Miracle-dz/UniFAR-FTUs huggingface dataset:
Convergence of adaptive markov chain monte carlo algorithms

In the thesis, we study ergodicity of adaptive Markov Chain Monte Carlo methods (MCMC) based on two conditions (Diminishing Adaptation and Containment which together imply ergodicity), explain the advantages of adaptive MCMC, and apply the theoretical result for some applications. First we show several facts: 1. Diminishing Adaptation alone may not guarantee ergodicity; 2. Containment is not necessary for ergodicity; 3. under some additional condition, Containment is necessary for ergodicity. Since Diminishing Adaptation is relatively easy to check and Containment is abstract, we focus on the sufficient conditions of Containment. In order to study Containment, we consider the quantitative bounds of the distance between samplers and targets in total variation norm. From early results, the quantitative bounds are connected with nested drift conditions for polynomial rates of convergence. For ergodicity of adaptive MCMC, assuming that all samplers simultaneously satisfy nested polynomial drift conditions, we find that either when the number of nested drift conditions is greater than or equal to two, or when the number of drift conditions with some specific form is one, the adaptive MCMC algorithm is ergodic. For adaptive MCMC algorithm with Markovian adaptation, the algorithm satisfying simultaneous polynomial ergodicity is ergodic without those restrictions. We also discuss some recent results related to this topic. Second we consider ergodicity of certain adaptive Markov Chain Monte Carlo algorithms for multidimensional target distributions, in particular, adaptive Metropolis and adaptive Metropolis-within-Gibbs algorithms. We derive various sufficient conditions to ensure Containment, and connect the convergence rates of algorithms with the tail properties of the corresponding target distributions. We also present a Summable Adaptive Condition which, when satisfied, proves ergodicity more easily. Finally, we propose a simple adaptive Metropolis-within-Gibbs algorithm attempting to study directions on which the Metropolis algorithm can be run flexibly. The algorithm avoids the wasting moves in wrong directions by proposals from the full dimensional adaptive Metropolis algorithm. We also prove its ergodicity, and test it on a Gaussian Needle example and a real-life Case-Cohort study with competing risks. For the Cohort study, we describe an extensive version of Competing Risks Regression model, define censor variables for competing risks, and then apply the algorithm to estimate coefficients based on the posterior distribution.
Logarithmically Completely Monotonic Rational Functions

This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as non-overshooting reference tracking. Conditions are proposed to ensure a rational function is LCM, a result that enables the known space of linear continuous-time externally positive systems to be enlarged and an efficient and optimal pole-placement procedure for the monotonic tracking controller synthesis problem to be developed. The presented conditions are shown to be less conservative than existing approaches whilst being computationally tractable.
Tests of fit for discrete distributions based on the probability generating function

The use of the probability generating function in testing the fit of discrete distributions was proposed by Kocherlakota & Kocherlakota (1986), and further studied by Marques and Perez-Abreu (1989). In Rueda et al. (1991), a quadratic statistic to test the fit of a discrete distribution was proposed using the probability generating function and its empirical counterpart. This was illustrated for the Poisson case with known parameter. Here, we deal with some extensions: the Poisson case with unknown parameter and the negative Binomial distribution with known or unknown parameter p. We find the asymptotic distribution of the test statistic in each case, and show with the aid of some Monte Carlo studies the closeness of these asymptotic distributions. A connection is established between this quadratic test and the Cramer von Mises test of fit described in Spinelli (1994) and Spinelli and Stephens (1997), thus providing additional insight into these procedures. Also, a correction is made on the expression of .
Interpretation of the Observed Neutrino Emission from Three Tidal Disruption Events

Three Tidal Disruption Event candidates (AT2019dsg, AT2019fdr, and AT2019aalc) have been associated with high-energy astrophysical neutrinos in multimessenger follow-ups. In all cases, the neutrino observation occurred (100) days after the maximum of the optical-ultraviolet (OUV) luminosity. We discuss unified fully time-dependent interpretations of the neutrino signals where the neutrino delays are not a statistical effect, but rather the consequence of a physical scale of the post-disruption system. Noting that X-ray flares and infrared (IR) dust echoes have been observed in all cases, we consider three models in which quasi-isotropic neutrino emission is due to the interactions of accelerated protons of moderate, medium, and ultra-high energies with X-rays, OUV, and IR photons, respectively. We find that the neutrino time delays can be well described in the X-ray model assuming magnetic confinement of protons in a calorimetric approach if the unobscured X-ray luminosity is roughly constant over time, and in the IR model, where the delay is directly correlated with the time evolution of the echo luminosity (for which a model is developed here). The OUV model exhibits the highest neutrino production efficiency. In all three models, the highest neutrino fluence is predicted for AT2019aalc, due to its high estimated supermassive black hole mass and low redshift. All models result in diffuse neutrino fluxes that are consistent with observations.
Revising Properties of Planet–Host Binary Systems. III. There Is No Observed Radius Gap for Kepler Planets in Binary Star Systems

