COHORT ANALYSIS OF FOOD CONSUMPTION: A CASE OF RAPIDLY CHANGING JAPANESE CONSUMPTION

Food Consumption/Nutrition/Food Safety,

Improved approximation rates for a parabolic control problem with an objective promoting directional sparsity

We discretize a directionally sparse parabolic control problem governed by a linear equation by means of control approximations that are piecewise constant in time and continuous piecewise linear in space. By discretizing the objective functional with the help of appropriate numerical quadrature formulas, we are able to show that the discrete optimal solution exhibits a directional sparse pattern alike the one enjoyed by the continuous solution. Error estimates are obtained and a comparison with the cases of having piecewise approximations of the control or a semilinear state equation are discussed. Numerical experiments that illustrate the theoretical results are included.The first two authors were partially supported by the Spanish Ministerio de Economía y Competitividad under projects MTM2014-57531-P and MTM2017-83185-P

Absorbing boundary conditions for the Westervelt equation

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation

A review on sparse solutions in optimal control of partial differential equations

In this paper a review of the results on sparse controls for partial differential equations is presented. There are two different approaches to the sparsity study of control problems. One approach consists of taking functions to control the system, putting in the cost functional a convenient term that promotes the sparsity of the optimal control. A second approach deals with controls that are Borel measures and the norm of the measure is involved in the cost functional. The use of measures as controls allows to obtain optimal controls supported on a zero Lebesgue measure set, which is very interesting for practical implementation. If the state equation is linear, then we can carry out a complete analysis of the control problem with measures. However, if the equation is nonlinear the use of measures to control the system is still an open problem, in general, and the use of functions to control the system seems to be more appropriate.This work was partially supported by the Spanish Ministerio de Economía y Competitividad under project MTM2014-57531-P

Analysis of optimal control problems of semilinear elliptic equations by BV-functions

Optimal control problems for semilinear elliptic equations with control costs in the space of bounded variations are analysed. BV-based optimal controls favor piecewise constant, and hence ’simple’ controls, with few jumps. Existence of optimal controls, necessary and sufficient optimality conditions of first and second order are analysed. Special attention is paid on the effect of the choice of the vector norm in the definition of the BV-seminorm for the optimal primal and adjoined variables.The first author was partially supported by Spanish Ministerio de Economía, Industria y Competitividad under research projects MTM2014-57531-P and MTM2017-83185-P. The second was partially supported by the ERC advanced grant 668998 (OCLOC) under the EUs H2020 research program

Contribution of glaciers to water, energy and food security in mountain regions: current perspectives and future priorities

Mountain glaciers are crucial sources of fresh water, contributing directly and indirectly to water, energy and food supplies for hundreds of millions of people. Assessing the impact of diminishing glacial meltwater contributions to the security of this resource is critical as we seek to manage and adapt to changing freshwater dynamics in a warming world. Both water quantity and quality influence water (in)security, so understanding the fluxes of water, sediment and contaminants through glacial and proglacial systems is required for holistic assessment of meltwater contribution to downstream resource security. In this paper we consider the socio-environmental role of and pressures on glacier-fed waters, discuss key research priorities for the assessment of both the quantity and quality of meltwater and reflect on the importance of situating our understanding within a transdisciplinary and inclusive research landscape

Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1d case

International audienceIn this paper we address some ill-posed problems involving the heat or the wave equation in one dimension, in particular the backward heat equation and the heat/wave equation with lateral Cauchy data. The main objective is to introduce some variational mixed formulations of quasi-reversibility which enable us to solve these ill-posed problems by using some classical La-grange finite elements. The inverse obstacle problems with initial condition and lateral Cauchy data for heat/wave equation are also considered, by using an elementary level set method combined with the quasi-reversibility method. Some numerical experiments are presented to illustrate the feasibility for our strategy in all those situations. 1. Introduction. The method of quasi-reversibility has now a quite long history since the pioneering book of Latt es and Lions in 1967 [1]. The original idea of these authors was, starting from an ill-posed problem which satisfies the uniqueness property, to introduce a perturbation of such problem involving a small positive parameter ε. This perturbation has essentially two effects. Firstly the perturbation transforms the initial ill-posed problem into a well-posed one for any ε, secondly the solution to such problem converges to the solution (if it exists) to the initial ill-posed problem when ε tends to 0. Generally, the ill-posedness in the initial problem is due to unsuitable boundary conditions. As typical examples of linear ill-posed problems one may think of the backward heat equation, that is the initial condition is replaced by a final condition, or the heat or wave equations with lateral Cauchy data, that is the usual Dirichlet or Neumann boundary condition on the boundary of the domain is replaced by a pair of Dirichlet and Neumann boundary conditions on the same subpart of the boundary, no data being prescribed on the complementary part of the boundary

Sparse initial data indentification for parabolic pde and its finite element approximations

We address the problem of inverse source identification for parabolic equations from the optimal control viewpoint employing measures of minimal norm as initial data. We adopt the point of view of approximate controllability so that the target is not required to be achieved exactly but only in an approximate sense. We prove an approximate inversion result and derive a characterization of the optimal initial measures by means of duality and the minimization of a suitable quadratic functional on the solutions of the adjoint system. We prove the sparsity of the optimal initial measures showing that they are supported in sets of null Lebesgue measure. As a consequence, approximate controllability can be achieved efficiently by means of controls that are activated in a finite number of pointwise locations. Moreover, we discuss the finite element numerical approximation of the control problem providing a convergence result of the corresponding optimal measures and states as the discretization parameters tend to zero.The first author was supported by Spanish Ministerio de Economía y Competitividad under project MTM2011-22711. The third author was supported by the Advanced Grant NUMERIWAVES/FP7-246775 of the European Research Council Executive Agency, FA9550-14-1-0214 of the EOARD-AFOSR, FA9550-15-1-0027 of AFOSR, the BERC 2014-2017 program of the Basque Government, the MTM2011-29306 and SEV-2013-0323 Grants of the MINECO, the CIMI-Toulouse Excellence Chair in PDEs, Control and Numerics and a Humboldt Award at the University of Erlangen-Nürnberg

Cryoconite: an efficient accumulator of radioactive fallout in glacial environments

Abstract. Cryoconite is rich in natural and artificial radioactivity, but a discussion about its ability to accumulate radionuclides is lacking. A characterization of cryoconite from two Alpine glaciers is presented here. Results confirm that cryoconite is significantly more radioactive than the matrices usually adopted for the environmental monitoring of radioactivity, such as lichens and mosses, with activity concentrations exceeding 10 000 Bq kg−1 for single radionuclides. This makes cryoconite an ideal matrix to investigate the deposition and occurrence of radioactive species in glacial environments. In addition, cryoconite can be used to track environmental radioactivity sources. We have exploited atomic and activity ratios of artificial radionuclides to identify the sources of the anthropogenic radioactivity accumulated in our samples. The signature of cryoconite from different Alpine glaciers is compatible with the stratospheric global fallout and Chernobyl accident products. Differences are found when considering other geographic contexts. A comparison with data from literature shows that Alpine cryoconite is strongly influenced by the Chernobyl fallout, while cryoconite from other regions is more impacted by events such as nuclear test explosions and satellite reentries. To explain the accumulation of radionuclides in cryoconite, the glacial environment as a whole must be considered, and particularly the interaction between ice, meltwater, cryoconite and atmospheric deposition. We hypothesize that the impurities originally preserved into ice and mobilized with meltwater during summer, including radionuclides, are accumulated in cryoconite because of their affinity for organic matter, which is abundant in cryoconite. In relation to these processes, we have explored the possibility of exploiting radioactivity to date cryoconite. </jats:p