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\"Imagine trying to understand a stained glass window by breaking it into pieces and examining it one shard at a time. While you could probably learn a lot about each piece, you would have no idea about what the entire picture looks like. This is reductionism--the idea that to understand the world we only need to study its pieces--and it is how most social scientists approach their work. In [this book], social scientist and economist John H. Miller shows why we need to start looking at whole pictures. For one thing, whether we are talking about stock markets, computer networks, or biological organisms, individual parts only make sense when we remember that they are part of larger wholes. And perhaps more importantly, those wholes can take on behaviors that are strikingly different from that of their pieces\"--Amazon.com.

Complex Analysis for Science and Technology is a textbook for undergraduate and postgraduate students undertaking science, technology, engineering and mathematics (STEM) courses. The book begins with an introduction to basic complex numbers, followed by chapters covering complex functions, integrals, transformations and conformal mapping. Topics such as complex series and residue theory are also covered. Key features of this textbook include: -simple, easy-to-understand explanations of relevant concepts -a wide range of simple and complex examples -several figures where appropriate

Special topic volume with invited peer reviewed papers only.

Background The effects of the coronavirus disease 2019 (COVID-19) pandemic and subsequent policies in the Netherlands extended beyond healthcare, impacting other societal systems such as education. This study aims to conceptualize a coupled education–healthcare system during a pandemic and identify key variables and relations that affect the accessibility of both systems. This is essential to address the interconnected nature of pandemic policymaking and design policies that account for possible unintended consequences that interventions in healthcare may have on education and vice versa. Methods Group model building and in-depth interviews with actors from healthcare and education were used to develop a coupled causal loop diagram of healthcare and education accessibility in the Netherlands during a pandemic. The causal loop diagram is analysed with cross-impact analysis to identify key leverage points, monitoring variables, feedback loops and relations between healthcare and education. Results Six causal relations were identified between healthcare and education, indicating a relevant impact of healthcare on education during pandemics. Cross-impact analysis identified 24 leverage points, of which 10 were in healthcare, 11 in education and 4 in the contextual environment. During the COVID-19 pandemic in the Netherlands, healthcare utilized all these leverage points, education utilized six and two were used not pertaining to healthcare or education but the contextual environment. Leverage points included the availability and wellbeing of personnel, number of patients, progress of pupils/students and resources. Seven monitoring variables included the availability of personnel, resources in education and progress of pupils/students, and were utilized in healthcare and education during the pandemic. Four feedback loops were found, of which three are reinforcing. One large balancing feedback loop is situated between the healthcare and education system, indicating mutual dependency to maintain staff for the accessibility of healthcare and education. Conclusions Group model building, in-depth interviews and cross-impact analysis identified key variables, causal relations and feedback loops illustrating the coupled nature of healthcare and education during pandemics. This highlights the need for integrated policymaking that addresses and considers coupled systems to ensure accessibility to both healthcare and education. The finalized model can serve as a tool to support such integrated policymaking.

This paper respectively considers passivity problem and pinning passivity problem for coupled delayed reaction–diffusion neural networks (CDRDNNs). By construction of appropriate Lyapunov functionals and utilization of inequality techniques, several passivity conditions are derived for the CDRDNNs. Moreover, the pinning control technique is developed to obtain some passivity criteria for CDRDNNs. Finally, two numerical examples are also provided to verify the correctness of the theoretical results.

Neural network algorithms on principal component analysis (PCA) and minor component analysis (MCA) are of importance in signal processing. Unified (dual purpose) algorithm is capable of both PCA and MCA, thus it is valuable for reducing the complexity and the cost of hardware implementations. Coupled algorithm can mitigate the speed-stability problem which exists in most noncoupled algorithms. Though unified algorithm and coupled algorithm have these advantages compared with single purpose algorithm and noncoupled algorithm, respectively, there are only few of unified algorithms and coupled algorithms have been proposed. Moreover, to the best of the authors’ knowledge, there is no algorithm which is both unified and coupled has been proposed. In this paper, based on a novel information criterion, we propose two self-stabilizing algorithms which are both unified and coupled. In the derivation of our algorithms, it is easier to obtain the results compared with traditional methods, because it is not needed to calculate the inverse Hessian matrix. Experiment results show that the proposed algorithms perform better than existing coupled algorithms and unified algorithms.

In the domain of science concerned with systems structure and behavior, the issue of the relationship between the micro and the macro level is of key importance. This book concentrates on the interplay between these levels and has a special focus on the level “in between” — the meso level. An investigation of those links is made through a number of cases from different domains of science, including physics, chemistry, ecology, social science, economics and technology. What is evident is that there are facets regarding meso-level issues that are similar between cases, but also that the domains differ in various ways. This is particularly exemplified by the differences in perspectives from which the natural and social sciences deal with scaling issues. The various examples provided in this book mirror its overriding theme: systems complexity.

High technology industries are in desperate need for adequate tools to assess the validity of simulations produced by ever faster computers for perennial unstable problems. In order to meet these industrial expectations, applied mathematicians are facing a formidable challenge summarized by these words — nonlinearity and coupling. This book is unique as it proposes truly original solutions: (1) Using hypercomputation in quadratic algebras, as opposed to the traditional use of linear vector spaces in the 20th century; (2) complementing the classical linear logic by the complex logic which expresses the creative potential of the complex plane.

Successfully coping with complex, real-world challenges, such as those related to sustainable development and the resilience of coupled human–environment systems, calls increasingly for adapted forms of education and extended competences. Hence, we argue that, beyond knowledge and expertise in professional domains, additionally, personal, systemic, creative, and sociocultural competences are required to meet such challenges. Herefor, institutions of higher and continuing education play a crucial role. In this paper, universities as institutions of higher education are critically considered in relation to delivering education for sustainable development by raising awareness and providing the necessary competences to cope with complex problems such as sustainable development through effective forms of higher and continuing education as well as training. Research on attitudes and perceptions regarding sustainable development and the perceived need for comprehensive competences required to deal with such complex problems is still lacking. Our study provides a first attempt to elucidate core aspects of these attitudes, perceptions, and competences aiming to contribute to future, more tailored education approaches. We discuss the outcomes of a survey on sustainability in teaching and learning conducted at four Austrian universities. The analyzed sample comprised 3200 students as the recipients of, and 498 lecturers as the providers of, sustainability education in various academic disciplines at four distinct Austrian universities. Applying a questionnaire-based investigation of self-reported sustainability-related perceptions, attitudes, and competences and conducting factor analysis and cluster analysis, five sustainability types were identified that revealed a type of specific core awareness of sustainability and the perception of required competences related to sustainable development. The results presented are positioned to build a basis for further investigation that goes beyond the self-reported assessments to enable a comparison with sustainability-related, real-world problem-solving performance.

A new reformulation of a free boundary problem for the Stokes equations, which govern a viscous flow with an overdetermined condition on the free boundary, is proposed. The idea of the method is to transform the governing equations into a boundary value problem with a complex Robin boundary condition that couples the two boundary conditions on the free boundary. The proposed formulation gives rise to a new cost functional that apparently has not been exploited in the context of free surface problems. The shape derivative of the cost function, constructed using the imaginary part of the velocity and pressure solution in the whole domain, is computed in order to identify the free boundary. The shape gradient information is then utilized in a domain variation method based on a preconditioned steepest descent algorithm to solve the shape optimization problem. Numerical results illustrating the applicability of the method are provided in both two and three spatial dimensions. For validation and evaluation of the method, the numerical results are compared with those obtained via the classical tracking-Dirichlet-data cost functional approach.