nils-herrmann/clean_scirepeval huggingface dataset:
Reducing Sampling Ratios and Increasing Number of Estimates Improve Bagging in Sparse Regression

Bagging, a powerful ensemble method from machine learning, has shown the ability to improve the performance of unstable predictors in difficult practical settings. Although Bagging is most well-known for its application in classification problems, here we demonstrate that employing Bagging in sparse regression improves performance compared to the baseline method ($\ell_{1}$ minimization). Although the original Bagging method uses a bootstrap sampling ratio of 1, such that the sizes of the bootstrap samples L are the same as the total number of data points m, we generalize the bootstrap sampling ratio to explore the optimal sampling ratios for various cases. The performance limits associated with different choices of bootstrap sampling ratio L/m and number of estimates K are analyzed theoretically. Simulation results show that a lower L/m ratio (0.6 - 0.9) leads to better performance than the conventional choice (L/ m = 1), especially in challenging cases with low levels of measurements. With the reduced sampling rate, SNR improves over the original Bagging method by up to 24% and over the base algorithm $\ell_{1}$ minimization by up to 367%. With a properly chosen sampling ratio, a reasonably small number of estimates (K = 30) gives a satisfying result, although increasing K is discovered to always improve or at least maintain performance.
A Bezout ring of stable range 2 which has square stable range 1

In this article, we introduced the concept of a ring of stable range 2 which has square stable range 1. We proved that a Hermitian ring R which has (right) square stable range 1 is an elementary divisor ring if and only if R is a duo ring of neat range 1. And we found that a commutative Hermitian ring R is a Toeplitz ring if and only if R is a ring of (right) square range 1. We proved that if R be a commutative elementary divisor ring of (right) square stable range 1, then for any matrix one can find invertible Toeplitz matrices P and Q such that where e1 is a divisor of e2.
Simulating X-ray Absorption Spectra with Linear-Response Density Cumulant Theory.

We present a new approach for simulating X-ray absorption spectra based on linear-response density cumulant theory (LR-DCT) [ Copan , A. V. ; Sokolov , A. Yu.  2018 , 14 , 4097 - 4108 ]. Our new method combines the LR-ODC-12 formulation of LR-DCT with core-valence separation approximation (CVS) that allows us to efficiently access high-energy core-excited states. We describe our computer implementation of the CVS-approximated LR-ODC-12 method (CVS-ODC-12) and benchmark its performance by comparing simulated X-ray absorption spectra to those obtained from experiment for several small molecules. Our results demonstrate that the CVS-ODC-12 method shows good agreement with experiment for relative spacings between transitions and their intensities, but the excitation energies are systematically overestimated. When compared to results from excited-state coupled cluster methods with single and double excitations, the CVS-ODC-12 method shows a similar performance for intensities and peak separations, while coupled cluster spectra are less shifted, relative to experiment. An important advantage of CVS-ODC-12 is that its excitation energies are computed by diagonalizing a Hermitian matrix, which enables efficient computation of transition intensities.
A General Approach to Domain Adaptation with Applications in Astronomy

The ability to build a model on a source task and subsequently adapt this model to a new target task is a pervasive need in many astronomical applications. The problem is generally known in the machine learning field as transfer learning, where domain adaptation is a popular scenario. An example is to build a predictive model on spectroscopic data to identify Type Ia supernovae (SNe Ia), while subsequently trying to adapt such a model to photometric data. In this paper we propose a new general approach to domain adaptation which does not rely on the proximity of source and target distributions. Instead we simply assume a strong similarity in model complexity across domains, and use active learning to mitigate the dependence on source examples. Our work leads to a new formulation for the likelihood as a function of empirical error using a theoretical learning bound; the result is a novel mapping from generalization error to a likelihood estimation. Results using two real astronomical problems, SN Ia classification and identification of Mars landforms, show two main advantages of our approach: increased performance accuracy and substantial savings in computational cost.
Bulk-Deformed Potentials for Toric Fano Surfaces, Wall-Crossing, and Period

We provide an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing techniques and a tropical–holomorphic correspondence theorem for holomorphic discs. As an application of the correspondence theorem, we also prove a big quantum period theorem for toric Fano surfaces, which relates the log descendant Gromov–Witten invariants with the oscillatory integrals of the bulk-deformed potentials.
Three Dimensional Reconstruction of Botanical Trees with Simulatable Geometry

