mathbb R$ via the compactness of this commutator.
Estimates on derivatives of Coulombic wave functions and their electron densities

Abstract We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions ψ, involving negative powers of the distance to the singularities of the many-body potential. We use these to derive bounds for all derivatives of the corresponding one-electron densities ρ, involving negative powers of the distance from the nuclei. The results are both natural and optimal, as seen from the ground state of Hydrogen.
On the Distribution of Zero Sets of Holomorphic Functions

Let M be a subharmonic function with Riesz measure νM in a domain D in the n-dimensional complex Euclidean space ℂn, and let f be a nonzero function that is holomorphic in D, vanishes on a set Z ⊂ D, and satisfies |f| ⩽ expM on D. Then restrictions on the growth of νM near the boundary of D imply certain restrictions on the dimensions or the area/volume of Z. We give a quantitative study of this phenomenon in the subharmonic framework.
Sutureless bioprosthesis for aortic valve replacement: Surgical and clinical outcomes

Aortic valve stenosis is the most common adult valve disease in industrialized countries. The aging population and the increase in comorbidities urge the development of safer alternatives to the current surgical treatment. Sutureless bioprosthesis has shown promising results, especially in complex procedures and in patients requiring concomitant surgeries.
Geometric and spectral estimates based on spectral Ricci curvature assumptions

Abstract We obtain a Bonnet–Myers theorem under a spectral condition: a closed Riemannian ( M n , g ) {(M^{n},g)} manifold for which the lowest eigenvalue of the Ricci tensor ρ is such that the Schrödinger operator Δ + ( n - 2 ) ⁢ ρ {\Delta+(n-2)\rho} is positive has finite fundamental group. Further, as a continuation of our earlier results, we obtain isoperimetric inequalities from Kato-type conditions on the Ricci curvature. We also obtain the Kato condition for the Ricci curvature under purely geometric assumptions.
Histological diagnosis of acute graft-versus-host disease in different sites of the upper gastrointestinal tract with correlation to endoscopic findings

Abstract Graft-versus-host disease (GvHD) involving the intestine is a threat to patients after allogeneic hematopoietic stem cell transplantation (alloHSCT). We evaluated biopsies from different sites of the upper gastrointestinal tract (GIT) of 97 patients after alloHSCT. Forty-six patients with clinical symptoms consistent with upper GI GvHD revealed histological features of GvHD in the esophagus, stomach, and/or duodenum. Biopsies of the duodenum and esophagus were significantly more sensitive for signs of GvHD than those of the gastric antrum or corpus. The histological features of GvHD were significantly correlated with the endoscopic findings of ulcers, erosion, atrophy, and white plaques; however, the sensitivity and specificity of the latter were low. In univariate analysis, overall mortality was significantly associated with histological GvHD signs in all four sites. Nonrelapse mortality was associated with histologic GvHD features in the antrum only. Regarding GvHD diagnosis, biopsies of the upper gastrointestinal tract should include the duodenum and/or esophagus.
Laplace pressure as a surface stress in fluid vesicles

Consider a surface enclosing a fixed volume, described by a free energy depending only on the local geometry; for example, the Canham–Helfrich energy quadratic in the mean curvature describes a fluid membrane. The stress at any point on the surface is determined completely by geometry. In equilibrium, its divergence is proportional to the Laplace pressure, normal to the surface, maintaining the constraint on the volume. It is shown that this source itself can be expressed as the divergence of a position-dependent surface stress. As a consequence, the equilibrium can be described in terms of a conserved effective surface stress. Various non-trivial geometrical consequences of this identification are explored. In a cylindrical geometry, the cross-section can be viewed as a closed planar Euler elastic curve. With respect to an appropriate centre the effective stress itself vanishes; this provides a remarkably simple relationship between the curvature and the position along the loop. In two or higher dimensions, it is shown that the only geometry consistent with the vanishing of the effective stress is spherical. It is argued that the appropriate generalization of the loop result will involve null stresses.
Anomalies and Holomorphy in Supersymmetric Chern-Simons-Matter Theories