Binary stars are ubiquitous; the majority of solar-type stars exist in binaries. Exoplanet occurrence rate is suppressed in binaries, but some multiples do still host planets. Binaries cause observational biases in planet parameters, with undetected multiplicity causing transiting planets to appear smaller than they truly are. We have analyzed the properties of a sample of 119 planet-host binary stars from the Kepler mission to study the underlying population of planets in binaries that fall in and around the radius valley, which is a demographic feature in period–radius space that marks the transition from predominantly rocky to predominantly gaseous planets. We found no statistically significant evidence for a radius gap for our sample of 122 planets in binaries when assuming that the primary stars are the planet hosts, with a low probability (p < 0.05) of the binary planet sample radius distribution being consistent with the single-star population of small planets via an Anderson–Darling test. These results reveal demographic differences in the planet size distribution between planets in binary and single stars for the first time, showing that stellar multiplicity may fundamentally alter the planet formation process. A larger sample and further assessment of circumprimary versus circumsecondary transits is needed to either validate this nondetection or explore other scenarios, such as a radius gap with a location that is dependent on binary separation.
Ion turbulence and thermal transport in laser-produced plasmas

In the interaction of high-intensity lasers with target plasmas the transport of thermal enelgy from the region in which the radiation is absorbed, to the cold dense plasma in the interior of the target, is an issue of central importance. It is also one of great complexity and as such is still largely unresolved. Ion-acoustic turbulence, self-generated magnetic fields and the inadequacy of classical transport theory have all been widely canvassed by way of explaining the observations which show thermal transport much reduced below what would be expected from conventional arguments. In this paper the role of ion turbulence as a flux limiter is addressed with particular regard to recent experiments in which target plasmas were irradiated by 1·06 µm neodymium laser light at irradiances of 1015W cm−2 and greater. Saturation levels of the ion-acoustic turbulence driven by a combination of a suprathermal electron current and a heat flux have been calculated on the basis of perturbed orbit theory. The levels of turbulence are found to be markedly lower than those commonly estimated from simple trapping arguments and too low to explain the thermal flux inhibition observed in the experiments used as a basis for the model.
Transport and diffusion of particles due to transverse drift waves

Transport and diffusion of plasma particles perpendicular and parallel to the magnetic field is discussed in the framework of the transverse drift wave theory. The starting model includes the density and magnetic field gradients perpendicular to the magnetic field vector. In such an inhomogeneous environment the transverse drift wave naturally develops. The transverse drift wave is a low frequency mode, with the frequency far below the ion gyro-frequency, it is driven by these gradients and it propagates perpendicular to them. The mode is also purely perpendicular to the magnetic field and it is electromagnetically transverse, which implies that when its wave vector is perpendicular to the magnetic field vector, the perturbed electric field is along the equilibrium magnetic field, while in the same time the perturbed magnetic field is in the direction of the background gradients. In application to the solar wind, it is shown that very small wave electric field amplitude, of the order of 10 −7 V/m, within one wave period can produce the drift of protons in both directions, perpendicular to the ecliptic plane and also along the background magnetic field, to distances measured in millions of kilometers. The electric field along the magnetic field vector implies particle acceleration in the same direction. When a critical threshold velocity of the particle is achieved, the particle motion becomes stochastic. This is a completely new nonlinear stochastic mechanism which follows from the very specific geometry of the transverse drift mode. Particle drift perpendicular to the magnetic field vector means a diffusion of particles, with the effective diffusion coefficient for ions that is at least 11 orders of magnitude larger than the classic diffusion coefficient. The features of this diffusion are: within certain time interval, initially faster particles will diffuse to larger distances, and the same holds for protons in comparison to heavier ions. For electrons the effective diffusion coefficient can easily match the one obtained from observations, i.e., to become of the order of 10 17 m 2 /s. It is also expected that the wave-induced stochastic motion will considerably increase the effective collision frequency in such an environment which is, with respect to its mean parameters, practically collision-lees. Hence, the solar wind regions affected by such a stochastic acceleration may show various unexpected features that are typical for collisional plasmas.
Quantum fluctuations, particles and entanglement: solving the quantum measurement problems