We tackle the challenging problem of creating full and accurate three dimensional reconstructions of botanical trees with the topological and geometric accuracy required for subsequent physical simulation, e.g. in response to wind forces. Although certain aspects of our approach would benefit from various improvements, our results exceed the state of the art especially in geometric and topological complexity and accuracy. Starting with two dimensional RGB image data acquired from cameras attached to drones, we create point clouds, textured triangle meshes, and a simulatable and skinned cylindrical articulated rigid body model. We discuss the pros and cons of each step of our pipeline, and in order to stimulate future research we make the raw and processed data from every step of the pipeline as well as the final geometric reconstructions publicly available.
A Scale Invariant Approach for Sparse Signal Recovery

In this paper, we study the ratio of the $L_1 $ and $L_2 $ norms, denoted as $L_1/L_2$, to promote sparsity. Due to the non-convexity and non-linearity, there has been little attention to this scale-invariant model. Compared to popular models in the literature such as the $L_p$ model for $p\in(0,1)$ and the transformed $L_1$ (TL1), this ratio model is parameter free. Theoretically, we present a strong null space property (sNSP) and prove that any sparse vector is a local minimizer of the $L_1 /L_2 $ model provided with this sNSP condition. Computationally, we focus on a constrained formulation that can be solved via the alternating direction method of multipliers (ADMM). Experiments show that the proposed approach is comparable to the state-of-the-art methods in sparse recovery. In addition, a variant of the $L_1/L_2$ model to apply on the gradient is also discussed with a proof-of-concept example of the MRI reconstruction.
Training of quantum circuits on a hybrid quantum computer

We train generative modeling circuits on a quantum hybrid computer showing an optimization strategy and a resource trade-off. Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. Here, we implement a data-driven quantum circuit training algorithm on the canonical Bars-and-Stripes dataset using a quantum-classical hybrid machine. The training proceeds by running parameterized circuits on a trapped ion quantum computer and feeding the results to a classical optimizer. We apply two separate strategies, Particle Swarm and Bayesian optimization to this task. We show that the convergence of the quantum circuit to the target distribution depends critically on both the quantum hardware and classical optimization strategy. Our study represents the first successful training of a high-dimensional universal quantum circuit and highlights the promise and challenges associated with hybrid learning schemes.
NOMA Aided Narrowband IoT for Machine Type Communications With User Clustering

To support machine type communications (MTCs) in next generation mobile networks, Narrowband-Internet of Things (NB-IoT) has been released by the third generation partnership project (3GPP) as a promising solution to provide extended coverage and low energy consumption for low cost MTC devices. However, the existing orthogonal multiple access (OMA) scheme in NB-IoT cannot provide connectivity for a massive number of MTC devices. In parallel with the development of NB-IoT and non-OMA (NOMA), introduced for the fifth generation wireless networks, is deemed to significantly improve the network capacity by providing massive connectivity through sharing the same spectral resources. To leverage NOMA in the context of NB-IoT, we propose a power domain NOMA scheme with user clustering for an NB-IoT system. In particular, the MTC devices are assigned to different ranks within the NOMA clusters where they transmit over the same frequency resources. Then, we formulate an optimization problem to maximize the total throughput of the network by optimizing the resource allocation of MTC devices and NOMA clustering while satisfying the transmission power and quality of service requirements. We prove the NP-hardness of the proposed optimization problem. We further design an efficient heuristic algorithm to solve the proposed optimization problem by jointly optimizing NOMA clustering and resource allocation of MTC devices. Furthermore, we prove that the reduced optimization problem of power control is a convex optimization task. Simulation results are presented to demonstrate the efficiency of the proposed scheme.
Enhanced continuous generation of non-Gaussianity through optomechanical modulation

We study the non-Gaussian character of quantum optomechanical systems evolving under the fully nonlinear optomechanical Hamiltonian. By using a measure of non-Gaussianity based on the relative entropy of an initially Gaussian state, we quantify the amount of non-Gaussianity induced by both a constant and time-dependent cubic light–matter coupling and study its general and asymptotic behaviour. We find analytical approximate expressions for the measure of non-Gaussianity and show that initial thermal phonon occupation of the mechanical element does not significantly impact the non-Gaussianity. More importantly, we also show that it is possible to continuously increase the amount of non-Gassuianity of the state by driving the light–matter coupling at the frequency of mechanical resonance, suggesting a viable mechanism for increasing the non-Gaussianity of optomechanical systems even in the presence of noise.
Variational Cross-domain Natural Language Generation for Spoken Dialogue Systems

Cross-domain natural language generation (NLG) is still a difficult task within spoken dialogue modelling. Given a semantic representation provided by the dialogue manager, the language generator should generate sentences that convey desired information. Traditional template-based generators can produce sentences with all necessary information, but these sentences are not sufficiently diverse. With RNN-based models, the diversity of the generated sentences can be high, however, in the process some information is lost. In this work, we improve an RNN-based generator by considering latent information at the sentence level during generation using conditional variational auto-encoder architecture. We demonstrate that our model outperforms the original RNN-based generator, while yielding highly diverse sentences. In addition, our model performs better when the training data is limited.
Using First Hitting Times to Find Sets that Maximize the Convergence Rate to Consensus

