Continuity of Optimal Control Costs and its application to Weak KAM Theory

We prove continuity of certain cost functions arising from optimal control of affine control systems. We give sharp sufficient conditions for this continuity. As an application, we prove a version of weak KAM theorem and consider the Aubry-Mather problems corresponding to these systems.Comment: 23 pages, 1 figures, added explanations in the proofs of the main theorem and the exampl

Optimal time decay of the non cut-off Boltzmann equation in the whole space

In this paper we study the large-time behavior of perturbative classical solutions to the hard and soft potential Boltzmann equation without the angular cut-off assumption in the whole space \threed_x with \DgE. We use the existence theory of global in time nearby Maxwellian solutions from \cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to determine the large time decay rates for the soft potential Boltzmann equation in the whole space, with or without the angular cut-off assumption \cite{MR677262,MR2847536}. For perturbative initial data, we prove that solutions converge to the global Maxwellian with the optimal large-time decay rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the L^2_\vel(L^r_x)-norm for any $2\leq r\leq \infty$.Comment: 31 pages, final version to appear in KR

Methyl 2-(methylthio)benzoate: the unique sulfur-containing sex pheromone of Phyllophaga crinita

The female-produced sex pheromone of Phyllophaga crinita (Burmeister) (Coleoptera: Scarabaeidae: Melolonthinae; the adult has no common name) is identified as methyl 2-(methylthio)benzoate. This is the first identification of a sulfur-containing, long-distance, female-produced sex attractant from any insect taxa. The root-feeding larvae of this species are serious pests in many crops in Texas and Mexico. In field tests, many P. crinita males were captured in traps baited with the authentic compound. Interestingly, a heteroatom analog, methyl 2-methoxybenzoate, also captured P. crinita males, but only at a dose 10,000 times higher than the lowest tested dose of the authentic pheromon

Celebrating Cercignani's conjecture for the Boltzmann equation

Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of the modern theory of the Boltzmann equation. 24 pages. V2: correction of some typos and one ref. adde

Global existence and full regularity of the Boltzmann equation without angular cutoff

We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the solutions thus obtained are shown to be non-negative and $C^\infty$ in all variables for any positive time. In this paper, we study the Maxwellian molecule type collision operator with mild singularity. One of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator. This norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated H-theorem

Mass Transportation on Sub-Riemannian Manifolds

We study the optimal transport problem in sub-Riemannian manifolds where the cost function is given by the square of the sub-Riemannian distance. Under appropriate assumptions, we generalize Brenier-McCann's Theorem proving existence and uniqueness of the optimal transport map. We show the absolute continuity property of Wassertein geodesics, and we address the regularity issue of the optimal map. In particular, we are able to show its approximate differentiability a.e. in the Heisenberg group (and under some weak assumptions on the measures the differentiability a.e.), which allows to write a weak form of the Monge-Amp\`ere equation

A Flexible Robotic Depalletizing System for Supermarket Logistics

Depalletizing robotic systems are commonly deployed to automatize and speed-up parts of logistic processes. Despite this, the necessity to adapt the preexisting logistic processes to the automatic systems often impairs the application of such robotic solutions to small business realities like supermarkets. In this work we propose a robotic depalletizing system designed to be easily integrated into supermarket logistic processes. The system has to schedule, monitor and adapt the depalletizing process considering both on-line perceptual information given by non-invasive sensors and constraints provided by the high-level management system or by a supervising user. We describe the overall system discussing two case studies in the context of a supermarket logistic process. We show how the proposed system can manage multiple depalletizing strategies and multiple logistic requests

The dissipative linear Boltzmann equation for hard spheres

We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard--spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The equilibrium state is a universal Maxwellian distribution function with the same velocity as field particles and with a non--zero temperature lower than the background one, which depends on the details of the binary collision. Thanks to the H--theorem we then prove strong convergence of the solution to the Boltzmann equation towards the equilibrium.Comment: 17 pages, submitted to Journal of Statistical Physic

Ukrainian refugee crisis management in the Local Health Authority Roma 1: the challenges of implementing public health policies and lessons learned

Background: The conflict between Russia and Ukraine has strained the health systems of countries that welcome war refugees on all levels, from national to local. Despite the Public Health guidelines regarding assistance being published on the topic, the scientific literature currently lacks evidence on the experience of applying theory in practice. This study aims to describe evidence-based practices that were implemented and to provide a detailed description of emerging problems and solutions pertaining Ukrainian refugee assistance in the context of one of the biggest Local Health Authorities in Italy (LHA Roma 1). Methods: LHA Roma 1 developed a strategic plan based on local expertise, national and international guidelines to ensure infectious disease prevention and control, as well as continuity of care for non-communicable diseases and mental health. Results: The insertion of Ukrainian refugees in the National Health System through an identification code assignment and other services such as COVID-19 swab and vaccination were provided either in one of the three major assistance hubs or in local district level ambulatories spread throughout the LHA. Many challenges were faced during the implementation phase of the outlined practice guidelines, which required sensible and timely solutions. These challenges include the necessity of rapid resource provision, overcoming linguistic and cultural barriers, guaranteeing a standard of care across multiple sites and coordination of interventions. Public Private Partnerships, the creation of a centralized multicultural and multidisciplinary team and the mutually beneficial collaboration with the local Ukrainian community were essential to guarantee the success of all operations. Conclusions: The experience of LHA Roma 1 helps shed light on the importance of leadership in emergency settings and how a dynamic relationship between policy and practice would allow each intervention to be modulated according to the local environment, to better realize the potential of local realities to provide appropriate health interventions to all those in need