nils-herrmann/clean_scirepeval huggingface dataset:
Entropy production in relativistic jet boundary layers

Hot relativistic jets, passing through a background medium with a pressure gradient p \propto r^{-\eta} where 2 < \eta <= 8/3, develop a shocked boundary layer containing a significant fraction of the jet power. In previous work, we developed a self-similar description of the boundary layer assuming isentropic flow, but we found that such models respect global energy conservation only for the special case \eta = 8/3. Here we demonstrate that models with \eta < 8/3 can be made self-consistent if we relax the assumption of constant specific entropy. Instead, the entropy must increase with increasing r along the boundary layer, presumably due to multiple shocks driven into the flow as it gradually collimates. The increase in specific entropy slows the acceleration rate of the flow and provides a source of internal energy that could be channeled into radiation. We suggest that this process may be important for determining the radiative characteristics of tidal disruption events and gamma-ray bursts from collapsars.
Black holes as particle detectors: evolution of superradiant instabilities

Superradiant instabilities of spinning black holes (BHs) can be used to impose strong constraints on ultralight bosons, thus turning BHs into effective particle detectors. However, very little is known about the development of the instability and whether its nonlinear time evolution accords to the linear intuition. For the first time, we attack this problem by studying the impact of gravitational-wave (GW) emission and gas accretion on the evolution of the instability. Our quasi-adiabatic, fully-relativistic analysis shows that: (i) GW emission does not have a significant effect on the evolution of the BH, (ii) accretion plays an important role, and (iii) although the mass of the scalar cloud developed through superradiance can be a sizeable fraction of the BH mass, its energy-density is very low and backreaction is negligible. Thus, massive BHs are well described by the Kerr geometry even if they develop bosonic clouds through superradiance. Using Monte Carlo methods and very conservative assumptions, we provide strong support to the validity of the linearized analysis and to the bounds of previous studies.
A nonparametric adaptive nonlinear statistical filter

We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty. We propose that these uncertainties can be estimated from (conditioned on) past observed data, and without making any assumptions of the system's prior distribution. The system's prior distribution at each time step is constructed from an ensemble of least-squares estimates on sub-sampled sets of the data via jackknife sampling. As new data is acquired, the state estimates, process uncertainty, and measurement uncertainty are updated accordingly, as described in this manuscript.
Visualizing the "heartbeat" of a city with tweets

Describing the dynamics of a city is a crucial step to both understanding the human activity in urban environments and to planning and designing cities accordingly. Here we describe the collective dynamics of New York City and surrounding areas as seen through the lens of Twitter usage. In particular, we observe and quantify the patterns that emerge naturally from the hourly activities in different areas of New York City, and discuss how they can be used to understand the urban areas. Using a dataset that includes more than 6 million geolocated Twitter messages we construct a movie of the geographic density of tweets. We observe the diurnal "heartbeat" of the NYC area. The largest scale dynamics are the waking and sleeping cycle and commuting from residential communities to office areas in Manhattan. Hourly dynamics reflect the interplay of commuting, work and leisure, including whether people are preoccupied with other activities or actively using Twitter. Differences between weekday and weekend dynamics point to changes in when people wake and sleep, and engage in social activities. We show that by measuring the average distances to the heart of the city one can quantify the weekly differences and the shift in behavior during weekends. We also identify locations and times of high Twitter activity that occur because of specific activities. These include early morning high levels of traffic as people arrive and wait at air transportation hubs, and on Sunday at the Meadowlands Sports Complex and Statue of Liberty. We analyze the role of particular individuals where they have large impacts on overall Twitter activity. Our analysis points to the opportunity to develop insight into both geographic social dynamics and attention through social media analysis.
Inflationary gravitational waves in the effective field theory of modified gravity

In the approach of the effective field theory of modified gravity, we derive the second-order action and the equation of motion for tensor perturbations on the flat isotropic cosmological background. This analysis accommodates a wide range of gravitational theories including Horndeski theories, its generalization, and the theories with spatial derivatives higher than second order (e.g., Horava-Lifshitz gravity). We obtain the inflationary power spectrum of tensor modes by taking into account corrections induced by higher-order spatial derivatives and slow-roll corrections to the de Sitter background. We also show that the leading-order spectrum in concrete modified gravitational theories can be mapped on to that in General Relativity under a disformal transformation. Our general formula will be useful to constrain inflationary models from the future precise measurement of the B-mode polarization in the cosmic microwave background.
Trajectories of point particles in cosmology and the Zel'dovich approximation

