nils-herrmann/clean_scirepeval huggingface dataset:
Symmetries of second-order PDEs and conformal Killing vectors

We study the Lie point symmetries of a general class of partial differential equations (PDE) of second order. An equation from this class naturally defines a second-order symmetric tensor (metric). In the case the PDE is linear on the first derivatives we show that the Lie point symmetries are given by the conformal algebra of the metric modulo a constraint involving the linear part of the PDE. Important elements in this class are the Klein--Gordon equation and the Laplace equation. We apply the general results and determine the Lie point symmetries of these equations in various general classes of Riemannian spaces. Finally we study the type II\ hidden symmetries of the wave equation in a Riemannian space with a Lorenzian metric.
Consistency Analysis of Nearest Subspace Classifier

The Nearest subspace classifier (NSS) finds an estimation of the underlying subspace within each class and assigns data points to the class that corresponds to its nearest subspace. This paper mainly studies how well NSS can be generalized to new samples. It is proved that NSS is strongly consistent under certain assumptions. For completeness, NSS is evaluated through experiments on various simulated and real data sets, in comparison with some other linear model based classifiers. It is also shown that NSS can obtain effective classification results and is very efficient, especially for large scale data sets.
Phase-Sensitive Detection in the undergraduate lab using a low-cost microcontroller

Phase-sensitive detection (PSD) is an important experimental technique that allows signals to be extracted from noisy data. PSD is also used in modulation spectroscopy and is used in the stabilization of optical sources. Commercial lock-in amplifiers that use PSD are often expensive and host a bewildering array of controls that may intimidate a novice user. Low-cost microcontrollers such as the Arduino family of devices seem like a good match for learning about PSD; however, making a self-contained device (reference signal, voltage input, mixing, filtering, and display) is difficult, but in the end the project teaches students "tricks" to turn the Arduino into a true scientific instrument.
Proof Normalisation in a Logic Identifying Isomorphic Propositions

We define a fragment of propositional logic where isomorphic propositions, such as $A\land B$ and $B\land A$, or $A\Rightarrow (B\land C)$ and $(A\Rightarrow B)\land(A\Rightarrow C)$ are identified. We define System I, a proof language for this logic, and prove its normalisation and consistency.
Randomized sketches for kernels: Fast and optimal non-parametric regression

Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given $n$ samples, the time and space complexity of computing the KRR estimate scale as $\mathcal{O}(n^3)$ and $\mathcal{O}(n^2)$ respectively, and so is prohibitive in many cases. We propose approximations of KRR based on $m$-dimensional randomized sketches of the kernel matrix, and study how small the projection dimension $m$ can be chosen while still preserving minimax optimality of the approximate KRR estimate. For various classes of randomized sketches, including those based on Gaussian and randomized Hadamard matrices, we prove that it suffices to choose the sketch dimension $m$ proportional to the statistical dimension (modulo logarithmic factors). Thus, we obtain fast and minimax optimal approximations to the KRR estimate for non-parametric regression.
Dynamics of Belief: Abduction, Horn Knowledge Base And Database Updates

The dynamics of belief and knowledge is one of the major components of any autonomous system that should be able to incorporate new pieces of information. In order to apply the rationality result of belief dynamics theory to various practical problems, it should be generalized in two respects: first it should allow a certain part of belief to be declared as immutable; and second, the belief state need not be deductively closed. Such a generalization of belief dynamics, referred to as base dynamics, is presented in this paper, along with the concept of a generalized revision algorithm for knowledge bases (Horn or Horn logic with stratified negation). We show that knowledge base dynamics has an interesting connection with kernel change via hitting set and abduction. In this paper, we show how techniques from disjunctive logic programming can be used for efficient (deductive) database updates. The key idea is to transform the given database together with the update request into a disjunctive (datalog) logic program and apply disjunctive techniques (such as minimal model reasoning) to solve the original update problem. The approach extends and integrates standard techniques for efficient query answering and integrity checking. The generation of a hitting set is carried out through a hyper tableaux calculus and magic set that is focused on the goal of minimality. The present paper provides a comparative study of view update algorithms in rational approach. For, understand the basic concepts with abduction, we provide an abductive framework for knowledge base dynamics. Finally, we demonstrate how belief base dynamics can provide an axiomatic characterization for insertion a view atom to the database. We give a quick overview of the main operators for belief change, in particular, belief update versus database update.
Online Optimization : Competing with Dynamic Comparators

Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop prediction methods that perform well against complex benchmarks. In this paper, we address these two directions together. We present a fully adaptive method that competes with dynamic benchmarks in which regret guarantee scales with regularity of the sequence of cost functions and comparators. Notably, the regret bound adapts to the smaller complexity measure in the problem environment. Finally, we apply our results to drifting zero-sum, two-player games where both players achieve no regret guarantees against best sequences of actions in hindsight.
Sequential sensing with model mismatch

We characterize the performance of sequential information guided sensing, Info-Greedy Sensing , when there is a mismatch between the true signal model and the assumed model, which may be a sample estimate. In particular, we consider a setup where the signal is low-rank Gaussian and the measurements are taken in the directions of eigenvectors of the covariance matrix Σ in a decreasing order of eigenvalues. We establish a set of performance bounds when a mismatched covariance matrix equation is used, in terms of the gap of signal posterior entropy, as well as the additional amount of power required to achieve the same signal recovery precision. Based on this, we further study how to choose an initialization for Info-Greedy Sensing using the sample covariance matrix, or using an efficient covariance sketching scheme.
Poisson matrix completion

We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper constraints on the matrix M of size d1-by-d2, and establish theoretical upper and lower bounds on the recovery error. Our bounds are nearly optimal up to a factor on the order of O(log(d1d2)). These bounds are obtained by adapting the arguments used for one-bit matrix completion  (although these two problems are different in nature) and the adaptation requires new techniques exploiting properties of the Poisson likelihood function and tackling the difficulties posed by the locally sub-Gaussian characteristic of the Poisson distribution. Our results highlight a few important distinctions of Poisson matrix completion compared to the prior work in matrix completion including having to impose a minimum signal-to-noise requirement on each observed entry. We also develop an efficient iterative algorithm and demonstrate its good performance in recovering solar flare images.
The Universe as a Topological Defect in a Higher-Dimensional Einstein-Yang-Mills Theory

An interpretation is suggested that a spontaneous compactification of space-time can be regarded as a topological defect in a higher-dimensional Einstein-Yang-Mills (EYM) theory. We start with $D$-dimensional EYM theory in our present analysis. A compactification leads to a $D-2$ dimensional effective action of Abelian gauge-Higgs theory. We find a "vortex" solution in the effective theory. Our universe appears to be confined in a center of a "vortex", which has $D-4$ large dimensions. In this paper we show an example with $SU(2)$ symmetry in the original EYM theory, and the resulting solution is found to be equivalent to the "instanton-induced compactification". The cosmological implication is also mentioned.
Analyzing data citation practices according to the Data Citation Index

We present an analysis on data citation practices based on the Data Citation Index from Thomson Reuters. This database launched in 2012 aims to link data sets and data studies with citations received from the rest of their citation indexes. Funding bodies and research organizations are increasingly demanding the need of researchers to make their scientific data available in a reusable and reproducible manner, aiming to maximize the allocation of funding while providing transparency on the scientific process. The DCI harvests citations to research data from papers indexed in the Web of Science. It relies on the information provided by the data repository as data citation practices are inconsistent or inexistent in many cases. The findings of this study show that data citation practices are far from common in most research fields. Some differences have been reported on the way researchers cite data: while in the areas of Science and Engineering & Technology data sets were the most cited, in Social Sciences and Arts & Humanities data studies play a greater role. 88.1% of the records have received no citation, but some repositories show very low uncitedness rates. While data citation practices are rare in most fields, they have expanded in disciplines such as Crystallography or Genomics. We conclude by emphasizing the role that the DCI could play in encouraging the consistent, standardized citation of research data – a role that would enhance its value as a means of following the research process from data collection to publication.
A game-based educational method relying on student-generated questions

Student-generated multiple-choice questions (MCQs) revised by the instructor were used to design an educational game and to set part of the exam in the framework of an elementary course in Photonics. An anonymous survey among the students revealed their general satisfaction with the method. The exam results of students who had been asked to author MCQs were compared to those of a control group subject to traditional teaching. The results of the former in the MCQ test of the exam were significantly better, without this being detrimental to their comparative performance in problem-solving.
IT-map: an Effective Nonlinear Dimensionality Reduction Method for Interactive Clustering

Scientists in many fields have the common and basic need of dimensionality reduction: visualizing the underlying structure of the massive multivariate data in a low-dimensional space. However, many dimensionality reduction methods confront the so-called "crowding problem" that clusters tend to overlap with each other in the embedding. Previously, researchers expect to avoid that problem and seek to make clusters maximally separated in the embedding. However, the proposed in-tree (IT) based method, called IT-map, allows clusters in the embedding to be locally overlapped, while seeking to make them distinguishable by some small yet key parts. IT-map provides a simple, effective and novel solution to cluster-preserving mapping, which makes it possible to cluster the original data points interactively and thus should be of general meaning in science and engineering.
Tensor Prediction, Rademacher Complexity and Random 3-XOR

