Wilmer Leal

University of Florida | UF · Department of Computer and Information Science and Engineering

For more than 150 years, the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is. Herein, based on the relations of order and similarity, we report a formal mathematical structure for the peri...

Chemical research unveils the structure of chemical space, spanned by all chemical species, as documented in more than 200 y of scientific literature, now available in electronic databases. Very little is known, however, about the large-scale patterns of this exploration. Here we show, by analyzing millions of reac- tions stored in the Reaxys datab...

The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of (hyper)edges, instead of vertices. For that purpose, we utilize so-called network curvatures. These curvatures quantify th...

The categorical modeling of Petri nets has received much attention recently. The Dialectica construction has also had its fair share of attention. We revisit the use of the Dialectica construction as a categorical model for Petri nets generalizing the original application to suggest that Petri nets with different kinds of transitions can be modeled...

The periodic system, which intertwines order and similarity among chemical elements, arose from knowledge about substances constituting the chemical space. Little is known, however, about how the expansion of the space contributed to the emergence of the system—formulated in the 1860s. Here, we show by analyzing the space between 1800 and 1869 that...

The Periodic Table (PT) is perhaps the most famous and widespread icon of chemistry. It orders chemical elements by their nuclear charge and groups them into families according to their similarity. Such arrangement was built using data about formulae of few compounds available in 19th century. Since then, the number of compounds has grown exponenti...

As a contribution to metaphor analysis, we introduce a statistical, data-based investigation with empirical analysis of long-standing conjectures and a first-ever empirical exploration of the systematic features of metaphors. Conversely, this also makes metaphor theory available as a basis of meaning emergence that can be quantitatively explored an...

Starting from the observation that substances and reactions are the central entities of chemistry, I have structured chemical knowledge into a formal space called a directed hypergraph, which arises when substances are connected by their reactions. I call this hypernet chemical space. In this thesis, I explore different levels of description of thi...

The periodic system arose from knowledge about substances, which constitute the chemical space. Despite the importance of this interplay, little is known about how the expanding space affected the system. Here we show, by analysing the space between 1800 and 1869, how the periodic system evolved until its formulation. We found that after an unstabl...

The periodic system arose from knowledge about substances, which constitute the chemical space. Despite the importance of this interplay, little is known about how the expanding space affected the system. Here we show, by analysing the space between 1800 and 1869, how the periodic system evolved until its formulation. We found that after an unstabl...

Hypergraphs serve as models of complex networks that capture more general structures than binary relations. For graphs, a wide array of statistics has been devised to gauge different aspects of their structures. Hypergraphs lack behind in this respect. The Forman–Ricci curvature is a statistics for graphs based on Riemannian geometry, which stresse...

The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of (hyper)edges, instead of vertices. For that purpose, we utilize so-called network curvatures. These curvatures quantify th...

Relationships in real systems are often not binary, but of a higher order, and therefore cannot be faithfully modelled by graphs, but rather need hypergraphs. In this work, we systematically develop formal tools for analyzing the geometry and the dynamics of hypergraphs. In particular, we show that Ricci curvature concepts, inspired by the correspo...

Networks encoding symmetric binary relations between pairs of elements are mathematically represented by (undirected) graphs. Graph theory is a well developed mathematical subject, but empirical networks are typically less regular and also often much larger than the graphs that are mathematically best understood. Several quantities have therefore b...

The collection of every species reported up to date constitutes the so-called Chemi- cal Space (CS). This space currently comprises well over 30 million substances and is growing exponentially [2]. In order to characterize this ever-growing space, chemists seek for similarity of substances on the CS based on the way they combine [3]. Mendeleev’s wo...

Meyer and Mendeleev came across with their periodic systems by classifying and ordering the known elements by about 1869. Order and similarity were based on knowledge of chemical compounds, which gathered together constitute the chemical space by 1869. Despite its importance, very little is known about the size and diversity of this space and even...

Mendeleev came across with his first attempt to a periodic system by classifying and ordering the known elements by 1869. Order and similarity were based on knowledge of chemical compounds, which gathered together constitute the chemical space by 1869. Despite its importance, very little is known about the size and diversity of this space and even...

For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is. Herein, based on the relations of order and similarity, we report a formal mathematical structure for the perio...

In contrast to graph-based models for complex networks, hypergraphs are more general structures going beyond binary relations of graphs. For graphs, statistics gauging different aspects of their structures have been devised and there is undergoing research for devising them for hypergraphs. Forman-Ricci curvature is a statistics for graphs, which i...

Background Hierarchical cluster analysis (HCA) is a widely used classificatory technique in many areas of scientific knowledge. Applications usually yield a dendrogram from an HCA run over a given data set, using a grouping algorithm and a similarity measure. However, even when such parameters are fixed, ties in proximity (i.e. two equidistant clus...

Similarity studies are important for chemistry and their applications range from the periodic table to the screening of large databases in the searching for new drugs. In this later case, it is assumed that similarity in molecular structure is related to similarity in reactivity. However, we state that structural formulas can be regarded as abstrac...

It has been claimed that relational properties among chemical substances are at the core of chemistry. Here we show that chemical elements and a wealth of their trends can be found by the study of a relational property: the formation of binary compounds. We say that two chemical elements A and B are similar if they form binary compounds AC and BC,...