nils-herrmann/clean_scirepeval huggingface dataset:
The Landau Hamiltonian with $\delta$-potentials supported on curves

The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian $A_\alpha =(i \nabla + A)^2 + \alpha\delta$ in $L^2(R^2)$ with a $\delta$-potential supported on a finite $C^{1,1}$-smooth curve $\Sigma$ are studied. Here $A = \frac{1}{2} B (-x_2, x_1)^\top$ is the vector potential, $B>0$ is the strength of the homogeneous magnetic field, and $\alpha\in L^\infty(\Sigma)$ is a position-dependent real coefficient modeling the strength of the singular interaction on the curve $\Sigma$. After a general discussion of the qualitative spectral properties of $A_\alpha$ and its resolvent, one of the main objectives in the present paper is a local spectral analysis of $A_\alpha$ near the Landau levels $B(2q+1)$. Under various conditions on $\alpha$ it is shown that the perturbation smears the Landau levels into eigenvalue clusters, and the accumulation rate of the eigenvalues within these clusters is determined in terms of the capacity of the support of $\alpha$. Furthermore, the use of Landau Hamiltonians with $\delta$-perturbations as model operators for more realistic quantum systems is justified by showing that $A_\alpha$ can be approximated in the norm resolvent sense by a family of Landau Hamiltonians with suitably scaled regular potentials.
Quicker ADC : Unlocking the Hidden Potential of Product Quantization With SIMD

Efficient Nearest Neighbor (NN) search in high-dimensional spaces is a foundation of many multimedia retrieval systems. A common approach is to rely on Product Quantization, which allows the storage of large vector databases in memory and efficient distance computations. Yet, implementations of nearest neighbor search with Product Quantization have their performance limited by the many memory accesses they perform. Following this observation, André et al. proposed Quick ADC with up to <inline-formula><tex-math notation="LaTeX">$6{\times }$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>6</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="lescouarnec-ieq1-2952606.gif"/></alternatives></inline-formula> faster implementations of PQ <inline-formula><tex-math notation="LaTeX">${m}{\times }math><inline-graphic xlink:href="lescouarnec-ieq2-2952606.gif"/></alternatives></inline-formula> product quantizers (PQ) leveraging specific SIMD instructions. Quicker ADC is a generalization of Quick ADC not limited to PQ <inline-formula><tex-math notation="LaTeX">${m}{\times }math><inline-graphic xlink:href="lescouarnec-ieq3-2952606.gif"/></alternatives></inline-formula> codes and supporting AVX-512, the latest revision of SIMD instruction set. In doing so, Quicker ADC faces the challenge of using efficiently 5,6 and 7-bit shuffles that do not align to computer bytes or words. To this end, we introduce (i) <italic>irregular product quantizers</italic> combining sub-quantizers of different granularity and (ii) <italic>split tables</italic> allowing lookup tables larger than registers. We evaluate Quicker ADC with multiple indexes including Inverted Multi-Indexes and IVF HNSW and show that it outperforms the reference optimized implementations (i.e., FAISS and polysemous codes) for numerous configurations. Finally, we release an open-source fork of FAISS enhanced with Quicker ADC.
Open source software in quantum computing

Open source software is becoming crucial in the design and testing of quantum algorithms. Many of the tools are backed by major commercial vendors with the goal to make it easier to develop quantum software: this mirrors how well-funded open machine learning frameworks enabled the development of complex models and their execution on equally complex hardware. We review a wide range of open source software for quantum computing, covering all stages of the quantum toolchain from quantum hardware interfaces through quantum compilers to implementations of quantum algorithms, as well as all quantum computing paradigms, including quantum annealing, and discrete and continuous-variable gate-model quantum computing. The evaluation of each project covers characteristics such as documentation, licence, the choice of programming language, compliance with norms of software engineering, and the culture of the project. We find that while the diversity of projects is mesmerizing, only a few attract external developers and even many commercially backed frameworks have shortcomings in software engineering. Based on these observations, we highlight the best practices that could foster a more active community around quantum computing software that welcomes newcomers to the field, but also ensures high-quality, well-documented code.
An Evaluation of Methods for Real-Time Anomaly Detection using Force Measurements from the Turning Process