Here we study the tensor prediction problem, where the goal is to accurately predict the entries of a low rank, third-order tensor (with noise) given as few observations as possible. We give algorithms based on the sixth level of the sum-of-squares hierarchy that work with roughly $m = n^{3/2}$observations, and we complement our result by showing that any attempt to solve tensor prediction with $m = n^{3/2 - \epsilon}$ observations through the sum-of-squares hierarchy needs $n^{2 \epsilon}$ rounds and consequently would run in moderately exponential time. In contrast, information theoretically roughly $m = n$ observations suffice. 
This work is part of a broader agenda of studying computational vs. statistical tradeoffs through the sum-of-squares hierarchy. In particular, for linear inverse problems (such as tensor prediction) the natural sum-of-squares relaxation gives rise to a sequence of norms. Our approach is to characterize their Rademacher complexity. Moreover, both our upper and lower bounds are based on connections between this, and the task of strongly refuting random $3$-XOR formulas, and the resolution proof system.
Jarzynski Equality in PT-Symmetric Quantum Mechanics.

We show that the quantum Jarzynski equality generalizes to PT-symmetric quantum mechanics with unbroken PT symmetry. In the regime of broken PT symmetry, the Jarzynski equality does not hold as also the CPT norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system-two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken PT symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.
Quantum Gross-Pitaevskii Equation

We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi) one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.
The systematic search for z ≳ 5 active galactic nuclei in the Chandra Deep Field South

We investigate early black hole (BH) growth through the methodical search for $z\gtrsim5$ AGN in the $Chandra$ Deep Field South. We base our search on the $Chandra$ 4-Ms data with flux limits of $9.1\times\ 10^{-18}$ (soft, 0.5 - 2 keV) and $5.5\times\ 10^{-17}\ \mathrm{erg}\ \mathrm{s}^{-1}\ \mathrm{cm}^{-2}$ (hard, 2 - 8 keV). At $z\sim5$ this corresponds to luminosities as low as $\sim10^{42}$ ($\sim10^{43}$) $\mathrm{erg}\ \mathrm{s}^{-1}$ in the soft (hard) band and should allow us to detect Compton-thin AGN with $M_\mathrm{BH}>10^7 M_{\odot}$ and Eddington ratios > 0.1. Our field ($0.03~\mathrm{deg}^2$) contains over 600 $z\sim5$ Lyman Break Galaxies. Based on lower redshift relations we would expect $\sim20$ of them to host AGN. After combining the $Chandra$ data with GOODS/ACS, CANDELS/WFC3 and $Spitzer$/IRAC data, the sample consists of 58 high-redshift candidates. We run a photometric redshift code, stack the GOODS/ACS data, apply colour criteria and the Lyman Break Technique and use the X-ray Hardness Ratio. We combine our tests and using additional data find that all sources are most likely at low redshift. We also find five X-ray sources without a counterpart in the optical or infrared which might be spurious detections. We conclude that our field does not contain any convincing $z\gtrsim5$ AGN. Explanations for this result include a low BH occupation fraction, a low AGN fraction, short, super-Eddington growth modes, BH growth through BH-BH mergers or in optically faint galaxies. By searching for $z\gtrsim5$ AGN we are setting the foundation for constraining early BH growth and seed formation scenarios.
Hadron Physics and QCD: Just the Basic Facts.

With discovery of the Higgs boson, the Standard Model of Particle Physics became complete. Its formulation is a remarkable story; and the process of verification is continuing, with the most important chapter being the least well understood. Quantum Chromodynamics (QCD) is that part of the Standard Model which is supposed to describe all of nuclear physics and yet, almost fifty years after the discovery of quarks, we are only just beginning to understand how QCD moulds the basic bricks for nuclei: pious, neutrons, protons. QCD is characterized by two emergent phenomena: confinement and dynamical chiral symmetry breaking (DCSB), whose implications are extraordinary. This contribution describes how DCSB, not the Higgs boson, generates more than 98% of the visible mass in the Universe, explains why confinement guarantees that condensates, those quantities that were commonly viewed as constant mass- scales that fill all spacetime, are instead wholly contained within hadrons, and elucidates a range of observable consequences of confinement and DCSB whose measurement is the focus of a vast international experimental programme.
Measuring academic influence: Not all citations are equal

