Miracle-dz/UniFAR-FTUs huggingface dataset:
A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings

We introduce a data-driven method and shows its skills for spatiotemporal prediction of high-dimensional chaotic dynamics and turbulence. The method is based on a finite-dimensional approximation of the Koopman operator where the observables are vector-valued and delay-embedded, and the nonlinearities are treated as external forcings. The predictive capabilities of the method are demonstrated for well-known prototypes of chaos such as the Kuramoto-Sivashinsky equation and Lorenz-96 system, for which the data-driven predictions are accurate for several Lyapunov timescales. Similar performance is seen for two-dimensional lid-driven cavity flows at high Reynolds numbers.
The Multidimensional Damped Wave Equation: Maximal Weak Solutions for Nonlinear Forcing via Semigroups and Approximation

Abstract The damped nonlinear wave equation, also known as the nonlinear telegraph equation, is studied within the framework of semigroups and eigenfunction approximation. The linear semigroup assumes a central role: it is bounded on the domain of its generator for all time This permits eigenfunction approximation within the semigroup framework, as a tool for the study of weak solutions. The semigroup convolution formula, known to be rigorous on the generator domain, is extended to the interpretation of weak solution on an arbitrary time interval. A separate approximation theory can be developed by using the invariance of the semigroup on eigenspaces of the Laplacian as the system evolves. For (locally) bounded continuous L 2 forcing, there is a natural derivation of a maximal solution, which can logically include a constraint on the solution as well. Operator forcing allows for the incorporation of concurrent physical processes. A significant feature of the proof in the nonlinear case is verification of successive approximation without standard fixed point analysis.
KL property of exponent $1/2$ for zero-norm composite quadratic functions

This paper is concerned with a class of zero-norm regularized and constrained composite quadratic optimization problems, which has important applications in the fields such as sparse eigenvalue problems, sparse portfolio problems, and nonnegative matrix factorizations. For this class of nonconvex and nonsmooth problems, we establish the KL property of exponent 1/2 of its objective function under a suitable assumption, and provide some examples to illustrate that the assumption holds.
A Scalable Algorithm for Identifying Multiple-Sensor Faults Using Disentangled RNNs

The problem of detecting and identifying sensor faults is critical for efficient, safe, regulatory-compliant, and sustainable operations of modern industrial processing systems. The increasing complexity of such systems brings, however, new challenges for sensor fault detection and sensor fault isolation (SFD-SFI). One of the key enablers for any SFD-SFI method is analytical redundancy, which is provided by an analytical model of sensor observations derived from first principles or identified from historical data. As defective sensors generate measurements that are inconsistent with their expected behavior as defined by the model, SFD amounts to the generation and monitoring of residuals between sensor observations and model predictions. In this article, we introduce a disentangled recurrent neural network (RNN) with the objective to cope with the smearing-out effect, i.e., where the propagation of a sensor fault to nonfaulty sensor results in large and misleading residuals. The introduction of a probabilistic model for the residual generation allows us to develop a novel procedure for the identification of the faulty sensors. The computational complexity of the proposed algorithm is linear in the number of sensors as opposed to the combinatorial nature of the SFI problem. Finally, we empirically verify the performance of the proposed SFD-SFI architecture using a real data set collected at a petrochemical plant.
A zero density estimate for Dedekind zeta functions

Given a finite group $G$, we establish a zero density estimate for Dedekind zeta functions associated to Galois extensions $K/\mathbb{Q}$ with $\mathrm{Gal}(K/\mathbb{Q})\cong G$ without assuming unproven progress toward the strong form of Artin's conjecture. As an application, we strengthen a recent breakthrough of Pierce, Turnage-Butterbaugh, and Wood on the average size of the error term in the Chebotarev density theorem.
Optimal Control and Stabilization for Networked Control Systems With Asymmetric Information

This article considers the optimal control and stabilization problems for networked control systems (NCSs) with asymmetric information. In this NCSs model, the remote controller can receive packet-dropout states of the plant, and the available information for the embedded controller are observations of states and packet-dropout states sent from the remote controller. The two controllers operate the plant simultaneously to make the quadratic performance minimized and stabilize the linear plant. For the finite-horizon case, since states of the plant cannot be obtained perfectly, we develop the optimal estimators for the embedded and remote controllers based on asymmetric information, respectively. Then we give the necessary and sufficient condition for the optimal control based on the solution to the forward–backward stochastic difference equations. For the infinite-horizon case, it is shown that the system is bounded in the mean-square sense if and only if there exist the solutions to the two coupled algebraic Riccati equations and the packet-dropout probability satisfies certain condition. Numerical examples on the unmanned underwater vehicle are presented to show the effectiveness of the given algorithm.
Distributed Word2Vec using Graph Analytics Frameworks

