Miracle-dz/UniFAR-FTUs huggingface dataset:
Robust analysis of variance based upon a likelihood ratio criterion

SUMMARY Robust tests of general linear hypotheses in linear models are developed. These are likeli- hood ratio type tests in the same sense that M-estimates are maximum likelihood type estimates. Construction of the tests suggests a decomposition of the data into terms analogous to classical sums of squares, providing a robust analysis of variance. Asymptotic efficiency and robustness properties of the tests are the same as those of the M-estimates upon which they are based. Parameter estimation is usually only a first step in the analysis of data arising fromn a linear model. A classical least squares analysis often focuses upon the analysis of variance, which tests simultaneous hypotheses on large subsets of the parameters. Since the terms in a classical analysis of variance are quadratic forms in least squares estimates, one would expect that the sensitivity of the estimates to departures from normality should be inherited by the tests. In fact, for moderate to heavy tailed error distributions or in the presence of outliers, it appears that the classical F test does lose power. Calculations of relative efficiency for proce- dures proposed in this paper substantiate on theoretical grounds the possible inefficiency and lack of power of classical F tests. In this paper, Huber's M-estimates are adapted to hypothesis tests which can be termed likelihood ratio type tests. These procedures naturally generalize and bear a striking re- semblance to classical F tests. Robustness and efficiency properties of M-estimates apply directly to the proposed tests. Hence the case to be made for using likelihood ratio type tests rather than classical F tests is the same as that for using M-estimates in favour of least squares estimates: possible poor performance of the classical methods may be overcome with methods which perform well both when classical assumptions are met and when they are not. The proposed methods are natural, intuitive and as easily computed as M-estimates.
A Two-Variable Artin Conjecture

Abstract Let a , b ∈ Q * be rational numbers that are multiplicatively independent. We study the natural density δ ( a , b ) of the set of primes p for which the subgroup of F * p generated by ( a mod p ) contains ( b mod p ). It is shown that, under assumption of the generalized Riemann hypothesis, the density δ ( a , b ) exists and equals a positive rational multiple of the universal constant S =∏ p prime (1− p /( p 3 −1)). An explicit value of δ ( a , b ) is given under mild conditions on a and b . This extends and corrects earlier work of Stephens (1976, J. Number Theory 8 , 313–332). We also discuss the relevance of the result in the context of second order linear recurrent sequences and some numerical aspects of the determination of δ ( a , b ).
The Non-Linear Schr\"odinger Equation with a periodic {\bf{$\delta$}}--interaction

We study the existence and stability of the standing waves for the periodic cubic nonlinear Schr\"odinger equation with a point defect determined by a periodic Dirac distribution at the origin. This equation admits a smooth curve of positive periodic solutions in the form of standing waves with a profile given by the Jacobi elliptic function of dnoidal type. Via a perturbation method and continuation argument, we obtain that in the case of an attractive defect the standing wave solutions are stable in $H^1_{per}$ with respect to perturbations which have the same period as the wave itself. In the case of a repulsive defect, the standing wave solutions are stable in the subspace of even functions of $H^1_{per}$ and unstable in $H^1_{per}$ with respect to perturbations which have the same period as the wave itself.
Stable Galerkin Finite Element Scheme for the Simulation of Problems Involving Conductors Moving Rectilinearly in Magnetic Fields

For the simulation of rectilinearly moving conductors across a magnetic field, the Galer-kin finite element method (GFEM) is generally employed. The inherent instability of GFEM is very often addressed by employing Streamline upwinding/Petrov-Galerkin (SU/PG) scheme. However, the SU/PG solution is known to suffer from distortion at the boundary transverse to the velocity and the remedial measures suggested in fluid dynamics literature are computationally demanding. Therefore, simple alternative schemes are essential. In an earlier effort, instead of conventional finite-difference based approach, the numerical instability was analyzed using the Z-transform. By employing the concept of pole-zero cancellation, stability of the numerical solution was achieved by a simple restatement of the input magnetic flux in terms of associated vector potential. This approach, however, is restricted for input fields, which vary only along the direction of the velocity. To overcome this, the present work proposes a novel approach in which the input field is restated as a weighted elemental average. The stability of the proposed scheme is proven analytically for both 1D and 2D cases. The error bound for the small oscillations remnant at intermittent Peclet numbers is also deduced. Using suitable numerical simulations, all the theoretical deductions are verified.
CARACTERIZAÇÃO DA BACIA HIDROGRÁFICA DO RIO ITAPECURU, MARANHÃO - BRASIL

