nils-herrmann/clean_scirepeval huggingface dataset:
A MOBILE WEB FOR ENHANCING STATISTICS AND MATHEMATICS EDUCATION

A freely available educational application (a mobile website) will be presented. This provides access to educational material and drilling on selected topics within mathematics and statistics with an emphasis on tablets and mobile phones. The application adapts to the student's performance, selecting from easy to difficult questions, or older material etc. These adaptations are based on statistical models and analyses of data from testing precursors of the system within several courses, from calculus and introductory statistics through multiple linear regression. The application can be used in both on-line and off-line modes. Results presented include analyses of how the internal algorithms relate to dropout rates, passing a course and general incremental improvement in knowledge during a semester.
Single-atom addressing in microtraps for quantum-state engineering using Rydberg atoms

We report on the selective addressing of an individual atom in a pair of single-atom microtraps separated by $3\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}$m. Using a tunable light shift, we render the selected atom off-resonant with a global Rydberg excitation laser which is resonant with the other atom, making it possible to selectively block this atom from being excited to the Rydberg state. Furthermore we demonstrate the controlled manipulation of a two-atom entangled state by using the addressing beam to induce a phase shift onto one component of the wave function of the system, transferring it to a dark state for the Rydberg excitation light. Our results are an important step towards implementing quantum information processing and quantum simulation with large arrays of Rydberg atoms.
Gravitational self-force in nonvacuum spacetimes

The gravitational self-force has thus far been formulated in background spacetimes for which the metric is a solution to the Einstein field equations in vacuum. While this formulation is sufficient to describe the motion of a small object around a black hole, other applications require a more general formulation that allows for a nonvacuum background spacetime. We provide a foundation for such extensions, and carry out a concrete formulation of the gravitational self-force in two specific cases. In the first we consider a particle of mass $m$ and scalar charge $q$ moving in a background spacetime that contains a background scalar field. In the second we consider a particle of mass $m$ and electric charge $e$ moving in an electrovac spacetime. The self-force incorporates all couplings between the gravitational perturbations and those of the scalar or electromagnetic fields. It is expressed as a sum of local terms involving tensors defined in the background spacetime and evaluated at the current position of the particle, as well as tail integrals that depend on the past history of the particle. Because such an expression is rarely a useful starting point for an explicit evaluation of the self-force, we also provide covariant expressions for the singular potentials, expressed as local expansions near the world line; these can be involved in the construction of effective extended sources for the regular potentials, or in the computation of regularization parameters when the self-force is computed as a sum over spherical-harmonic modes.
Linear technique to understand non-normal turbulence applied to a magnetized plasma.

In nonlinear dynamical systems with highly nonorthogonal linear eigenvectors, linear nonmodal analysis is more useful than normal mode analysis in predicting turbulent properties. However, the nontrivial time evolution of nonmodal structures makes quantitative understanding and prediction difficult. We present a technique to overcome this difficulty by modeling the effect that the advective nonlinearities have on spatial turbulent structures. The nonlinearities are taken as a periodic randomizing force with time scale consistent with critical balance arguments. We apply this technique to a model of drift wave turbulence in the Large Plasma Device [W. Gekelman et al.,  (1991)], where nonmodal effects dominate the turbulence. We compare the resulting growth rate spectra to the spectra obtained from a nonlinear simulation, showing good qualitative agreement, especially in comparison to the eigenmode growth rate spectra.
Higgs-Dilaton cosmology: Universality versus criticality

The Higgs-Dilaton model is able to produce an early inflationary expansion followed by a dark energy dominated era responsible for the late time acceleration of the Universe. At tree level, the model predicts a small tensor-to-scalar ratio (0.0021 <= r <= 0.0034), a tiny negative running of the spectral tilt (-0.00057 <= dn(s)/d ln k <= -0.00034) and a nontrivial consistency relation between the spectral tilt of scalar perturbations and the dark energy equation of state, which turns out to be close to a cosmological constant (0 <= 1 + w(DE) <= 0.014). We reconsider the validity of these predictions in the vicinity of the critical value of the Higgs self-coupling giving rise to an inflection point in the inflationary potential. The value of the inflationary observables in this case strongly depends on the parameters of the model. The tensor-to-scalar ratio can be large [ r similar to O(0.1)] and notably exceed its tree-level value. If that happens, the running of the scalar tilt becomes positive and rather big [dn(s)/d ln k similar to O(0.01)] and the equation-of-state parameter of dark energy can significantly differ from a cosmological constant [1 + w(DE) similar to O(0.1)].
Generalized Dantzig Selector: Application to the k-support norm

