nils-herrmann/clean_scirepeval huggingface dataset:
Two-Dimensional Collisions and Conservation of Momentum

Analysis of collisions is standardly included in the introductory physics course. In one dimension (1D), there do not seem to be any unusual issues: Typically, the initial velocities of the two colliding objects are specified, and the problem is to find the final velocities. In 1D there are therefore two unknown variables. One can write the equation for conservation of momentum, and either the equation for conservation of energy for the perfectly elastic case, or the expression for the coefficient of restitution (COR) otherwise. Thus, one has two equations for two unknowns, and one may solve the problem fully. An issue arises, however, in two-dimensional (2D) collisions: There are four unknown variables (two components of the final velocity of each object), but now there appear to be only three equations: two components of the equation of conservation of momentum, and the energy condition. The problem may appear therefore to be underdetermined. If this problem were in principle an underdetermined one, one would fail in predicting the outcome of the collision experiment. We describe how one may assign students an appropriate lab exercise and problems for an interesting class of 2D collisions for which one can determine uniquely the outcome of the collision.Analysis of collisions is standardly included in the introductory physics course. In one dimension (1D), there do not seem to be any unusual issues: Typically, the initial velocities of the two colliding objects are specified, and the problem is to find the final velocities. In 1D there are therefore two unknown variables. One can write the equation for conservation of momentum, and either the equation for conservation of energy for the perfectly elastic case, or the expression for the coefficient of restitution (COR) otherwise. Thus, one has two equations for two unknowns, and one may solve the problem fully. An issue arises, however, in two-dimensional (2D) collisions: There are four unknown variables (two components of the final velocity of each object), but now there appear to be only three equations: two components of the equation of conservation of momentum, and the energy condition. The problem may a...
A Probabilistic Graph Model for Trust Opinion Estimation in Online Social Networks

Trust assessment plays a key role in many online applications, such as online money lending, product reviewing and active friending. Trust models usually employ a group of parameters to represent the trust relation between a trustor-trustee pair. These parameters are originated from the trustor's bias and opinion on the trustee. Naturally, these parameters can be regarded as a vector. To address this problem, we propose a framework to accurately convert the single values to the parameters needed by 3VSL. The framework firstly employs a probabilistic graph model (PGM) to derive the trustor's opinion and bias to his rating on the trustee.
Inducing Constituency Trees through Neural Machine Translation

Latent tree learning(LTL) methods learn to parse sentences using only indirect supervision from a downstream task. Recent advances in latent tree learning have made it possible to recover moderately high quality tree structures by training with language modeling or auto-encoding objectives. In this work, we explore the hypothesis that decoding in machine translation, as a conditional language modeling task, will produce better tree structures since it offers a similar training signal as language modeling, but with more semantic signal. We adapt two existing latent-tree language models--PRPN andON-LSTM--for use in translation. We find that they indeed recover trees that are better in F1 score than those seen in language modeling on WSJ test set, while maintaining strong translation quality. We observe that translation is a better objective than language modeling for inducing trees, marking the first success at latent tree learning using a machine translation objective. Additionally, our findings suggest that, although translation provides better signal for inducing trees than language modeling, translation models can perform well without exploiting the latent tree structure.
On the Essential Spectrum of Schr\"odinger Operators on Graphs

This work studies geometrical characterizations of the essential spectrum $\sigma_{\text ess}$ of Schrodinger operators on graphs. Especially we focus on generalizing characterizations which are given in terms of the concept of right limits. Intuitively the set of right limits of a Schrodinger operator $H$ on $\ell^2(\mathbb{N})$ includes the limit operators which are obtained by a sequence of left-shifts (moving away to infinity) of $H$. One characterization, which is known for such operators is that $\sigma_{\text ess}(H)$ is equal to the union over the spectra of right limits of $H$. Additionally, the essential spectrum equals to the union over the sets of "eigenvalues" corresponding to bounded eigenfunctions of the right limits of $H$. The first characterization above (and its generalization to $\mathbb{Z}^n$) is essentially due to a work by Last-Simon from 2006. In this work we study the possibility of generalizing these characterizations of $\sigma_{ess}(H)$ to Schrodinger operators on graphs. The work is composed of the following chapters: 
Chapter 1. An overview, including the setting and the proposed generalization of the concept of right limits to general graphs. 
Chapter 2. On extending the original Last-Simon argument for the proof of the first characterization to graphs. We give both a partial positive result and an example of a graph on which this characterization fails. 
Chapter 3. A Focus on characterizing the essential spectrum on trees. 
Chapter 4. A study of the possible generalization of the second characterization to graphs, from which we also get the first characterization on a general family of graphs.
Algorithms for certain classes of Tamil Spelling correction