We examined the use of three conventional anomaly detection methods and assess their potential for on-line tool wear monitoring. Through efficient data processing and transformation of the algorithm proposed here, in a real-time environment, these methods were tested for fast evaluation of cutting tools on CNC machines. The three-dimensional force data streams we used were extracted from a turning experiment of 21 runs for which a tool was run until it generally satisfied an end-of-life criterion. Our real-time anomaly detection algorithm was scored and optimised according to how precisely it can predict the progressive wear of the tool flank. Most of our tool wear predictions were accurate and reliable as illustrated in our off-line simulation results. Particularly when the multivariate analysis was applied, the algorithm we develop was found to be very robust across different scenarios and against parameter changes. It shall be reasonably easy to apply our approach elsewhere for real-time tool wear analytics.
Gushel–Mukai varieties: Moduli

We describe the moduli stack of Gushel–Mukai varieties as a global quotient stack and its coarse moduli space as the corresponding GIT quotient. The construction is based on a comprehensive study of the relation between this stack and the stack of so-called Lagrangian data defined in our previous works; roughly speaking, we show that the former is a generalized root stack of the latter. As an application, we define the period map for Gushel–Mukai varieties and construct some complete nonisotrivial families of smooth Gushel–Mukai varieties. In an appendix, we describe a generalization of the root stack construction used in our approach to the moduli stack.
Factorizing the Top-Loc adjunction through positive topologies

We characterize the category of Sambin's positive topologies as a fibration over the category of locales Loc. The fibration is obtained by applying the Grothendieck construction to a doctrine over Loc. We then construct an adjunction between the category of positive topologies and that of topological spaces Top, and show that the well-known adjunction between Top and Loc factors through the newly constructed adjunction.
Sources of Complexity in Semantic Frame Parsing for Information Extraction

This paper describes a Semantic Frame parsing System based on sequence labeling methods, precisely BiLSTM models with highway connections, for performing information extraction on a corpus of French encyclopedic history texts annotated according to the Berkeley FrameNet formalism. The approach proposed in this study relies on an integrated sequence labeling model which jointly optimizes frame identification and semantic role segmentation and identification. The purpose of this study is to analyze the task complexity, to highlight the factors that make Semantic Frame parsing a difficult task and to provide detailed evaluations of the performance on different types of frames and sentences.
Learning to Navigate the Web

Learning in environments with large state and action spaces, and sparse rewards, can hinder a Reinforcement Learning (RL) agent's learning through trial-and-error. For instance, following natural language instructions on the Web (such as booking a flight ticket) leads to RL settings where input vocabulary and number of actionable elements on a page can grow very large. Even though recent approaches improve the success rate on relatively simple environments with the help of human demonstrations to guide the exploration, they still fail in environments where the set of possible instructions can reach millions. We approach the aforementioned problems from a different perspective and propose guided RL approaches that can generate unbounded amount of experience for an agent to learn from. Instead of learning from a complicated instruction with a large vocabulary, we decompose it into multiple sub-instructions and schedule a curriculum in which an agent is tasked with a gradually increasing subset of these relatively easier sub-instructions. In addition, when the expert demonstrations are not available, we propose a novel meta-learning framework that generates new instruction following tasks and trains the agent more effectively. We train DQN, deep reinforcement learning agent, with Q-value function approximated with a novel QWeb neural network architecture on these smaller, synthetic instructions. We evaluate the ability of our agent to generalize to new instructions on World of Bits benchmark, on forms with up to 100 elements, supporting 14 million possible instructions. The QWeb agent outperforms the baseline without using any human demonstration achieving 100% success rate on several difficult environments.
Complexity of Partitioning Hypergraphs

For a given $\pi=(\pi_0, \pi_1,..., \pi_k) \in \{0, 1, *\}^{k+1}$, we want to determine whether an input $k$-uniform hypergraph $G=(V, E)$ has a partition $(V_1, V_2)$ of the vertex set so that for all $X \subseteq V$ of size $k$, $X \in E$ if $\pi_{|X\cap V_1|}=1$ and $X \notin E$ if $\pi_{|X\cap V_1|}=0$. We prove that this problem is either polynomial-time solvable or NP-complete depending on $\pi$ when $k=3$ or $4$. We also extend this result into $k$-uniform hypergraphs for $k \geq 5$.
Quantum control in infinite dimensions and Banach-Lie algebras

In finite dimensions, controllability of bilinear quantum control systems can be decided quite easily in terms of the "Lie algebra rank condition" (LARC), such that only the systems Lie algebra has to be determined from a set of generators. In this paper we study how this idea can be lifted to infinite dimensions. To this end we look at control systems on an infinite dimensional Hilbert space which are given by an unbounded drift Hamiltonian H0 and bounded control Hamiltonians H1,…,HN. The drift H0 is assumed to have empty continuous spectrum. We use recurrence methods and the theory of Abelian von Neumann algebras to develop a scheme, which allows us to use an approximate version of LARC, in order to check approximate controllability of the control system in question.
Nonparametric Feature Extraction from Dendrograms

