Guillermo Restrepo

Max Planck Institute for Mathematics in the Sciences | MIS

In an effort to expand the domain of mathematical chemistry and inspire research beyond the realms of graph theory and quantum chemistry, we explore five mathematical chemistry spaces and their interconnectedness. These spaces comprise the chemical space, which encompasses substances and reactions; the space of reaction conditions, spanning the phy...

High-order structures have been recognised as suitable models for systems going beyond the binary relationships for which graph models are appropriate. Despite their importance and surge in research on these structures, their random cases have been only recently become subjects of interest. One of these high-order structures is the chemical hypergr...

Neue Forschungsansätze zur Geschichte der Chemie präsentierte die Tagung Multidisciplinary approaches to the history of chemistry in Leipzig Ende Januar.

In an effort to expand the domain of mathematical chemistry and inspire research beyond the realms of graph theory and quantum chemistry, I explore five mathematical chemistry spaces and their interconnectedness through mappings. These spaces are characterised by their elements and the concept of proximity that binds these elements within the space...

High-order structures have been recognised as suitable models for systems going beyond the binary relationships for which graph models are appropriate. Despite their importance and surge in research on these structures, their random cases have been only recently become subjects of interest. One of these high-order structures is the oriented hypergr...

We propose a program for a computational analysis, based on large scale datasets, of deep conceptual and formal structures, representing the mechanisms of historical transformations in different domains ranging from biological to social, cultural, and knowledge systems. We conceptualize such systems as consisting of complex multi-layer networks. St...

The careers of two pioneers of modern physical organic chemistry, Sir Christopher K. Ingold and Saul Winstein, are discussed and compared. Despite the fact that Ingold received 112 nominations from 77 nominees for the Nobel Prize in Chemistry (NPch), he never received that award. Winstein, also a non‐recipient of the NPch, died prematurely at the a...

The solicitation of nominations for the Nobel Prizes in Chemistry (NPch) is and has been the first step in the selection process since the very first awards were made in 1901. The number of nominations solicited by and provided to the Nobel Committee for Chemistry supports the belief by the nominators that their nominations are meaningful. In this...

The periodic system encodes order and similarity among chemical elements arising from known substances at a given time that constitute the chemical space. Although the system has incorporated new elements, the connection with the remaining space is still to be analysed, which leads to the question of how the exponentially growing space has affected...

Correction for ‘Chemical space: limits, evolution and modelling of an object bigger than our universal library’ by Guillermo Restrepo et al. , Digital Discovery , 2022, 1 , 568–585, https://doi.org/10.1039/D2DD00030J.

Chemistry is concerned with a subject that is not static, but evolving in time, chemical space, that is, the collection of all substances and reactions reported over time. If we accept that premise, we can identify the path dependencies and self-reinforcing mechanisms that determined its current space and selected it across historical alternatives....

Edited by Carmen J. Giunta, Vera V. Mainz, and Gregory S. Girolami. Pp. vii+460, illus., index. Springer: Cham. 2021. £109.99 (hardback). ISBN: 978-3-030-67909-5.

The periodic system emerges by intertwining order and similarity relationships among chemical elements, which in turn arise from known substances at a given time that constitute the chemical space. Although the system has been adjusted to accommodate new elements, the connection with the chemical space has been largely forgotten and the question th...

The evolution of the three constitutive systems of chemical knowledge is presented. In the social system, we see the growth of and the changes and developments in the chemical community and its institutions and the network-like framework connecting the various actors. The evolution of the semiotic system is presented as a shift of mathematical fram...

Chemistry is not only of interest for chemists, but rather for the society at large, as the output of this discipline generates both welfare and hazard for our civilisation. Therefore, understanding chemical knowledge and its evolution is of central importance. In this book we introduced a formal setting for chemical knowledge as a complex dynamica...

We present chemical knowledge as a complex dynamical system emerging from the interaction of the more fundamental material, social and semiotic systems of chemistry. These three latter systems are characterised and further discussed in terms of their constitutive objects and the relations they establish.

We present some instances of binary interactions among the social, material and semiotic systems of chemical knowledge. We highlight the relevance of the different temporalities of each system for the purposes of modelling the evolution of chemical knowledge. Finally, we discuss the relationship of chemical knowledge with other kinds of scientific...

We present the mathematical and computational frameworks to analyse the data pertaining to the material, social and semiotic systems of chemistry. These include, but are not limited to, hypergraphs, complexity measures, time series analysis, statistical physics methods, agent-based modelling, language theory, formal concept analysis, machine learni...

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...

Chemical space entails substances endowed with a notion of nearness that comes in two flavours: similarity and synthetic reachability. What is the maximum size for the chemical space? Is there an upper bound for its classes of similar substances? How many substances and reactions can it house? Can we store these features of the chemical space? Here...

