Miracle-dz/UniFAR-FTUs huggingface dataset:
Interpolation in the Presence of Domain Inhomogeneity

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity, characterized by different, potentially overlapping, subdomains. By introducing a domain-similarity metric for each sample, the interpolation process is then based on a domain-informed consistency principle. We illustrate and demonstrate the feasibility of domain-informed linear interpolation in 1D, and also, on a real fMRI image in 2D. The results show the benefit of incorporating domain knowledge so that, for example, sharp domain boundaries can be recovered by the interpolation, if such information is available.
Analytic isomorphisms of compressed local algebras

In this paper we consider Artin local K-algebras with maximal length in the class of Artin algebras with given embedding dimension and socle type. They have been widely studied by several authors, among others by Iarrobino, Froberg and Laksov. If the local K-algebra is Gorenstein of socle degree 3, then the authors proved that it is canonically graded, i.e. analytically isomorphic to its associated graded ring, see (6). This unexpected result has been extended to compressed level K-algebras of socle degree 3 in (4). In this paper we end the investigation proving that extremal Artin Gorenstein local K-algebras of socle degree s � 4 are canonically graded, but the result does not extend to extremal Artin Gorenstein local rings of socle degree 5 or to compressed level local rings of socle degree 4 and type > 1. As a consequence we present results on Artin compressed local K-algebras having a specified socle type.
A quantitative bounded distance theorem and a Margulis’ lemma for $\mathbb Z^n$-actions, with applications to homology

We consider the stable norm associated to a discrete, torsionless abelian group of isometries Γ ∼ = Z n of a geodesic space ( X, d ). We show that the diﬀerence between the stable norm (cid:107) (cid:107) st and the distance d is bounded by a constant only depending on the rank n and on upper bounds for the diameter of ¯ X = Γ \ X and the asymptotic volume ω (Γ , d ). We also prove that the upper bound on the asymptotic volume is equivalent to a lower bound for the stable systole of the action of Γ on ( X, d ); for this, we establish a Lemma `a la Margulis for Z n -actions, which gives optimal estimates of ω (Γ , d ) in terms of stsys(Γ , d ), and vice versa, and characterize the cases of equality. Moreover, we show that all the parameters n, diam( ¯ X ) and ω (Γ , d ) (or stsys(Γ , d )) are necessary to bound the diﬀerence d −(cid:107) (cid:107) st , by providing explicit counterexamples for each case. As an application in Riemannian geometry, we prove that the number of connected components of any optimal, integral 1-cycle in a closed Riemannian manifold ¯ X either is bounded by an explicit function of the ﬁrst Betti number, diam( ¯ X ) and ω ( H 1 ( ¯ X, Z )), or is a sublinear function of the mass.
Continuous Univariate Distributions.

Continuous Univariate Distributions.1-2Characterizations of Univariate Continuous DistributionsCharacterizations of Univariate Continuous DistributionsDictionary and Classified Bibliography of Statistical Distributions in Scientific Work: Continuous univariate modelsDistributions in StatisticsUnivariate Discrete DistributionsContinuous univariate distributions. IIDistributions in StatisticsContinuous Univariate DistributionsContinuous Univariate Distributions. Vol. 2Continuous Univariate DistributionsContinuous Multivariate Distributions, Volume 1Continuous Univariate Distributions. Vol. 1Distributions in StatisticsContinuous Univariate DistributionsFitting Statistical DistributionsDistributions in Statistics: Continuous Multivariate DistributionsDistributions in Statistics: Continuous univariate distributionsField Guide to Continuous Probability DistributionsStatistics for Criminal Justice and Criminology in Practice and ResearchDistributions in StatisticsDistributions in Statistics: Continuous univariate distributions 1-2Continuous Univariate Distributions, Volume 2Continuous Univariate DistributionsA Survey of Some Recent Results in Continuous Univariate DistributionsContinuous Univariate Distributions-1Probability Distributions Used in Reliability EngineeringBeyond BetaSimulating Data with SASContinuous Bivariate DistributionsDistributions in StatisticsContinuous Univariate DistributionsMultivariate Statistical SimulationRecordsContinuous Univariate DistributionsDistributions in StatisticsContinuous Univariate DistributionsContinuous Multivariate DistributionsDistributions in StatisticsDistributions in Statistics
Stable limit laws and structure of the scaling function for reaction-diffusion in random environment