Este trabalho é fruto da reunião de algumas bibliografias sobre o Rio Itapecuru bacia, com o objetivo congregar a informações e dados sobre o mesmo, para servir de referência para os interessados neste rio fascinante. A bacia hidrográfica do Rio de Itapecuru se localiza no centro-leste do Estado do Maranhão, entre as coordenadas 2°51 6°56 Lat. S e 43°02 43°58 Long. W. Esta bacia se apresenta zona de transição de climassemi-árido do nordeste para úmido equatorial de Amazônia, que norte da bacia é refletido nas formações vegetais que transicionais de cerrado (pasto Aberto), no sul, para a Floresta Estacional Decidual e Semidecidual, na parte norte.
Bifurcation from Zero or Infinity in Sturm–Liouville Problems Which Are Not Linearizable

We consider the nonlinear Sturm–Liouville problem[formula][formula]whereai, biare real numbers with |ai| + |bi| > 0,i = 0, 1, λ is a real parameter, and the functionspandaare strictly positive on [0, π]. Suppose that the nonlinearityhsatisfies a condition of the form[formula]as either |(ξ, η)| → 0 or |(ξ, η)| → ∞, for some constantsM0, M1. Then we show that there exist global continua of nontrivial solutions (λ, u) bifurcating fromu = 0 or “u = ∞,” respectively. These global continua have properties similar to those of the continua found in Rabonowitz' well-known global bifurcation theorem.
Modulation detection thresholds for cochlear implants: Dependence on stimulation site and stimulus level

Amplitude modulation of pulse trains is the strategy of choice for transmission of temporal‐envelope information in most modern auditory prostheses. Previous studies by Fu, Colletti, and Shannon have shown high negative correlations between modulation detection thresholds (MDTs) (measured at only one site in the electrode array) and speech recognition with cochlear or brainstem auditory prostheses. The objective of this study was to characterize MDTs across the parameter space used in cochlear prosthesis speech processors: all usable stimulation sites at multiple stimulus levels. Across‐site patterns of MDTs varied considerably from subject to subject. In general, sites with the poorest MDTs were located in the basal third of the scala‐tympani electrode array, but this pattern did not hold for all subjects or all stimulus conditions. The mean MDT for two levels (30% and 70% of dynamic range) was highly correlated with the mean for five levels. Mean MDTs at these two levels averaged over four adjacent elec.
Strict inequalities for the time constant in first passage percolation

In this work we are interested in the variations of the asymptotic shape in first passage percolation on Z2 according to the passage time distribution. Our main theorem extends a result proved by van den Berg and Kesten, which says that the time constant strictly decreases when the distribution of the passage time is modified in a certain manner (according to a convex order extending stochastic comparison). Van den Berg and Kesten’s result requires, when the minimum r of the support of the passage time distribution is strictly positive, that the mass given to r is less than the critical threshold of an embedded oriented percolation model. We get rid of this assumption in the two-dimensional case, and to achieve this goal, we entirely determine the flat edge occurring when the mass given to r is greater than the critical threshold, as a functional of the asymptotic speed of the supercritical embedded oriented percolation process, and we give a related upper bound for the time constant.
Narrative macrostructure and microstructure profiles of bilingual children with autism spectrum disorder: differentiation from bilingual children with developmental language disorder and typical development

Abstract Children with autism spectrum disorder (ASD) show heterogeneous language profiles beyond early language delays. Understanding the second language profiles of bilingual children with ASD is important for clinical practice in diverse societies. Accordingly, we examined the narrative abilities of bilinguals with ASD, with developmental language disorder (DLD), and with typical development (TD) to determine which narrative components best differentiate bilinguals with ASD from the other groups. Participants were 29 bilingual children with ASD, DLD, and TD who were matched for age (mean = 6;8), nonverbal intelligence, and receptive vocabulary. Narratives were coded for macrostructure (story grammar (SG) scores, number of individual SG components) and microstructure (syntactic complexity, mean length of utterance, lexical diversity, and story length). The TD group had superior SG scores, included more SG components, and used longer utterances and more complex syntax than the ASD group, whereas no differences were found between the clinical groups. For SG components requiring perspective-taking abilities, the ASD group had worse performance than the TD and DLD groups. Our results suggest that bilingual children with ASD show weaknesses in both macrostructure and microstructure, which can overlap with children with DLD. The linguistic profiles of bilingual children with ASD and DLD are thus both overlapping and distinct.
Connected components of affine Deligne–Lusztig varieties in mixed characteristic

