Oportunidades Públicas

High-order boundary integral equation methods for Stokes flow problems

I invite applications of highly motivated undergraduate students to pursue research on novel boundary integral equation methods for the solution of Stokes flow problems with applications in biology. Successful candidates are expected to have basic knowledge in the following areas: fluid mechanics, scientific computing, and programming in Matlab, Julia, or Python.

Cellular Automata + Neural Networks + Visualization

Los automatas celulares son modelos que evolucionan por reglas locales, que incluyen el famoso "Conway game of life". La idea de la ipre es desarrollar esta herramienta en conjunto con redes neuronales.

Empezaremos con entender la creacion de automatas celulares auto-regenerantes por redes neuronales, ver este paper: https://distill.pub/2020/growing-ca/

Sucesivamente, el objetivo es desarrollar mas herramientas para generacion de patrones similares a las activaciones de neuronas reales, con modelos de automatas celulares aprendidos por redes neuronales, con el enfoque en hacer posible la exploracion visual directa de modelos de aprendizaje y memoria para el usuario.

Para esta investigacion se necesitan bases de teoria de redes neuronales, y curiosidad de entender el proceso de aprendizaje por inteligencia artificial. Un interes previo en cosas como automatas celulares, neurociencia o patrones geometricos, hara el avance del proyecto mas facil.

Graph Neural Networks for molecules

Graph-based deep learning models have recently surpassed other classical methods in computational chemistry for searching for molecules with specific properties, such as drugs and bioprocess catalysts. The goal of IPRE is to develop neural networks on graphs to calculate the optimal fit of molecule pairs from a database. It's not necessary to start from scratch with neural networks to make smooth progress, and it's useful for those with a passion for tackling difficult problems with combinatorial and geometric aspects.

No-Show y recalendarización en tratamientos médicos

This research aims to explicitly incorporate patient no-show probabilities into stochastic modeling frameworks designed to support appointment scheduling and rescheduling decisions. In particular, the study seeks to account for the uncertainty associated with actual patient attendance and to leverage this information to design policies that improve resource utilization and overall service performance.

Referencias:
• Nesterov, Y., Spokoiny, V. Random Gradient-Free Minimization of Convex Functions. Found Comput Math 17, 527–566 (2017)
• Diakonikolas J., Guzmán C.: Optimization on a Finer Scale: Bounded Local Subgradient Variation Perspective. ArXiv:2403.16317 (2024)

Relational indices in graph queries

In this project we will look into configuring PostgreSQL and MySQL-InnoDB index schemes to support graph database queries. The idea is to compare their performance against native graph solutions using the Wikidata knowledge graph.

B+tree index compression - a case study

We will study index compression schemes for B+tree storage supported in popular relational and graph engines. In particular, the project consists of testing schemes that were already implemented in the MillenniumDB graph engine and showing what is their effect on query performance and data storage. We will do an experimental suite on the Wikidata knowledge graph which comprises multiple TB of data, underlying the importance of good compression scheme.

Are columnstores wortless when it comes to knowledge graph data management?

He we test how well modern columns store systems perform when managing real world knowledge graph query/data load. The main objective of the project will be to set up multiple columnar systems and tune them sufficiently enough to be able to handle the reduced version of the Wikidata knowledge graph. We will then test their performance on a realistic query load consisting of user posted Wikidata queries.

Transaction processing in IIC3413DB

In this project we will add basic support for several transaction processing pipelines to IIC3413DB which is used in our database course. The project will start by implementing basic MVCC mechanism supporting the READ COMMITED isolation level and progress to Snapshot Isolation. Finally, we will add support for SERIALIZABLE isolation level using simple in-memory metadata mechanisms. Knowledge of C++ is required for this project.

Managing the full Knowledge Graph Stack

In this project we will learn how to manage a full knowledge graph stack developed as open source at IMFD Chile, a research institute that forms a part of our university. The project will teach you how to approach this problem, starting from data extraction using LLMs, loading them into the MillenniumDB graph database engine, and making this data publicly available. You will also learn how to create and manipulate vector indices which can represent LLM created data, query multimedia files, and make your project available to the general public. The project mainly leverages using existing database systems and might require a mild level of Python programming.

Automatic detection of audio signatures in underwater acoustic scenes

Marine ecosystems can be studied through recordings of underwater acoustic scenes using hydrophones. The objective of this project is to develop and to implement efficient methods for the detection of acoustic signatures of distinct fish species living in these ecosystems. This problem is part of an interdisciplinary collaboration with marine biologists which poses interesting computational challenges. This is due to the length of the audio recordings, the reduced number of acoustic signatures, and the low signal to noise ratio due to the diversity of the acoustic scene.

From a mathematical perspective, the detection is formulated similarly to blind deconvolution. The signal is modeled as a superposition of a few components modulated in frequency and corrupted by additive noise. To identify these components, we avoid a black-box approach, solving instead a semidefinite program. The computational challenge involves developing efficient solvers able to scale up to long audio recordings with low signal to noise ratio.

Analysis of vortices in rotating Bose–Einstein condensates.

Bose–Einstein condensates constitute one of the most remarkable examples of macroscopic quantum behavior. When a gas of bosons is cooled to extremely low temperatures, a macroscopic fraction of its particles occupies the same quantum state, which makes it possible to describe the system by means of a single effective wave function. From the mathematical point of view, the phenomenological model most commonly used to study this phenomenon is the Gross–Pitaevskii theory, a nonlinear variational model closely related to the Ginzburg–Landau model of superconductivity.

One of the most interesting properties of these condensates appears when the system is subjected to rotation. Beyond a certain critical angular velocity, the condensate is no longer free of singularities and quantized vortices begin to appear. In two dimensions these vortices are observed as points, whereas in three dimensions they take the form of vortex lines. These structures are not only of physical interest, but also give rise to deep mathematical problems: when they first appear, where they localize, how they interact with one another, and how they depend on the geometry of the system and on the intensity of the rotation.

There is a very strong mathematical connection between this phenomenon and the theory of type-II superconductors. In both cases, the system develops topological singularities governed by a competition between different energy terms, and many of the tools needed to describe them come from the calculus of variations, partial differential equations, and geometric measure theory. However, in the case of Bose–Einstein condensates there is an additional difficulty: the density of the condensate is not constant, but depends on the confining potential. This means that the energetic cost associated with vortices varies in space, which makes the problem richer and more delicate from the analytical point of view.

This research opportunity is situated precisely at that intersection between superconductivity and superfluidity. The aim is to study the appearance, localization, and interaction of vortex lines in rotating Bose–Einstein condensates, based on the analogy with recent advances in three-dimensional superconductivity. In particular, the goal is to gain a better understanding of the regime near the first critical velocity and to explore how the tools developed for superconductors can be adapted to the study of Bose–Einstein condensates.