Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

Peroxisome proliferator-activated receptor structures: ligand specificity, molecular switch and interactions with regulators.

Peroxisome proliferator-activated receptors (PPARs) compose a family of nuclear receptors that mediate the effects of lipidic ligands at the transcriptional level. In this review, we highlight advances in the understanding of the PPAR ligand binding domain (LBD) structure at the atomic level. The overall structure of PPARs LBD is described, and important protein ligand interactions are presented. Structure-activity relationships between isotypes structures and ligand specificity are addressed. It is shown that the numerous experimental three-dimensional structures available, together with in silico simulations, help understanding the role played by the activating function-2 (AF-2) in PPARs activation and its underlying molecular mechanism. The relation between the PPARs constitutive activity and the intrinsic stability of the active conformation is discussed. Finally, the interactions of PPARs LBD with co-activators or co-repressors, as well as with the retinoid X receptor (RXR) are described and considered in relation to PPARs activation.

The 16p11.2 locus modulates brain structures common to autism, schizophrenia and obesity

Anatomical structures and mechanisms linking genes to neuropsychiatric disorders are not deciphered. Reciprocal copy number variants at the 16p11.2 BP4-BP5 locus offer a unique opportunity to study the intermediate phenotypes in carriers at high risk for autism spectrum disorder (ASD) or schizophrenia (SZ). We investigated the variation in brain anatomy in 16p11.2 deletion and duplication carriers. Beyond gene dosage effects on global brain metrics, we show that the number of genomic copies negatively correlated to the gray matter volume and white matter tissue properties in cortico-subcortical regions implicated in reward, language and social cognition. Despite the near absence of ASD or SZ diagnoses in our 16p11.2 cohort, the pattern of brain anatomy changes in carriers spatially overlaps with the well-established structural abnormalities in ASD and SZ. Using measures of peripheral mRNA levels, we confirm our genomic copy number findings. This combined molecular, neuroimaging and clinical approach, applied to larger datasets, will help interpret the relative contributions of genes to neuropsychiatric conditions by measuring their effect on local brain anatomy.Molecular Psychiatry advance online publication, 25 November 2014; doi:10.1038/mp.2014.145.

Model structures on the category of small double categories

In this paper we obtain several model structures on DblCat, the category of small double categories. Our model structures have three sources. We first transfer across a categorification-nerve adjunction. Secondly, we view double categories as internal categories in Cat and take as our weak equivalences various internal equivalences defined via Grothendieck topologies. Thirdly, DblCat inherits a model structure as a category of algebras over a 2-monad. Some of these model structures coincide and the different points of view give us further results about cofibrant replacements and cofi brant objects. As part of this program we give explicit descriptions and discuss properties of free double categories, quotient double categories, colimits of double categories, and several nerves and categorifications.

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Inheritance of ductile and brittle structures in the development of large rock slope instabilities: Examples from western Norway

The high density of slope failures in western Norway is due to the steep relief and to the concentration of various structures that followed protracted ductile and brittle tectonics. On the 72 investigated rock slope instabilities, 13 were developed in soft weathered mafic and phyllitic allochthons. Only the intrinsic weakness of such rocks increases the susceptibility to gravitational deformation. In contrast, the gravitational structures in the hard gneisses reactivate prominent ductile or/and brittle fabrics. At 30 rockslides along cataclinal slopes, weak mafic layers of foliation are reactivated as basal planes. Slope-parallel steep foliation forms back-cracks of unstable columns. Folds are specifically present in the Storfjord area, together with a clustering of potential slope failures. Folding increases the probability of having favourably orientated planes with respect to the gravitational forces and the slope. High water pressure is believed to seasonally build up along the shallow-dipping Caledonian detachments and may contribute to destabilization of the rock slope upwards. Regional cataclastic faults localized the gravitational structures at 45 sites. The volume of the slope instabilities tends to increase with the amount of reactivated prominent structures and the spacing of the latter controls the size of instabilities.

Formal deformations of Poisson structures in low dimensions

In this paper, we study formal deformations of Poisson structures, especially for three families of Poisson varieties in dimensions two and three. For these families of Poisson structures, using an explicit basis of the second Poisson cohomology space, we solve the deformation equations at each step and obtain a large family of formal deformations for each Poisson structure which we consider. With the help of an explicit formula, we show that this family contains, modulo equivalence, all possible formal eformations. We show moreover that, when the Poisson structure is generic, all members of the family are non-equivalent.