We determine the set of connected components of minuscule affine Deligne–Lusztig varieties for hyperspecial maximal compact subgroups of unramified connected reductive groups. Partial results are also obtained for non-minuscule closed affine Deligne–Lusztig varieties. We consider both the function field case and its analog in mixed characteristic. In particular, we determine the set of connected components of unramified Rapoport–Zink spaces.
Determination of Takeover Time Budget Based on Analysis of Driver Behavior

An automated driving system notifies a fallback-ready human driver to resume driving when critical operational and functional limits have been or are about to be exceeded. The point between notification and critical limit is the time budget. Previous studies indicate that interdependencies exist between takeover variables and the time budget leading to performance variations and sometimes accidents. It is known that drivers may delay or respond inadequately depending on the time budget. This contribution focuses on utilizing these interdependencies to evaluate the suitability of the time budget for specific scenarios. A 7 s time budget, eight scenarios, and three secondary tasks were studied in a driving simulator with 70 participants aged between 19 Yrs and 41 Yrs. The results indicate that drivers prioritize takeover effort in decreasing order of relative speed, traffic agents, and junctions. Furthermore, 7 s is suitable at a vehicle speed of 80 Km/h to 130 km/h, maximum two traffic agents and three junctions, and handsfree tasks but too high for lower complexities. Generally, the time budget is a sum of the takeover time and maneuver (e.g., lane change) response time. These results are relevant to safety and adaptive variation of the time budget for successful takeover.
A Maass Lifting of $\Theta^3$ and Class Numbers of Real and imaginary Quadratic Fields

We give an explicit construct of a harmonic weak Maass form $F_{\Theta}$ that is a "lift" of $\Theta^3$, where $\Theta$ is the classical Jacobi theta function. Just as the Fourier coefficients of $\Theta^3$ are related to class numbers of imaginary quadratic fields, the Fourier coefficients of the "holomorphic part" of $F_{\Theta}$ are associated to class numbers of real quadratic fields.
Distance graphs and sets of positive upper
density in ℝd

We present a sharp extension of a result of Bourgain on finding configurations of $k+1$ points in general position in measurable subset of $\mathbb{R}^d$ of positive upper density whenever $d\geq k+1$ to all proper $k$-degenerate distance graphs.
A note on the stochastic weakly* almost periodic homogenization of fully nonlinear elliptic equations

A function $f\in \BUC(\R^d)$ is said to be weakly* almost periodic, denoted $f\in\APs(\R^d)$, if there is $g\in\AP(\R^d)$, such that, $\oM(|f-g|)=0$, where $\BUC(\R^d)$ and $\AP(\R^d)$ are, respectively, the space of bounded uniformly continuous functions and the space of almost periodic functions, in $\R^d$, and $\oM(h)$ denotes the mean value of $h$, if it exists. We give a very simple direct proof of the stochastic homogenization property of the Dirichlet problem for fully nonlinear uniformly elliptic equations of the form $F(\om,\frac{x}{\ve},D^2u)=0$, $x\in U$, in a bounded domain $U\subset\R^d$, in the case where for almost all $\om\in \Om$, the realization $F(\om,\cdot,M)$ is a weakly* almost periodic function, for all $M\in\S^d$, where $\S^d$ is the space of $d\X d$ symmetric matrices. Here $(\Om,\mu,\FF)$ is a probability space with probability measure $\mu$ and $\s$-algebra $\FF$ of $\mu$-measurable subsets of $\Om$. For each fixed $M\in\S^d$, $F(\om,y,M)$ is a stationary process, that is, $F(\om,y,M)=\tilde F(T(y)\om,M):= F(T(y)\om,0,M)$, where $T(y):\Om\to\Om$ is an ergodic group of measure preserving mappings such that the mapping $(\om,y)\to T(y)\om$ is measurable. Also, $F(\om,y,M)$, $M\in\S^d$, is uniformly elliptic, with ellipticity constants $0<\l<\gL$ independent of $(\om,y)\in\Om\X\R^d$. The result presented here is a particular instance of the general theorem of Caffarelli, Souganidis and Wang, in CPAM 2005. Our point here is just to show a straightforward proof for this special case, which serves as a motivation for that general theorem, whose proof involves much more intricate arguments. We remark that any continuous stationary process verifies the property that almost all realizations belong to an ergodic algebra, and that $\APs(\R^d)$ is, so far, the greatest known ergodic algebra on $\R^d$.
Grothendieck ring of pretriangulated categories

