Related papers: Representing Vineyard Modules
In this work, we present a generalization of extended persistent homology to filtrations of graded sub-groups by defining relative homology in this setting. Our work provides a more comprehensive and flexible approach to get an algebraic…
Developmental constraints have been postulated to limit the space of feasible phenotypes and thus shape animal evolution. These constraints have been suggested to be the strongest during either early or mid-embryogenesis, which corresponds…
We introduce a hybrid metaphor for the visualization of the reconciliations of co-phylogenetic trees, that are mappings among the nodes of two trees. The typical application is the visualization of the co-evolution of hosts and parasites in…
The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the…
Zigzag persistent homology is a powerful generalisation of persistent homology that allows one not only to compute persistence diagrams with less noise and using less memory, but also to use persistence in new fields of application.…
Neural representations are not unique objects. Even when two systems realize the same downstream computation, their hidden coordinates may differ by reparameterization. A probe family intended to reveal structure already present in a…
Multidimensional persistence has been proposed to study the persistence of topological features in data indexed by multiple parameters. In this work, we further explore its algebraic complications from the point of view of higher…
We study families of cellular resolutions by looking at them as a category and applying tools from representation stability. We obtain sufficient conditions on the structure of the family to have a noetherian representation category and…
Traditional saliency map methods, popularized in computer vision, highlight individual points (pixels) of the input that contribute the most to the model's output. However, in time series, they offer limited insights, as semantically…
Interpretable machine learning and explainable artificial intelligence have become essential in many applications. The trade-off between interpretability and model performance is the traitor to developing intrinsic and model-agnostic…
Rooted phylogenetic networks provide an explicit representation of the evolutionary history of a set $X$ of sampled species. In contrast to phylogenetic trees which show only speciation events, networks can also accommodate reticulate…
Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from…
In this paper, we present a new compositing approach to obtain stylized reflections and refractions with a simple control. Our approach does not require any mask or separate 3D rendering. Moreover, only one additional image is sufficient to…
We define a class of invariants, which we call homological invariants, for persistence modules over a finite poset. Informally, a homological invariant is one that respects some homological data and takes values in the free abelian group…
Recently we have started a program to describe the action of Lie algebras associated with Dynkin-type diagrams on generic Verma modules in terms of polynomial vector fields. In this paper we explain that the results for the classical ABCD…
Assessing the boundedness and stability of vector nonlinear systems with variable delays and coefficients remains a challenging problem with broad applications in science and engineering. Existing methods tend to produce overly conservative…
The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a…
Ordered sets and maps play important roles as index structures in relational data models. When a shared index in a multi-user system is modified concurrently, the current state of the index will diverge into multiple versions containing the…
A representation invariant is a property that holds of all values of abstract type produced by a module. Representation invariants play important roles in software engineering and program verification. In this paper, we develop a…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…