Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

On linear order and computation : The expressiveness of interactive computations on linear orders and computations indexed by ordinals

We solve the Dynamic Ehrenfeucht-Fra\"iss\'e Game on linear orders for both players, yielding a normal form for quantifier-rank equivalence classes of linear orders in first-order logic, infinitary logic, and generalized-infinitary logics with linearly ordered clocks. We show that Scott Sentences can be manipulated quickly, classified into local information, and consistency can be decided effectively in the length of the Scott Sentence. We describe a finite set of linked automata moving continuously on a linear order. Running them on ordinals, we compute the ordinal truth predicate and compute truth in the constructible universe of set-theory. Among the corollaries are a study of semi-models as efficient database of both model-theoretic and formulaic information, and a new proof of the atomicity of the Boolean algebra of sentences consistent with the theory of linear order -- i.e., that the finitely axiomatized theories of linear order are dense.

Integrating pest population models with biophysical crop models to better represent the farming system

Farming systems frameworks such as the Agricultural Production Systems simulator (APSIM) represent fluxes through the soil, plant and atmosphere of the system well, but do not generally consider the biotic constraints that function within the system. We designed a method that allowed population models built in DYMEX to interact with APSIM. The simulator engine component of the DYMEX population-modelling platform was wrapped within an APSIM module allowing it to get and set variable values in other APSIM models running in the simulation. A rust model developed in DYMEX is used to demonstrate how the developing rust population reduces the crop's green leaf area. The success of the linking process is seen in the interaction of the two models and how changes in rust population on the crop's leaves feedback to the APSIM crop modifying the growth and development of the crop's leaf area. This linking of population models to simulate pest populations and biophysical models to simulate crop growth and development increases the complexity of the simulation, but provides a tool to investigate biotic constraints within farming systems and further moves APSIM towards being an agro-ecological framework.

Making the most of spatial information in health: A tutorial in Bayesian disease mapping for areal data

Disease maps are effective tools for explaining and predicting patterns of disease outcomes across geographical space, identifying areas of potentially elevated risk, and formulating and validating aetiological hypotheses for a disease. Bayesian models have become a standard approach to disease mapping in recent decades. This article aims to provide a basic understanding of the key concepts involved in Bayesian disease mapping methods for areal data. It is anticipated that this will help in interpretation of published maps, and provide a useful starting point for anyone interested in running disease mapping methods for areal data. The article provides detailed motivation and descriptions on disease mapping methods by explaining the concepts, defining the technical terms, and illustrating the utility of disease mapping for epidemiological research by demonstrating various ways of visualising model outputs using a case study. The target audience includes spatial scientists in health and other fields, policy or decision makers, health geographers, spatial analysts, public health professionals, and epidemiologists.

Problems and Algorithms for Sequence Segmentations

The analysis of sequential data is required in many diverse areas such as telecommunications, stock market analysis, and bioinformatics. A basic problem related to the analysis of sequential data is the sequence segmentation problem. A sequence segmentation is a partition of the sequence into a number of non-overlapping segments that cover all data points, such that each segment is as homogeneous as possible. This problem can be solved optimally using a standard dynamic programming algorithm. In the first part of the thesis, we present a new approximation algorithm for the sequence segmentation problem. This algorithm has smaller running time than the optimal dynamic programming algorithm, while it has bounded approximation ratio. The basic idea is to divide the input sequence into subsequences, solve the problem optimally in each subsequence, and then appropriately combine the solutions to the subproblems into one final solution. In the second part of the thesis, we study alternative segmentation models that are devised to better fit the data. More specifically, we focus on clustered segmentations and segmentations with rearrangements. While in the standard segmentation of a multidimensional sequence all dimensions share the same segment boundaries, in a clustered segmentation the multidimensional sequence is segmented in such a way that dimensions are allowed to form clusters. Each cluster of dimensions is then segmented separately. We formally define the problem of clustered segmentations and we experimentally show that segmenting sequences using this segmentation model, leads to solutions with smaller error for the same model cost. Segmentation with rearrangements is a novel variation to the segmentation problem: in addition to partitioning the sequence we also seek to apply a limited amount of reordering, so that the overall representation error is minimized. We formulate the problem of segmentation with rearrangements and we show that it is an NP-hard problem to solve or even to approximate. We devise effective algorithms for the proposed problem, combining ideas from dynamic programming and outlier detection algorithms in sequences. In the final part of the thesis, we discuss the problem of aggregating results of segmentation algorithms on the same set of data points. In this case, we are interested in producing a partitioning of the data that agrees as much as possible with the input partitions. We show that this problem can be solved optimally in polynomial time using dynamic programming. Furthermore, we show that not all data points are candidates for segment boundaries in the optimal solution.

