Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

On the signature of positive braids and adjacency for torus knots

The objects of study in this thesis are knots. More precisely, positive braid knots, which include algebraic knots and torus knots. In the first part of this thesis, we compare two classical knot invariants - the genus g and the signature σ - for positive braid knots. Our main result on positive braid knots establishes a linear lower bound for the signature in terms of the genus. In the second part of the thesis, a positive braid approach is applied to the study of the local behavior of polynomial functions from the complex affine plane to the complex numbers. After endowing polynomial function germs with a suitable topology, the adjacency problem arises: for a fixed germ f, what classes of germs g can be found arbitrarily close to f? We introduce two purely topological notions of adjacency for knots and discuss connections to algebraic notions of adjacency and the adjacency problem.

A Case for CDN-as-a-Service in the Cloud: A Mobile Cloud Networking Argument

Content Distribution Networks are mandatory components of modern web architectures, with plenty of vendors offering their services. Despite its maturity, new paradigms and architecture models are still being developed in this area. Cloud Computing, on the other hand, is a more recent concept which has expanded extremely quickly, with new services being regularly added to cloud management software suites such as OpenStack. The main contribution of this paper is the architecture and the development of an open source CDN that can be provisioned in an on-demand, pay-as-you-go model thereby enabling the CDN as a Service paradigm. We describe our experience with integration of CDNaaS framework in a cloud environment, as a service for enterprise users. We emphasize the flexibility and elasticity of such a model, with each CDN instance being delivered on-demand and associated to personalized caching policies as well as an optimized choice of Points of Presence based on exact requirements of an enterprise customer. Our development is based on the framework developed in the Mobile Cloud Networking EU FP7 project, which offers its enterprise users a common framework to instantiate and control services. CDNaaS is one of the core support components in this project as is tasked to deliver different type of multimedia content to several thousands of users geographically distributed. It integrates seamlessly in the MCN service life-cycle and as such enjoys all benefits of a common design environment, allowing for an improved interoperability with the rest of the services within the MCN ecosystem.

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.

A Parametric Test of Perfect Ranking in Balanced Ranked Set Sampling

Many techniques based on data which are drawn by Ranked Set Sampling (RSS) scheme assume that the ranking of observations is perfect. Therefore it is essential to develop some methods for testing this assumption. In this article, we propose a parametric location-scale free test for assessing the assumption of perfect ranking. The results of a simulation study in two special cases of normal and exponential distributions indicate that the proposed test performs well in comparison with its leading competitors.

Mobility and bandwidth prediction in virtualized LTE systems: Architecture and challenges

Long Term Evolution (LTE) represents the fourth generation (4G) technology which is capable of providing high data rates as well as support of high speed mobility. The EU FP7 Mobile Cloud Networking (MCN) project integrates the use of cloud computing concepts in LTE mobile networks in order to increase LTE's performance. In this way a shared distributed virtualized LTE mobile network is built that can optimize the utilization of virtualized computing, storage and network resources and minimize communication delays. Two important features that can be used in such a virtualized system to improve its performance are the user mobility and bandwidth prediction. This paper introduces the architecture and challenges that are associated with user mobility and bandwidth prediction approaches in virtualized LTE systems.

A Hennessy-Milner Property for Many-Valued Modal Logics

A Hennessy-Milner property, relating modal equivalence and bisimulations, is defined for many-valued modal logics that combine a local semantics based on a complete MTL-chain (a linearly ordered commutative integral residuated lattice) with crisp Kripke frames. A necessary and sufficient algebraic condition is then provided for the class of image-finite models of these logics to admit the Hennessy-Milner property. Complete characterizations are obtained in the case of many-valued modal logics based on BL-chains (divisible MTL-chains) that are finite or have universe [0,1], including crisp Lukasiewicz, Gödel, and product modal logics.