Miracle-dz/UniFAR-FTUs huggingface dataset:
A Stochastic Gronwall Lemma

We prove a stochastic Gronwall lemma of the following type: if $Z$ is an adapted nonnegative continuous process which satisfies a linear integral inequality with an added continuous local martingale $M$ and a process $H$ on the right hand side, then for any $p \in (0,1)$ the $p$-th moment of the supremum of $Z$ is bounded by a constant $\kappa_p$ (which does not depend on $M$) times the $p$-th moment of the supremum of $H$. Our main tool is a martingale inequality which is due to D. Burkholder. We provide an alternative simple proof of the martingale inequality which provides an explicit numerical value for the constant $c_p$ appearing in the inequality which is at most four times as large as the optimal constant.
A model‐free method for identification of mass modifications

In this paper, a model‐free methodology for off‐line identification of modifications of structural mass is proposed and verified experimentally. The methodology of the virtual distortion method is used: the modifications are modeled by the equivalent pseudo‐loads that act in the related degrees of freedom of the unmodified structure; their influence on the response is computed using a convolution of the pseudo‐loads with the experimentally obtained local impulse responses. As a result, experimentally measured data are directly used to model the response of the modified structure in a non‐parametric way. The approach obviates the need for a parametric numerical model of the structure and for laborious initial updating of its parameters. Moreover, no topological information about the structure is required, besides potential locations of the modifications. The identification is stated as a problem of minimization of the discrepancy between the measured and the modeled responses of the modified structure. The formulation allows the adjoint variable method to be used for a quick first‐ and second‐order sensitivity analysis, so that Hessian‐based optimization algorithms can be used for fast convergence. The proposed methodology was experimentally verified using a 3D truss structure with 70 elements. Mass modifications in a single node and in two nodes were considered. Given the initially measured local impulse responses, a single sensor and single excitation were sufficient for the identification. Copyright © 2010 John Wiley & Sons, Ltd.
Evolution of Quasi-Two-Dimensional Squall Lines. Part I: Kinematic and Reflectivity Structure

Abstract Doppler radar observations that establish common patterns in the evolution of the reflectivity and flow structures of squall lines are described. A number of squall lines have been analyzed with unprecedented time resolution in order to identity these patterns. All of the squall lines appeared to be approximately two-dimensional and featured a solid leading edge at some time during their life cycle, instead of being composed of discrete cells separated by echo-free regions. A large variety of intensities and evolution lime scales was observed. It is shown that squall lines of this type evolve through identifiable stages of reflectivity structure. This evolution appears to be strongly related to changes that occur in the kinematic structure. As a typical system evolves, a rearward-sloping zone of horizontal vorticity, predominantly associated with vertical shear, develops on the scale of the system, presumably driven by the horizontal buoyancy gradients across the system. The vorticity that is gen.
Int\'egralit\'e des coefficients de Taylor de racines d'applications miroir

We prove the integrality of the Taylor coefficients of roots of mirror maps at the origin. By mirror maps, we mean formal power series z.exp(G(z)/F(z)), where F(z) and G(z)+log(z)F(z) are particular solutions of certain generalized hypergeometric differential equations. This enables us to prove a conjecture stated by Zhou in "Integrality properties of variations of Mahler measures" [arXiv:1006.2428v1 math.AG]. The proof of these results is an adaptation of the techniques used in our article "Crit\`ere pour l'int\'egralit\'e des coefficients de Taylor des applications miroir", [J. Reine Angew. Math. (to appear)].
Doped silicon single electron transistors with single island characteristics

Uniformly doped single electron transistors nominally consisting of a single island and two silicon tunneling barriers have been fabricated on silicon–on–insulator material. Two operation regimes are found depending upon the gate voltages applied. The structure acts either as a multiple tunnel junction device or as a single electron transistor consisting of a single dot corresponding to the geometrical shape of the device. The multiple tunnel junction behavior is attributed to the formation of additional tunneling barriers, introduced into the structure by the high doping level. We demonstrate that these barriers can be removed by raising the Fermi level via the application of an appropriate gate voltage.
Existence, Uniqueness and Convergence of Simultaneous Distributed-Boundary Optimal Control Problems

