A set of elementary building blocks undergoes self-assembly if local interactions govern how this set forms intricate structures. Self-assembly has been widely observed in nature, ranging from the field of crystallography to the study of viruses and multicellular organisms. A natural question is whether a model of self-assembly can capture the hierarchical growth seen in nature or in other fields of mathematics. In this work, we consider hierarchical growth in substitution rules; informally, a substitution rule describes the iterated process by which the polygons of a given set are individually enlarged and dissected. We develop the Polygonal Two-Handed Assembly Model (p-2HAM) where building blocks, or tiles, are polygons and growth occurs when tiles bind to one another via matching, complementary bonds on adjacent sides; the resulting assemblies can then be used to construct new, larger structures. The p-2HAM is based on a handful of well-studied models, notably the Two-Handed Assembly Model and the polygonal free-body Tile Assembly Model. The primary focus of our work is to provide conditions which are either necessary or sufficient for the ``bordered simulation'' substitution rules. By this, we mean that a border made up of tiles is allowed to form around an assembly which then coordinates how the assembly interacts with other assemblies. In our main result, we provide a construction which gives a sufficient condition for bordered simulation. This condition is presented in graph theoretic terms and considers the adjacency of the polygons in the tilings associated to a given substitution rule. Alongside our results, we consider a collection of over one hundred substitution rules from various sources. We show that only the substitution rules in this collection which satisfy our sufficient condition admit bordered simulation. We conclude by considering open questions related to simulating substitution rules and to hierarchical growth in general.

<p>The minimum ecologically viable population size (MEVP) of a species describes the minimum size at which the species itself or another species in the same ecosystem goes extinct as a result of the loss of inter-specific interactions. The MEVP shows a good potential for use as a tool for exploring the mechanisms behind species extinctions, but presently only a small amount of research has been done that takes advantage of this. In this study the MEVP is used to investigate what properties of species can be used as good indicators of ecological importance. 100 large computer generated food webs were created with an assembly model and the reduction in density that was necessary to induce an extinction event in the web was subsequently determined for each species within the webs. This change in density was then correlated with 28 different properties, measured for each species. The results show that properties that measure how well connected a species is, as well as measures of the species role as a prey item in the web are the ones with the greatest potential to find species with high MEVP. Further, the results put emphasis on the importance of regarding the web as a whole when working with species extinctions, while also highlighting the usefulness of the MEVP concept.</p>

The minimum ecologically viable population size (MEVP) of a species describes the minimum size at which the species itself or another species in the same ecosystem goes extinct as a result of the loss of inter-specific interactions. The MEVP shows a good potential for use as a tool for exploring the mechanisms behind species extinctions, but presently only a small amount of research has been done that takes advantage of this. In this study the MEVP is used to investigate what properties of species can be used as good indicators of ecological importance. 100 large computer generated food webs were created with an assembly model and the reduction in density that was necessary to induce an extinction event in the web was subsequently determined for each species within the webs. This change in density was then correlated with 28 different properties, measured for each species. The results show that properties that measure how well connected a species is, as well as measures of the species role as a prey item in the web are the ones with the greatest potential to find species with high MEVP. Further, the results put emphasis on the importance of regarding the web as a whole when working with species extinctions, while also highlighting the usefulness of the MEVP concept.

<p>Doktorska disertacija ukazuje na model dijagnostike stanja koji zbog svog istraživačkog karaktera može dovesti do novih naučnih saznanja i metoda praćenja uticaja najvažnijih parametara na pouzdanost vozila, izučavanja ključnih performansi iz oblasti održavanja motornih vozila. Njen cilj je da teorijski i empirijski, kritički, sistematski i kontrolisano defini&scaron;e model dijagnostike stanja kao i da izvr&scaron;i izbor optimalnih parametara, radne temperature i pohabanosti ležajeva, a sve u cilju određivanja sigurnosti funkcionisanja sastavnih komponenti motornih vozila. Proces istraživanja modela predstavlja vezu između periodičnosti provere parametara stanja u radu i otkaza sastavnih komponenata motornih vozila. Simulacijom se može prognozirati vremenski trenutak zamene komponenata pre nego &scaron;to dođe do njihovog otkaza. Dati model je univerzalnog tipa iz razloga &scaron;to se može primeniti i na složene sisteme, bez obzira na dimenzije komponenti sklopova motornih vozila.</p> / <p>PhD dissertation indicates a model of state diagnostics, which due to its research nature, could lead to new scientific knowledge and methods of monitoring the impact of the most important parameters on vehicle reliability, the study of key performance in the field of maintenance of motor vehicles. Its aim is to theoretically and empirically, critically, systematically and in a controlled way define the model of conditions diagnostic and to make the selection of optimal parameters, operating temperature and wear of bearings, all for the purpose of determining the security of functioning of the parts and components of motor vehicles. The research process of a model represents the relationship between the periodicity of testing parameters of the operating mode and cancellation of integral components of motor vehicles. The simulation can predict time for replacement of components before they cancel. The present model is of a universal type because it can be applied to complex systems, regardless of the dimensions of the components of motor vehicles.</p>

DNA nanotechnology is a rapidly developing field that creates nanoscale devices from DNA, which enables novel interfaces with biological material. Their therapeutic use is envisioned and applications in other areas of basic science have already been found. These devices function at physiological conditions and, owing to their molecular scale, are subject to thermal fluctuations during both preparation and operation of the device. Troubleshooting a failed device is often difficult and we develop models to characterise two separate devices: DNA walkers and DNA origami. Our framework is that of continuous-time Markov chains, abstracting away much of the underlying physics. The resulting models are coarse but enable analysis of system-level performance, such as ‘the molecular computation eventually returns the correct answer with high probability’. We examine the applicability of probabilistic model checking to provide guarantees on the behaviour of nanoscale devices, and to this end we develop novel model checking methodology. We model a DNA walker that autonomously navigates a series of junctions, and we derive design principles that increase the probability of correct computational output. We also develop a novel parameter synthesis method for continuous-time Markov chains, for which the synthesised models guarantee a predetermined level of performance. Finally, we develop a novel discrete stochastic assembly model of DNA origami from first principles. DNA origami is a widespread method for creating nanoscale structures from DNA. Our model qualitatively reproduces experimentally observed behaviour and using the model we are able to rationally steer the folding pathway of a novel polymorphic DNA origami tile, controlling the eventual shape.