We prove the emergence of stable fluctuations for reaction-diffusion in random environment with Weibull tails. This completes our work around the quenched to annealed transition phenomenon in this context of reaction diffusion. In [9], we had already considered the model treated here and had studied fully the regimes where the law of large numbers is satisfied and where the fluctuations are Gaussian, but we had left open the regime of stable fluctuations. Our work is based on a spectral approach centered on the classical theory of rank-one perturbations. It illustrates the gradual emergence of the role of the higher peaks of the environments. This approach also allows us to give the delicate exact asymptotics of the normalizing constants needed in the stable limit law.
COREGISTRATION OF DSM AND 3D POINT CLOUDS ACQUIRED BY A MOBILE MAPPING SYSTEM

The development of 3D mapping databases is a matter of increasing interest. Databases have recently been developed at different scales (national, European, international) and to meet different needs. Such development has been made possible by the implementation of efficient 3D mapping technologies. 3D mapping strategies are based on multi-sensor data fusion usually performed after a preprocessing step that includes registration and filtering. In this paper, we present our work on registration methods applied to solve problems in 3D urban environment representations issued from a Mobile Mapping System. We improve the stability of convergence, the computation time and handle heterogeneous data sets in various scenarios.
Descorrelacionador Aliado à Diversidade de Percursos

—A asynchronous unicellular DS-CDMA system is modeled considering a slow fading frequency selective multipath mobile radio channel. The system performance is evaluated in bit error rate terms analyzing the beneﬁces which derives from decorrelator implementation and path diversity. Finally, it veriﬁes the superiority in performance at condition of identical numbers of ﬁngers and of paths.
Bulk Acoustic Wave Filter Using Piezoelectrically Coupled Resonators

New configurations for bulk acoustic wave (BAW) filters suitable for the ultra high frequency (UHF) band are proposed. In contrast with a monolithic crystal filter, the resonators of the proposed filter are electrically coupled through a piezoelectric film deposited on the filter substrate. Equivalent circuit analysis and simulation results are described. The simulation results suggest the possibility of BAW filters in the UHF band. Because the proposed filter is suitable for the silicon diaphragm structure, development of highly sophisticated integrated electronic circuits with piezoelectric filters is expected.
El problema del multicubrimiento: una aplicación para la selección de paradas en la red de transporte de la Ciudad de México

In this paper an heuristic algorithm is developed. Its implementation is developedas well, in order to solve a sampling problem in the urban transportation network in Mexico City. The problem consist of the selection of at least 2 points (stops) on each ofthe 236 routes in the study comprising a total of 8390 stops. This problem is presentedas a multicover problem subject to 236 restrictions and 8390 binary variables. Giventhat this an NP-hard problem, it was implemented an heuristic algorithm to determinethe sampling points.Keywords: Multicover problem, heuristic methods, greedy algorithms, combinatorial optimization.
Parabolic induction and extensions

Let $G$ be a $p$-adic reductive group. We determine the extensions between admissible smooth mod $p$ representations of $G$ parabolically induced from supersingular representations of Levi subgroups of $G$, in terms of extensions between representations of Levi subgroups of $G$ and parabolic induction. This proves for the most part a conjecture formulated by the author in a previous article and gives some strong evidence for the remaining part. In order to do so, we use the derived functors of the left and right adjoints of the parabolic induction functor, both related to Emerton's $\delta$-functor of derived ordinary parts. We compute the latter on parabolically induced representations of $G$ by pushing to their limits the methods initiated and expanded by the author in previous articles.
Bin decompositions

