Arturo Merino, PhD(c) at Technische Universität Berlin (Germany), MSc. on Applied Math, Universidad de Chile.
ID Zoom: 98844302627
Combinatorial generation is the task of computing all solutions to a combinatorial problem instead of only one of them. For example, we may be interested in all spanning trees of a given graph or all optimal weight perfect matchings of a given weighted graph. In recent years, there has been much interest in unifying techniques or general approaches that simultaneously apply to various combinatorial generation problems. We propose a new simple general approach for combinatorial generation. Given some binary strings X⊆{0,1}ⁿ, our approach consists of greedily computing a Hamilton path in a polytope with X as vertices, namely conv(X). Our main result shows that this approach works for all X⊆{0,1}ⁿ and is efficient whenever optimization over X can be efficiently solved, showing an unexplored relation between combinatorial optimization and generation. More specifically, if we can solve certain linear optimization problems for X in time O(T), we can compute a Hamilton path in conv(X) in roughly O(T⋅log(n)) time per vertex. As a consequence, we obtain new efficient algorithms for combinatorial generation problems that can be binary encoded, like spanning tree generation, 0/1 vertex enumeration, and perfect matching generation. Furthermore, consecutive objects visited by our generation algorithms differ only in one local operation, like an edge exchange in the case of spanning trees or an alternating cycle exchange in the case of perfect matchings. This is joint work with Torsten Mütze.

Pedro P. B. de Oliveira, Adjunct Professor, Faculdade de Computação e Informática, Universidade Presbiteriana Mackenzie (Sao Paulo, Brasil).
ID Zoom: 95379368546
In the context of the propagation of infectious diseases, when a sufficient degree of immunisation is achieved within a population, the spread of the disease is ended or significantly decreased, leading to collective immunity, meaning the indirect protection given by immune individuals to susceptible individuals. Here we describe the estimates of the collective immunity to COVID-19 from a stochastic cellular automaton based model designed to emulate the spread of SARS-CoV-2 in a population of static individuals interacting only via a Moore neighbourhood of radius one, with a view to analyze the impact of initially immune individuals on the dynamics of COVID-19. This impact was measured by comparing a progression of initial immunity ratio—the percentage of immunised individuals before patient zero starts infecting its neighbourhood—from 0 to 95% of the initial population, with the number of susceptible individuals not contaminated, the peak value of active cases, the total number of deaths and the emulated pandemic duration in days. The influence of this range of immunities over the model was tested with different parameterisations regarding the uncertainties involved in the model such as the durations of the cellular automaton states, the contamination contributions of each state and the state transition probabilities. A collective immunity threshold of 55% +- 2:5% on average was obtained from this procedure, under four distinct parameterisations, which is in tune with the estimates of the currently available medical literature, even increasing the uncertainty of the input parameters.

André P. Vieira, Profesor Asociado, Instituto de Física, Departamento de Física Geral, Universidade de São Paulo, Brasil.
ID Zoom: 97912982114
The contact process [T. E. Harris, Annals of Probability 2, 969 (1974)] is a stochastic process which can be interpreted as a model for the spreading of an infectious disease. In this process, the agents seating on the sites of a regular lattice can be either infected or susceptible. Infected agents heal with a rate m, while susceptible agents having a fraction x of infected neighbors become infected with a rate xl. For a fixed value of m, there is a critical value of l separating an active phase, in which the infection fails to propagate throughout the lattice, from an active phase, in which the infection becomes endemic. The critical point is characterized by a set of critical exponents in the directed-percolation universality class and, in particular, the critical fraction of infected agents decays as a power law of time with vanishing relative noise. In this talk, we report on the effects, on this phase transition, of imposing time-dependent rates following aperiodic but deterministic sequences obtained from substitution rules [Fogg et al., Substitutions in Dynamics, Arithmetics, and Combinatorics, Springer (2002)] such as a→ab, b→a, which yields the celebrated Fibonacci sequence abaaba…. Dependending on the strength of the temporal fluctuations induced by a sequence, we show that the critical exponents can be affected and that the critical point can be associated with huge density fluctuations characterized by an infinitely broad probability distribution.