Das Periodensystem der Elemente steht seit über 100 Jahren für eine verlässliche Ordnung in der verwirrenden Vielfalt der chemischen Substanzen. Doch angesichts neuer Entdeckungen muss man sich fragen: Gibt es vielleicht etwas Besseres?

In this essay it is shown how mathematical and computational approaches can be used to model the underlying mechanisms of historical processes, which transform the structure, dynamics and function of chemistry. By chemical knowledge, I refer to a complex dynamical system emerging from the interaction of the social, material and semiotic systems of...

Chemistry shapes and creates the disposition of the world's resources and provides novel substances for the welfare and hazard of our civilisation at an exponential rate. Can we model the evolution of chemical knowledge? This book not only provides a positive answer to the question, it provides the formal models and available data to model chemical...

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 deluge of biological sequences ranging from those of proteins, DNA and RNA to genomes has increased the models for their representation, which are further used to contrast those sequences. Here we present a brief bibliometric description of the research area devoted to representation of biological sequences and highlight the semiotic reaches of...

Meyer und Mendelejew ordneten und klassifizierten im 19. Jahrhundert die Elemente nach chemischen Verbindungen. Wenn Chemiker jetzt immer mehr Verbindungen synthetisieren und charakterisieren, sollte ein Periodensystem dann nicht irgendwann ganz anders aussehen?

A chemical element, treated as a concept, entails objects and attributes. From the eighteenth century to date, objects include substances up to quasi-molecular species and nuclides. Attributes range from non-decomposability up to lifetimes of 10 ⁻¹⁴ seconds. By analyzing the historical changes of the concept, we found the central role “chemical rea...

Chemistry shapes and creates the disposition of the world's resources and exponentially provides new substances for the welfare and hazard of our civilisation. Over the history chemists-driven by social, semiotic and material forces-have shaped the discipline, while creating a colossal corpus of information and knowledge. Historians and sociologist...

As a compliment to several other publications that present and honor Rolf Huisgen's research achievements, the first part of this paper reveals the human side of this eminent chemist. From excerpts from many of his personal and professional writings, Huisgen's personality and philosophies of life are revealed. Also revealed is Huisgen functioning a...

As a compliment to several other publications that present Rolf Huisgen’s research achievements, the first part of this paper reveals the human side of this eminent chemist as he edges closer to his 100th birthday. From excerpts from many of his personal and professional writings, Huisgen’s personality and philosophies of life are revealed. Also re...

Over the past several decades, the Nobel Prize program has slowly but steadily been modified in both transparent and opaque ways. A transparent change has been the creation of the Nobel Prize in Economic Sciences, officially known as the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. An opaque change has been the mutation o...

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...

The periodic system of chemical elements was historically devised by assessing order and similarity relationships among the elements from their compounds, that is, using the accumulated results of chemical practice and knowledge. However, the current approach to the system is based on an ontology of isolated atoms where similarities, especially, ar...

Over the past several decades, the Nobel Prize program has slowly but steadily been modified in both transparent and opaque ways. A transparent change has been the creation of the Nobel Prize in Economic Sciences, more officially known as the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. An opaque change has been the mutat...

We celebrate 150 years of periodic systems that reached their maturity in the 1860s. They began as pedagogical efforts to project corpuses of substances on the similarity and order relationships of the chemical elements. However, these elements are not the canned substances wrongly displayed in many periodic tables, but rather the abstract preserve...

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...

Unveiling numerical trends among either atomic or equivalent weights that somehow preserved resemblances among elements was frequent in the 1860s. Standing out from the crowd, Meyer and Mendeleev went beyond numerical relationships, certainly motivated by a pedagogical aim. Both were after a system synthesizing the chemical knowledge of their times...

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...

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...

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...

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...

Since 1969, the international chemistry community has only held conferences on the topic of the Periodic Table three times, and the 2012 conference in Cusco, Peru was the first in almost a decade. The conference was highly interdisciplinary, featuring papers on geology, physics, mathematical and theoretical chemistry, the history and philosophy of...

We explore the meaning of the periodic table and of some of its related terms. In so doing we highlight a few common mistakes that arise from confusion of those terms and from misinterpretation of others, e.g. element, periodic system, table and law. An approach to the structure of the periodic system we follow in this chapter is through similarity...

Analysing order relationships among objects is central for decision making processes or for optimisation, which are also relevant in the field of chemistry. A mathematical tool to carry out ordering studies is the Hasse diagram technique, whose Hasse diagram summarises a large amount of order information. However, when the number of objects is larg...

Since 1969, the international chemistry community has only held conferences on the topic of the Periodic Table three times, and the 2012 conference in Cusco, Peru was the first in almost a decade. The conference was highly interdisciplinary, featuring papers on geology, physics, mathematical and theoretical chemistry, the history and philosophy of...

