nils-herrmann/clean_scirepeval huggingface dataset:
Symmetric Weighted First-Order Model Counting

The FO Model Counting problem (FOMC) is the following: given a sentence Φ in FO and a number n, compute the number of models of Φ over a domain of size n; the Weighted variant (WFOMC) generalizes the problem by associating a weight to each tuple and defining the weight of a model to be the product of weights of its tuples. In this paper we study the complexity of the symmetric WFOMC, where all tuples of a given relation have the same weight. Our motivation comes from an important application, inference in Knowledge Bases with soft constraints, like Markov Logic Networks, but the problem is also of independent theoretical interest. We study both the data complexity, and the combined complexity of FOMC and WFOMC. For the data complexity we prove the existence of an FO3 formula for which FOMC is #P1-complete, and the existence of a Conjunctive Query for which WFOMC is #P1-complete. We also prove that all γ-acyclic queries have polynomial time data complexity. For the combined complexity, we prove that, for every fragment FOk, k ≥ 2, the combined complexity of FOMC (or WFOMC) is #P-complete.
Probabilistic Q-function distributions in fermionic phase-space

We obtain a positive probability distribution or Q-function for an arbitrary fermionic many-body system. This is different to previous Q-function proposals, which were either restricted to a subspace of the overall Hilbert space, or used Grassmann methods that do not give probabilities. The fermionic Q-function obtained here is constructed using normally ordered Gaussian operators, which include both non-interacting thermal density matrices and BCS states. We prove that the Q-function exists for any density matrix, is real and positive, and has moments that correspond to Fermi operator moments. It is defined on a finite symmetric phase-space equivalent to the space of real, antisymmetric matrices. This has the natural SO(2M) symmetry expected for Majorana fermion operators. We show that there is a physical interpretation of the Q-function: it is the relative probability for observing a given Gaussian density matrix. The distribution has a uniform probability across the space at infinite temperature, while for pure states it has a maximum value on the phase-space boundary. The advantage of probabilistic representations is that they can be used for computational sampling without a sign problem.
Role of Magnetic Field in Self-Oscillation of Nanomagnet Excited by Spin Torque

The critical current of the self-oscillation of a spin torque oscillator consisting of a perpendicularly magnetized free layer and an in-plane magnetized pinned layer was studied by solving the Landau-Lifshitz-Gilbert equation. We found that the critical current diverged at certain field directions, indicating that the self-oscillation does not occur at these directions. It was also found that the sign of the critical current changed depending on the applied field direction.
Bosons star at finite temperature

By using a simple thermodynamical method we confirm the finding of Chavanis and Harko that stable Bose-Einstein condensate stars can form. However, by using a thermodynamically consistent boson equation of state, we obtain a less massive Bose-Einstein condensate star compared to the one predicted by Chavanis and Harko. We also obtain that the maximum mass of a boson star is insensitive to the change of matter temperature. However, the mass of boson star with relatively large radius depends significantly on the temperature of the boson matter.
Iterative Subsampling in Solution Path Clustering of Noisy Big Data

We develop an iterative subsampling approach to improve the computational efficiency of our previous work on solution path clustering (SPC). The SPC method achieves clustering by concave regularization on the pairwise distances between cluster centers. This clustering method has the important capability to recognize noise and to provide a short path of clustering solutions; however, it is not sufficiently fast for big datasets. Thus, we propose a method that iterates between clustering a small subsample of the full data and sequentially assigning the other data points to attain orders of magnitude of computational savings. The new method preserves the ability to isolate noise, includes a solution selection mechanism that ultimately provides one clustering solution with an estimated number of clusters, and is shown to be able to extract small tight clusters from noisy data. The method's relatively minor losses in accuracy are demonstrated through simulation studies, and its ability to handle large datasets is illustrated through applications to gene expression datasets. An R package, SPClustering, for the SPC method with iterative subsampling is available at this http URL
LightLDA: Big Topic Models on Modest Computer Clusters