Stability of Growth Models with Generalised Lag Structures

This paper considers the lag structures of dynamic models in economics, arguing that the standard approach is too simple to capture the complexity of actual lag structures arising, for example, from production and investment decisions. It is argued that recent (1990s) developments in the the theory of functional differential equations provide a means to analyse models with generalised lag structures. The stability and asymptotic stability of two growth models with generalised lag structures are analysed. The paper concludes with some speculative discussion of time-varying parameters.

Free Mobility and Taste-Homogeneity of Jurisdiction Structures

We consider a population of agents distributed on the unit interval. Agents form jurisdictions in order to provide a public facility and share its costs equally. This creates an incentive to form large entities. Individuals also incur a transportation cost depending on their location and that of the facility which makes small jurisdictions advantageous. We consider a fairly general class of distributions of agents and generalize previous versions of this model by allowing for non-linear transportation costs. We show that, in general, jurisdictions are not necessarily homogeneous. However, they are if facilities are always intraterritory and transportation costs are superadditive. Superadditivity can be weakened to strictly increasing and strictly concave when agents are uniformly distributed. Keywords: Consecutiveness, stratification, local public goods, coalition formation, country formation. JEL Classification: C71 (Cooperative Games), D71 (Social Choice; Clubs; Committees; Associations), H73 (Interjurisdictional Differentials and Their Effects).

Structures and failure mechanisms analysis of Turtle Mountain

The 30 M m3 rockslide that occurred on the east face of Turtle Mountain in the Crowsnest Pass area (Alberta) in 1903 is one of the most famous landslides in the world. In this paper, the structural features of the South part of Turtle Mountain are investigated in order to understand the present-day scar morphology and to identify the most important failure mechanisms. The structural features were mapped using a high resolution digital elevation model (DEM) in order to have a large overview of the relevant structural features. At the same time, a field survey was carried out and small scale fractures were analyzed in different parts of southern Turtle Mountain in order to confirm the DEM analysis. Results allow to identify six main discontinuity sets that influence the Turtle Mountain morphology. These discontinuity sets were then used to identify the potential failure mechanisms affecting Third Peak and South Peak area.

Moduli of flat conformal structures of hyperbolic type

"Vegeu el resum a l'inici del document del fitxer adjunt."

Condensation of polyhedric structures onto soap films

We study the existence of solutions to general measure-minimization problems over topological classes that are stable under localized Lipschitz homotopy, including the standard Plateau problem without the need for restrictive assumptions such as orientability or even rectifiability of surfaces. In case of problems over an open and bounded domain we establish the existence of a “minimal candidate”, obtained as the limit for the local Hausdorff convergence of a minimizing sequence for which the measure is lower-semicontinuous. Although we do not give a way to control the topological constraint when taking limit yet— except for some examples of topological classes preserving local separation or for periodic two-dimensional sets — we prove that this candidate is an Almgren-minimal set. Thus, using regularity results such as Jean Taylor’s theorem, this could be a way to find solutions to the above minimization problems under a generic setup in arbitrary dimension and codimension.

Complex landslide behaviour and structural controlled by the structures: A 3D conceptual model example of Åknes rockslide, Norway

Åknes is an active complex large rockslide of approximately 30?40 Mm3 located within the Proterozoic gneisses of western Norway. The observed surface displacements indicate that this rockslide is divided into several blocks moving in different directions at velocities of between 3 and 10 cm year?1. Because of regional safety issues and economic interests this rockslide has been extensively monitored since 2004. The understanding of the deformation mechanism is crucial for the implementation of a viable monitoring system. Detailed field investigations and the analysis of a digital elevation model (DEM) indicate that the movements and the block geometry are controlled by the main schistosity (S1) in gneisses, folds, joints and regional faults. Such complex slope deformations use pre-existing structures, but also result in new failure surfaces and deformation zones, like preferential rupture in fold-hinge zones. Our interpretation provides a consistent conceptual three-dimensional (3D) model for the movements measured by various methods that is crucial for numerical stability modelling. In addition, this reinterpretation of the morphology confirms that in the past several rockslides occurred from the Åknes slope. They may be related to scars propagating along the vertical foliation in folds hinges. Finally, a model of the evolution of the Åknes slope is presented.