Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models

The paper is mostly devoted to applications of a novel optimal control theory for perturbed sweeping/Moreau processes to two practical dynamical models. The first model addresses mobile robot dynamics with obstacles, and the second one concerns control and optimization of traffic flows. Describing these models as controlled sweeping processes with pointwise/hard control and state constraints and applying new necessary optimality conditions for such systems allow us to develop efficient procedures to solve naturally formulated optimal control problems for the models under consideration and completely calculate optimal solutions in particular situations

Implicación das proteínas reguladas por Hakai en cancro

[Abstract]: Most human malignant tumours are carcinomas, and the most common cause of mortality is due to metastasis. The E3 ubiquitin-ligase Hakai protein is responsible of the degradation of the E-cadherin at post-traslational level, and in consequence the activation of the epithelial-to-mesenchymal transition programme (EMT). In this study, I analysed the expression levels of the heat shock proteins Hsp70 and Hsp90, previously identified as Hakai-regulated proteins and notoriously related to cancer. I analysed the expression of these proteins in healthy colon tissues, adenoma and different TNM-tumour stages. Then, the expression levels of Hsp90 were analysed by transiently overexpressing Hakai in colon epithelial tumour cells. The Hsp90 levels increase in the transition from healthy and adenoma to carcinoma in human colon adenocarcinoma progression. Furthermore, by immunofluorescence it was detected an increase Hsp90 protein expression in Hakai-transfected LoVo cells.[Resumen]: La mayoría de los tumores malignos humanos son carcinomas y la mayoría de las muertes por cáncer son debidas a las metástasis. La proteína E3 ubiquitin-ligasa Hakai es responsable de la degradación de E-cadherina a nivel postraduccional, y en consecuencia se activa el programa de transición epitelio-mesénquima (EMT). En este estudio, analicé los niveles de expresión de las proteínas de choque térmico Hsp70 y Hsp90, previamente identificadas como proteínas reguladas por Hakai y con un papel relevante en cáncer. Analicé la expresión de estas proteínas en tejidos de colon sanos, adenomas y diferentes estadios TNM de progresión tumoral. A continuación, los niveles de expresión de Hsp90 fueron analizados tras la sobreexpresion transitoria de Hakai en células epiteliales tumorales de colon. Mis resultados indican que los niveles de Hsp90 se incrementan en la transición de tejidos sanos y adenoma a carcinoma en la progresión tumoral de adenocarcinoma humano. Además, por immunofluorescencia detecté un incremento en los niveles de expresión de proteína Hsp90 en las células LoVo transfectadas con Hakai.[Resumo]: A maioría dos tumores malignos en humanos son carcinomas e a maioría das mortes por cancro son debidas á metástase. A proteína E3 ubiquitín-ligasa Hakai é responsable da degradación de E-cadherina a nivel postraduccional, e en consecuencia actívase o programa de transición epitelio-mesénquima (EMT). Neste estudo, analicei os niveis de expresión das proteínas de choque térmico Hsp70 e Hsp90, previamente identificadas como proteínas reguladas por Hakai e con un papel relevante no cancro. Analicei a expresión destas proteínas en tecidos de colon sans, adenomas e diferentes estadios TNM de progresión tumoral. A continuación, os niveis de expresión de Hsp90 foron analizados tra a sobreexpresión transitoria de Hakai en células epiteliais tumorais de colon. Os meus resultados indican que os niveis de Hsp90 increméntanse na transición de texidos sanos e adenoma a carcinoma na progresión tumoral de adenocarcinoma humano. Ademais, por inmunofluorescencia detectei un incremento dos niveis de expresión da proteína Hsp90 nas células LoVo transfectadas con Hakai.Traballo fin de mestrado (UDC.CIE). Bioloxía molecular, celular e xenética. Curso 2017/201

The Grand Challenges: A Potential Boost for a Responsible Research and Innovation

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Estimating Fiscal Multipliers: News From A Non-linear World

open4siCaggiano acknowledges the financial support received by the Visiting Research Scholar programme offered by the University of MelbourneWe estimate non-linear VARs to assess to what extent fiscal spending multipliers are countercyclical in the US. We deal with the issue of non-fundamentalness due to fiscal foresight by appealing to sums of revisions of expectations of fiscal expenditures. This measure of anticipated fiscal shocks is shown to carry valuable information about future dynamics of public spending. Results based on generalised impulse responses suggest that fiscal spending multipliers in recessions are greater than one, but not statistically larger than those in expansions. However, non-linearities arise when focusing on 'extreme' events, that is, deep recessions versus strong expansionary periods.openCaggiano, Giovanni; Castelnuovo, Efrem; Colombo, Valentina; Nodari, GabrielaCaggiano, Giovanni; Castelnuovo, Efrem; Colombo, Valentina; Nodari, Gabriel