Recent chemical applications of Formal Concept Analysis are reviewed, showing that molecular structure and activity of substances may be related through association rules, which is exemplified for mutagenicity and hepatotoxicity cases. Nuclear chemistry and nuclear medicine cases are explored, where attributes of radionuclides are related. A study...

Similarity is one of the key concepts of the periodic table, which was historically addressed by assessing the resemblance of chemical elements through that of their compounds. A contemporary approach to the similarity among elements is through quantum chemistry, based on the resemblance of the electronic properties of the atoms involved. In spite...

This paper describes the bibliometric characteristics of 2398 articles published in the Journal of Mathematical Chemistry in the period 1987–2015. These articles have been analysed using data from the Web of Science Core Collection and demonstrate the contribution of the journal not only to mathematical chemistry but also to science more generally.

Este texto, personal y anecdótico, es un intento de mostrar el humano que habita en el sabio José Luis Villaveces. No es más que la narración –no cronológica– de varios acontecimientos de su vida en los que el autor y algunos colegas han tenido relación.

Antes de analizar las aproximaciones desde la semejanza al sistema periódico, definimos "ley periódica", "tabla periódica" y "sistema periódico" y criticamos algunas confusiones que se dan en estos términos. Resaltamos la importancia de sustancias "simples" y "básicas" como lados realista y trascendental del concepto de elemento químico. Además, re...

Uranium contamination is of global concern and several approaches have been applied to cleanse U-contaminated ecosystems. Among them, biotechnological techniques using microorganisms have proven to be eco-friendly. However, knowing which of them behave better for U trapping is still an open question. In this study, a general and a detailed comparis...

The philosophy of chemistry has emerged in recent years as a new and autonomous field within the Anglo-American philosophical tradition. With the development of this new discipline, Eric Scerri and Grant Fisher’s “Essays in the Philosophy of Chemistry” is a timely and definitive guide to all current thought in this field. This edited volume will se...

THE AIM OF THIS chapter is to ponder and discuss the relationship between chemistry and mathematics, taking into account some early research we have performed on the subject (Restrepo and Schummer 2014; Restrepo and Villaveces 2012, 2013; Restrepo 2013). In those works we have discussed some criticism and some support throughout history regarding t...

This paper describes the bibliometric characteristics of 1,319 articles published in the journal MATCH Communications in Mathematical and in Computer Chemistry, in the period 1995-2014. These articles have been analysed using data from the Web of Science Core Collection and demonstrate the contribution of the journal not only to mathematical and co...

A clear and concise depiction of the "state of the art" of the fundamental concepts of mathematical chemistry and their relevant applications by a large number of reputed contributors of the scientific discipline KEY FEATURES  Brings together both the theoretical and practical aspects of the fundamental concepts of mathematical chemistry  Covers...

A clear and concise depiction of the "state of the art" of the fundamental concepts of mathematical chemistry and their relevant applications by a large number of reputed contributors of the scientific discipline KEY FEATURES  Brings together both the theoretical and practical aspects of the fundamental concepts of mathematical chemistry  Covers...

Chemical reactions can be prioritised according to either their attributes or according to properties of their substances. Such a prioritisation can be extended to entire synthetic routes and thus makes it possible to assessing synthesis plans and looking for suitable reactions. The combination of properties of substances to evaluate objects such a...

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...

We give some basic mathematical ideas of partially ordered sets (posets), which frame into the mathematical way of thinking illustrated in the Erlangen Programme by Felix Klein. The programme entails extracting relevant variables to study, symbolising them and relating them through a function. We show several examples where the mathematical way of...

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...

Advances in Mathematical Chemistry and Applications highlights the recent progress in the emerging discipline of discrete mathematical chemistry. Editors Subhash C. Basak, Guillermo Restrepo, and Jose Luis Villaveces have brought together 27 chapters written by 68 internationally renowned experts in these two volumes. Each volume comprises a wise i...

In continuing with the research program initiated by Llored and Harré of exploring the part/whole (mereological) discourses of chemistry, we analyse Quantitative Structure-Activity Relationships (QSAR) studies, which are widespread approaches for modeling substances’ properties. The study is carried out by analyzing a particular QSAR model, and it...

In this eBook we introduce our readers to one of the most comprehensive and thematically diverse treatise on the emerging discipline of mathematical chemistry, or, more accurately, discrete mathematical chemistry. Although mathematical representation and characterization of chemical objects were known for a long time, the incursion of discrete math...

Advances in Mathematical Chemistry and Applications (eBook), Volume 2 Edited By Subhash C. Basak, International Society of Mathematical Chemistry, and UMD-NRRI, Duluth MN, USA Guillermo Restrepo, Laboratorio de Química Teórica, Universidad de Pamplona, Colombia & José L. Villaveces, Universidad de los Andes, Bogotá, D. C., Colombia CONTENTS Forewo...

