Accepted Posters / Pôsteres Aceitos
FGV EMAp 15 Years: Multidisciplinarity in Mathematics and Data Science
Undergraduate Posters / Pôsteres de Graduação (20)
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Modeling the impact of long-acting injectable PrEP on HIV dynamics
Computational models make it possible to investigate the dynamics of infectious diseases and evaluate prevention and control strategies. COMORBUSS is an individual based model that integrates social, epidemiological and biological models, allowing it to represent individual heterogeneity and interactions, which are key aspects of HIV transmission.
This study proposes extending COMORBUSS to model HIV transmission by incorporating infection progression, diagnosis, antiretroviral treatment, prevention strategies, and viral load dynamics. The model will enable the evaluation of different prevention scenarios, accounting for agents’ individual characteristics and sexual interaction networks.
Considering that the impact of pre-exposure prophylaxis (PrEP) depends on both its effectiveness and its population-level distribution, and that inequalities in access to PrEP persist in Rio de Janeiro (Coelho et al., submitted), this study aims to assess the epidemiological impact of replacing oral PrEP with long-acting injectable PrEP while maintaining current coverage levels, and to investigate whether this change could help reduce HIV transmission.
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Interdisciplinaridade: um superpoder para meninas e mulheres combaterem desigualdades nas Ciências Exatas
O projeto “Interdisciplinaridade: um superpoder para meninas e mulheres combaterem desigualdades nas Ciências Exatas” consiste em uma intervenção piloto voltada a meninas do ensino médio de escolas públicas da periferia do Rio de Janeiro e a graduandas de áreas ETEC (Ciências Exatas e da Terra, Tecnologias, Engenharias e Computação). A iniciativa privilegia a interdisciplinaridade e o desenvolvimento do raciocínio lógico, buscando ampliar o interesse das estudantes pelas áreas quantitativas. Para isso, as alunas participam, sob a orientação de suas professoras, de atividades que articulam conteúdos de português, história, sociologia e biologia a conceitos e aplicações das áreas ETEC. O percurso formativo também inclui seminários com profissionais, visitas externas e atividades práticas de pesquisa, estatística, ciência de dados e programação. Como resultados parciais, o projeto consolidou uma dinâmica formativa continuada, disponibilizou videoaulas em um canal público no YouTube e deu início ao desenvolvimento de projetos individuais pelas participantes. Avaliações subjetivas e métricas objetivas como a aplicação da escala S-STEM permitirão avaliar a viabilidade, aceitação e efetividade da intervenção.
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Estudo de R_0 e Pontos de Equilíbrio de Modelo SEIR com Compartimento Ambiental
Este trabalho apresenta um estudo teórico e numérico de modelos epidemiológicos compartimentais, com ênfase na determinação de pontos de equilíbrio, no cálculo do número básico de reprodução (R_0) e na análise da dinâmica de transmissão de doenças infecciosas. Inicialmente, são investigadas essas propriedades em um modelo do tipo Suscetíveis–Infectados–Recuperados (SIR), permitindo compreender o papel do R_0 como parâmetro de limiar epidemiológico e introduzir o método da Matriz de Próxima Geração. Em seguida, os conhecimentos desenvolvidos são aplicados a uma adaptação de um modelo de transmissão da Influenza Aviária de Alta Patogenicidade (HPAI) em rebanhos de gado leiteiro, estruturado em compartimentos de suscetíveis, expostos, infectados e recuperados (SEIR), acrescido de um reservatório ambiental de patógenos. Para o modelo proposto, são demonstradas a existência e unicidade global de soluções biologicamente admissíveis, sua não negatividade e limitação. A análise dos equilíbrios permite determinar as condições de existência do equilíbrio endêmico e examinar os efeitos da introdução externa de patógenos no ambiente. Adicionalmente, realiza-se uma análise de elasticidade do R_0, identificando a influência relativa dos mecanismos de transmissão direta e ambiental. Por fim, simulações numéricas do sistema adimensionalizado ilustram os regimes de extinção e persistência da doença, evidenciando a influência das condições iniciais sobre a dinâmica transitória e a aproximação aos equilíbrios correspondentes. Os resultados contribuem para a compreensão matemática dos mecanismos de transmissão e fornecem uma base para investigações futuras sobre estratégias de controle da infecção em rebanhos bovinos.
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An empirical study of robust high-dimensional mean algorithmic estimators
We compare robust estimators of a high-dimensional mean on synthetic data, building on the empirical study of Anderson and Phillips (2025). The Gaussian experiments adapt their design with n = 10,000 observations, dimensions from 20 to 1020, and contamination fractions up to 0.45, run the iterative solvers un- til numerical saturation, and add a breakdown experiment with point-mass and tail-replacement attacks. The non-Gaussian experiments replace the inliers with standardized heavy-tailed families. With Gaussian inliers, projected gradient de- scent (PGD) matches the error of the mean of the uncontaminated observations in the median over scenarios, and eigenvalue filtering and QUE stay close to it except under diagonal covariance. When the informed contamination parameter is half the true fraction, the weight cap of PGD forces weight onto the outliers and its error follows the lower bound implied by the cap. With heavy-tailed inliers, skew- ness reverses the ranking of the coordinate-wise estimators, whose error comes from a shift of the estimation target that does not shrink with n and disappears after a Haar rotation.
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Integrated Egg Production Planning: Mixed-Integer Linear Programming and a Lexicographic Approach with Relax-and-Fix
This study aims to support integrated egg production planning by coordinating chick purchases, flock allocation, transfers between pullet and laying houses, and whole-flock culling over a weekly planning horizon. A mixed-integer linear programming model represents initial flock inventories, age-dependent egg production, housing capacities, occupancy and cleaning constraints. A lexicographic approach prioritizes the minimization of egg production shortfall, followed by the minimization of feeding and transportation costs. A Relax-and-Fix heuristic generates a feasible solution for the first stage, and its shortfall value defines a tolerance-based upper bound for the second stage. The computational analysis evaluates the quality of the solutions obtained by Relax-and-Fix against solver bounds and reference solutions, where available. Sensitivity analyses examine how feed prices and sanitary downtime requirements for pullet and laying houses affect production shortfall, operating costs, and flock replacement decisions.