A study of the deformation slip lines in quenched and aged Al-2% Ge alloy

Optical microscopy has been employed to observe the slip lines in deformed Al-2% Ge alloy samples. Slip lines have been observed in the as-quenched, partially-aged, fully-aged and over-aged states. The lines tend to traverse fairly straight paths in the case of quenched and partially-aged conditions. Fully-aged samples also reveal such straight running lines when tested at low-temperatures. However, the density of the lines generally decreases as the peak-aged state is approached. These results are in agreement with the idea that thermally activated shearing of the precipitates is occurring in the alloy aged up to peak-hardness. The irregular lines for the over-aged specimens support the view that the moving dislocations by-pass the precipitates during deformation. The influence of test-temperature on the appearance of slip traces has been briefly examined.

Mixed reality stories: How creative writers integrate virtual and physical realities

Mixed reality stories (MRS) unfold simultaneously in the physical and the virtual world. Advancements in digital technologies, which are now able to capture more contextual information about our physical environments, are enabling novel ways of blending the two worlds. To explore the process of creating stories from this perspective, we conducted a study with creative writers, in which we asked them to write a MRS script for outdoor running. While we saw instances of intentional connections between physical and virtual worlds in their work, we also observed the use of ambiguity or even deliberate contradiction with available contextual information. In this paper we discuss how these approaches can be beneficial for MRS and propose directions for future work.

Being chased by zombies!: Understanding the experience of mixed reality quests

Both researchers and practitioners show increasing interest in exploring mixed reality games: games, where physical environments blend together with digital technologies. In this paper we have extended earlier work by bringing attention to the role of narrative in mixed reality games. For our case study we chose a mobile phone application Zombies Run!, which is designed to support actual running. This application contains a fictional story about a zombie apocalypse and provides runners with various quests (in the form of missions) to complete during their run. We investigated different aspects of participants' experience with the application and how it changed their running. Our findings show how the app changed running in three major ways. Firstly, it changed the way runs were organised. Secondly, it shook up established running routines. And lastly, it shaped the meanings associated with running.

Effect of long-wave UV radiation on mouse melanoma: an in vitro and in vivo study

The skin cancer incidence has increased substantially over the past decades and the role of ultraviolet (UV) radiation in the etiology of skin cancer is well established. Ultraviolet B radiation (280-320 nm) is commonly considered as the more harmful part of the UV-spectrum due to its DNA-damaging potential and well-known carcinogenic effects. Ultraviolet A radiation (320-400 nm) is still regarded as a relatively low health hazard. However, UVA radiation is the predominant component in sunlight, constituting more than 90% of the environmentally relevant solar ultraviolet radiation. In the light of the recent scientific evidence, UVA has been shown to have genotoxic and immunologic effects, and it has been proposed that UVA plays a significant role in the development of skin cancer. Due to the popularity of skin tanning lamps, which emit high intensity UVA radiation and because of the prolonged sun tanning periods with the help of effective UVB blockers, the potential deleterious effects of UVA has emerged as a source of concern for public health. The possibility that UV radiation may affect melanoma metastasis has not been addressed before. UVA radiation can modulate various cellular processes, some of which might affect the metastatic potential of melanoma cells. The aim of the present study was to investigate the possible role of UVA irradiation on the metastatic capacity of mouse melanoma both in vitro and in vivo. The in vitro part of the study dealt with the enhancement of the intercellular interactions occurring either between tumor cells or between tumor cells and endothelial cells after UVA irradiation. The use of the mouse melanoma/endothelium in vitro model showed that a single-dose of UVA to melanoma cells causes an increase in melanoma cell adhesiveness to non-irradiated endothelium after 24-h irradiation. Multiple-dose irradiation of melanoma cells already increased adhesion at a 1-h time-point, which suggests the possible cumulative effect of multiple doses of UVA irradiation. This enhancement of adhesiveness might lead to an increase in binding tumor cells to the endothelial lining of vasculature in various internal organs if occurring also in vivo. A further novel observation is that UVA induced both decline in the expression of E-cadherin adhesion molecule and increase in the expression of the N-cadherin adhesion molecule. In addition, a significant decline in homotypic melanoma-melanoma adhesion (clustering) was observed, which might result in the reduction of E-cadherin expression. The aim of the in vivo animal study was to confirm the physiological significance of previously obtained in vitro results and to determine whether UVA radiation might increase melanoma metastasis in vivo. The use of C57BL/6 mice and syngeneic melanoma cell lines B16-F1 and B16-F10 showed that mice, which were i.v. injected with B16-F1 melanoma cells and thereafter exposed to UVA developed significantly more lung metastases when compared with the non-UVA-exposed group. To study the mechanism behind this phenomenon, the direct effect of UVA-induced lung colonization capacity was examined by the in vitro exposure of B16-F1 cells. Alternatively, the UVA-induced immunosuppression, which might be involved in increased melanoma metastasis, was measured by standard contact hypersensitivity assay (CHS). It appears that the UVA-induced increase of metastasis in vivo might be caused by a combination of UVA-induced systemic immunosuppression, and to the lesser extent, it might be caused by the increased adhesiveness of UVA irradiated melanoma cells. Finally, the UVA effect on gene expression in mouse melanoma was determined by a cDNA array, which revealed UVA-induced changes in the 9 differentially expressed genes that are involved in angiogenesis, cell cycle, stress-response, and cell motility. These results suggest that observed genes might be involved in cellular response to UVA and a physiologically relevant UVA dose have previously unknown cellular implications. The novel results presented in this thesis offer evidence that UVA exposure might increase the metastatic potential of the melanoma cells present in blood circulation. Considering the wellknown UVA-induced deleterious effects on cellular level, this study further supports the notion that UVA radiation might have more potential impact on health than previously suggested. The possibility of the pro-metastatic effects of UVA exposure might not be of very high significance for daily exposures. However, UVA effects might gain physiological significance following extensive sunbathing or solaria tanning periods. Whether similar UVA-induced pro-metastatic effects occur in people sunbathing or using solaria remains to be determined. In the light of the results presented in this thesis, the avoidance of solaria use could be well justified.

