International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Biological Protein Patterning Systems across the Domains of Life: from Experiments to Modelling

Distinct localisation of macromolecular structures relative to cell shape is a common feature across the domains of life. One mechanism for achieving spatiotemporal intracellular organisation is the Turing reaction-diffusion system (e.g. Min system in the bacterium Escherichia coli controlling in cell division). In this thesis, I explore potential Turing systems in archaea and eukaryotes as well as the effects of subdiffusion. Recently, a MinD homologue, MinD4, in the archaeon Haloferax volcanii was found to form a dynamic spatiotemporal pattern that is distinct from E. coli in its localisation and function. I investigate all four archaeal Min paralogue systems in H. volcanii by identifying four putative MinD activator proteins based on their genomic location and show that they alter motility but do not control MinD4 patterning. Additionally, one of these proteins shows remarkably fast dynamic motion with speeds comparable to eukaryotic molecular motors, while its function appears to be to control motility via interaction with the archaellum. In metazoa, neurons are highly specialised cells whose functions rely on the proper segregation of proteins to the axonal and somatodendritic compartments. These compartments are bounded by a structure called the axon initial segment (AIS) which is precisely positioned in the proximal axonal region during early neuronal development. How neurons control these self-organised localisations is poorly understood. Using a top-down analysis of developing neurons in vitro, I show that the AIS lies at the nodal plane of the first non-homogeneous spatial harmonic of the neuron shape while a key axonal protein, Tau, is distributed with a concentration that matches the same harmonic. These results are consistent with an underlying Turing patterning system which remains to be identified. The complex intracellular environment often gives rise to the subdiffusive dynamics of molecules that may affect patterning. To simulate the subdiffusive transport of biopolymers, I develop a stochastic simulation algorithm based on the continuous time random walk framework, which is then applied to a model of a dimeric molecular motor. This provides insight into the effects of subdiffusion on motor dynamics, where subdiffusion reduces motor speed while increasing the stall force. Overall, this thesis makes progress towards understanding intracellular patterning systems in different organisms, across the domains of life

Music : healing and meaning

vii, 52 leaves ; 29 cm. --This project considers music's relationship to humanity. A perspective from the informational basis of academic music therapy is interwoven with reflective theory about music's healing capacity. The writer's music healing experiences as a professional musician and apprentice to the music healing tradition of Indigenous South (Quechua) and Central (Huichol) America guide the reflective theory. In this way, the writer desires to integrate the Western academic and South/Central indigenous American understandings of music therapy. Diverse genres are employed, including poetry, narrative, and academic styles to invoke and relate different perspectives of the same understanding of music's therapeutic and curative potential

Fractional Calculus and the Future of Science

Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding