Vertex-degree-based molecular structure descriptors of benzenoid systems and phenylenes

Several recently published papers report expressions for various vertex-degree-based molecular structure descriptors of benzenoid systems and phenylenes. We deduce here the general expression for these descriptors, and show that a simple and generally valid relation exists between such structure descriptors of phenylenes and their hexagonal squeezes

O umanjivanju korelacije izme|u topolo{kih indeksa

A very large number of molecular-graph-based structure descriptors, the so-called topological indices (TIs), have been proposed in the recent and current chemical literature. Many of these are highly intercorrelated, which makes their application in QSPR and QSAR studies difficult and purposeless. A class of such TIs (including the Platt number, the connectivity index, and the Zagreb indices) has been examined by methods of mathematical statistics and probability theory, and the reasons for their mutual correlation are revealed. The analysis has shown that by a slight modification of these TIs, their mutual correlation can be reduced or completely eliminated. These theoretical inferences have been corroborated by a computer experiment done on a database consisting of over 126000 distinct molecular structures.U novijoj je kemijskoj literaturi predložen veliki broj strukturnih deskriptora zasnovanih na molekularnome grafu, takozvanih topoloških indeksa. Mnogi od njih su u velikoj mjeri međusobno korelirani što otežava ili onemogućava njihovu primjenu u QSPR i QSAR studijama. Jedna skupina ovakvih topoloških indeksa (koja obuhvaća Plattov broj, indeks povezanosti kao i Zagrebačke indekse) proučavana je s pomoću metoda matematičke statistike i teorije vjerojatnosti. Otkriveni su razlozi za njihovu uzajamnu koreliranost. Analiza je pokazala, da se malom modifikacijom ovih topoloških indeksa njihova koreliranost može umanjiti ili potpuno otkloniti. Dobiveni teorijski zaključci potvrđeni su kompjutorskim eksperimentom u kojem je upotrebljena jedna baza podataka s više od 126000 molekularnih struktura

Two Stability Criteria for Benzenoid Hydrocarbons and Their Relation

A new, simple, relation is established between the total π-electron energy and the HOMO-LUMO gap, applicable to benzenoid hydrocarbons. This work is licensed under a Creative Commons Attribution 4.0 International License

Constructing NSSD molecular graphs

A graph is said to be non-singular if it has no eigenvalue equal to zero; otherwise it is singular. Molecular graphs that are non-singular and also have the property that all subgraphs of them obtained by deleting a single vertex are themselves singular, known as NSSD graphs, are of importance in the theory of molecular π-electron conductors; NSSD = non-singular graph with a singular deck. Whereas all non-singular bipartite graphs (therefore, the molecular graphs of all closed-shell alternant conjugated hydrocarbons) are NSSD, the non-bipartite case is much more complicated. Only a limited number of non-bipartite molecular graphs have the NSSD property. Several methods for constructing such molecular graphs are presented.peer-reviewe

The Total π-Electron Energy Saga

The total π-electron energy, as calculated within the Hückel tight-binding molecular orbital approximation, is a quantum-theoretical characteristic of conjugated molecules that has been conceived as early as in the 1930s. In 1978, a minor modification of the definition of total π-electron energy was put forward, that made this quantity interesting and attractive to mathematical investigations. The concept of graph energy, introduced in 1978, became an extensively studied graph-theoretical topic, with many hundreds of published papers. A great variety of graph energies is being considered in the current mathematical-chemistry and mathematical literature. Recently, some unexpected applications of these graph energies were discovered, in biology, medicine, and image processing. We provide historic, bibliographic, and statistical data on the research on total π-electron energy and graph energies, and outline its present state of art. The goal of this survey is to provide, for the first time, an as-complete-as-possible list of various existing variants of graph energy, and thus help the readers to avoid getting lost in the jungle of references on this topic. This work is licensed under a Creative Commons Attribution 4.0 International License

