The goal of this thesis is to build an interactive tool for analyzing the quality of a digital image and predicting the scale at which it may be published. Since edges are present almost everywhere in most digital images, we use a mathematical edge model as the basis of analysis. In particular, we are interested in the luminance and chromaticity behavior at edge boundaries. We use this model to develop PhETA — Photograph Edge Transition Analyzer — an interactive tool that allows novice users to view and understand the results gained from this analysis in a clear and simple manner. / Master of Science

Exploring coordinated relationships is an important task in data analytics. For example, an intelligence analyst may want to find three suspicious people who all visited the same four cities. However, existing techniques that display individual relationships, such as between lists of entities, require repetitious manual selection and significant mental aggregation in cluttered visualizations to find coordinated relationships. This work presents a visual analytics approach that applies biclusters to support coordinated relationships exploration. Each computed bicluster aggregates individual relationships into coordinated sets. Thus, coordinated relationships can be formalized as biclusters. However, how to incorporate biclusters into a visual analytics tool to support sensemaking tasks is challenging. To address this, this work features three key contributions: 1) a five-level design framework for bicluster visualizations, 2) BiSet, highlighting bicluster-based edge bundling, seriation-based multiple lists ordering, and interactions for dynamic information foraging and management, and 3) an evaluation of BiSet. / Ph. D.

Edge computing is an emerging technology that can overcome the limitations of centralized cloud computing by enabling distributed, low-latency computation at a network edge. Particularly, in edge computing, some of the cloud's functionalities such as storage, processing, and computing are migrated to end-user devices called edge nodes so as to reduce the round-trip delay needed to reach the cloud data center. Despite the major benefits and practical applications of using edge computing, one must address many technical challenges that include edge network formation, computational task allocation, and radio resource allocation, while considering the uncertainties innate in edge nodes, such as incomplete future information on their wireless channel gains and computing capabilities. The goal of this dissertation is to develop foundational science for the deployment, performance analysis, and low-complexity optimization of edge computing under the aforementioned uncertainties. First, the problems of edge network formation and task distribution are jointly investigated while considering a hybrid edge-cloud architecture under uncertainty on the arrivals of computing tasks. In particular, a novel online framework is proposed to form an edge network, distribute the computational tasks, and update a target competitive ratio defined as the ratio between the latency achieved by the proposed online algorithm and the optimal latency. The results show that the proposed framework achieves the target competitive ratio that is affected by the wireless data rate and computing speeds of edge nodes. Next, a new notion of ephemeral edge computing is proposed in which edge computing must occur under a stringent requirement on the total computing time period available for the computing process. To maximize the number of computed tasks in ephemeral edge networks under the uncertainty on future task arrivals, a novel online framework is proposed to enable a source edge node to offload computing tasks from sensors and allocate them to neighboring edge nodes for distributed task computing, within the limited total time period. Then, edge computing is applied for mobile blockchain and online caching systems, respectively. First, a mobile blockchain framework is designed to use edge devices as mobile miners, and the performance is analyzed in terms of the probability of forking event and energy consumption. Second, an online computational caching framework is designed to minimize the edge network latency. The proposed caching framework enables each edge node to store intermediate computation results (IRs) from previous computations and download IRs from neighboring nodes under uncertainty on future computation. Subsequently, online optimization is extended to investigate other edge networking applications. In particular, the problem of online ON/OFF scheduling of self-powered small cell base stations is studied, in the presence of energy harvesting uncertainty with the goal of minimizing the operational costs that consist of energy consumption and transmission delay of a network. Such a framework can enable the self-powered base stations to be functioned as energy-efficient edge nodes. Also, the problem of radio resource allocation is studied when a base station is assisted by self-powered reconfigurable intelligent surfaces (RIS). To this end, a deep reinforcement learning approach is proposed to jointly optimize the transmit power, phase shifting, and RIS reflector's ON/OFF states under the uncertainties on the downlink wireless channel information and the harvested energy at the RIS. Finally, the online problem of dynamic channel allocation is studied for full-duplex device-to-device (D2D) networks so that D2D users can share their data with a low communication latency when users dynamically arrive on the network. In conclusion, the analytical foundations and frameworks presented in this dissertation will provide key guidelines for effective design of edge computing in wireless networks. / Doctor of Philosophy / Smart cities will rely on an Internet of Things (IoT) system that interconnects cars, drones, sensors, home appliances, and other digital devices. Modern IoT systems are inherently designed to process real-time information such as temperature, humidity, or even car navigational data, at any time and location. A unique challenge in the design of such an IoT is the need to process large volumes of data over a wireless network that consists of heterogeneous IoT devices such as smartphones, vehicles, home access points, robots, and drones. These devices must perform local (on-device or so-called edge) processing of their data without relying on a remote cloud. This vision of a smart city seen as a mobile computing platform gives rise to the emerging concept of edge computing using which smartphones, sensors, vehicles, and drones can exchange and process data locally on their own devices. Edge computing allows overcoming the limitations of centralized cloud computation by enabling distributed, low-latency computation at the network edge. Despite the promising opportunities of edge computing as an enabler for smart city services such as autonomous vehicles, drones, or smart homes, one must address many challenges related to managing time-varying resources such as energy and storage, in a dynamic way. For instance, managing communication, energy, and computing resources in an IoT requires handling many uncertain factors such as the intermittent availability of wireless connectivity and the fact that the devices do not know a priori what type of tasks they need to process. The goal of this dissertation is to address the fundamental challenges in edge computing under uncertainty in an IoT. In particular, this dissertation introduces novel mathematical algorithms and frameworks that exploit ideas from the fields of online optimization, machine learning, and wireless communication to enable future IoT services such as smart factories, virtual reality, and autonomous systems. In this dissertation, holistic frameworks are developed by designing, analyzing, and optimizing wireless communications systems with an emphasize on emerging IoT applications. To this end, various mathematical frameworks and efficient algorithms are proposed by drawing on tools from wireless communications, online optimization, and machine learning to yield key innovations. The results show that the developed solutions can enable an IoT to operate efficiently in presence of uncertainty stemming from time-varying dynamics such as mobility of vehicles or changes in the wireless networking environment. As such, the outcomes of this research can be used as a building block for the large deployment of smart city technologies that heavily rely on the IoT.

