The expansion of chemical space in 1826 and in the 1840s prompted the convergence to the periodic system.

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 after an unstable period culminating around 1826, chemical space led the system to converge to a backbone structure clearly recognizable in the 1840s. Hence, the system was already encoded in the space for about two and half decades before its formulation. Chemical events in 1826 and in the 1840s were driven by the discovery of new forms of combination standing the test of time. Emphasis of the space upon organic chemicals after 1830 prompted the recognition of relationships among elements participating in the organic turn and obscured some of the relationships among transition metals. To account for the role of nineteenth century atomic weights upon the system, we introduced an algorithm to adjust the space according to different sets of weights, which allowed for estimating the resulting periodic systems of chemists using one or the other weights. By analyzing these systems, from Dalton up to Mendeleev, Gmelin's atomic weights of 1843 produce systems remarkably similar to that of 1869, a similarity that was reinforced by the atomic weights on the years to come. Although our approach is computational rather than historical, we hope it can complement other tools of the history of chemistry.

The Uncertain Role of Nominations for the Nobel Prize in Chemistry†.

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 publication, we examine data culled from the Nobel Prize Nomination Archives for the period 1901-1970 of the variable role of nominations in the selection process for the Nobel Prize in Chemistry. The evidence is overwhelming that nominations, in general, during the 1901-1970 period have not been the deciding, overriding factor in the selection of the recipients of the NPch. Rather, we posit that nominations from the preselected nominator-pool have been a source of information for the Committee, used to suggest future years' contenders and possibly served as motivation for the Committee to seek nominations for specific nominees for future years. It is also clear that selections are often influenced by personal prejudices, for example, friendships, rivalries, and nationality.

Exploration of the chemical space and its three historical regimes.

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 reactions stored in the Reaxys database, that chemists have reported new compounds in an exponential fashion from 1800 to 2015 with a stable 4.4% annual growth rate, in the long run neither affected by World Wars nor affected by the introduction of new theories. Contrary to general belief, synthesis has been the means to provide new compounds since the early 19th century, well before Wöhler's synthesis of urea. The exploration of chemical space has followed three statistically distinguishable regimes. The first one included uncertain year-to-year output of organic and inorganic compounds and ended about 1860, when structural theory gave way to a century of more regular and guided production, the organic regime. The current organometallic regime is the most regular one. Analyzing the details of the synthesis process, we found that chemists have had preferences in the selection of substrates and we identified the workings of such a selection. Regarding reaction products, the discovery of new compounds has been dominated by very few elemental compositions. We anticipate that the present work serves as a starting point for more sophisticated and detailed studies of the history of chemistry.

Rolf Huisgen, Eminent Chemist and Polymath (1920-2020): In His Own Words and In His Publication Metrics.

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 as a historian of chemistry. The second part of this paper examines the scientometrics of Huisgen's publication history. In the late 1950s and early 1960s, Huisgen's career experienced a major transition in terms of publication metrics and the influence these papers had on the organic chemistry community. This was the result of his research into 1,3-dipolar cycloadditions. Citations to his scientific contributions are well spread over many of his papers, demonstrating his constant work and the building up of a research topic, which continued after his official retirement in 1988. In fact, 17 % of his more than 600 publications appeared after 1988. The majority of Huisgen's papers were co-authored with his many graduate and postdoctoral students. Consistent with the trend of that era, Huisgen was the sole author of most of his Review articles, and not just those of his many plenary lectures, and it is those Review articles that proved to be his most cited publications. This demonstrates the power and influence of Review articles-secondary sources, in the vocabulary of historians and sociologists of science. In those Review articles, Huisgen principally described the state of the art of 1,3-dipolar cycloadditions-his golden offspring.

The Mutation of the "Nobel Prize in Chemistry" into the "Nobel Prize in Chemistry or Life Sciences": Several Decades of Transparent and Opaque Evidence of Change within the Nobel Prize Program.

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 of the Nobel Prize in Chemistry into what is effectively the "Nobel Prize in Chemistry or Life Sciences." This paper presents a detailed study of this opaque change, including evidence that the disciplines of chemistry and biochemistry cover, today, intellectually quite distinct and generally scientifically-unrelated intellectual territory. This paper supports the evolution of the Nobel Prizes, and encourages the Nobel Prize program to move from opaque to transparent change processes for the next generations of achievement in the sciences.

Challenges for the Periodic Systems of Elements: Chemical, Historical and Mathematical Perspectives.

