Applications of random set theory in econometrics

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.

Cloud-based Orchestration of Multimedia Services and Applications

The Mobile Cloud Networking project develops among others, several virtualized services and applications, in particular: (1) IP Multimedia Subsystem as a Service that gives the possibility to deploy a virtualized and on-demand instance of the IP Multimedia Subsystem platform, (2) Digital Signage Service as a Service that is based on a re-designed Digital Signage Service architecture, adopting the cloud computing principles, and (3) Information Centric Networking/Content Delivery Network as a Service that is used for distributing, caching and migrating content from other services. Possible designs for these virtualized services and applications have been identified and are being implemented. In particular, the architectures of the mentioned services were specified, adopting cloud computing principles, such as infrastructure sharing, elasticity, on-demand and pay-as-you-go. The benefits of Reactive Programming paradigm are presented in the context of Interactive Cloudified Digital Signage services in a Mobile Cloud Platform, as well as the benefit of interworking between different Mobile Cloud Networking Services as Digital Signage Service and Content Delivery Network Service for better performance of Video on Demand content deliver. Finally, the management of Service Level Agreements and the support of rating, charging and billing has also been considered and defined.

Explicit mathematics and operational set theory: some ontological comparisons

We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.

Hand-held 3D light field photography and applications

We propose a method to acquire 3D light fields using a hand-held camera, and describe several computational photography applications facilitated by our approach. As our input we take an image sequence from a camera translating along an approximately linear path with limited camera rotations. Users can acquire such data easily in a few seconds by moving a hand-held camera. We include a novel approach to resample the input into regularly sampled 3D light fields by aligning them in the spatio-temporal domain, and a technique for high-quality disparity estimation from light fields. We show applications including digital refocusing and synthetic aperture blur, foreground removal, selective colorization, and others.

Simulation of SLA-based VM-scaling algorithms for cloud-distributed applications

Cloud Computing has evolved to become an enabler for delivering access to large scale distributed applications running on managed network-connected computing systems. This makes possible hosting Distributed Enterprise Information Systems (dEISs) in cloud environments, while enforcing strict performance and quality of service requirements, defined using Service Level Agreements (SLAs). {SLAs} define the performance boundaries of distributed applications, and are enforced by a cloud management system (CMS) dynamically allocating the available computing resources to the cloud services. We present two novel VM-scaling algorithms focused on dEIS systems, which optimally detect most appropriate scaling conditions using performance-models of distributed applications derived from constant-workload benchmarks, together with SLA-specified performance constraints. We simulate the VM-scaling algorithms in a cloud simulator and compare against trace-based performance models of dEISs. We compare a total of three SLA-based VM-scaling algorithms (one using prediction mechanisms) based on a real-world application scenario involving a large variable number of users. Our results show that it is beneficial to use autoregressive predictive SLA-driven scaling algorithms in cloud management systems for guaranteeing performance invariants of distributed cloud applications, as opposed to using only reactive SLA-based VM-scaling algorithms.

Service Level Agreements-Driven Management of Distributed Applications in Cloud Computing Environments

Cloud Computing enables provisioning and distribution of highly scalable services in a reliable, on-demand and sustainable manner. However, objectives of managing enterprise distributed applications in cloud environments under Service Level Agreement (SLA) constraints lead to challenges for maintaining optimal resource control. Furthermore, conflicting objectives in management of cloud infrastructure and distributed applications might lead to violations of SLAs and inefficient use of hardware and software resources. This dissertation focusses on how SLAs can be used as an input to the cloud management system, increasing the efficiency of allocating resources, as well as that of infrastructure scaling. First, we present an extended SLA semantic model for modelling complex service-dependencies in distributed applications, and for enabling automated cloud infrastructure management operations. Second, we describe a multi-objective VM allocation algorithm for optimised resource allocation in infrastructure clouds. Third, we describe a method of discovering relations between the performance indicators of services belonging to distributed applications and then using these relations for building scaling rules that a CMS can use for automated management of VMs. Fourth, we introduce two novel VM-scaling algorithms, which optimally scale systems composed of VMs, based on given SLA performance constraints. All presented research works were implemented and tested using enterprise distributed applications.

Regularity conditions in the realisability problem in applications to point processes and random closed sets

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive ex-tension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extens ion can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed sets with given two-point covering function or contact distribution function. It is shown that the regularity condition can be efficiently checked in many cases in order to ensure that the obtained point processes are indeed locally finite and random sets have closed realisations.

