On spectral types of semialgebraic sets

In this work we prove that a semialgebraic set $M\subset{\mathbb R}^m$ is determined (up to a semialgebraic homeomorphism) by its ring ${\mathcal S}(M)$ of (continuous) semialgebraic functions while its ring ${\mathcal S}^*(M)$ of (continuous) bounded semialgebraic functions only determines $M$ besides a distinguished finite subset $\eta(M)\subset M$. In addition it holds that the rings ${\mathcal S}(M)$ and ${\mathcal S}^*(M)$ are isomorphic if and only if $M$ is compact. On the other hand, their respective maximal spectra $\beta_s M$ and $\beta_s^* M$ endowed with the Zariski topology are always homeomorphic and topologically classify a `large piece' of $M$. The proof of this fact requires a careful analysis of the points of the remainder $\partial M:=\beta_s^* M\setminus M$ associated with formal paths.Comment: 22 page

Solving the Constraints of General Relativity

I show in this letter that it is possible to solve some of the constraints of the $SO(3)$-ADM formalism for general relativity by using an approach similar to the one introduced by Capovilla, Dell and Jacobson to solve the vector and scalar constraints in the Ashtekar variables framework. I discuss the advantages of using the ADM formalism and compare the result with similar proposals for different Hamiltonian formulations of general relativity.Comment: 8 pages, LATEX, no figures, Preprint CGPG-94/11-

Combating catastrophic forgetting with developmental compression

Generally intelligent agents exhibit successful behavior across problems in several settings. Endemic in approaches to realize such intelligence in machines is catastrophic forgetting: sequential learning corrupts knowledge obtained earlier in the sequence, or tasks antagonistically compete for system resources. Methods for obviating catastrophic forgetting have sought to identify and preserve features of the system necessary to solve one problem when learning to solve another, or to enforce modularity such that minimally overlapping sub-functions contain task specific knowledge. While successful, both approaches scale poorly because they require larger architectures as the number of training instances grows, causing different parts of the system to specialize for separate subsets of the data. Here we present a method for addressing catastrophic forgetting called developmental compression. It exploits the mild impacts of developmental mutations to lessen adverse changes to previously-evolved capabilities and `compresses' specialized neural networks into a generalized one. In the absence of domain knowledge, developmental compression produces systems that avoid overt specialization, alleviating the need to engineer a bespoke system for every task permutation and suggesting better scalability than existing approaches. We validate this method on a robot control problem and hope to extend this approach to other machine learning domains in the future

A liquid crystal analogue of the cosmic string

We consider the propagation of light in a anisotropic medium with a topological line defect in the realm of geometrical optics. It is shown that the effective geometry perceived by light propagating in such medium is that of a spacial section of the cosmic string spacetime.Comment: 3 pages, 2 figures. Modern Physics Letters A, accepted for publicatio

Characterization and mapping of surface physical properties of Mars from CRISM multi-angular data: application to Gusev Crater and Meridiani Planum

The analysis of the surface texture from the particle (grain size, shape and internal structure) to its organization (surface roughness) provides information on the geological processes. CRISM multi-angular observations (varied emission angles) allow to characterize the surface scattering behavior which depends on the composition but also the material physical properties (e.g., grain size, shape, internal structure, the surface roughness). After an atmospheric correction by the Multi-angle Approach for Retrieval of the Surface Reflectance from CRISM Observations, the surface reflectances at different geometries are analyzed by inverting the Hapke photometric model depending on the single scattering albedo, the 2-term phase function, the macroscopic roughness and the 2-term opposition effects. Surface photometric maps are created to observe the spatial variations of surface scattering properties as a function of geological units at the CRISM spatial resolution (200m/pixel). An application at the Mars Exploration Rover (MER) landing sites located at Gusev Crater and Meridiani Planum where orbital and in situ observations are available, is presented. Complementary orbital observations (e.g. CRISM spectra, THermal EMission Imaging System, High Resolution Imaging Science Experiment images) are used for interpreting the estimated Hapke photometric parameters in terms of physical properties. The in situ observations are used as ground truth to validate the interpretations. Varied scattering properties are observed inside a CRISM observation (5x10km) suggesting that the surfaces are controlled by local geological processes (e.g. volcanic resurfacing, aeolian and impact processes) rather than regional or global. Consistent results with the in situ observations are observed thus validating the approach and the use of photometry for the characterization of Martian surface physical properties

Using choreographies to support the gamification process on the development of an application to reduce electricity costs

Building automation systems contribute to reduce electricity costs by managing distributed energy resources in an efficient way. However, a large share of consumption cannot be optimized through automation alone, since it mainly depends on human interactions. Gamification can be used as one form of changing users’ behaviours [1], but its implementation does require assumptions on the behaviour patterns that need to be identified, encouraged, or discouraged. To tackle this problem, we propose a framework that joins building automation solutions with gamification techniques to enable behavioural demand response.info:eu-repo/semantics/publishedVersio