The so-called quantum measurement problems are solved from a new perspective. One of the main observations is that the basic entities of our world are particles, elementary or composite. It follows that each elementary process, hence each measurement process at its core, is a spacetime, pointlike, event. Another key idea is that, when a microsystem ψ gets into contact with the experimental device, factorization of ψ rapidly fails and entangled mixed states appear. The wave functions for the microsystem-apparatus coupled system for different measurement outcomes then lack overlapping spacetime support. It means that the aftermath of each measurement is a single term in the sum: a “wave-function collapse”. Our discussion leading to a diagonal density matrix, ρ = diag(|c 1|2,…,|cn |2,…) shows how the information encoded in the wave function |ψ〉=∑ncn|n〉 gets transcribed, via entanglement with the experimental device and environment, into the relative frequencies Pn = |cn |2 for various experimental outcomes F = fn . Our discussion represents the first, significant steps towards filling in the logical gaps in the conventional interpretation based on Born’s rule, replacing it with a clearer understanding of quantum mechanics. Accepting objective reality of quantum fluctuations, independent of any experiments, and independently of human presence, one renounces the idea that in a fundamental, complete theory of Nature the result of each single experiment must necessarily be predictable.
Low profile antenna study using the physical optics hybrid method (POHM)

POHM is applied to the design of the low-profile IFF (identification of friend or foe) airborne antenna whose height is less than 1 in. The basic idea of the POHM is that the physical optics technique is used to extend the application of the method of moments to a larger class of problems. The POHM program is tested with geometrical optics, geometrical theory of diffraction, and measured data. It is seen that the accuracy of the POHM is quite satisfactory for large ground plates. In the angular region, z>or=0, the accuracy of the POHM is very high because the physical optics currents on the body are included. However, the accuracy decreases because the POHM assumes that no currents exist on the shadow area (z<0) of the surface on the body. <<ETX>>
Exploiting Unlabeled Data for Feedback Efficient Human Preference based Reinforcement Learning

Preference Based Reinforcement Learning has shown much promise for utilizing human binary feedback on queried trajectory pairs to recover the underlying reward model of the Human in the Loop (HiL). While works have attempted to better utilize the queries made to the human, in this work we make two observations about the unlabeled trajectories collected by the agent and propose two corresponding loss functions that ensure participation of unlabeled trajectories in the reward learning process, and structure the embedding space of the reward model such that it reflects the structure of state space with respect to action distances. We validate the proposed method on one locomotion domain and one robotic manipulation task and compare with the state-of-the-art baseline PEBBLE. We further present an ablation of the proposed loss components across both the domains and find that not only each of the loss components perform better than the baseline, but the synergic combination of the two has much better reward recovery and human feedback sample efficiency.
On the scintillation response of NaI(TI)-crystals

Several articles have been reviewed on the scintillation response of NaI(Tl). Those publications which report results obtained with radioactive sources either dispersed throughout the NaI(Tl)-lattice or located inside the wells of NaI(Tl)-crystals match within a /spl plusmn/0.9% standard deviation of a linear scintillation response between 3 MeV and 3 keV. Several authors who plated their sources outside the crystals measured nonlinear responses of NaT(TI) with up to /spl plusmn/7% of standard deviations between 700 and 4.5 keV. The presented analysis suggests that the observed nonlinearity is not an intrinsic effect of NaI(TI) but could be caused, at least partly, by effects occurring at the radiation entrance surfaces of the crystals.
On the convergence result of the gradient-push algorithm on directed graphs with constant stepsize

Gradient-push algorithm has been widely used for decentralized optimization problems when the connectivity network is a direct graph. This paper shows that the gradient-push algorithm with stepsize $\alpha>0$ converges exponentially fast to an $O(\alpha)$-neighborhood of the optimizer under the assumption that each cost is smooth and the total cost is strongly convex. Numerical experiments are provided to support the theoretical convergence results.
Analytic elastic coefficients in molecular calculations: Finite strain, nonaffine displacements, and many-body interatomic potentials

Elastic constants are among the most fundamental and important properties of solid materials, which is why they are routinely characterized in both experiments and simulations. While conceptually simple, the treatment of elastic constants is complicated by two factors not yet having been concurrently discussed: finite-strain and non-affine, internal displacements. Here, we revisit the theory behind zero-temperature, finite-strain elastic constants and extend it to explicitly consider non-affine displacements. We further present analytical expressions for second-order derivatives of the potential energy for two-body and generic many-body interatomic potentials, such as cluster and empirical bond-order potentials. Specifically, we revisit the elastic constants of silicon, silicon carbide and silicon dioxide under hydrostatic compression and dilatation. Based on existing and new results, we outline the effect of multiaxial stress states as opposed to volumetric deformation on the limits of stability of their crystalline lattices.
Quantum symmetry in multigraphs (part I)

