Oportunidades Públicas

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.

Optimización de procesos de selección en una exportadora

Se analizará y desarrollará un algoritmo para la asignación de personal a las bocas de salida de una máquina de selección automática de fruta. Se evaluará el beneficio de contar con mejor información de la condición de recepción de la fruta en packing.

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)

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.

Electricity Systems Planning and Public Policy

Research on the use and development of planning models for power systems and the design of public policies. In particular, the SWITCH model for generation and transmission expansion will be applied to the Chilean power system. The impact of integrating new technologies into power systems will be quantified, along with other elements such as increasing the use of electricity in the energy matrix and leveraging demand-side flexibility, among others.

Sensitivity and identifiability analysis of parameters in thermodynamic models

This research opportunity will study how thermodynamic model parameters influence the prediction of properties and phase equilibrium. For this task, simple models from the literature will be implemented and the sensitivity of their parameters will be analyzed using programming tools (Python and/or Julia) and numerical analysis. The expected result is the identification of the most influential parameters and the evaluation of possible identifiability problems in the estimation of parameters from experimental data.

Dynamic Analysis and Optimization Algorithms for the Control of Multivariable Systems

Many modern high-tech systems require controlling multiple critical variables simultaneously. Although this is traditionally addressed through cascade control schemes, current trends point towards Model Predictive Control (MPC) formulations, which consolidate regulation tasks into a single real-time optimization problem.

In this IPRE we will focus on analyzing the dynamic behavior of this type of formulations. The mathematical model of the system is already fully developed and available, so the student's work will consist of the theoretical characterization and simulation of the performance of the algorithms.

The project will address two main objectives:

System Dynamics Analysis: Study the properties of the resulting multivariable model, evaluating the couplings between states and control actions, as well as the linearization of the system.

Algorithm Evaluation (Solvers): Implement and compare different numerical optimization methods to evaluate the trade-off between mathematical precision, computational effort and feasibility of execution in real time.

Study application:
The practical case study where these tools will be evaluated corresponds to energy balance and current regulation in advanced power converters (used in smart grids, energy storage and electromobility).

Profile and Prerequisites:
Tools: MATLAB/Simulink or Python.

Prerequisites: Solid knowledge of Dynamic Systems and Automatic Control. Basic notions of mathematical optimization and programming.

Impact and Learning:
The student will develop advanced skills in the analysis of multivariable systems, formulation of optimization algorithms and simulation of predictive control strategies, skills highly transferable to both postgraduate research and technological development in the industry.