Miracle-dz/UniFAR-FTUs huggingface dataset:
Minimum-Violation Planning for Autonomous Systems: Theoretical and Practical Considerations

This paper considers the problem of computing an optimal trajectory for an autonomous system that is subject to a set of potentially conflicting rules. First, we introduce the concept of prioritized safety specifications, where each rule is expressed as a temporal logic formula with its associated weight and priority. The optimality is defined based on the violation of such prioritized safety specifications. We then introduce a class of temporal logic formulas called si-FLTLGxand develop an efficient, incremental sampling-based approach to solve this minimum-violation planning problem with guarantees on asymptotic optimality. We illustrate the application of the proposed approach in autonomous vehicles, showing that si-FLTLGx formulas are sufficiently expressive to describe many traffic rules. Finally, we discuss practical considerations and present simulation results for a vehicle overtaking scenario.
A Convergence Analysis of the Multipole Expansion Method

The multipole expansion method (MEM) is a spatial discretization technique that is widely used in applications that feature scattering of waves from multiple spheres and circular cylinders. Moreover, it also serves as a key component in several other numerical methods in which scattering computations involving arbitrarily shaped objects are accelerated by enclosing the objects in artificial spheres or cylinders. A fundamental question is that of how fast the approximation error of the MEM converges to zero as the truncation number goes to infinity. Despite the fact that the MEM was introduced in 1913, and has been in widespread usage as a numerical technique since as far back as 1955, to the best of the authors' knowledge, a precise, quantitative characterization of the asymptotic rate of convergence of the MEM has not been obtained. In this work, we finally provide a resolution to this issue for the two-dimensional case. We begin by deriving bounds which are tight as long as the cylinders are not too close together. When some cylinders are, in fact, in close proximity to one another, these bounds become pessimistic. To obtain a more accurate characterization of the convergence in this regime, we formulate a first-order scattering approximation and derive its rate of convergence. Numerical simulations show that this approximation provides a far more accurate estimate of the convergence in the closely spaced regime than the aforementioned bounds. Our results establish MEM convergence rates that hold for all boundary conditions and boundary integral equation solution representations.
Towards Debiasing NLU Models from Unknown Biases

NLU models often exploit biases to achieve high dataset-specific performance without properly learning the intended task. Recently proposed debiasing methods are shown to be effective in mitigating this tendency. However, these methods rely on a major assumption that the types of bias should be known a-priori, which limits their application to many NLU tasks and datasets. In this work, we present the first step to bridge this gap by introducing a self-debiasing framework that prevents models from mainly utilizing biases without knowing them in advance. The proposed framework is general and complementary to the existing debiasing methods. We show that it allows these existing methods to retain the improvement on the challenge datasets (i.e., sets of examples designed to expose models' reliance on biases) without specifically targeting certain biases. Furthermore, the evaluation suggests that applying the framework results in improved overall robustness.
Bremsstrahlung emission and plasma characterization driven by moderately relativistic laser–plasma interactions

Relativistic electrons generated by the interaction of petawatt-class short laser pulses with solid targets can be used to generate bright x-rays via bremsstrahlung. The efficiency of laser energy transfer into these electrons depends on multiple parameters including the focused intensity and pre-plasma level. This paper reports experimental results from the interaction of a high intensity petawatt-class glass laser pulses with solid targets at a maximum intensity of 1019 W cm−2. In-situ measurements of specularly reflected light are used to provide an upper bound of laser absorption and to characterize focused laser intensity, the pre-plasma level and the generation mechanism of second harmonic light. The measured spectrum of electrons and bremsstrahlung radiation provide information about the efficiency of laser energy transfer.
Whispers from the dark side: Confronting light new physics with NANOGrav data

The NANOGrav collaboration has recently observed first evidence of a gravitational wave background (GWB) in pulsar timing data. Here we explore the possibility that this GWB is due to new physics, and show that the signal can be well fit also with peaked spectra like the ones expected from phase transitions (PTs) or from the dynamics of axion like particles (ALPs) in the early universe. We find that a good fit to the data is obtained for a very strong PT at temperatures around 1~MeV to 10~MeV. For the ALP explanation the best fit is obtained for a decay constant of F \approx 5\times 10^{17}F≈5×1017~GeV and an axion mass of 2\times 10^{-13}2×10−13~eV. We also illustrate the ability of PTAs to constrain the parameter space of these models, and obtain limits which are already comparable to other cosmological bounds.
Extrema of multi-dimensional Gaussian processes over random intervals