Non-Lipschitz points and the SBV regularity of the minimum time function

This paper is devoted to the study of the Hausdorff dimension of the singular set of the minimum time function $T$ under controllability conditions which do not imply the Lipschitz continuity of $T$. We consider first the case of normal linear control systems with constant coefficients in $\mathbb{R}^N$. We characterize points around which $T$ is not Lipschitz as those which can be reached from the origin by an optimal trajectory (of the reversed dynamics) with vanishing minimized Hamiltonian. Linearity permits an explicit representation of such set, that we call $\mathcal{S}$. Furthermore, we show that $\mathcal{S}$ is $\mathcal{H}^{N-1}$-rectifiable with positive $\mathcal{H}^{N-1}$-measure. Second, we consider a class of control-affine \textit{planar} nonlinear systems satisfying a second order controllability condition: we characterize the set $\mathcal{S}$ in a neighborhood of the origin in a similar way and prove the $\mathcal{H}^1$-rectifiability of $\mathcal{S}$ and that $\mathcal{H}^1(\mathcal{S})>0$. In both cases, $T$ is known to have epigraph with positive reach, hence to be a locally $BV$ function (see \cite{CMW,GK}). Since the Cantor part of $DT$ must be concentrated in $\mathcal{S}$, our analysis yields that $T$ is $SBV$, i.e., the Cantor part of $DT$ vanishes. Our results imply also that $T$ is locally of class $\mathcal{C}^{1,1}$ outside a $\mathcal{H}^{N-1}$-rectifiable set. With small changes, our results are valid also in the case of multiple control input.Comment: 23 page

Optimal control of the sweeping process over polyhedral controlled sets

The paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping/Moreau process while using controls to determine the best shape of moving convex polyhedra in order to optimize the given Bolza-type functional, which depends on control and state variables as well as their velocities. Besides the highly non-Lipschitzian nature of the unbounded differential inclusion of the controlled sweeping process, the optimal control problems under consideration contain intrinsic state constraints of the inequality and equality types. All of this creates serious challenges for deriving necessary optimality conditions. We develop here the method of discrete approximations and combine it with advanced tools of first-order and second-order variational analysis and generalized differentiation. This approach allows us to establish constructive necessary optimality conditions for local minimizers of the controlled sweeping process expressed entirely in terms of the problem data under fairly unrestrictive assumptions. As a by-product of the developed approach, we prove the strong $W^{1,2}$-convergence of optimal solutions of discrete approximations to a given local minimizer of the continuous-time system and derive necessary optimality conditions for the discrete counterparts. The established necessary optimality conditions for the sweeping process are illustrated by several examples

Discrete Approximations of a Controlled Sweeping Process

The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhe- dral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of equality and inequality types. It makes challenging and difficult their anal- ysis and optimization. In this paper we establish some existence results for the sweeping process under consideration and develop the method of discrete approximations that allows us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type sweeping process by their discrete counterparts

Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins

In this work we propose an Uncertainty Quantification methodology for sedimentary basins evolution under mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only) system of PDEs with uncertain parameters. While in previous works (Formaggia et al. 2013, Porta et al., 2014) we assumed a simplified depositional history with only one material, in this work we consider multi-layered basins, in which each layer is characterized by a different material, and hence by different properties. This setting requires several improvements with respect to our earlier works, both concerning the deterministic solver and the stochastic discretization. On the deterministic side, we replace the previous fixed-point iterative solver with a more efficient Newton solver at each step of the time-discretization. On the stochastic side, the multi-layered structure gives rise to discontinuities in the dependence of the state variables on the uncertain parameters, that need an appropriate treatment for surrogate modeling techniques, such as sparse grids, to be effective. We propose an innovative methodology to this end which relies on a change of coordinate system to align the discontinuities of the target function within the random parameter space. The reference coordinate system is built upon exploiting physical features of the problem at hand. We employ the locations of material interfaces, which display a smooth dependence on the random parameters and are therefore amenable to sparse grid polynomial approximations. We showcase the capabilities of our numerical methodologies through two synthetic test cases. In particular, we show that our methodology reproduces with high accuracy multi-modal probability density functions displayed by target state variables (e.g., porosity).Comment: 25 pages, 30 figure