Hybrid supercapacitors possess high power and energy density, while the cascaded H-bridge converter features rapid response capability. Integrating these two components leads to an energy storage system capable of swiftly responding to power demands, effectively mitigating voltage and frequency instability in weak-grid renewable energy stations. Based on this system, in this paper, a novel automatic frequency–voltage regulation strategy is proposed. First, a fast fault severity detection method is proposed. It evaluates the system’s fault condition by monitoring the voltage response and generates auxiliary signals to enable subsequent rapid compensation of voltage and frequency. Subsequently, fast automatic voltage and frequency regulation strategies are developed. These strategies leverage real-time fault assessment to deliver immediate power support to weak-grid renewable stations following a disturbance, thereby effectively stabilizing the terminal voltage magnitude and system frequency. The effectiveness of the proposed method is validated through simulations. A grid-connected model of a weak-grid renewable energy station is established in MATLAB (2023b)/Simulink. Tests under various fault scenarios with different short-circuit ratios and voltage sag depths demonstrate that the proposed strategy can rapidly stabilize both voltage and frequency after large disturbances.
Abstract Psycholinguistic research methods like self‐paced reading and eye‐tracking during reading yield precise data in milliseconds that indicate how much time participants spend looking at and reading specific words in a stimulus sentence. Collecting and analyzing such time‐based data entails some special considerations and three fundamental ones are covered in this entry. First, the design of stimulus sentences is an exacting task that must address multiple extraneous variables, such as word length and frequency, which might otherwise affect the data and obscure the effects of interest to the researchers. The easiest and most efficient way to ensure experimental control is to design stimulus sentences that are nearly identical across conditions except for a single word that is related to the manipulated variable. Second, stimulus items are random rather than fixed, meaning that they are similar to participants in that they are a sample drawn from a larger population and that the goal is to generalize results to a broader population. Statistical analysis should therefore capture random variation between stimulus items. Current practice accomplishes this with mixed‐effects models that include crossed random effects for subject and item with unaveraged data. Finally, recent attention to effect sizes in applied linguistics research has generated interest in establishing specific effect size guidelines that are appropriate for research with different methods. For self‐paced reading and eye‐tracking, it appears that effect sizes tend to be small, probably because reading is a largely automatic and unconscious process and because random variation in the data is relatively high.
Adriana Palos, Ismael Caballero, Daniel de Mercado
et al.
Centro Español de Metrología (CEM) is developing a quantum frequency standard based on trapped calcium ions, marking its entry into the landscape of the second quantum revolution. Optical frequency standards offer unprecedented precision by referencing atomic transitions that are fundamentally stable and immune to environmental drift. However, the challenge of developing such a system from scratch is unaffordable for a medium-sized National Metrology Institute (NMI), which seems to limit the ability of an institute such as CEM to contribute to this field of research. To overcome this, CEM has adopted a hybrid strategy, combining commercially available components with custom integration to accelerate deployment. This paper defines and implements an architecture adapted to the constraints of a medium-size NMI, where the main contribution is the systematic design, selection, and interconnection of the subsystems required to realize this standard. The rationale behind the system design is presented, detailing the integration of key elements for ion trapping, laser stabilization, frequency measurement, and system control. Current progress, ongoing developments, and future research directions are outlined, establishing the foundation for spectroscopic measurements and uncertainty evaluation. The project represents a strategic step toward strengthening national capabilities in quantum metrology for a medium-sized NMI.
Porawat Visutsak, Xiabi Liu, Chalothon Choothong
et al.