We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS. Thereafter, non-asymptotic high-probability bounds are established on the estimation error, which rely on Gaussian widths of the unit norm ball and the error set. Further, we consider a non-trivial example of the GDS using k-support norm. We derive an efficient method to compute the proximal operator for k-support norm since existing methods are inapplicable in this setting. For statistical analysis, we provide upper bounds for the Gaussian widths needed in the GDS analysis, yielding the first statistical recovery guarantee for estimation with the k-support norm. The experimental results confirm our theoretical analysis.
Semi-supervised Learning with Deep Generative Models

The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models that allow for effective generalisation from small labelled data sets to large unlabelled ones. Generative approaches have thus far been either inflexible, inefficient or non-scalable. We show that deep generative models and approximate Bayesian inference exploiting recent advances in variational methods can be used to provide significant improvements, making generative approaches highly competitive for semi-supervised learning.
Towards a deeper geometric, analytic and algorithmic understanding of margins

Given a matrix A, a linear feasibility problem (of which linear classification is a special case) aims to find a solution to a primal problem or a certificate for the dual problem which is a probability distribution . Inspired by the continued importance of ‘large-margin classifiers’ in machine learning, this paper studies a condition measure of A called its margin that determines the difficulty of both the above problems. To aid geometrical intuition, we first establish new characterizations of the margin in terms of relevant balls, cones and hulls. Our second contribution is analytical, where we present generalizations of Gordan's theorem, and variants of Hoffman's theorems, both using margins. We end by proving some new results on a classical iterative scheme, the Perceptron, whose convergence rates famously depends on the margin. Our results are relevant for a deeper understanding of margin-based learning and proving convergence rates of iterative schemes, apart from providing a unifying perspective on this vast topic.
Sums of permanental minors using Grassmann algebra

We show that a formalism proposed by Creutz to evaluate Grassmann integrals provides an algorithm of complexity $O(2^n n^3)$ to compute the generating function for the sum of the permanental minors of a matrix of order $n$. This algorithm improves over the Brualdi-Ryser formula, whose complexity is at least $O(2^{\frac{5n}{2}})$. In the case of a banded matrix with band width $w$ and rank $n$ the complexity is $O(2^{min(2w, n)} (w + 1) n^2)$. Related algorithms for the matching and independence polynomials of graphs are presented.
Predicting the future behavior of a time-varying probability distribution

We study the problem of predicting the future, though only in the probabilistic sense of estimating a future state of a time-varying probability distribution. This is not only an interesting academic problem, but solving this extrapolation problem also has many practical application, e.g. for training classifiers that have to operate under time-varying conditions. Our main contribution is a method for predicting the next step of the time-varying distribution from a given sequence of sample sets from earlier time steps. For this we rely on two recent machine learning techniques: embedding probability distributions into a reproducing kernel Hilbert space, and learning operators by vector-valued regression. We illustrate the working principles and the practical usefulness of our method by experiments on synthetic and real data. We also highlight an exemplary application: training a classifier in a domain adaptation setting without having access to examples from the test time distribution at training time.
Spectral Ranking using Seriation

We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a similarity matrix from pairwise comparisons, using seriation methods to reorder this matrix and construct a ranking. We first show that this spectral seriation algorithm recovers the true ranking when all pairwise comparisons are observed and consistent with a total order. We then show that ranking reconstruction is still exact when some pairwise comparisons are corrupted or missing, and that seriation based spectral ranking is more robust to noise than classical scoring methods. Finally, we bound the ranking error when only a random subset of the comparions are observed. An additional benefit of the seriation formulation is that it allows us to solve semi-supervised ranking problems. Experiments on both synthetic and real datasets demonstrate that seriation based spectral ranking achieves competitive and in some cases superior performance compared to classical ranking methods.
PSR J1756-2251: a pulsar with a low-mass neutron star companion

