# Guillermo RestrepoMax Planck Institute for Mathematics in the Sciences | MIS

Guillermo Restrepo

Doctor rerum natura

## About

125

Publications

34,370

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987

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Introduction

Additional affiliations

Education

December 2005 - February 2008

September 2001 - December 2003

February 1993 - December 1998

## Publications

Publications (125)

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 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...

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 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...

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...

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...

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...

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...

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 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...

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,...

Ranking chemicals according to their potential environmental hazard is a well accepted preparatory step in risk assessment. A study of Halfon et al. ranked pesticides by applying simple tools on the partially ordered set (poset) induced by chemical properties as proxies for their groundwater contamination hazard. In this contribution, we present so...

The appearance of three scientific journals devoted to mathematical chemis-try, the foundation of an academy of mathematical chemistry, various books on the subject as well as regular conferences all testify to the establishment of an international community of mathematical chemistry since the mid-20 th century and a new subdiscipline, according to...

En la edición 1490 de la revista Semana apareció el ranking de presidentes colombianos realizado por la Fundación Liderazgo y Democracia. El resultado ha suscitado algunas reacciones, cinco de ellas pueden seguirse a través de la página en Internet de la fundación que realizó el ranking. El estudio se hizo con ayuda de 20 académicos, en su mayoría...

We analyze the connections of Lavoisier system of nomenclature with Leibniz’s philosophy, pointing out to the resemblance between what we call Leibnizian and Lavoisian programs. We argue that Lavoisier’s contribution to chemistry is something more subtle, in so doing we show that the system of nomenclature leads to an algebraic system of chemical s...

The nitrocubane substitution network shows the pattern by which single nitro-substitutions starting from cubane lead ultimately
to octanitrocubane. Of the 22 member species, densities have been experimentally measured for only 8, and we utilise these
to estimate the densities of the other 14 members. The network is viewed as a partially ordered set...

There are at least two significant applications of partial order theory in chemistry: Ranking methods and substances' properties prediction. In both cases, a set of objects is endowed with a partial order relation e.g. "more polluting than", "can be obtained from", "more reactive than" etc. The couple of set and partial order relation is known in m...

We have shown in several papers the importance of using topology, particularly set-point topology, to deal with chemical questions related to the concept of similarity. The procedure developed has been called "chemotopology" and it has been applied to different chemical sets e.g. chemical elements, benzimidazoles, sterorids, amino acids and hydride...

Fifteen quantitative structure-activity relationship (QSAR) models developed by various authors for the prediction of mutagenicity of aromatic and heteroaromatic amines were analyzed and thirteen of them, based on 95 amines, were compared using their respective statistics and order theory (Hasse Diagram Technique, HDT) to obtain an ordering of QSAR...

Ranking objects means pairwise comparing their features, mostly using certain parameters, for example real–valued functions, the values of which allow to put the objects in a certain order. However, due to the ordinal character of ranking not all slight numerical differences in the values of features should be considered as relevant. The possible a...