When building large-scale machine learning (ML) programs, such as massive topic models or deep neural networks with up to trillions of parameters and training examples, one usually assumes that such massive tasks can only be attempted with industrial-sized clusters with thousands of nodes, which are out of reach for most practitioners and academic researchers. We consider this challenge in the context of topic modeling on web-scale corpora, and show that with a modest cluster of as few as 8 machines, we can train a topic model with 1 million topics and a 1-million-word vocabulary (for a total of 1 trillion parameters), on a document collection with 200 billion tokens --- a scale not yet reported even with thousands of machines. Our major contributions include: 1) a new, highly-efficient O(1) Metropolis-Hastings sampling algorithm, whose running cost is (surprisingly) agnostic of model size, and empirically converges nearly an order of magnitude more quickly than current state-of-the-art Gibbs samplers; 2) a model-scheduling scheme to handle the big model challenge, where each worker machine schedules the fetch/use of sub-models as needed, resulting in a frugal use of limited memory capacity and network bandwidth; 3) a differential data-structure for model storage, which uses separate data structures for high- and low-frequency words to allow extremely large models to fit in memory, while maintaining high inference speed. These contributions are built on top of the Petuum open-source distributed ML framework, and we provide experimental evidence showing how this development puts massive data and models within reach on a small cluster, while still enjoying proportional time cost reductions with increasing cluster size.
End-to-end Continuous Speech Recognition using Attention-based Recurrent NN: First Results

We replace the Hidden Markov Model (HMM) which is traditionally used in in continuous speech recognition with a bi-directional recurrent neural network encoder coupled to a recurrent neural network decoder that directly emits a stream of phonemes. The alignment between the input and output sequences is established using an attention mechanism: the decoder emits each symbol based on a context created with a subset of input symbols elected by the attention mechanism. We report initial results demonstrating that this new approach achieves phoneme error rates that are comparable to the state-of-the-art HMM-based decoders, on the TIMIT dataset.
Spanning trees of the World Trade Web: real-world data and the gravity model of trade

In this paper, we investigate the statistical features of the weighted international-trade network. By finding the maximum weight spanning trees for this network we make the extraction of the truly relevant connections forming the network's backbone. We discuss the role of large-sized countries (strongest economies) in the tree. Finally, we compare the topological properties of this backbone to the maximum weight spanning trees obtained from the gravity model of trade. We show that the model correctly reproduces the backbone of the real-world economy.
Metanetworks of artificially evolved regulatory networks

We study metanetworks arising in genotype and phenotype spaces, in the context of a model population of Boolean graphs evolved under selection for short dynamical attractors. We define the adjacency matrix of a graph as its genotype, which gets mutated in the course of evolution, while its phenotype is its set of dynamical attractors. Metanetworks in the genotype and phenotype spaces are formed, respectively, by genetic proximity and by phenotypic similarity, the latter weighted by the sizes of the basins of attraction of the shared attractors. We find that evolved populations of Boolean graphs form tree-like giant clusters in genotype space, while random populations of Boolean graphs are typically so far removed from each other genetically that they cannot form a metanetwork. In phenotype space, the metanetworks of evolved populations are super robust both under the elimination of weak connections and random removal of nodes.
Stess-testing the system: Financial shock contagion in the realm of uncertainty

This work proposes an augmented variant of DebtRank with uncertainty intervals as a method to investigate and assess systemic risk in financial networks, in a context of incomplete data. The algorithm is tested against a default contagion algorithm on three ensembles of networks with increasing density, estimated from real-world banking data related to the largest 227 EU15 financial institutions indexed in a stock market. Results suggest that DebtRank is capable of capturing increasing rates of systemic risk in a more sensitive and continuous way, thereby acting as an early-warning signal. The paper proposes three policy instruments based on this approach: the monitoring of systemic risk over time by applying the augmented DebtRank on time snapshots of interbank networks, a stress-testing framework able to test the systemic importance of financial institutions on different shock scenarios, and the evaluation of distribution of systemic losses in currency value.
How Many Communities Are There?

Stochastic blockmodels and variants thereof are among the most widely used approaches to community detection for social networks and relational data. A stochastic blockmodel partitions the nodes of a network into disjoint sets, called communities. The approach is inherently related to clustering with mixture models; and raises a similar model selection problem for the number of communities. The Bayesian information criterion (BIC) is a popular solution, however, for stochastic blockmodels, the conditional independence assumption given the communities of the endpoints among different edges is usually violated in practice. In this regard, we propose composite likelihood BIC (CL-BIC) to select the number of communities, and we show it is robust against possible misspecifications in the underlying stochastic blockmodel assumptions. We derive the requisite methodology and illustrate the approach using both simulated and real data.
Applying Conceptual Blending to Model Coordinated Use of Multiple Ontological Metaphors

