Related papers: Functional Data Representation with Merge Trees

We introduce a framework for the reconstruction and representation of functions in a setting where these objects cannot be directly observed, but only indirect and noisy measurements are available, namely an inverse problem setting. The…

We build on recent work of Yeats, Courtiel, and others involving connected chord diagrams. We first derive from a Hopf-algebraic foundation a class of tree-like functional equations and prove that they are solved by weighted generating…

We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…

Symbolic regression (SR) poses a significant challenge for randomized search heuristics due to its reliance on the synthesis of expressions for input-output mappings. Although traditional genetic programming (GP) algorithms have achieved…

In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse-Smale complexes play an essential role in capturing the shape of scalar field data. We…

Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this…

Functional-structural models provide detailed representations of tree growth and their application to forestry seems full of prospects. However, owing to the complexity of tree architecture, parametric identification of such models remains…

Transformer-based models have demonstrated significant success in various source code representation tasks. Nonetheless, traditional positional embeddings employed by these models inadequately capture the hierarchical structure intrinsic to…

This paper investigates the execution of tree-shaped task graphs using multiple processors. Each edge of such a tree represents some large data. A task can only be executed if all input and output data fit into memory, and a data can only…

Tree data are ubiquitous because they model a large variety of situations, e.g., the architecture of plants, the secondary structure of RNA, or the hierarchy of XML files. Nevertheless, the analysis of these non-Euclidean data is difficult…

One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…

Can we do arithmetic in a completely different way, with a radically different data structure? Could this approach provide practical benefits, like operations on giant numbers while having an average performance similar to traditional…

Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…

The positioning of this research falls within the scalar-on-function classification literature, a field of significant interest across various domains, particularly in statistics, mathematics, and computer science. This study introduces an…

Search trees are fundamental data structures in computer science. We study functionals on random search trees that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal…

Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…

Model performance is frequently reported only for the overall population under consideration. However, due to heterogeneity, overall performance measures often do not accurately represent model performance within specific subgroups. We…

The tree is an essential data structure in many applications. In a distributed application, such as a distributed file system, the tree is replicated.To improve performance and availability, different clients should be able to update their…

This work considers the problem of fitting functional models with sparsely and irregularly sampled functional data. It overcomes the limitations of the state-of-the-art methods, which face major challenges in the fitting of more complex…

The remarkable growth and significant success of machine learning have expanded its applications into programming languages and program analysis. However, a key challenge in adopting the latest machine learning methods is the representation…