We propose feature extraction from dendrograms in a nonparametric way. The Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level function and a distance function over that. Therefore, we extend this method to arbitrary dendrograms. We develop a generalized framework wherein different distance measures can be inferred from different types of dendrograms, level functions and distance functions. Via an appropriate embedding, we compute a vector-based representation of the inferred distances, in order to enable many numerical machine learning algorithms to employ such distances. Then, to address the model selection problem, we study the aggregation of different dendrogram-based distances respectively in solution space and in representation space in the spirit of deep representations. In the first approach, for example for the clustering problem, we build a graph with positive and negative edge weights according to the consistency of the clustering labels of different objects among different solutions, in the context of ensemble methods. Then, we use an efficient variant of correlation clustering to produce the final clusters. In the second approach, we investigate the sequential combination of different distances and features sequentially in the spirit of multi-layered architectures to obtain the final features. Finally, we demonstrate the effectiveness of our approach via several numerical studies.
A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint

A firm is selling a product to different types (based on the features such as education backgrounds, ages, etc.) of customers over a finite season with non-replenishable initial inventory. The type label of an arriving customer can be observed but the demand function associated with each type is initially unknown. The firm sets personalized prices dynamically for each type and attempts to maximize the revenue over the season. We provide a learning algorithm that is near-optimal when the demand and capacity scale in proportion. The algorithm utilizes the primal-dual formulation of the problem and learns the dual optimal solution explicitly. It allows the algorithm to overcome the curse of dimensionality (the rate of regret is independent of the number of types) and sheds light on novel algorithmic designs for learning problems with resource constraints.
Symbolic Inductive Bias for Visually Grounded Learning of Spoken Language

A widespread approach to processing spoken language is to first automatically transcribe it into text. An alternative is to use an end-to-end approach: recent works have proposed to learn semantic embeddings of spoken language from images with spoken captions, without an intermediate transcription step. We propose to use multitask learning to exploit existing transcribed speech within the end-to-end setting. We describe a three-task architecture which combines the objectives of matching spoken captions with corresponding images, speech with text, and text with images. We show that the addition of the speech/text task leads to substantial performance improvements on image retrieval when compared to training the speech/image task in isolation. We conjecture that this is due to a strong inductive bias transcribed speech provides to the model, and offer supporting evidence for this.
Persistence Bag-of-Words for Topological Data Analysis

Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit, however, complex structure and are difficult to integrate in today's machine learning workflows. This paper introduces persistence bag-of-words: a novel and stable vectorized representation of PDs that enables the seamless integration with machine learning. Comprehensive experiments show that the new representation achieves state-of-the-art performance and beyond in much less time than alternative approaches.
Ground state energy: Can it really be reached with quantum annealers?

Finding the ground state energy of a Hamiltonian $H$, which describes a quantum system of several interacting subsystems, is crucial as well for many-body physics as for various optimization problems. Variety of algorithms and simulation procedures (either hardware or software based) rely on the separability approximation, in which one seeks for the minimal expectation value of $H$ among all product states. We demonstrate that already for systems with nearest neighbor interactions this approximation is inaccurate, which implies fundamental restrictions for precision of computations performed with near-term quantum annealers. Furthermore, for generic Hamiltonians this approximation leads to significant systematic errors as the minimal expectation value among separable states asymptotically tends to zero. As a result, we introduce an effective entanglement witness based on a generic observable that is applicable for any multipartite quantum system.
Twisted Holography.

We derive and test a novel holographic duality in the B-model topological string theory. The duality relates the B-model on certain Calabi-Yau three-folds to two-dimensional chiral algebras defined as gauged $\beta\gamma\,$ systems. The duality conjecturally captures a topological sector of more familiar $\mathrm{AdS}_5 / \mathrm{CFT}_4$ holographic dualities.
Improvement of functionals in density functional theory by the inverse Kohn–Sham method and density functional perturbation theory

We propose a way to improve energy density functionals (EDFs) in the density functional theory based on the combination of the inverse Kohn--Sham method and the density functional perturbation theory. Difference between the known EDF and the exact one is treated as the first-order perturbation. As benchmark calculations, we reproduce the theoretical exchange and correlation functionals in the local density approximation. Systems of noble-gas atoms are used for benchmark calculations, and the ground-state energies and densities, as well as the functionals, are reproduced with good accuracies.
Communication: Relating the pure and ensemble density matrix functional.