The pulsar PSR J1756$-$2251 resides in a relativistic double neutron star (DNS) binary system with a 7.67-hr orbit. We have conducted long-term precision timing on more than 9 years of data acquired from five telescopes, measuring five post-Keplerian parameters. This has led to several independent tests of general relativity (GR), the most constraining of which shows agreement with the prediction of GR at the 4% level. Our measurement of the orbital decay rate disagrees with that predicted by GR, likely due to systematic observational biases. We have derived the pulsar distance from parallax and orbital decay measurements to be 0.73$_{-0.24}^{+0.60}$ kpc (68%) and < 1.2 kpc (95% upper limit), respectively; these are significantly discrepant from the distance estimated using Galactic electron density models. We have found the pulsar mass to be 1.341$\pm$0.007 M$_\odot$, and a low neutron star (NS) companion mass of 1.230$\pm$0.007 M$_\odot$. We also determined an upper limit to the spin-orbit misalignment angle of 34{\deg} (95%) based on a system geometry fit to long-term profile width measurements. These and other observed properties have led us to hypothesize an evolution involving a low mass loss, symmetric supernova progenitor to the second-formed NS companion, as is thought to be the case for the double pulsar system PSR J0737$-$3039A/B. This would make PSR J1756$-$2251 the second compact binary system providing concrete evidence for this type of NS formation channel.
SOME STARS ARE TOTALLY METAL: A NEW MECHANISM DRIVING DUST ACROSS STAR-FORMING CLOUDS, AND CONSEQUENCES FOR PLANETS, STARS, AND GALAXIES

Dust grains in neutral gas behave as aerodynamic particles, so they can develop large local density fluctuations entirely independent of gas density fluctuations. Specifically, gas turbulence can drive order-of-magnitude “resonant” fluctuations in the dust density on scales where the gas stopping/drag timescale is comparable to the turbulent eddy turnover time. Here we show that for large grains (size ≳ 0.1 μm, containing most grain mass) in sufficiently large molecular clouds (radii ≳ 1–10 pc, masses ≳ 104 M☉), this scale becomes larger than the characteristic sizes of prestellar cores (the sonic length), so large fluctuations in the dust-to-gas ratio are imprinted on cores. As a result, star clusters and protostellar disks formed in large clouds should exhibit significant abundance spreads in the elements preferentially found in large grains (C, O). This naturally predicts populations of carbon-enhanced stars, certain highly unusual stellar populations observed in nearby open clusters, and may explain the “UV upturn” in early-type galaxies. It will also dramatically change planet formation in the resulting protostellar disks, by preferentially “seeding” disks with an enhancement in large carbonaceous or silicate grains. The relevant threshold for this behavior scales simply with cloud densities and temperatures, making straightforward predictions for clusters in starbursts and high-redshift galaxies. Because of the selective sorting by size, this process is not necessarily visible in extinction mapping. We also predict the shape of the abundance distribution—when these fluctuations occur, a small fraction of the cores may actually be seeded with abundances Z ∼ 100 〈Z〉 such that they are almost “totally metal” (Z ∼ 1)! Assuming the cores collapse, these totally metal stars would be rare (1 in ∼104 in clusters where this occurs), but represent a fundamentally new stellar evolution channel.
GJ 832c: A SUPER-EARTH IN THE HABITABLE ZONE

We report the detection of GJ 832c, a super-Earth orbiting near the inner edge of the habitable zone of GJ 832, an M dwarf previously known to host a Jupiter analog in a nearly circular 9.4 yr orbit. The combination of precise radial-velocity measurements from three telescopes reveals the presence of a planet with a period of 35.68 ± 0.03 days and minimum mass (m sin i) of 5.4 ± 1.0 Earth masses. GJ 832c moves on a low-eccentricity orbit (e = 0.18 ± 0.13) toward the inner edge of the habitable zone. However, given the large mass of the planet, it seems likely that it would possess a massive atmosphere, which may well render the planet inhospitable. Indeed, it is perhaps more likely that GJ 832c is a “super-Venus,” featuring significant greenhouse forcing. With an outer giant planet and an interior, potentially rocky planet, the GJ 832 planetary system can be thought of as a miniature version of our own solar system.
Transpose-free Fast Fourier Transform for Turbulence Simulation

Pseudo-spectral method is one of the most accurate techniques for simulating turbulent flows. Fast Fourier transform (FFT) is an integral part of this method. In this paper, we present a new procedure to compute FFT in which we save operations during interprocess communications by avoiding transpose of the array. As a result, our transpose-free FFT is 15\% to 20\% faster than FFTW.
Statistical arbitrage in the Black–Scholes framework

In this study we prove the existence of statistical arbitrage opportunities in the Black-Scholes framework by considering trading strategies that consists of borrowing from the risk free rate and taking a long position in the stock until it hits a deterministic barrier level. We derive analytical formulas for the expected value, variance, and probability of loss for the discounted cumulative trading profits. No-statistical arbitrage condition is derived for the Black-Scholes framework, which imposes a constraint on the Sharpe ratio of the stock. Furthermore, we verify our theoretical results via extensive Monte Carlo simulations.
On semidefinite relaxations for the block model

