nils-herrmann/clean_scirepeval huggingface dataset:
Nucleon tensor charges and electric dipole moments

A symmetry-preserving Dyson-Schwinger equation treatment of a vector-vector contact interaction is used to compute dressed-quark-core contributions to the nucleon σ-term and tensor charges. The latter enable one to directly determine the effect of dressed-quark electric dipole moments (EDMs) on neutron and proton EDMs. The presence of strong scalar and axial-vector diquark correlations within ground-state baryons is a prediction of this approach. These correlations are active participants in all scattering events and thereby modify the contribution of the singly represented valence quark relative to that of the doubly represented quark. Regarding the proton σ-term and that part of the proton mass which owes to explicit chiral symmetry breaking, with a realistic d-u mass splitting, the singly represented d quark contributes 37% more than the doubly represented u quark; and in connection with the proton’s tensor charges, δTu, δTd, the ratio δTd/δTu is 18% larger than anticipated from simple quark models. Of particular note, the size of δTu is a sensitive measure of the strength of dynamical chiral symmetry breaking; and δTd measures the amount of axial-vector diquark correlation within the proton, vanishing if such correlations are absent.
Learning Theory for Distribution Regression

We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point estimation problems without analytical solution (such as hyperparameter or entropy estimation). Despite the large number of available heuristics in the literature, the inherent two-stage sampled nature of the problem makes the theoretical analysis quite challenging, since in practice only samples from sampled distributions are observable, and the estimates have to rely on similarities computed between sets of points. To the best of our knowledge, the only existing technique with consistency guarantees for distribution regression requires kernel density estimation as an intermediate step (which often performs poorly in practice), and the domain of the distributions to be compact Euclidean. In this paper, we study a simple, analytically computable, ridge regression-based alternative to distribution regression, where we embed the distributions to a reproducing kernel Hilbert space, and learn the regressor from the embeddings to the outputs. Our main contribution is to prove that this scheme is consistent in the two-stage sampled setup under mild conditions (on separable topological domains enriched with kernels): we present an exact computational-statistical efficiency trade-off analysis showing that our estimator is able to match the one-stage sampled minimax optimal rate [Caponnetto and De Vito, 2007; Steinwart et al., 2009]. This result answers a 17-year-old open question, establishing the consistency of the classical set kernel [Haussler, 1999; Gaertner et. al, 2002] in regression. We also cover consistency for more recent kernels on distributions, including those due to [Christmann and Steinwart, 2010].
The Emergence of Spacetime: Transactions and Causal Sets

This paper discusses how the transactional interpretation of quantum mechanics can provide for a natural account of the emergence of spacetime events from a quantum substratum. In this account, spacetime is not a substantive manifold that becomes occupied with events; rather, spacetime itself exists only in virtue of specific actualized events. This implies that spacetime is discrete rather than continuous, and that properties attributed to spacetime based on the notion of a continuum are idealizations that do not apply to the real physical world. It is further noted that the transactional picture of the emergence of spacetime can provide the quantum dynamics that underlie the causal set approach as proposed by Sorkin and others.
Covariate-assisted spectral clustering

Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides insight into the systems that generated the graphs. Moreover, in applications such as connectomics, social networks, and genomics, graph data are accompanied by contextualizing measures on each node. We utilize these node covariates to help uncover latent communities in a graph, using a modification of spectral clustering. Statistical guarantees are provided under a joint mixture model that we call the node-contextualized stochastic blockmodel, including a bound on the misclustering rate. The bound is used to derive conditions for achieving perfect clustering. For most simulated cases, covariate-assisted spectral clustering yields results superior both to regularized spectral clustering without node covariates and to an adaptation of canonical correlation analysis. We apply our clustering method to large brain graphs derived from diffusion MRI data, using the node locations or neurological region membership as covariates. In both cases, covariate-assisted spectral clustering yields clusters that are easier to interpret neurologically.
The history of the Universe is an elliptic curve