Using a Green's function approach, we compare the trajectories of classical Hamiltonian point particles in an expanding space-time to the effectively inertial trajectories in the Zel'dovich approximation. It is shown that the effective gravitational potential accelerating the particles relative to the Zel'dovich trajectories vanishes exactly initially as a consequence of the continuity equation, and acts only during a short, early period. The Green's function approach suggests an iterative scheme for improving the Zel'dovich trajectories, which can be analytically solved. We construct these trajectories explicitly and show how they interpolate between the Zel'dovich and the exact trajectories. The effective gravitational potential acting on the improved trajectories is substantially smaller at late times than the potential acting on the exact trajectories. The results may be useful for Lagrangian perturbation theory and for numerical simulations.
The disappearance of causality at small scale in almost-commutative manifolds

This paper continues the investigations of noncommutative ordered spaces put forward by one of the authors. These metaphoric spaces are defined dually by so-called \emph{isocones} which generalize to the noncommutative setting the convex cones of order-preserving functions. In this paper we will consider the case of isocones inside almost-commutative algebras of the form ${\cal C}(M)\otimes A_f$, with $M$ a compact metrizable space. We will give a family of isocones in such an algebra with the property that every possible isocone is contained in exactly one member of the family. We conjecture that this family is in fact a complete classification, a hypothesis related with the noncommutative Stone-Weierstrass conjecture. We also obtain that every isocone in ${\cal C}(M)\otimes A_f$, with $A_f$ noncommutative, induces an order relation on $M$ with the property that every point in $M$ lies in a neighbourhood of incomparable points. Thus, if the causal order relation on spacetime is induced by an isocone in an almost-commutative (but not commutative) algebra, then causality must disappear at small scale.
Kernel Mean Estimation via Spectral Filtering

The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference step of modern kernel methods (e.g., kernel-based non-parametric tests) that rely on embedding probability distributions in RKHSs. Previous work  has shown that shrinkage can help in constructing "better" estimators of the kernel mean than the empirical estimator. The present paper studies the consistency and admissibility of the estimators in , and proposes a wider class of shrinkage estimators that improve upon the empirical estimator by considering appropriate basis functions. Using the kernel PCA basis, we show that some of these estimators can be constructed using spectral filtering algorithms which are shown to be consistent under some technical assumptions. Our theoretical analysis also reveals a fundamental connection to the kernel-based supervised learning framework. The proposed estimators are simple to implement and perform well in practice.
Simple approximate MAP Inference for Dirichlet processes

The Dirichlet process mixture (DPM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as Gibb's sampling are required. As a result, DPM-based methods, which have considerable potential, are restricted to applications in which computational resources and time for inference is plentiful. For example, they would not be practical for digital signal processing on embedded hardware, where computational resources are at a serious premium. Here, we develop simplified yet statistically rigorous approximate maximum a-posteriori (MAP) inference algorithms for DPMs. This algorithm is as simple as K-means clustering, performs in experiments as well as Gibb's sampling, while requiring only a fraction of the computational effort. Unlike related small variance asymptotics, our algorithm is non-degenerate and so inherits the "rich get richer" property of the Dirichlet process. It also retains a non-degenerate closed-form likelihood which enables standard tools such as cross-validation to be used. This is a well-posed approximation to the MAP solution of the probabilistic DPM model.
Iterated geometric harmonics for data imputation and reconstruction of missing data

The method of geometric harmonics is adapted to the situation of incomplete data by means of the iterated geometric harmonics (IGH) scheme. The method is tested on natural and synthetic data sets with 50–500 data points and dimensionality of 400– 10,000. Experiments suggest that the algorithm converges to a near optimal solution within 4–6 iterations, at runtimes of less than 30 minutes on a medium-grade desktop computer. The imputation of missing data values is applied to collections of damaged images (suffering from data annihilation rates of up to 70%) which are reconstructed with a surprising degree of accuracy.
A statistical model for tensor PCA