We consider a steady-state heat conduction problem $P$ for the Poisson equation with mixed boundary conditions in a bounded multidimensional domain $\Omega$. We also consider a family of problems $P_{\alpha}$ for the same Poisson equation with mixed boundary conditions being $\alpha>0$ the heat transfer coefficient defined on a portion $\Gamma_{1}$ of the boundary. We formulate simultaneous \emph{distributed and Neumann boundary} optimal control problems on the internal energy $g$ within $\Omega$ and the heat flux $q$, defined on the complementary portion $\Gamma_{2}$ of the boundary of $\Omega$ for quadratic cost functional. Here the control variable is the vector $(g,q)$. We prove existence and uniqueness of the optimal control $(\overline{\overline{g}},\overline{\overline{q}})$ for the system state of $P$, and $(\overline{\overline{g}}_{\alpha},\overline{\overline{q}}_{\alpha})$ for the system state of $P_{\alpha}$, for each $\alpha>0$, and we give the corresponding optimality conditions. We prove strong convergence, in suitable Sobolev spaces, of the vectorial optimal controls, system and adjoint states governed by the problems $P_{\alpha}$ to the corresponding vectorial optimal control, system and adjoint states governed by the problem $P$, when the parameter $\alpha$ goes to infinity. We also obtain estimations between the solutions of these vectorial optimal control problems and the solution of two scalar optimal control problems characterized by fixed $g$ (with boundary optimal control $\overline{q}$) and fixed $q$ (with distributed optimal control $\overline{g}$), respectively, for both cases $\alpha>0$ and $\alpha=\infty$.
Effectiveness of a psychoeducational group intervention developed by primary care nurses on symptom control of pediatric patients with ADHD. ADHD parent study

ABSTRACT Attention Deficit Hyperactivity Disorder (ADHD) is a common childhood disorder with an estimated prevalence of 5%. The purpose of this study is to evaluate the effectiveness of a psychoeducational intervention performed by primary care nurses on parents of children with ADHD. We recruited participants composed of parents and children between 6 and 12 years with ADHD. We conducted a two-branch randomized control trial. The intervention programme consisted of nine group sessions (5-12 parents) with a duration of 10 months. The primary outcomes were the attention tasks measured with the Test of Variables of Attention (TOVA) and the ADHD symptomatology. Forty-eight children were included in the study. The average age of the parents was 42.6 years (standard deviation, SD: 6.3), and of the children 10.1 years (SD: 1.9), 81.3% were boys. TOVA and the symptoms after the intervention showed no statistically changes in both groups. The intervention group showed more knowledge of ADHD (17.3 vs 11.5, p = 0.008) and knowledge of drugs (6.1 vs. 4.5, p = 0.005) than the control group after the intervention. A psychoeducational intervention performed by primary care nurses on parents of children with ADHD did not show any modification in the attention tasks, and only changed the knowledge of ADHD of the parents that received the intervention.
Is virtual reality training superior to conventional treatment in improving lower extremity motor function in chronic hemiplegic patients?

Objectives This study aims to examine the effect of virtual reality (VR) training, frequently included in rehabilitation programs, on lower extremity functional status, mobility, balance, and walking speed in chronic stroke patients. Patients and methods This randomized, controlled study was conducted with 60 chronic stroke patients (26 males, 34 females; mean age: 64.0 years; range, 33 to 80 years) who presented to the physical therapy and rehabilitation outpatient clinic of the Kütahya Health Sciences University Evliya Çelebi Training and Research Hospital between February 2019 and February 2020. The participants were randomized to the VR group and the control group by simple randomization with 1:1 allocation. The VR group received 30 min of VR training and 30 min of conventional physiotherapy, while the control group received 60 min of conventional physiotherapy. The patients were evaluated before and after treatment using the Fugl-Meyer Assessment-Lower Extremity (FMA-LE), Rivermead Mobility Index (RMI), 10-m walk test (10MWT), and Berg Balance Scale (BBS). Results The FMA-LE, RMI, 10MWT, and BBS scores significantly improved in both groups after treatment (p<0.001). The post-treatment change in the FMA-LE score was significantly higher in the VR group than in the control group (Z=-3.560, p<0.001). Similarly, the change in the BBS score was significantly higher in the VR group (Z=-3.769, p<0.001). Post-treatment changes in the RMI and 10MWT were not significant (p>0.05). Conclusion Virtual reality training combined with conventional physiotherapy was found to be superior to conventional physiotherapy alone in improving lower extremity functional status in chronic stroke patients; therefore, adding a VR component to rehabilitation programs will have a favorable impact on treatment outcomes.
Almost full entropy subshifts uncorrelated to the M\"obius function

