Ph.D. in Complex Systems Engineering

December 9-10, 2021: Online Workshop The Automata Factory 4

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Ph.D. in Complex Systems Engineering

November 11, 2021: María José Quinteros graduates from DISC program

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Ph.D. in Complex Systems Engineering

October 21, 2021: Catalina Canals graduates from DISC program

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Next Seminar (13/05/2022, 14.30am, Hybrid): «Biología de Sistemas para el desarrollo de Biotecnología, estudio de enfermedades, nutrición y medio ambiente»

Mauricio Latorre, Profesor Asociado, UOH. ID Zoom: 92861624153
La Biología de Sistemas es el campo de investigación interdisciplinaria de los procesos biológicos, donde las interacciones de los componentes involucrados se representan con un sistema matemático o modelo complejo. Este enfoque «holístico» o «global» permite comprender integradamente el funcionamiento de los sistemas (procesos) lo que conlleva a la aparición de nuevas propiedades. En este contexto, describiremos diferentes estrategias experimentales para abordar preguntas desde una escala global relacionadas Biotecnología, estudio de Enfermedades Humanas y caracterización de Ambientes Extremos. Principalmente, nos enfocaremos en mostrar diversos modelos de Redes Biológicas del tipo Transcripcionales, Metabólicos y Microbiomas, destacando su potencial para describir fenómenos a escala global, identificar nuevos componentes explicando el tipo de interacciones que se establecen entre genes, reguladores, metabolitos y microorganismos. Entendemos que tanto la construcción como el análisis de estos modelos tiene un fuerte componente matemático, donde la colaboración interdisciplinaria juega un papel fundamental para poder resolver estas y otras interrogantes dentro del campo de la Biología de Sistemas.

06 May

Next Seminar (6/05/2022, 14.30am, Hybrid): «Moreau envelope of supremum functions with applications to stochastic programming»

Emilio Vilches, Profesor Asociado, UOH. ID Zoom: 91988911006
In this talk, we present results about the Moreau envelope of the supremum of a family of convex, proper, and lower semicontinuous functions. Under mild assumptions, we prove that the Moreau envelope of a supremum is the supremum of Moreau envelopes, which allows us to approximate possibly nonsmooth supremum functions by smooth functions that are also the suprema of functions. Consequently, we propose and study approximated optimization problems from stochastic programming, for which we obtain zero-duality gap results and optimality conditions without the verification of constraint qualification conditions.

05 May

Next Seminar (08/04/2022, 14.30am, Hybrid): «Multidimensional Apportionment Through Discrepancy Theory»

Victor Verdugo, Profesor Asociado, UOH. ID Zoom: 96080651738
Deciding how to allocate the seats of a house of representatives is one of the most fundamental problems in the political organization of societies, and has been widely studied over already two centuries. The idea of proportionality is at the core of most approaches to tackle this problem, and this notion is captured by the divisor methods, such as the Jefferson/D’Hondt method. In a seminal work, Balinski and Demange extended the single-dimensional idea of divisor methods to the setting in which the seat allocation is simultaneously determined by two dimensions, and proposed the so-called biproportional apportionment method. The method, currently used in several electoral systems, is however limited to two dimensions and the question of extending it is considered to be an important problem both theoretically and in practice. In this work we initiate the study of multidimensional proportional apportionment. We first formalize a notion of multidimensional proportionality that naturally extends that of Balinski and Demange. By means of analyzing an appropriate integer linear program we are able to prove that, in contrast to the two-dimensional case, the existence of multidimensional proportional apportionments is not guaranteed and deciding its existence is NP-complete. Interestingly, our main result asserts that it is possible to find approximate multidimensional proportional apportionments that deviate from the marginals by a small amount. The proof arises through the lens of discrepancy theory, mainly inspired by the celebrated Beck-Fiala Theorem. We evaluate various methods based of 3-dimensional proportionality, using the data from the recent 2021 Chilean Constitutional Convention election. Besides the classical political and geographical dimensions, this election required the convention to be balanced in gender. The methods we consider are 3-dimensional in spirit but include further characteristics such as plurality constraints and/or minimum quotas for representation.
This is joint work with José Correa, Javier Cembrano and Gonzalo Diaz (PNAS 2022, EC 2021 and EAAMO 2021).

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Ph.D. in Complex Systems Engineering

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