Word embeddings capture semantic and syntactic similarities of words, represented as vectors. Word2Vec is a popular implementation of word embeddings; it takes as input a large corpus of text and learns a model that maps unique words in that corpus to other contextually relevant words. After training, Word2Vec's internal vector representation of words in the corpus map unique words to a vector space, which are then used in many downstream tasks. Training these models requires significant computational resources (training time often measured in days) and is difficult to parallelize. Most word embedding training uses stochastic gradient descent (SGD), an "inherently" sequential algorithm where at each step, the processing of the current example depends on the parameters learned from the previous examples. Prior approaches to parallelizing SGD do not honor these dependencies and thus potentially suffer poor convergence. This paper introduces GraphWord2Vec, a distributedWord2Vec algorithm which formulates the Word2Vec training process as a distributed graph problem and thus leverage state-of-the-art distributed graph analytics frameworks such as D-Galois and Gemini that scale to large distributed clusters. GraphWord2Vec also demonstrates how to use model combiners to honor data dependencies in SGD and thus scale without giving up convergence. We will show that GraphWord2Vec has linear scalability up to 32 machines converging as fast as a sequential run in terms of epochs, thus reducing training time by 14x.
Projectively self-concordant barriers on convex sets

Self-concordance is the most important property required for barriers in convex programming. We introduce an alternative, stronger notion, which we call projective self-concordance, define the corresponding Dikin sets by a quadratic inequality, and develop a corresponding duality theory. Our notion is equivariant with respect to the group of projective transformations, which is larger than the affine group corresponding to the classical notion. Our Dikin sets are larger than the classical Dikin ellipsoids, depend on the gradient of the barrier at the center point, are non-symmetric, and may even be unbounded. From the derivatives of the barrier at a given point we construct a quadratic set which overbounds the underlying convex set, which is not possible for the classical notion of self-concordance. This opens the way to design algorithms which make larger steps and hence have a faster convergence rate than traditional interior-point methods. We give many examples of convex sets with projectively self-concordant barriers.
Neural Rule Grounding for Low-Resource Relation Extraction

While deep neural models have gained successes on information extraction tasks, they become less reliable when the amount of labeled data is limited. In this paper, we study relation extraction (RE) under low-resource setting, where only some (hand-built) labeling rules are provided for learning a neural model over a large, unlabeled corpus. To overcome the low-coverage issue of current bootstrapping methods (i.e., hard grounding of rules), we propose a Neural Rule Grounding (REGD) framework for jointly learning a relation extraction module (with flexible neural architecture) and a sentence-rule soft matching module. The soft matching module extends the coverage of rules on semantically similar instances and augments the learning on unlabeled corpus. Experiments on two public datasets demonstrate the effectiveness of REGD when compared with both rule-based and semi-supervised baselines. Additionally, the learned soft matching module is able to predict on new relations with unseen rules, and can provide interpretation on matching results.
Node classification framework

GCN is a recent effective algorithm which effectively learns a function incorporate both graph structure and node features for semisupervised graph based node classification. Although GCN exceeds other state-of-the-art methods, the number of parameters that need to be learned are still significantly more than the number of used samples. Because only labeled nodes and their 2-hop neighbors are used for learning parameters in GCN. As a consequence the accuracy of node classification declines sharply when decreasing the size of train data. In order to reducing parameters and making better use of unlabeled nodes, we proposes to use unsupervised representation algorithm such as autoencoder to pretrain a embedding for each node, which captures effective information from input features and reduce parameters in graph convolution layers. Experiments show that our model has increased by 0.87%, 1.96%, 1.87% compared to baseline on Cora, Citeseer and Pubmed data respectively. The performance of our model declines slower than GCN when decreasing the train samples.
An Efficient Motion Planning Strategy for Automated Lane Change based on Mixed-Integer Optimization and Neural Networks

To guarantee safe and efficient driving for automated vehicles in complicated traffic conditions, the motion planning module of automated vehicles are expected to generate collision-free driving policies as soon as possible in varying traffic environment. However, there always exist a tradeoff between efficiency and accuracy for the motion planning algorithms. Besides, most motion planning methods cannot find the desired trajectory under extreme scenarios (e.g., lane change in crowded traffic scenarios). This study proposed an efficient motion planning strategy for automated lane change based on Mixed-Integer Quadratic Optimization (MIQP) and Neural Networks. We modeled the lane change task as a mixed-integer quadratic optimization problem with logical constraints, which allows the planning module to generate feasible, safe and comfortable driving actions for lane changing process. Then, a hierarchical machine learning structure that consists of SVM-based classification layer and NN-based action learning layer is established to generate desired driving policies that can make online, fast and generalized motion planning. Our model is validated in crowded lane change scenarios through numerical simulations and results indicate that our model can provide optimal and efficient motion planning for automated vehicles.
The Effect of Residency Requirements on Police as Capable Guardians

