nils-herrmann/clean_scirepeval huggingface dataset:
Mechanization of Separation in Generic Extensions

We mechanize, in the proof assistant Isabelle, a proof of the axiom-scheme of Separation in generic extensions of models of set theory by using the fundamental theorems of forcing. We also formalize the satisfaction of the axioms of Extensionality, Foundation, Union, and Powerset. The axiom of Infinity is likewise treated, under additional assumptions on the ground model. In order to achieve these goals, we extended Paulson's library on constructibility with renaming of variables for internalized formulas, improved results on definitions by recursion on well-founded relations, and sharpened hypotheses in his development of relativization and absoluteness.
Compactification of the space of Hamiltonian stationary Lagrangian submanifolds with bounded total extrinsic curvature and volume

For a sequence of immersed connected closed Hamiltonian stationary Lagrangian submaniolds in $\mathbb{C}^{n}$ with uniform bounds on their volumes and the total extrinsic curvatures, we prove that a subsequence converges either to a point or to a Hamiltonian stationary Lagrangian $n$-varifold locally uniformly in $C^{k}$ for any nonnegative integer $k$ away from a finite set of points, and the limit is Hamiltonian stationary in ${\mathbb{C}}^{n}$. We also obtain a theorem on extending Hamiltonian stationary Lagrangian submanifolds $L$ across a compact set $N$ of Hausdorff codimension at least 2 that is locally noncollapsing in volumes matching its Hausdorff dimension, provided the mean curvature of $L$ is in $L^{n}$ and a condition on local volume of $L$ near $N$ is satisfied.
Accelerated Flow for Probability Distributions

This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in (wibisono, et. al. 2016) from vector valued variables to probability distributions. The variational problem is modeled as a mean-field optimal control problem. The maximum principle of optimal control theory is used to derive Hamilton's equations for the optimal gradient flow. The Hamilton's equation are shown to achieve the accelerated form of density transport from any initial probability distribution to a target probability distribution. A quantitative estimate on the asymptotic convergence rate is provided based on a Lyapunov function construction, when the objective functional is displacement convex. Two numerical approximations are presented to implement the Hamilton's equations as a system of $N$ interacting particles. The continuous limit of the Nesterov's algorithm is shown to be a special case with $N=1$. The algorithm is illustrated with numerical examples.
Laboratory Photochemistry of Covalently Bonded Fluorene Clusters: Observation of an Interesting PAH Bowl-forming Mechanism

The fullerene C60, one of the largest molecules identified in the interstellar medium (ISM), has been proposed to form top-down through the photochemical processing of large (more than 60 C atoms) polycyclic aromatic hydrocarbon (PAH) molecules. In this article, we focus on the opposite process, investigating the possibility that fullerenes form from small PAHs, in which bowl-forming plays a central role. We combine laboratory experiments and quantum chemical calculations to study the formation of larger PAHs from charged fluorene clusters. The experiments show that with visible laser irradiation, the fluorene dimer cation—[C13H9−C13H9]+—and the fluorene trimer cation—[C13H9−C13H8−C13H9]+—undergo photodehydrogenation and photoisomerization, resulting in bowl-structured aromatic cluster ions, C26H12+ and C39H20+, respectively. To study the details of this chemical process, we employ quantum chemistry that allows us to determine the structures of the newly formed cluster ions, to calculate the dissociation energies for hydrogen loss, and to derive the underlying reaction pathways. These results demonstrate that smaller PAH clusters (with less than 60 C atoms) can convert to larger bowled geometries that might act as building blocks for fullerenes, because the bowl-forming mechanism greatly facilitates the conversion from dehydrogenated PAHs to cages. Moreover, the bowl-forming induces a permanent dipole moment that—in principle—allows one to search for such species using radio astronomy.
A New Tensioning Method using Deep Reinforcement Learning for Surgical Pattern Cutting

Surgeons normally need surgical scissors and tissue grippers to cut through a deformable surgical tissue. The cutting accuracy depends on the skills to manipulate these two tools. Such skills are part of basic surgical skills training as in the Fundamentals of Laparoscopic Surgery. The gripper is used to pinch a point on the surgical sheet and pull the tissue to a certain direction to maintain the tension while the scissors cut through a trajectory. As the surgical materials are deformable, it requires a comprehensive tensioning policy to yield appropriate tensioning direction at each step of the cutting process. Automating a tensioning policy for a given cutting trajectory will support not only the human surgeons but also the surgical robots to improve the cutting accuracy and reliability. This paper presents a multiple pinch point approach to modelling an autonomous tensioning planner based on a deep reinforcement learning algorithm. Experiments on a simulator show that the proposed method is superior to existing methods in terms of both performance and robustness.
Phase transitions and gravitational wave tests of pseudo-Goldstone dark matter in the softly broken 
U(1)
 scalar singlet model

