Renormalization: an advanced overview

We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond standard QFT textbook material, and may be little-known to specialists of each other approach. This review is aimed at bridging this gap.Comment: Review, 130 pages, 33 figures; v2: misprints corrected, refs. added, minor improvements; v3: some changes to sect. 5, refs. adde

Symmetry in Graph Theory

This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view

Review of the Marine Monitoring Program (MMP)

The Marine Monitoring Program (MMP) monitors the condition of inshore water quality and aims to link this to changes in the health of key inshore environments (coral reefs and seagrass). This report provides a review of each of the 5 programs based on the best available information that was provided by the MMP providers at the time of the review

Modelling deadlock in queueing systems

Motivated by the needs of Aneurin Bevan University Health Board, this thesis ex- plores three themes: the phenomenon of deadlock in queueing systems, the develop- ment of discrete event simulation software, and applying modelling to the evaluation of the effects of a new healthcare intervention, Stay Well Plans, for older people in Gwent. When customers in a restricted queueing network become mutually blocked, and all possible movement ceases, that system becomes deadlocked. This thesis novelly investigates deadlock. A graph theoretical method of detecting deadlock in discrete event simulations is given, analytical models of deadlocking systems are built, and these are used to investigate the effect of system parameters on the expected time until reaching deadlock. Furthermore a deadlock resolution procedure is proposed. An open source discrete event simulation software, Ciw, is developed. This software is designed and developed using best practice principles. Furthermore it permits the use of best practice, such as reproducibility, in simulation modelling. Ciw is used for the modelling of a healthcare system, in order to evaluate the effect of Stay Well Plans. During the development of these models, a number of techniques are employed to overcome the difficulties of lack of data. Insightful results from these models are obtained, indicating a shift in demand from residential care services to community care services

Statistical Methods for High Dimensional Networked Data Analysis.

Networked data are frequently encountered in many scientific disciplines. One major challenges in the analysis of such data are its high dimensionality and complex dependence. My dissertation consists of three projects. The first project focuses on the development of sparse multivariate factor analysis regression model to construct the underlying sparse association map between gene expressions and biomarkers. This is motivated by the fact that some associations may be obscured by unknown confounding factors that are not collected in the data. I have shown that accounting for such unobserved confounding factors can increase both sensitivity and specificity for detecting important gene-biomarker associations and thus lead to more interpretable association maps. The second project concerns the reconstruction of the underlying gene regulatory network using directed acyclic graphical models. My project aims to reduce false discoveries by identifying and removing edges resulted from shared confounding factors. I propose sparse structural factor equation models, in which structural equation models are used to capture directed graphs while factor analysis models are used to account for potential latent factors. I have shown that the proposed method enables me to obtain a simpler and more interpretable topology of a gene regulatory network. The third project is devoted to the development of a new regression analysis methodology to analyze electroencephalogram (EEG) neuroimaging data that are correlated among electrodes within an EEG-net. To address analytic challenges pertaining to the integration of network topology into the analysis, I propose hybrid quadratic inference functions that utilize both prior and data-driven correlations among network nodes into statistical estimation and inference. The proposed method is conceptually simple and computationally fast and more importantly has appealing large-sample properties. In a real EEG data analysis I applied the proposed method to detect significant association of iron deficiency on event-related potential measured in two subregions, which was not found using the classical spatial ANOVA random-effects models.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111595/1/zhouyan_1.pd

Dynamical Systems; Proceedings of an IIASA Workshop, Sopron, Hungary, September 9-13, 1985

The investigation of special topics in systems dynamics -- uncertain dynamic processes, viability theory, nonlinear dynamics in models for biomathematics, inverse problems in control systems theory -- has become a major issue at the System and Decision Sciences Research Program of IIASA. The above topics actually reflect two different perspectives in the investigation of dynamic processes. The first, motivated by control theory, is concerned with the properties of dynamic systems that are stable under variations in the systems' parameters. This allows us to specify classes of dynamic systems for which it is possible to construct and control a whole "tube" of trajectories assigned to a system with uncertain parameters and to resolve some inverse problems of control theory within numerically stable solution schemes. The second perspective is to investigate generic properties of dynamic systems that are due to nonlinearity (as bifurcations theory, chaotic behavior, stability properties, and related problems in the qualitative theory of differential systems). Special stress is given to the applications of nonlinear dynamic systems theory to biomathematics and ecology. The proceedings of a workshop on the "Mathematics of Dynamic Processes", dealing with these topics is presented in this volume