The stochastic block model (SBM) is a popular tool for community detection in networks, but fitting it by maximum likelihood (MLE) involves a computationally infeasible optimization problem. We propose a new semidefinite programming (SDP) solution to the problem of fitting the SBM, derived as a relaxation of the MLE. We put ours and previously proposed SDPs in a unified framework, as relaxations of the MLE over various sub-classes of the SBM, revealing a connection to sparse PCA. Our main relaxation, which we call SDP-1, is tighter than other recently proposed SDP relaxations, and thus previously established theoretical guarantees carry over. However, we show that SDP-1 exactly recovers true communities over a wider class of SBMs than those covered by current results. In particular, the assumption of strong assortativity of the SBM, implicit in consistency conditions for previously proposed SDPs, can be relaxed to weak assortativity for our approach, thus significantly broadening the class of SBMs covered by the consistency results. We also show that strong assortativity is indeed a necessary condition for exact recovery for previously proposed SDP approaches and not an artifact of the proofs. Our analysis of SDPs is based on primal-dual witness constructions, which provides some insight into the nature of the solutions of various SDPs. We show how to combine features from SDP-1 and already available SDPs to achieve the most flexibility in terms of both assortativity and block-size constraints, as our relaxation has the tendency to produce communities of similar sizes. This tendency makes it the ideal tool for fitting network histograms, a method gaining popularity in the graphon estimation literature, as we illustrate on an example of a social networks of dolphins. We also provide empirical evidence that SDPs outperform spectral methods for fitting SBMs with a large number of blocks.
Parallel Algorithms for Counting Triangles in Networks with Large Degrees

Finding the number of triangles in a network is an important problem in the analysis of complex networks. The number of triangles also has important applications in data mining. Existing distributed memory parallel algorithms for counting triangles are either Map-Reduce based or message passing interface (MPI) based and work with overlapping partitions of the given network. These algorithms are designed for very sparse networks and do not work well when the degrees of the nodes are relatively larger. For networks with larger degrees, Map-Reduce based algorithm generates prohibitively large intermediate data, and in MPI based algorithms with overlapping partitions, each partition can grow as large as the original network, wiping out the benefit of partitioning the network. 
In this paper, we present two efficient MPI-based parallel algorithms for counting triangles in massive networks with large degrees. The first algorithm is a space-efficient algorithm for networks that do not fit in the main memory of a single compute node. This algorithm divides the network into non-overlapping partitions. The second algorithm is for the case where the main memory of each node is large enough to contain the entire network. We observe that for such a case, computation load can be balanced dynamically and present a dynamic load balancing scheme which improves the performance significantly. Both of our algorithms scale well to large networks and to a large number of processors.
An Unconventional Attempt to Tame Mandelbrot's Grey Swans

We suggest an original physical approach to describe the mechanism of market pricing. The core of our approach is to consider pricing at different time scales separately, using independent equations of motion. Such an approach leads to a pricing model that not only allows estimating the volatility of future market prices, but also permits forecasting the direction of the price move. Alongside with that, it is crucial that our model implies no calibration on historical market data. And last but not least, properties of the model's solution are consistent with those of real markets: it has fat tails, possesses scaling and evinces nonlinear market memory. As our model has been derived with the tip of the pen, it may be not a yet another confirmation of the known empirical facts, but a theoretical justification thereto. Tests on real financial instruments prove the competence of our approach.
Reduction of Systemic Risk by Means of Pigouvian Taxation

We analyze the possibility of reduction of systemic risk in financial markets through Pigouvian taxation of financial institutions, which is used to support the rescue fund. We introduce the concept of the cascade risk with a clear operational definition as a subclass and a network related measure of the systemic risk. Using financial networks constructed from real Italian money market data and using realistic parameters, we show that the cascade risk can be substantially reduced by a small rate of taxation and by means of a simple strategy of the money transfer from the rescue fund to interbanking market subjects. Furthermore, we show that while negative effects on the return on investment (ROI) are direct and certain, an overall positive effect on risk adjusted return on investments (ROI RA) is visible. Please note that the taxation is introduced as a monetary/regulatory, not as a _scal measure, as the term could suggest. The rescue fund is implemented in a form of a common reserve fund.
A Brief History of Long Memory: Hurst, Mandelbrot and the Road to ARFIMA, 1951-1980

Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is exhibiting long memory since that impacts the accuracy and confidence with which one may predict future events on the basis of a small amount of historical data. A major force in the development and study of long memory was the late Benoit B. Mandelbrot. Here, we discuss the original motivation of the development of long memory and Mandelbrot’s influence on this fascinating field. We will also elucidate the sometimes contrasting approaches to long memory in different scientific communities.