Miracle-dz/UniFAR-FTUs huggingface dataset:
Fundamental limits of low-rank matrix estimation

We consider the high-dimensional inference problem where the signal is a low-rank matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension setting for the mutual information between the signal and the observations, as well as the matrix minimum mean square error, while the rank of the signal remains constant. This allows to locate the information-theoretic threshold for this estimation problem, i.e. the critical value of the signal intensity below which it is impossible to recover the low-rank matrix.
Exponential relaxation of the Nos\'e-Hoover equation under Brownian heating

We study a stochastic perturbation of the Nos\'e-Hoover equation (called the Nos\'e-Hoover equation under Brownian heating) and show that the dynamics converges at a geometric rate to the augmented Gibbs measure in a weighted total variation distance. The joint marginal distribution of the position and momentum of the particles in turn converges exponentially fast in a similar sense to the canonical Boltzmann-Gibbs distribution. The result applies to a general number of particles interacting through wide class of potential functions, including the usual polynomial type as well as the singular Lennard-Jones variety.
Magneto-optical conductivity in graphene

Landau level quantization in graphene reflects the Dirac nature of its quasiparticles and has been found to exhibit an unusual integer quantum Hall effect. In particular, the lowest Landau level can be thought of as shared equally by electrons and holes, and this leads to characteristic behaviour of the magneto-optical conductivity as a function of frequency Ω for various values of the chemical potential μ. Particular attention is paid to the optical spectral weight under various absorption peaks and its redistribution as μ is varied. We also provide results for magnetic field B as well as chemical potential sweeps at selected fixed frequencies, which can be particularly useful for possible measurements in graphene. Both diagonal and Hall conductivities are considered.
Two-Dimensional Accretion Disks at Subcritical Luminosity

To examine subcritical accretion disks, we performed two-dimensional axisymmetric calculations by solving a set of fully non-linear hydrodynamic equations coupled with radiation transport. Focusing on the accretion disks of neutron stars near to the Eddington luminosity LE, we obtained thermally stable accretion disks where the radiation pressure and electron scattering are dominant. The thermally stable disks are interpreted in terms of the slim accretion-disk theory. While the accretion disks are unstable to convection and convective cells generally stretch from the disk mid-plane to the disk surface in the inner disk. It has been found that convection is an important energy-transfer mechanism along the vertical direction of the disk. A very rarefied, hot, and optically thin region is formed along the rotational axis of the disk. The relativistic jet with a collimation angle of less than 10° is generated in the rarefied optically thin region, mainly due to the dominant radiation-pressure force. The results of subcritical accretion onto a neutron star are discussed in relation to SS 433.
Convexity of a stochastic control functional related to importance sampling of It\^o diffusions

We consider the problem of rare event importance sampling, where the random variable of interest is a path functional of an Ito diffusion computed up to the first exit from a $d$-dimensional bounded domain. Dupuis and Wang (\textit{Ann. Appl. Probab.}, 15 (2005), pp. 1-38) studied the importance sampling problem by formulating it as a stochastic optimal control problem, where the value function is related to the conditional cumulant generating function of the random variable. In this paper, we show that the sufficient conditions for the value function to be twice-differentiable and $\alpha$-uniformly Holder continuous on the closure of the domain are also sufficient conditions for positive definiteness of the second variation of the control functional on the space of differentiable, $\alpha$-uniformly Holder continuous $\mathbb{R}^d$-valued feedback controls. We derive an expression for the second variation using Kazamaki's sufficient condition for $L^q$-boundedness of exponential martingales, and using Fredholm theory to prove the finiteness of the moment generating function of the first exit time over any bounded interval containing the origin. The strict convexity result suggests that one may be able to solve the corresponding Hamilton-Jacobi-Bellman boundary value problem in a dimension-robust way, by combining convex optimisation and Monte Carlo methods. We apply the result to analyse a gradient descent algorithm proposed by Hartmann and Schutte (\textit{J. Stat. Mech. Theor. Exp.} (2012), P11004) for efficient rare event simulation.
Adjoint L-Functions for GL(3) and U2,1

We show that the finite part of the adjoint $L$-function (including contributions from all non-archimedean places, including ramified places) is holomorphic in ${\textrm{Re}}(s) \ge 1/2$ for a cuspidal automorphic representation of ${\textrm{GL}}_3$ over a number field. This improves the main result of [21]. We obtain more general results for twisted adjoint $L$-functions of both ${\textrm{GL}}_3$ and quasisplit unitary groups. For unitary groups, we explicate the relationship between poles of twisted adjoint $L$-functions, endoscopy, and the structure of the stable base change lifting.
Reducing the Candidate Line List for Practical Integration of Switching into Power System Operation