We study phase transitions in a softly broken $U(1)$ complex singlet scalar model in which the dark matter is the pseudo-scalar part of a singlet whose direct detection coupling to matter is strongly suppressed. Our aim is to find ways to test this model with the stochastic gravitational wave background from the scalar phase transition. We find that the phase transition which induces vacuum expectation values for both the Higgs boson and the singlet - necessary to provide a realistic dark matter candidate - is always of the second order. If the stochastic gravitational wave background characteristic to a first order phase transition will be discovered by interferometers, the soft breaking of $U(1)$ cannot be the explanation to the suppressed dark matter-baryon coupling, providing a conclusive negative test for this class of singlet models.
Global spacetime structure of compactified inflationary universe

We investigate the global spacetime structure of torus de Sitter universe, which is exact de Sitter space with torus identification based on the flat chart. We show that past incomplete null geodesics in torus de Sitter universe are locally extendible. Then we give an extension of torus de Sitter universe so that at least one of the past incomplete null geodesics in the original spacetime becomes complete. However, we find that extended torus de Sitter universe has two ill behaviors. The first one is a closed causal curve. The second one is so called quasi regular singularity, which means that there is no global, consistent extension of spacetime where all curves become complete, nevertheless each curve is locally extensible.
Developing a reasoning inventory for measuring physics quantitative literacy

In an effort to improve the quality of citizen engagement in workplace, politics, and other domains in which quantitative reasoning plays an important role, Quantitative Literacy (QL) has become the focus of considerable research and development efforts in mathematics education. QL is characterized by sophisticated reasoning with elementary mathematics. In this project, we extend the notions of QL to include the physics domain and call it Physics Quantitative Literacy (PQL). We report on early stage development from a collaboration that focuses on reasoning inventory design and data analysis methodology for measuring the development of PQL across the introductory physics sequence. We have piloted a prototype assessment designed to measure students' PQL in introductory physics: Physics Inventory of Quantitative Literacy (PIQL). This prototype PIQL focuses on two components of PQL: proportional reasoning, and reasoning with negative quantities. We present preliminary results from approximately 1,000 undergraduate and 20 graduate students.
RetinaMask: Learning to predict masks improves state-of-the-art single-shot detection for free

Recently two-stage detectors have surged ahead of single-shot detectors in the accuracy-vs-speed trade-off. Nevertheless single-shot detectors are immensely popular in embedded vision applications. This paper brings single-shot detectors up to the same level as current two-stage techniques. We do this by improving training for the state-of-the-art single-shot detector, RetinaNet, in three ways: integrating instance mask prediction for the first time, making the loss function adaptive and more stable, and including additional hard examples in training. We call the resulting augmented network RetinaMask. The detection component of RetinaMask has the same computational cost as the original RetinaNet, but is more accurate. COCO test-dev results are up to 41.4 mAP for RetinaMask-101 vs 39.1mAP for RetinaNet-101, while the runtime is the same during evaluation. Adding Group Normalization increases the performance of RetinaMask-101 to 41.7 mAP. Code is at:this https URL
When does privatization spur entrepreneurial performance? The moderating effect of institutional quality in an emerging market

We explore how institutional quality moderates the effectiveness of privatization on entrepreneurs sales performance. To do this, we blend agency theory and entrepreneurial cognition theory with insights from institutional economics to develop a model of emerging market venture performance. Using data from the World Banks Enterprise Survey of entrepreneurs in China, our results suggest that private-owned enterprises (POEs) outperform state-owned enterprises (SOEs) but only in environments with high-quality market institutions. In environments with low-quality market institutions, SOEs outperform POEs. These findings suggest that the effectiveness of privatization on entrepreneurial performance is context-specific, which reveals more nuance than previously has been attributed.
Measurements of inclusive and differential fiducial cross-sections of $t\bar{t}\gamma$ production in leptonic final states at $\sqrt{s}$ = 13 TeV

The latest results of the ATLAS experiment for the production of a top-quark pair in association with a photon using proton-proton collision data from the LHC at a centre-of-mass energy of 13 TeV are summarised here. This includes inclusive and differential cross-sections measurements performed in single-lepton and dilepton final states in a fiducial volume corresponding to the experimental acceptance.
Unsupervised Moving Object Detection via Contextual Information Separation

We propose an adversarial contextual model for detecting moving objects in images. A deep neural network is trained to predict the optical flow in a region using information from everywhere else but that region (context), while another network attempts to make such context as uninformative as possible. The result is a model where hypotheses naturally compete with no need for explicit regularization or hyper-parameter tuning. Although our method requires no supervision whatsoever, it outperforms several methods that are pre-trained on large annotated datasets. Our model can be thought of as a generalization of classical variational generative region-based segmentation, but in a way that avoids explicit regularization or solution of partial differential equations at run-time.
Continuous Regular Functions