This paper describes a proposed method for preserving tangible cultural heritage by reconstructing a 3D model of cultural heritage using 2D captured images. The input data represent a set of multiple 2D images captured using different views around the object. An image registration technique is applied to configure the overlapping images with the depth of images computed to construct the 3D model. The automatic 3D reconstruction system consists of three steps: (1) Image registration for managing the overlapping of 2D input images; (2) Depth computation for managing image orientation and calibration; and (3) 3D reconstruction using point cloud and stereo-dense matching. We collected and recorded 2D images of tangible cultural heritage objects, such as high-relief and round-relief sculptures, using a low-cost digital camera. The performance analysis of the proposed method, in conjunction with the generation of 3D models of tangible cultural heritage, demonstrates significantly improved accuracy in depth information. This process effectively creates point cloud locations, particularly in high-contrast backgrounds.
James V. Roggeveen, Erik Y. Wang, Will Flintoft
et al.
Large language models (LLMs) have shown remarkable progress in mathematical problem-solving, but evaluation has largely focused on problems that have exact analytical solutions or involve formal proofs, often overlooking approximation-based problems ubiquitous in applied science and engineering. To fill this gap, we build on prior work and present HARDMath2, a dataset of 211 original problems covering the core topics in an introductory graduate applied math class, including boundary-layer analysis, WKB methods, asymptotic solutions of nonlinear partial differential equations, and the asymptotics of oscillatory integrals. This dataset was designed and verified by the students and instructors of a core graduate applied mathematics course at Harvard. We build the dataset through a novel collaborative environment that challenges students to write and refine difficult problems consistent with the class syllabus, peer-validate solutions, test different models, and automatically check LLM-generated solutions against their own answers and numerical ground truths. Evaluation results show that leading frontier models still struggle with many of the problems in the dataset, highlighting a gap in the mathematical reasoning skills of current LLMs. Importantly, students identified strategies to create increasingly difficult problems by interacting with the models and exploiting common failure modes. This back-and-forth with the models not only resulted in a richer and more challenging benchmark but also led to qualitative improvements in the students' understanding of the course material, which is increasingly important as we enter an age where state-of-the-art language models can solve many challenging problems across a wide domain of fields.
Alessandra Aimi, Giulia Di Credico, Heiko Gimperlein
This article studies a boundary element method for dynamic frictional contact between linearly elastic bodies. We formulate these problems as a variational inequality on the boundary, involving the elastodynamic Poincaré-Steklov operator. The variational inequality is solved in a mixed formulation using boundary elements in space and time. In the model problem of unilateral Tresca friction contact with a rigid obstacle we obtain an a priori estimate for the resulting Galerkin approximations. Numerical experiments in two space dimensions demonstrate the stability, energy conservation and convergence of the proposed method for contact problems involving concrete and steel in the linearly elastic regime. They address both unilateral and two-sided dynamic contact with Tresca or Coulomb friction.
Laiane Morais de Almeida, Carlos Erick Brito de Sousa
Ao longo dos anos, a divulgação científica e a educação ambiental vêm sendo alvo de muitas discussões e pesquisas no mundo todo, evidenciando a preocupação com a forma como as informações científicas e ambientais estão sendo divulgadas ao público geral, bem como sobre os materiais utilizados para essa divulgação. Nesse sentido, esses estudos apontam o texto de divulgação científica como potencial recurso didático para auxiliar no processo de difusão desses conhecimentos por tratar de temáticas atuais de forma clara e objetiva. Nesse sentido, o presente estudo analisa as propostas de atuação ambiental apresentadas nos textos da Revista Ciência Hoje das Crianças. Trata-se de uma pesquisa de abordagem qualitativa e de tipologia documental, na qual realizamos um estudo a partir do referencial da análise de conteúdo. A análise foi realizada em 34 revistas que correspondem às edições de junho de 2018 a junho de 2021, totalizando 81 textos que compõem o nosso corpus de análise. Em nossas análises, constatamos que a divulgação científica das questões ambientais na revista partem de uma concepção conservacionista do meio ambiente, priorizando os aspectos físicos e biológicos da crise ambiental, preocupando-se demasiadamente com a resolução de problemas ambientais, deixando de apresentar reflexões significativas sobre as relações sociais e políticas que são intrínsecas à questão ambiental, resultando numa leitura considerada simples, superficial e despolitizada do meio ambiente aos seus leitores.