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Turing Instability in Reaction-Diffusion Systems
This work investigates Turing instability in reaction-diffusion systems, aiming to understand how diffusion can destabilize a spatially homogeneous equilibrium and promote pattern formation. First, the mathematical foundations of the phenomenon were reviewed, followed by a linear stability analysis. The system was linearized around a steady state, and the Jacobian matrix and its eigenvalues were used to establish stability conditions in the absence of diffusion. Next, perturbations were expanded in eigenfunctions of the Laplacian to derive conditions for diffusion-driven instability. The theory was then applied to a reduced epidemiological SIR model, which divides the population into susceptible, infected, and recovered individuals. The analysis yielded explicit conditions for instability and showed that, in this model, susceptible individuals must diffuse sufficiently faster than infected individuals. These findings connect the mathematical properties of the system to the emergence of nonhomogeneous spatial structures, illustrated by a simulation developed as part of related research.
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STA: An Interpretable Vector Similarity Measure for Spatiotemporal Analogue Retrieval
STA (Spatio-Temporal Analogue) searches a historical record for gridded trajectories resembling a supplied model forecast. A cosine over area-weighted anomaly and tendency fields measures similarity of their combined state vectors, and a ratio of anomaly norms measures amplitude proximity. Their product is the score, with both components retained for interpretation. STA requires no training. The developing 2026/27 El Niño was selected for an initial exploratory case study after forecasts and specialist and general media described it as potentially record-setting [16–18]. Six-month SEAS5 forecasts of Niño 3.4 initialized from May to October 2026 are compared with the 1991–2020 ERA5 record, with OISST v2.1 and HadISST 1.1 as alternative observational references. Supporting undetrended series show the highest monthly ERA5 Niño 3.4 anomaly since 1990 in September 2026. This latest value comes from preliminary ERA5T data and remains subject to revision. For October, pairwise Kendall's $\tau$ among the three source rankings ranges from 0.94 to 0.97, and 1997/98 and 2015/16 remain the leading analogues. From May to October, the top ERA5 STA falls from 0.93 to 0.65 while the combined-vector cosine remains 0.95–0.97 and amplitude proximity drops from 0.98 to 0.68. The decomposition distinguishes alignment of the combined anomaly–tendency vectors from agreement in their anomaly norms. The event's eventual seasonal peak remains unobserved. Broader hyperparameter validation and comparative benchmarks remain necessary. Numerical prediction has improved, but forecasts remain imperfect because of model limitations and the atmosphere's sensitivity to initial conditions. Analogue retrieval can help identify past episodes whose documented consequences may inform planning alongside forecasts, although similar SST trajectories do not necessarily imply similar atmospheric conditions or impacts [22].
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When Does Flow-Matching Augmentation with FLUX.1 Help Few-Shot Object Detection?
Object detectors need many labeled images per class, but in many real problems only a few are available. Our objective is to determine when generative augmentation with flow matching helps a detector trained on very few real images, and what makes the generated images useful. We simulate this scarcity on the African Wildlife dataset by sampling only 5 or 10 real images per class. We fine-tune FLUX.1, a flow-matching text-to-image model, with LoRA on each class and add the synthetic images to the training set of a YOLOv11 detector. We compare four training conditions: real images only, real plus classical augmentation, real plus FLUX.1 images, and real plus both. We measure detection with mAP@0.5, the generated images with FID, and their scene composition from the bounding boxes. We ran the full pipeline twice. In the first run, every image came from one fixed close-up prompt. In the second, the captions and prompts followed the mix of scenes in the real photos. In the first run, the synthetic images lowered mAP@0.5 by 15 to 20 points. They looked realistic, but 94% showed a single animal, against 56% of the real photos. In the second run the result flipped. The synthetic images alone raised mAP@0.5 by 6 to 8 points over the real-only baseline, and combined with classical augmentation they gave the best result with 5 images per class, 13.2 points above it. The two classes absent from COCO pre-training gained the most, while FID did not follow the change. Since the runs also differ in seed, this is evidence, not proof. With so few images, what the synthetic set shows matters more than how real each image looks.
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Cálculo Funcional de Itô e Gregas de Opções Dependentes do Caminho: aplicação a uma opção asiática com strike flutuante
Objetivos: O trabalho aplica o Cálculo Funcional de Itô (FITO) ao cálculo de gregas de derivativos dependentes do caminho, contrastando-o com o método tradicional de diferenças finitas. O objetivo central é mostrar, de forma aplicada e reprodutível, que o formalismo funcional permite expressar o Delta de uma opção asiática com strike flutuante como uma expectativa ponderada, obtendo estimadores de Monte Carlo com variância significativamente menor.
Metodologia: Considera-se o modelo de Black-Scholes com payoff dependente da média aritmética do ativo em uma janela de tempo. A partir da derivada vertical do funcional de preço e da representação de martingales para funcionais fracamente dependentes do caminho (Jazaerli & Saporito, 2017), obtém-se a fórmula fechada para o Delta como E[g(X_T)·W_{t1}/(t1·σ·X_0)]. Simulações de Monte Carlo com variáveis antitéticas e 100 mil trajetórias, em 252 passos temporais, são utilizadas para estimar preço e Delta simultaneamente. Os resultados são comparados a diferenças finitas centrais com bump de 1% e common random numbers, usando X_0=100, σ=0,2, t_1=0,2 e T=1.
Resultados: O método FITO forneceu Delta = 0,03994 ± 0,00280, enquanto as diferenças finitas produziram 0,03890 ± 0,01075. Os estimadores concordam dentro do erro de Monte Carlo, validando a implementação, e o FITO reduz o erro padrão por um fator de aproximadamente 3,84× com o mesmo custo computacional — equivalente a cerca de 16 vezes menos trajetórias para atingir a mesma precisão. Conclui-se que o formalismo funcional oferece uma alternativa eficiente, não enviesada e diretamente aplicável a derivativos dependentes do caminho em finanças quantitativas.
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Tangent Categories: A Bridge Between Geometry and Category Theory
Tangent categories are a developing area of category theory that seeks to formalize geometric reasoning in categorical terms. In recent years, significant progress has been made in the field, with an increasing number of geometric structures successfully described within this framework. Nevertheless, tangent categories remain a relatively niche topic and are still largely unknown in Brazil. This provides an introduction to the subject, highlighting its significance, and presenting an important application: the axiomatization of vector fields and differential equations within the framework of tangent categories.
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Pet Analytics: A Multisensor Data Acquisition Weareble for Canine Behavior Research
Objectives: To develop a raw data acquisition platform for canine wearable research, emphasizing data collection optimization and reduced prototype costs to support the creation of a robust canine behavior database for subsequent use with machine learning algorithms.
