Estimation of Parameters for Gaussian Random Variables using Robust Differential Geometric Techniques

Most signal processing systems today need to estimate parameters of the underlying probability distribution, however quantifying the robustness of this system has always been difficult. This thesis attempts to quantify the performance and robustness of the Maximum Likelihood Estimator (MLE), and a robust estimator, which is a Huber-type censored form of the MLE. This is possible using diff erential geometric concepts of slope. We compare the performance and robustness of the robust estimator, and its behaviour as compared to the MLE. Various nominal values of the parameters are assumed, and the performance and robustness plots are plotted. The results showed that the robustness was high for high values of censoring and was lower as the censoring value decreased. This choice of the censoring value was simplifi ed since there was an optimum value found for every set of parameters. This study helps in future studies which require quantifying robustness for di fferent kinds of estimators

Robust Framework for System Architecture and Hand-offs in Wireless and Cellular Communication Systems

Robustness of a system has been defined in various ways and a lot of work has been done to model the robustness of a system, but quantifying or measuring robustness has always been very difficult. In this research, we develop a framework for robust system architecture. We consider a system of a linear estimator (multiple tap filter) and then attempt to model the system performance and robustness in a graphical manner, which admits an analysis using the differential geometric concepts. We compare two different perturbation models, namely the gradient with biased perturbations (sub-optimal model) of a surface and the gradient with unbiased perturbations (optimal model), and observe the values to see which of them can alternately be used in the process of understanding or measuring robustness. In this process we have worked on different examples and conducted many simulations to find if there is any consistency in the two models. We propose the study of robustness measures for estimation/prediction in stationary and non-stationary environment using differential geometric tools in conjunction with probability density analysis. Our approach shows that the gradient can be viewed as a random variable and therefore used to generate probability densities, allowing one to draw conclusions regarding the robust- ness. As an example, one can apply the geometric methodology to the prediction of time varying deterministic data in imperfectly known non-stationary distribution. We also compare stationary to non-stationary distribution and prove that robustness is reduced by admitting residual non-stationarity. We then research and develop a robust iterative handoff algorithm, relating generally to methods, devices and systems for reselecting and then handing over a mobile communications device from a first cell to a second cell in a cellular wireless communications system (GPRS, W-CDMA or OFDMA). This algorithm results in significant decrease in amount of power and/or result is a decrease of break in communications during an established voice call or other connection, in the field, thereby outperforming prior art

Towards Interpretability and Robustness of Machine Learning Models

Modern machine learning models can be difficult to probe and understand after they have been trained. This is a major problem for the field, with consequences for trustworthiness, diagnostics, debugging, robustness, and a range of other engineering and human interaction issues surrounding the deployment of a model. Another problem of modern machine learning models is their vulnerability to small adversarial perturbations to the input, which incurs a security risk when they are applied to critical areas.In this thesis, we develop systematic and efficient tools for interpreting machine learning models and evaluating their adversarial robustness. Part I focuses on model interpretation. We derive an efficient feature scoring method by exploiting the graph structure in data. We also develop a learning-based method under an information-based framework. As an attempt to leverage prior knowledge about what constitutes a satisfying interpretation in a given domain, we propose a systematic approach to exploiting syntactic constituency structure by leveraging a parse tree for interpretation of models in the setting of linguistic data. Part II focuses on the evaluation of adversarial robustness. We first propose a probabilistic framework for generating adversarial examples on discrete data, and develop two algorithms to implement it. We also introduce a novel attack method in the setting where the attacker has access to model decisions alone. We investigate the robustness of various machine learning models and existing defense mechanisms under the proposed attack method. In Part III, we build a connection between the two fields by developing a method for detecting adversarial examples via tools in model interpretation

On Statistics and Dynamics of Cosmic Structure

Die vorliegende Arbeit soll einen Einblick in aktuelle Entwicklungen der Statistik und Dynamik großräumiger Strukturen im Universum geben. Breiter Raum wird dabei der statistischen Auswertung mit Hilfe von Minkowskifunktionalen eingeräumt. Dieses übergeordnete Thema illustrieren wir exemplarisch durch die detailierte Darlegung dreier Anwendungsbereiche, die ganz unterschiedliche Arten kosmologisch relevanter Daten verwerten. Wir hoffen, mit diesem Überblick einen Beitrag zu der wachsenden Akzeptanz zu leisten, die die Minkowskifunktionale in letzter Zeit als Alternative zu den weit verbreiteten Zweipunktstatistiken gewinnen

