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Propulsion by growing actin networks is a universal mechanism used in many different biological systems. Although the core molecular machinery for actin network growth is well preserved in most cases, the geometry of the propelled obstacle…
Interpretability is crucial for doctors, hospitals, pharmaceutical companies and biotechnology corporations to analyze and make decisions for high stakes problems that involve human health. Tree-based methods have been widely adopted for…
Extracting the optimal amount of power from an array of tidal turbines requires an intricate understanding of tidal dynamics and the effects of turbine placement on the local and regional scale flow. Numerical models have contributed…
Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer.…
This paper shows a mathematical formalization, algorithms and computation software of volume optimal cycles, which are useful to understand geometric features shown in a persistence diagram. Volume optimal cycles give us concrete and…
The precise delineation of blood vessels in medical images is critical for many clinical applications, including pathology detection and surgical planning. However, fully-automated vascular segmentation is challenging because of the…
Coronary arteries and their branches supply blood to myocardium. The obstruction of coronary arteries results in significant loss of myocardium, called acute myocardial infarction, and the number one cause of death globally. Hence,…
Vascular tracking of angiographic image sequences is one of the most clinically important tasks in the diagnostic assessment and interventional guidance of cardiac disease. However, this task can be challenging to accomplish because of…
In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an $n$-vertex graph $G=(V,E,w)$ with positive real edge weights, and our goal is to maintain a tree which is a good…
Blood vessel segmentation is one of the most studied topics in computer vision, due to its relevance in daily clinical practice. Despite the evolution the field has been facing, especially after the dawn of deep learning, important…
Compact and I/O-efficient data representations play an important role in efficient algorithm design, as memory bandwidth and latency can present a significant performance bottleneck, slowing the computation by orders of magnitude. While…
We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any…
Complex systems have motivated continuing interest from the scientific community, leading to new concepts and methods. Growing systems represent a case of particular interest, as their topological, geometrical, and also dynamical properties…
Anatomical trees are critical for clinical diagnosis and treatment planning, yet their complex and diverse geometry make accurate representation a significant challenge. Motivated by the latest advances in large language models, we…
We present computer simulations of three systems of randomly branching polymers in d=3 dimensions: ideal trees and self-avoiding trees with annealed and quenched connectivities. In all cases, we performed a detailed analysis of trees…
Statistical shape modeling (SSM) is a valuable and powerful tool to generate a detailed representation of complex anatomy that enables quantitative analysis and the comparison of shapes and their variations. SSM applies mathematics,…
Modeling the sequential information of image sequences has been a vital step of various vision tasks and convolutional long short-term memory (ConvLSTM) has demonstrated its superb performance in such spatiotemporal problems. Nevertheless,…
Tumor growth beyond a critical size relies on the development of a functional vascular network, which ensures adequate oxygen and nutrient supply. In this work, we present a modeling framework based on an optimization-based 3D-1D coupling…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
Tree-based models are increasingly popular due to their ability to identify complex relationships that are beyond the scope of parametric models. Survival tree methods adapt these models to allow for the analysis of censored outcomes, which…