The Effect of User Experience on Designing Interactive Tool: A Case Study of Learning Images Compression

Technology has significantly emerged in various fields, including healthcare, government, and education. In the education field, students of all ages and backgrounds turn to modern technologies for learning instead of traditional methods, especially under challenging courses such as mathematics. However, students face many problems in understanding mathematical concepts and understanding how to benefit from them in real-life. Therefore, it can be challenging to design scientific materials suitable for learning mathematics and clarifying their applications in life that meet the students’ preferences. To solve this issue, we designed and developed an interactive platform based on user experience to learn an advanced concept in the idea of linear algebra called Singular Value Decomposition (SVD) and its applicability in image compression. The proposed platform considered the common design principles to map between the provider in terms of clear mathematical explanation and the receiver in terms of matching good user experience. Twenty participants between the ages of 16 and 30 tested the proposed platform. The results showed that learning using it gives better results than learning traditionally in terms of the number of correct and incorrect actions, effectiveness, efficiency, and safety factors. Consequently, we can say that designing an interactive learning platform to explain an advanced mathematical concept and clarify its applications in real-life is preferable by considering and following the common design principles.

Model Smoke Stream Adsorption over Cellulose Acetate Stick with Three-dimensional Temperature Gradient by Combining in-situ DRIFTS with Infrared Thermal Imaging

Understanding the adsorption of the smoke stream (SR) on cellulose acetate stick as cigarette filter with different temperatures is beneficial for controlling chemical emissions and reducing the toxic effect of smoking on human health. However the investigation of corresponding adsorption properties was missing because the adsorption of smoke stream (SR) on cigarette cellulose acetate stick is sensitive with the three-dimensional temperature gradient. In this work, the adsorption of typical smoke stream substances, such as CO, propylene glycol, formaldehyde, and acetone, on cellulose acetate stick were studied by in-situ diffuse reflectance Fourier transform infrared spectroscopy with different temperatures assisted by the infrared thermal imaging method. The adsorption capacities of cellulose acetate stick to these typical smoke stream substances is dependent on the adsorption time and temperature. The adsorption properties all fitted well with the Freundlich model. By a spectroscopic and mathematical explanation, quantifying contours of adsorption was performed. The 3D model of the normalized CO adsorption of cellulose acetate stick versus the spatial coordinates and time was established. This study gives unparalleled insight into smoking release characteristics of tobacco filtered by cellulose acetate and regulating cellulose acetate stick for reducing the negative effect of smoke on human health.

Understanding small Chinese cities as COVID-19 hotspots with an urban epidemic hazard index

Multiple small- to middle-scale cities, mostly located in northern China, became epidemic hotspots during the second wave of the spread of COVID-19 in early 2021. Despite qualitative discussions of potential social-economic causes, it remains unclear how this unordinary pattern could be substantiated with quantitative explanations. Through the development of an urban epidemic hazard index (EpiRank) for Chinese prefectural districts, we came up with a mathematical explanation for this phenomenon. The index is constructed via epidemic simulations on a multi-layer transportation network interconnecting local SEIR transmission dynamics, which characterizes intra- and inter-city population flow with a granular mathematical description. Essentially, we argue that these highlighted small towns possess greater epidemic hazards due to the combined effect of large local population and small inter-city transportation. The ratio of total population to population outflow could serve as an alternative city-specific indicator of such hazards, but its effectiveness is not as good as EpiRank, where contributions from other cities in determining a specific city’s epidemic hazard are captured via the network approach. Population alone and city GDP are not valid signals for this indication. The proposed index is applicable to different epidemic settings and can be useful for the risk assessment and response planning of urban epidemic hazards in China. The model framework is modularized and the analysis can be extended to other nations.

MATHEMATICAL EXPLANATION OF SUSTAINABLE POLITICAL DEVELOPMENT OF THE SOCIETY

Обсуждается возможность математического объяснения современных социально-политических событий в Российской Федерации и за рубежом, что проявляют скрытые закономерности расслоения и изоляции общества на всех уровнях его организации. Формируются новые модели дистанционного взаимодействия - коммуникации разных социальных слоев, объединение их в комплексы сетей информационно-функциональных связей. Эти закономерности сквозным образом в разных масштабах описываются метатеоретическими моделями и методами расслоения с использованием универсальных математических уравнений, аксиоматической теории деятельности и устойчивого развития, раскрывающими этические, правовые и политические аспекты сосуществования. Содержательная интерпретация формального подхода основывается на идеях трансцендентальной аргументации И.Канта - автора морально-нравственного категорического императива, концепции правового государства и политической философии. Формулируется безусловная идея устойчивого мироустройства, которая берется за основу всякого общественного закона как выражения идеала, прообраза будущего, что становится основанием для предсказания прогрессивных форм политической деятельности. The opportunity of a mathematical explanation of modern socio-political events in the Russian Federation and abroad is discussed. It reveals hidden patterns of stratification and isolation of society at all levels of its organization. New models of remote interaction are being formed: communication of different social strata, combining them into complexes of networks of information and functional connections. These laws are described in a through manner at different scales by meta-theoretical models and bundle methods using universal mathematical equations, axiomatic theory of activity and sustainable development, which combines the ethical, legal and political aspects of coexistence. The content interpretation of the formal approach is based on the ideas of the transcendental argumentation of I. Kant as the author of moral categorical imperative and the concept of the rule of law and political philosophy. An unconditional idea of a stable world order is formed, which is taken as social law expressing an ideal prototype of the future and the basis for predicting progressive forms of political activity.

Supplemental Material: Emergent simplicity despite local complexity in eroding fluvial landscapes

Movies S1 and S2 (showing examples of the time dependent behavior of the threshold model), and a simple mathematical explanation for how models of physical erosion can be simplified to few parameters.<br>

Supplemental Material: Emergent simplicity despite local complexity in eroding fluvial landscapes

Movies S1 and S2 (showing examples of the time dependent behavior of the threshold model), and a simple mathematical explanation for how models of physical erosion can be simplified to few parameters.<br>