Tamil language has an agglutinative, diglossic, alpha-syllabary structure which provides a significant combinatorial explosion of morphological forms all of which are effectively used in Tamil prose, poetry from antiquity to the modern age in an unbroken chain of continuity. However, for the language understanding, spelling correction purposes some of these present challenges as out-of-dictionary words. In this paper the authors propose algorithmic techniques to handle specific problems of conjoined-words (out-of-dictionary) (transliteration)[thendRalkattRu] = [thendRal]+[kattRu] when parts are alone present in word-list in efficient way. Morphological structure of Tamil makes it necessary to depend on synthesis-analysis approach and dictionary lists will never be sufficient to truly capture the language. In this paper we have attempted to make a summary of various known algorithms for specific classes of Tamil spelling errors. We believe this collection of suggestions to improve future spelling checkers. We also note do not cover many important techniques like affix removal and other such techniques of key importance in rule-based spell checkers.
Towards Explainability for a Civilian UAV Fleet Management using an Agent-based Approach

This paper presents an initial design concept and specification of a civilian Unmanned Aerial Vehicle (UAV) management simulation system that focuses on explainability for the human-in-the-loop control of semi-autonomous UAVs. The goal of the system is to facilitate the operator intervention in critical scenarios (e.g. avoid safety issues or financial risks). Explainability is supported via user-friendly abstractions on Belief-Desire-Intention agents. To evaluate the effectiveness of the system, a human-computer interaction study is proposed.
Deep Structured Neural Network for Event Temporal Relation Extraction

We propose a novel deep structured learning framework for event temporal relation extraction. The model consists of 1) a recurrent neural network (RNN) to learn scoring functions for pair-wise relations, and 2) a structured support vector machine (SSVM) to make joint predictions. The neural network automatically learns representations that account for long-term contexts to provide robust features for the structured model, while the SSVM incorporates domain knowledge such as transitive closure of temporal relations as constraints to make better globally consistent decisions. By jointly training the two components, our model combines the benefits of both data-driven learning and knowledge exploitation. Experimental results on three high-quality event temporal relation datasets (TCR, MATRES, and TB-Dense) demonstrate that incorporated with pre-trained contextualized embeddings, the proposed model achieves significantly better performances than the state-of-the-art methods on all three datasets. We also provide thorough ablation studies to investigate our model.
The Brauer-Manin obstruction for constant curves over global function fields.

Let $\mathbb{F}$ be a finite field and $C,D$ smooth, geometrically irreducible proper curves over $\mathbb{F}$ and set $K = \mathbb{F}(D)$. We consider Brauer-Manin and abelian descent obstructions to the existence of rational points and to weak approximation for the curve $C \otimes_\mathbb{F} K$. In particular, we show that Brauer-Manin is the only obstruction to weak approximation and the Hasse principle in the case that the genus of $D$ is less than that of $C$. We also show that we can identify the points corresponding to non-constant maps $D \to C$ using Frobenius descents.
Sensitivity of collective outcomes identifies pivotal components

A social system is susceptible to perturbation when its collective properties depend sensitively on a few pivotal components. Using the information geometry of minimal models from statistical physics, we develop an approach to identify pivotal components to which coarse-grained, or aggregate, properties are sensitive. As an example, we introduce our approach on a reduced toy model with a median voter who always votes in the majority. The sensitivity of majority–minority divisions to changing voter behaviour pinpoints the unique role of the median. More generally, the sensitivity identifies pivotal components that precisely determine collective outcomes generated by a complex network of interactions. Using perturbations to target pivotal components in the models, we analyse datasets from political voting, finance and Twitter. Across these systems, we find remarkable variety, from systems dominated by a median-like component to those whose components behave more equally. In the context of political institutions such as courts or legislatures, our methodology can help describe how changes in voters map to new collective voting outcomes. For economic indices, differing system response reflects varying fiscal conditions across time. Thus, our information-geometric approach provides a principled, quantitative framework that may help assess the robustness of collective outcomes to targeted perturbation and compare social institutions, or even biological networks, with one another and across time.
Towards Best Experiment Design for Evaluating Dialogue System Output

To overcome the limitations of automated metrics (e.g. BLEU, METEOR) for evaluating dialogue systems, researchers typically use human judgments to provide convergent evidence. While it has been demonstrated that human judgments can suffer from the inconsistency of ratings, extant research has also found that the design of the evaluation task affects the consistency and quality of human judgments. We conduct a between-subjects study to understand the impact of four experiment conditions on human ratings of dialogue system output. In addition to discrete and continuous scale ratings, we also experiment with a novel application of Best-Worst scaling to dialogue evaluation. Through our systematic study with 40 crowdsourced workers in each task, we find that using continuous scales achieves more consistent ratings than Likert scale or ranking-based experiment design. Additionally, we find that factors such as time taken to complete the task and no prior experience of participating in similar studies of rating dialogue system output positively impact consistency and agreement amongst raters.
Verified Uncertainty Calibration

