WAlexandru T. Balaban is a Romanian chemist who significantly contributed to the fields of organic chemistry, theoretical chemistry, mathematical chemistry, and chemical graph theory.
WIn graph theory, a caterpillar or caterpillar tree is a tree in which all the vertices are within distance 1 of a central path.
WThe circuit topology of a linear polymer refers to arrangement of its intra-molecular contacts. Examples of linear polymers with intra-molecular contacts are nucleic acids and proteins. For defining the circuit topology, contacts are defined depending on the context. For proteins with disulfide bonds, these bonds could be considered as contacts. In a context where beta-beta interactions in proteins are more relevant, these interactions are used to define the circuit topology. As such, circuit topology framework can be applied to a wide range of applications including protein folding and analysis of genome architecture. In particular, data from Hi-C and related technologies can be readily analysed using circuit topology framework.
WErnesto Estrada is a Cuban-Spanish scientist. He is Senior ARAID Research at the Institute of Mathematics and Applications at the University of Zaragoza, Spain since 2019. Before he was the Chair in Complexity Science, Full Professor at the Department of Mathematics and Statistics of the University of Strathclyde, Glasgow, United Kingdom. He is known by his contributions in different disciplines including mathematical chemistry, and complex network theory.
WThe Hosoya index, also known as the Z index, of a graph is the total number of matchings in it. The Hosoya index is always at least one, because the empty set of edges is counted as a matching for this purpose. Equivalently, the Hosoya index is the number of non-empty matchings plus one. The index is named after Haruo Hosoya.
WIn chemical graph theory and in mathematical chemistry, a molecular graph or chemical graph is a representation of the structural formula of a chemical compound in terms of graph theory. A chemical graph is a labeled graph whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds. Its vertices are labeled with the kinds of the corresponding atoms and edges are labeled with the types of bonds. For particular purposes any of the labelings may be ignored.
WA Savitzky–Golay filter is a digital filter that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase the precision of the data without distorting the signal tendency. This is achieved, in a process known as convolution, by fitting successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares. When the data points are equally spaced, an analytical solution to the least-squares equations can be found, in the form of a single set of "convolution coefficients" that can be applied to all data sub-sets, to give estimates of the smoothed signal, at the central point of each sub-set. The method, based on established mathematical procedures, was popularized by Abraham Savitzky and Marcel J. E. Golay, who published tables of convolution coefficients for various polynomials and sub-set sizes in 1964. Some errors in the tables have been corrected. The method has been extended for the treatment of 2- and 3-dimensional data.
WTomaž (Tomo) Pisanski is a Slovenian mathematician working mainly in discrete mathematics and graph theory. He is considered by many Slovenian mathematicians to be the "father of Slovenian discrete mathematics."
WMilan Randić is a Croatian American scientist who is one of the leading experts in the field of computational chemistry.