Structures such as isoprotonic-isoelectronic molecules can be mathematically represented by Young diagrams (or integer partitions), whose columns correspond to the different nuclear charges in a molecule. We found that these Young diagrams, when ordered by majorization, produce a partially ordered set, which is equivalent to the ordering of ground-...

The relationship between molecular structures of drugs and their hepatotoxicity was studied by characterizing their structure in a new way and using formal concept analysis, a mathematical technique to condense knowledge into particular rules, which does not imply linearly assumptions as many conventional statistical techniques. The structural char...

After lecturing at the Second Mathematical Chemistry Workshop of the Americas , organised by Guillermo Restrepo and José L. Villaveces in Bogota (Colombia) in July 2010, Joachim Schummer, editor-in-chief of HYLE--International Journal for Philosophy of Chemistry (HYLE), discussed with Restrepo the possibility of editing a special issue of HYLE devo...

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...

This is a personal account of few months of mathematical chemistry, a hurricane and the luck of having shared a few months with Douglas Jay Klein (Doug). After having read several Doug's scientific papers on partial orders (posets) in chemistry and their uses, being in touch with him by email, I finally met him in a scientific conference. I followe...

Douglas Jay Klein and other researchers have seen that there is a great potential in applying partial order in the field of QSAR. The basic idea is to deduce from order relations among chemicals, properties of the ordered chemicals. Despite the satisfactory results found by Klein’s methods, we think it is worth exploring another feature of the pose...

We studied 27 β+ radionuclides taking into account some of their variants encoding information of their production, such as integral yield, threshold energy and energy of projectiles used to generate them; these radionuclides are of current use in clinical diagnostic imaging by positron emission tomography (PET). The study was conducted based on ph...

This book provides innovative chapters covering new methodologies and important applications in the fields of nanoscience and computational chemistry. The book offers scope for academics, researchers, and engineering professionals to present their research and development works that have potential for applications in several disciplines of nano and...

We discuss two complexity indicators reported in the literature for partially ordered sets (posets), the first one based on linear extensions and the second one on incomparabilities. Later, we introduce a novel indicator that combines comparabilities and incomparabilities with a Shannon's entropy approach. The possible values the novel complexity i...

We thought an appropriate way to celebrate the seminal contribution of Kier is to explore his influence on science, looking for the impact of his research through the citation of his scientific production. From a bibliometric approach the impact of Kier's work is addressed as an individual within a community. Reviewing data from his curriculum vita...

We first show some successes of discrete mathematical chemistry (DMC), a branch of theoretical chemistry born in the 1960s and 1970s. Then we explore the social context in which the emergence of DMC took place, ini-tiated mainly in East European countries. The availability of knowledge, espe-cially of mathematical knowledge, and the lack of researc...

Between mathematics, the deductive science par excellence, and chemistry, which has long been the epitome of the experimental laboratory science, the epistemological differences can hardly be overestimated. The first part of this special issue on 'Mathematics and Chemistry' (HYLE, vol. 18, no. 1) has focused on general aspects and the early history...

By analysing a contemporary criticism to the so called “mathematical chemistry”, we discuss what we understand by mathematizing chemistry and its implications. We then pass to ponder on some positions on the subject by considering the cases of Laszlo, Venel and Diderot, opponents to the idea of mathematization of chemistry. In contrast, we analyse...

We carried out a chemotopological study of two groups of positron emitter radionuclides of current and potential use in positron emission tomography (PET) diagnostic imaging. The aim was to look for potential β+ radionuclides not yet in use for PET imaging, taking into account the similarities of these radionuclides with radionuclides already used...

Often a ranking based on a multi-indicator system is performed by construction of a composite indicator, which is generally computed as a weighted average of the indicators. The set of weight-tuples is introduced: the g-space. Each point of this space represents a tuple of weight values, which lead together with the indicators of an object to a cer...

This special issue of Foundations of Chemistry collects five of the papers presented at the International Society for the Philosophy of Chemistry—Summer symposium 2011 (ISPC 2011), held in Latin America for the first time at the Universidad de los Andes (Bogota, Colombia). The symposium was sponsored by the Universidad de los Andes and organised by...

Background/Question/Methods Identification of appropriate conservation surrogates is essential to the design of effective protected area networks. Indicator species have been frequently used as surrogates, but their selection often requires detailed biological data that is time consuming or expensive to collect. Here we present a technique based...

Mathematical chemistry is often thought to be a 20 th -century sub-discipline of chemistry, but in this paper we discuss several early chemical ide-as and some landmarks of chemistry as instances of the mathematical way of thinking; many of them before 1900. By the mathematical way of thinking, we follow Weyl's description of it in terms of functio...