It is well known that every positive integer can be expressed as a sum of nonconsecutive Fibonacci numbers provided the Fibonacci numbers satisfy $F_n =F_{n-1}+F_{n-2}$ for $n\geq 3$, $F_1 =1$ and $F_2 =2$. In this paper, for any $n,m\in\mathbb{N}$ we create a sequence called the $(n,m)$-bin sequence with which we can define a notion of a legal decomposition for every positive integer. These sequences are not always positive linear recurrences, which have been studied in the literature, yet we prove, that like positive linear recurrences, these decompositions exist and are unique. Moreover, our main result proves that the distribution of the number of summands used in the $(n,m)$-bin legal decompositions displays Gaussian behavior.
Combinatorics of Orbit Configuration Spaces

From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this “orbit configuration space” is the complement of an arrangement of subvarieties inside the Cartesian product, and we use this structure to study its topology. We give an abstract combinatorial description of its poset of layers (connected components of intersections from the arrangement), which turns out to be of much independent interest as a generalization of partition and Dowling lattices. The close relationship to these classical posets is then exploited to give explicit cohomological calculations.
A full-chain constitutive model for bidisperse blends of linear polymers

We develop a full-chain tube-based constitutive model [along the lines of Graham et al. J. Rheol. 47, 1171 (2003)] for the nonlinear rheology of bidisperse blends of long and short linear polymers. For a test chain in the blend, we use the physical picture of a fat tube, representing long-lived entanglements with long chains, and a thin tube, representing entanglements with all chains. The model includes the processes of reptation, contour length fluctuation (CLF), constraint release, and stretch relaxation. In the linear rheology regime, we identify a new relaxation process: CLF along the fat tube contour, achieved via a combination of chain motion along the thin tube, and local constraint release of the thin tube as it explores the width of the fat tube. This process is sufficiently fast to relax a significant portion of the long chains before reptation. It provides an explanation of the decrease in terminal time of long chains upon dilution with short chains in a framework where motion along the thin t.
On the Gopakumar–Ooguri–Vafa correspondence
 for Clifford–Klein 3-manifolds

Gopakumar, Ooguri and Vafa famously proposed the existence of a correspondence between a topological gauge theory on one hand ($U(N)$ Chern-Simons theory on the three-sphere) and a topological string theory on the other (the topological A-model on the resolved conifold). On the physics side, this duality provides a concrete instance of the large $N$ gauge/string correspondence where exact computations can be performed in detail; mathematically, it puts forward a triangle of striking relations between quantum invariants (Reshetikhin-Turaev-Witten) of knots and 3-manifolds, curve-counting invariants (Gromov-Witten/Donaldson-Thomas) of local Calabi-Yau 3-folds, and the Eynard-Orantin recursion for a specific class of spectral curves. I quickly survey recent results on the most general frame of validity of this correspondence and discuss some of its implications.
Plasma production by low-field side injection of electron cyclotron waves in a simple magnetized torus

The mechanisms leading to ionization of neutral gas by means of microwaves in the electron cyclotron range of frequencies in a simple toroidal plasma configuration are investigated in the TORPEX device (Fasoli A et al 2003 Bull. Am. Phys. Soc. 48 119). The role of the upper hybrid resonance, where most of the ionization events occur once the plasma is formed, is clearly demonstrated. The fast phenomena related to ionization are discriminated from the slower mechanisms leading to the stationary background profiles by measuring the density perturbation caused by a modulation of the injected microwave power. The same method permits reconstruction of the spatial profile of the particle source. The ionization processes are then related to experimental control parameters such as the injected microwave power.
Properties of Pseudocontractive Updates in Convex Optimization