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 preserved entities in compound transformations. We celebrate the systems, rather than their tables or ultimate table. The periodic law, we argue, is not an all-encompassing achievement, as it does not apply to every property of all elements and compounds. Periodic systems have been generalised as ordered hypergraphs, which solves the long-lasting question on the mathematical structure of the systems. In this essay, it is shown that these hypergraphs may solve current issues such as order reversals in super-heavy elements and lack of system predictive power. We discuss research in extending the limits of the systems in the super-heavy-atom region and draw attention to other limits: the antimatter region and the limit arising from compounds under extreme conditions. As systems depend on the known chemical substances (chemical space) and such a space grows exponentially, we wonder whether systems still aim at projecting knowledge of compounds on the relationships among the elements. We claim that systems are not based on compounds anymore, rather on 20th century projections of the 1860s systems of elements on systems of atoms. These projections bring about oversimplifications based on entities far from being related to compounds. A linked oversimplification is the myth of vertical group similarity, which raises questions on the approaches to locate new elements in the system. Finally, we propose bringing back chemistry to the systems by exploring similarity and order relationships of elements using the current information of the chemical space. We ponder whether 19th century periodic systems are still there or whether they have faded away, leaving us with an empty 150th celebration.

The six stages of the convergence of the periodic system to its final structure.

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 the periodic system. Here we show, by analysing the space between 1800 and 2021, that the system has converged towards its current stable structure through six stages, respectively characterised by the finding of elements (1800-1826), the emergence of the core structure of the system (1826-1860), its organic chemistry bias (1860-1900) and its further stabilisation (1900-1948), World War 2 new chemistry (1948-1980) and the system final stabilisation (1980-). Given the self-reinforced low diversity of the space and the limited chemical possibilities of the elements to be synthesised, we hypothesise that the periodic system will remain largely untouched.

Iatrogenic dural arteriovenous fistula and aneurysmal subarachnoid hemorrhage.

The authors present the case of a patient who presented acutely with aneurysmal subarachnoid hemorrhage (SAH) and a contralateral iatrogenic dural arteriovenous fistula (DAVF). Diagnostic angiography was performed, revealing a right-sided middle cerebral artery (MCA) aneurysm and a left-sided DAVF immediately adjacent to the entry of the ventriculostomy and bur hole site. A craniotomy was performed for clipping of the ruptured MCA aneurysm, and the patient subsequently underwent endovascular obliteration of the DAVF 3 days later. The authors present their treatment of an iatrogenic DAVF in a patient with an aneurysmal SAH, considerations in management options, and a literature review on the development of iatrogenic DAVFs.

Semiotic Thoughts on Biological Sequence Representations.

The deluge of biological sequences ranging from those of proteins, DNA and RNA to genomes has motivated to devise models to represent them, which are further used to contrast those sequences. Here we present a brief bibliometric description of the research area devoted to the representation of biological sequences and highlight the semiotic elements of this process. Finally, we argue that this research area must learn from the evolution of mathematical chemistry and try to avoid its pitfalls.

Formal structure of periodic system of elements.

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 periodic system, which corresponds to an ordered hypergraph. It is shown that the current periodic system of chemical elements is an instance of the general structure. The definition is used to devise a tailored periodic system of polarizability of single covalent bonds, where order relationships are quantified within subsets of similar bonds and among these classes. The generalized periodic system allows envisioning periodic systems in other disciplines of science and humanities.

How frequently do clusters occur in hierarchical clustering analysis? A graph theoretical approach to studying ties in proximity.

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 clusters from a third one) may produce several different dendrograms, having different possible clustering patterns (different classifications). This situation is usually disregarded and conclusions are based on a single result, leading to questions concerning the permanence of clusters in all the resulting dendrograms; this happens, for example, when using HCA for grouping molecular descriptors to select that less similar ones in QSAR studies. RESULTS: Representing dendrograms in graph theoretical terms allowed us to introduce four measures of cluster frequency in a canonical way, and use them to calculate cluster frequencies over the set of all possible dendrograms, taking all ties in proximity into account. A toy example of well separated clusters was used, as well as a set of 1666 molecular descriptors calculated for a group of molecules having hepatotoxic activity to show how our functions may be used for studying the effect of ties in HCA analysis. Such functions were not restricted to the tie case; the possibility of using them to derive cluster stability measurements on arbitrary sets of dendrograms having the same leaves is discussed, e.g. dendrograms from variations of HCA parameters. It was found that ties occurred frequently, some yielding tens of thousands of dendrograms, even for small data sets. CONCLUSIONS: Our approach was able to detect trends in clustering patterns by offering a simple way of measuring their frequency, which is often very low. This would imply, that inferences and models based on descriptor classifications (e.g. QSAR) are likely to be biased, thereby requiring an assessment of their reliability. Moreover, any classification of molecular descriptors is likely to be far from unique. Our results highlight the need for evaluating the effect of ties on clustering patterns before classification results can be used accurately.Graphical abstractFour cluster contrast functions identifying statistically sound clusters within dendrograms considering ties in proximity.

