Integration of Lie Algebroid Comorphisms

We show that the path construction integration of Lie algebroids by Lie groupoids is an actual equivalence from the category of integrable Lie algebroids and complete Lie algebroid comorphisms to the category of source 1-connected Lie groupoids and Lie groupoid comorphisms. This allows us to construct an actual symplectization functor in Poisson geometry. We include examples to show that the integrability of comorphisms and Poisson maps may not hold in the absence of a completeness assumption.Comment: 28 pages, references adde

Symplectic Microgeometry III: Monoids

We show that the category of Poisson manifolds and Poisson maps, the category of symplectic microgroupoids and lagrangian submicrogroupoids (as morphisms), and the category of monoids and monoid morphisms in the microsymplectic category are equivalent symmetric monoidal categories.Comment: 19 pages, 2 figure

Chromatographic test facility. Analysis and design of a capsule landing system and surface vehicle control system for Mars exploration

Test facility to verify design concepts and mathematical models of chromatograph for atmospheric composition analysis of Mar

On the persistence of two small-scale problems in {\Lambda}CDM

We investigate the degree to which the inclusion of baryonic physics can overcome two long-standing problems of the standard cosmological model on galaxy scales: (i) the problem of satellite planes around Local Group galaxies, and (ii) the "too big to fail" problem. By comparing dissipational and dissipationless simulations, we find no indication that the addition of baryonic physics results in more flattened satellite distributions around Milky-Way-like systems. Recent claims to the contrary are shown to derive in part from a non-standard metric for the degree of flattening, which ignores the satellites' radial positions. If the full 3D positions of the satellite galaxies are considered, none of the simulations we analyse reproduce the observed flattening nor the observed degree of kinematic coherence of the Milky Way satellite system. Our results are consistent with the expectation that baryonic physics should have little or no influence on the structure of satellite systems on scales of hundreds of kiloparsecs. Claims that the "too big to fail" problem can be resolved by the addition of baryonic physics are also shown to be problematic.Comment: 13 pages, 5 figures. Accepted for publication in ApJ. Partially written in response to arXiv:1412.274

Specialization of the rostral prefrontal cortex for distinct analogy processes

Analogical reasoning is central to learning and abstract thinking. It involves using a more familiar situation (source) to make inferences about a less familiar situation (target). According to the predominant cognitive models, analogical reasoning includes 1) generation of structured mental representations and 2) mapping based on structural similarities between them. This study used functional magnetic resonance imaging to specify the role of rostral prefrontal cortex (PFC) in these distinct processes. An experimental paradigm was designed that enabled differentiation between these processes, by temporal separation of the presentation of the source and the target. Within rostral PFC, a lateral subregion was activated by analogy task both during study of the source (before the source could be compared with a target) and when the target appeared. This may suggest that this subregion supports fundamental analogy processes such as generating structured representations of stimuli but is not specific to one particular processing stage. By contrast, a dorsomedial subregion of rostral PFC showed an interaction between task (analogy vs. control) and period (more activated when the target appeared). We propose that this region is involved in comparison or mapping processes. These results add to the growing evidence for functional differentiation between rostral PFC subregions

Stable fractal sums of pulses: the cylindrical case

A class of α-stable, 0\textlessα\textless2, processes is obtained as a sum of ’up-and-down’ pulses determined by an appropriate Poisson random measure. Processes are H-self-affine (also frequently called ’self-similar’) with H\textless1/α and have stationary increments. Their two-dimensional dependence structure resembles that of the fractional Brownian motion (for H\textless1/2), but their sample paths are highly irregular (nowhere bounded with probability 1). Generalizations using different shapes of pulses are also discussed

Formal symplectic groupoid

The multiplicative structure of the trivial symplectic groupoid over $\mathbb R^d$ associated to the zero Poisson structure can be expressed in terms of a generating function. We address the problem of deforming such a generating function in the direction of a non-trivial Poisson structure so that the multiplication remains associative. We prove that such a deformation is unique under some reasonable conditions and we give the explicit formula for it. This formula turns out to be the semi-classical approximation of Kontsevich's deformation formula. For the case of a linear Poisson structure, the deformed generating function reduces exactly to the CBH formula of the associated Lie algebra. The methods used to prove existence are interesting in their own right as they come from an at first sight unrelated domain of mathematics: the Runge--Kutta theory of the numeric integration of ODE's.Comment: 28 pages, 4 figure

The vibrational dynamics of vitreous silica: Classical force fields vs. first-principles

We compare the vibrational properties of model SiO_2 glasses generated by molecular-dynamics simulations using the effective force field of van Beest et al. (BKS) with those obtained when the BKS structure is relaxed using an ab initio calculation in the framework of the density functional theory. We find that this relaxation significantly improves the agreement of the density of states with the experimental result. For frequencies between 14 and 26 THz the nature of the vibrational modes as determined from the BKS model is very different from the one from the ab initio calculation, showing that the interpretation of the vibrational spectra in terms of calculations using effective potentials can be very misleading.Comment: 7 pages of Latex, 4 figure