Mauricio Galleguillos, Ph.D en Ciencias Agronómicas mención aguas continentales y sociedad, Montpellier SupAGRO (Francia). Profesor FIC-UAI.
Los cambios globales están impulsando profundas transformaciones al funcionamiento del sistema terrestre. De particular interés resultan aquellos cambios vinculados al ciclo hidrológico los cuales son de vital importancia para las sociedades por lo que conocer en detalle las causas y consecuencias de estos procesos se vuelve imprescindible para afrontar los desafíos por venir. Para abordar el complejo sistema vinculado al ciclo del agua, donde interactúan tanto los componentes físicos del sistema terrestre, así como aquellos biológicos y antrópicos, se proponen diversas alternativas metodológicas siendo los modelos numéricos basados en procesos los más reconocidos. Estos modelos pueden operar de manera espacialmente explicita considerando un área finita correspondiente a una cuenca hidrográfica resolviendo una serie de ecuaciones que reproducen diversos procesos del funcionamiento de los componentes de este sistema. Gracias a estas herramientas es posible reproducir el funcionamiento de la naturaleza en un tiempo presente para poder proyectar tanto para el pasado y/o futuro lo que pudo o podría ser el devenir de este sistema. Existen diversos estudios reportados a nivel global que utilizan estas metodologías, con algunos escasos ejemplos en Chile.
En específico se ha evaluado el efecto de políticas de ordenamiento del territorio (o la ausencia de) y políticas
de fomento forestal sobre la provisión de agua en las cuencas de Cauquenes y de Lumaco, así como también se ha investigado sobre la atribución de las causas de la desaparición de la Laguna de Acúleo. El general los resultados muestran un importante efecto del cambio climático futuro y las sequías presentes en la disminución del recurso hídrico, no obstante, el efecto de las modificaciones al uso de la tierra también ha demostrado ser de gran importancia.

Andrea Vega, Doctor en Ciencias Biológicas con mención en Genético Molecular y Microbiología, PUC. Profesora FIC-UAI.
Nitrogen (N) is one of the main limiting nutrients for plant growth and crop yield. Despite its role as a nutrient, nitrate play an important role act as a signaling molecule that modulates gene expression networks of a wide range of plant processes. It is well documented that changes in nitrate availability, the main N source found in agricultural soils, influences a myriad of developmental programs and the plant’s ability to cope with environmental challenges such as plant pathogen attacks. We show that Solanum lycopersicum defense response to the necrotrophic fungus Botrytis cinerea is affected by plant N availability, with higher susceptibility in nitrate-limiting conditions. Genome-wide expression responses of tomato against infection by the fungus under contrasting nitrate conditions reveals that genes involved in several functions explain this connection. Using a systems biology approach, we identified transcriptional regulatory networks implicated in plant response to the fungus infection under contrasting nitrate conditions. Interestingly, hub genes in this network are known key transcription factors involved in ethylene (ET) and jasmonic acid (JA). Gene expression analysis revealed trends in nutrient, hormonal signal and plant defense. Our results provide insights into potential crosstalk mechanisms between necrotrophic defense response and N status in plants.

Bernard Cazelles, Institut de Biologie de l’École Normale Supérieure UMR8197, Eco-Evolutionary Mathematics, École Normale Supérieure, Paris, France and Unité Mixte Internationale 209, Mathematical and Computational Modeling of Complex Systems, Sorbonne Université, Paris, France.
There are many reasons for this non-stationarity in ecological dynamics. For instance, recent studies have shown switch between different dynamics at multi-decadal scales, triggered by small environmental changes in different regions for different species. Long-term changes in climate and/or human activities have also considerable effects on the dynamics of numerous ecological systems explaining they transient behaviors. Wavelet analysis has been suggested as a way to overcome this complexities. Wavelet analysis performs a time-scale decomposition of the signal, which means the estimation of its spectral characteristics as a function of time. This approach provides no information about the underlying ecological mechanisms, yet can provide useful clues about the non-stationary nature of the underlying ecological processes , which then can be incorporated in mathematical models. In this context, I will also demonstrate the efficiency of stochastic models with time varying parameters coupled with Bayesian approachesand discuss their advantages.

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.

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.

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).

Pedro Montealegre, FIC-UAI. ID Zoom: 92016440388
There are more and more distributed algorithms specially designed to work on specific graph classes, such as interval graphs or planar graphs. Before running such algorithms, one would like to be sure that the graph does belong to the class. In this talk, we tackle the problem of locally certifying graph classes. Specifically, we explain recent results showing the design compact certification (i.e. proof-labeling schemes with logarithmic certificates) for planar, bounded genus, chordal, interval, circular-arc, permutation and bounded treewidth graphs.