Special aspects of education, Applied mathematics. Quantitative methods
In this paper, we have proposed a mathematical compartmental model with non-monotonic incidence and saturated treatment and we have validated the model with SARS infection in Hong Kong, 2003. We have analysed the stability of disease free and endemic equilibria as well as different bifurcations. We have shown that the epidemic disappears if the cure rate of treatment crosses a threshold value. We have obtained a necessary and sufficient condition for backward bifurcation, which shows the basic reproduction number less than unity is not sufficient to eradicate the disease completely. Saddle–node and Hopf bifurcation with respect to awareness factor have been investigated, which shows that the awareness factor is effective to change the disease dynamics. The model has been fitted to SARS cases in Hong Kong. The most effective parameters for controlling infections have been identified through sensitivity analysis. Moreover, we have investigated how the number of infected cases reduces if there was some vaccination polices in SARS infection. Finally, the model has been also used as an optimal control problem as vaccination and treatment controls are time dependent functions.
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective dimensions of mathematics. These approaches aim to make mathematics humanize. It proposes novel directions in mathematics, stressing that the ideas presented here are provisional. Furthermore, it argues that mathematics can take multiple humanized forms. Even traditional mathematics can be interpreted as a form of humanized mathematics. To support this perspective, several mathematical observations are provided. Additionally, a general approach to addressing the Riemann Hypothesis, focusing on proof by contradiction and mathematical logic, particularly model theory, is outlined. The paper also briefly reflects on my prior research through this idea on humanization and concludes with general remarks and future directions.
This is an exposition of the contributions of László Lovász to mathematics and computer science written on the occasion of the bestowal of the Abel Prize~2021 to him. Our survey, of course, cannot be exhaustive. We sketch remarkable results that solved well-known open and important problems and that -- in addition -- had lasting impact on the development of subsequent research and even started whole new theories. Although discrete mathematics is what one can call the Lovász home turf, his interests were, from the beginning of his academic career, much broader. He employed algebra, geometry, topology, analysis, stochastics, statistical physics, optimization, and complexity theory, to name a few, to contribute significantly to the explosive growth of combinatorics; but he also exported combinatorial techniques to many other fields, and thus built enduring bridges between several branches of mathematics and computer science. Topics such as computational convexity or topological combinatorics, for example, would not exist without his fundamental results. We also briefly mention his substantial influence on various developments in applied mathematics such as the optimization of real-world applications and cryptography.
Arnulf Jentzen, Benno Kuckuck, Philippe von Wurstemberger
This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including different artificial neural network (ANN) architectures (such as fully-connected feedforward ANNs, convolutional ANNs, recurrent ANNs, residual ANNs, and ANNs with batch normalization) and different optimization algorithms (such as the basic stochastic gradient descent (SGD) method, accelerated methods, and adaptive methods). We also cover several theoretical aspects of deep learning algorithms such as approximation capacities of ANNs (including a calculus for ANNs), optimization theory (including Kurdyka-Łojasiewicz inequalities), and generalization errors. In the last part of the book some deep learning approximation methods for PDEs are reviewed including physics-informed neural networks (PINNs) and deep Galerkin methods. We hope that this book will be useful for students and scientists who do not yet have any background in deep learning at all and would like to gain a solid foundation as well as for practitioners who would like to obtain a firmer mathematical understanding of the objects and methods considered in deep learning.