Uncertainty based online planning for UAV target finding in cluttered and GPS-denied environments

There are some scenarios in which Unmmaned Aerial Vehicle (UAV) navigation becomes a challenge due to the occlusion of GPS systems signal, the presence of obstacles and constraints in the space in which a UAV operates. An additional challenge is presented when a target whose location is unknown must be found within a confined space. In this paper we present a UAV navigation and target finding mission, modelled as a Partially Observable Markov Decision Process (POMDP) using a state-of-the-art online solver in a real scenario using a low cost commercial multi rotor UAV and a modular system architecture running under the Robotic Operative System (ROS). Using POMDP has several advantages to conventional approaches as they take into account uncertainties in sensor information. We present a framework for testing the mission with simulation tests and real flight tests in which we model the system dynamics and motion and perception uncertainties. The system uses a quad-copter aircraft with an board downwards looking camera without the need of GPS systems while avoiding obstacles within a confined area. Results indicate that the system has 100% success rate in simulation and 80% rate during flight test for finding targets located at different locations.

Two-level k-means clustering algorithm for k-tau relationship establishment and linear-time classification

Partitional clustering algorithms, which partition the dataset into a pre-defined number of clusters, can be broadly classified into two types: algorithms which explicitly take the number of clusters as input and algorithms that take the expected size of a cluster as input. In this paper, we propose a variant of the k-means algorithm and prove that it is more efficient than standard k-means algorithms. An important contribution of this paper is the establishment of a relation between the number of clusters and the size of the clusters in a dataset through the analysis of our algorithm. We also demonstrate that the integration of this algorithm as a pre-processing step in classification algorithms reduces their running-time complexity.

2-Chloro-3-hydroxymethyl-7,8-dimethylquinoline

All non-H atoms of the title compound, C12H12ClNO, are co-planar (r.m.s. deviation = 0.055 angstrom). The hydroxy H atom is disordered over two positions of equal occupancy. In the crystal, molecules are linked by O-H center dot center dot center dot O hydrogen bonds, generating zigzag chains running along the b axis.

2-Chloro-3-hydroxymethyl-6-methoxyquinoline

All the non-H atoms of the title compound, C11H10ClNO2, are roughly coplanar (r.m.s. deviation = 0.058 angstrom). In the crystal, adjacent molecules are linked by an O-H center dot center dot center dot N hydrogen bond, generating chains running along the a axis.

Compact fiber Bragg grating dynamic strain sensor cum broadband thermometer for thermally unstable ambience

An instrument for simultaneous measurement of dynamic strain and temperature in a thermally unstable ambience has been proposed, based on fiber Bragg grating technology. The instrument can function as a compact and stand-alone broadband thermometer and a dynamic strain gauge. It employs a source wavelength tracking procedure for linear dependence of the output on the measurand, offering high dynamic range. Two schemes have been demonstrated with their relative merits. As a thermometer, the present instrumental configuration can offer a linear response in excess of 500 degrees C that can be easily extended by adding a suitable grating and source without any alteration in the procedure. Temperature sensitivity is about 0.06 degrees C for a bandwidth of 1 Hz. For the current grating, the upper limit of strain measurement is about 150 mu epsilon with a sensitivity of about 80 n epsilon Hz(-1/2). The major source of uncertainty associated with dynamic strain measurement is the laser source intensity noise, which is of broad spectral band. A low noise source device or the use of optical power regulators can offer improved performance. The total harmonic distortion is less than 0.5% up to about 50 mu epsilon, 1.2% at 100 mu epsilon and about 2.3% at 150 mu epsilon. Calibrated results of temperature and strain measurement with the instrument have been presented. Traces of ultrasound signals recorded by the system at 200 kHz, in an ambience of 100-200 degrees C temperature fluctuation, have been included. Also, the vibration spectrum and engine temperature of a running internal combustion engine has been recorded as a realistic application of the system.

2-[2-(Hydroxymethyl)phenyl]-1-(1-naphthyl)ethanol

The molecular conformation of the title compound, C19H18O2, is stabilized by an intramolecular O-H-O hydrogen bond. In addition, intermolecular O-H-O interactions link the molecules into zigzag chains running along the c axis.