Methodology: The hardware consists of an ESP32-S3 Super Mini connected to three inertial sensors (ICM-20948) and two barometers (BMP390) through an I2C multiplexer. FreeRTOS tasks allocate data acquisition and microSD logging to separate processor cores, communicating through a queue. The system records 79-byte binary packets at 100 Hz, with barometer and magnetometer polling rates of 25 and 20 Hz, respectively. Controlled prototype tests included stationary periods, sequential movements, abrupt signal changes, and assessment of communication robustness between acquisition and storage. Recorded data were plotted and converted into physical units to assess sensor responses and system robustness. Based on the literature used as a reference for the project, sensor data are acquired without filtering.
Results: Continuous recordings lasting more than 30 minutes showed no detected packet losses or CRC failures. The hardware has a compact form intended for discreet integration into a dog harness and minimal discomfort. The system supports data collection for building a database to train machine learning algorithms in future research.
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Robustifying Markowitz
Objectives. This study investigates whether global minimum variance (GMV) portfolios built with robust estimation of the covariance action Σw show lower weight instability and better net out-of-sample performance than GMV portfolios based on the sample covariance or shrinkage estimators. It adapts the framework of Robustifying Markowitz to Brazilian equities, where heavy tails and noisy covariance estimates can make classical Markowitz weights unstable and costly to trade.
Methodology. The experiment uses a frozen universe of 54 Ibovespa-based stocks, rolling estimation windows of T = 252 and T = 500 days, monthly rebalancing, and transaction costs of 50 basis points. The robust portfolio solves the GMV problem by projected gradient descent with budget projection, avoiding covariance inversion. At each step, Σw is estimated by pairwise centering, block splitting, norm-based truncation, and Hopkins–Li–Zhang spectral reweighting. Benchmarks are equal weight, sample GMV, long-only GMV, linear and nonlinear shrinkage, and the Ibovespa. Performance is assessed with Sharpe, Calmar, drawdown, turnover, and weight statistics.
Results. For T = 252, the robust portfolio achieved the highest net Sharpe ratio (0.713) and cut turnover to 0.370, versus 0.988 for sample GMV and 0.528–0.733 for shrinkage. For T = 500, it achieved the highest Calmar ratio (0.824) and lower turnover (0.280) than sample GMV and both shrinkage methods, although linear shrinkage had the highest Sharpe (1.010). The robust portfolio did not dominate every metric, so the hypothesis is partially supported. There is clear evidence of greater weight stability and competitive net performance.
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Comparing Monocular and Multi-View 3D Pedestrian Reconstruction Strategies for Urban Intersection Sensing
Analyzing pedestrian movement at urban intersections is central to traffic safety and mobility planning. It depends on physical measurements such as 3D pose, metric trajectories, stature, and walking speed, which 2D video does not provide directly. Moreover, fixed cameras have oblique viewpoints, suffer from occlusions, and rarely come with 3D reference annotations. This work, published and presented at SIBGRAPI 2026, compares two 3D pedestrian reconstruction strategies in order to offer practical guidelines for choosing between them. Using the StreetAware dataset, with eight synchronized cameras at an urban intersection, we compare two pipelines. The first is monocular and estimates depth with learned models (SAM 3, ByteTrack, and SAM 3D Body). The second is multi-view and measures depth through projective geometry (2D pose with YOLOv11-pose, cross-camera association, and triangulation). Since no 3D ground truth is available, we propose a reference-free evaluation protocol based on pedestrian coverage, anthropometric plausibility, walking-speed distributions, and computational cost. The results reveal complementary trade-offs. The monocular pipeline detects many more pedestrians and produces stable measurements, but it systematically underestimates stature because it lacks absolute scale. The multi-view pipeline discards pedestrians seen by only one camera, but it yields measurements closer to reality and is considerably more efficient. On the other hand, it suffers from association errors in dense crowds. We conclude that no strategy is universally superior. The multi-view approach is preferable for safety analyses that require absolute measurements, while the monocular approach is better suited to isolated cameras and pedestrian-flow studies.
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Spatial dynamics in epidemiological models
The primary objective of this research is to develop and apply mathematical models (such as SIR, SIS, and their variations), supplemented by spatial dynamics, to simulate the spread of infectious diseases. We aim to investigate the interactions between epidemiological dynamics and the spatial movement of the population. The study involves a mathematical and computational analysis of the model, which consists of a system of partial differential equations (PDEs) incorporating diffusion. The research seeks to produce intuitive visualizations—such as graphs and animations—to facilitate the communication of results, in alignment with the Sustainable Development Goals.
Activities carried out in 2025–2026
Theoretical mathematical studies: Differential equations applied to epidemiology, partial differential equations, the diffusion equation, boundary conditions, and the application of partial differential equations in an epidemiological context.
Computational applications: Use of the Euler method to approximate differential equations; simulation of epidemiological disease spread; modeling the diffusivity of population groups via the diffusion equation; and investigation into the existence of Turing patterns.
Results achieved
Development of an SIR (Susceptible, Infected, Recovered) model incorporating disease spread and population diffusivity, implemented in Python. The project includes the generation of graphs and GIFs, as well as the identification of Turing patterns.
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Bayesian Poisson Forecasting and Tournament Simulation for the 2026 FIFA World Cup
This study addresses probabilistic forecasting of the 2026 FIFA World Cup from historical
international-match results. It aimed to produce match-outcome and scoreline probabilities,
translate them into stage-reach and title probabilities for the 48 teams, and evaluate forecasts
against the tournament. We fitted a ranking-informed Bayesian independent-Poisson attack-
defence model, estimated with the No-U-Turn Sampler and a weighted likelihood combining
tournament-category weights and exponential time decay. Posterior draws were propagated
through 100,000 Monte Carlo replications; nine cutoff-specific snapshots retrained the model at
each cutoff. Evaluation of 104 matches used the Brier score, ranked probability score, logarith-
mic score, calibration diagnostics, score-point errors, and paired bootstrap comparisons with
the frozen pre-tournament forecast. The cutoff-specific model obtained Brier 0.515, ranked
probability score 0.158, and log score 0.876, versus 0.548, 0.175, and 0.917 for the static FIFA-
ranking logistic benchmark. Yet updating did not detectably improve average accuracy: the
Brier difference versus the pre-tournament forecast was 0.0007, with 95% bootstrap interval [-
0.0157, 0.0179]. Draws were a key limitation: across 28 realised draws, the mean assigned draw
probability was 23.3% and the mean three-way Brier score was 0.984, versus 0.341 and 0.347
for home-win and away-win outcomes. Spain was the leading pre-tournament title candidate
at 14.7% and had 62.213% probability before defeating Argentina 1-0 in the final, although the
model favoured France 58.69% to 41.31% in the third-place match won 6-4 by England. The re-
sults support transparent uncertainty quantification while exposing draw and score-dependence
limitations; probabilities refer to recorded regulation scores and do not separately model stop-
page time, extra time, or penalty shootouts.
