Proyectos

Fair resource allocation is a topic that has been studied extensively in game theory, operations research and computer science. Much progress has been done in different directions by integrating techniques from different areas, but many questions still remain open. Representation and proportionality of the solutions is a characteristic that in many situations is desirable, and has been object of study from different perspectives. In this project we aim to provide a deep mathematical and algorithmic treatment of problems arising in this context. Proportional allocations have been widely studied and used in different contexts, ranging from parliament seat allocations to optimal transport and statistical estimation, but there are still many gaps in the theory. Furthermore, many methods widely used in practice to solve an integer version of this problem are far from being fully understood, and even some of them have not been shown to be correct in every instance, neither to be efficient. In this project we look for a formal treatment and development of efficient algorithms to find proportional allocations. From a mechanism design point of view, it is also relevant to understand the fairness implications of the solutions implemented. Proportionality was introduced as a way of ensuring representation, and in this project we plan to study multidimensional representation aspects. We hope to contribute in the understanding of trade-offs between representation and algorithmic efficiency, which is a very active area of study nowadays. The study of this topic requires the use and development of tools from convex optimization, algorithmic analysis and mechanism design. We expect during the project to contribute in the understanding of related questions, as well as bringing provable methods and algorithms that could be used in practice.

Fair resource allocation is a topic that has been studied extensively in game theory, operations research and computer science. Much progress has been done in different directions by integrating techniques from different areas, but many questions still remain open. Representation and proportionality of the solutions is a characteristic that in many situations is desirable, and has been object of study from different perspectives. In this project we aim to provide a deep mathematical and algorithmic treatment of problems arising in this context. Proportional allocations have been widely studied and used in different contexts, ranging from parliament seat allocations to optimal transport and statistical estimation, but there are still many gaps in the theory. Furthermore, many methods widely used in practice to solve an integer version of this problem are far from being fully understood, and even some of them have not been shown to be correct in every instance, neither to be efficient. In this project we look for a formal treatment and development of efficient algorithms to find proportional allocations. From a mechanism design point of view, it is also relevant to understand the fairness implications of the solutions implemented. Proportionality was introduced as a way of ensuring representation, and in this project we plan to study multidimensional representation aspects. We hope to contribute in the understanding of trade-offs between representation and algorithmic efficiency, which is a very active area of study nowadays. The study of this topic requires the use and development of tools from convex optimization, algorithmic analysis and mechanism design. We expect during the project to contribute in the understanding of related questions, as well as bringing provable methods and algorithms that could be used in practice.

Fluid impacts are present in a large variety of situations. For instance, the craters formed by rain--drops impacting the soil are relevant in agricultural applications. Also, wave--impact can damage coastal structures, and impact of sloshing--waves may produce over--turning of trucks or vessels that transport fluids. Therefore, the relevance (I would say the impact) of fluid impact goes from industry to environmental sciences. And also because of its beauty and scientific challenges, fluid impact is currently (and largely) studied by communities of physicist and applied mathematicians. As the field of fluid impact is vast, we focus in one particular problem: the bottle flip challenge, as (1) it provides more contoured problems to be tackled experimentally during the time limits of this proposal; (2) it could give insights about other relevant and applied problems; (3) as it already received press coverage worldwide, it is likely to have a large visibility of the results obtained. The bottle flip challenge is a game consisting in spinning a plastic bottle partially filled with water, in order to make it landing vertically after completing a single turn, or more. In recent years the challenge received huge attention in social media and some press coverage including Las Ultimas Noticias. In our opinion, such effervescence for a physical phenomenon relies in the counter-intuitiveness of the trick: as the bottle is turning, one expect it to continue turning until falling down, instead of the abrupt and stable stop in a vertical position that actually occurs. Some of the videos, magazine publication and the available physics article (Dekker et al., 2018), focus their attention in the conservation of angular momentum and the variations of momentum of inertia to explain the successful landing. Dekker et al. recognize that the physics of water sloshing is highly complex in itself and approached the problem by the side of classical mechanics. What we propose here, is indeed to take the challenge of fluid dynamics to carry conserved-quantities explanations to a greater depth. Our starting point is a high--speed camera recording of a successful throw and landing. There, one can observe at least two key fluid-dynamical events that contribute to the vertical stabilization of the bottle: (1) the impact of a water jet into the wall, strongly reducing the bottle-angular-momentum during the free traveling of the system, and (2) a violent redistribution of water taking place at landing, where water captures an important amount of the kinetic energy carried by the bottle. After describing these two key events, we can already summarize this proposal as a committed experimental study of both events, plus an effort to translate these ideas into a (engineering inspired) sloshing dynamics application. We propose first to study the landing stage asking the following question (Question 1): for a container partially filled with fluid, can fluid motion act as a shock-absorber for the impact? We propose to perform an experiment where the bottle is rotated on its vertical axis before it is released (also vertically). Then we will study the effect of fluid motion, by simply defining a restitution coefficient (valid at landing impact) and to see when the loss of bottle-energy is maximized. Bottle-energy loss implies fluid-energy absorption: a balance that will be experimentally checked. Maximal loss of bottle-energy indeed ensures greater bottle stability at landing. Then, we will focus on the effect of water--jet--impact asking Question 2: On which circumstances jet-impact may stabilize a freely rotating container? On one side, we will perform experiments of bottle throwing just as the challenge proposes (that is, throwing the bottle by hand). Also, we will construct a quasi-2D experiment, to perform computer-controlled rotations of the bottle in order to produce jet--impact on the bottle walls. In both cases, we will study angular momentum transfer and deviations from bottles without impact by filming with a high-speed camera and applying mass conservation models. In order to return to the general problem of fluid impact, our final question (3) is Can we take advantage of jet-impact to stabilize any moving container? Here we will apply the previous knowledge to the study a classical configuration exhibiting wave impact: a container subjected to horizontal excitation. After characterizing impact conditions in the solid container, we will study the consequences (in wall acceleration for instance) of having a freely moving wall.