We show that if $y=(y_n)_{n\ge 1}$ is a bounded sequence with zero average along every infinite arithmetic progression then for every $N\ge 2$ there exist (unilateral or bilateral) subshifts $\Sigma$ over $N$ symbols, with entropy arbitrarily close to $\log N$, uncorrelated to $y$. In particular, for $y=\mu$ being the Mobius function, we get that there exist subshifts as above which satisfy the assertion of Sarnak's conjecture. The existence of positive entropy systems uncorrelated to the Mobius function is claimed in Sarnak's survey \cite{sarnak} (and attributed to Bourgain), however, to our knowledge no examples have ever been published. We fill in this gap and by the way we show that this has nothing to do with more advanced algebraic properties (for instance multiplicativity) of the considered sequence.
Iron K-shell emission from NGC 1068

The X-ray iron line emission from NGC 1068 is modeled using the new multiline, multilevel, non-LTE radiative transport code Altair and a detailed atomic model for Ne-like through-stripped iron. The X-rays passing through the ionized gas induce iron K-alpha line emission. The atomic model was constructed to describe in detail the K-shell ionization and K-alpha line emission, as well as to calculate the ionization state properly. A greater equivalent width than previously predicted is found because the observed K-alpha line is produced not only by fluorescence but also by line scattering of the continuum into the line of sight. The K-alpha equivalent width and energy are functions not only of the ionization parameter, but also of the column depth and temperature. For a likely model of NGC 1068, it is found that the iron abundance is about twice solar, but that modifications of this model may permit a smaller abundance. 35 refs.
Bootstrap Prediction Intervals for Autoregressive Models of Unknown or Infinite Lag Order

Recent studies on bootstrap prediction intervals for autoregressive (AR) model provide simulation findings when the lag order is known. In practical applications, however, the AR lag order is unknown or can even be infinite. This paper is concerned with prediction intervals for AR models of unknown or infinite lag order. Akaike's information criterion is used to estimate (approximate) the unknown (infinite) AR lag order. Small-sample properties of bootstrap and asymptotic prediction intervals are compared under both normal and non-normal innovations. Bootstrap prediction intervals are constructed based on the percentile and percentile-t methods, using the standard bootstrap as well as the bootstrap-after-bootstrap. It is found that bootstrap-after-bootstrap prediction intervals show small-sample properties substantially better than other alternatives, especially when the sample size is small and the model has a unit root or near-unit root. Copyright © 2002 by John Wiley & Sons, Ltd.
Simulation of the prompt energization and transport of radiation belt particles during the March 24, 1991 SSC

The authors model the rapid ([approximately]1 min) formation of a new electron radiation belt at L [approx equal] 2.5 that resulted from the Storm Sudden Commencement (SSC) of March 24, 1991 as observed by the CRRES satellite. Guided by the observed electric and magnetic fields, the authors represent the time-dependent magnetospheric electric field during the SSC by an asymmetric bipolar pulse that is associated with the compression and relaxation of the Earth's magnetic field. The authors follow the electrons using a relativistic guiding center code. The test-particle simulations show that electrons with energies of a few MeV at L > 6 were energized up to 40 MeV and transported to L [approx equal] 2.5 during a fraction of their drift period. The energization process conserves the first adiabatic invariant and is enhanced due to resonance of the electron drift motion with the time-varying electric field. Their simulation results, with an initial W[sup [minus]8] energy flux spectra, reproduce the observed electron drift echoes and show that the interplanetary shock impacted the magnetosphere between 1500 and 1800 MLT. 121 refs., 5 figs.
On categories of (phi, Gamma)-modules