Optimized operation of the transmission network is one solution to supply extra demand by more efficient use of transmission facilities, and line switching is one main tool to achieve this goal. In this paper, we add extra constraints to OPF formulation to limit the maximum number of switching operations in every hour based on network conditions, and add switching cost in the objective function to represent extra maintenance cost as a result of frequent switching. We also propose an algorithm to remove less important lines for switching in different loading conditions, so OPF with transmission switching will be solved faster for real-time operation. It is applied to a case study with several operation hours.
A spectral surface plasmon resonance sensor based on transmission grating: architecture analysis dedicated to spectral sensors

Surface Plasmons Resonance (SPR) architectures based on grating coupler/disperser combination is an attractive alternative for spectral-based sensing. We present a new concept where the plasmon coupling occurs through thin film grating and sensing occurs via the first diffraction order in reflective or transmitive mode. The developed geometry is dedicated to droplet sensing. The extension of the architecture to bi-dimensional array of sensors is also facilitated. This paper describes several designs of sensors. The analysis of their theoretical performances is demonstrated and compared, including a sensitivity evaluation.
Weight-Lattice Discretization of Weyl-Orbit Functions

Weyl-orbit functions have been defined for each simple Lie algebra, and permit Fourier-like analysis on the fundamental region of the corresponding affine Weyl group. They have also been discretized, using a refinement of the coweight lattice, so that digitized data on the fundamental region can be Fourier-analyzed. The discretized orbit function has arguments that are redundant if related by the affine Weyl group, while its labels, the Weyl-orbit representatives, invoke the dual affine Weyl group. Here we discretize the orbit functions in a novel way, by using the weight lattice. A cleaner theory results, with symmetry between the arguments and labels of the discretized orbit functions. Orthogonality of the new discretized orbit functions is proved, and leads to the construction of unitary, symmetric matrices with Weyl-orbit-valued elements. For one type of orbit function, the matrix coincides with the Kac-Peterson modular $S$ matrix, important for Wess-Zumino-Novikov-Witten conformal field theory.
A finite element model based on triangular mesh for convection-dominated stationary flows

The fluctuation distribution method is presented in this work to deal with the convection terms of the general transport equation. The fluctuation represents the convective surface exchange within an element. The solution method consists of defining numerical schemes to distribute this fluctuation. To that end, we introduce a new variable to rewrite the variational formulation with linear triangular element and weighted functions appropriately selected. The method is found to be accurate with minimum of dispersion or diffusion in the vicinity of the discontinuity. This method is interesting because there are no parameters to choose and can be an alternative to the famous streamline upwind Petrov–Galerkin method.
Scaling functions in the square Ising model

We show and give the linear differential operators  q scal ? > of order q = n 2 / 4 + n + 7 / 8 + ( − 1 ) n / 8 ? > , for the integrals I n ( r ) ? > which appear in the two-point correlation scaling function of Ising model F ± ( r ) = lim scaling  ± − 2 < &sgr; 0,0 &sgr; M , N > = ∑ n I n ( r ) ? > . The integrals I n ( r ) ? > are given in expansion around r = 0 ? > in the basis of the formal solutions of  q scal ? > with transcendental combination coefficients. We find that the expression r 1 / 4 exp ( r 2 / 8 ) ? > is a solution of the Painlevé VI equation in the scaling limit. Combinations of the (analytic at r = 0 ? > ) solutions of  q scal ? > sum to exp ( r 2 / 8 ) ? > . We show that the expression r 1 / 4 exp ( r 2 / 8 ) ? > is the scaling limit of the correlation function C ( N , N ) ? > and C ( N , N + 1 ) ? > . The differential Galois groups of the factors occurring in the operators  q scal ? > are given.
Work-Related Stress and Turnover Intention during Covid-19 among Nurses in

