Fondos para apoyar la realizacion de la Fourth Latin American Summer School on Robotics (LACORO 2025). La primera edición se realizó online en octubre de 2020; la segunda fue presencial en enero de 2023; la tercera 2024 en la Universidad de O'Higgins en Rancagua, Chile. La cuarta edición tendrá lugar en diciembre de 2025 en la Universidad de O'Higgins. https://lacoro.org/ Esta Escuela de Verano beneficiará principalmente a Estudiantes y Académicos de las Américas interesados en la Investigación en Inteligencia Artificial aplicada a la Robótica. Nuestro objetivo es fomentar la colaboración nacional y regional en esta área de investigación. Para la primera edición, alcanzamos 241 inscripciones para actividades online de todo el mundo, y la segunda versión tuvo 166 inscripciones para actividades presenciales en enero de 2023, principalmente de Chile, México, Argentina, Brasil y Uruguay.

Fondos para apoyar la realizacion de la Fourth Latin American Summer School on Robotics (LACORO 2025). La primera edición se realizó online en octubre de 2020; la segunda fue presencial en enero de 2023; la tercera 2024 en la Universidad de O'Higgins en Rancagua, Chile. La cuarta edición tendrá lugar en diciembre de 2025 en la Universidad de O'Higgins. https://lacoro.org/ Esta Escuela de Verano beneficiará principalmente a Estudiantes y Académicos de las Américas interesados en la Investigación en Inteligencia Artificial aplicada a la Robótica. Nuestro objetivo es fomentar la colaboración nacional y regional en esta área de investigación. Para la primera edición, alcanzamos 241 inscripciones para actividades online de todo el mundo, y la segunda versión tuvo 166 inscripciones para actividades presenciales en enero de 2023, principalmente de Chile, México, Argentina, Brasil y Uruguay.

This research proposal aims to study the long-term behavior of solutions to partial differential equations arising from dispersive dynamics, kinetic models, and integro-differential dynamics in ecology; and to study extremals of functional inequalities in connection to the ground states of partial differential equations arising from quantum mechanics and diffusion phenomena. Five major topics are proposed: Relativistic quantum mechanics, Dirac operators and functional inequalities; Symmetry breaking in weighted functional inequalities and weighted diffusions; long time dynamics in dispersive PDEs in one space dimension; long-term dynamics in nonlocal models from ecology; and hypocoercivity and decay to equilibrium in kinetic models with heavy tails. The first topic focuses on establishing connections between spectral problems and functional inequalities for Dirac operators. The aim is to analyse the symmetry of optimal spinors in inequalities of Keller-Lieb-Thirring type, and to obtain the solitary waves of Soler-type nonlinear Dirac equations as optimizers of a nonlinear inequality. The second topic aims to characterize a symmetry range in which optimal functions are radially symmetric for weighted logarithmic Sobolev inequalities and a new family of Caffarelli-Kohn-Nirenberg inequalities. A nonlinear carré-du-champ method will be adapted to prove entropy-type estimates. Rigidity, perturbation, and stability issues will be addressed. The third topic seeks to study the asymptotic stability of topological and non-topological solitions for a class of dispersive PDEs in dimension one. A new method is proposed, based on perturbations in weighted spaces with exponential weights, on the so-called virial identities, and on the study of existence of breathers. The fourth topic concerns the description of evolutionary stable strategies of long-term dynamics of integro-differential models that arise in the modeling of structured populations, and to obtain qualitative and quantitative insights on the concentration dynamics. In the fifth topic, the aim is to extend the Dolbeault-Mouhot-Schmeiser method to study the large-time behavior of solutions for a broad family of kinetic equations in which the confinement potential exhibits heavy tails. The goals of this project are multiple: to strengthen and to create new collaborative research networks between France and Chile in the field of nonlinear partial differential equations and applications, to publish co-authored articles in top-tier journals and disseminate the results in international meetings, and to promote the formation of advanced human capital. In order to achieve these goals, yearly workshops will be organized in France and Chile to account for the progress of the investigations as well as to encourage the participation of students and young researchers. International training of doctoral and postdoctoral researchers will be ensured by allocating resources from this project for exchanges. Considering the history of successful collaboration amongst the members of this project, and their expertise in their research fields, we are confident about the successful termination of the project. In particular, we expect to pave the way for new research avenues. The main scientific contribution of this proposal involves adapting state-of-the-art techniques from PDEs and nonlinear analysis to obtain qualitative and quantitative results for variational problems and partial differential equations, in which the setting plays a crucial role: complex-valued matrices (first topic), nonlinear and weighted (second topic), strongly nonlinear and dispersive (third topic), nonlocal (fourth topic), general assumption on the tail of the confining potential (fifth topic). This proposed research will provide insights into spectral theory, stability theory of equilibria of differential equations, optimal rates of convergence to equilibria, and their relation to optimal constants in functional inequalities. The expected results will help improving the understanding of various real-life phenomena, including population-dynamics, relativistic quantum mechanics, and diffussion processes. The viability of the project is sustained on the expertise of the members of the Chilean and French research teams, including experts in partial differential equations, nonlinear analysis, calculus of variations, and mathematical physics. Their successful collaboration record and significant contributions to these fields only strengthen the potential of this proposal. In conclusion, the present research project will not only foster the scientific cooperation between Chile and France but it will also provide meaningful advancements in the aforementioned fields and their application to various physical phenomena.