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Exploring Nitisinone as a Complementary Strategy for Malaria Vector Control Using PopGEM
Malaria remains a serious public health problem worldwide, with an estimated 282 million cases in 2024. The disease is transmitted by female Anopheles mosquitoes, and the growing resistance of these vectors to conventional insecticides highlights the need for new control strategies. In this context, nitisinone (NTBC), a drug that inhibits the enzyme 4-hydroxyphenylpyruvate dioxygenase (HPPD), has shown potential as an alternative approach, as mosquitoes that feed on blood containing NTBC may die due to the disruption of tyrosine metabolism. This study proposes modifications to the Population Genetics and Ecology in Mosquitoes (PopGEM) model to investigate the effects of NTBC on mosquito populations. PopGEM is a deterministic model that simulates the mosquito life cycle in daily time steps, including aquatic and adult stages, blood-feeding behavior, reproduction, and insecticide resistance genetics. The proposed modifications include a pharmacokinetic module to describe how NTBC concentrations in human blood change over time and a concentration-dependent mortality function based on experimental studies found in the scientific literature. These changes are incorporated into the existing blood-feeding and survival processes in PopGEM. The study uses simulations to compare different levels of NTBC treatment coverage, both alone and combined with insecticide-treated nets (ITNs), to investigate their effects on mosquito population dynamics.
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Dynamics of a Predator-Prey Model with Infectious Disease in Predators
Objectives: This study mainly aims to investigate the dynamics of a predator-prey ecological system in which the predator population is affected by an infectious disease, modeled by an SIR (Susceptible-Infected-Recovered) system. The purpose is to analytically understand how the introduction of epidemic dynamics influences biological interactions and affects the population growth of both species.
Methodology: The research is based on mathematical modeling through systems of autonomous non-linear ordinary differential equations (ODEs). The qualitative analysis consisted of the mathematical identification of the system's equilibrium points and the evaluation of their local stability using linearization via the Jacobian matrix. The basic reproduction number (\(R_{0}\)) was also defined to understand its relationship with the system. Additionally, numerical simulations were performed in the phase space using Python.
Results: The mathematical and numerical study showed the existence of multiple equilibrium states, encompassing both disease-free scenarios and endemic equilibria. Among the main results, stable coexistence between subpopulations was observed, as well as the emergence of limit cycles (sustained oscillations) generated by loss of stability, bistability regimes (where more than one equilibrium proves to be attractive), and scenarios of complete population instability.
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Self-Supervised Learning for Detecting Climate Patterns and Changes in Brazil
With the growing need to understand complex climate patterns and changes in atmospheric conditions, particularly in the context of extreme events, deep learning methods offer an alternative for exploring large volumes of climate data without relying on manual labeling. This work aims to identify and characterize recurring patterns of climate anomalies in Brazil and investigate their association with extreme events and changes over time.
The approach combines Vision Transformers (ViT) and Masked Siamese Networks (MSN) to learn latent representations of daily temperature and relative humidity anomalies derived from ERA5 reanalysis data. Climatological references are used to estimate expected conditions and standardize deviations. The resulting clusters are examined through anomaly distributions, quantiles, spatial patterns, and temporal behavior. An independent analysis of temperature, humidity, and precipitation supports the interpretation of individual, persistent, and compound events.
Results for the Amazon region reveal states with distinct temperature and humidity signatures and associations with cold events, prolonged periods of low rainfall, and precipitation anomalies. Including relative humidity produces more persistent states. A state supported by a substantial number of observations combines warmer conditions, low humidity, and precipitation deficits, although precipitation is not used as a model input. These findings suggest that MSN can organize daily anomalies into physically interpretable states, supporting the characterization of multivariate conditions associated with extreme events, the approach provides a basis for investigating how anomalous conditions combine and persist over time.
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Certification of Tabular Foundation Models
Prior-data fitted networks (PFNs) have gained popularity across scientific applications due to their competitive performance against tree-based models. However, the reliability of PFNs in the presence of noisy or corrupted observations remains understudied, with limited mathematical guarantees on the robustness of complete PFN architectures. In this work, we address this gap by developing a certification framework that establishes proven upper bounds on the worst-case change in model predictions under context poi-soning. To this end, we use a simple Taylor expansion that captures how noise propagates in Transformer-like architectures. We evaluate our framework on state-of-the-art PFN architectures such as nanoTabPFN and TabPFN-3 models, obtaining bounds that match certified adversarial lower bounds almost exactly. By leveraging our proposed scheme, we obtain robustness certificates up to 150x tighter than prior approaches. We showcase the effectiveness of our work on a variety of tasks atop PFN models, spanning evaluation of adversarial robustness, model interpretability and fine-grained data attribution.
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Variational approximations for the normalised power prior
Borrowing information from previous studies in a principled manner is a fundamental problem in the Bayesian analysis of randomised clinical trials (RCTs) and statistical analyses more broadly.
The normalised power prior (NPP) has emerged as an important method for eliciting informative prior distributions by raising the likelihood of the historical data to a discounting factor between zero and one -- it is thus a variation of the larger class of Gibbs posteriors, here employed as a prior.
Despite its popularity, adoption of the NPP is hampered by double intractability induced by the need to compute the prior normalisation constant.
Moreover, current approximate methods do not scale well with model dimension or data size because they depend on approximating high-dimensional integrals with respect to the power prior for many values of the discounting factor, without theoretical guarantees for the resulting approximation.
In this work, we first establish important asymptotic results for the power prior (PP) and its normalised version, including posterior consistency and a Bernstein–von Mises theorem.
This then motivates the development of variational approaches which scale well with reliable guarantees.
We finish by providing empirical evidence that the variational normalised power prior (VNPP) works well in real-world settings including model selection in logistic regression to evaluate HIV treatment protocols and survival analysis in melanoma trials.