Friedmann–Lemaître equations with contributions coming from matter, curvature, cosmological constant, and radiation, when written in terms of conformal time u rather than in terms of cosmic time t, can be solved explicitly in terms of standard Weierstrass elliptic functions. The spatial scale factor, the temperature, the densities, the Hubble function, and almost all quantities of cosmological interest (with the exception of t itself) are elliptic functions of u, in particular they are bi-periodic with respect to a lattice of the complex plane, when one takes u complex. After recalling the basics of the theory, we use these explicit expressions, as well as the experimental constraints on the present values of density parameters (we choose for the curvature density a small value in agreement with experimental bounds) to display the evolution of the main cosmological quantities for one real period 2 &ohgr; r ?> of conformal time (the cosmic time t ‘never ends’ but it goes to infinity for a finite value u f < 2 &ohgr; r ?> of u). A given history of the Universe, specified by the measured values of present-day densities, is associated with a lattice in the complex plane, or with an elliptic curve, and therefore with two Weierstrass invariants g 2 , g 3 ?> . Using the same experimental data we calculate the values of these invariants, as well as the associated modular parameter and the corresponding Klein j-invariant. If one takes the flat case k = 0, the lattice is only defined up to homotheties, and if one, moreover, neglects the radiation contribution, the j-invariant vanishes and the corresponding modular parameter τ can be chosen in one corner of the standard fundamental domain of the modular group (equihanharmonic case: τ = exp ( 2 i &pgr; / 3 ) ?> ). Several exact—i.e., non-numerical—results of independent interest are obtained in that case.
Discovering the QCD Axion with Black Holes and Gravitational Waves

Advanced LIGO may be the first experiment to detect gravitational waves. Through superradiance of stellar black holes, it may also be the first experiment to discover the QCD axion with decay constant above the grand unification scale. When an axion’s Compton wavelength is comparable to the size of a black hole, the axion binds to the black hole, forming a “gravitational atom.” Through the superradiance process, the number of axions occupying the bound levels grows exponentially, extracting energy and angular momentum from the black hole. Axions transitioning between levels of the gravitational atom and axions annihilating to gravitons can produce observable gravitational wave signals. The signals are long lasting, monochromatic, and can be distinguished from ordinary astrophysical sources. We estimate up to O(1) transition events at aLIGO for an axion between 10-11 and 10-10  eV and up to 104 annihilation events for an axion between 10-13 and 10-11  eV. In the event of a null search, aLIGO can constrain the axion mass for a range of rapidly spinning black hole formation rates. Axion annihilations are also promising for much lighter masses at future lower-frequency gravitational wave observatories; the rates have large uncertainties, dominated by supermassive black hole spin distributions. Our projections for aLIGO are robust against perturbations from the black hole environment and account for our updated exclusion on the QCD axion of 6×10-13  eV
Model-Parallel Inference for Big Topic Models

In real world industrial applications of topic modeling, the ability to capture gigantic conceptual space by learning an ultra-high dimensional topical representation, i.e., the so-called "big model", is becoming the next desideratum after enthusiasms on "big data", especially for fine-grained downstream tasks such as online advertising, where good performances are usually achieved by regression-based predictors built on millions if not billions of input features. The conventional data-parallel approach for training gigantic topic models turns out to be rather inefficient in utilizing the power of parallelism, due to the heavy dependency on a centralized image of "model". Big model size also poses another challenge on the storage, where available model size is bounded by the smallest RAM of nodes. To address these issues, we explore another type of parallelism, namely model-parallelism, which enables training of disjoint blocks of a big topic model in parallel. By integrating data-parallelism with model-parallelism, we show that dependencies between distributed elements can be handled seamlessly, achieving not only faster convergence but also an ability to tackle significantly bigger model size. We describe an architecture for model-parallel inference of LDA, and present a variant of collapsed Gibbs sampling algorithm tailored for it. Experimental results demonstrate the ability of this system to handle topic modeling with unprecedented amount of 200 billion model variables only on a low-end cluster with very limited computational resources and bandwidth.
Similarity Learning for High-Dimensional Sparse Data

A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of the data. In this paper, we propose a method that can learn efficiently similarity measure from high-dimensional sparse data. The core idea is to parameterize the similarity measure as a convex combination of rank-one matrices with specific sparsity structures. The parameters are then optimized with an approximate Frank-Wolfe procedure to maximally satisfy relative similarity constraints on the training data. Our algorithm greedily incorporates one pair of features at a time into the similarity measure, providing an efficient way to control the number of active features and thus reduce overfitting. It enjoys very appealing convergence guarantees and its time and memory complexity depends on the sparsity of the data instead of the dimension of the feature space. Our experiments on real-world high-dimensional datasets demonstrate its potential for classification, dimensionality reduction and data exploration.
Sparse Estimation with Generalized Beta Mixture and the Horseshoe Prior

In this paper, the use of the Generalized Beta Mixture (GBM) and Horseshoe distributions as priors in the Bayesian Compressive Sensing framework is proposed. The distributions are considered in a two-layer hierarchical model, making the corresponding inference problem amenable to Expectation Maximization (EM). We present an explicit, algebraic EM-update rule for the models, yielding two fast and experimentally validated algorithms for signal recovery. Experimental results show that our algorithms outperform state-of-the-art methods on a wide range of sparsity levels and amplitudes in terms of reconstruction accuracy, convergence rate and sparsity. The largest improvement can be observed for sparse signals with high amplitudes.
Parity-violating and anisotropic correlations in pseudoscalar inflation

