Rasmussen's spectral sequences and the \germslN-concordance invariants

Combining known spectral sequences with a new spectral sequence relating reduced and unreduced slN-homology yields a relations hip between the Homflypt-homology of a knot and its slN-concordance invariants. As an application, some of the slN-concordance invariants are shown to be linearly independent.

Heterotic T-folds with a small number of neutral moduli

We discuss non-geometric supersymmetric heterotic string models in D=4, in the framework of the free fermionic construction. We perform a systematic scan of models with four a priori left-right asymmetric Z2 projections and shifts. We analyze some 220 models, identifying 18 inequivalent classes and addressing variants generated by discrete torsions. They do not contain geometrical or trivial neutral moduli, apart from the dilaton. However, we show the existence of flat directions in the form of exactly marginal deformations and identify patterns of symmetry breaking where product gauge groups, realized at level one, are broken to their diagonal at higher level. We also describe an “inverse Gepner map” from Heterotic to Type II models that could be used, in certain non geometric settings, to define “effective” topological invariants.

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.

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.

A Unified Approach to Architecture Conformance Checking

Software erosion can be controlled by periodically checking for consistency between the de facto architecture and its theoretical counterpart. Studies show that this process is often not automated and that developers still rely heavily on manual reviews, despite the availability of a large number of tools. This is partially due to the high cost involved in setting up and maintaining tool-specific and incompatible test specifications that replicate otherwise documented invariants. To reduce this cost, our approach consists in unifying the functionality provided by existing tools under the umbrella of a common business-readable DSL. By using a declarative language, we are able to write tool-agnostic rules that are simple enough to be understood by non-technical stakeholders and, at the same time, can be interpreted as a rigorous specification for checking architecture conformance

On the Evaluation of a DSL for Architectural Consistency Checking

Software architecture erodes over time and needs to be constantly monitored to be kept consistent with its original intended design. Consistency is rarely monitored using automated techniques. The cost associated to such an activity is typically not considered proportional to its benefits. To improve this situation, we propose Dicto, a uniform DSL for specifying architectural invariants. This language is designed to reduce the cost of consistency checking by offering a framework in which existing validation tools can be matched to newly-defined language constructs. In this paper we discuss how such a DSL can be qualitatively and qualitatively evaluated in practice.