Abstract This paper studies the joint tail asymptotics of extrema of the multi-dimensional Gaussian process over random intervals defined as $P(u)\;:\! =\; \mathbb{P}\{\cap_{i=1}^n (\sup_{t\in[0,\mathcal{T}_i]} ( X_{i}(t) +c_i t )>a_i u )\}$ , $u\rightarrow\infty$ , where $X_i(t)$ , $t\ge0$ , $i=1,2,\ldots,n$ , are independent centered Gaussian processes with stationary increments, $\boldsymbol{\mathcal{T}}=(\mathcal{T}_1, \ldots, \mathcal{T}_n)$ is a regularly varying random vector with positive components, which is independent of the Gaussian processes, and $c_i\in \mathbb{R}$ , $a_i>0$ , $i=1,2,\ldots,n$ . Our result shows that the structure of the asymptotics of P(u) is determined by the signs of the drifts $c_i$ . We also discuss a relevant multi-dimensional regenerative model and derive the corresponding ruin probability.
Novel black-bounce geometries

We develop a number of novel "black-bounce" spacetimes. These are specific regular black holes where the "area radius" always remains non-zero, thereby leading to a "throat" that is either timelike (corresponding to a traversable wormhole), spacelike (corresponding to a "bounce" into a future universe), or null (corresponding to a "one-way wormhole"). We shall first perform a general analysis of the regularity conditions for such a spacetime, and then consider a number of specific examples. The examples are constructed using a mass function similar to that of Fan--Wang, and fall into several particular cases, such as the original Simpson--Visser model, a Bardeen-type model, and other generalizations thereof. We shall analyse the regularity, the energy conditions, and the causal structure of these models. The main results are several new geometries, more complex than before, with two or more horizons, with the possibility of an extremal case. We shall derive a general theorem regarding static space-time regularity, and another general theorem regarding (non)-satisfaction of the classical energy conditions.
Compressive Spectral Image Classification using 3D Coded Neural Network

Hyperspectral image classification (HIC) is an active research topic in remote sensing. However, the huge volume of three-dimensional (3D) hyperspectral images poses big challenges in data acquisition, storage, transmission and processing. To overcome these limitations, this paper develops a novel deep learning HIC approach based on the compressive measurements of coded-aperture snapshot spectral imaging (CASSI) system, without reconstructing the complete hyperspectral data cube. A new kind of deep learning strategy, namely 3D coded convolutional neural network (3D-CCNN) is proposed to efficiently solve for the HIC problem, where the hardware-based coded aperture is regarded as a pixel-wise connected network layer. An end-to-end training method is developed to jointly optimize the network parameters and the coded aperture pattern with periodic structure. The accuracy of HIC approach is effectively improved by involving the degrees of optimization freedom from the coded aperture. The superiority of the proposed method is assessed on some public hyperspectral datasets over the state-of-the-art HIC methods.
Influence of segmentation accuracy in structural MR head scans on electric field computation for TMS and tES

In several diagnosis and therapy procedures based on electrostimulation effect, the internal physical quantity related to the stimulation is the induced electric field. To estimate the induced electric field in an individual human model, the segmentation of anatomical imaging, such as magnetic resonance image (MRI) scans, of the corresponding body parts into tissues is required. Then, electrical properties associated with different annotated tissues are assigned to the digital model to generate a volume conductor. However, the segmentation of different tissues is a tedious task with several associated challenges specially with tissues appear in limited regions and/or low-contrast in anatomical images. An open question is how segmentation accuracy of different tissues would influence the distribution of the induced electric field. In this study, we applied parametric segmentation of different tissues to exploit the segmentation of available MRI to generate different quality of head models using deep learning neural network architecture, named ForkNet. Then, the induced electric field are compared to assess the effect of model segmentation variations. Computational results indicate that the influence of segmentation error is tissue-dependent. In brain, sensitivity to segmentation accuracy is relatively high in cerebrospinal fluid (CSF), moderate in gray matter (GM) and low in white matter for transcranial magnetic stimulation (TMS) and transcranial electrical stimulation (tES). A CSF segmentation accuracy reduction of 10% in terms of Dice coefficient (DC) lead to decrease up to 4% in normalized induced electric field in both applications. However, a GM segmentation accuracy reduction of 5.6% DC leads to increase of normalized induced electric field up to 6%. Opposite trend of electric field variation was found between CSF and GM for both TMS and tES. The finding obtained here would be useful to quantify potential uncertainty of computational results.
Restrained Italian domination in graphs

