Related papers: Mathematical Interpretation between Genotype and P…
Geometric and Topological Deep Learning are rapidly growing research areas that enhance machine learning through the use of geometric and topological structures. Within this framework, Group Equivariant Non-Expansive Operators (GENEOs) have…
This paper introduces a rigorous mathematical framework for neural network explainability, and more broadly for the explainability of equivariant operators called Group Equivariant Operators (GEOs) based on Group Equivariant Non-Expansive…
Our main problem is to find finite topological spaces to within homeomorphism, given (also to within homeomorphism) the quotient-spaces obtained by identifying one point of the space with each one of the other points. In a previous version…
Natural phenomenon of coevolution is the reciprocally induced evolutionary change between two or more species or population. Though this biological occurrence is a natural fact, there are only few attempts to use this as a simile in…
All possible phenotypes are not equally accessible to evolving populations. In fact, only phenotypes of large size, i.e. those resulting from many different genotypes, are found in populations of sequences, presumably because they are…
The genotype-phenotype map is an essential object in our understanding of organismal complexity and adaptive properties, determining at once genomic plasticity and those constraints that may limit the ability of genomes to attain…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the…
The connection between contextuality and graph theory has led to many developments in the field. In particular, the sets of probability distributions in many contextuality scenarios can be described using well known convex sets from graph…
Interpretable regression models are important for many application domains, as they allow experts to understand relations between variables from sparse data. Symbolic regression addresses this issue by searching the space of all possible…
Linear mixed models (LMMs) are a powerful and established tool for studying genotype-phenotype relationships. A limiting assumption of LMMs is that the residuals are Gaussian distributed, a requirement that rarely holds in practice.…
Cross fields play a critical role in various geometry processing tasks, especially for quad mesh generation. Existing methods for cross field generation often struggle to balance computational efficiency with generation quality, using slow…
Deep generative models open new avenues for simulating realistic genomic data while preserving privacy and addressing data accessibility constraints. While previous studies have primarily focused on generating gene expression or haplotype…
We develop a generally covariant description of evolutionary dynamics that operates consistently in both genotype and phenotype spaces. We show that the maximum entropy principle yields a fundamental identification between the inverse…
Causal inference approaches in systems genetics exploit quantitative trait loci (QTL) genotypes to infer causal relationships among phenotypes. The genetic architecture of each phenotype may be complex, and poorly estimated genetic…
We study metanetworks arising in genotype and phenotype spaces, in the context of a model population of Boolean graphs evolved under selection for short dynamical attractors. We define the adjacency matrix of a graph as its genotype, which…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
We study properties of a category after quotienting out a suitable chosen group of isomorphisms on each object. Coproducts in the original category are described in its quotient by our new weaker notion of a 'phased coproduct'. We examine…
Models of invasive species spread often assume that landscapes are spatially homogeneous; thus simplifying analysis but potentially reducing accuracy. We extend a recently developed partial differential equation model for invasive conifer…
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…