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.

Gehring-Hayman theorem for conformal deformations

We study conformal deformations of a uniform space that satisfies the Ahlfors Q-regularity condition on balls of Whitney type. We verify the Gehring–Hayman Theorem by using a Whitney Covering of the space.

A Small Baseline DIFSAR Approach for Investigating Deformations on Full Resolution SAR Interferograms

This paper presents a differential synthetic apertureradar (SAR) interferometry (DIFSAR) approach for investigatingdeformation phenomena on full-resolution DIFSAR interferograms.In particular, our algorithm extends the capabilityof the small-baseline subset (SBAS) technique that relies onsmall-baseline DIFSAR interferograms only and is mainly focusedon investigating large-scale deformations with spatial resolutionsof about 100 100 m. The proposed technique is implemented byusing two different sets of data generated at low (multilook data)and full (single-look data) spatial resolution, respectively. Theformer is used to identify and estimate, via the conventional SBAStechnique, large spatial scale deformation patterns, topographicerrors in the available digital elevation model, and possibleatmospheric phase artifacts; the latter allows us to detect, onthe full-resolution residual phase components, structures highlycoherent over time (buildings, rocks, lava, structures, etc.), as wellas their height and displacements. In particular, the estimation ofthe temporal evolution of these local deformations is easily implementedby applying the singular value decomposition technique.The proposed algorithm has been tested with data acquired by theEuropean Remote Sensing satellites relative to the Campania area(Italy) and validated by using geodetic measurements.

Mapping cell-matrix stresses during stretch reveals inelastic reorganization of the cytoskeleton.

The mechanical properties of the living cell are intimately related to cell signaling biology through cytoskeletal tension. The tension borne by the cytoskeleton (CSK) is in part generated internally by the actomyosin machinery and externally by stretch. Here we studied how cytoskeletal tension is modified during stretch and the tensional changes undergone by the sites of cell-matrix interaction. To this end we developed a novel technique to map cell-matrix stresses during application of stretch. We found that cell-matrix stresses increased with imposition of stretch but dropped below baseline levels on stretch release. Inhibition of the actomyosin machinery resulted in a larger relative increase in CSK tension with stretch and in a smaller drop in tension after stretch release. Cell-matrix stress maps showed that the loci of cell adhesion initially bearing greater stress also exhibited larger drops in traction forces after stretch removal. Our results suggest that stretch partially disrupts the actin-myosin apparatus and the cytoskeletal structures that support the largest CSK tension. These findings indicate that cells use the mechanical energy injected by stretch to rapidly reorganize their structure and redistribute tension.

Contractions in the 2-wasserstein lenght space and thermalization of granular media

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) | if uniformly controlled | will quantify contractivity (limit expansivity) of the flow.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

An alternative way to model merit good arguments

Besley (1988) uses a scaling approach to model merit good arguments in commodity tax policy. In this paper, I question this approach on the grounds that it produces 'wrong' recommendations--taxation (subsidisation) of merit (demerit) goods--whenever the demand for the (de)merit good is inelastic. I propose an alternative approach that does not suffer from this deficiency, and derive the ensuing first and second best tax rules, as well as the marginal cost expressions to perform tax reform analysis.

Is bundling anticompetitive?

I analyze the implications of bundling on price competition in a market for complementary products. Using a model of imperfect competition with product differentiation, I identify the incentives to bundle for two types of demand functions and study how they change with the size of the bundle. With an inelastic demand, bundling creates an advantage over uncoordinated rivals who cannot improve by bundling. I show that this no longer holds with an elastic demand. The incentives to bundle are stronger and the market outcome is symmetric bundling, the most competitive one. Profits are lowest and consumer surplus is maximized.

The demand elasticity on tolled motorways

This paper analyses the elasticities of demand in tolled motorways in Spain with respect to the main variables influencing it. The demand equation is estimated using a panel data set where the cross-section observations correspond to the different Spanish tolled motorways sections, and the temporal dimension ranges from the beginning of the eighties until the end of the nineties. The results show a high elasticity with respect to the economic activity level. The average elasticity with respect to petrol price falls around -0.3, while toll elasticities clearly vary across motorway sections. These motorway sections are classified into four groups according to the estimated toll elasticity with values that range from -0.21 for the most inelastic to -0.83 for the most elastic. The main factors that explain such differences are the quality of the alternative road and the length of the section. The long-term effect is about 50 per cent higher than the short term one; however, the period of adjustment is relatively short.

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.

Pareto-improving optimal capital and labor taxes

We show a standard model where the optimal tax reform is to cut labor taxes and leave capital taxes very high in the short and medium run. Only in the very long run would capital taxes be zero. Our model is a version of Chamley??s, with heterogeneous agents, without lump sum transfers, an upper bound on capital taxes, and a focus on Pareto improving plans. For our calibration labor taxes should be low for the first ten to twenty years, while capital taxes should be at their maximum. This policy ensures that all agents benefit from the tax reform and that capital grows quickly after when the reform begins. Therefore, the long run optimal tax mix is the opposite from the short and medium run tax mix. The initial labor tax cut is financed by deficits that lead to a positive long run level of government debt, reversing the standard prediction that government accumulates savings in models with optimal capital taxes. If labor supply is somewhat elastic benefits from tax reform are high and they can be shifted entirely to capitalists or workers by varying the length of the transition. With inelastic labor supply there is an increasing part of the equilibrium frontier, this means that the scope for benefitting the workers is limited and the total benefits from reforming taxes are much lower.

Terrestrial laser scanning for landslides deformation monitoring

Within last few years a new type of instruments called Terrestrial Laser Scanners (TLS) entered to the commercial market. These devices brought a possibility to obtain completely new type of spatial, three dimensional data describing the object of interest. TLS instruments are generating a type of data that needs a special treatment. Appearance of this technique made possible to monitor deformations of very large objects, like investigated here landslides, with new quality level. This change is visible especially with relation to the size and number of the details that can be observed with this new method. Taking into account this context presented here work is oriented on recognition and characterization of raw data received from the TLS instruments as well as processing phases, tools and techniques to do them. Main objective are definition and recognition of the problems related with usage of the TLS data, characterization of the quality single point generated by TLS, description and investigation of the TLS processing approach for landslides deformation measurements allowing to obtain 3D deformation characteristic and finally validation of the obtained results. The above objectives are based on the bibliography studies and research work followed by several experiments that will prove the conclusions.