Real rank boundaries and loci of forms

In this article we study forbidden loci and typical ranks of forms with respect to the embeddings of $\mathbb P^1\times \mathbb P^1$ given by the line bundles $(2,2d)$. We introduce the Ranestad-Schreyer locus corresponding to supports of non-reduced apolar schemes. We show that, in those cases, this is contained in the forbidden locus. Furthermore, for these embeddings, we give a component of the real rank boundary, the hypersurface dividing the minimal typical rank from higher ones. These results generalize to a class of embeddings of $\mathbb P^n\times \mathbb P^1$. Finally, in connection with real rank boundaries, we give a new interpretation of the $2\times n \times n$ hyperdeterminant.Comment: 17 p

Production Process Modelling Architecture to Support Improved Cyber-Physical Production Systems

With the proliferation of intelligent networks in industrial environments, manufacturing SME’s have been in a continuous search for integrating and retrofitting existing assets with modern technologies that could provide low-cost solutions for optimizations in their production processes. Their willingness to support a technological evolution is firmly based on the perception that, in the future, better tools will guarantee process control, surveillance and maintenance. For this to happen, the digitalization of valuable and extractable information must be held in a cost-effective manner, through contemporary approaches such as IoT, creating the required fluidity between hardware and software, for implementing Cyber-Physical modules in the manufacturing process. The goal of this work is to develop an architecture that will support companies to digitize their machines and processes through an MDA approach, by modeling their production processes and physical resources, and transforming into an implementation model, using contemporary CPS and IoT concepts, to be continuously improved using forecasting/predictive algorithms and analytics.authorsversionpublishe

Continuous non-perturbative regularization of QED

We regularize in a continuous manner the path integral of QED by construction of a non-local version of its action by means of a regularized form of Dirac's $\delta$ functions. Since the action and the measure are both invariant under the gauge group, this regularization scheme is intrinsically non-perturbative. Despite the fact that the non-local action converges formally to the local one as the cutoff goes to infinity, the regularized theory keeps trace of the non-locality through the appearance of a quadratic divergence in the transverse part of the polarization operator. This term which is uniquely defined by the choice of the cutoff functions can be removed by a redefinition of the regularized action. We notice that as for chiral fermions on the lattice, there is an obstruction to construct a continuous and non ambiguous regularization in four dimensions. With the help of the regularized equations of motion, we calculate the one particle irreducible functions which are known to be divergent by naive power counting at the one loop order.Comment: 23 pages, LaTeX, 5 Encapsulated Postscript figures. Improved and revised version, to appear in Phys. Rev.

Goal-Based Selection of Visual Representations for Big Data Analytics

The H2020 TOREADOR Project adopts a model-driven architecture to streamline big data analytics and make it widely available to companies as a service. Our work in this context focuses on visualization, in particular on how to automate the translation of the visualization objectives declared by the user into a suitable visualization type. To this end we first define a visualization context based on seven prioritizable coordinates for assessing the user's objectives and describing the data to be visualized; then we propose a skyline-based technique for automatically translating a visualization context into a set of suitable visualization types. Finally, we evaluate our approach on a real use case excerpted from the pilot applications of TOREADOR

Regularization as quantization in reducible representations of CCR

A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials is tested on the example of quantum electrodynamic fields produced by a classical current. The scheme implies a modified but very physically looking Hamiltonian. We solve Heisenberg equations of motion and compute photon statistics. Poisson statistics naturally occurs and no infrared divergence is found even for pointlike sources. Classical fields produced by classical sources can be obtained if one computes coherent-state averages of Heisenberg-picture operators. It is shown that the new form of representation automatically smears out pointlike currents. We discuss in detail Poincar\'e covariance of the theory and the role of Bogoliubov transformations for the issue of gauge invariance. The representation we employ is parametrized by a number that is related to R\'enyi's $\alpha$. It is shown that the ``Shannon limit" $\alpha\to 1$ plays here a role of correspondence principle with the standard regularized formalism.Comment: minor extensions, version submitted for publicatio

Confining Properties of the Homogeneous Self-Dual Field and the Effective Potential in SU(2) Yang-Mills Theory

We examine in non-Abelian gauge theory the heavy quark limit in the presence of the (anti-)self-dual homogeneous background field and see that a confining potential emerges, consistent with the Wilson criterion, although the potential is quadratic and not linear in the quark separation. This builds upon the well-known feature that propagators in such a background field are entire functions. The way in which deconfinement can occur at finite temperature is then studied in the static temporal gauge by calculation of the effective potential at high temperature. Finally we discuss the problems to be surmounted in setting up the calculation of the effective potential nonperturbatively on the lattice.Comment: 31 pages, LaTeX, expanded discussion and derivations in Sections 2 and

Matrilineal diversity and population history of Norwegians

Background While well known for its Viking past, Norway's population history and the influences that have shaped its genetic diversity are less well understood. This is particularly true with respect to its demography, migration patterns, and dialectal regions, despite there being curated historical records for the past several centuries. In this study, we undertook an analysis of mitochondrial DNA (mtDNA) diversity within the country to elaborate this history from a matrilineal genetic perspective. Methods We aggregated 1174 partial modern Norwegian mtDNA sequences from the published literature and subjected them to detailed statistical and phylogenetic analysis by dialectal regions and localities. We further contextualized the matrilineal ancestry of modern Norwegians with data from Mesolithic, Iron Age, and historic period populations. Results Modern Norwegian mtDNAs fell into eight West Eurasian (N, HV, JT, I, U, K, X, W), five East Eurasian (A, F, G, N11, Z), and one African (L2) haplogroups. Pairwise analysis of molecular variance (AMOVA) estimates for all Norwegians indicated they were differentiated from each other at 1.68% (p < 0.001). Norwegians within the same dialectal region also showed genetic similarities to each other, although differences between subpopulations within dialectal regions were also observed. In addition, certain mtDNA lineages in modern Norwegians were also found among prehistoric and historic period populations, suggesting some level of genetic continuity over hundreds to many thousands of years. Conclusions This analysis of mtDNA diversity provides a detailed picture of the genetic variation within Norway in light of its topography, settlement history, and historical migrations over the past several centuries.publishedVersio

Enabling agile web development through in-browser code generation and evaluation

Rapid evolution and flexibility are the key of modern web application development. Rapid Prototyping approaches try to facilitate evolution by reducing the time between the elicitation of a new requirement and the evaluation of a prototype by both developers and customers. Software generation, with disciplines such as Software Product Lines Engineering or Model Driven Engineering, favours the required flexibility for the development process. Nevertheless, each small change in the design of an application requires a full redeployment of complex environments in order to allow customers to test and evaluate the new configuration. In this work we present an approach that improves the development process reducing the complexity of deploying evaluation prototypes and enabling an agile development cycle. The approach can be applied using software generation and it is based on in-browser generation and evaluation. We also describe two real world tools that have integrated the proposed approach in their development cycle