In a model of communication in a social network described by a simple consensus model, we pose the problem of finding a subset of nodes with given cardinality and fixed consensus values that enable the fastest convergence rate to equilibrium of the values of the remaining nodes. Given a network topology and a subset, called the stubborn nodes, the equilibrium exists and is a convex sum of the initial values of the stubborn nodes. The value at a non-stubborn node converges to its consensus value exponentially with a rate constant determined by the expected first hitting time of a random walker starting at the node and ending at the first stubborn node it visits. In this paper, we will use the sum of the expected first hitting times to the stubborn nodes as an objective function for a minimization problem. Its solution is a set with the fastest convergence rate. We present a polynomial time method for obtaining approximate solutions of the optimization problem for fixed cardinality less than that of a reference vertex cover. Under the assumption that the transition matrix for the random walk is irreducible and reversible, we also obtain an upper bound for the expected first hitting time and therefore an upper bound on the rate of convergence to consensus, using results from the mixing theory of Markov chains
Calibrating Lévy Process from Observations Based on Neural Networks and Automatic Differentiation with Convergence Proofs

The L\'evy process has been widely applied to mathematical finance, quantum mechanics, peridynamics, and so on. However, calibrating the nonparametric multivariate distribution related to the L\'evy process from observations is a very challenging problem due to the lack of explicit distribution functions. In this paper, we propose a novel algorithm based on neural networks and automatic differentiation for solving this problem. We use neural networks to approximate the nonparametric part and discretize the characteristic exponents using accuracy numerical quadratures. Automatic differentiation is then applied to compute gradients and we minimize the mismatch between empirical and exact characteristic exponents using first-order optimization approaches. Another distinctive contribution of our work is that we made an effort to investigate the approximation ability of neural networks and the convergence behavior of algorithms. We derived the estimated number of neurons for a two-layer neural network. To achieve an accuracy of $\varepsilon$ with the input dimension $d$, it is sufficient to build $\mathcal{O}\left(\left(\frac{d}{\varepsilon} \right)^2\right)$ and $\mathcal{O}\left(\frac{d}{\varepsilon} \right)$ for the first and second layers. The numbers are polynomial in the input dimension compared to the exponential $\mathcal{O}\left(\varepsilon^{-d} \right)$ for one. We also give the convergence proof of the neural network concerning the training samples under mild assumptions and show that the RMSE decreases linearly in the number of training data in the consistency error dominancy region for the 2D problem. It is the first-ever convergence analysis for such an algorithm in literature to our best knowledge. Finally, we apply the algorithms to the stock markets and reveal some interesting patterns in the pairwise $\alpha$ index.
Pre-training with non-expert human demonstration for deep reinforcement learning

Deep reinforcement learning (deep RL) has achieved superior performance in complex sequential tasks by using deep neural networks as function approximators to learn directly from raw input images. However, learning directly from raw images is data inefficient. The agent must learn feature representation of complex states in addition to learning a policy. As a result, deep RL typically suffers from slow learning speeds and often requires a prohibitively large amount of training time and data to reach reasonable performance, making it inapplicable to real-world settings where data are expensive. In this work, we improve data efficiency in deep RL by addressing one of the two learning goals, feature learning. We leverage supervised learning to pre-train on a small set of non-expert human demonstrations and empirically evaluate our approach using the asynchronous advantage actor-critic algorithms in the Atari domain. Our results show significant improvements in learning speed, even when the provided demonstration is noisy and of low quality.
A possibility of Lorentz violation in the Higgs sector

In string theory, a scalar field often appears as a moduli of a geometrical configuration of D-branes in higher-dimensional space. In the low energy effective theory on D-branes, the distance between D-branes is translated into the energy scale of the gauge symmetry breaking. In this paper, we study a phenomenological consequence of a possibility that the Higgs field is such a moduli field and the D-brane configuration is stabilized by a stationary motion, in particular, revolution of D-branes on which we live. Then, due to the Coriolis force, Higgs mode is mixed with the angular fluctuation of branes and the Lorentz symmetry is violated in the dispersion relation of the Higgs boson. The Higgs boson mass measurements at LHC experiments give an upper bound GeV for the angular frequency of the revolution of D-branes.
Internal migration and education: A cross-national comparison