For a graph G = (V(G), E(G)), an Italian dominating function (ID function) f : V(G) → {0,1,2} has the property that for every vertex v ∈ V(G) with f(v) = 0, either v is adjacent to a vertex assigned 2 under f or v is adjacent to least two vertices assigned 1 under f. The weight of an ID function is ∑v∈V(G) f(v). The Italian domination number is the minimum weight taken over all ID functions of G. In this paper, we initiate the study of a variant of ID functions. A restrained Italian dominating function (RID function) f of G is an ID function of G for which the subgraph induced by {v ∈ V(G) | f(v) = 0} has no isolated vertices, and the restrained Italian domination number γrI (G) is the minimum weight taken over all RID functions of G. We first prove that the problem of computing this parameter is NP-hard, even when restricted to bipartite graphs and chordal graphs as well as planar graphs with maximum degree five. We prove that γrI(T) for a tree T of order n ≥ 3 different from the double star S2,2 can be bounded from below by (n + 3)/2. Moreover, all extremal trees for this lower bound are characterized in this paper. We also give some sharp bounds on this parameter for general graphs and give the characterizations of graphs G with small or large γrI (G).
A Unified Description of Spin Transport, Weak Antilocalization and Triplet Superconductivity in Systems with Spin-Orbit Coupling

The Eilenberger equation is a standard tool in the description of superconductors with an arbitrary degree of disorder. It can be generalized to systems with linear-in-momentum spin-orbit coupling (SOC), by exploiting the analogy of SOC with a non-abelian background field. Such field mixes singlet and triplet components and yields the rich physics of magnetoelectric phenomena. In this work we show that the application of this equation extends further, beyond superconductivity. In the normal state, the linearized Eilenberger equation describes the coupled spin-charge dynamics. Moreover, its resolvent corresponds to the so called Cooperons, and can be used to calculate the weak localization corrections. Specifically, we show how to solve this equation for any source term and provide a closed-form solution for the case of Rashba SOC. We use this solution to address several problems of interest for spintronics and superconductivity. Firstly, we study spin injection from ferromagnetic electrodes in the normal state, and describe the spatial evolution of spin density in the sample, and the complete crossover from the diffusive to the ballistic limit. Secondly, we address the so-called superconducting Edelstein effect, and generalize the previously known results to arbitrary disorder. Thirdly, we study weak localization correction beyond the diffusive limit, which can be a valuable tool in experimental characterization of materials with very strong SOC. We also address the so-called pure gauge case where the persistent spin helices form. Our work establishes the linearized Eilenberger equation as a powerful and a very versatile method for the study of materials with spin-orbit coupling, which often provides a simpler and more intuitive picture compared to alternative methods.
Mirror Descent and the Information Ratio

We establish a connection between the stability of mirror descent and the information ratio by Russo and Van Roy [2014]. Our analysis shows that mirror descent with suitable loss estimators and exploratory distributions enjoys the same bound on the adversarial regret as the bounds on the Bayesian regret for information-directed sampling. Along the way, we develop the theory for information-directed sampling and provide an efficient algorithm for adversarial bandits for which the regret upper bound matches exactly the best known information-theoretic upper bound.
Safe Coverage of Moving Domains for Vehicles With Second-Order Dynamics

Autonomous coverage of a specified area by robots operating in close proximity with each other has many potential applications such as real-time monitoring of rapidly changing environments, and search and rescue; however, coordination and safety are two fundamental challenges. For coordination, we propose a distributed controller for covering moving, compact domains which consists in a double integrator with bounded input forces. This control policy is based on artificial potentials and alignment forces designed to promote desired vehicle-domain and intervehicle separations and relative velocities. We prove that certain coverage configurations are locally asymptotically stable. For safety, we establish energy conditions for collision-free motion and utilize Hamilton–Jacobi (HJ) reachability theory for last-resort pairwise collision avoidance. We derive an analytical solution to the associated HJ partial differential equation corresponding to the collision avoidance problem between two double integrator vehicles. We demonstrate our approach in several numerical simulations involving vehicles covering convex and nonconvex moving domains.
GANs with Variational Entropy Regularizers: Applications in Mitigating the Mode-Collapse Issue

Building on the success of deep learning, Generative Adversarial Networks (GANs) provide a modern approach to learn a probability distribution from observed samples. GANs are often formulated as a zero-sum game between two sets of functions; the generator and the discriminator. Although GANs have shown great potentials in learning complex distributions such as images, they often suffer from the mode collapse issue where the generator fails to capture all existing modes of the input distribution. As a consequence, the diversity of generated samples is lower than that of the observed ones. To tackle this issue, we take an information-theoretic approach and maximize a variational lower bound on the entropy of the generated samples to increase their diversity. We call this approach GANs with Variational Entropy Regularizers (GAN+VER). Existing remedies for the mode collapse issue in GANs can be easily coupled with our proposed variational entropy regularization. Through extensive experimentation on standard benchmark datasets, we show all the existing evaluation metrics highlighting difference of real and generated samples are significantly improved with GAN+VER.
Botsing, a Search-based Crash Reproduction Framework for Java

