Related papers: Studying Morphological Variation: Exploring the Sh…
In this working paper, we present a simple theoretical framework based on network theory to study how speciation, the process by which new species appear, shapes spatial patterns of diversity. We show that this framework can be expanded to…
The rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in the appearance of shapes. While the shapes are kept unanalyzed as a computation moves forward, part-structures for shapes can be…
This review is an introduction to theoretical models and mathematical calculations for biological evolution, aimed at physicists. The methods in the field are naturally very similar to those used in statistical physics, although the…
The evolution of biological morphology is critical for understanding the diversity of the natural world, yet traditional analyses often involve subjective biases in the selection and coding of morphological traits. This study employs deep…
We illustrate shape mode analysis as a simple, yet powerful technique to concisely describe complex biological shapes and their dynamics. We characterize undulatory bending waves of beating flagella and reconstruct a limit cycle of…
Cities are complex products of human culture, characterised by a startling diversity of visible traits. Their form is constantly evolving, reflecting changing human needs and local contingencies, manifested in space by many urban patterns.…
A simplified model of the bird skeleton along with elongation parameters for the flight feathers is used to explore the diversity of bird shapes. Varying a small number of parameters simulates a wide range of observed bird silhouettes. The…
Understanding of the evolutionary origins of protein structures represents a key component of the understanding of molecular evolution as a whole. Here we seek to elucidate how the features of an underlying protein structural "space" might…
This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian…
Possibilities for using geometry and topology to analyze statistical problems in biology raise a host of novel questions in geometry, probability, algebra, and combinatorics that demonstrate the power of biology to influence the future of…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
An applied problem facing all areas of data science is harmonizing data sources. Joining data from multiple origins with unmapped and only partially overlapping features is a prerequisite to developing and testing robust, generalizable…
The basic problem of shape complementarity analysis appears fundamental to applications as diverse as mechanical design, assembly automation, robot motion planning, micro- and nano-fabrication, protein-ligand binding, and rational drug…
For nearly three decades, spatial games have produced a wealth of insights to the study of behavior and its relation to population structure. However, as different rules and factors are added or altered, the dynamics of spatial models often…
We cast shape matching as metric learning with convolutional networks. We break the end-to-end process of image representation into two parts. Firstly, well established efficient methods are chosen to turn the images into edge maps.…
Several biological tissues undergo changes in their geometry and in their bulk material properties by modelling and remodelling processes. Modelling synthesises tissue in some regions and removes tissue in others. Remodelling overwrites old…
This paper introduces a new mathematical and numerical framework for surface analysis derived from the general setting of elastic Riemannian metrics on shape spaces. Traditionally, those metrics are defined over the infinite dimensional…
We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric…
This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of…
Multimodal tasks, such as image-text retrieval and generation, require embedding data from diverse modalities into a shared representation space. Aligning embeddings from heterogeneous sources while preserving shared and modality-specific…