Applications such as weather forecasting and personalized medicine demand models that output calibrated probability estimates---those representative of the true likelihood of a prediction. Most models are not calibrated out of the box but are recalibrated by post-processing model outputs. We find in this work that popular recalibration methods like Platt scaling and temperature scaling are (i) less calibrated than reported, and (ii) current techniques cannot estimate how miscalibrated they are. An alternative method, histogram binning, has measurable calibration error but is sample inefficient---it requires $O(B/\epsilon^2)$ samples, compared to $O(1/\epsilon^2)$ for scaling methods, where $B$ is the number of distinct probabilities the model can output. To get the best of both worlds, we introduce the scaling-binning calibrator, which first fits a parametric function to reduce variance and then bins the function values to actually ensure calibration. This requires only $O(1/\epsilon^2 + B)$ samples. Next, we show that we can estimate a model's calibration error more accurately using an estimator from the meteorological community---or equivalently measure its calibration error with fewer samples ($O(\sqrt{B})$ instead of $O(B)$). We validate our approach with multiclass calibration experiments on CIFAR-10 and ImageNet, where we obtain a 35% lower calibration error than histogram binning and, unlike scaling methods, guarantees on true calibration. In these experiments, we also estimate the calibration error and ECE more accurately than the commonly used plugin estimators. We implement all these methods in a Python library: this https URL
Consistent and efficient pricing of SPX and VIX options under multiscale stochastic volatility

This study provides a consistent and efficient pricing method for both Standard & Poor's 500 Index (SPX) options and the Chicago Board Options Exchange's Volatility Index (VIX) options under a multiscale stochastic volatility model. To capture the multiscale volatility of the financial market, our model adds a fast scale factor to the well-known Heston volatility and we derive approximate analytic pricing formulas for the options under the model. The analytic tractability can greatly improve the efficiency of calibration compared to fitting procedures with the finite difference method or Monte Carlo simulation. Our experiment using options data from 2016 to 2018 shows that the model reduces the errors on the training sets of the SPX and VIX options by 9.9% and 13.2%, respectively, and decreases the errors on the test sets of the SPX and VIX options by 13.0\% and 16.5\%, respectively, compared to the single-scale model of Heston. The error reduction is possible because the additional factor reflects short-term impacts on the market, which is difficult to achieve with only one factor. It highlights the necessity of modeling multiscale volatility.
Machine Learning Optimization Algorithms & Portfolio Allocation

Portfolio optimization emerged with the seminal paper of Markowitz (1952). The original mean-variance framework is appealing because it is very efficient from a computational point of view. However, it also has one well-established failing since it can lead to portfolios that are not optimal from a financial point of view. Nevertheless, very few models have succeeded in providing a real alternative solution to the Markowitz model. The main reason lies in the fact that most academic portfolio optimization models are intractable in real life although they present solid theoretical properties. By intractable we mean that they can be implemented for an investment universe with a small number of assets using a lot of computational resources and skills, but they are unable to manage a universe with dozens or hundreds of assets. However, the emergence and the rapid development of robo-advisors means that we need to rethink portfolio optimization and go beyond the traditional mean-variance optimization approach. Another industry has faced similar issues concerning large-scale optimization problems. Machine learning has long been associated with linear and logistic regression models. Again, the reason was the inability of optimization algorithms to solve high-dimensional industrial problems. Nevertheless, the end of the 1990s marked an important turning point with the development and the rediscovery of several methods that have since produced impressive results. The goal of this paper is to show how portfolio allocation can benefit from the development of these large-scale optimization algorithms. Not all of these algorithms are useful in our case, but four of them are essential when solving complex portfolio optimization problems. These four algorithms are the coordinate descent, the alternating direction method of multipliers, the proximal gradient method and the Dykstra's algorithm.
Heterogeneous-Temporal Graph Convolutional Networks: Make the Community Detection Much Better