The construction of intelligent logistics by intelligent wireless sensing is a modern trend. Hence, this study uses the multistate flow network (MFN) to explore the actual environment of logistics delivery and to consider the different types of transportation routes available for logistics trucks in today’s practical environment, which have been neglected in previous studies. Two road types, namely highways and slow roads, with different speed limits are explored. The speed of the truck is fast on the highway, so the completion time of the single delivery is, of course, fast. However, it is also because of its high speed that it is subject to many other conditions. For example, if the turning angle of the truck is too large, there will be a risk of the truck overturning, which is a quite serious and important problem that must be included as a constraint. Moreover, highways limit the weight of trucks, so this limit is also included as a constraint. On the other hand, if the truck is driving on a slow road, where its speed is much slower than that of a highway, it is not limited by the turning angle. Nevertheless, regarding the weight capacity of trucks, although the same type of trucks running on slow roads can carry a weight capacity that is higher than the load weight limit of driving on the highway, slow roads also have a load weight limit. In addition to a truck’s aforementioned turning angle and load weight capacity, in today’s logistics delivery, time efficiency is extremely important, so the delivery completion time is also included as a constraint. Therefore, this study uses the improved d-MP method to study the reliability of logistics delivery in trucks driving on two types of roads under constraints to help enhance the construction of intelligent logistics with intelligent wireless sensing. An illustrative example in an actual environment is introduced.
Michael J. MacCoss, Javier Alfaro, Meni Wanunu
et al.
Mammalian cells have about 30,000-fold more protein molecules than mRNA molecules. This larger number of molecules and the associated larger dynamic range have major implications in the development of proteomics technologies. We examine these implications for both liquid chromatography-tandem mass spectrometry (LC-MS/MS) and single-molecule counting and provide estimates on how many molecules are routinely measured in proteomics experiments by LC-MS/MS. We review strategies that have been helpful for counting billions of protein molecules by LC-MS/MS and suggest that these strategies can benefit single-molecule methods, especially in mitigating the challenges of the wide dynamic range of the proteome. We also examine the theoretical possibilities for scaling up single-molecule and mass spectrometry proteomics approaches to quantifying the billions of protein molecules that make up the proteomes of our cells.
A key goal in studies of ecology and evolution is understanding the causes of phenotypic diversity in nature. Most traits of interest, such as those relating to morphology, life-history, immunity and behaviour are quantitative, and phenotypic variation is driven by the cumulative effects of genetic and environmental variation. The field of quantitative genetics aims to quantify the additive genetic component of this trait variance (i.e. the "heritability"), often with the underlying assumption that trait variance is driven by many loci of infinitesimal effects throughout the genome. This approach allows us to understand the evolutionary potential of natural populations and can be extended to examine the genetic covariation with fitness to predict responses to selection. Therefore, quantitative genetic studies are fundamental to understanding evolution in the wild. Over the last two decades, there has been a wealth of studies investigating trait heritabilities and genetic correlations, but these were initially limited to long-term studies of pedigreed populations or common-garden experiments. However, genomic technologies have since allowed quantitative genetic studies in a more diverse range of wild systems and has increased the opportunities for addressing outstanding questions in ecology and evolution. In particular, genomic studies can uncover the genetic basis of fitness-related quantitative traits, allowing a better understanding of their evolutionary dynamics. We organised this special issue to highlight new work and review recent advances at the cutting edge of "Wild Quantitative Genomics". In this Editorial, we will present some history of wild quantitative genetic and genomic studies, before discussing the main themes in the papers published in this special issue and highlighting the future outlook of this dynamic field.
A polynomial conjecture, associated with rational solutions including rogue wave solutions of the KdV equation, is presented. The conjecture can be used to show that for the bilinear KdV equation, an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders will again be a solution.
Church's simple type theory is often deemed too simple for elaborate mathematical constructions. In particular, doubts were raised whether schemes could be formalized in this setting and a challenge was issued. Schemes are sophisticated mathematical objects in algebraic geometry introduced by Alexander Grothendieck in 1960. In this article we report on a successful formalization of schemes in the simple type theory of the proof assistant Isabelle/HOL, and we discuss the design choices which make this work possible. We show in the particular case of schemes how the powerful dependent types of Coq or Lean can be traded for a minimalist apparatus called locales.