We consider the abelian group PT generated by quasi-equivalence classes of pretriangulated DG categories with relations coming from semiorthogonal decompositions of corresponding triangulated categories. We introduce an operation of “multiplication” • on the collection of DG categories, which makes this abelian group into a commutative ring. A few applications are considered: representability of “standard” functors between derived categories of coherent sheaves on smooth projective varieties and a construction of an interesting motivic measure.
Polynôme de Bernstein-Sato générique local

Given a family of analytic functions near 0 \in C^n parametrized by a smooth space, we study the Bernstein polynomial of the fiber on an irreducible variety V of the space of parameters and we show that it is generically constant. We prove that this polynomial b(s) satisfies a functional equation on V from which we derive a contructible stratification of the space of parameters by the Bernstein polynomial of the fiber. When the hypersurface admits generically a unique singularity at 0 \in C^n, we prove that b(s) is the generic Bernstein polynomial in the sense of Brian\c{c}on-Geandier-Maisonobe. The tools for the proofs are a formal generalization of an algorithm by Oaku and the generic standard bases studied by the author.
Effect of Tensor Conductivity on Rotating Superposed Plasmas

Die Stabilitat einer Wirbelflache zwischen zwei rotierenden hydromagnetischen Flussigkeiten mit tensorieller Leitfahigkeit wird untersucht. Ebenso wird die Stabilitat des Systems fur den Fall diskutiert, das es anfanglich ruht, aber einer zur Trennflache senkrechten Beschleunigung unterliegt. Man findet, das die tensorielle Leitfahigkeit das System destabilisiert, das aber die Rotation je nach der Lange der Storungswellen stabilisierend oder destabilisierend wirken kann. The stability of a vortex sheet between two hydromagnetic, rotating liquids having tensor conductivity is examined. The stability of the system without initial motion but subject to an acceleration perpendicular to the interface is also discussed. It is found that tensor conductivity destabilizes the system but rotation might be stabilizing or destabilizing depending upon the wave length of perturbation.
Large girth graphs with bounded diameter-by-girth ratio

We provide an explicit construction of finite regular graphs $(\Gamma_k)_{k\in \mathbb N}$ with girth $\Gamma_k\to\infty$ as $k\to\infty$ and $\frac{\text{diam } \Gamma_k}{\text{girth }\Gamma_k}\leqslant D$ for some $D>0$ and all $k\in\mathbb{N}$. For each dimension $n\in \{2, q^t+1\},$ where $q$ is a prime and $t\in\mathbb N$, we find a pair of matrices in $SL_{n}(\mathbb{Z})$ such that (i) they generate a free subgroup, (ii)~their reduction $\mod p$ generate $SL_{n}(\mathbb{F}_{p})$ for all sufficiently large primes $p$, (iii) the corresponding Cayley graphs of $SL_{n}(\mathbb{F}_{p})$ have girth at least $c_n\log p$ for some $c_n>0$. Relying on growth results (with no use of expansion properties of the involved graphs), we observe that the diameter of those Cayley graphs is at most $O(\log p)$. This gives infinite sequences of finite $4$-regular Cayley graphs as in the title. These are the first explicit examples in infinitely many dimensions $n\geqslant 2$. Moreover, they happen to be expanders.
Hyperbaric Oxygen Therapy-Induced Molecular and Pathway Changes in a Rat Model of Spinal Cord Injury: A Proteomic Analysis

Hyperbaric Oxygen Therapy (HBOT) has definitive therapeutic effects on spinal cord injury (SCI), but its mechanism of action is still unclear. Here, we’ve conducted a systemic proteomic analysis to identify differentially expressed proteins (DEPs) between SCI rats and HBOT + SCI rats. The function clustering analysis showed that the top enriched pathways of DEPs include oxygen transport activity, oxygen binding, and regulation of T cell proliferation. The results of functional and signal pathway analyses indicated that metabolic pathways, thermogenesis, LXR/RXR activation, acute phase response signaling, and the intrinsic prothrombin pathway in the SCI + HBOT group was higher than SCI group.
Delay-dependent guaranteed cost control for uncertain neutral systems with nonlinear parameter perturbations