Let K be a complete discretely valued field of mixed characteristics (0, p) with perfect residue field. One of the central objects of study in p-adic Hodge theory is the category of continuous representations of the absolute Galois group of K on finite-dimensional Qp-vector spaces. In recent years, it has become clear that this category can be studied more effectively by embedding it into the larger category of (phi, Gamma)-modules; this larger category plays a role analogous to that played by the category of vector bundles on a compact Riemann surface in the Narasimhan-Seshadri theorem on unitary representations of the fundamental group of said surface. This category turns out to have a number of distinct natural descriptions, which on one hand suggests the naturality of the construction, but on the other hand forces one to use different descriptions for different applications. We provide several of these descriptions and indicate how to translate certain key constructions, which were originally given in the context of modules over power series rings, to the more modern context of perfectoid algebras and spaces.
Computing an Exact Confidence Interval for the Common Odds Ratio in Several 2×2 Contingency Tables

Abstract A quadratic time network algorithm is provided for computing an exact confidence interval for the common odds ratio in several 2×2 independent contingency tables. The algorithm is shown to be a considerable improvement on an existing algorithm developed by Thomas (1975), which relies on exhaustive enumeration. Problems that would formerly have consumed several CPU hours can now be solved in a few CPU seconds. The algorithm can easily handle sparse data sets where asymptotic results are suspect. The network approach, on which the algorithm is based, is also a powerful tool for exact statistical inference in other settings.
Exponential instability for inverse elliptic problems with unknown boundaries

We prove that the inverse problem of determining unknown defects of various types in a conductor by performing electrostatic measurements at the boundary is severely ill-posed. We show that the ill-posedness does not depend on the nature of the defects to be determined and, more importantly, by the kind, choice and number of measurements performed.
Euler-Mellin integrals and A-hypergeometric functions

We consider integrals that generalize both Mellin transforms of rational functions of the form 1/f and classical Euler integrals. The domains of integration of our so-called Euler Mellin integrals are naturally related to the coamoeba of f, and the components of the complement of the closure of this coamoeba give rise to a family of these integrals. After performing an explicit meromorphic continuation of Euler Mellin integrals, we interpret them as A-hypergeometric functions and discuss their linear independence and relation to Mellin Barnes integrals.
An extremely high velocity CO outflow from NGC 7538 IRS 9

New observations of the luminous protostellar object NGC 7538 IRS 9 are presented. Lines of CO J = 3-2 show an extremely high velocity (EHV) red wing, with outflow velocities of 110 km/s. The EHV-emitting region is compact and is centered at a position 5 arcsec east of IRS 9. The emission in lower velocity (classical HV) gas is spatially extended and bipolar. The different spatial distribution and kinematics of the HV and EHV gas imply that the outflow activity of IRS 9 has been discontinuous. The activity which produced the extended HV outflow began roughly 16,000 yr ago, while the activity which produced the EHV gas began roughly 1200 yr ago. The EHV gas has only 3 percent of the mass of the HV gas, but 1.5 times the kinetic energy. 13 refs.
Bogomolov multipliers of all groups of order 128

This note is an implementation of the algorithm for computing Bogomolov multipliers as given in \cite{Mor11} in combination with \cite{Eic08} to effectively determine the multipliers of groups of order $128$. The two serving purposes are a continuation of the results \cite{Chu08,Chu09}, and an application \cite{Jez13}.
Classification of actions of compact abelian groups on subfactors with index less than 4

We classify actions of discrete abelian groups on some inclusions of von Neumann algebras, up to cocycle conjugacy. As an application, we classify actions of compact abelian groups on the inclusions of approximately finite dimensional (AFD) factors of type II1 with index less than 4, up to stable conjugacy.
On special subvarieties of Kuga varieties II