Combinatorial objects frequently appear in various areas of computer science and discrete mathematics. These objects are central to questions in algorithmic design, where we aim to program a computer to efficiently perform tasks involving them. These tasks may include counting objects based on certain parameters, sampling an object uniformly at random, optimizing with respect to an objective function, searching for objects that satisfy specific properties, or generating all objects exactly once. This project focuses on two of these problems: combinatorial generation and the search for highly distinct combinatorial objects. While many of the aforementioned tasks have general-purpose techniques that allow them to tackle multiple problems simultaneously, the situation becomes less clear when dealing with combinatorial generation or the search for distant objects. Much of the effort in these areas has been devoted to developing ad hoc methods. Despite this, these last two problems can be naturally phrased in the language of flip graphs, which encode the similarity between combinatorial objects. In this context, the problem transforms into the traditional graph problems of Hamiltonicity (finding a path that traverses all the vertices exactly once) and diameter (finding two vertices that are farthest apart). Recent research has highlighted the significant value of exploiting polytopal properties and symmetry of flip graphs, leading to unified frameworks that can address many problems simultaneously. The main objective of this project is to contribute to this perspective. Specifically, it aims to enhance our understanding of the polytopal and symmetric properties of flip graphs and use this knowledge to develop efficient algorithms for tackling Hamiltonicity and diameter problems

Plants, with their two-layered immune system, are equipped to combat pathogen invasion. The first layer, Pattern Triggered Immunity (PTI), is a powerful defense mechanism. It relies on Pattern Recognition Receptors (PRRs) to detect Microbe-Associated Molecular Patterns (MAMPs) from microbes, triggering a robust defense response. This response, including signaling cascades, gene expression changes, and production of antimicrobials and defense hormones, contributes to restricting pathogen colonization. PTI activation can trigger a systemic response known as Induced Systemic Resistance (IRS), enhancing plant defenses throughout the organism and leading to Non-Host-Resistance. The potential of PTI activation to enhance a plant's overall defensive capacity is a promising strategy to improve crop health. PTI activation at infection sites triggers the production of mobile signals within the plant, which then spread IRS throughout the plant, enhancing its overall defensive capacity. Flg22 and xyn11, two well-known MAMPs, trigger PTI in tomato, activating various defense responses and, interestingly, including IRS in tomatoes and other plants. Plant roots, often overlooked in discussions of plant immune systems, possess their own immune system, though less potent than leaves. They respond to MAMPs like Flg22 and chitin, but with weaker production of defense chemicals. Despite this difference, roots activate various defenses like PR proteins and callose deposition. Uniquely, roots secrete antifungal secondary metabolites like flavonoids. These root exudates play a crucial role in shaping the surrounding microbiome, attracting beneficial microbes, and possess antimicrobial activity itself. Studies have shown that root exudate composition can be manipulated to influence the soil microbiome and potentially enhance plant growth. This underlines the importance of considering roots in our understanding of plant immune systems, particularly how defense responses are displayed in the root after immune activation in leaves in terms of a systemic immune response. This often overlooked aspect is crucial for a comprehensive understanding of plant immunity. Plants and microbes communicate two-way, establishing an interaction, by instance, plant root exudates influence the composition of the rhizosphere microbiome, which in turn regulates plant growth and immunity. Research suggests that specific bacteria within the rhizosphere microbiome can enhance plant immunity. In fact, transplanting the microbiome from a resistant tomato variety to a susceptible one improved disease resistance. Understanding this plant-microbiome-soil interaction is crucial for developing sustainable agriculture. Our ongoing research investigates how soil type influences tomato immunity and its connection to the soil microbiome. Preliminary results show that different soil types affect the strength of plant immunity responses, even though the overall bacterial types (phyla) are similar. Interestingly, specific bacterial isolates from a soil type with higher immunity were able to directly trigger plant defense mechanisms. Unraveling the intricate interplay between soil type, the rhizosphere microbiome, and tomato immunity holds the key to unlocking sustainable and resilient agricultural practices. This proposal aims to investigate the potential of targeted Pattern-Triggered Immunity (PTI) activation in tomato leaves to enhance plant defense against diverse pathogens. We hypothesize that leaf application of microbial elicitors (flg22 and Xyn11) will trigger PTI, leading to changes in root gene expression and root exudate composition. These alterations are expected to enrich beneficial bacteria in the rhizosphere microbiome, ultimately enhancing resistance against both the foliar pathogen Pseudomonas syringae pv. tomato and the soil-borne pathogen Fusarium oxysporum f.sp. lycopersici. To achieve this, we have defined three specific objectives: 1) Evaluate the impact of leaf-applied elicitors on pathogen susceptibility, root gene expression, root exudate composition, and soil microbiome composition. 2) Develop synthetic exudates mimicking PTI-activated plants and construct synthetic microbial communities potentially containing beneficial bacteria. 3) Assess the effectiveness of leaf-applied elicitors and synthetic microbial communities on the root microbiome and plant health under field conditions. With this, we aim to elucidate the mechanisms by which leaf-based PTI activation influences root-level processes and shapes the rhizosphere microbiome to enhance tomato plant defense against various pathogens. The findings hold promise for developing novel and sustainable strategies for disease management in tomato production.