Approaches for automatic crash reproduction aim to generate test cases that reproduce crashes starting from the crash stack traces. These tests help developers during their debugging practices. One of the most promising techniques in this research field leverages search-based software testing techniques for generating crash reproducing test cases. In this paper, we introduce Botsing, an open-source search-based crash reproduction framework for Java. Botsing implements state-of-the-art and novel approaches for crash reproduction. The well-documented architecture of Botsing makes it an easy-to-extend framework, and can hence be used for implementing new approaches to improve crash reproduction. We have applied Botsing to a wide range of crashes collected from open source systems. Furthermore, we conducted a qualitative assessment of the crash-reproducing test cases with our industrial partners. In both cases, Botsing could reproduce a notable amount of the given stack traces.Demo. video: https://www.youtube. com/watch? v=k6XaQjHqe48 Botsing website: https://stamp-project.github. io/botsing/
Fast-Response Liquid Crystal Phase Modulators with an Excellent Photostability

We report a new mixture, which is modified from Merck TL-216, for liquid-crystal-on-silicon spatial light modulators (SLMs). To achieve 2π phase change at λ = 633 nm with 5 V operation voltage, the measured response time is about 3 ms at 50 °C. Meanwhile, our mixture exhibits no sign of photodegradation and even the total dosage has exceeded 400 MJ/cm2 at a blue laser wavelength λ = 465 nm. In comparison, E7 died at about 30 MJ/cm2. Widespread applications of this material for high brightness SLMs, near-eye displays, and head-up displays are foreseeable.
Tracy-Widom law for the extreme eigenvalues of large signal-plus-noise matrices

Let $\bY =\bR+\bX$ be an $M\times N$ matrix, where $\bR$ is a rectangular diagonal matrix and $\bX$ consists of $i.i. d. $ entries. This is a signal-plus-noise type model. Its signal matrix could be full rank, which is rarely studied in literature compared with the low rank cases. This paper is to study the extreme eigenvalues of $\bY\bY^*$. We show that under the high dimensional setting ($M/N\rightarrow c\in(0,1]$) and some regularity conditions on $\bR$ the rescaled extreme eigenvalue converges in distribution to Tracy-Widom distribution ($TW_1$).
Microsoft Word-789-795.docx

Most of the researchers in positivist paradigm develop conceptual frameworks to test the research hypothese quantitative study it is very common to identify the relationship between independent and dependent variables. In that, most of the conceptual models consist of moderating mediating variables. Hence, it is very critical to test these effects and similarly it is very serious, as to how to interpret results properly. Hence, the objectives of this study are; to explain the correlation, moderating and mediating effects; to explain how to interpret the test results of correlation, moderation and mediating effects in a social science research.
An introduction to totally disconnected locally compact groups

These are notes of the expository lectures that will be delivered for the LMS Autumn Algebra School, 21-25 September 2020. The aim is to introduce beginning Ph.D. students to the theory of totally disconnected locally compact groups. The exposition then includes basic properties of topological groups, a proof of van Dantzig’s theorem and some of the most popular examples of totally disconnected locally compact groups. The focus is on totally disconnected locally compact groups that satisfy some finiteness conditions with more emphasis on compact generation: for compactly generated totally disconnected locally compact groups, the notion of Cayley-Abels graph permits to deal with the topological group as a geometric object.
Derivation of fragility curves using inelastic time-history analysis and damage statistics

A methodology is presented for the derivation of seismic vulnerability (fragility) curves based on the hybrid approach, which combines statistical data with appropriately postprocessed (on the basis of repair cost models) nonlinear dynamic analyses that permit extrapolation of statistical data to earthquake intensities for which no data are available. An extensive numerical study is carried out, wherein a large number of building types (representing most of the typologies common in S. Europe) are modelled and subjected to a set of ground motions. Fragility curves expressed as cumulative lognormal distributions are then derived using the aforementioned hybrid approach; the curves correlate peak ground acceleration (PGA) to the probability that a building type exceeds a particular damage state.
Pebble-Depth

In this paper we introduce a new formulation of Bennett's logical depth based on pebble transducers. This notion is defined based on the difference between the minimal length descriptional complexity of strings from the perspective of finite-state transducers and pebble transducers. Our notion of pebble-depth satisfies the three fundamental properties of depth: i.e. easy sequences and random sequences are not deep, and the existence of a slow growth law. We also compare pebble-depth to other depth notions based on finite-state transducers, pushdown compressors and the Lempel-Ziv $78$ compression algorithm. We first demonstrate how there exists a normal pebble-deep sequence even though there is no normal finite-state-deep sequence. We next build a sequence which has a pebble-depth level of roughly $1$, a pushdown-depth level of roughly $1/2$ and a finite-state-depth level of roughly $0$. We then build a sequence which has pebble-depth level of roughly $1/2$ and Lempel-Ziv-depth level of roughly $0$.