Energy is an abstract science concept, so the ways that we think and talk about energy rely heavily on ontological metaphors: metaphors for what kind of thing energy is. Two commonly used ontological metaphors for energy are energy as a substance and energy as a vertical location. Our previous work has demonstrated that students and experts can productively use both the substance and location ontologies for energy. In this paper, we use Fauconnier and Turner's conceptual blending framework to demonstrate that experts and novices can successfully blend the substance and location ontologies into a coherent mental model in order to reason about energy. Our data come from classroom recordings of a physics professor teaching a physics course for the life sciences, and from an interview with an undergraduate student in that course. We analyze these data using predicate analysis and gesture analysis, looking at verbal utterances, gestures, and the interaction between them. This analysis yields evidence that the speakers are blending the substance and location ontologies into a single blended mental space.
A LEGO Watt balance: An apparatus to determine a mass based on the new SI

A global effort to redefine our International System of Units (SI) is underway, and the change to the new system is expected to occur in 2018. Within the newly redefined SI, the present base units will still exist but be derived from fixed numerical values of seven reference constants. In particular, the unit of mass (the kilogram) will be realized through a fixed value of the Planck constant h. A so-called watt balance, for example, can then be used to realize the kilogram unit of mass within a few parts in 108. Such a balance has been designed and constructed at the National Institute of Standards and Technology. For educational outreach and to demonstrate the principle, we have constructed a LEGO tabletop watt balance capable of measuring a gram-level masses to 1% relative uncertainty. This article presents the design, construction, and performance of the LEGO watt balance and its ability to determine h.
Nonparametric modal regression

Modal regression estimates the local modes of the distribution of $Y$ given $X=x$, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of the joint distribution of $Y$ and $X$. We derive asymptotic error bounds for this method, and propose techniques for constructing confidence sets and prediction sets. The latter is used to select the smoothing bandwidth of the underlying KDE. The idea behind modal regression is connected to many others, such as mixture regression and density ridge estimation, and we discuss these ties as well.
Stochastic Covariance Compression

Covariance matrices are an effective way to capture global spread across local interest points in images. Often, these image descriptors are more compact, robust and informative than, for example, bags of visual words. However, they are symmetric and positive definite (SPD) and therefore live on a non-Euclidean Riemannian manifold, which gives rise to non-Euclidean metrics. These are slow to compute and can make the use of covariance features prohibitive in many settings, in particular k-nearest neighbors (kNN) classification. In this paper we present Stochastic Covariance Compression, an algorithm that compresses a data set of SPD matrices to a much smaller set with similar kNN characteristics. We show that we can reduce the data sets to 1/6 and in some cases even up to 1/50 of their original size, while approximately matching the test error of full kNN classification. In fact, because the compressed set is learned to perform well on kNN tasks, it sometimes even outperforms the original data set, while requiring only a fraction of the space and drastically reduced test-time computation.
Improved methods for simulating nearly extremal binary black holes

Astrophysical black holes could be nearly extremal (that is, rotating nearly as fast as possible); therefore, nearly extremal black holes could be among the binaries that current and future gravitational-wave observatories will detect. Predicting the gravitational waves emitted by merging black holes requires numerical-relativity simulations, but these simulations are especially challenging when one or both holes have mass m and spin S exceeding the Bowen–York limit of S / m 2 = 0.93 ?> . We present improved methods that enable us to simulate merging, nearly extremal black holes (i.e., black holes with S / m 2 > 0.93 ?> ) more robustly and more efficiently. We use these methods to simulate an unequal-mass, precessing binary black hole (BBH) coalescence, where the larger black hole has S / m 2 = 0.99 ?> . We also use these methods to simulate a non-precessing BBH coalescence, where both black holes have S / m 2 = 0.994 ?> , nearly reaching the Novikov–Thorne upper bound for holes spun up by thin accretion disks. We demonstrate numerical convergence and estimate the numerical errors of the waveforms; we compare numerical waveforms from our simulations with post-Newtonian and effective-one-body waveforms; we compare the evolution of the black hole masses and spins with analytic predictions; and we explore the effect of increasing spin magnitude on the orbital dynamics (the so-called ‘orbital hangup’ effect).
Quantum Entanglement of Matter and Geometry in Large Systems

Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard quantum field theory with general relativity on macroscopic scales can be reconciled by nonstandard, nonlocal entanglement of field states with quantum states of geometry. Wave functions of particle world lines are used to estimate scales of geometrical entanglement and emergent locality. Simple models of entanglement predict coherent fluctuations in position of massive bodies, of Planck scale origin, measurable on a laboratory scale, and may account for the fact that the information density of long lived position states in Standard Model fields, which is determined by the strong interactions, is the same as that determined holographically by the cosmological constant.
KNOWLEDGE, JUSTIFICATION, AND ADEQUATE REASONS