Migration the main process shaping patterns of human settlement within and between countries. It is widely acknowledged to be integral to the process of human development as it plays a significant role in enhancing educational outcomes. At regional and national levels, internal migration underpins the efficient functioning of the economy by bringing knowledge and skills to the locations where they are needed. It is the multi-dimensional nature of migration that underlines its significance in the process of human development. Human mobility extends in the spatial domain from local travel to international migration, and in the temporal dimension from short-term stays to permanent relocations. Classification and measurement of such phenomena is inevitably complex, which has severely hindered progress in comparative research, with very few large-scale cross-national comparisons of migration. The linkages between migration and education have been explored in a separate line of inquiry that has predominantly focused on country-specific analyses as to the ways in which migration affects educational outcomes and how educational attainment affects migration behaviour. A recurrent theme has been the educational selectivity of migrants, which in turn leads to an increase of human capital in some regions, primarily cities, at the expense of others. Questions have long been raised as to the links between education and migration in response to educational expansion, but have not yet been fully answered because of the absence, until recently, of adequate data for comparative analysis of migration. In this paper, we bring these two separate strands of research together to systematically explore links between internal migration and education across a global sample of 57 countries at various stages of development, using data drawn from the IPUMS database.
Scalar quasinormal modes of 
Kerr−AdS5

An analytic expression for the scalar quasinormal modes of generic, spinning Kerr-AdS5 black holes was previously proposed by the authors [ (2017) 094JHEPFG1029-847910.1007/JHEP08(2017)094], in terms of transcendental equations involving the Painleve VI (PVI) τ function. In this work, we carry out a numerical investigation of the modes for generic rotation parameters, comparing implementations of expansions for the PVI τ function in terms of both conformal blocks (Nekrasov functions) and Fredholm determinants. We compare the results with standard numerical methods for the subcase of Schwarzschild black holes. We then derive asymptotic formulas for the angular eigenvalues and the quasinormal modes in the small black hole limit for generic scalar mass and discuss, both numerically and analytically, the appearance of superradiant modes.
Slimmable Neural Networks

We present a simple and general method to train a single neural network executable at different widths (number of channels in a layer), permitting instant and adaptive accuracy-efficiency trade-offs at runtime. Instead of training individual networks with different width configurations, we train a shared network with switchable batch normalization. At runtime, the network can adjust its width on the fly according to on-device benchmarks and resource constraints, rather than downloading and offloading different models. Our trained networks, named slimmable neural networks, achieve similar (and in many cases better) ImageNet classification accuracy than individually trained models of MobileNet v1, MobileNet v2, ShuffleNet and ResNet-50 at different widths respectively. We also demonstrate better performance of slimmable models compared with individual ones across a wide range of applications including COCO bounding-box object detection, instance segmentation and person keypoint detection without tuning hyper-parameters. Lastly we visualize and discuss the learned features of slimmable networks. Code and models are available at: this https URL
Neural Diffusion Model for Microscopic Cascade Prediction

The prediction of information diffusion or cascade has attracted much attention over the last decade. Most cascade prediction works target on predicting cascade-level macroscopic properties such as the final size of a cascade. Existing microscopic cascade prediction models which focus on user-level modeling either make strong assumptions on how a user gets infected by a cascade or limit themselves to a specific scenario where "who infected whom" information is explicitly labeled. The strong assumptions oversimplify the complex diffusion mechanism and prevent these models from better fitting real-world cascade data. Also, the methods which focus on specific scenarios cannot be generalized to a general setting where the diffusion graph is unobserved. 
To overcome the drawbacks of previous works, we propose a Neural Diffusion Model (NDM) for general microscopic cascade prediction. NDM makes relaxed assumptions and employs deep learning techniques including attention mechanism and convolutional network for cascade modeling. Both advantages enable our model to go beyond the limitations of previous methods, better fit the diffusion data and generalize to unseen cascades. Experimental results on diffusion prediction task over four realistic cascade datasets show that our model can achieve a relative improvement up to 26% against the best performing baseline in terms of F1 score.
Lectures on 4d $N$=1 dynamics and related topics

This lecture series consists of mostly independent three parts: Part 1: a tour of basic 4d N=1 supersymmetric dynamics, covering the pure super Yang-Mills, the Seiberg duality for classical groups, the supersymmetric index on S^3, and the a-maximization. Part 2: a brief look at 2d N=(2,2) and N=(0,2) dynamics, covering the Landau-Ginzburg and Calabi-Yau models, the elliptic genera on T^2, and the triality of Gadde-Gukov-Putrov.  a review of basic properties of supersymmetries in various dimensions. 
Part of the content is based on an unpublished collaboration with F. Yagi and another with K. Kikuchi.