nils-herrmann/clean_scirepeval huggingface dataset:
On using the Microsoft Kinect$^{\rm TM}$ sensors in the analysis of human motion

The present paper aims at providing the theoretical background required for investigating the use of the Microsoft Kinect$^{\rm TM}$ (`Kinect', for short) sensors (original and upgraded) in the analysis of human motion. Our methodology is developed in such a way that its application be easily adaptable to comparative studies of other systems used in capturing human-motion data. Our future plans include the application of this methodology to two situations: first, in a comparative study of the performance of the two Kinect sensors; second, in pursuing their validation on the basis of comparisons with a marker-based system (MBS). One important feature in our approach is the transformation of the MBS output into Kinect-output format, thus enabling the analysis of the measurements, obtained from different systems, with the same software application, i.e., the one we use in the analysis of Kinect-captured data; one example of such a transformation, for one popular marker-placement scheme (`Plug-in Gait'), is detailed. We propose that the similarity of the output, obtained from the different systems, be assessed on the basis of the comparison of a number of waveforms, representing the variation within the gait cycle of quantities which are commonly used in the modelling of the human motion. The data acquisition may involve commercially-available treadmills and a number of velocity settings: for instance, walking-motion data may be acquired at $5$ km/h, running-motion data at $8$ and $11$ km/h. We recommend that particular attention be called to systematic effects associated with the subject's knee and lower leg, as well as to the ability of the Kinect sensors in reliably capturing the details in the asymmetry of the motion for the left and right parts of the human body. The previous versions of the study have been withdrawn due to the use of a non-representative database.
Multi-Target Shrinkage

Stein showed that the multivariate sample mean is outperformed by "shrinking" to a constant target vector. Ledoit and Wolf extended this approach to the sample covariance matrix and proposed a multiple of the identity as shrinkage target. In a general framework, independent of a specific estimator, we extend the shrinkage concept by allowing simultaneous shrinkage to a set of targets. Application scenarios include settings with (A) additional data sets from potentially similar distributions, (B) non-stationarity, (C) a natural grouping of the data or (D) multiple alternative estimators which could serve as targets. 
We show that this Multi-Target Shrinkage can be translated into a quadratic program and derive conditions under which the estimation of the shrinkage intensities yields optimal expected squared error in the limit. For the sample mean and the sample covariance as specific instances, we derive conditions under which the optimality of MTS is applicable. We consider two asymptotic settings: the large dimensional limit (LDL), where the dimensionality and the number of observations go to infinity at the same rate, and the finite observations large dimensional limit (FOLDL), where only the dimensionality goes to infinity while the number of observations remains constant. We then show the effectiveness in extensive simulations and on real world data.
Gravitational Field Tensor

We present a tensorial relative of the familiar affine connection and argue that it should be regarded as the gravitational field tensor. Remarkably, the Lagrangian density expressed in terms of this tensor has a simple form, which depends only on the metric and its first derivatives and, moreover, is a true scalar quantity. The geodesic equation, moreover, shows that our tensor plays a role that is strongly reminiscent of the gravitational field in Newtonian mechanics and this, together with other evidence, which we present, leads us to identify it as the gravitational field tensor. We calculate the gravitational field tensor for the Schwarzschild metric. We suggest some of the advantages to be gained from applying our tensor to the study of gravitational waves.
Anti-de Sitter momentum space