We consider the Principal Component Analysis problem for large tensors of arbitrary order $k$ under a single-spike (or rank-one plus noise) model. On the one hand, we use information theory, and recent results in probability theory, to establish necessary and sufficient conditions under which the principal component can be estimated using unbounded computational resources. It turns out that this is possible as soon as the signal-to-noise ratio $\beta$ becomes larger than $C\sqrt{k\log k}$ (and in particular $\beta$ can remain bounded as the problem dimensions increase). 
On the other hand, we analyze several polynomial-time estimation algorithms, based on tensor unfolding, power iteration and message passing ideas from graphical models. We show that, unless the signal-to-noise ratio diverges in the system dimensions, none of these approaches succeeds. This is possibly related to a fundamental limitation of computationally tractable estimators for this problem. 
We discuss various initializations for tensor power iteration, and show that a tractable initialization based on the spectrum of the matricized tensor outperforms significantly baseline methods, statistically and computationally. Finally, we consider the case in which additional side information is available about the unknown signal. We characterize the amount of side information that allows the iterative algorithms to converge to a good estimate.
Wave functions of S U ( 3 ) pure gauge glueballs on the lattice

The Bethe-Salpeter wave functions of SU(3) pure gauge glueballs are revisited in this study. The ground and the first excited states of the scalar and tensor glueballs are identified unambiguously through the variational method. We calculate the wave functions in the Coulomb gauge and use two lattice spacings to check the discretization artifacts. For the ground states, the radial wave functions are approximately Gaussian, and the size of the tensor glueball is roughly twice as large as that of the scalar glueball. For the first excited states, the radial nodes are clearly observed for both the scalar and the tensor glueballs, such that they can be interpreted as the first radial excitations. These observations may shed light on the theoretical understanding of the inner structure of glueballs.
Fast Exact Matrix Completion with Finite Samples

Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this problem. However, the sample complexity in all these results is sub-optimal in its dependence on the rank, condition number and the desired accuracy. 
In this paper, we present a fast iterative algorithm that solves the matrix completion problem by observing $O(nr^5 \log^3 n)$ entries, which is independent of the condition number and the desired accuracy. The run time of our algorithm is $O(nr^7\log^3 n\log 1/\epsilon)$ which is near linear in the dimension of the matrix. To the best of our knowledge, this is the first near linear time algorithm for exact matrix completion with finite sample complexity (i.e. independent of $\epsilon$). 
Our algorithm is based on a well known projected gradient descent method, where the projection is onto the (non-convex) set of low rank matrices. There are two key ideas in our result: 1) our argument is based on a $\ell_{\infty}$ norm potential function (as opposed to the spectral norm) and provides a novel way to obtain perturbation bounds for it. 2) we prove and use a natural extension of the Davis-Kahan theorem to obtain perturbation bounds on the best low rank approximation of matrices with good eigen-gap. Both of these ideas may be of independent interest.
Expectation-Maximization for Learning Determinantal Point Processes

A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by maximizing the log-likelihood of the available data. However, log-likelihood is non-convex in the entries of the kernel matrix, and this learning problem is conjectured to be NP-hard . Thus, previous work has instead focused on more restricted convex learning settings: learning only a single weight for each row of the kernel matrix , or learning weights for a linear combination of DPPs with fixed kernel matrices . In this work we propose a novel algorithm for learning the full kernel matrix. By changing the kernel parameterization from matrix entries to eigenvalues and eigenvectors, and then lower-bounding the likelihood in the manner of expectation-maximization algorithms, we obtain an effective optimization procedure. We test our method on a real-world product recommendation task, and achieve relative gains of up to 16.5% in test log-likelihood compared to the naive approach of maximizing likelihood by projected gradient ascent on the entries of the kernel matrix.
Multilayer stochastic block models reveal the multilayer structure of complex networks

In complex systems, the network of interactions we observe between system's components is the aggregate of the interactions that occur through different mechanisms or layers. Recent studies reveal that the existence of multiple interaction layers can have a dramatic impact in the dynamical processes occurring on these systems. However, these studies assume that the interactions between systems components in each one of the layers are known, while typically for real-world systems we do not have that information. Here, we address the issue of uncovering the different interaction layers from aggregate data by introducing multilayer stochastic block models (SBMs), a generalization of single-layer SBMs that considers different mechanisms of layer aggregation. First, we find the complete probabilistic solution to the problem of finding the optimal multilayer SBM for a given aggregate observed network. Because this solution is computationally intractable, we propose an approximation that enables us to verify that multilayer SBMs are more predictive of network structure in real-world complex systems.
Learning of Agent Capability Models with Applications in Multi-agent Planning