In this paper we prove the equidistribution of certain families of special subvarieties in Kuga varieties, which is a special case of the general Andre-Oort conjecture formulated for mixed Shimura varieties proposed by R.Pink. Our approach is parallel to the pure case treated in the works of L.Clozel, E.Ullmo, and A.Yafaev using tools from ergodic theory.
Optimized Acoustic Phantom Design for Characterizing Body Sound Sensors

Many commercial and prototype devices are available for capturing body sounds that provide important information on the health of the lungs and heart; however, a standardized method to characterize and compare these devices is not agreed upon. Acoustic phantoms are commonly used because they generate repeatable sounds that couple to devices using a material layer that mimics the characteristics of skin. While multiple acoustic phantoms have been presented in literature, it is unclear how design elements, such as the driver type and coupling layer, impact the acoustical characteristics of the phantom and, therefore, the device being measured. Here, a design of experiments approach is used to compare the frequency responses of various phantom constructions. An acoustic phantom that uses a loudspeaker to generate sound and excite a gelatin layer supported by a grid is determined to have a flatter and more uniform frequency response than other possible designs with a sound exciter and plate support. When measured on an optimal acoustic phantom, three devices are shown to have more consistent measurements with added weight and differing positions compared to a non-optimal phantom. Overall, the statistical models developed here provide greater insight into acoustic phantom design for improved device characterization.
Diffusional-thermal instability of diffusion flames

The diffusional–thermal instability, which gives rise to striped quenching patterns that have been observed for diffusion flames, is analysed by studying the model of a one-dimensional convective diffusion flame in the diffusion-flame regime of activation-energy asymptotics. Attention is focused principally on near-extinction conditions with Lewis numbers less than unity, in which the reactants with high diffusivity diffuse into the strong segments of the reaction sheet, so that the regions between the strong segments become deficient in reactant and subject to the local quenching that leads to the striped patterns. This analysis differs from other flame stability analyses in that the complete description of the dispersion relation is obtained from a composite expansion of the results of an analysis with the conventional convective-diffusive scaling and one with reaction-zone scaling. The results predict that striped patterns will occur, for flames sufficiently close to quasi-steady extinction, with a finite wavenumber that in convective–diffusive scaling is proportional to the cube root of the Zel'dovich number. The convective–diffusive response contributes to the stabilization of long-wavelength disturbances by through positive excess enthalpies by which the flame becomes more resistant to instability, while the reaction-zone response provides stabilization of short-wavelength disturbances by transverse diffusion, within the reactive inner layer, which relaxes the perturbed scalar fields towards their unperturbed states. As quasi-steady extinction is approached, marginal stability arises first at an intermediate range between these two scalings. Parametric results for this bifurcation point are obtained through numerical solutions of the associated generalized eigenvalue problems. Comparisons with measured pattern dimensions for different sets of reactants and diluents reveal excellent qualitative agreement.
Talbot effect application: measurement of distance with a Fourier-transform method

In this work, we use the diffraction properties of gratings (Talbot effect) to obtain a distance measurement through a Fourier transform method. The proposed technique is easy to use and requires low mechanical stability. Furthermore, it is suitable for out-of-laboratory applications and provides real-time (frame refresh) data acquisition capability.
Ping pong on CAT(0) cube complexes

Let $G$ be a group acting properly and essentially on an irreducible, non-Euclidean finite dimensional CAT(0) cube complex $X$ without fixed points at infinity. We show that for any finite collection of simultaneously inessential subgroups $\{H_1, \ldots, H_k\}$ in $G$, there exists an element $g$ of infinite order such that $\forall i$, $\langle H_i, g\rangle \cong H_i * \langle g\rangle$. We apply this to show that any group, acting faithfully and geometrically on a non-Euclidean possibly reducible CAT(0) cube complex, has property $P_{naive}$ i.e. given any finite list $\{g_1, \ldots, g_k\}$ of elements from $G$, there exists $g$ of infinite order such that $\forall i$, $\langle g_i, g\rangle \cong \langle g_i \rangle *\langle g\rangle$. This applies in particular to the Burger-Moses simple groups that arise as lattices in products of trees. The arguments utilize the action of the group on its Poisson boundary and moreover, allow us to summarise equivalent conditions for the reduced $C^*$-algebra of the group to be simple.