A pseudo-scalar inflaton field can have interesting phenomenological signatures associated with parity violation. The existing analyses of these signatures typically assume statistical isotropy. In the present work we instead investigate the possibility that a pseudo-scalar inflaton is coupled to a vector field carrying a small but non-negligible vacuum expectation value (vev) coherent over our Hubble patch. We show that, in such case, correlators involving the primordial curvature perturbations and gravitational waves violate both statistical isotropy and parity symmetry. We compute the Cosmic Microwave Background (CMB) temperature anisotropies (T) and polarization (E/B) generated by these primordial modes. The CMB two-point correlation functions present distinct signals of broken rotational and parity invariance. Specifically, we find non-vanishing TT, TE, EE and BB correlators between ℓ1 and ℓ2 = ℓ1 ± 1 multipoles, and non-vanishing TB and EB correlators between ℓ1 and ℓ2 = ℓ1 ± 2 multipoles. Such signatures are specific of the models under consideration and they cannot be generated if one of parity and isotropy is preserved. As a specific example we consider the simple case in which the vector field has just an "electric" background component decaying in the standard way as a−2. In this case a strong scale-dependent quadrupolar modulation of the primordial power spectra is generated and we find that almost noiseless data of the large-scale temperature and E-mode polarization anisotropies (like, e.g., the ones provided by WMAP or Planck) should be able to constrain the quadrupolar amplitude coefficients g2M of the primordial scalar power spectrum (normalized at the pivot scale comparable to the present horizon size k−10 = 14 Gpc) down to g2M = 30 (68%CL).
Optimising Credit Portfolio Using a Quadratic Nonlinear Projection Method

A novel optimisation framework through quadratic nonlinear projection is introduced for credit portfolio when the portfolio risk is measured by Conditional Value-at-Risk (CVaR). The whole optimisation procedure to search toward the optimal portfolio state is conducted by a series of single-step optimisations under the local constraints described in the multi-dimensional constraint parameter space as functions of the total amount of portfolio adjustment. Each single-step optimisation is approximated by the first-order variation of the weight increments with respect to the total amount of portfolio adjustment and is solved in the form of locally exact formula formulated in the general Lagrange multiplier method. Our method can deal with optimisation for general nonlinear objective functions, such as the return-to-risk ratio maximisation or the diversification index, as well as the risk minimisation or the return maximisation.
Parameter Estimation in Spherical Symmetry Groups

This letter considers statistical estimation problems where the probability distribution of the observed random variable is invariant with respect to actions of a finite topological group. It is shown that any such distribution must satisfy a restricted finite mixture representation. When specialized to the case of distributions over the sphere that are invariant to the actions of a finite spherical symmetry group G, a group-invariant extension of the Von Mises Fisher (VMF) distribution is obtained. The G-invariant VMF is parameterized by location and scale parameters that specify the distribution's mean orientation and its concentration about the mean, respectively. Using the restricted finite mixture representation these parameters can be estimated using an Expectation Maximization (EM) maximum likelihood (ML) estimation algorithm. This is illustrated for the problem of mean crystal orientation estimation under the spherically symmetric group associated with the crystal form, e.g., cubic or octahedral or hexahedral. Simulations and experiments establish the advantages of the extended VMF EM-ML estimator for data acquired by Electron Backscatter Diffraction (EBSD) microscopy of a polycrystalline Nickel alloy sample.
Statistical distributions of sequencing by synthesis with probabilistic nucleotide incorporation

Sequencing by synthesis is used in many next-generation DNA sequencing technologies. Some of the technologies, especially those exploring the principle of single-molecule sequencing, allow incomplete nucleotide incorporation in each cycle. We derive statistical distributions for sequencing by synthesis by taking into account the possibility that nucleotide incorporation may not be complete in each flow cycle. The statistical distributions are expressed in terms of nucleotide probabilities of the target sequences and the nucleotide incorporation probabilities for each nucleotide. We give exact distributions both for fixed number of flow cycles and for fixed sequence length. Explicit formulas are derived for the mean and variance of these distributions. The results are generalizations of our previous work for pyrosequencing. Incomplete nucleotide incorporation leads to significant change in the mean and variance of the distributions, but still they can be approximated by normal distributions with the same mean and variance. The results are also generalized to handle sequence context dependent incorporation. The statistical distributions will be useful for instrument and software development for sequencing by synthesis platforms.
Deep Exponential Families