14 Definition of the Issue.15 Introduction.15 History and Background of the Problem.17 Operationalization.20 Statement of the Problem.20 Research Question.21 Conceptual Assumptions.21 Delineation of the Research Problem.21 Hypotheses.22
Asynchronous time-parallel method based on Laplace transform

Laplace transform method has proved to be very efficient and easy to parallelize for the solution of time-dependent problems. However, the synchronization delay among processors implies an upper bound on the expectable acceleration factor, which leads to a lot of wasted time. In this paper, we propose an original asynchronous Laplace transform method formalized for quasilinear problems based on the well-known Gaver–Stehfest algorithm. Parallel experiments show the convergence of our new method, as well as several interesting properties compared with the classical algorithms.
The long-lived inner bar of NGC 1291

Abstract The question whether stellar bars are either transitory features or long-lived structures is still matter of debate. This problem is more acute for double-barred systems where even the formation of the inner bar remains a challenge for numerical studies. We present a thorough study of the central structures of the double-barred galaxy NGC 1291. We used a two-dimensional multi-component photometric decomposition performed on the 3.6 μm images from S4 G, combined with both stellar kinematics and stellar population analysis carried out using integral field data from the MUSE TIMER project. We report on the discovery of the first Box-Peanut (B/P) structure in an inner bar detected in the face-on galaxy NGC 1291. The B/P structure is detected as bi-symmetric minima of the h4 moment of the line-of-sight velocity distribution along the major axis of the inner bar, as expected from numerical simulations. Our observations demonstrate that inner bars (similarly as outer bars) can suffer buckling instabilities, thus suggesting they can survive a long time after bar formation. The analysis of the star formation history for the structural components shaping the central regions of NGC 1291 also constrains the epoch of dynamical assembly of the inner bar, which took place >6.5 Gyr ago for NGC 1291. Our results imply that the inner bar of NGC 1291 is a long-lived structure.
Graph representation learning: a survey

Abstract Research on graph representation learning has received great attention in recent years since most data in real-world applications come in the form of graphs. High-dimensional graph data are often in irregular forms. They are more difficult to analyze than image/video/audio data defined on regular lattices. Various graph embedding techniques have been developed to convert the raw graph data into a low-dimensional vector representation while preserving the intrinsic graph properties. In this review, we first explain the graph embedding task and its challenges. Next, we review a wide range of graph embedding techniques with insights. Then, we evaluate several stat-of-the-art methods against small and large data sets and compare their performance. Finally, potential applications and future directions are presented.
Finding Salient Context based on Semantic Matching for Relevance Ranking

We propose a salient-context based semantic matching method to improve relevance ranking in information retrieval. We first propose a new notion of salient context and then define how to measure it. Then we show how the most salient context can be located with a sliding window technique. Finally, we use the semantic similarity between a query term and the most salient context terms in a corpus of documents to rank those documents. Experiments on various TREC collections show the effectiveness of our model compared to the state-of-the-art methods.
GNU-Octave Como Alternativa de Simulación de Sistemas Dinámicos No Lineales en la Enseñanza de la Ingeniería

This paper presents a proposed alternative to simulate non-linear dynamical systems. This has an application in bachelor programs like: Electrical and mechanical engineering, Networks and Telecommunications engineering, Mechanical engineering and more, than they are taught in several public universities in Guerrero state. Commonly, the computer devices used for simulations require of high hardware capacity to support the simulation software. Moreover, the simulation software in the majority of the cases is under license permission. For these reasons, implementing a simulation lab in a public university is very high cost. Thus, we show an alternative by using a commercial development board Raspberry Pi supporting the GNU-Octave software, which is a free software, to simulate non-linear dynamical systems like a 4 grades of freedom SCARA robot and a rotational inverted pendulum. The comparision of the simulated dynamical models in both the specialized software and the proposed free software, exhibit the viability of the proposed alternative.
Directionally-Unbiased Unitary Optical Devices in Discrete-Time Quantum Walks

The optical beam splitter is a widely-used device in photonics-based quantum information processing. Specifically, linear optical networks demand large numbers of beam splitters for unitary matrix realization. This requirement comes from the beam splitter property that a photon cannot go back out of the input ports, which we call “directionally-biased”. Because of this property, higher dimensional information processing tasks suffer from rapid device resource growth when beam splitters are used in a feed-forward manner. Directionally-unbiased linear-optical devices have been introduced recently to eliminate the directional bias, greatly reducing the numbers of required beam splitters when implementing complicated tasks. Analysis of some originally directional optical devices and basic principles of their conversion into directionally-unbiased systems form the base of this paper. Photonic quantum walk implementations are investigated as a main application of the use of directionally-unbiased systems. Several quantum walk procedures executed on graph networks constructed using directionally-unbiased nodes are discussed. A significant savings in hardware and other required resources when compared with traditional directionally-biased beam-splitter-based optical networks is demonstrated.
Computer simulations of colloidal gels: how hindered particle rotation affects structure and rheology.

