Synthon Model of Organic Chemistry and Synthesis Design

Koča, Jaroslav; Kratochvíl, Milan; Kvasnička, Vladimı́r; Matyska, Luděk; Pospı́chal, Jiřı́

doi:10.1007/978-3-642-93416-2

Cited by 24 publications

(11 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Jain [33] also considers an extension of the chemical distance, limited to the Frobenius norm, that incorporates edge attributes. However, it is not immediately clear how to relax the above metrics [33,37] to attain tractability.…”

Section: Related Workmentioning

confidence: 99%

“…Both are metrics and are hard to compute, while existing heuristics [49,25] are not metrics. The reaction distance [37] is also a metric directly related to the chemical distance [41] when edits are restricted to edge additions and deletions. Jain [33] also considers an extension of the chemical distance, limited to the Frobenius norm, that incorporates edge attributes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Family of Tractable Graph Distances

Bento¹,

Ioannidis²

2018

Proceedings of the 2018 SIAM International Conference on Data Mining

View full text Add to dashboard Cite

Important data mining problems such as nearestneighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in diverse areas, including, e.g., image processing and social networks. Unfortunately, popular distance scores used in these applications, that scale over large graphs, are not metrics and thus come with no guarantees. Classic graph distances such as, e.g., the chemical and the CKS distance are arguably natural and intuitive, and are indeed also metrics, but they are intractable: as such, their computation does not scale to large graphs. We define a broad family of graph distances, that includes both the chemical and the CKS distance, and prove that these are all metrics. Crucially, we show that our family includes metrics that are tractable. Moreover, we extend these distances by incorporating auxiliary node attributes, which is important in practice, while maintaining both the metric property and tractability.arXiv:1801.04301v1 [math.CO]

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Family of Tractable Graph Distances

Bento¹,

Ioannidis²

2018

Proceedings of the 2018 SIAM International Conference on Data Mining

View full text Add to dashboard Cite

show abstract

“…7. A concept of similarity is determined graph-theoretically [22] by maximal common subgraph of ph and ph' determined by intersections of subsets for pair matching and subsets for unmatched vertices, respectively (see Fig. 8 For larger values on n this optimization problem represents an extremely complicated computational problem, which will be approached in the forthcoming part of this paper by a chemostat technique specified al ready above in the previous Section.…”

Section: A Set-theory Formalismmentioning

confidence: 99%

“…(30a-b)). All possible phenotypes create a set Ph, we put .For the set Ph we may define a similarity (metrics) as follows[22]: Let ( ) ( ) ( )…”

mentioning

confidence: 99%

Artificial Chemistry and Molecular Darwinian Evolution in silico

Kvasnička

Pospı́chal

2003

Collect. Czech. Chem. Commun.

View full text Add to dashboard Cite

A simplified model of Darwinian evolution at the molecular level is studied by applying the methods of artificial chemistry. A chemical reactor (chemostat) contains molecules that are represented by binary strings, the strings being capable of replication with a probability proportional to their fitness. Moreover, the process of replication is not fully precise, sporadic mutations may produce new offspring strings, which are slightly different from their parent templates. The dynamics of such an autoreplicating system is described by Eigen's differential equations. These equations have a unique asymptotically stable state, which corresponds to those strings that have the highest rate constants (fitness). Fitness of binary string is calculated as a graph-theory similarity between a folding (phenotype) of respective string and the so-called required folding. The presented method offers a detailed view of mechanisms of the molecular Darwinian evolution, in particular of the meaning and importance of neutral mutations.

show abstract

“…Graphs are connectivity schemes that put across a quantum object such as a molecule in a succinct representation. In their work 1 on the synthon model of organic chemistry Koča et al classify mathematical models as physical or nonphysical, a distinction that is admittedly of a relative nature. However, they note the trend toward “physicalization” of nonphysical models.…”

Section: Introductionmentioning

confidence: 99%

Functional groups expressed as graphs extracted from the Laplacian of the electron density

Popelier

Burke

Malcolm

2003

Int J of Quantum Chemistry

View full text Add to dashboard Cite

ABSTRACT:The valence charge concentration shell, as determined by the Laplacian of the electron density, is used as a source of quantum topological graphs, called Lgraphs. A considerable number of such graphs are extracted from the ab initio wave functions of 31 molecules calculated at the B3LYP/6-311ϩG(2d,p)//B3LYP/6-311ϩG(2d,p) level, covering common functional groups in organic chemistry. We show how L-graphs can be constructed from a largely transferable subgraph called atomic L-graph. We investigate the topological stability of the L-graphs as a function of the basis set. Reliable and consistent atomic L-graphs are only obtained with basis sets of triple-zeta quality or higher. The recurrence of invariant motifs or subgraphs in the Lgraphs enables the isolation of 16 atomic L-graphs.

show abstract

Synthon Model of Organic Chemistry and Synthesis Design

Cited by 24 publications

References 0 publications

A Family of Tractable Graph Distances

A Family of Tractable Graph Distances

Artificial Chemistry and Molecular Darwinian Evolution in silico

Functional groups expressed as graphs extracted from the Laplacian of the electron density

Contact Info

Product

Resources

About