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This paper analyzes the controllability of constant coefficient linear differential equations and presents two proofs of a major theorem on controllability. Properties of nearly-non-negative matrices are discussed and in particular a theorem on the behavior of the exponential matrix of nearly-non-negative matrices is proven. These results are then used to prove that the reachable set for systems with nearly-non-negative matrices is limited to the positive hyperoctant.

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A Thurston map whose postcritical set consists of exactly four points and for which the local degree at each of its critical points is 2 is called textit{nearly Euclidean}. These maps were specified to parse Thurston's combinatorial characterization of rational functions. We determine an extension of the half-space theorem which provides an open hyperbolic half-space such that the negative reciprocal of any fixed slope value is excluded from the boundary of the half-space. / Master of Science / Thurston proved necessary and sufficient conditions under which a certain class of mappings defined topologically are equivalent, in a precise sense which can be considered less strict than topological conjugacy, to a rational map. The conditions presented in the proof of this theorem are not ones for which computational algorithms are easily admitted in all settings. Nearly Euclidean Thurston maps are a sub-class of the maps to which this theorem is applicable and for which an abundance of information is algorithmically attainable. We extend a theorem in this setting. One main example which speaks to the utility of this extension is in determining when certain rational maps arise as matings of polynomials.

Για ένα, μάλλον, μακρύ διάστημα, (1950-1975) οι Μαθηματικοί ασχολήθηκαν με την εμφύτευση μιας αντιμεταθετικής τοπολογικής ημιομάδας σε ομάδα. Είναι γνωστό ότι για ημιομάδα S έχουμε αλγεβρική εμφύτευση στο σχέση ισοδυναμίας = , όπου στοιχεία της καινούργιας ομάδας). Το νέο στοιχείο είναι ότι ενώ η συνθήκη εμφύτευσης αναφέρεται σε Ομοιόμορφο χώρο, έχει εισαχθεί ο Η- μι-Ομοιόμορφος χώρος. Οι διαφορές μεταξύ των δύο χώρων είναι τεράστιες και ακριβώς, εκεί έγκειται η δημιουργικότητα της νέας δομής. Έτσι, η πρώτη θεώρηση για τη διατριβή είναι η προσπάθεια επιστημόνων να βρούνε συνθήκες, ώστε να μπορεί μια τοπολογική αντιμεταθετική ημιομάδα ( S,.,τ) (με τη συνήθη έννοια των . και τ ) να εμφυτεύεται στη δομή η γνωστή ισοδυ- ναμία ad=bc αν ). Τα έξη πρώτα εδάφια είναι εισαγωγικά. Στη συνέχεια εκθέτουμε όλη τη μεθοδο- λογία του θέματος / --

The study of crowding effects on particle diffusion is a large subject with implications in many scientific areas. The studies span from pure theoretical calculations to experiments actually measuring the movement of proteins diffusing in a cell. Even though the subject is important and has been studied heavily there are still aspects not fully understood.   This report describes a Monte Carlo simulation approach (Gillespie algorithm) to study the effects of crowding on particle diffusion in a quasi one-dimensional system. With quasi meaning that the particles diffuses on a one-dimensional lattice but has the possibility to disassociate from the lattice and then rebind at a latter stage. Different binding strategies are considered: rebinding to the same location and randomly choosing the binding location. The focus of the study is how these strategies affects the mobility (diffusion coefficient) of a tracer particle. The main result of this thesis is a graph showing the diffusion coefficient as a function of the binding rate for different binding strategies and particle densities. We provide analytical estimates for the diffusion coefficient in the unbinding rate limits which show good agreement with the simulations. / Hur "trängsel" (från engelskans "crowding" t ex molecular crowding) påverkar diffusionsprocesser är viktigt inom många olika vetenskapliga områden. Forskningen som för tillfället utförs sträcker sig från rent teoretiska beräkningar till experiments där man kan följa enskilda proteiners rörelse i en cell. Även fast ämnet är viktig och väl undersökt finns det fortfarande många aspekter som man inte förstår till fullo. I det här examensarbetet beskrivs en Monte Carlo metod (Gillespie algoritmen) för att studera hur trängsel påverkar en partikel som diffunderar i ett "nästan" en-dimensonellt system. Det är nästan en-dimensionellt i det avsedde att partiklarna diffunderar på ett gitter men kan binda av från gittret och binda tillbaka i ett senare skedde. Olika metoder för hur partiklarna binder till gittret undersöks: Återbinding till avbindingsplatsen och slumpmässigt vald återbindingsplats. Fokus ligger på att förklara hur dessa påverkar mobiliteten (diffusionskonstanten) av en spårningspartikel (tracer particle). Resultatet är en graf som visar diffusionskonstanten för spårningspartikeln som en funktion av avbindingsfrekvens för olika bindingstrategier och partikeldensiteter. Vi ger också analytiska resultat i gränsvärdet för höga och låga avbindingstakter vilka stämmer bra överens med simuleringar.