The outbreak of COVID-19 had significantly impacted the healthcare system, placing it under tremendous strain. Nurses were shown to have suffered the impact of the pandemic, suggested traumatization and estimated a mass turnover intention among nurses globally due to the pandemic [1] . The objective of this cross-sectional study is to assess the prevalence of work-related stress and turnover intention among nurses in the Hospital Universiti Sains Malaysia (Hospital USM). This hospital is a teaching hospital with 830 beds that offers various specialties recognized as Hybrid COVID Hospital in managing patients. This study utilized multi-stage sampling. The population was stratified into three strata which were, Medical-Surgical wards, Specialty wards (Pediatric, Obstetrics and Gynecology), and Critical Care wards. Next, the wards were selected through a simple random method. The nurses from the selected wards who follow inclusion criteria; nurses with grade U29 or U32 (KUP) with at least one year of working experience [2] were invited to join the study. A total of 365 nurses participated in this study by answering a self-administered questionnaire through Google Forms sent to them. The questionnaire included three parts; Part A sociodemographic data, Part B Nurse Stress Index (NSI) with scoring ranging from 30-150 and Part C Turnover Intention Scale (TIS-6) with a scoring of 9-18 [3] . The NSI is categorized into four categories: 30-60= no pressure, 61-90= This study found that work-related stress was significant among nurses although the data were collected towards the end of the pandemic approaching endemic phase. This could be explained by the uncertainty of the disease which was among the factors that could contribute to stress among frontliners [4] . Although the stress level is significant, the nurses in this study have low intention to leave. This could be possibly due to the job security working in government sector as this study was done in a semi-government hospital where the nurses receives benefits and securities such as salary remuneration and pension scheme [5] . Findings of the study shows a positive correlation between work-related stress and turnover intention. It is known that prolonged stress causes negative impact towards the physical and mental health of nurses, subsequently being the contributing factor towards turnover intention [6] . Nevertheless, this study implies that healthcare personnel should be alert regarding the issues and consequences related to work-related stress and turnover intention. Appropriate strategies or recommendations should be done to improve nurses’ satisfaction and addressing issues related that surround the nursing practice environment to improve the quality of work life among nurses and thus, improve the quality of care delivered and patient safety, thus retaining highly skilled nurses.
Offline Evaluation for Reinforcement Learning-Based Recommendation

In this paper, we argue that the paradigm commonly adopted for offline evaluation of sequential recommender systems is unsuitable for evaluating reinforcement learning-based recommenders. We find that most of the existing offline evaluation practices for reinforcement learning-based recommendation are based on a next-item prediction protocol, and detail three shortcomings of such an evaluation protocol. Notably, it cannot reflect the potential benefits that reinforcement learning (RL) is expected to bring while it hides critical deficiencies of certain offline RL agents. Our suggestions for alternative ways to evaluate RL-based recommender systems aim to shed light on the existing possibilities and inspire future research on reliable evaluation protocols.
Global weak solutions for generalized SQG in bounded domains

We prove the existence of global $L^2$ weak solutions for a family of generalized inviscid surface-quasi geostrophic (SQG) equations in bounded domains of the plane. In these equations, the active scalar is transported by a velocity field which is determined by the scalar through a more singular nonlocal operator compared to the SQG equation. The result is obtained by establishing appropriate commutator representations for the weak formulation together with good bounds for them in bounded domains.
A Geometric Homology Representative in the Space of Long Knots

We produce explicit geometric representatives of nontrivial homology classes in the space of long knots in R^d, when d is even. We generalize results of Cattaneo, Cotta-Ramusino and Longoni to define cycles which live off of the vanishing line of a homology spectral sequence due to Sinha. We use configuration space integrals to show our classes pair nontrivially with cohomology classes due to Longoni.
WFC3 Near-IR Channel: PSF and Plate Scale Study

This report focuses on the PSF properties and plate scale optimization for the Near-IR channel of WFC3. We discuss how various effects lead to the final observed PSF in NICMOS Camera 2 and suggest apodization of the cold stop as a possible way to improve contrast for the Near-IR channel of WFC3. We derive a model for the pixel response of the NICMOS arrays and use this model to produce simulated images which are then employed to evaluate the WFC3 photometric accuracy as a function of pixel scale. We find that images with a pixel size of 0.15’’ are shallower than those with a pixel size of 0.10’’ by about 0.3 mag. This can be compensated by longer exposure times still maintaing a 45 percent discovery efficiency advantage for the larger pixel size. The difference between the two pixel sizes in the presence of crowding is much smaller than the deviation of both from the ideal case of infinite resolution.
General maximum principles for optimal control problems of stochastic Volterra integral equations

Optimal control problems of forward stochastic Volterra integral equations (SVIEs) are formulated and studied. When control region is arbitrary subset of Euclidean space and control enters into the diffusion, necessary conditions of Pontryagin's type for optimal controls are established via spike variation. Our conclusions naturally cover the analogue of stochastic differential equations (SDEs), and our developed methodology drops the reliance on Ito formula and second-order adjoint equations. Some new features, that are concealed in the SDEs framework, are revealed in our situation. For example, instead of using second-order adjoint equations, it is more appropriate to introduce second-order adjoint processes. Moreover, the conventional way of using one second-order adjoint equation is inadequate here. In other words, two adjoint processes, which just merge into the solution of second-order adjoint equation in SDEs situation, are actually required and proposed in our setting.
Alignment of a nematic liquid crystal induced by anisotropic photo-oxidation of photosensitive polyimide films