Following Chaudhuri, Sankaranarayanan, and Vardi, we say that a function $f:[0,1] \to [ if there is a Buchi automaton that accepts precisely the set of base $r \in \mathbb{N}$ representations of elements of the graph of $f$. We show that a continuous $r$-regular function $f$ is locally affine away from a nowhere dense, Lebesgue null, subset of $[0,1]$. As a corollary we establish that every differentiable $r$-regular function is affine. It follows that checking whether an $r$-regular function is differentiable is in $\operatorname{PSPACE}$. Our proofs rely crucially on connections between automata theory and metric geometry developed by Charlier, Leroy, and Rigo.
On determinantal equations for curves and Frobenius split hypersurfaces

I consider the problem of existence of intrinsic determinantal equations for plane projective curves and hypersurfaces in projective space and prove that in many cases of interest there exist intrinsic determinantal equations. In particular I prove (1) in characteristic two any ordinary, plane projective curve of genus at least one is given by an intrinsic determinantal equation (2) in characteristic three any plane projective curve is an intrinsic Pfaffian (3) in any positive characteristic any plane projective curve is set theoretically the determinant of an intrinsic matrix (4) in any positive characteristic, any Frobenius split hypersurface in ${\bf P}^n$ is given by set theoretically as the determinant of an intrinsic matrix with homogeneous entries of degree between $1$ and $n-1$. In particular this implies that any smooth, Fano hypersurface is set theoretically given by an intrinsic determinantal equation and the same is also true for any Frobenius split Calabi-Yau hypersurface.
Time reversal symmetry in cosmology and the quantum creation of universes

The classical evolution of the universe can be seen as a parametrised worldline of the minisuperspace, with the time variable $t$ being the parameter that parametrises the worldline. The time reversal symmetry of the classical action implies then that for any positive oriented solution it must be a symmetric negative oriented one that, in terms of the same time variable, represent an expanding and a contracting universe, respectively. However, the choice of the time variable induced by the correct value of the Schrodinger equation in the two universes makes that their physical time variables are reversely related. Thus, the two universes turn out to be expanding universes from the point of view of their internal inhabitants, who identify matter with the particles that move in their spacetimes and antimatter with the particles that move in the symmetric universe. This might explain two of the main problems in cosmology: the time asymmetry observed in the context of a single universe and the matter-antimatter asymmetry of the primordial universe.
Effect of scalar boson on fermionic dark stars

The role of scalar boson exchange as a mediator of the fermionic dark particle interaction and the mass of dark particle on the bulk properties of fermionic dark stars including their moment of inertia and tidal deformability are studied. We have found that the role of the attractive nature of the scalar boson exchange and the fermionic dark particle mass can control the stiffness of the fermionic dark star equation-of-state. By increasing the strength of scalar boson coupling, the fermionic dark star becomes more compact. As a consequence, if scalar boson exchange contribution is included the compactness of a dark star can exceed  see text] = 0.22. We also compare the fermionic dark stars moment of inertia and tidal deformability to those of neutron stars (with and without hyperons in neutron star core) predicted by relativistic mean field model. It is evident that the properties of both types of stars are quite different. We also have found that the universal I-Love relation in fermionic dark stars is not affected by scalar boson exchange contribution and the fermionic dark particle mass. Possible observations of fermionic dark stars are also discussed.
Detecting Overfitting of Deep Generative Networks via Latent Recovery

State of the art deep generative networks have achieved such realism that they can be suspected of memorizing training images. It is why it is not uncommon to include visualizations of training set nearest neighbors, to suggest generated images are not simply memorized. We argue this is not sufficient and motivates studying overfitting of deep generators with more scrutiny. We address this question by i) showing how simple losses are highly effective at reconstructing images for deep generators ii) analyzing the statistics of reconstruction errors for training versus validation images. Using this methodology, we show that pure GAN models appear to generalize well, in contrast with those using hybrid adversarial losses, which are amongst the most widely applied generative methods. We also show that standard GAN evaluation metrics fail to capture memorization for some deep generators. Finally, we note the ramifications of memorization on data privacy. Considering the already widespread application of generative networks, we provide a step in the right direction towards the important yet incomplete picture of generative overfitting.
Characterizing and Evaluating Adversarial Examples for Offline Handwritten Signature Verification