25 Years of Self-Organized Criticality: Solar and Astrophysics

Shortly after the seminal paper {\sl "Self-Organized Criticality: An explanation of 1/f noise"} by Bak, Tang, and Wiesenfeld (1987), the idea has been applied to solar physics, in {\sl "Avalanches and the Distribution of Solar Flares"} by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme.Comment: 139 pages, 28 figures, Review based on ISSI workshops "Self-Organized Criticality and Turbulence" (2012, 2013, Bern, Switzerland

Wearable Sensors in the Evaluation of Gait and Balance in Neurological Disorders

The aging population and the increased prevalence of neurological diseases have raised the issue of gait and balance disorders as a major public concern worldwide. Indeed, gait and balance disorders are responsible for a high healthcare and economic burden on society, thus, requiring new solutions to prevent harmful consequences. Recently, wearable sensors have provided new challenges and opportunities to address this issue through innovative diagnostic and therapeutic strategies. Accordingly, the book “Wearable Sensors in the Evaluation of Gait and Balance in Neurological Disorders” collects the most up-to-date information about the objective evaluation of gait and balance disorders, by means of wearable biosensors, in patients with various types of neurological diseases, including Parkinson’s disease, multiple sclerosis, stroke, traumatic brain injury, and cerebellar ataxia. By adopting wearable technologies, the sixteen original research articles and reviews included in this book offer an updated overview of the most recent approaches for the objective evaluation of gait and balance disorders

Joint University Program for Air Transportation Research, 1989-1990

Research conducted during the academic year 1989-90 under the NASA/FAA sponsored Joint University Program for Air Transportation research is discussed. Completed works, status reports and annotated bibliographies are presented for research topics, which include navigation, guidance and control theory and practice, aircraft performance, human factors, and expert systems concepts applied to airport operations. An overview of the year's activities for each university is also presented

A Socio-Hydrologic Assessment of Mountain Water Supply Vulnerability to Changing Snowmelt

Climate change is accelerating disconnects between snowmelt-driven water supply and downstream demand. Identifying what makes people and places vulnerable to these disconnects can improve understanding of present conditions and help anticipate future changes in water management. This dissertation seeks to understand the potential for increasing disconnects between downstream agriculturally productive regions and their primary water supply—higher elevation, mountainous (upland) environments. We do so by focusing on agriculturally productive regions in the western United States (US) that are heavily reliant on seasonal snowmelt-driven streamflow, and using interdisciplinary tools such as big data, conceptual modeling, social science, and computational hydrology to assess vulnerability from the source (mountains) to demand (agriculture) We find that a process-based framework isolating three dominant mechanisms linking snow to streamflow helps explain changes in snowmelt-driven streamflow in 537 upland catchments throughout the US. We then use a hydrogeological framework and optimized averaging in a subset of our initial 537 catchments, highlighting the critical and often overlooked role of groundwater contributions in high, arid, and deep mountain catchments. Equipped with a more robust understanding of surface water and groundwater supplies in the western US, we then quantify the benefits of adaptation to changing snow resources particularly in hay-dominated agriculturally productive systems with smaller declines in snow relative to reservoir storage. Finally, we derive a flexible approach for expanding vulnerability assessments beyond the mountains and show that robust consideration of multiple aspects of vulnerability requires better measures of the social value of water as well as demand

The effect of noise on dynamics and the influence of biochemical systems

Understanding a complex system requires integration and collective analysis of data from many levels of organisation. Predictive modelling of biochemical systems is particularly challenging because of the nature of data being plagued by noise operating at each and every level. Inevitably we have to decide whether we can reliably infer the structure and dynamics of biochemical systems from present data. Here we approach this problem from many fronts by analysing the interplay between deterministic and stochastic dynamics in a broad collection of biochemical models. In a classical mathematical model we first illustrate how this interplay can be described in surprisingly simple terms; we furthermore demonstrate the advantages of a statistical point of view also for more complex systems. We then investigate strategies for the integrated analysis of models characterised by different organisational levels, and trace the propagation of noise through such systems. We use this approach to uncover, for the first time, the dynamics of metabolic adaptation of a plant pathogen throughout its life cycle and discuss the ecological implications. Finally, we investigate how reliably we can infer model parameters of biochemical models. We develop a novel sensitivity/inferability analysis framework that is generally applicable to a large fraction of current mathematical models of biochemical systems. By using this framework to quantify the effect of parametric variation on system dynamics, we provide practical guidelines as to when and why certain parameters are easily estimated while others are much harder to infer. We highlight the limitations on parameter inference due to model structure and qualitative dynamical behaviour, and identify candidate elements of control in biochemical pathways most likely of being subjected to regulation