As compared to traditional cloud computing, edge computing provides computational, sensor, and storage resources co-located with client requests, thereby reducing network transmission and providing context-awareness. While server farms can allocate cloud computing resources on demand at runtime, edge-based heterogeneous devices, ranging from stationary servers to mobile, IoT, and energy harvesting devices are not nearly as reliable and abundant. As a result, edge application developers face the following obstacles: 1) heterogeneous devices provide hard-to-access resources, due to dissimilar capabilities, operating systems, execution platforms, and communication interfaces; 2) unreliable resources cause high failure rates, due to device mobility, low energy status, and other environmental factors; 3) resource scarcity hinders the performance; 4) the dissimilar and dynamic resources across edge environments make QoS impossible to guarantee. Edge environments are characterized by the prevalence of equivalent functionalities, which satisfy the same application requirements by different means. The thesis of this research is that equivalent functionalities can be exploited to improve the reliability, efficiency, and adaptiveness of edge-based services. To prove this thesis, this dissertation comprises three key interrelated research thrusts: 1) create a system architecture and programming support for providing edge services that run on heterogeneous and ever changing edge devices; 2) introduce programming abstractions for executing equivalent functionalities; 3) apply equivalent functionalities to improve the reliability, efficiency, and adaptiveness of edge services. We demonstrate how the connected devices with unreliable, dynamic, and scarce resources can automatically form a reliable, adaptive, and efficient execution environment for sensing, computing, and other non-trivial tasks. This dissertation is based on 5 conference papers, presented at ICDCS'20, ICWS'19, EDGE'19, CLOUD'18, and MobileSoft'18 / Doctor of Philosophy / As mobile and IoT devices are generating ever-increasing volumes of sensor data, it has become impossible to transfer this data to remote cloud-based servers for processing. As an alternative, edge computing coordinates nearby computing resources that can be used for local processing. However, while cloud computing resources are abundant and reliable, edge computing ones are scarce and unreliable. This dissertation research introduces novel execution strategies that make it possible to provide reliable, efficient, and flexible edge-based computing services in dissimilar edge environments.

Vertex-distinguishing edge-colorings (vdec colorings) are a restriction of proper edge-colorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively new field of study. We present a survey of known results concerning vdec colorings. We also define a new matrix which may be used to study vdec colorings, and examine its properties. We find several bounds on the eigenvalues of this matrix, as well as results concerning its determinant, and other properties. We finish by examining related topics and open problems.

Mainly used for decorative purpose in the textile industry, lace is a type of lightweight, openwork fabric. The process of lace manufacturing is complex but much of it has been highly automated with the advancement of modern technology. One exception is the lace cutting operation which is used to cut the wide lace webs (as wide as 3.8 m) knitted from automatic knitting machines into individual lace breadths. Currently, lace cutting IS carried out by skilled operators or a low speed mechanical cutting system, leading to high cost and increased product lead times. Therefore the lace cutting operation has become a bottleneck of the whole process oflace manufacturing and its automation is highly desired. Based on the combination of machine vision and laser cutting technology, two automatic lace cutting systems have been developed in Loughborough University, which have fully demonstrated the feasibility of replacing the slow and expensive traditional lace cutting methods. However, the edge quality of the lace cut by these systems is not satisfactory enough to meet the requirements of demanding lace markets. In this thesis, based on the investigation of the effect of handling tension on lace cutting edge quality and the microstructure of lace, a strategic lace cutting solution has been presented. The cutting strategy is aimed at tensioning and exposing the loop thread by strategically tensioning and cutting individual threads. The loop thread is considered critical to cutting lace with a high quality finish. To automatically implement the cutting strategy, a machine vision system has been developed. An automatic lace transport and tensioning rig has been designed and manufactured. The long term aim of this rig is to be able to transport and tension lace continuously for lace cutting and apply localised tension on individual threads with the vision system providing feedback for tension control. The work in this thesis has been limited to manual adjustment of the rig to prove the initial ideas for this concept. An integrated vision guided, pulsed laser cutting system for lace cutting has been developed, based on which two types of representative lace have been cut. According to the assessment results of using a combination of user trials, microscopic and newly developed measurement techniques, the lace cut by this newly developed system has shown significant improvement in cutting edge quality, when compared to the lace cut by the previous laser cutting systems.