Theoretical Physics, Blackett Laboratory, Imperial College, London, SW7 2BZ, United Kingdom(Dated: December 8, 2014)We investigate the anti-de Sitter (AdS) counterpart to the well studied de Sitter (dS) model forenergy-momentum space, viz \-momentum space" space (with a structure based on the propertiesof the -Poincare Hopf algebra). On the basis of previous preliminary results one might expect thetwo models to be \dual": dS exhibiting an invariant maximal spatial momentum but unboundedenergy, AdS a maximal energy but unbounded momentum. If that were the case AdS momentumspace could be used to implement a principle of maximal Planck-scale energy, just as several studiesuse dS momentum space to postulate of maximal Planck-scale spatial momentum. However severalunexpected features are uncovered in this paper, which limit the scope of the expected duality,and interestingly they take di erent forms in di erent coordinatizations of AdS momentum space.\Cosmological" AdS coordinates mimic the dS construction used for -momentum space, and pro-duce a Carrol limit in the ultraviolet. However, unlike the -momentum space, the boundary of thecovered patch breaks Lorentz invariance, thereby introducing a preferred frame. In \horospherical"coordinates we achieve full consistency with frame independence as far as boost transformationsare concerned, but nd that rotational symmetry is broken, leading to an anisotropic model for thespeed of light. Finally, in \static" coordinates we nd a way of deforming relativistic transforma-tions that successfully enforces frame invariance and isotropy, and produces a Carrol limit in theultraviolet. However, the phenomenological implications appear to be too weak for any realisticchance of detection. Our results are also relevant for a long-standing debate on whether or not coor-dinate rede nitions in momentum space lead to physically equivalent theories: our three proposalsare evidently physically inequivalent, leading to alternative models of Planck-scale e ects. As acorollary we study the UV running of the Hausdor dimension of momentum space in the rst andthird model, obtaining di erent results.
An iterative step-function estimator for graphons

Exchangeable graphs arise via a sampling procedure from measurable functions known as graphons. A natural estimation problem is how well we can recover a graphon given a single graph sampled from it. One general framework for estimating a graphon uses step-functions obtained by partitioning the nodes of the graph according to some clustering algorithm. We propose an iterative step-function estimator (ISFE) that, given an initial partition, iteratively clusters nodes based on their edge densities with respect to the previous iteration's partition. We analyze ISFE and demonstrate its performance in comparison with other graphon estimation techniques.
Proton annihilation at hadron colliders and Kamioka: High energy versus high luminosity

We examine models and prospects for proton annihilation to dileptons, a process which violates baryon and lepton number each by two. We determine that currently Super-Kamiokande would place the most draconian bound on $pp \rightarrow \ell^+ \ell^+$, ruling out new physics below a scale of $\sim 1.6$ TeV. We also find present and future hadron collider sensitivity to these processes. While 8 TeV LHC data excludes new physics at a scale below $\sim 800$ GeV, the reach of a 14 TeV LHC run is $\sim 1.8$ TeV, putting it on par with the sensitivity of Super-Kamiokande. On the other hand, a 100 TeV proton-proton collider would be sensitive to proton annihilation at a scale up to 10 TeV, allowing it to far exceed the reach of both Super-Kamiokande and the projected 2 TeV reach of Hyper-Kamiokande. Constraints from neutron star observation and cosmological evolution are not competitive. Therefore, although high-luminosity water Cherenkov experiments currently place the leading bounds on baryon and lepton number violation, next generation high-energy hadron colliders will begin surpassing them in sensitivity to some $B/L$-violating processes.
Polarization-dependent exciton dynamics in tetracene single crystals.

We conduct polarization-dependent ultrafast spectroscopy to study the dynamics of singlet fission (SF) in tetracene single crystals. The spectrotemporal species for singlet and triplet excitons in transient absorption spectra are found to be strongly dependent on probe polarization. By carefully analyzing the polarization dependence, the signals contributed by different transitions related to singlet excitons have been disentangled, which is further applied to construct the correlation between dynamics of singlet and triplet excitons. The anisotropy of exciton dynamics provides an alternative approach to tackle the long-standing challenge in understanding the mechanism of singlet fission in organic semiconductors.
Declarative Statistical Modeling with Datalog

Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the probability space to a conditional subspace (the posterior). Use cases of such formalisms include the development of algorithms in machine learning and artificial intelligence. We propose and investigate a declarative framework for specifying statistical models on top of a database, through an appropriate extension of Datalog. By virtue of extending Datalog, our framework offers a natural integration with the database, and has a robust declarative semantics. Our Datalog extension provides convenient mechanisms to include numerical probability functions; in particular, conclusions of rules may contain values drawn from such functions. The semantics of a program is a probability distribution over the possible outcomes of the input database with respect to the program; these outcomes are minimal solutions with respect to a related program with existentially quantified variables in conclusions. Observations are naturally incorporated by means of integrity constraints over the extensional and intensional relations. We focus on programs that use discrete numerical distributions, but even then the space of possible outcomes may be uncountable (as a solution can be infinite). We define a probability measure over possible outcomes by applying the known concept of cylinder sets to a probabilistic chase procedure. We show that the resulting semantics is robust under different chases. We also identify conditions guaranteeing that all possible outcomes are finite (and then the probability space is discrete). We argue that the framework we propose retains the purely declarative nature of Datalog, and allows for natural specifications of statistical models.
The growth index of matter perturbations using the clustering of dark energy