We describe \textit{deep exponential families} (DEFs), a class of latent variable models that are inspired by the hidden structures used in deep neural networks. DEFs capture a hierarchy of dependencies between latent variables, and are easily generalized to many settings through exponential families. We perform inference using recent "black box" variational inference techniques. We then evaluate various DEFs on text and combine multiple DEFs into a model for pairwise recommendation data. In an extensive study, we show that going beyond one layer improves predictions for DEFs. We demonstrate that DEFs find interesting exploratory structure in large data sets, and give better predictive performance than state-of-the-art models.
Optimization of the geometrical stability in square ring laser gyroscopes

Ultra-sensitive ring laser gyroscopes are regarded as potential detectors of the general relativistic frame-dragging effect due to the rotation of the Earth. Our project for this goal is called GINGER (gyroscopes in general relativity), and consists of a ground-based triaxial array of ring lasers aimed at measuring the rotation rate of the Earth with an accuracy of 10 − 14 rad s − 1 ?> . Such an ambitious goal is now within reach, as large-area ring lasers are very close to the required sensitivity and stability. However, demanding constraints on the geometrical stability of the optical path of the laser inside the ring cavity are required. Thus, we have begun a detailed study of the geometry of an optical cavity in order to find a control strategy for its geometry that could meet the specifications of the GINGER project. As the cavity perimeter has a stationary point for the square configuration, we identify a set of transformations on the mirror positions that allows us to adjust the laser beam steering to the shape of a square. We show that the geometrical stability of a square cavity strongly increases by implementing a suitable system to measure the mirror distances, and that the geometry stabilization can be achieved by measuring the absolute lengths of the two diagonals and the perimeter of the ring.
Global structure of black holes via the dynamical system

We have recast the system of Einstein field equations for locally rotationally symmetric spacetimes into an autonomous system of covariantly defined geometrical variables. The analysis of this autonomous system gives all the important global features of the maximal extension of these spacetimes. We have concluded that the dynamical system analysis can be a powerful mathematical tool for qualitative understanding of the global structure of spacetimes covariantly, without actually solving the field equations.
The topological long range order in QCD. Applications to heavy ion collisions and cosmology

We argue that the local violation of P invariance in heavy ion collisions is a consequence of the long range topological order which is inherent feature of strongly coupled QCD. A similar phenomenon is known to occur in some topologically ordered condensed matter systems with a gap. We also discuss possible cosmological applications of this long range order in strongly coupled gauge theories. In particular, we argue that the de Sitter behaviour might be dynamically generated as a result of the long range order. In this framework the inflaton is an auxiliary field which effectively describes the dynamics of topological sectors in a gauge theory in the expanding universe, rather than a new dynamical degree of freedom.
The Bayesian Echo Chamber: Modeling Social Influence via Linguistic Accommodation

We present the Bayesian Echo Chamber, a new Bayesian generative model for social interaction data. By modeling the evolution of people's language usage over time, this model discovers latent influence relationships between them. Unlike previous work on inferring influence, which has primarily focused on simple temporal dynamics evidenced via turn-taking behavior, our model captures more nuanced influence relationships, evidenced via linguistic accommodation patterns in interaction content. The model, which is based on a discrete analog of the multivariate Hawkes process, permits a fully Bayesian inference algorithm. We validate our model's ability to discover latent influence patterns using transcripts of arguments heard by the US Supreme Court and the movie "12 Angry Men." We showcase our model's capabilities by using it to infer latent influence patterns from Federal Open Market Committee meeting transcripts, demonstrating state-of-the-art performance at uncovering social dynamics in group discussions.
Bayesian group latent factor analysis with structured sparsity

Latent factor models are the canonical statistical tool for exploratory analyses of low-dimensional linear structure for an observation matrix with p features across n samples. We develop a structured Bayesian group factor analysis model that extends the factor model to multiple coupled observation matrices; in the case of two observations, this reduces to a Bayesian model of canonical correlation analysis. The main contribution of this work is to carefully define a structured Bayesian prior that encourages both element-wise and column-wise shrinkage and leads to desirable behavior on high-dimensional data. In particular, our model puts a structured prior on the joint factor loading matrix, regularizing at three levels, which enables element-wise sparsity and unsupervised recovery of latent factors corresponding to structured variance across arbitrary subsets of the observations. In addition, our structured prior allows for both dense and sparse latent factors so that covariation among either all features or only a subset of features can both be recovered. We use fast parameter-expanded expectation-maximization for parameter estimation in this model. We validate our method on both simulated data with substantial structure and real data, comparing against a number of state-of-the-art approaches. These results illustrate useful properties of our model, including i) recovering sparse signal in the presence of dense effects; ii) the ability to scale naturally to large numbers of observations; iii) flexible observation- and factor-specific regularization to recover factors with a wide variety of sparsity levels and percentage of variance explained; and iv) tractable inference that scales to modern genomic and document data sizes.