The effects of particle roughness and short-ranged non-central forces on colloidal gels are studied using computer simulations in which particles experience a sinusoidal variation in energy as they rotate. The number of minima n and energy scale K are the key parameters; for large K and n, particle rotation is strongly hindered, but for small K and n particle rotation is nearly free. A series of systems are simulated and characterized using fractal dimensions, structure factors, coordination number distributions, bond-angle distributions and linear rheology. When particles rotate easily, clusters restructure to favor dense packings. This leads to longer gelation times and gels with strand-like morphology. The elastic moduli of such gels scale as G' ∝ ω0.5 at high shear frequencies ω. In contrast, hindered particle rotation inhibits restructuring and leads to rapid gelation and diffuse morphology. Such gels are stiffer, with G' ∝ ω0. 35. The viscous moduli G'' in the low-barrier and high-barrier regimes scale according to exponents 0.53 and 0.5, respectively. The crossover frequency between elastic and viscous behaviors generally increases with the barrier to rotation. These findings agree qualitatively with some recent experiments on heterogeneously-surface particles and with studies of DLCA-type gels and gels of smooth spheres.
Duality Regularization for Unsupervised Bilingual Lexicon Induction

Unsupervised bilingual lexicon induction naturally exhibits duality, which results from symmetry in back-translation. For example, EN-IT and IT-EN induction can be mutually primal and dual problems. Current state-of-the-art methods, however, consider the two tasks independently. In this paper, we propose to train primal and dual models jointly, using regularizers to encourage consistency in back translation cycles. Experiments across 6 language pairs show that the proposed method significantly outperforms competitive baselines, obtaining the best-published results on a standard benchmark.
Transverse-mode coupling effects in scanning cavity microscopy

Tunable open-access Fabry–Pérot microcavities enable the combination of cavity enhancement with high resolution imaging. To assess the limits of this technique originating from background variations, we perform high-finesse scanning cavity microscopy of pristine planar mirrors. We observe spatially localized features of strong cavity transmission reduction for certain cavity mode orders, and periodic background patterns with high spatial frequency. We show in detailed measurements that the localized structures originate from resonant transverse-mode coupling and arise from the topography of the planar mirror surface, in particular its local curvature and gradient. We further examine the background patterns and find that they derive from non-resonant mode coupling, and we attribute it to the micro roughness of the mirror. Our measurements and analysis elucidate the impact of imperfect mirrors and reveal the influence of their microscopic topography. This is crucial for the interpretation of scanning cavity images, and could provide relevant insight for precision applications such as gravitational wave detectors, laser gyroscopes, and reference cavities.
Real-time image processing with a 2D semiconductor neural network vision sensor

In recent years, machine vision has taken huge leaps and is now becoming an integral part of various intelligent systems, including autonomous vehicles, robotics, and many others. Usually, visual information is captured by a frame-based camera, converted into a digital format, and processed afterwards using a machine learning algorithm such as an artificial neural network (ANN). A large amount of (mostly redundant) data being passed through the entire signal chain, however, results in low frame rates and large power consumption. Various visual data preprocessing techniques have thus been developed that allow to increase the efficiency of the subsequent signal processing in an ANN. Here, we demonstrate that an image sensor itself can constitute an ANN that is able to simultaneously sense and process optical images without latency. Our device is based on a reconfigurable two-dimensional (2D) semiconductor photodiode array, with the synaptic weights of the network being stored in a continuously tunable photoresponsivity matrix. We demonstrate both supervised and unsupervised learning and successfully train the sensor to classify and encode images, that are optically projected onto the chip, with a throughput of 20 million bins per second.
Fuller Singularities for Generic Control-Affine Systems with an Even Number of Controls

In this article we study how bad can be the singularities of a time-optimal trajectory of a generic control affine system. In the case where the control is scalar and belongs to a closed interval it was recently shown in [6] that singularities cannot be, generically, worse than finite order accumulations of Fuller points, with order of accumulation lower than a bound depending only on the dimension of the manifold where the system is set. We extend here such a result to the case where the control has an even number of scalar components and belongs to a closed ball.