# Some dimension problems in molecular databases

@article{Mezey2009SomeDP, title={Some dimension problems in molecular databases}, author={Paul G. Mezey}, journal={Journal of Mathematical Chemistry}, year={2009}, volume={45}, pages={1-6} }

Molecular databases obtained either by combinatorial chemistry tools or by more traditional methods are usually organized according to a set of molecular properties. A database may be regarded as a multidimensional collection of points within a space spanned by the various molecular properties of interest, the property space. Some properties are likely to be more important than others, those considered important form the essential dimensions of the molecular database. How many properties are…

## 15 Citations

### On the dimension dependence of the level of optimality of certain multidimensional sampling strategies

- Computer ScienceJ. Comput. Methods Sci. Eng.
- 2016

A volume-constrained hypersphere – hypercube combination is explored if a switch of strategy might become desirable, and the advantages of modifying these strategies to make them more compatible with one another in a dimension-dependent way are discussed.

### Mathematical and Computational Techniques for Drug Discovery: Prom- ises and Developments

- Biology, Chemistry
- 2019

Computational techniques derived from high level quantum chemical computations such as QM/MM ONIOM methods, quantum chemical optimization of geometries complexes, and molecular dynamics methods for providing insights into protein-drug interactions are considered.

### From quantum similarity measures to quantum analogy functors: tools for QShAR, quantitative shape-activity relations

- ChemistryTheoretical Chemistry Accounts
- 2021

An analogy can be regarded as a relation between two families of similarities, and the mathematical tool of functor has been proposed for certain chemical applications where not just one type of…

### Computational combinatorics of hyperplane colorings of 6D-hypercube for all irreducible representations and applications

- MathematicsJournal of Mathematical Chemistry
- 2019

Computational generating function techniques are outlined for combinatorics of colorings of all hyperplanes of the 6D-hypercube for 65 irreducible representations of the 6D-hyperoctahedral group…

### Distance degree vector and scalar sequences of corona and lexicographic products of graphs with applications to dynamic NMR and dynamics of nonrigid molecules and proteins

- MathematicsTheoretical Chemistry Accounts
- 2021

We have developed novel topological techniques to generate distance degree vector sequences (DDS) and distance degree scalar sequences (SS) of corona and lexicographic products of graphs both of…

### Computations of Colorings 7D‐Hypercube's Hyperplanes for All Irreducible Representations

- Mathematics, Computer ScienceJ. Comput. Chem.
- 2020

In the present study, we compute and enumerate the colorings of 7D‐hypercube for all of its hyperplanes (q = 1–7) for all 110 irreducible representations (IRs) of the seventh‐dimensional…

### Computational multinomial combinatorics for colorings of 5D-hypercubes for all irreducible representations and applications

- MathematicsJournal of Mathematical Chemistry
- 2018

We have developed computational multinomial techniques for colorings of 5D-hypercubes for all irreducible representations of the five-dimensional hyperoctahedral group up to 10 different color types.…

### Nonrigid water octamer: Computations with the 8‐cube

- PhysicsJ. Comput. Chem.
- 2020

A 8‐cube model of the fully nonrigid water octamer is considered within the 8‐dimensional hyperoctahedral wreath product group with 10,321,920 operations and 185 irreducible representations by…

### Combinatorial multinomial generators for colorings of 4D-hypercubes and their applications

- MathematicsJournal of Mathematical Chemistry
- 2018

Combinatorial enumeration of colorings of vertices, edges, faces and cells of 4D-hypercubes are considered for all irreducible representations of the 4D-hyperoctahedral group. We have developed…

### Enumeration of relativistic states for superheavy and transactinide dimers in the periodic table

- PhysicsJournal of Mathematical Chemistry
- 2019

We have employed combinatorial techniques based on multinomial symmetric function (S-function) techniques for exhaustive enumeration and generation of relativistic (ω–ω states) states originating…

## References

SHOWING 1-10 OF 13 REFERENCES

### The degree of similarity of three-dimensional bodies: Application to molecular shape analysis

- Physics
- 1991

Similarity of shape features of three-dimensional bodies is of importance in many fields. Computational methods that are suitable to provide numerical measures for such similarities are expected to…

### QUANTUM CHEMICAL SHAPE : NEW DENSITY DOMAIN RELATIONS FOR THE TOPOLOGY OF MOLECULAR BODIES, FUNCTIONAL GROUPS, AND CHEMICAL BONDING

- Chemistry
- 1994

A density domain (DD) is the formal body enclosed by a molecular isodensity contour (MIDCO) surface. Individual nuclear neighborhoods and various formal molecular fragments can be regarded as fuzzy…

### A Functional Group Database: A Charge Density – DARC Approach

- Chemistry
- 1998

The principle of the DARC approach of hierarchical organization is applied to a molecular electron density representation of functional groups, designed to represent some of the large-scale features…

### Dimension Concepts and Reduced Dimensions in Toxicological QShAR Databases as Tools for Data Quality Assessment

- Computer Science
- 2001

Some of the tools for effective dimension reduction and dimension expansion are reviewed in the context of database quality control and conditions for database compatibility are presented.

### Relations among functional groups within a stoichiometry: A nuclear configuration space approach

- Mathematics
- 1992

A general scheme is proposed for the study of the interrelations and transformations of flexible functional groups within the configuration space M of all possible chemical species of a fixed overall…

### Local Electron Densities and Functional Groups in Quantum Chemistry

- Chemistry
- 1999

The connections between the quantum chemical concept of local electron densities and the traditional concept of functional groups of organic chemistry are explored. The Density Domain criterion of…

### Quantum chemistry of macromolecular shape

- Chemistry
- 1997

Some of the new developments in the quantum-chemical study of macromolecular shapes are reviewed, with special emphasis on the additive fuzzy electron density fragmentation methods and on the…

### Computational Aspects of Combinatorial Quantum Chemistry

- Chemistry
- 2001

The Additive Fuzzy Density Fragmentation (AFDF) principle and the Adjustable Density Matrix Assembler (ADMA) methods are proposed for a combinatorial construction of electron density representations…