The convergence of mobile computing and cloud computing enables new mobile applications that are both resource-intensive and interactive. For these applications, end-to-end network bandwidth and latency matter greatly when cloud resources are used to augment the computational power and battery life of a mobile device. This dissertation designs and implements a new architectural element called a cloudlet, that arises from the convergence of mobile computing and cloud computing. Cloudlets represent the middle tier of a 3-tier hierarchy, mobile device — cloudlet—cloud, to achieve the right balance between cloud consolidation and network responsiveness. We first present quantitative evidence that shows cloud location can affect the performance of mobile applications and cloud consolidation. We then describe an architectural solution using cloudlets that are a seamless extension of todays cloud computing infrastructure. Finally, we define minimal functionalities that cloudlets must offer above/beyond standard cloud computing, and address corresponding technical challenges.

Several studies carried out in boreal forests have found significant edge effects in Scots pine although, none of them in southern Sweden. The aim of this study was to investigate edge effects in adjacent Scots pine stands and its influence on tree growth and field vegetation composition. This was carried out in 10 selected forest edges in southeastern Sweden. Results showed reduced number of stems, height, diameter and basal area growth among young trees in particular within 2 m from the forest edge. In the older stands number of stems, diameter and basal area growth increased within the first 2 m from the edge. Field vegetation inventory showed differences in composition in the adjacent stands. In the older stands lichens, lingonberry and blueberry were more frequent, while heather and grasses showed a higher appearance in young stands.

Le Cloud offre le calcul, stockage etréseau en tant que services. Pour réduire le coûtde cette offre, les opérateurs ont tendance à s’appuyer sur des infrastructures centralisées et gigantesques. Cependant, cette configuration entrave la satisfaction des exigences de latence et de bande passante des applications de nouvelle génération. L'Edge cherche à relever ce défi en s'appuyant sur des ressources massivement distribuées. Afin de satisfaire les attentes des opérateurs et des utilisateurs du Edge, des services de gestion ayant des capacités similaires à celles qui ont permis le succès du Cloud doivent être conçus. Dans cette thèse, nous nous concentrons sur le service de supervision. Nous proposons un canevas logiciel pour la mise en place d’un service holistique. Ce canevas permet de déterminer une architecture de déploiement pair-à-pair pour les fonctions d'observation, de traitement et d'exposition des mesures. Il vérifie que cette architecture satisfait les exigences fonctionnelles et de qualité de service des utilisateurs. Ces derniers peuvent être exprimés à l'aide d'un langage de description offert par le canevas. Le canevas offre également un langage de description pour unifier la description de l'infrastructure Edge. L’architecture de déploiement est déterminée avec l’objectif de minimiser l'empreinte de calcul et réseau du service de supervision. Pour cela, les fonctions de supervision sont mutualisées entre les différents utilisateurs. Les tests que nous avons faits ont montré la capacité de notre proposition à réduire l'empreinte de supervision avec un gain qui atteint -28% pour le calcul et -24% pour leréseau. / Cloud offers compute, storage and network as services. To reduce the offer cost, the operators tend to rely on centralized and massive infrastructures. However, such a configuration hinders the satisfaction of the latency and bandwidth requirements of new generation applications. The Edge aims to rise this challenge by relying on massively distributed resources. To satisfy the operators and the users of Edge, management services similar to the ones that made the success of Cloud should be designed. In this thesis, we focus on the monitoring service. We design a framework to establish a holistic monitoring service. This framework determines a peer-to-peer deployment architecture for the observation, processing, and exposition of measurements. It verifies that this architecture satisfies the functional and quality of service constraints of the users. For this purpose, it relies on a description of users requirement sand a description of the Edge infrastructure.The expression of these two elements can be unified with two languages offered by the Framework. The deployment architecture is determined with the aim of minimizing the compute and network footprint of the monitoring service. For this purpose, the functions are mutualized as much as possible among the different users. The tests we did showed the relevance of our proposal for reducing monitoring footprint with a gain of -28% for the compute and -24% for the network.

Boundary value problems on manifolds with conical singularities or edges contain potential operators as well as trace and Green operators which play a similar role as the corresponding operators in (pseudo-differential) boundary value problems on a smooth manifold. There is then a specific asymptotic behaviour of these operators close to the singularities. We characterise potential operators in terms of actions of cone or edge pseudo-differential operators (in the neighbouring space) on densities supported by sbmanifolds which also have conical or edge singularities. As a byproduct we show the continuity of such potentials as continuous perators between cone or edge Sobolev spaces and subspaces with asymptotics.