A crucial theorem in Reduced Density Matrix Functional Theory (RDMFT) suggests that the universal pure and ensemble functionals coincide on their common domain of pure N-representable one-matrices. We refute this by a comprehensive analysis of the geometric picture underlying Levy's constrained search. Moreover, we then show that the ensemble functional follows instead as the lower convex envelop of the pure functional. It is particularly remarkable that the pure functional determines the ensemble functional even outside its own domain of pure N-representable one-matrices. From a general perspective, this demonstrates that relaxing pure RDMFT to ensemble RDMFT does not necessarily circumvent the complexity of the one-body pure N-representability conditions (generalized Pauli constraints). Instead, the complexity may simply be transferred from the underlying space of pure N-representable one-matrices to the structure of the universal one-matrix functional.
Analytification of mapping stacks

Derived mapping stacks are a fundamental source of examples of derived enhancements of classical moduli problems. For instance, they appear naturally in Gromov-Witten theory and in some branches of geometric representation theory. In this paper, we show that in many cases the mapping stacks construction commutes with the (complex or non-archimedean) analytification functor. Along the way, we establish several properties of the stack of analytic perfect complexes and study some incarnations of analytic Tannaka duality.
Growth, Industrial Externality, Prospect Dynamics, and Well-Being on Markets

Functions or 'functionings' enable to give a structure to any economic activity whether they are used to describe a good or a service that is exchanged on a market or they constitute the capability of an agent to provide the labor market with specific work and skills. That structure encompasses the basic law of supply and demand and the conditions of growth within a transaction and of the inflation control. Functional requirements can be followed from the design of a product to the delivery of a solution to a customer needs with different levels of externalities while value is created integrating organizational and technical constraints whereas a budget is allocated to the various entities of the firm involved in the production. Entering the market through that structure leads to designing basic equations of its dynamics and to finding canonical solutions out of particular equilibria. This approach enables to tackle behavioral foundations of Prospect Theory within a generalization of its probability weighting function turned into an operator which applies to Western, Educated, Industrialized, Rich, and Democratic societies as well as to the poorest ones. The nature of reality and well-being appears then as closely related to the relative satisfaction reached on the market, as it can be conceived by an agent, according to business cycles. This reality being the result of the complementary systems that govern human mind as structured by rational psychologists.
Multiple topic identification in telephone conversations

This paper deals with the automatic analysis of conversations between a customer and an agent in a call centre of a customer care service. The purpose of the analysis is to hypothesize themes about problems and complaints discussed in the conversation. Themes are defined by the application documentation topics. A conversation may contain mentions that are irrelevant for the application purpose and multiple themes whose mentions may be interleaved portions of a conversation that cannot be well defined. Two methods are proposed for multiple theme hypothesization. One of them is based on a cosine similarity measure using a bag of features extracted from the entire conversation. The other method introduces the concept of thematic density distributed around specific word positions in a conversation. In addition to automatically selected words, word bigrams with possible gaps between successive words are also considered and selected. Experimental results show that the results obtained with the proposed methods outperform the results obtained with support vector machines on the same data. Furthermore, using the theme skeleton of a conversation from which thematic densities are derived, it will be possible to extract components of an automatic conversation report to be used for improving the service performance.
Local Estimation of a Multivariate Density and its Derivatives.

We present methods for estimating the multivariate probability density (or the $\log$-density) and its first and second order derivatives simultaneously. Two methods, local log-likelihood and Hyv\"arinen score estimation, are in terms of weighted scoring rules with local polynomials. A third approach is matching of local moments. Consistency and asymptotic convergence results are shown and compared with corresponding results for kernel density estimators.
Unsupervised Speech Recognition via Segmental Empirical Output Distribution Matching

We consider the problem of training speech recognition systems without using any labeled data, under the assumption that the learner can only access to the input utterances and a phoneme language model estimated from a non-overlapping corpus. We propose a fully unsupervised learning algorithm that alternates between solving two sub-problems: (i) learn a phoneme classifier for a given set of phoneme segmentation boundaries, and (ii) refining the phoneme boundaries based on a given classifier. To solve the first sub-problem, we introduce a novel unsupervised cost function named Segmental Empirical Output Distribution Matching, which generalizes the work in (Liu et al., 2017) to segmental structures. For the second sub-problem, we develop an approximate MAP approach to refining the boundaries obtained from Wang et al. (2017). Experimental results on TIMIT dataset demonstrate the success of this fully unsupervised phoneme recognition system, which achieves a phone error rate (PER) of 41.6%. Although it is still far away from the state-of-the-art supervised systems, we show that with oracle boundaries and matching language model, the PER could be improved to 32.5%.This performance approaches the supervised system of the same model architecture, demonstrating the great potential of the proposed method.