The importance of a research article is routinely measured by counting how many times it has been cited. However, treating all citations with equal weight ignores the wide variety of functions that citations perform. We want to automatically identify the subset of references in a bibliography that have a central academic influence on the citing paper. For this purpose, we examine the effectiveness of a variety of features for determining the academic influence of a citation. By asking authors to identify the key references in their own work, we created a data set in which citations were labeled according to their academic influence. Using automatic feature selection with supervised machine learning, we found a model for predicting academic influence that achieves good performance on this data set using only four features. The best features, among those we evaluated, were those based on the number of times a reference is mentioned in the body of a citing paper. The performance of these features inspired us to design an influence‐primed h‐index (the hip‐index). Unlike the conventional h‐index, it weights citations by how many times a reference is mentioned. According to our experiments, the hip‐index is a better indicator of researcher performance than the conventional h‐index.
Online Nonparametric Regression with General Loss Functions

This paper establishes minimax rates for online regression with arbitrary classes of functions and general losses. 1 We show that below a certain threshold for the complexity of the function class, the minimax rates dependon both thecurvatureof the lossfunction andthe sequentialcomplexities of theclass. Abovethis threshold, the curvatureof the loss does not affect the rates. Furthermore,for the case of square loss, our results point to the interesting phenomenon: whenever sequential and i.i.d. empirical entropies match, the rates for statistical and online learning are the same. In addition to the study of minimax regret, we derive a generic forecaster that enjoys the established optimal rates. We also provide a recipe for designing online prediction algorithms that can be computationally efficient for certain problems. We illustrate the techniques by deriving existing and new forecasters for the case of finite experts and for online linear regression.
A CONSISTENCY LEMMA IN STATISTICAL PHYLOGENETICS

= T). Let θbe a vector of continuous parameters – including the branch lengthsof T, along with possibly other continuous parameters required to specify a model of characterevolution on T. Let Θ denote the set of values θ may take. Branch lengths, in particular,are assumed to be strictly positive and ﬁnite; and in general Θ will be some open subset ofEuclidean space. Consider any stochastic process (e.g. Markov process, or mixture of Markovprocesses) which assigns to each pair (T,θ) a probability distribution s = s(T,θ) on discrete,ﬁnite-state characters at the tips of the tree. We assume throughout that the map θ→ s(T,θ) iscontinuous. Such models are central to statistical phylogenetics and methods for reconstructingphylogenetic trees from aligned genetic (e.g. DNA) sequences. A tree reconstruction method ψisany method that reconstructs a set of one or more unrooted phylogenetic trees from any givendistribution ˆf of site pattern frequencies. Suppose we generate ksites i.i.d. from (T,θ), and let ˆsbe the random variable equal to the resulting proportion of site patterns (character types). Themethod ψis a statistically consistent estimator of the unrooted topology of Tif the probabilitythat ψ(ˆs) = {T
maxDNN: An Efficient Convolution Kernel for Deep Learning with Maxwell GPUs

This paper describes maxDNN, a computationally efficient convolution kernel for deep learning with the NVIDIA Maxwell GPU. maxDNN reaches 96.3% computational efficiency on typical deep learning network architectures. The design combines ideas from cuda-convnet2 with the Maxas SGEMM assembly code. We only address forward propagation (FPROP) operation of the network, but we believe that the same techniques used here will be effective for backward propagation (BPROP) as well.
Particle Gibbs with Ancestor Sampling for Probabilistic Programs

Particle Markov chain Monte Carlo techniques rank among current state-of-the-art methods for probabilistic program inference. A drawback of these techniques is that they rely on importance resampling, which results in degenerate particle trajectories and a low effective sample size for variables sampled early in a program. We here develop a formalism to adapt ancestor resampling, a technique that mitigates particle degeneracy, to the probabilistic programming setting. We present empirical results that demonstrate nontrivial performance gains.
Quantifying sudden changes in dynamical systems using symbolic networks

We characterize the evolution of a dynamical system by combining two well-known complex systems’ tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time series we construct a network in which every node weight represents the probability of an ordinal pattern (OP) to appear in the symbolic sequence and each edge's weight represents the probability of transitions between two consecutive OPs. Several network-based diagnostics are then proposed to characterize the dynamics of different systems: logistic, tent, and circle maps. We show that these diagnostics are able to capture changes produced in the dynamics as a control parameter is varied. We also apply our new measures to empirical data from semiconductor lasers and show that they are able to anticipate the polarization switchings, thus providing early warning signals of abrupt transitions.