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This article, titled "Historic Behavior in Nonautonomous Rock-Paper-Scissors Dynamics," explores the concept of historic behavior in dynamical systems. The author challenges the widely held belief that replicator equations in evolutionary game theory satisfy the "Folk Theorem of Evolutionary Game Theory." The paper proposes a class of replicator equations that exhibit historic behavior, where the time averages of the orbit do not converge. The article also presents some auxiliary results and provides a proof for the main theorem. The research was supported by ongoing institutional funding, and the author declares no conflicts of interest. [Extracted from the article]

Interventions targeting cognitive control processes, such as Executive Functions (EF) have recently been experimented to enhance early math skills. This pilot study explored the feasibility and effectiveness of an intervention integrating EF activities into the mathematical domain among second‐grade students. One hundred and four typically‐developing‐children were assigned to either a group that underwent the intervention (Trained Group; n = 58) or a group that continued with daily didactic activities (Control Group; n = 46). The training lasted for 8 weeks and included both home‐based digital and school‐based paper activities. According to teachers' feedback, the intervention was highly appreciated by children and compatible with classical school curricula. The Trained Group improved in behavioral self‐regulation, math abilities and problem‐solving in comparison to the Control Group. Notably, within the Trained Group, benefits of the training were higher in children with high working memory. This training offers a model to support math learning in primary school, considering inter‐individual differences in EF. Early mathematical skills can be enhanced through cognitive control processes, notably Executive Functions (EF). This study proposes an intervention that combines EF activities with mathematical and problem‐solving exercises. The evaluation by participating teachers indicates that the intervention was both feasible and integrated into the school curriculum. The results show that the Trained Group exhibited improvements in behavioral self‐regulation, mathematical skills and problem‐solving, surpassing the achievement of the Control Group. [ABSTRACT FROM AUTHOR]

[Display omitted] • Acidification defines the preservation state of Xuan paper in museums. • Photochemical damage to Xuan paper is owing to oxidation and hydrolysis reactions. • FTIR combined with PCA is able to evaluate photochemical damage law of Xuan paper. • pH values, λ, and their interaction promotes photochemical damage to Xuan paper. • Photochemical damage is fitted as a mathematical function of pH values and λ. In museums, there is a huge storage of Xuan paper cultural relics with profound historical and artistic significances. Exploring the photochemical damage behavior of Xuan paper that is generally in acidification, namely its damage mechanisms and laws, is crucial for the preventive lighting protection for paper cultural relics. In this study, the accelerated aging experiments in the range of visible light were conducted on Xuan paper samples with different degrees of acidification. The photochemical damage mechanisms of samples were traced, which is related with the synergistic effects of oxidation and hydrolysis reactions. It can be found that there is an effect of acidification, a long-standing material property of Xuan paper, on its damage, which further defines its preservation state in museums. On this basis, a spectral quantification method of infrared spectra combined with the principal component analysis was proposed to comprehensively analyze the photochemical damage law of Xuan paper in different preservation states. The analysis shows that the effect of acidification degree (pH values), spectra wavelength (λ), and their interaction on the damage to Xuan paper are statistically significant. Furthermore, the fitted mathematical function of pH values and λ is of great importance for evaluating photochemical damage, in order to further develop preventive lighting protection applications. [ABSTRACT FROM AUTHOR]

The aim of this research is to advance in the teaching-learning process of representing quadratic functions, both with pencil and paper and with a technological tool. For this purpose, a didactic experience is presented. Firstly, it is explained in the traditional way how to graph a quadratic function; secondly, students are introduced to the GeoGebra software. It provides a categorization of the different errors and difficulties of the students, the comparison between a graphic representation with paper and pencil and a representation with GeoGebra, and the improvement with the technological tool. [ABSTRACT FROM AUTHOR]