The delay-dependent guaranteed cost control problem for uncertain neutral systems with nonlinear time-varying parameter perturbations is studied. By using a newly established integral inequality, the delay-dependent conditions for the existence of memoryless and memory state feedback guaranteed cost controllers are derived in terms of nonlinear matrix inequalities without involving model transformation and bounding technique for cross terms. An iterative algorithm involving convex optimisation is presented to solve these nonlinear matrix inequalities. A numerical example is given to demonstrate the effectiveness and superiority of the proposed results.
Caccioppoli--type estimates and Hardy--type inequalities derived from degenerated $p$--harmonic problems

We obtain Caccioppoli--type estimates for nontrivial and nonnegative solutions to the anticoercive partial differential inequalities of elliptic type involving degenerated $p$--Laplacian: $-\Delta_{p,a} u:= -\mathrm{div}(a(x)|\na u|^{p-2}\na u)\ge b(x)\Phi (u)$, where $u$ is defined in a domain $\Omega$. Using Caccioppoli--type estimates, we obtain several variants of Hardy--type inequalities in weighted Sobolev spaces.
Star-cluster formation and evolution

Abstract Star clusters are observed to form in a highly compact state and with low star-formation efficiencies, and only 10 per cent of all clusters appear to survive to middle- and old-dynamical age. If the residual gas is expelled on a dynamical time the clusters disrupt. Massive clusters may then feed a hot kinematical stellar component into their host-galaxy's field population thereby thickening galactic disks, a process that theories of galaxy formation and evolution need to accommodate. If the gas-evacuation time-scale depends on cluster mass, then a power-law embedded-cluster mass function may transform within a few dozen Myr to a mass function with a turnover near 105M, thereby possibly explaining this universal empirical feature. Discordant empirical evidence on the mass function of star clusters leads to the insight that the physical processes shaping early cluster evolution remain an issue of cutting-edge research.
Laplace Subspectrality

Exploring the relationship between geometry and the resonant frequencies of a shape is of interest to pure and applied mathematicians. These resonant frequencies are related to the spectrum of the Laplacian, a partial differential operator. A long-standing research program asks: What geometric information can one deduce from these harmonics? This dissertation explores a related question. Say one shape is subspectral to another provided each successive resonant frequency of the one is less than the corresponding frequency of the other. What information can be deduced about the relationship between the shapes' geometries? We use variational arguments to study subspectrality of self-adjoint operators. We develop analytical tools to study Laplace subspectrality. We then study subspectrality in rectangles, construct counterexamples in more general classes of domains, and use the heat trace to relate length subspectrality to Laplace subspectrality. Finally, we discuss a more general question relating eigenvalues to functions, stemming from a 1961 conjecture of Polya.
Differential principal factors and Pólya property of pure metacyclic fields

Barrucand and Cohn’s theory of principal factorizations in pure cubic fields [Formula: see text] and their Galois closures [Formula: see text] with [Formula: see text] types is generalized to pure quintic fields [Formula: see text] and pure metacyclic fields [Formula: see text] with [Formula: see text] possible types. The classification is based on the Galois cohomology of the unit group [Formula: see text], viewed as a module over the automorphism group [Formula: see text] of [Formula: see text] over the cyclotomic field [Formula: see text], by making use of theorems by Hasse and Iwasawa on the Herbrand quotient of the unit norm index [Formula: see text] by the number [Formula: see text] of primitive ambiguous principal ideals, which can be interpreted as principal factors of the different [Formula: see text]. The precise structure of the group of differential principal factors is determined with the aid of kernels of norm homomorphisms and central orthogonal idempotents. A connection with integral representation theory is established via class number relations by Parry and Walter involving the index of subfield units [Formula: see text]. Generalizing criteria for the Pólya property of Galois closures [Formula: see text] of pure cubic fields [Formula: see text] by Leriche and Zantema, we prove that pure metacyclic fields [Formula: see text] of only one type cannot be Pólya fields. All theoretical results are underpinned by extensive numerical verifications of the [Formula: see text] possible types and their statistical distribution in the range [Formula: see text] of [Formula: see text] normalized radicands.