For Chern-Simons-matter theories in three dimensions, gauge invariance may require the Chern-Simons level k to be half-integral, in which case parity is violated. As noted by Pasquetti for abelian theories with N=2 supersymmetry, the partition function on the ellipsoid also admits a suitable holomorphic factorization precisely when the value of k is properly quantized. Using known formulas for the partition function, we investigate analytic aspects of this factorization for non-abelian gauge groups and general matter representations. We verify that factorization occurs in accord with the parity anomaly for the classical matrix groups and for the exceptional group G_2. In an appendix, we discuss the analytic continuation of torus knot observables in the SU(2) Chern-Simons-matter theory.
Large $N$ duality for compact Calabi-Yau threefolds

We study geometric transitions for topological strings on compact Calabi-Yau hypersurfaces in toric varieties. Large N duality predicts an equivalence between topological open and closed string theories connected by an extremal transition. We develop new open string enumerative techniques and perform a high precision genus zero test of this conjecture for a certain class of toric extremal transitions. Our approach is based on a) an open string version of Gromov-Witten theory with convex obstruction bundle and b) an extension of Chern-Simons theory treating the framing as a formal variable.
On the invariance of Welschinger invariants

We collect in this note some observations about original Welschinger invariants of real symplectic fourfolds. None of their proofs is difficult, nevertheless these remarks do not seem to have been made before. Our main result is that when $X$ is a real rational algebraic surface, Welschinger invariants only depend on the number of real interpolated points, and some homological data associated to $X$. This strengthened the invariance statement initially proved by Welschinger. This main result follows easily from a formula relating Welschinger invariants of two real symplectic manifolds differing by a surgery along a real Lagrangian sphere. In its turn, once one believes that such formula may hold, its proof is a mild adaptation of the proof of analogous formulas previously obtained by the author on the one hand, and by Itenberg, Kharlamov and Shustin on the other hand. We apply the two aforementioned results to complete the computation of Welschinger invariants of real rational algebraic surfaces, and to obtain vanishing, sign, and sharpness results for these invariants that generalize previously known statements. We also discuss some hypothetical relations of our work with tropical refined invariants defined by Block-G\"ottsche and G\"ottsche-Schroeter.
Outcomes of bovine versus porcine surgical aortic valve replacement

There are no guidelines regarding the use of bovine pericardial or porcine valves for aortic valve replacement, and prior studies have yielded conflicting results. The current study sought to compare short‐ and long‐term outcomes in propensity‐matched cohorts of patients undergoing isolated aortic valve replacement (AVR) with bovine versus porcine valves.
Integral representation of one-dimensional three particle scattering for δ function interactions

The Schrodinger equation, in hyperspherical coordinates, is solved in closed form for a system of three particles on a line, interacting via pair delta functions. This is for the case of equal masses and potential strengths. The interactions are replaced by appropriate boundary conditions. This leads then to requiring the solution of a free-particle Schrodinger equation subject to these boundary conditions. A generalized Kontorovich–Lebedev transformation is used to write this solution as an integral involving a product of Bessel functions and pseudo-Sturmian functions. The coefficient of the product is obtained from a three-term recurrence relation, derived from the boundary condition. The contours of the Kontorovich–Lebedev representation are fixed by the asymptotic conditions. The scattering matrix is then derived from the exact solution of the recurrence relation. The wavefunctions that are obtained are shown to be equivalent to those derived by McGuire. The method can clearly be applied to a larger n.
Endogenous antioxidants predicted outcome and increased after treatment: A benzoate dose‐finding, randomized, double‐blind, placebo‐controlled trial for Alzheimer's disease

Previous pilot studies suggest that sodium benzoate may be a potential cognitive enhancer for patients with Alzheimer's disease (AD), schizophrenia, or late‐life depression. Especially for AD treatment, a confirmatory trial with predictive biomarkers is urgently needed. This study aimed to confirm benzoate as a novel treatment for AD and to discover its optimal dose and biomarkers.