Progress in the field of metal-templated self-assembly has made it possible to design and build supramolecular architectures with increasingly complex structures and topologies1,2. As well as the synthetic challenges and aesthetic appeal associated with such structures, current activities in this area are also driven by the desire to produce functional systems. This can be achieved in a number ...

Molecular Field Topology Analysis (MFTA) [1] is a QSAR approach based on the local (atomic) descriptors. First, a so-called molecular supergraph is constructed which is a simple graph such that the molecular graphs of all training set structures can be represented as its subgraphs. A uniform descriptor set for the statistical analysis is obtained by superimposing each training set structure ont...

The goal of this research will be to provide sufficient conditions and tractable algorithms that guarantee the topological embedding of geometric approximations commonly used by modern geometric design systems. Particular focus is on the use of ambient isotopy as the measure of topological equivalence, which is stricter than the more traditional use of homeomorphism. Such topological guarantees...

We have developed the topology-aware parallel molecular dynamics (TAPMD) algorithm, in which the processors are rearranged automatically according to resource topology so as to minimize the cost required for the simulation. It is demonstrated that TAPMD can reduce the communication time to less than half compared to the time in the worst case on a distributed PC clusters. This improvement is ex...

let g = (v,e) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. in this paper, we associate a topology to g, called graphic topology of g and we show that it is an alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. then we investigate some properties of this topology. our motivation is to give an e...

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

Understanding the relationship between molecular structure and folding is a central problem in disciplines ranging from biology to polymer physics and DNA origami. Topology can be a powerful tool to address this question. For a folded linear chain, the arrangement of intra-chain contacts is a topological property because rearranging the contacts requires discontinuous deformations. Conversely, ...

modeling and simulation of processing plants are widely used in industry. construction of a mathematical model for a plant is a time-consuming and error-prone task. in light of extensive advancements in computer science (both hardware and software), computers are becoming a necessary instrument in industrial activities. many software tools for modeling, simulation and optimization of processing...

Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational transitions that are associated with changes in molecular topology. For folded linear biomolecules, arrangement of intramolecular contacts is identified as a k...