Community detection has long been an important yet challenging task to analyze complex networks with a focus on detecting topological structures of graph data. Essentially, real-world graph data contains various features, node and edge types which dynamically vary over time, and this invalidates most existing community detection approaches. To cope with these issues, this paper proposes the heterogeneous-temporal graph convolutional networks (HTGCN) to detect communities from hetergeneous and temporal graphs. Particularly, we first design a heterogeneous GCN component to acquire feature representations for each heterogeneous graph at each time step. Then, a residual compressed aggregation component is proposed to represent "dynamic" features for "varying" communities, which are then aggregated with "static" features extracted from current graph. Extensive experiments are evaluated on two real-world datasets, i.e., DBLP and IMDB. The promising results demonstrate that the proposed HTGCN is superior to both benchmark and the state-of-the-art approaches, e.g., GCN, GAT, GNN, LGNN, HAN and STAR, with respect to a number of evaluation criteria.
Whitney Numbers of Combinatorial Geometries and Higher-Weight Dowling Lattices

We study the Whitney numbers of the first kind of combinatorial geometries. The first part of the paper is devoted to general results relating the Mobius functions of nested atomistic lattices, extending some classical theorems in combinatorics. We then specialize our results to restriction geometries, i.e., to sublattices $\mathcal{L}(A)$ of the lattice of subspaces of an $\mathbb{F}_q$-linear space, say $X$, generated by a set of projective points $A \subseteq X$. In this context, we introduce the notion of subspace distribution, and show that partial knowledge of the latter is equivalent to partial knowledge of the Whitney numbers of $\mathcal{L}(A)$. This refines a classical result by Dowling. 
The most interesting applications of our results are to be seen in the theory of higher-weight Dowling lattices (HWDLs), to which we dovote the second and most substantive part of the paper. These combinatorial geometries were introduced by Dowling in 1971 in connection with fundamental problems in coding theory, and further studied, among others, by Zaslavsky, Bonin, Kung, Brini, and Games. To date, still very little is known about these lattices. In particular, the techniques to compute their Whitney numbers have not been discovered yet. In this paper, we bring forward the theory of HWDLs, computing their Whitney numbers for new infinite families of parameters. Moreover, we show that the second Whitney numbers of HWDLs are polynomials in the underlying field size $q$, whose coefficients are expressions involving the Bernoulli numbers. This reveals a new link between combinatorics, coding theory, and number theory. We also study the asymptotics of the Whitney numbers of HWDLs as the field size grows, giving upper bounds and exact estimates in some cases. In passing, we obtain new results on the density functions of error-correcting codes.
Sliding window property testing for regular languages

We study the problem of recognizing regular languages in a variant of the streaming model of computation, called the sliding window model. In this model, we are given a size of the sliding window $n$ and a stream of symbols. At each time instant, we must decide whether the suffix of length $n$ of the current stream ("the active window") belongs to a given regular language. 
Recent works showed that the space complexity of an optimal deterministic sliding window algorithm for this problem is either constant, logarithmic or linear in the window size $n$ and provided natural language theoretic characterizations of the space complexity classes. Subsequently, those results were extended to randomized algorithms to show that any such algorithm admits either constant, double logarithmic, logarithmic or linear space complexity. 
In this work, we make an important step forward and combine the sliding window model with the property testing setting, which results in ultra-efficient algorithms for all regular languages. Informally, a sliding window property tester must accept the active window if it belongs to the language and reject it if it is far from the language. We consider deterministic and randomized sliding window property testers with one-sided and two-sided errors. In particular, we show that for any regular language, there is a deterministic sliding window property tester that uses logarithmic space and a randomized sliding window property tester with two-sided error that uses constant space.
The Hellmann–Feynman theorem at finite temperature

We present a simple derivation of the Hellmann–Feynman theorem at finite temperature. We illustrate its validity by considering three relevant examples, which can be used in quantum mechanics lectures: the one-dimensional harmonic oscillator, the one-dimensional Ising model, and the Lipkin model. We show that the Hellmann–Feynman theorem allows one to calculate expectation values of operators that appear in the Hamiltonian. This is particularly useful when the total free energy is available, but there is no direct access to the thermal average of the operators themselves.
Deep Multi-Facial patches Aggregation Network for Expression Classification from Face Images

Emotional Intelligence in Human-Computer Interaction has attracted increasing attention from researchers in multidisciplinary research fields including psychology, computer vision, neuroscience, artificial intelligence, and related disciplines. Human prone to naturally interact with computers face-to-face. Human Expressions is an important key to better link human and computers. Thus, designing interfaces able to understand human expressions and emotions can improve Human-Computer Interaction (HCI) for better communication. In this paper, we investigate HCI via a deep multi-facial patches aggregation network for Face Expression Recognition (FER). Deep features are extracted from facial parts and aggregated for expression classification. Several problems may affect the performance of the proposed framework like the small size of FER datasets and the high number of parameters to learn. For That, two data augmentation techniques are proposed for facial expression generation to expand the labeled training. The proposed framework is evaluated on the extended Cohn-Konade dataset (CK+) and promising results are achieved.