Graduate Posters / Pôsteres de Pós-graduação (20)
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Hierarchical Cooperative GFlowNets
Generative Flow Networks (GFlowNets) are trained to sample objects from compositional spaces with probability proportional to a reward function, but ineffective exploration can cause learned samplers to concentrate on a few high-reward regions. An intuitive remedy is to train multiple GFlowNets independently in parallel and combine their samples. However, this does not prevent multiple models from collapsing onto the same high-reward areas, leaving large regions of the state space unexplored. With this in mind, we propose Hierarchical Cooperative GFlowNets (HCG), an approach that dynamically partitions the search space to coordinate discovery without relying on hand-crafted boundaries. HCG imposes an ordering in which the highest-ranked model may explore the entire space, while lower-ranked models are progressively pushed toward regions not covered by higher-ranked ones. We provide a theoretical characterization of how specific learning objectives can shift probability mass away from designated areas, instantiating this mechanism within our architecture. A shared classifier coordinates the hierarchy by partitioning the search space, keeping the GFlowNets independently parameterized and enabling asynchronous training. Furthermore, we derive a normalizer-weighted aggregation rule for the ensemble and prove that it recovers the target reward-proportional distribution under the stated assumptions. Finally, experiments across multimodal distributions, sequence generation, combinatorial optimization, and biological sequence design show that HCG improves mode coverage and target approximation, translating increases in the number of coordinated samplers into broader, complementary exploration.
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Actuarial Modelling of Parametric Climate Insurance for Soybean Production
This study evaluates the feasibility of implementing a parametric agricultural insurance product for soybean crops, covering drought events at the municipal level in the states of Paraná, Mato Grosso, and Goiás, Brazil. The modeling framework is based on the Standardized Precipitation-Evapotranspiration Index (SPEI) at a quarterly scale and the application of quantile regression to capture the relationship between water deficit and yield losses. Using yield data from IBGE (SIDRA) and climate variables from the Brazilian Daily Weather Gridded Data, models were estimated for the lower tail of the yield distribution, enabling the definition of triggers, indemnities, and premiums. The results show that the drought index has strong explanatory power for agricultural losses in the state of Paraná, where the model presented higher coefficients, coverage of approximately 90% of historical losses, and positive hedging effectiveness. Additionally, the selection of the 30th percentile proved more suitable for contract design, balancing trigger frequency and adherence to observed losses. In contrast, in the states of Mato Grosso and Goiás, lower sensitivity of yield to the selected index was observed, resulting in weaker model performance. Overall, the findings demonstrate that the use of climate indices for structuring parametric insurance is technically robust and promising, particularly in regions where drought is a key driver of yield variability, while also highlighting the importance of regionalized approaches to maximize efficiency and reduce basis risk.
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Modelos de Precificação Atuarial de Letra de Risco e Seguro para Catástrofe Climática no Brasil
Este trabalho analisa a viabilidade da adaptação dos Cat Bonds, instrumentos de transferência de risco amplamente utilizados em mercados internacionais, ao contexto brasileiro. Foram revisadas as estruturas de Insurance-Linked Securities (ILS) no cenário global e utilizados dados da Susep sobre inundações (2016–2021), complementados por registros recentes de eventos climáticos extremos. A modelagem considerou três abordagens: duas não sazonais, baseadas em estudos internacionais com intensidade constante das perdas, e uma terceira que incorporou explicitamente a sazonalidade das inundações. Os resultados indicam que, embora mais complexa, a modelagem sazonal proporciona maior aderência à realidade do risco, reforçando sua relevância para a precificação de Cat Bonds em contextos climáticos bem definidos.
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Spatial co-occurrence of extreme drought and the risk diversification potential of the Brazilian soybean area
Objectives. Drought causes most climate-related agricultural losses in Brazil, and insurers cannot rely on the law of large numbers when many farms dry at the same time. We measure how much of the drought risk of Brazilian soybean can be diversified across space, which regions hedge each other, and how diversification changes in the tail.
Methodology. Extreme drought is represented by excursion sets of the daily SPEI-30 below a local quantile, on a 0.1° grid covering 63 crop years (1961/62-2023/24), applied counterfactually to the entire 2024 soybean area (46 Mha), reading each historical season as if it occurred today. Because every cell exceeds its own quantile on the same fraction of days, all margins are equal and co-occurrence maps exactly onto portfolio quantities: the effective number of independent units, its Euler allocation across regions and an expected-shortfall version for the tail. Pools of four drought regions are compared through buffer funds of a loss proxy (production value under extreme drought, not indemnities), with exact independence counterfactuals. A climate-only ranking of municipalities is validated against 577,326 federal crop-insurance (PSR) policies.
Results. At the 5% rarity level, Brazilian soybean behaves like about eight independent units on a typical day, but only five on the worst 1% of days. A national pool needs a buffer fund of 37% of the sum of local buffers, and 0.60 of the sum of regional buffers (0.50 if regions were independent). Pooling the Centre-North with the South diversifies better than independence (0.59 against 0.76), because their drought seasons rarely coincide; Mato Grosso with the Centre-North (0.98) and Paraná-São Paulo-Mato Grosso do Sul with the South (0.92) barely diversify. Two or more regions have a 1-in-10 bad season together once every 10.5 years, twice the independent rate. The climate-only ranking reproduces the ranking from claims (Spearman 0.72, 509 municipalities).
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Bayesian borrowing of historical information from multiple historical datasets via the power prior
The use of historical information has become an important tool for improving inference in medical research, often through the elicitation of informative priors from historical data. In this context, a widely used approach is the power prior, which introduces a discounting parameter to control the influence of the historical data likelihood. While this is usually done for a single historical dataset, here we study the much less explored setting of multiple historical datasets, which may be collected across different time periods or regions, where the analyst might wish to assign a greater weight to datasets that are more consistent with the current study.
We study three design choices that arise in this setting: (i) whether to normalize the combined power prior jointly or sequentially across datasets; (ii) whether to impose an order constraint on the discounting parameters; and (iii) whether varying hyperparameter choice leads to different inferences. We show that joint normalization is coherent, corresponding to a Bayesian update of the historical datasets, while sequential normalization leads to inconsistencies. Through simulated experiments, we show that enforcing ordering sometimes leads to a better inference due to improved shrinkage, and normalizing sequentially leads to poor estimates in most scenarios. We also characterize the properties of each setting studied based on metrics such as bias, mean squared error (MSE) and weighted interval score (WIS), and finally, we use these findings to derive simpler priors that offer practitioners a more accessible alternative.
