A set of semi-analytic techniques based on Fourier analysis is used to solve wave-scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are the newly developed conformal mapping methods, wave splitting, Fourier series expansions in eigenfunctions to non-normal operators, the building block method or the cascade technique, Dirichlet-to-Neumann operators, and reformulation in terms of stable differential equations for reflection and transmission matrices. For an example, the results show good correspondence with a finite element method solution to the same problem in the low- and medium-frequency domains. The Fourier method complements finite element analysis as a waveguide simulation tool. For inverse engineering involving tuning of straight waveguide parts joining complicated waveguide elements, the Fourier method is an attractive alternative including time aspects. The prime motivation for the Fourier method is its added physical understanding primarily at low frequencies.

Evolutionary rescue is the process whereby a declining population may start growing again, thus avoiding extinction, via an increase in the frequency of fitter genotypes. These genotypes may either already be present in the population in small numbers, or arise by mutation as the population declines. We present a simple two-type discrete-time branching process model and use it to obtain results such as the probability of rescue, the shape of the population growth curve of a rescued population, and the time until the first rescuing mutation occurs. Comparisons are made to existing results in the literature in cases where both the mutation rate and the selective advantage of the beneficial mutations are small.

Speciation is characterized by the development of reproductive isolating barriers between diverging groups. A seminal paper of a mathematical model of speciation was published by Orr (1995), extended by Livingstone et al. (2012) to incorporate interaction networks. Here, we further develop the model to take into account the possibility of different substitution rates for network nodes of different connectivity. Mathematically, this amounts to sampling nodes from an undirected graph where the inclusion probability for a given node depends on its degree (number of connecting edges). We establish formulas for the rate of speciation and identify a crucial parameter that is a measure of the deviation from simple random sampling.

The pandemic has forced teaching as well as as the Software Development industry, to be performed remotely. The educational institutions are therefore facing the situation of training and steering the students in, not only complex work, but also in remote-based work and it processes. Specific challenges here relate to project work with larger groups of developers, with testing, and integration of technical components for complete solutions, but the psychosocial factors come into play as well. This paper considers the situation that has arisen as a consequence of the pandemic and regards how project-based courses should be adapted to ‘The New Normal’. In focus is a course in Software Engineering, where a large-scaled project shall be developed remotely. Representatives from IT-companies act at the course remote, and at specific occurrences. The course is observed by the teachers to see its outcome, as well as different aspects on attitudes towards future remote work. Interviews and surveys regarding attitudes of students, as well as involved company representatives are presented, where the focus is on process, productivity, work environment, interest in remote work, as well as social aspects. The main findings, based on the surveys, motivates hybrid solutions for university courses, to meet the corresponding companies’ way of future working style.