Many convex optimization methods are conceived of and analyzed in a largely separate fashion. In contrast to this traditional separation, this manuscript points out and demonstrates the utility of an important but largely unremarked common thread running through many prominent optimization methods. In particular, we show that methods such as successive orthogonal projection, gradient descent, projected gradient descent, the proximal-point method, forward-backward splitting, the alternating direction method of multipliers, and under- or over-relaxed variants of the preceding all involve updates that are of a common type --- namely, the updates satisfy a property known as pseudocontractivity. Moreover, since the property of pseudocontractivity is preserved under both composition and convex combination, updates constructed via these operations from pseudocontractive updates are themselves pseudocontractive. Having demonstrated that pseudocontractive updates are to be found in many optimization methods, we then provide a unified basic analysis of methods with pseudocontractive updates. Specifically, we prove a novel bound satisfied by the norm of the difference in iterates of pseudocontractive updates and we then use this bound to establish that the error criterion $\left\Vert x^{N}-Tx^{N}\right\Vert ^{2}$ is $o(1/N)$ for any method involving pseudocontractive updates (where $N$ is the number of iterations and $T$ is the iteration operator).
Efficacy and safety of proprioceptive neuromuscular facilitation for chronic low back pain: A meta-analysis of randomized controlled trials

Objectives This study aimed to evaluate the effectiveness and safety of proprioceptive neuromuscular facilitation for chronic low back pain. Materials and methods: Eleven databases were searched from their inception through January 2021. The primary outcomes were pain intensity, individual activities, quality of life, and adverse events. Results Four randomized controlled trials (RCTs) with 184 patients (mean age: 37.8±3.1 years; range, 35 to 50 years) met the inclusion criteria. The pooled effect size showed proprioceptive neuromuscular facilitation, relieved pain (standard means difference [SMD]: -0.835, 95% CI: -1.139 to -0.531, p<0.001, n=4), and improved individual activity (Roland Morris Disability Questionnaire, SMD: -1.765, 95% CI: -2.642 to -0.888, p<0.001, n=2; Oswestry Disability Index, SMD: -0.893, 95% CI: -1.434 to -0.352, p=0.001, n=1) for chronic low back pain (CLBP). Conclusion This study verified that proprioceptive neuromuscular facilitation could relieve pain and improve individual activities without serious adverse events in patients with CLBP; however, it should be cautiously recommended due to the small number of included RCTs.
Efficient Knowledge Distillation for Brain Tumor Segmentation

Deep learning has allowed great progress to be made in obtaining more accurate prediction results for brain tumor segmentation. The current mainstream research approaches obtain segmentation accuracy improvements by modifying deep-learning model architectures, while ignoring the computational and storage efficiency issues of segmentation. In this paper, we proposed an improved knowledge distillation method: coordinate distillation (CD), which integrates channel and space information and completes brain tumor segmentation by training the student network with the teacher network without changing the original network architecture. Experimental results showed that the method was effective and that it could enhance the segmentation accuracy of brain tumors without changing the segmentation efficiency.
Solutions to ABS Lattice Equations via Generalized Cauchy Matrix Approach

The usual Cauchy matrix approach starts from a known plain wave factor vector r and known dressed Cauchy matrix M . In this paper, we start from a determining matrix equation set with undetermined r and M . From the determining equation set we can build shift relations for some defined scalar functions and then derive lattice equations. The determining equation set admits more choices for r and M and in the paper we give explicit formulae for all possible r and M . As applications, we get more solutions than usual multisoliton solutions for many lattice equations including the lattice potential KdV equation, the lattice potential modified KdV equation, the lattice Schwarzian KdV equation, NQC equation, and some lattice equations in ABS list.
Convergence of persistence diagrams for topological crackle