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A Mean Field Game Model For Educational Choices
This thesis studies the allocation of time between working and studying as a mean field game.
Education trades current wage income for future productivity, and its return is not exogenous: wages
and interest rates are the marginal products of an aggregate production function, evaluated at quantities
that are themselves aggregates of the choices of the whole population. The motivation is concrete: the
2023 Brazilian Continuous National Household Sample Survey reports that 45% of individuals aged 15
to 29 who are not enrolled in school give the necessity of working as their reason.
We make two contributions: a mean field game model of educational choices and a numerical method
for McKean–Vlasov forward-backward stochastic differential equations with common noise. We develop
the numerical method in order to solve the mean field game model numerically.
In the numerical method, the forward-backward coupling is handled by a Picard iteration over the
whole time horizon, and the dependence on the stochastic measure flow by elicitability: the statistic of the
conditional law that the coefficients require is learned by minimizing an empirical score, parameterized
as a recurrent network acting on the common-noise path. Conditional expectations are thus obtained
without nested simulation, and interactions mediated by quantiles or tail-risk measures are handled by
the same algorithm. We prove whole-interval error bounds and validate the method on three problems,
one of which has a closed-form solution.
With regard to the educational choices model, agents are heterogeneous in financial wealth and skill
and control two margins, consumption and the fraction of time spent working rather than studying,
and the mean field interaction operates through both factor prices. We characterize the Nash equilibria
as the solution of a McKean–Vlasov forward-backward system and establish its well posedness over
short horizons. In the computed equilibrium education is front-loaded, a non-negligible mass of agents
chooses no education at all, and cumulative education is strongly increasing in initial wealth, so that
the association between low wealth and school dropout emerges as an equilibrium outcome rather than
as an assumption. Applying the model to a money transfer conditioned on school attendance, of the
type of Bolsa Família and Pé de Meia, shifts that distribution upward among agents of below-median
wealth. The model is stylized and not calibrated to data, so its results are qualitative properties of the
equilibrium
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A mechanistic multiscale framework coupling within-host resistance evolution and between-host transmission
Objective: Antimicrobial resistance (AMR) emerges from processes across multiple scales. As these scales are often modeled separately, we propose a mechanistic framework linking within- and between-host dynamics to investigate how treatment non-adherence influences the emergence and spread of resistance.
Methods: A pharmacokinetic/pharmacodynamic model provides concentration-dependent, strain-specific death rates for sensitive and resistant pathogen populations, described by continuous-time Markov chains. Each stochastic trajectory generates strain-specific transmission rates, which determine the force of infection in a two-strain SEIRS model, analyzed first in a homogeneous population and then in a two-patch metapopulation connected by human mobility. Stochastic simulations assess three non-adherence scenarios (intermittent missed doses, early discontinuation, delayed initiation) and different levels of connectivity.
Results: In the non-spatial model, non-adherence progressively reduces infection control. Adherence of 100% and 95% eliminates or nearly eliminates both strains, 75% allows resistant strains to escape and rebound after treatment, and 50% results in a community outbreak. Early discontinuation, especially after 30 days, produces the largest outbreaks, while delays of 30 days or more favor resistant strains. In the two-patch model, with 50% adherence in Patch 1 (hotspot) and 100% in Patch 2 (community), connectivity determines the fate of resistance. Under near isolation, Patch 2 eliminates infections. Under empirical migration, the continuous influx of infected individuals enables stochastic rescue of the resistant strain, which becomes endemic in Patch 2. Under very high connectivity, both patches converge to a resistant-dominated state. When symptomatic individuals leave Patch 1 at five times the rate, empirical migration mainly causes sensitive-strain outbreaks in Patch 2, while late resistant-strain rescue occurs only under very high connectivity.
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Divide to Conquer: Nonparametric Inference for Nonstationary Spatial Point Processes
Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying intensity function. These features are difficult to capture with standard modeling approaches. This work proposes a spatial Cox process model in which nonstationarity is induced through a random partition of the spatial domain, with conditionally independent Gaussian process priors specified across the resulting regions. This construction allows for heterogeneous spatial behavior, including sharp transitions in intensity. A discretization-free MCMC algorithm is developed to target the infinite-dimensional posterior distribution without approximation, thus ensuring exact inference. The random partition framework via Voronoi tessellation also reduces the computational burden associated with Gaussian process models. Spatial covariates can be incorporated to account for structured variation in intensity. The proposed methodology is evaluated through synthetic examples and real-world applications, demonstrating its ability to flexibly capture complex spatial structures. The model performs competitively, outperforming stationary and nonstationary alternatives in a variety of scenarios. Recent computational methods are used, enabling scalability to large datasets while preserving exactness.
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Preserving Utility in Continual LLM Unlearning via Orthogonal Projections
Unlearning concerns the task of removing the influence of a sensitive portion of the training data, such as protected, copyrighted or private text, from a model without retraining it from scratch. While unlearning requests happen continuously during a model's lifetime, the vast majority of LLM unlearning methods are ill-suited for iterated removal, yielding steep decay in forgetting and utility upon sequential unlearning. This decay stems from interference between successive updates, as each new deletion can undo earlier ones or push the model further along directions already degraded by them.
To address this, we introduce Continual Orthogonal Projection (COP), a gradient-projection scheme that restricts each update to the orthogonal complement of activation subspaces cached from prior forget sets. This approach provably guarantees first-order non-interference with earlier deletions.
COP stores only a low-rank basis per layer, requiring neither past gradients nor previous forget sets, and plugs into unlearning methods that update the model through gradient steps on a differentiable loss without modifying its objective.
We evaluate COP on TOFU and RWKU with Llama-3.2 models over five sequential requests. On TOFU with the 1B model, gradient ascent and IDK collapse (model utility of 0.16 and 0.04 after the fifth request), whereas their COP variants retain 0.46 and 0.47; on the 3B model, COP raises the final utility of gradient ascent from 0.22 to 0.57. For NPO and SimNPO, forgetting stays comparable while utility degrades more slowly. The continual baselines O3 and ALKN either fail to forget or lose most of their utility.