We have put forward a new unified framework which provides a consistent and rather complete account of the growth index of matter perturbations in the regime where the dark energy is allowed to have clustering. In particular, we find that the growth index is not only affected by the cosmological parameters but rather it depends on the choice of the considered dark energy (homogeneous or clustered). Using the {\em Planck} priors and performing a standard $\chi^2$-minimization between theoretical expectations and growth data, we statistically quantify the ability of the growth index to represent the observations. Finally, based on the growth index analysis we find that the growth data favour the clustered dark energy scenario.
Visual Causal Feature Learning

We provide a rigorous definition of the visual cause of a behavior that is broadly applicable to the visually driven behavior in humans, animals, neurons, robots and other perceiving systems. Our framework generalizes standard accounts of causal learning to settings in which the causal variables need to be constructed from micro-variables. We prove the Causal Coarsening Theorem, which allows us to gain causal knowledge from observational data with minimal experimental effort. The theorem provides a connection to standard inference techniques in machine learning that identify features of an image that correlate with, but may not cause, the target behavior. Finally, we propose an active learning scheme to learn a manipulator function that performs optimal manipulations on the image to automatically identify the visual cause of a target behavior. We illustrate our inference and learning algorithms in experiments based on both synthetic and real data.
Riemannian Geometry: Definitions, Pictures, and Results

A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints, some of which would seem to be novel to the literature. Topics are avoided which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations. As much material as possible is developed for manifolds with connection (omitting a metric) to make clear which aspects can be readily generalized to gauge theories. The presentation in most cases does not assume a coordinate frame or zero torsion, and the coordinate-free, tensor, and Cartan formalisms are developed in parallel.
Dimensionality Reduction with Subspace Structure Preservation

Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that $2K$ projection vectors are sufficient for the independence preservation of any $K$ class data sampled from a union of independent subspaces. It is this non-trivial observation that we use for designing our dimensionality reduction technique. In this paper, we propose a novel dimensionality reduction algorithm that theoretically preserves this structure for a given dataset. We support our theoretical analysis with empirical results on both synthetic and real world data achieving \textit{state-of-the-art} results compared to popular dimensionality reduction techniques.
MLitB: Machine Learning in the Browser

With few exceptions, the field of Machine Learning (ML) research has largely ignored the browser as a computational engine. Beyond an educational resource for ML, the browser has vast potential to not only improve the state-of-the-art in ML research, but also, inexpensively and on a massive scale, to bring sophisticated ML learning and prediction to the public at large. This paper introduces MLitB, a prototype ML framework written entirely in Javascript, capable of performing large-scale distributed computing with heterogeneous classes of devices. The development of MLitB has been driven by several underlying objectives whose aim is to make ML learning and usage ubiquitous (by using ubiquitous compute devices), cheap and eff ortlessly distributed, and collaborative. This is achieved by allowing every internet capable device to run training algorithms and predictive models with no software installation and by saving models in universally readable formats. Our prototype library is capable of training deep neural networks with synchronized, distributed stochastic gradient descent. MLitB off ers several important opportunities for novel ML research, including: development of distributed learning algorithms, advancement of web GPU algorithms, novel field and mobile applications, privacy preserving computing, and green grid-computing. MLitB is available as open source software.
Probabilistic low-rank matrix completion on finite alphabets