Esta Propuesta de Instalación se da en el contexto de una Universidad nueva que se encuentra en pleno periodo de conformación de su planta académica; el Dr. Diego Muñoz Carpintero será el primer experto en el área de control automático del Instituto de Ciencias de la Ingeniería y la Universidad, complementado de este modo la planta docente y de investigación en Ingeniería Eléctrica. La Universidad y el Instituto de Ciencias de la Ingeniería consideran como aspectos centrales de su misión una vocación de excelencia académica y profesional, y de responsabilidad social con un sentido de pertenencia regional. Respecto del último punto, es prioritaria la investigación relevante para las actividades principales de la región, minera y agroindustrial, y en temáticas de relevancia local y global, como energía, sustentabilidad, y en ciencias físicas y matemáticas. La selección del investigador para este concurso cumple todos los criterios de excelencia en investigación, docencia, y de relevancia de su investigación en un contexto regional y global. La propuesta de investigación se centra en temas de electro-movilidad y eficiencia energética. En particular, abordará problemáticas relacionadas con vehículos eléctricos (EVs): ruteo de flotas de EVs para maximización de vida útil de las baterías, control tolerante a fallas de EVs, diseño de estrategias de control de servicios auxiliares brindadas por estaciones de carga de EVs, y el diseño y análisis de estrategias de control y optimización para estos problemas. La investigación en estos temas posee relevancia local por su impacto en sustentabilidad y utilidad para las principales actividades económicas de la región (minería y agroindustrial), y también poseen relevancia global por enmarcarse en las tendencias globales de conversión al uso de energías limpias y eficientes. Finalmente, existen sinergias entre este proyecto de investigación y el perfil del Dr. Muñoz, con otros proyectos y el perfil de otros académicos del Instituto.

In general, machine learning aims to learn a model from the input data in order to make reliable and repeatable decisions. The learning of a model is either done automatically or semiautomatically. While deep learning can be used to automatically learn a model from arbitrary raw data, the number of successful application domains is still very restricted. This proposal is concerned with supervised learning - a machine-learning technique that aims at learning a model from input-output examples. A crucial task in supervised learning is the engineering of the features. Features are used to extract the relevant information from the raw data in order to learn a classifier that is based on the extracted data. A classifier is a function that partitions the input data into different categories. Feature engineering is a time-consuming process that includes a lot of trial and error, and stepwise addition or deletion of features. We aim at automating that process and learn a classifier based on some automatically generated features.

En este proyecto se busca diseñar técnicas para resolver problemas de optimización polinomial. Este tipo de modelos está dentro de los modelos de optimización más complejos y poseen una amplia gama de importantes aplicaciones.

En este proyecto se busca diseñar técnicas para resolver problemas de optimización polinomial. Este tipo de modelos está dentro de los modelos de optimización más complejos y poseen una amplia gama de importantes aplicaciones.