We introduce various notions of quantum symmetry in a directed or undirected multigraph with no isolated vertex and explore relations among them. If the multigraph is single edged (that is, a simple graph where loops are allowed), all our notions of quantum symmetry reduce to already existing notions of quantum symmetry provided by Bichon and Banica. Our constructions also show that any multigraph with at least two pairs of vertices with multiple edges among them possesses genuine quantum symmetry.
An Optimal Projection Framework for Structure-Preserving Model Reduction of Linear Systems

This paper presents a structure-preserving model reduction framework for linear systems, in which the $\mathcal{H}_2$ optimization is incorporated with the Petrov-Galerkin projection to preserve structural features of interest, including dissipativity, passivity, and bounded realness. The model reduction problem is formulated in a nonconvex optimization setting on a noncompact Stiefel manifold, aiming to minimize the $\mathcal{H}_2$ norm of the approximation error between the full-order and reduced-order models. The explicit expression for the gradient of the objective function is derived, and two gradient descent procedures are applied to seek for a (local) minimum, followed by a theoretical analysis on the convergence properties of the algorithms. Finally, the performance of the proposed method is demonstrated by two numerical examples which consider stability-preserving and passivity-preserving model reduction problems, respectively.
Meta-Album: Multi-domain Meta-Dataset for Few-Shot Image Classification

We introduce Meta-Album, an image classification meta-dataset designed to facilitate few-shot learning, transfer learning, meta-learning, among other tasks. It includes 40 open datasets, each having at least 20 classes with 40 examples per class, with verified licences. They stem from diverse domains, such as ecology (fauna and flora), manufacturing (textures, vehicles), human actions, and optical character recognition, featuring various image scales (microscopic, human scales, remote sensing). All datasets are preprocessed, annotated, and formatted uniformly, and come in 3 versions (Micro $\subset$ Mini $\subset$ Extended) to match users' computational resources. We showcase the utility of the first 30 datasets on few-shot learning problems. The other 10 will be released shortly after. Meta-Album is already more diverse and larger (in number of datasets) than similar efforts, and we are committed to keep enlarging it via a series of competitions. As competitions terminate, their test data are released, thus creating a rolling benchmark, available through OpenML.org. Our website https://meta-album.github. io/ contains the source code of challenge winning methods, baseline methods, data loaders, and instructions for contributing either new datasets or algorithms to our expandable meta-dataset.
Deep comparisons of Neural Networks from the EEGNet family

A preponderance of brain–computer interface (BCI) publications proposing artificial neural networks for motor imagery (MI) electroencephalography (EEG) signal classification utilize one of the BCI Competition datasets. However, these databases encompass MI EEG data from a limited number of subjects, typically less than or equal to 10. Furthermore, the algorithms usually include only bandpass filtering as a means of reducing noise and increasing signal quality. In this study, we conducted a comparative analysis of five renowned neural networks (Shallow ConvNet, Deep ConvNet, EEGNet, EEGNet Fusion, and MI-EEGNet) utilizing open-access databases with a larger subject pool in conjunction with the BCI Competition IV 2a dataset to obtain statistically significant results. We employed the FASTER algorithm to eliminate artifacts from the EEG as a signal processing step and explored the potential for transfer learning to enhance classification results on artifact-filtered data. Our objective was to rank the neural networks; hence, in addition to classification accuracy, we introduced two supplementary metrics: accuracy improvement from chance level and the effect of transfer learning. The former is applicable to databases with varying numbers of classes, while the latter can underscore neural networks with robust generalization capabilities. Our metrics indicated that researchers should not disregard Shallow ConvNet and Deep ConvNet as they can outperform later published members of the EEGNet family.
Complexity Function of Jammed Configurations of Rydberg Atoms

In this article, we determine the complexity function (configurational entropy) of jammed configurations of Rydberg atoms on a one-dimensional lattice. Our method consists of providing asymptotics for the number of jammed configurations determined by direct combinatorial reasoning. In this way we reduce the computation of complexity to solving a constrained optimization problem for the Shannon's entropy function. We show that the complexity can be expressed explicitly in terms of the root of a certain polynomial of degree $b$, where $b$ is the so-called blockade range of a Rydberg atom. Our results are put in a relation with the model of irreversible deposition of $k$-mers on a one-dimensional lattice.
Infinite Action Contextual Bandits with Reusable Data Exhaust

For infinite action contextual bandits, smoothed regret and reduction to regression results in state-of-the-art online performance with computational cost independent of the action set: unfortunately, the resulting data exhaust does not have well-defined importance-weights. This frustrates the execution of downstream data science processes such as offline model selection. In this paper we describe an online algorithm with an equivalent smoothed regret guarantee, but which generates well-defined importance weights: in exchange, the online computational cost increases, but only to order smoothness (i.e., still independent of the action set). This removes a key obstacle to adoption of smoothed regret in production scenarios.