Network based data oriented methods for application driven problems

Networks are amazing. If you think about it, some of them can be found in almost every single aspect of our life from sociological, financial and biological processes to the human body. Even considering entities that are not necessarily connected to each other in a natural sense, can be connected based on real life properties, creating a whole new aspect to express knowledge. A network as a structure implies not only interesting and complex mathematical questions, but the possibility to extract hidden and additional information from real life data. The data that is one of the most valuable resources of this century. The different activities of the society and the underlying processes produces a huge amount of data, which can be available for us due to the technological knowledge and tools we have nowadays. Nevertheless, the data without the contained knowledge does not represent value, thus the main focus in the last decade is to generate or extract information and knowledge from the data. Consequently, data analytics and science, as well as data-driven methodologies have become leading research fields both in scientific and industrial areas. In this dissertation, the author introduces efficient algorithms to solve application oriented optimization and data analysis tasks built on network science based models. The main idea is to connect these problems along graph based approaches, from virus modelling on an existing system through understanding the spreading mechanism of an infection/influence and maximize or minimize the effect, to financial applications, such as fraud detection or cost optimization in a case of employee rostering

Networking - A Statistical Physics Perspective

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.Comment: (Review article) 71 pages, 14 figure

Automated retinal layer segmentation and pre-apoptotic monitoring for three-dimensional optical coherence tomography

The aim of this PhD thesis was to develop segmentation algorithm adapted and optimized to retinal OCT data that will provide objective 3D layer thickness which might be used to improve diagnosis and monitoring of retinal pathologies. Additionally, a 3D stack registration method was produced by modifying an existing algorithm. A related project was to develop a pre-apoptotic retinal monitoring based on the changes in texture parameters of the OCT scans in order to enable treatment before the changes become irreversible; apoptosis refers to the programmed cell death that can occur in retinal tissue and lead to blindness. These issues can be critical for the examination of tissues within the central nervous system. A novel statistical model for segmentation has been created and successfully applied to a large data set. A broad range of future research possibilities into advanced pathologies has been created by the results obtained. A separate model has been created for choroid segmentation located deep in retina, as the appearance of choroid is very different from the top retinal layers. Choroid thickness and structure is an important index of various pathologies (diabetes etc.). As part of the pre-apoptotic monitoring project it was shown that an increase in proportion of apoptotic cells in vitro can be accurately quantified. Moreover, the data obtained indicates a similar increase in neuronal scatter in retinal explants following axotomy (removal of retinas from the eye), suggesting that UHR-OCT can be a novel non-invasive technique for the in vivo assessment of neuronal health. Additionally, an independent project within the computer science department in collaboration with the school of psychology has been successfully carried out, improving analysis of facial dynamics and behaviour transfer between individuals. Also, important improvements to a general signal processing algorithm, dynamic time warping (DTW), have been made, allowing potential application in a broad signal processing field.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Intrinsic randomness in non-local theories: quantification and amplification

Quantum mechanics was developed as a response to the inadequacy of classical physics in explaining certain physical phenomena. While it has proved immensely successful, it also presents several features that severely challenge our classicality based intuition. Randomness in quantum theory is one such and is the central theme of this dissertation. Randomness is a notion we have an intuitive grasp on since it appears to abound in nature. It a icts weather systems and nancial markets and is explicitly used in sport and gambling. It is used in a wide range of scienti c applications such as the simulation of genetic drift, population dynamics and molecular motion in fluids. Randomness (or the lack of it) is also central to philosophical concerns such as the existence of free will and anthropocentric notions of ethics and morality. The conception of randomness has evolved dramatically along with physical theory. While all randomness in classical theory can be fully attributed to a lack of knowledge of the observer, quantum theory qualitatively departs by allowing the existence of objective or intrinsic randomness. It is now known that intrinsic randomness is a generic feature of hypothetical theories larger than quantum theory called the non-signalling theories. They are usually studied with regards to a potential future completion of quantum mechanics or from the perspective of recognizing new physical principles describing nature. While several aspects have been studied to date, there has been little work in globally characterizing and quantifying randomness in quantum and non-signalling theories and the relationship between them. This dissertation is an attempt to ll this gap. Beginning with the unavoidable assumption of a weak source of randomness in the universe, we characterize upper bounds on quantum and non-signalling randomness. We develop a simple symmetry argument that helps identify maximal randomness in quantum theory and demonstrate its use in several explicit examples. Furthermore, we show that maximal randomness is forbidden within general non-signalling theories and constitutes a quantitative departure from quantum theory. We next address (what was) an open question about randomness ampli cation. It is known that a single source of randomness cannot be ampli ed using classical resources alone. We show that using quantum resources on the other hand allows a full ampli cation of the weakest sources of randomness to maximal randomness even in the presence of supra-quantum adversaries. The signi cance of this result spans practical cryptographic scenarios as well as foundational concerns. It demonstrates that conditional on the smallest set of assumptions, the existence of the weakest randomness in the universe guarantees the existence of maximal randomness. The next question we address is the quanti cation of intrinsic randomness in non-signalling correlations. While this is intractable in general, we identify cases where this can be quanti ed. We nd that in these cases all observed randomness is intrinsic even relaxing the measurement independence assumption. We nally turn to the study of the only known resource that allows generating certi able intrinsic randomness in the laboratory i.e. entanglement. We address noisy quantum systems and calculate their entanglement dynamics under decoherence. We identify exact results for several realistic noise models and provide tight bounds in some other cases. We conclude by putting our results into perspective, pointing out some drawbacks and future avenues of work in addressing these concerns

The SXS Collaboration catalog of binary black hole simulations

Accurate models of gravitational waves from merging black holes are necessary for detectors to observe as many events as possible while extracting the maximum science. Near the time of merger, the gravitational waves from merging black holes can be computed only using numerical relativity. In this paper, we present a major update of the Simulating eXtreme Spacetimes (SXS) Collaboration catalog of numerical simulations for merging black holes. The catalog contains 2018 distinct configurations (a factor of 11 increase compared to the 2013 SXS catalog), including 1426 spin-precessing configurations, with mass ratios between 1 and 10, and spin magnitudes up to 0.998. The median length of a waveform in the catalog is 39 cycles of the dominant $\ell=m=2$ gravitational-wave mode, with the shortest waveform containing 7.0 cycles and the longest 351.3 cycles. We discuss improvements such as correcting for moving centers of mass and extended coverage of the parameter space. We also present a thorough analysis of numerical errors, finding typical truncation errors corresponding to a waveform mismatch of $\sim 10^{-4}$. The simulations provide remnant masses and spins with uncertainties of 0.03% and 0.1% ($90^{\text{th}}$ percentile), about an order of magnitude better than analytical models for remnant properties. The full catalog is publicly available at https://www.black-holes.org/waveforms .Comment: 33+18 pages, 13 figures, 4 tables, 2,018 binaries. Catalog metadata in ancillary JSON file. v2: Matches version accepted by CQG. Catalog available at https://www.black-holes.org/waveform

Glosarium Matematika

273 p.; 24 cm