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Audio Features and Song Longevity on Spotify Charts: An Andersen–Gill Recurrent Event Analysis
This study investigates associations between audio features and song longevity on Spotify’s weekly global Top 200 chart from December 2016 to June 2024. Because songs can leave the chart and subsequently return, chart exits are treated as recurrent events. The prepared dataset comprises 5,699 tracks and 8,058 risk intervals, constructed from 390 weekly chart editions and combined with audio features obtained from the Spotify API. The Andersen-Gill extension of the Cox proportional hazards model is used to retain successive chart spells, with time measured in accumulated weeks on the chart and robust standard errors clustered by track. Candidate covariates include audio features, chart positions, artist indicators, and indicators for remix- and Christmas-labelled tracks. Backward selection retained ten covariates. In the final model, a three-decibel increase in loudness was associated with an estimated 8.9% lower exit intensity, while remix-labelled tracks had a 15.3% lower intensity. Christmas-labelled tracks had a 123.4% higher exit intensity. Worse peak positions and higher liveness were also associated with higher exit intensity. These findings describe adjusted associations among charting songs. The recurrent-event framework preserves information on successive exits that would be discarded in an analysis restricted to the first exit.
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ManyProofs: A Crowdsourcing Platform for Certifying LaTeX-to-Lean Translations with LLM-Assisted Alignment
Autoformalization tools now translate mathematics into Lean 4 at growing scale, and AI systems have begun to solve open problems that mathematicians must still check. Lean verifies that a formal statement type-checks and that its proof is complete, but it cannot tell whether the formalization means what the LaTeX source says. That judgment still rests with mathematicians, usually in isolation and without a shared record of what was accepted. We present ManyProofs, a crowdsourcing platform, currently under development, where mathematicians share, discuss, correct and certify translations between LaTeX and Lean 4. Users organized in groups propose pairs of informal and formal statements and proofs, one at a time or by importing existing formalization projects (math-OpenAI, Hexagon+Palomar and LeanBlueprint). Lean checks every proposal, reviewers vote within their group, and a pair is certified only when the group accepts both sides; every revision and discussion is kept. To support reviewers, the platform includes automatic alignment tools: an LLM links spans of the LaTeX text to the Lean code that encodes them, currently at the level of theorem statements, shown as an interactive map that proposers and reviewers inspect and edit. Unmatched text or code points to the omissions and additions where mistranslations hide. To select the alignment prompt, four annotators built a gold standard for 10 statements from Google DeepMind’s formal-conjectures and we compared five prompts by token-level IoU; the best one (few-shot with three external examples, explicit rules and JSON output) reaches a mean IoU of 0.935 with Gemini 3.6 Flash. The next step is a first deployment with formalization research groups. Once in use, its discussions, corrections and interaction logs will form a dataset of LaTeX/Lean pairs in which agreements and disagreements are documented, useful for evaluating autoformalization models and for designing new visual encodings for formalization review.
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Learning Context-Dependent Costs: Functional Inverse Optimization in Reproducing Kernel Hilbert Spaces
Inverse optimization (IO) recovers the cost that makes observed decisions optimal, and almost all of it recovers a single cost vector shared by every observation. Decision makers, however, price their options differently in different situations. We let the cost be a function $p^\star(z)$ of an exogenous context and learn it in a vector-valued reproducing kernel hilbert space. The loss is inspired by Zattoni's augmented suboptimality loss, which needs neither optimal experts nor consistent data. A representer theorem reduces the problem to a finite-dimensional convex program, the Kernelized Augmented Suboptimality Loss (K-ASL), which contains constant-cost IO as the special case of a constant kernel. The K-ASL is minimized by stochastic first-order methods that query only a forward oracle, so they apply when the feasible set is continuous or combinatorially large. We compare two step geometries, Euclidean in the representer coefficients and gradient descent in the RKHS. They differ by a Gram preconditioner, and only the RKHS step stays well conditioned as the bandwidth grows. We prove a uniform deviation bound of order $N^{-1/2}$ and the consistency of the Tikhonov-regularized estimator. In experiments the learned cost follows piecewise-constant and continuous targets that no constant cost can represent.
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ContraVis: Evidence-Grounded Visual Analytics for Contradiction Review in Legal Contracts
Legal contracts are structurally complex documents in which contradictions may emerge across distant and interconnected provisions. Although large language models (LLMs) improve legal language understanding, contradiction analysis remains a human-centered and evidence-grounded review task. We present ContraVis, a visual analytics system for human-in-the-loop contradiction analysis in legal contracts. The system models contracts as typed paragraph graphs that combine explicit contractual references with semantic relationships between paragraphs. This graph plays a dual role: it conditions LLM reasoning and serves as the interactive representation the analyst explores, keeping model context and human inspection aligned across coordinated views. In a controlled comparison, graph-conditioned reasoning recovered more injected contradictions than standalone LLM analysis as contract length grew, while surfacing additional candidates for analyst validation. A formative study with contract-domain lawyers indicated that in-context evidence comparison supported contradiction validation, and we distill design implications for evidence-grounded, LLM-assisted document review.
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Stochastic Simulation of Dengue Spread: A Multi-Strain SEIR Approach
Dengue is hyperendemic in Brazil, with four co-circulating serotypes and a record epidemic in 2024 (>6 million notifications). Immunity is permanent only for the same serotype; heterologous cross-protection is transient, and secondary infections may undergo Antibody-Dependent Enhancement (ADE). This work aims to model dengue spread in Rio de Janeiro state with a stochastic two-strain SEIR model in which ADE increases secondary-infection severity while reducing onward transmission, since severe cases are removed from circulation earlier. Methodology: the model has 14 compartments and follows the two-step Aguiar–Stollenwerk structure, in which cross-immunity wanes at a constant rate before secondary infection occurs; ADE enters the force of infection through a factor φ < 1 that down-weights secondary infectious individuals, revising our original single-step formulation (φ > 1). Exact stochastic trajectories are generated with the Gillespie algorithm. For each municipality, R0 is estimated with EPISCANNER, β is back-calculated as R0(γ + µ) keeping γ at its biological value (~7 days of viremia), and population sizes come from IBGE. Results: for Petrópolis, simulated incidence reproduces the observed 2024 epidemic curve (InfoDengue data), indicates substantial underreporting, and shows the divergence between primary and secondary infection dynamics. A K-means clustering (K = 2, silhouette-selected) of 34 municipalities separates lower/stable from higher/volatile R0 regimes, placing Petrópolis and Duque de Caxias in the former and Volta Redonda in the latter. Future work includes seasonality, case importation and Erlang-distributed waning of cross-immunity.
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Scaling limit under equilibrium Surface under the Random Average Process.