Is knowledge definable as justified true belief (“JTB”)? We argue that one can legitimately answer positively or negatively, depending on whether or not one’s true belief is justified by what we call adequate reasons. To facilitate our argument we introduce a simple propositional logic of reason-based belief, and give an axiomatic characterization of the notion of adequacy for reasons. We show that this logic is sufficiently flexible to accommodate various useful features, including quantification over reasons. We use our framework to contrast two notions of JTB: one internalist, the other externalist. We argue that Gettier cases essentially challenge the internalist notion but not the externalist one. Our approach commits us to a form of infallibilism about knowledge, but it also leaves us with a puzzle, namely whether knowledge involves the possession of only adequate reasons, or leaves room for some inadequate reasons. We favor the latter position, which reflects a milder and more realistic version of infallibilism.
Statistical Physics of Adaptation

All living things exhibit adaptations that enable them to survive and reproduce in the natural environment that they inhabit. From a biological standpoint, it has long been understood that adaptation comes from natural selection, whereby maladapted individuals do not pass their traits effectively to future generations. However, we may also consider the phenomenon of adaptation from the standpoint of physics, and ask whether it is possible to delineate what the difference is in terms of physical properties between something that is well-adapted to its surrounding environment, and something that is not. In this work, we undertake to address this question from a theoretical standpoint. Building on past fundamental results in far-from-equilibrium statistical mechanics, we demonstrate a generalization of the Helmholtz free energy for the finite-time stochastic evolution of driven Newtonian matter. By analyzing this expression term by term, we are able to argue for a general tendency in driven many-particle systems towards self-organization into states formed through exceptionally reliable absorption and dissipation of work energy from the surrounding environment. Subsequently, we illustrate the mechanism of this general tendency towards physical adaptation by analyzing the process of random hopping in driven energy landscapes.
Document clustering using graph based document representation with constraints

Document clustering is an unsupervised approach in which a large collection of documents (corpus) is subdivided into smaller, meaningful, identifiable, and verifiable sub-groups (clusters). Meaningful representation of documents and implicitly identifying the patterns, on which this separation is performed, is the challenging part of document clustering. We have proposed a document clustering technique using graph based document representation with constraints. A graph data structure can easily capture the non-linear relationships of nodes, document contains various feature terms that can be non-linearly connected, and hence a graph can easily represents this information. Constrains, are explicit conditions for document clustering where background knowledge is used to set the direction for Linking or Not-Linking a set of documents for a target clusters, thus guiding the clustering process. We deemed clustering is an ill-define problem, there can be many clustering results. Background knowledge can be used to drive the clustering algorithm in the right direction. We have proposed three different types of constraints, Instance level, corpus level and cluster level constraints. A new algorithm Constrained HAC is also proposed which will incorporate Instance level constraints as prior knowledge; it will guide the clustering process leading to better results. Extensive set of experiments have been performed on both synthetic and standard document clustering datasets .Results are then compared on standard clustering measures like: purity, entropy and F-measure. These clearly establish that our proposed approach leads to improvement in cluster quality.
Lefschetz-thimble techniques for path integral of zero-dimensional $O(n)$ sigma models

Zero-dimensional $O(n)$-symmetric sigma models are studied by using Picard--Lefschetz integration method in the presence of small symmetry-breaking perturbations. Due to approximate symmetry, downward flows turn out to show significant structures: They slowly travel along the set of pseudo classical points, and branch into other directions so as to span middle-dimensional integration cycles. We propose an efficient way to find such slow motions for computing Lefschetz thimbles. In the limit of symmetry restoration, we figure out that only special combinations of Lefschetz thimbles can survive as convergent integration cycles: Other integrations become divergent due to non-compactness of the complexified group of symmetry. We also compute downward flows of $O(2)$-symmetric fermionic systems, and confirm that all of these properties are true also with fermions.
Taming Reverse Mathematics zoo

Mathematics is a program in the foundations of mathematics. Its results give rise to an elegant classification of theorems of ordinary mathematics based on computability. In particular, the majority of theorems fall into only five categories of which the associated logical systems are dubbed `the Big Five'. Recently, a lot of effort has been directed towards finding exceptional principles, i.e. which fall outside the Big Five categories. The so-called Reverse Mathematics zoo is a collection of such exceptional principles (and their relations). In this paper, we show that uniform versions of the principles from this zoo do fall in line with the Big Five categorisation, i.e. the zoo seems to disappear at the uniform level. In particular, we shall formulate a general template which establishes equivalence between uniform zoo-principles and arithmetical comprehension, the third Big Five category.