Related papers: Decomposition tables for experiments I. A chain of…

Similarity analyses between multiple correlation or covariance tables constitute the cornerstone of network neuroscience. Here, we introduce covSTATIS, a versatile, linear, unsupervised multi-table method designed to identify structured…

Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…

Lattice models parameterized using first-principles calculations constitute an effective framework to simulate the thermodynamic behavior of physical systems. The cluster expansion method is a flexible lattice-based method used extensively…

We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of the braid arrangement and show that all…

A stepped wedge cluster randomized trial is a type of longitudinal cluster design that sequentially switches clusters to intervention over time until all clusters are treated. While the traditional posttest-only parallel design requires…

We consider experiments for comparing treatments using units that are ordered linearly over time or space within blocks. In addition to the block effect, we assume that a trend effect influences the response. The latter is modeled as a…

Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected…

We study holographic entropy inequalities and their structural properties by making use of a judicious grouping of terms into certain multipartite information quantities. This allows us to recast cumbersome entropic expressions into much…

We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…

This article defines a partial order structure to study the relationship between levels and contents of conscious subjective experience in a single mathematical set-up. We understand phenomenal structure as extrapolated relationships among…

The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement and led by ADERSA, a French company of research under contract. The aim was to study the techniques of regular…

This paper presents an algorithmic method to study structural properties of nonlinear control systems in dependence of parameters. The result consists of a description of parameter configurations which cause different control-theoretic…

This paper considers a process for the creation and subsequent firing of sequences of neuronal patterns, as might be found in the human brain. The scale is one of larger patterns emerging from an ensemble mass, possibly through some type of…

In this work we introduce declarative statistics, a suite of declarative modelling tools for statistical analysis. Statistical constraints represent the key building block of declarative statistics. First, we introduce a range of relevant…

One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…

We consider the demixing problem of two (or more) structured high-dimensional vectors from a limited number of nonlinear observations where this nonlinearity is due to either a periodic or an aperiodic function. We study certain families of…

Reproducible research in Machine Learning has seen a salutary abundance of progress lately: workflows, transparency, and statistical analysis of validation and test performance. We build on these efforts and take them further. We offer a…

Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…

We propose a novel structure, the data-sharing graph, for characterizing sharing patterns in large-scale data distribution systems. We analyze this structure in two such systems and uncover small-world patterns for data-sharing…

This paper describes the many image decomposition models that allow to separate structures and textures or structures, textures, and noise. These models combined a total variation approach with different adapted functional spaces such as…