The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image processing, quantum physics or multi-class classificationto name a few. Most works have focused on recovering an unknown real-valued low-rankmatrix from randomly sub-sampling its entries.Here, we investigate the case where the observations take a finite number of values, corresponding for examples to ratings in recommender systems or labels in multi-class classification.We also consider a general sampling scheme (not necessarily uniform) over the matrix entries.The performance of a nuclear-norm penalized estimator is analyzed theoretically.More precisely, we derive bounds for the Kullback-Leibler divergence between the true and estimated distributions.In practice, we have also proposed an efficient algorithm based on lifted coordinate gradient descent in order to tacklepotentially high dimensional settings.
Physics of microswimmers—single particle motion and collective behavior: a review

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.
Provable Methods for Training Neural Networks with Sparse Connectivity

We provide novel guaranteed approaches for training feedforward neural networks with sparse connectivity. We leverage on the techniques developed previously for learning linear networks and show that they can also be effectively adopted to learn non-linear networks. We operate on the moments involving label and the score function of the input, and show that their factorization provably yields the weight matrix of the first layer of a deep network under mild conditions. In practice, the output of our method can be employed as effective initializers for gradient descent.
Patterns of text reuse in a scientific corpus

In the modern electronic format it is both easier to reuse text and easier to detect reused text. This is the first comprehensive study of patterns of text reuse within the full texts of an important large scientific corpus, covering a 20-y timeframe. It provides an important baseline for what is regarded as standard practice within the affected research communities, a standard somewhat more lenient than that currently applied to journalists, popular authors, and public figures. We consider the incidence of text “reuse” by researchers via a systematic pairwise comparison of the text content of all articles deposited to arXiv.org from 1991 to 2012. We measure the global frequencies of three classes of text reuse and measure how chronic text reuse is distributed among authors in the dataset. We infer a baseline for accepted practice, perhaps surprisingly permissive compared with other societal contexts, and a clearly delineated set of aberrant authors. We find a negative correlation between the amount of reused text in an article and its influence, as measured by subsequent citations. Finally, we consider the distribution of countries of origin of articles containing large amounts of reused text.
Thin film detection of High Energy Materials: Optical Pumping Approach

We present our work on High Energy Material detection based on thin film of Lithium using the phenomenon of Optical Pumping. The Li atoms present in the thin film are optically pumped to one of the ground hyperfine energy levels so that they can no more absorb light from the resonant light source. Now in presence of a RF signal, which quantifies the ambient magnetic field, this polarized atomic system is again randomized thus making it reabsorb the resonant light. This gives a quantified measurement of the magnetic field surrounding the thin film detector. This is then mapped to the presence of magnetic HEM and hence the HEM are detected. Our approach in this regard starts with verifying the stability of Lithium atoms in various solvents so as to get a suitable liquid medium to form a thin film. In this regard, various UV-visible characterization spectra are presented to finally approach a stable system for the detection. We have worked on around 10 polar and non- polar solvents to see the stability criteria. UV-Vis probe has been found to be quite effective in addressing issue of hosting Lithium atoms by various solvents. Further results on the atomic system size as dispersed in the various solvents are presented. Atomic system size gives us a good quantitative estimate of the density of Lithium dispersed system in the thin film. Finally a separate atomic system under Ultrahigh vacuum is presented to achieve optical pumping wherein the polarization and depolarization of atomic system is seen using a 670 nm diode laser system which is electronically locked using a double window Hollow cathode lamp. These both systems will finally be combined together to give the final form to the detection system. As this whole system measures relative change in magnetic field due to the presence of HEM,it gives a more reliable and accurate detection method compared to the absolute measurement detectors.
Ocean Wave Model and Wave Drift Caused by the Asymmetry of Crest and Trough

It follows from the review on classical wave models that the asymmetry of crest and trough is the direct cause for wave drift. Based on this, a new model of Lagrangian form is constructed. Relative to the Gerstner model, its improvement is reflected in the horizontal motion which includes an explicit drift term. On the one hand, the depth-decay factor for the new drift accords well with that of the particle’s horizontal velocity. It is more rational than that of Stokes drift. On the other hand, the new formula needs no Taylor expansion as for Stokes drift and is applicable for the waves with big slopes. In addition, the new formula can also yield a more rational magnitude for the surface drift than that of Stokes.