Service level agreements-driven management of distributed applications in cloud computing environments

Advancements in cloud computing have enabled the proliferation of distributed applications, which require management and control of multiple services. However, without an efficient mechanism for scaling services in response to changing workload conditions, such as number of connected users, application performance might suffer, leading to violations of Service Level Agreements (SLA) and possible inefficient use of hardware resources. Combining dynamic application requirements with the increased use of virtualised computing resources creates a challenging resource Management context for application and cloud-infrastructure owners. In such complex environments, business entities use SLAs as a means for specifying quantitative and qualitative requirements of services. There are several challenges in running distributed enterprise applications in cloud environments, ranging from the instantiation of service VMs in the correct order using an adequate quantity of computing resources, to adapting the number of running services in response to varying external loads, such as number of users. The application owner is interested in finding the optimum amount of computing and network resources to use for ensuring that the performance requirements of all her/his applications are met. She/he is also interested in appropriately scaling the distributed services so that application performance guarantees are maintained even under dynamic workload conditions. Similarly, the infrastructure Providers are interested in optimally provisioning the virtual resources onto the available physical infrastructure so that her/his operational costs are minimized, while maximizing the performance of tenants’ applications. Motivated by the complexities associated with the management and scaling of distributed applications, while satisfying multiple objectives (related to both consumers and providers of cloud resources), this thesis proposes a cloud resource management platform able to dynamically provision and coordinate the various lifecycle actions on both virtual and physical cloud resources using semantically enriched SLAs. The system focuses on dynamic sizing (scaling) of virtual infrastructures composed of virtual machines (VM) bounded application services. We describe several algorithms for adapting the number of VMs allocated to the distributed application in response to changing workload conditions, based on SLA-defined performance guarantees. We also present a framework for dynamic composition of scaling rules for distributed service, which used benchmark-generated application Monitoring traces. We show how these scaling rules can be combined and included into semantic SLAs for controlling allocation of services. We also provide a detailed description of the multi-objective infrastructure resource allocation problem and various approaches to satisfying this problem. We present a resource management system based on a genetic algorithm, which performs allocation of virtual resources, while considering the optimization of multiple criteria. We prove that our approach significantly outperforms reactive VM-scaling algorithms as well as heuristic-based VM-allocation approaches.

On degeneracy and invariances of random fields paths with applications in Gaussian process modelling

We study pathwise invariances and degeneracies of random fields with motivating applications in Gaussian process modelling. The key idea is that a number of structural properties one may wish to impose a priori on functions boil down to degeneracy properties under well-chosen linear operators. We first show in a second order set-up that almost sure degeneracy of random field paths under some class of linear operators defined in terms of signed measures can be controlled through the two first moments. A special focus is then put on the Gaussian case, where these results are revisited and extended to further linear operators thanks to state-of-the-art representations. Several degeneracy properties are tackled, including random fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process modelling. In a first numerical experiment, it is shown that dedicated kernels can be used to infer an axis of symmetry. Our second numerical experiment deals with conditional simulations of a solution to the heat equation, and it is found that adapted kernels notably enable improved predictions of non-linear functionals of the field such as its maximum.

A toolbox with DERIVE: calculus on several variables, Applications of Computer Algebra

A toolbox is a set of procedures taking advantage of the computing power and graphical capacities of a CAS. With these procedures the students can solve math problems, apply mathematics to engineering or simply reinforce the learning of certain mathematical concepts. From the point of view of their construction, we can consider two types of toolboxes: (i) the closed box, built by the teacher, in which the utility files are provided to the students together with the respective tutorials and several worksheets with proposed exercises and problems,

Computer simulation of the interplay between fractal structures and surrounding heterogeneous multifractal distributions. Applications

In a large number of physical, biological and environmental processes interfaces with high irregular geometry appear separating media (phases) in which the heterogeneity of constituents is present. In this work the quantification of the interplay between irregular structures and surrounding heterogeneous distributions in the plane is made For a geometric set image and a mass distribution (measure) image supported in image, being image, the mass image gives account of the interplay between the geometric structure and the surrounding distribution. A computation method is developed for the estimation and corresponding scaling analysis of image, being image a fractal plane set of Minkowski dimension image and image a multifractal measure produced by random multiplicative cascades. The method is applied to natural and mathematical fractal structures in order to study the influence of both, the irregularity of the geometric structure and the heterogeneity of the distribution, in the scaling of image. Applications to the analysis and modeling of interplay of phases in environmental scenarios are given.

Fluid dynamics and applications,

Reproduced from typewritten copy.

A study of arithmetic recoding with applications in multiplication and division.

Vita.

Théorie du potentiel et ses applications à l'électrostatique et au magnétisme,

Available on demand as hard copy or computer file from Cornell University Library.

Traité des applications de l'analyse mathématique au jeu des échecs, précédé d'une introduction à l'usage des lecteurs soit étrangers aux échecs, soit peu versés dans l'analyse.

Available on demand as hard copy or computer file from Cornell University Library.