Lemont B. Kier: a bibliometric exploration of his scientific production and its use.

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 vitae, as well as from the ISI Web of Knowledge (ISI), his role within the scientific community is established and the way his scientific results circulate is studied. His curriculum vitae is explored emphasising the approaches he used in his research activities and the social ties with other actors of the community. The circulation of Kier's publications in the ISI is studied as a means for spreading and installing his discourse within the community. The citation patterns found not only show the usage of Kier's scientific results, but also open the possibility to identify some characteristics of this discursive community, such as a common vocabulary and common research goals. The results show an interdisciplinary research work that consolidates a scientific community on the topic of drug discovery.

Chemotopology: beyond neighbourhoods.

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 hydrides. The idea behind chemotopology is to run a hierarchical cluster analysis study on a set of objects characterised by different attributes. From this study a dendrogram is obtained, which gathers similarity neighbourhoods for the set of objects. By using a mathematical characterisation of a dendrogram it is possible to select a collection of objects' neighbourhoods which in turn become a basis for a topology. With this basis at hand different properties of subsets of objects can be calculated, all of them related to the concept of similarity e.g. closures, derived sets, boundaries, interiors and exteriors. We have also shown the chemical meaning of each one of these properties. In this manuscript, we review the foundations of the chemotopological method as well as its different applications to chemical sets. By means of examples we illustrate how the method can be used as a versatile tool for drug discovery. We also study the relationship between the topologies generated from dendrograms of a given set of objects and the dendrograms that can be obtained for particular topologies on the set of objects.

Comparison of QSARs and characterization of structural basis of bioactivity using partial order theory and formal concept analysis: a case study with mutagenicity.

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 models. The technique of Formal Concept Analysis (FCA) was applied to the set of 95 amines to extract concepts and, in general, knowledge about the relationship between structural attributes and mutagenicity. HDT may be useful as a general tool for the comparison of different classes of QSAR models. FCA turns out to be a novel mathematical technique for seeking for relationships between molecular structure and activity.

Partially ordered sets: ranking and prediction of substances' properties.

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 mathematics as a partially ordered set (poset). Ranking methods, such as the Hasse diagram technique, lead to a partial order where several incomparabilities (lack of order) appear between pairs of objects. This phenomenon is quite common in ranking studies, and it often is circumvented by a combination of object features leading to a total order. However, such a combination introduces subjectivities and bias in the ranking process. Here a step-by-step procedure is shown to turn incomparabilities into comparabilities taking into account all the possible bias by a linear combination of features. In such a manner, it is possible to predict how probable it is to obtain a particular total order from a given poset. Similarly, it is possible to calculate the needed bias over certain attributes to obtain a particular total order. An example application is shown where substances are ranked according to their bioconcentration factor and biodegradation potential. Another application of partial order theory to chemistry has to do with the prediction of properties for a set of substances related in a (preferably systematic) chemical fashion. A customary relation is "can be obtained from"; if such a relation is set up for a given molecular structure e.g. benzene, and all its substituted derivatives (say chlorinated ones) are considered, then the set of benzene and its chlorinated derivatives are partially ordered. Taking advantage of the poset generated, different methods can be applied to predict properties of the substances considered in the poset. Such methods include the poset-average, cluster expansion, and splinoid methods. In this paper we discuss each one of these methods, its advantages and disadvantages and we outline its applicability to estimate cooperative free energies of hemoglobins with different degree of oxygenation.

Ranking of refrigerants.

Environmental ranking of refrigerants is of need in many instances. The aim is to assess the relative environmental hazard posed by 40 refrigerants, including those used in the past, those presently used, and some proposed substitutes. Ranking is based upon ozone depletion potential, global warming potential, and atmospheric lifetime and is achieved by applying the Hasse diagram technique, a mathematical method that allows us to assess order relationships of chemicals. The refrigerants are divided into 13 classes, of which the chlorofluorocarbons, hydrofluorocarbons, hydrochlorofluorocarbons, hydrofluoroethers, and hydrocarbons contain the largest number of single substances. The dominance degree, a method for measuring order relationships among classes, is discussed and applied to the 13 refrigerant classes. The results show that some hydrofluoroethers are as problematic as the hydrofluorocarbons. Hydrocarbons and ammonia are the least problematic refrigerants with respect to the three environmental properties.