We consider the equilibrium surface of the Random Average Process started from an inclined plane, as seen from the height of the origin, obtained in [8], where its fluctuations were shown to be of order of the square root of the distance to the origin in one dimension, and the square root of the log of that distance in two dimensions (and constant in higher dimensions). Remarkably, even if not pointed out explicitly in [8], the covariance structure of those fluctuations is given in terms of the Green’s function of a certain random walk, and thus corresponds to those of Discrete Gaussian Free Fields. In the present paper we obtain the scaling limit of those fluctuations in one and two dimensions, in terms of Gaussian processes, in the sense of finite dimensional distributions. In one dimension, the limit is given by Brownian Motion; in two dimensions, we get a process with a discontinuous covariance function.
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Hierarchical Agglomerative Clustering via Relaxed Representatives
Due to their simplicity and interpretability, linkage methods are a central class of hierarchical agglomerative clustering (HAC). In particular, representative-based methods, such as centroid and medoid approaches, are appealing because their representatives provide intuitive summaries of the clusters. However, many representative-based linkage methods suffer from important drawbacks, such as high computational cost and the generation of inversions, which limit their broader applicability. We introduce relaxed-representative clustering, a principled generalization of representative-based linkages that preserves their interpretability while addressing these limitations. This framework yields (i) RMM*, a quadratic-time variant of the cubic-time minimax method, and (ii) CRM*, an inversion-free variant of the centroid method whose representatives belong to the input set. On the theoretical side, we prove that for every k our methods are O(min{k, log n})-approximation algorithms for the k-center objective. Empirically, experiments on tabular, biological, and textual datasets show that RMM* consistently outperforms several baselines and achieves clustering quality comparable to minimax at a fraction of the computational cost. Meanwhile, CRM* remains competitive with the centroid method while producing inversion-free dendrograms and interpretable representatives.
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Central limit theorems for optimal controls under parametric uncertainty
Many control problems involve dynamics with uncertain parameters, where a single control must perform well on average over all possible scenarios. In practice, the expected cost is replaced by an average over a finite sample of parameters (sample average approximation). Our goal is to quantify the statistical error of this approximation, not only for the optimal value but also for the optimal control itself.
We consider control-affine systems with uncertain parameters and initial states, an expected terminal cost with a Tikhonov regularization term, and pointwise convex control constraints. Exploiting the affine structure, we show that the cost is twice differentiable in a Hilbert space, with a Hessian that is a Hilbert–Schmidt perturbation of a multiple of the identity. This enables a second-order analysis in the Hilbert space and the use of limit theorems.
We prove central limit theorems for the optimal values and for the sampled optimal controls in the Hilbert space. The limit is Gaussian when the constraints are inactive, and is the solution of a random quadratic problem on the critical cone under active polyhedral constraints.
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Study of SARS-CoV-2 spread dynamic using data assimilation techniques
We aimed to reconstruct the evolution of the COVID-19 pandemic in Ecuador from its onset (March 2020) to the start of mass vaccination (August 2021), and to assess whether estimates produced in real time from official data captured the true epidemic dynamics. We applied variational data assimilation to jointly estimate the parameters and initial conditions of a SEIR-type model distinguishing documented and undocumented infections, with observational, parameter and initial-state uncertainty encoded in error covariance matrices. The optimization problem was solved with a projected BFGS method, and the resulting maximum-a-posteriori estimates were complemented with a Laplace approximation of the posterior distribution. Two data sources were assimilated: positive PCR test counts from the Public Health Ministry (MSP), available in real time, and infections inferred retrospectively from excess mortality recorded by the Civil Registry (RC), computed with a SARIMA forecast of expected deaths and case fatality rates. The analysis focused on Guayas and Pichincha, the two most populous provinces of Ecuador. Excess mortality far exceeded officially reported COVID-19 deaths (23,672 excess vs. 5,995 reported deaths in Guayas; 15,174 vs. 6,750 in Pichincha). In Guayas, the RC-based peak of documented active infections was five times higher than the MSP-based peak, revealing substantial underreporting and reporting delays, whereas Pichincha experienced a later and more moderate first wave. Despite differences in parameters and case counts, effective reproduction numbers estimated from both sources showed coinciding trends and overlapping uncertainty intervals in most weeks. This indicates that the methodology, applied in real time with MSP data can captured the epidemic’s evolution, and it highlights marked heterogeneity within the country.
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Adaptive Truncation for a Sentinel-Observation Chain-Size Model
Likelihood-based inference for transmission-chain sizes must account for the observation mechanism when chains are recorded only if at least one member is identified as a sentinel. This selection mechanism induces a conditional distribution whose likelihood involves an infinite normalising series. Approximating this series through fixed truncation can leave the omitted tail uncontrolled, potentially affecting both computational efficiency and parameter estimation.
The framework considers a subcritical Galton–Watson model with negative-binomial offspring and independent sentinel identification. The probability of a chain being missed is expressed as an infinite sum of total-progeny probabilities weighted by the probability that none of its members is identified as a sentinel. Lower and upper bounds for the uncomputed tail are derived by exploiting the monotonicity of consecutive-term ratios and their explicit limiting value. These bounds provide an interval containing the infinite sum and yield an adaptive stopping rule based on a prescribed interval width. The resulting procedure is incorporated into the observed-data log-likelihood, with stable numerical evaluation performed on the log scale. Numerical experiments compare adaptive and fixed truncation in terms of approximation accuracy, number of terms, computational time, and sensitivity of likelihood-based parameter estimates.
Initial numerical experiments indicate that adaptive truncation is particularly useful in challenging settings with low sentinel identification probabilities. In these regimes, the slower decay of the series requires more terms to achieve accurate approximations, making fixed truncation more susceptible to numerical error. Such inaccuracies can propagate to the observed-data likelihood and potentially affect parameter estimates. These preliminary findings motivate the use of adaptive bounds, although a broader numerical assessment remains necessary.
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Ducking the Curve: A Mean Field Game Model for Household Battery Incentives in Brazil’s Solar Transition
Considering a calibrated model of Brazilian energy dispatch, we focus on solar generation
and study different incentive structures for battery operation at different penetration levels.
Our main focus is on a mean field game model, motivated by decentralized tariff-based coordination, which we compare with the other approaches in terms of duck-curve attenuation
and operating costs. We also present numerical methods for the different models and establish
existence and uniqueness of the MFG equilibrium through a convex potential formulation. Our
aim is to understand how much of the benefit of coordinated storage can be achieved through
individual responses to price incentives.
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