The alignment of a nematic liquid crystal (LC) could be induced by three polyimide (PI) films exposed to linearly polarized ultraviolet (UV) light of long wavelength (366 nm). The alignment could also be modified by changing the direction of polarization of the linearly polarized light (LPL). Infrared (IR) and UV-visible spectroscopy indicated that among the three PI films the PI with a benzophenone moiety and the PI with a diphenyl methane moiety were sensitive to UV radiation and susceptible to remarkable ablation after irradiation with LPL in air. Polarized UV-visible spectroscopy indicated that dichroism of the PI films was caused by LPL and altered by changing the polarization of the LPL. Furthermore, the PI films irradiated under vacuum showed little reduction in intensity of IR bands, which is in sharp contrast to the marked decreases in samples irradiated in atmospheres containing oxygen. This proves that oxygen is necessary to the ablative process of the PI films. Our results indicate that the me.
Frequency of Recurrent Events at Failure Time

Recurrent events arise in many longitudinal medical studies where time to a terminal event or failure is the primary endpoint. With incomplete follow-up data, the analysis of recurrent events is a challenge owing to their association with the failure. One specific quantity of interest rarely addressed in the statistical literature is the recurrence frequency at the failure time; an example is hospitalization frequency, which is often used as a rough measure of lifetime medical cost. In this article we show that a marginal model (e.g., the log-linear model) of the recurrence frequency, although desirable, is typically not identifiable. For this reason, we advocate modeling the recurrent events and the failure time jointly, and propose an approach to forming semiparametric joint models from prespecified marginal ones. We suggest two conceptually simple and nested regression models aiming at the recurrence frequency as a mark of the failure and at the process of recurrent events. We formulate monotone estimating functions and propose novel interval-estimation procedures to accommodate non-smooth estimating functions. The resulting estimators are consistent and asymptotically normal. Simulation studies and the application to an AIDS clinical trial exhibit that these proposals are easy to implement and reliable for practical use. Finally, we generalize our proposals to marked recurrent events, and also devise a global inference procedure for recurrent events of multiple types.
A Liouville Theorem for Solutions of Degenerate Monge-Ampère Equations

In this paper, we give a new proof of a celebrated theorem of Jörgens which states that every classical convex solution of has to be a second order polynomial. Our arguments do not use complex analysis, and can be applied to establish such Liouville type theorems for solutions of a class of degenerate Monge-Ampère equations. We prove that every convex generalized (or Alexandrov) solution of where α > −1, has to be for some constants a > 0, b and a linear function ℓ(x 1, x 2). This work is motivated by the Weyl problem with nonnegative Gauss curvature.
A Feasible Approach For The Force Control Of Traction Wheels Driven By Electric Motors

This study proposes a novel approach to evaluating and controlling the traction force of a wheel directly driven by an electric motor on different road surfaces. Instead of slip ratio measurements, the database of the motor called the current‐RPM‐torque database can evaluate the traction force of the wheel. The feedback of the measured current and the rotational speed can assist the autonomous traction controller synthesized from this database by the neural network approach when one traction wheel of the vehicle is traveling on different kinds of road surfaces. The adequate gains which are the training data for the neural network control synthesis have to satisfy the assigned specifications in time domain for different slip ratios. This paper also finds that the adequate gains mainly depend on slip ratio slope rather than slip ratio. Based on a scenario similar to real situations, the simulated results in this study show that it is feasible to evaluate and control the traction force through the motor database by the feedback of the current and the RPM.
Human UPF 3 A and UPF 3 B enable fault-tolerant activation of nonsense-mediated mRNA decay

The paralogous human proteins UPF 3 A and UPF 3 B are involved in recognizing mRNAs targeted by nonsense-mediated mRNA decay (NMD). UPF 3 B has been demonstrated to support NMD, presum-ably by bridging an exon junction complex (EJC) to the NMD factor UPF 2 . The role of UPF 3 A has been described either as a weak NMD activator or an NMD inhibitor. Here, we present a comprehensive functional analysis of UPF 3 A and UPF 3 B in human cells using combinatory experimental approaches. Overexpression or knockout of UPF 3 A as well as knockout of UPF 3 B did not substantially change global NMD activity. In contrast, the co-depletion of UPF 3 A and UPF 3 B resulted in a marked NMD inhibition and a transcriptome-wide upregulation of NMD substrates, demonstrat-ing a functional redundancy between both NMD factors. In rescue experiments, UPF 2 or EJC binding-deficient UPF 3 B largely retained NMD activity. However, combinations of different mutants, including deletion of the middle domain, showed additive or synergistic effects and therefore failed to maintain NMD. Collectively, UPF 3 A and UPF 3 B emerge as fault-tolerant, functionally redundant NMD activators in human cells.