The phenomenon of adversarial examples is attracting increasing interest from the machine learning community, due to its significant impact on the security of machine learning systems. Adversarial examples are similar (from a perceptual notion of similarity) to samples from the data distribution, that “fool” a machine learning classifier. For computer vision applications, these are images with carefully crafted but almost imperceptible changes, which are misclassified. In this paper, we characterize this phenomenon under an existing taxonomy of threats to biometric systems, in particular identifying new attacks for offline handwritten signature verification systems. We conducted an extensive set of experiments on four widely used datasets: MCYT-75, CEDAR, GPDS-160, and the Brazilian PUC-PR, considering both a CNN-based system and a system using a handcrafted feature extractor. We found that attacks that aim to get a genuine signature rejected are easy to generate, even in a limited knowledge scenario, where the attacker does not have access to the trained classifier nor the signatures used for training. Attacks that get a forgery to be accepted are harder to produce, and often require a higher level of noise—in most cases, no longer “imperceptible” as previous findings in object recognition. We also evaluated the impact of two countermeasures on the success rate of the attacks and the amount of noise required for generating successful attacks.
Mean Estimation from One-Bit Measurements

We consider the problem of estimating the mean of a symmetric log-concave distribution under the following constraint: only a single bit per sample from this distribution is available to the estimator. We study the mean squared error (MSE) risk in this estimation as a function of the number of samples, and hence the number of bits, from this distribution. Under an adaptive setting in which each bit is a function of the current sample and the previously observed bits, we show that the optimal relative efficiency compared to the sample mean is the efficiency of the median. For example, in estimating the mean of a normal distribution, a constraint of one bit per sample incurs a penalty of $\pi/2$ in sample size compared to the unconstrained case. We also consider a distributed setting where each one-bit message is only a function of a single sample. We derive lower bounds on the MSE in this setting, and show that the optimal efficiency can only be attained at a finite number of points in the parameter space. Finally, we analyze a distributed setting where the bits are obtained by comparing each sample against a prescribed threshold. Consequently, we consider the threshold density that minimizes the maximal MSE. Our results indicate that estimating the mean from one-bit measurements is equivalent to estimating the sample median from these measurements. In the adaptive case, this estimate can be done with vanishing error for any point in the parameter space. In the distributed case, this estimate can be done with vanishing error only for a finite number of possible values for the unknown mean.
Deep Learning for Anomaly Detection: A Survey

Anomaly detection is an important problem that has been well-studied within diverse research areas and application domains. The aim of this survey is two-fold, firstly we present a structured and comprehensive overview of research methods in deep learning-based anomaly detection. Furthermore, we review the adoption of these methods for anomaly across various application domains and assess their effectiveness. We have grouped state-of-the-art deep anomaly detection research techniques into different categories based on the underlying assumptions and approach adopted. Within each category, we outline the basic anomaly detection technique, along with its variants and present key assumptions, to differentiate between normal and anomalous behavior. Besides, for each category, we also present the advantages and limitations and discuss the computational complexity of the techniques in real application domains. Finally, we outline open issues in research and challenges faced while adopting deep anomaly detection techniques for real-world problems.
Towards platform-independent specification and verification of the standard trigonometry functions

Research project "Platform-independent approach to formal specification and verification of standard mathematical functions" is aimed onto a development of an incremental combined approach to the specification and verification of the standard mathematical functions like sqrt, cos, sin, etc. Platform-independence means that we attempt to design a relatively simple axiomatization of the computer arithmetic in terms of real, rational, and integer arithmetic (i.e. the fields R and Q of real and rational numbers, the ring Z of integers) but don't specify neither base of the computer arithmetic, nor a format of numbers' representation. Incrementality means that we start with the most straightforward specification of the simplest easy to verify algorithm in real numbers and finish with a realistic specification and a verification of an algorithm in computer arithmetic. We call our approach combined because we start with a manual (pen-and-paper) verification of some selected algorithm in real numbers, then use these algorithm and verification as a draft and proof-outlines for the algorithm in computer arithmetic and its manual verification, and finish with a computer-aided validation of our manual proofs with some proof-assistant system (to avoid appeals to "obviousness" that are very common in human-carried proofs). In the paper we present first steps towards a platform-independent incremental combined approach to specification and verification of the standard functions cos and sin that implement mathematical trigonometric functions cos and sin.
Preventing Posterior Collapse with delta-VAEs

Due to the phenomenon of "posterior collapse," current latent variable generative models pose a challenging design choice that either weakens the capacity of the decoder or requires augmenting the objective so it does not only maximize the likelihood of the data. In this paper, we propose an alternative that utilizes the most powerful generative models as decoders, whilst optimising the variational lower bound all while ensuring that the latent variables preserve and encode useful information. Our proposed $\delta$-VAEs achieve this by constraining the variational family for the posterior to have a minimum distance to the prior. For sequential latent variable models, our approach resembles the classic representation learning approach of slow feature analysis. We demonstrate the efficacy of our approach at modeling text on LM1B and modeling images: learning representations, improving sample quality, and achieving state of the art log-likelihood on CIFAR-10 and ImageNet $32\times 32$.