Structure–activity relationship and quantitative SAR are modeling methods largely used in assessing biological properties of chemical substances. QSAR is based on the hypothesis that the chemical structure is responsible for the activity; it follows that similar molecules are expected to have similar properties. Similarity plays an important role in read across, which categorizes molecules primarily on the basis of similarity. Similarity, and chemical similarity too, is a property differently perceived by humans. The various proposed metrics often disagree with human (...) judgment, and no a unique metric for chemical similarity is universally adopted. Researchers argued that categorization is not only explained by similarity but depends as well on abstract knowledge and the task to accomplish. Moreover, similarity cannot be the unique explanation of a categorization, as different perceptual processes take place in category formation. Assuming that similarity judgments are deeply rooted in human knowledge and perception, cognitive sciences contributions are as important as the mathematical considerations of the classical theories. After an excursus in the many views of similarity in philosophy, mathematics, and cognitive science, the paper explores how connectionist systems, which loosely mimic the human cognitive system, could improve similarity-based choices. A case study on building SARs using connectionism and deep neural networks shows the role of similarity in building and explaining those models. A discussion about deep learning for QSAR and as a modeling tool for science concludes the presentation. (shrink)

This paper aims to develop an account of the pursuitworthiness of models based on a view of models as epistemic tools. This paper is motivated by the historical question of why, in the 1960s, when many scientists hardly found QSAR models attractive, some pharmaceutical scientists pursued Quantitative Structure–Activity Relationship (QSAR) models despite the lack of potential for theoretical development or empirical success. This paper addresses this question by focusing on how models perform their heuristic functions as epistemic tools (...) rather than as potential theories. I argue that models perform their heuristic function by “constructing” phenomena from data in the sense that they allow the model users who interact with the medium of the models to recognise the phenomena as such. The constructed phenomena assist model users in identifying which conditional hypotheses that are focused on low-level regularities concerning entities such as chemical compounds are more “testworthy,” a concept that links the costs associated with hypothesis testing with the fertility of the hypothesis. (shrink)

Topological indices are quantitative measurements that describe a molecule’s topology and are quantified from the molecule’s graphical representation. The significance of topological indices is linked to their use in QSPR/QSAR modelling as descriptors. Mathematical associations between a particular molecular or biological activity and one or several biochemical and/or molecular structural features are QSPRs and QSARs. In this paper, we give explicit expressions of two recently defined novel ev-degree- and ve-degree-based topological indices of two classes of benzenoid, namely, linear hexagonal (...) chain and hammer-like benzenoid. (shrink)

Topological indices are numeric parameters which portray the topology of a subatomic structure. In QSAR/QSPR analysis, topological descriptors play a vital role to examine the topology of a network. An interconnection network is a structure whose components are connected physically according to some pattern. In this paper, an interconnection network, ternary hypertree, which is a structural combination of complete ternary tree and hypertree, is introduced. We have evaluated the topological descriptors grounded on the distances for the ternary hypertree. The (...) analytical expressions for Wiener, different types of Szeged, and Mostar indices are determined. (shrink)

Mathematical chemistry is often thought to be a 20th-century subdiscipline of chemistry, but in this paper we discuss several early chemical ideas 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 functional thinking, i.e. setting up variables, symbolizing them, and seeking for functions relating them. The cases we discuss are Plato's triangles, Geoffroy's affinity table, Lavoisier's classification (...) of substances and their relationships, Mendeleev's periodic table, Cayley's enumeration of alkanes, Sylvester's association of algebra and chemistry, and Wiener's relationship between molecular structure and boiling points. These examples show that mathematical chemistry has much more than a century of history. (shrink)