In this paper we study the persistent homology associated with topological crackle generated by distributions with an unbounded support. Persistent homology is a topological and algebraic structure that tracks the creation and destruction of homological cycles (generalizations of loops or holes) in different dimensions. Topological crackle is a term that refers to homological cycles generated by "noisy" samples where the support is unbounded. We aim to establish weak convergence results for persistence diagrams - a point process representation for persistent homology, where each homological cycle is represented by its (birth,death) coordinates. In this work we treat persistence diagrams as random closed sets, so that the resulting weak convergence is defined in terms of the Fell topology. In this framework we show that the limiting persistence diagrams can be divided into two parts. The first part is a deterministic limit containing a densely-growing number of persistence pairs with a short lifespan. The second part is a two-dimensional Poisson process, representing persistence pairs with a longer lifespan.
Long range particle dynamics and the linear Boltzmann equation

This thesis aims to give full and complete details of the first proof that the particle density for a tagged particle interacting with a background of particles via a long range potential ϕ converges weak-* to a weak solution of the linear Boltzmann equation for ϕ . This convergence is shown to hold for potentials where there is a τ > 0, and such that for sufficiently large [x] we have ∇∅(x)≤Ce-|x|3/2÷τ The main difficulty in this context are the many grazing collisions in the particle dynamics which prevents a Markovian structure of the dynamics. We remove grazing collisions via the use of a regularisation parameter. This enables us to consider an associated short range evolution, which we describe on a space of marked trees to encode the collisional history of the tagged particle. This description then enables a specification of Markovian dynamics by removing a set of trees that exhibit recollisions. We then relate this evolution with the Markovian evolution of the linear Boltzmann equation on this space. The difference between dynamics with and without grazing collisions are estimated by comparing the contribution from near collisions with a bound on the time of collision, and the contribution from grazing collisions by using an L∞ estimate on the potential. The remaining error for the contribution of the grazing collisions on solutions of the linear Boltzmann equation are estimated by estimating the difference between deviation angles with and without grazing collisions.
Sign changing solutions of the Hardy–Sobolev–Maz'ya equation

Abstract. In this article we will study the existence, multiplicity and Morse index of sign changing solutions for the Hardy–Sobolev–Maz'ya (HSM) equation in bounded domain and involving critical growth. We obtain infinitely many sign changing solutions for HSM equation. We also establish an estimate on the Morse index for the sign changing solutions.
Electronic transport in graphene : A semiclassical approach including midgap states

Using the semi-classical Boltzmann theory, we calculate the conductivity as function of the carrier density. As usually, we include the scattering from charged impurities, but conclude that the estimated impurity density is too low in order to explain the experimentally observed mobilities. We thus propose an additional scattering mechanism involving midgap states which leads to a similar k-dependence of the relaxation time as charged impurities. The new scattering mechanism can account for the experimental findings such as the sublinear behavior of the conductivity versus gate voltage and the increase of the minimal conductivity for clean samples. We also discuss temperature dependent scattering due to acoustic phonons.
On the Lower Bound for the Number of Facets of a k-Neighborly Polytope

We pose the conjecture that the number of facets $f_{d-1}(P)$ of a $k$-neighborly $d$-polytope $P$ cannot be less than the number of its vertices $f_0(P)$ for $k \ge 2$. We prove that the statement of conjecture is true in two cases: 1) when $d \le 2k+2\lfloor k/2\rfloor$, and 2) when $f_0(P) \le d + 1 + k^2$. For the case $f_0(P) = d + 3$, we have found the tight lower bound: $f_{d-1}(P) - f_{0}(P) \ge (k + 2)(k^2 + k - 3)/3$ if $k\in \{2, 3\}$, and $f_{d-1}(P) - f_{0}(P) \ge 2 (k^2 - 1)$ if $k \ge 4$.
A Multiple State Model for Disability Using the Decomposition of Death Probabilities and Cross-Sectional Data

ABSTRACT We split the components corresponding to the disability-free survival probability, and the disability survival probability. Our analysis is conducted for men and women separately, for age groups over 64 years. We discuss the estimation of a multiple state model under several scenarios when only a single survey of cross-sectional data is available. The conclusions are used to discuss the disability level of the Spanish elderly population and are helpful to develop welfare programs and insurance products.