One important challenge for a set of agents to achieve more efficient collaboration is for these agents to maintain proper models of each other. An important aspect of these models of other agents is that they are often partial and incomplete. Thus far, there are two common representations of agent models: MDP based and action based, which are both based on action modeling. In many applications, agent models may not have been given, and hence must be learnt. While it may seem convenient to use either MDP based or action based models for learning, in this paper, we introduce a new representation based on capability models, which has several unique advantages. First, we show that learning capability models can be performed efficiently online via Bayesian learning, and the learning process is robust to high degrees of incompleteness in plan execution traces (e.g., with only start and end states). While high degrees of incompleteness in plan execution traces presents learning challenges for MDP based and action based models, capability models can still learn to  useful information out of these traces. As a result, capability models are useful in applications in which such incompleteness is common, e.g., robot learning human model from observations and interactions. Furthermore, when used in multi-agent planning (with each agent modeled separately), capability models provide flexible abstraction of actions. The limitation, however, is that the synthesized plan is incomplete and abstract.
Projecting Markov Random Field Parameters for Fast Mixing

Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful techniques to sample from almost arbitrary distributions. The flaw in practice is that it can take a large and/or unknown amount of time to converge to the stationary distribution. This paper gives sufficient conditions to guarantee that univariate Gibbs sampling on Markov Random Fields (MRFs) will be fast mixing, in a precise sense. Further, an algorithm is given to project onto this set of fast-mixing parameters in the Euclidean norm. Following recent work, we give an example use of this to project in various divergence measures, comparing univariate marginals obtained by sampling after projection to common variational methods and Gibbs sampling on the original parameters.
Science and Ethnicity: How Ethnicities Shape the Evolution of Computer Science Research Community

Globalization and the world wide web has resulted in academia and science being an international and multicultural community forged by researchers and scientists with different ethnicities. How ethnicity shapes the evolution of membership, status and interactions of the scientific community, however, is not well understood. This is due to the difficulty of ethnicity identification at the large scale. We use name ethnicity classification as an indicator of ethnicity. Based on automatic name ethnicity classification of 1.7+ million authors gathered from Web, the name ethnicity of computer science scholars is investigated by population size, publication contribution and collaboration strength. By showing the evolution of name ethnicity from 1936 to 2010, we discover that ethnicity diversity has increased significantly over time and that different research communities in certain publication venues have different ethnicity compositions. We notice a clear rise in the number of Asian name ethnicities in papers. Their fraction of publication contribution increases from approximately 10% to near 50% from 1970 to 2010. We also find that name ethnicity acts as a homophily factor on coauthor networks, shaping the formation of coauthorship as well as evolution of research communities.
Global Convergence of Stochastic Gradient Descent for Some Non-convex Matrix Problems

Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a low-rank least-squares problem, and we prove that, under broad sampling conditions, our method converges globally from a random starting point within $O(\epsilon^{-1} n \log n)$ steps with constant probability for constant-rank problems. Our modification of SGD relates it to stochastic power iteration. We also show experiments to illustrate the runtime and convergence of the algorithm.
Oxidation of a Graphite Surface: The Role of Water

On the basis of density functional calculations, we demonstrate a significant difference in oxidation patterns between graphene and graphite and the formation of defects after oxidation. Step-by-step modeling demonstrates that oxidation of 80% of the graphite surface is favorable. Oxidation above half of the graphite surface significantly decreases the energy costs of vacancy formation with CO2 production. The presence of water is crucial in the transformation of epoxy groups to hydroxyl, intercalation with further bundling, and exfoliation. In water-rich conditions, water intercalates graphite at the initial stages of oxidation and oxidation, which is similar to the oxidation process of free-standing graphene; in contrast, in water-free conditions, large molecules intercalate graphite only after oxidation occurs on more than half of the surface.
Berk-Nash Equilibrium: A Framework for Modeling Agents with Misspecified Models

We develop an equilibrium framework that relaxes the standard assumption that people have a correctly-specified view of their environment. Each player is characterized by a (possibly misspecified) subjective model, which describes the set of feasible beliefs over payoff-relevant consequences as a function of actions. We introduce the notion of a Berk-Nash equilibrium: Each player follows a strategy that is optimal given her belief, and her belief is restricted to be the best fit among the set of beliefs she considers possible. The notion of best fit is formalized in terms of minimizing the Kullback-Leibler divergence, which is endogenous and depends on the equilibrium strategy profile. Standard solution concepts such as Nash equilibrium and self-confirming equilibrium constitute special cases where players have correctly-specified models. We provide a learning foundation for Berk-Nash equilibrium by extending and combining results from the statistics literature on misspecified learning and the economics literature on learning in games.