Holomorphic symplectic geometry: a problem list

A list of open problems on holomorphic symplectic, contact and Poisson manifolds

Modelling and analyzing adaptive self-assembling strategies with Maude

Building adaptive systems with predictable emergent behavior is a challenging task and it is becoming a critical need. The research community has accepted the challenge by introducing approaches of various nature: from software architectures, to programming paradigms, to analysis techniques. We recently proposed a conceptual framework for adaptation centered around the role of control data. In this paper we show that it can be naturally realized in a reflective logical language like Maude by using the Reflective Russian Dolls model. Moreover, we exploit this model to specify and analyse a prominent example of adaptive system: robot swarms equipped with obstacle-avoidance self-assembly strategies. The analysis exploits the statistical model checker PVesta

Measurement of the total cross section for e^+e^-→hadrons at √s=10.52 GeV

Using the CLEO detector at the Cornell Electron Storage Ring, we have made a measurement of R≡σ(e^+e^-→hadrons)/σ(e^+e^-→μ^+μ^-)=3.56±0.01±0.07 at √s=10.52 GeV. This implies a value for the strong coupling constant of α_s(10.52 GeV)=0.20±0.01±0.06, or α_s(MZ)=0.13±0.005±0.03

Lagrangian fibrations of holomorphic-symplectic varieties of K3^[n]-type

Let X be a compact Kahler holomorphic-symplectic manifold, which is deformation equivalent to the Hilbert scheme of length n subschemes of a K3 surface. Let L be a nef line-bundle on X, such that the 2n-th power of c_1(L) vanishes and c_1(L) is primitive. Assume that the two dimensional subspace H^{2,0}(X) + H^{0,2}(X), of the second cohomology of X with complex coefficients, intersects trivially the integral cohomology. We prove that the linear system of L is base point free and it induces a Lagrangian fibration on X. In particular, the line-bundle L is effective. A determination of the semi-group of effective divisor classes on X follows, when X is projective. For a generic such pair (X,L), not necessarily projective, we show that X is bimeromorphic to a Tate-Shafarevich twist of a moduli space of stable torsion sheaves, each with pure one dimensional support, on a projective K3 surface.Comment: 34 pages. v3: Reference [Mat5] and Remark 1.8 added. Incorporated improvement to the exposition and corrected typos according to the referees suggestions. To appear in the proceedings of the conference Algebraic and Complex Geometry, Hannover 201

Data protection in elderly health care platforms

Ambient Assisted Living provides solutions to the increasing cognitive problems that affect the elderly population. To provide all features possible, Ambient Assisted Living projects require access to personal and private information of their users. Currently, the legal issues arisen in Ambient Assisted Living are a hot topic in the European Union, especially aspects regarding unsupervised data processing and cross-sharing of personal information. In this paper it is presented the iGenda project, which is a Cognitive Assistant inserted in the Ambient Assisted Living area which aims to build safe environments that adapt themselves to one’s individual needs. However, one of the issues is the protection of the data flowing within the system and the protection of user’s fundamental rights. It is also presented the principles and legal guarantees of data protection and transmission, and legal aspects are explained, embracing appropriate solutions to technological features that may be a threat.FEDER - Federación Española de Enfermedades Raras(TIN2015-65515-C4-1-R). COMPETE: POCI-01-0145-FEDER-007043 and FCT-Fundação para a Ciência e Tecnologia within the Project Scope UID/ CEC/00319/2013. A. Costa thanks the Fundação para a Ciência e a Tecnologia (FCT) the Post-Doc scholarship with the Ref. SFRH/BPD/102696/2014. This work is also partially supported by the MINECO/FEDER TIN2015-65515-C4-1-R

Identifying component modules

A computer-based system for modelling component dependencies and identifying component modules is presented. A variation of the Dependency Structure Matrix (DSM) representation was used to model component dependencies. The system utilises a two-stage approach towards facilitating the identification of a hierarchical modular structure. The first stage calculates a value for a clustering criterion that may be used to group component dependencies together. A Genetic Algorithm is described to optimise the order of the components within the DSM with the focus of minimising the value of the clustering criterion to identify the most significant component groupings (modules) within the product structure. The second stage utilises a 'Module Strength Indicator' (MSI) function to determine a value representative of the degree of modularity of the component groupings. The application of this function to the DSM produces a 'Module Structure Matrix' (MSM) depicting the relative modularity of available component groupings within it. The approach enabled the identification of hierarchical modularity in the product structure without the requirement for any additional domain specific knowledge within the system. The system supports design by providing mechanisms to explicitly represent and utilise component and dependency knowledge to facilitate the nontrivial task of determining near-optimal component modules and representing product modularity

Cities in fiction: Perambulations with John Berger

This paper explores selected novels by John Berger in which cities play a central role. These cities are places, partially real and partially imagined, where memory, hope, and despair intersect. My reading of the novels enables me to trace important themes in recent discourses on the nature of contemporary capitalism, including notions of resistance and universality. I also show how Berger?s work points to a writing that can break free from the curious capacity of capitalism to absorb and feed of its critique

The Tate conjecture for K3 surfaces over finite fields

Artin's conjecture states that supersingular K3 surfaces over finite fields have Picard number 22. In this paper, we prove Artin's conjecture over fields of characteristic p>3. This implies Tate's conjecture for K3 surfaces over finite fields of characteristic p>3. Our results also yield the Tate conjecture for divisors on certain holomorphic symplectic varieties over finite fields, with some restrictions on the characteristic. As a consequence, we prove the Tate conjecture for cycles of codimension 2 on cubic fourfolds over finite fields of characteristic p>3.Comment: 20 pages, minor changes. Theorem 4 is stated in greater generality, but proofs don't change. Comments still welcom

Magnetization of ferrofluids with dipolar interactions - a Born--Mayer expansion

For ferrofluids that are described by a system of hard spheres interacting via dipolar forces we evaluate the magnetization as a function of the internal magnetic field with a Born--Mayer technique and an expansion in the dipolar coupling strength. Two different approximations are presented for the magnetization considering different contributions to a series expansion in terms of the volume fraction of the particles and the dipolar coupling strength.Comment: 19 pages, 11 figures submitted to PR