The Total π-Electron Energy Saga

The total π-electron energy, as calculated within the Hückel tight-binding molecular orbital approximation, is a quantum-theoretical characteristic of conjugated molecules that has been conceived as early as in the 1930s. In 1978, a minor modification of the definition of total π-electron energy was put forward, that made this quantity interesting and attractive to mathematical investigations. The concept of graph energy, introduced in 1978, became an extensively studied graph-theoretical topic, with many hundreds of published papers. A great variety of graph energies is being considered in the current mathematical-chemistry and mathematical literature. Recently, some unexpected applications of these graph energies were discovered, in biology, medicine, and image processing. We provide historic, bibliographic, and statistical data on the research on total π-electron energy and graph energies, and outline its present state of art. The goal of this survey is to provide, for the first time, an as-complete-as-possible list of various existing variants of graph energy, and thus help the readers to avoid getting lost in the jungle of references on this topic. This work is licensed under a Creative Commons Attribution 4.0 International License

Fed-BioMed: A general open-source frontendframework for federated learning in healthcare

International audienceWhile data in healthcare is produced in quantities never imagined before, the feasibility of clinical studies is often hindered by the problem of data access and transfer, especially regarding privacy concerns. Federated learning allows privacy-preserving data analyses using decentralized optimization approaches keeping data securely decentralized. There are currently initiatives providing federated learning frameworks , which are however tailored to specific hardware and modeling approaches, and do not provide natively a deployable production-ready environment. To tackle this issue, herein we propose an open-source fed-erated learning frontend framework with application in healthcare. Our framework is based on a general architecture accommodating for different models and optimization methods. We present software components for clients and central node, and we illustrate the workflow for deploying learning models. We finally provide a real-world application to the federated analysis of multi-centric brain imaging data

McClellandov broj konjugiranih ugljikovodika

The McClelland number of a conjugated hydrocarbon is the integer k, satisfying the condition 2superscript(–(1/2))superscript(k) sqrt (2nm) ≤ E < 22superscript(–(1/2))2superscript(k+1) sqrt(2nm), where E is the HMO total Π-electron energy, n the number of carbon atoms, and m the number of carbon-carbon bonds. If k = 3, then the respective conjugated system is said to be energy-regular. If k ≤ 2 and k ≥ 4, then one speaks of energy-poor and energy-rich Π-electron systems, respectively. We found that all polycyclic Kekuléan hydrocarbons, possessing condensed rings, are energy-regular, with only three exceptions: naphthalene, phenanthrene, and triphenylene (which are energy-rich). Energy-poor Π-electron systems are some (but not all) non-Kekuléans, whereas many of the polycyclic Kekuléan hydrocarbons with non-condensed rings (polyphenyls, phenyl-substituted polyenes and similar) are energy-rich.McClellandov broj konjugiranoga ugljikovodika cijeli je broj k, koji zadovoljava uvjet 2superscript(-(1/2))superscript(k) sqrt (2nm) ≤ E < 22superscript(-(1/2))2superscript(k+1) sqrt(2nm), gdje je E ukupna HMO Π-elektronska energija, n broj ugljikovih atoma, a m broj ugljik-ugljik veza. Ako je k = 3, onda se za odgovarajući konjugirani sustav kaže da je energijski regularan. Ako je k ≤ 2 odn. k ≥ 4, onda govorimo o energijski siroma{nome odn. energijski bogatome Π-elektronskom sustavu. Našli smo da su svi policiklički Kekuléovski ugljikovodici s kondenziranim prstenima energijski regularni, uz jedina tri izuzetka: naftalen, fenantren i trifenilen (koji su energijski bogati). Energijski siromašni su neki (ali ne svi) ne-Kekuléovski Π-elektronski sustavi, dok su mnogi policiklički Kekuléovski ugljikovodici bez kondenziranih prstenova (polifenili, fenil-substituirani polieni i slični) energijski bogati