In their celebrated paper (Furst et al., Math. Syst. Theory 17(1), 13-27 (12)), Furst, Saxe, and Sipser used random restrictions to reveal the weakness of Boolean circuits of bounded depth, establishing that constant-depth and polynomial-size circuits cannot compute the parity function. Such local restrictions have played important roles and have found many applications in complexity analysis and algorithm design over the past three decades. In this article, we give a brief overview of two intriguing applications of local restrictions: the first one is for the Isomorphism Conjecture and the second one is for moderately exponential time algorithms for the Boolean formula satisfiability problem. [ABSTRACT FROM AUTHOR]

Abstract: The study used the simulated e-paper to investigate how the bending radius of curvature (−10cm, plane, and 10cm) and 12 text/background color-combinations of e-paper affect subjects’ visual performance and subjective preference under various ambient illuminance conditions (200 and 500lx). Analysis results indicated that the bending curvature and ambient illuminance did not significantly affect subjects’ visual performance. However, subjects visual performance differed significantly for different text/background color combinations of the simulated e-paper. When the background color of the simulated e-paper was set to yellow-like condition and the luminance of the text was low (2.2 and 4.6cd/m2), subjects’ visual performance was best. Regarding the subjective preferences of subjects, the results of this research also demonstrated that the bending curvature, text/background color combinations and ambient illuminance all significantly affected the subjective preferences of subjects. Subjects exhibited the best preference under the following settings: bending curvature of the simulated e-paper set to plane; background color of the simulated e-paper set to yellow-like condition and low text luminance (2.2 or 4.6cd/m2); high ambient illuminance (500lx). [Copyright &y& Elsevier]

In citation networks, the content relativity of papers is a precondition of engendering citations, which is hard to model by a topological graph. A geometric graph is proposed to predict some features of the citation networks with exponentially growing papers, which addresses the precondition by using coordinates of nodes to model the research contents of papers, and geometric distances between nodes to diversities of research contents between papers. Citations between modeled papers are drawn according to a geometric rule, which addresses the precondition as well as some other factors engendering citations, namely academic influences of papers, aging of those influences, and incomplete copying of references. Instead of cumulative advantage of degree, the model illustrates that the scale-free property of modeled networks arises from the inhomogeneous academic influences of modeled papers. The model can also reproduce some other statistical features of citation networks, e.g. in- and out-assortativities, which show the model provides a suitable tool to understand some aspects of citation networks by geometry. [ABSTRACT FROM AUTHOR]

Many results have been obtained when studying scientific papers citations databases in a network perspective. Articles can be ranked according to their current in-degree and their future popularity or citation counts can even be predicted. The dynamical properties of such networks and the observation of the time evolution of their nodes started more recently. This work adopts an evolutionary perspective and proposes an original algorithm for the construction of genealogical trees of scientific papers on the basis of their citation count evolution in time. The fitness of a paper now amounts to its in-degree growing trend and a “dying” paper will suddenly see this trend declining in time. It will give birth and be taken over by some of its most prevalent citing “offspring”. Practically, this might be used to trace the successive published milestones of a research field. [ABSTRACT FROM AUTHOR]

A simple scheme that achieves the capacity and the reliability function of the wideband Costa dirty-paper channel is proposed. The scheme can be interpreted as an opportunistic version of pulse position modulation (PPM). This interpretation suggests a natural generalization of the scheme which we show to achieve the capacity per unit cost of Gel'fand-Pinsker channels with a zero-cost input letter. [ABSTRACT FROM AUTHOR]

In this tutorial note we consider the class of non-convex semi-infinite optimization problems which are defined by (one or) finitely many objective functions as well as infinitely many constraints in a finitedimensional space. We present an overview of recent results on the so-called p-power transformation which changes the original problem equivalently locally around a solution point. This transformation is a convexification procedure for the Lagrangian where the functions in the original problem are substituted by their p-th powers. As a consequence, the convexity of the so-transformed Lagrangian allows the application of local duality theory and corresponding solution methods locally around this solution point of the original problem. [ABSTRACT FROM AUTHOR]