The primary objective of this research is to evaluate the feasibility of using ultrasonic acoustic imaging as a non-intrusive, in situ technique to assess the plastic behavior of commercial metals and alloys. Specifically, it aims to explore the potential of ultrasonic acoustic imaging to identify and monitor various plastic deformation mechanisms in stainless steel and aluminum. The selection of materials is based on their distinct plastic deformation behaviors: aluminum releases internal energy through dislocation mechanisms, while stainless steel releases energy through deformation, first by dislocation and then by twinning. To achieve this goal, the study will continuously measure changes in sound velocity and the nonlinear acoustic parameter β while subjecting the materials to uniaxial tensile tests at different levels of applied stress. Previous studies conducted by our research group have demonstrated that changes in sound velocity, in relation to strain, offer a reliable means of quantifying dislocation density in local measurements on aluminum, copper, and stainless steel specimens. Furthermore, these studies have observed that alterations in the nonlinear acoustic parameter, specifically second harmonic generation, exhibit more pronounced changes compared to variations in linear acoustics (speed of sound). Building upon these findings, the proposed research involves the generation of both linear and nonlinear acoustic images over wider spatial regions to advance our understanding of the plastic behavior of materials undergoing different microstructural changes. The challenge of applying the results of this research to in situ measurements in the industry is not trivial, as the highly controlled laboratory conditions are not maintained in service components. In this regard, the incorporation of machine learning tools in the proposal aims to identify the parameters most sensitive to the various deformation mechanisms through clustering techniques. It is expected that the correlation of different acoustic parameters with the various plastic deformation mechanisms of both materials under study will generate an optimal database that reflects the variety of scenarios present in service components, thus paving the way for the industrial use of the proposed characterization system. The adoption of diagnostic techniques and the utilization of metallic material state analysis in service significantly enhance our ability to comprehend and control plastic deformation mechanisms, contributing to improved material reliability and robustness, and facilitating informed decision-making and maintenance strategies. Additionally, ex-situ standard microstructural tests, including XRD (X-ray diffraction), EBSD (electron backscatter diffraction), and TEM (transmission electron microscopy), will be performed to characterize the material’s state after deformation. These complementary tests will provide valuable microstructural information, enabling the correlation of deformation states with the acquired acoustic images. All the acoustic and microstructural information described above, in conjunction with previous research group data, will be stored in a robust and comprehensive database. This database will serve as the input for a Machine Learning algorithm, which will facilitate the identification of patterns of correspondence between acoustic and microstructural parameters. This approach aims to enable the future prediction, with a high level of probability, of the specific type of plastic deformation mechanism that a material is undergoing based on the acoustic parameter measurements. The successful development of this research proposal would yield several significant outcomes. Firstly, it would enable the early detection of microstructural changes in materials long before fractures occur. Moreover, it would establish a non-intrusive tool for characterizing materials by identifying the underlying mechanisms driving plastic deformation and monitoring the evolution of materials in service over time. Ultimately, this research has the potential to advance our understanding of the plastic behavior of stainless steel and aluminum, opening avenues for improved analysis, design, and performance evaluation of materials in various industrial applications.