This thesis consists of four papers that concern error estimates for the Born-Oppenheimer molecular dynamics, and adaptive algorithms for the Car-Parrinello and Ehrenfest molecular dynamics. In Paper I, we study error estimates for the Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces. The paper first proves an error estimate showing that the difference of the values of observables for the time-independent Schrödinger equation, with matrix valued potentials, and the values of observables for the ab initio Born-Oppenheimer molecular dynamics of the ground state depends on the probability to be in the excited states and the nuclei/electron mass ratio. Then we present a numerical method to determine the probability to be in the excited states, based on the Ehrenfest molecular dynamics, and stability analysis of a perturbed eigenvalue problem. In Paper II, we present an approach, motivated by the so called Landau-Zener probability estimation, to systematically choose the artificial electron mass parameters appearing in the Car-Parrinello and Ehrenfest molecular dynamics methods to approximate the Born-Oppenheimer molecular dynamics solutions. In Paper III, we extend the work presented in Paper II for a set of more general problems with more than two electron states. A main conclusion of Paper III is that it is necessary to resolve the near avoided conical intersections between all electron eigenvalue gaps, including gaps between the occupied states. In Paper IV, we numerically compare, using simple model problems, the Ehrenfest molecular dynamics using the adaptive mass algorithm proposed in Paper II and III and the Born-Oppenheimer molecular dynamics based on the so called purification of the density matrix method concluding that the Born-Oppenheimer molecular dynamics based on purification of density matrix method performed better in terms of computational efficiency. / <p>QC 20161102</p>

Suppose there is a systematic effect or trend that influences the observations in addition to the block and treatment effects. The problem of experimental designs in the presence of trends was first studied by Cox (1951,1952). Bradley and Yeh (1980) define the concept of trend-free block designs, i.e., the designs in which the analysis of treatment effects are essentially the same whether the trend effects are present or not. If the trend effect within each blocks are the same and linear, Yeh and Bradley (1983) derive a simple necessary condition for designs to be linear trend-free, 　　r_i(k+1)≡0 (mod 2), 1≦i≦v,　　　　　(1) 　　where r_i is the replication of treatment i, for 1≦i≦v, and k is block size. 　　In case where a trend-free version does not exist Yeh et al. (1985) suggest the use of “ nearly trend-free version”. Chai (1995) pays attention to situations where (1) does not hold. He also shows that often, under these circumstances, a nearly linear trend-free design could be constructed. 　　Designs that are derived by extending or deleting m disjoint and binary blocks from BIBD (v,b,k,r,λ)'s are considered. If the resulting designs have linear trend-free versions, by Constantine (1981), they are E-optimal designs with the corresponding classes. When k is even, however, it is impossible to have linear trend-free versions since not all the r_i's are even in such type of designs and (1) is violated. In this paper, we shall convert the designs to be nearly linear trend-free versions of them by permuting the treatment symbols within blocks, and investigate that the resulting designs remain to be E-optimal.

This thesis questions the connection between knowledge and finance and advances an account that links both in a two-folded way. The first level departs from what separates the two opposite views or alternative explanations about the value of knowledge. The source and essence of the extra profits in information goods or commodities, such as digital media contents and software, featuring increasing returns to scale owing to their peculiar cost structure manifested by a high fixed cost and very low constant marginal cost, is what separates the two views about the value of knowledge. In light of the near-decomposability/modularity hypothesis, the extra profits in information commodities should arise from &#039 / information hiding,&#039 / which is intrinsic to nearly-decomposable systems or modular architecture because they are built on an ignorance on the parts in regard to the other parts and the whole of system. Such (hidden) design information that gives rise to parts or modules creates, at the same time, the future paths of action or (real) options, according to real-options perspective. When the two perspectives are combined, knowledge production, as distinct from subsequent knowledge commodity production, basically becomes an option creation process. Then, it becomes possible to argue that the concurrence of knowledge and finance is not a coincidence at all because the logics of accumulation is no different but almost identical, which is the second level of the two-folded account attempted in this study. The main contribution of this thesis is to build an account that links financialization to knowledge via the notion of modularity. Such an account sees financialization as a reflection and consequence of a value-driven permanent innovation economy developed under the &#039 / IT paradigm&#039 / in order to exploit a surplus peculiar and intrinsic to the modular structure that makes &#039 / information hiding&#039 / an integral part of such architectures since they are by definition built on an ignorance on the parts in regard to the other parts and the whole of system.

This thesis questions the connection between knowledge and finance and advances an account that links both in a two-folded way. The first level departs from what separates the two opposite views or alternative explanations about the value of knowledge. The source and essence of the extra profits in information goods or commodities, such as digital media contents and software, featuring increasing returns to scale owing to their peculiar cost structure manifested by a high fixed cost and very low constant marginal cost, is what separates the two views about the value of knowledge. In light of the near-decomposability/modularity hypothesis, the extra profits in information commodities should arise from &#039 / information hiding,&#039 / which is intrinsic to nearly-decomposable systems or modular architecture because they are built on an ignorance on the parts in regard to the other parts and the whole of system. Such (hidden) design information that gives rise to parts or modules creates, at the same time, the future paths of action or (real) options, according to real-options perspective. When the two perspectives are combined, knowledge production, as distinct from subsequent knowledge commodity production, basically becomes an option creation process. Then, it becomes possible to argue that the concurrence of knowledge and finance is not a coincidence at all because the logics of accumulation is no different but almost identical, which is the second level of the two-folded account attempted in this study. The main contribution of this thesis is to build an account that links financialization to knowledge via the notion of modularity. Such an account sees financialization as a reflection and consequence of a value-driven permanent innovation economy developed under the &#039 / IT paradigm&#039 / in order to exploit a surplus peculiar and intrinsic to the modular structure that makes &#039 / information hiding&#039 / an integral part of such architectures since they are by definition built on an ignorance on the parts in regard to the other parts and the whole of system.