Information entropy changes in chemical reactions

From Local Atomic Environments to Molecular Information Entropy

The similarity of local atomic environments is an important concept in many machine learning techniques, which find applications in computational chemistry and material science. Here, we present and discuss a connection between the information entropy and the similarity matrix of a molecule. The resulting entropy can be used as a measure of the complexity of a molecule. Exemplarily, we introduce and evaluate two specific choices for defining the similarity: one is based on a SMILES representation of local substructures, and the other is based on the SOAP kernel. By tuning the sensitivity of the latter, we can achieve good agreement between the respective entropies. Finally, we consider the entropy of two molecules in a mixture. The gain of entropy due to the mixing can be used as a similarity measure of the molecules. We compare this measure to the average and best-match kernel. The results indicate a connection between the different approaches and demonstrate the usefulness and broad applicability of the similarity-based entropy approach.

Bidimensional ensemble entropy: Concepts and application to emphysema lung computerized tomography scans

BACKGROUND AND OBJECTIVE

Bidimensional entropy algorithms provide meaningful quantitative information on image textures. These algorithms have the advantage of relying on well-known one-dimensional entropy measures dedicated to the analysis of time series. However, uni- and bidimensional algorithms require the adjustment of some parameters that influence the obtained results or even findings. To address this, ensemble entropy techniques have recently emerged as a solution for signal analysis, offering greater stability and reduced bias in data patterns during entropy estimation. However, such algorithms have not yet been extended to their two-dimensional forms.

METHODS

We therefore propose six bidimensional algorithms, namely ensemble sample entropy, ensemble permutation entropy, ensemble dispersion entropy, ensemble distribution entropy, and two versions of ensemble fuzzy entropy based on different models or parameters initialization of an entropy algorithm. These new measures are first tested on synthetic images and further applied to a biomedical dataset.

RESULTS

The results suggest that ensemble techniques are able to detect different levels of image dynamics and their degrees of randomness. These methods lead to more stable entropy values (lower coefficients of variations) for the synthetic data. The results also show that these new measures can obtain up to 92.7% accuracy and 88.4% sensitivity when classifying patients with pulmonary emphysema through a k-nearest neighbors algorithm.

CONCLUSIONS

This is a further step towards the potential clinical deployment of bidimensional ensemble approaches to detect different levels of image dynamics and their successful performance on emphysema lung computerized tomography scans. These bidimensional ensemble entropy algorithms have potential to be used in various imaging applications thanks to their ability to distinguish more stable and less biased image patterns compared to their original counterparts.

Digitalizing Structure–Symmetry Relations at the Formation of Endofullerenes in Terms of Information Entropy Formalism

Information entropy indices are widely used for numerical descriptions of chemical structures, though their applications to the processes are scarce. We have applied our original information entropy approach to filling fullerenes with a guest atom. The approach takes into account both the topology and geometry of the fullerene structures. We have studied all possible types of such fillings and found that information entropy (ΔhR) and symmetry changes correlate. ΔhR is negative, positive or zero if symmetry is increased, reduced or does not change, respectively. The ΔhR value and structural reorganization entropy, a contribution to ΔhR, are efficient parameters for the digital classification of the fullerenes involved into the filling process. Based on the calculated values, we have shown that, as the symmetry of the fullerene cage becomes higher, the structural changes due to the filling it with a guest atom become larger. The corresponding analytical expressions and numerical data are discussed.

Complexity of Molecular Nets: Topological Approach and Descriptive Statistics

The molecular net complexity (HmolNet) is an extension of the combinatorial complexity (Hmol) of a crystal structure introduced by Krivovichev. It was calculated for a set of 4152 molecular crystal structures with the composition of CxHyOz characterized by the structural class P21/c, Z = 4 (1). The molecular nets were derived from the molecular Voronoi–Dirichlet Polyhedra (VDPmol). The values of the molecular coordination number (CNmol) and critical coordination number (CNcrit) are discussed in relation with the complexity of the crystal structures. A statistical distribution of the set of molecular crystals based on the values of CNmol, CNcrit, and the complexity parameters is obtained. More than a half of the considered structures has CNmol = 14 and CNmol′ = 9 with the Wyckoff set of edges e5dcba. The average multiplicity of intermolecular contacts statistically significantly decreases from 1.58 to 1.51 upon excluding all contacts except those bearing the molecular net. The normalized value of HmolNet is of the logistic distribution type and is distributed near 0.85HmolNet with a small standard deviation. The contribution of Hmol into HmolNet ranges from 35 to 95% (mean 79%, SD 6%), and the subset of bearing intermolecular contacts accounts for 41 to 100% (mean 62%, SD 11%) of the complexity of the full set of intermolecular contacts.

Molecular size and molecular structure: Discriminating their changes upon chemical reactions in terms of information entropy

Structural descriptors take the central place in the digitalization of chemical reactions. Information entropy is one of such descriptors that has been a seminal for numerous derivative indices. Previously, we have studied the rules of calculating information entropies of molecular ensembles based on the corresponding values of constituting molecules and found that the complexity of the ensemble has the contributions from the molecular structure and the size of the molecules. Considering chemical reaction as the conversion of one molecular ensemble to another allows calculating the change in information entropy as well as its components associated with molecular-structure and molecular-size changes. We demonstrate that both total information entropy change and its contributions are characteristic for the selected classes of chemical reactions and exemplify this approach with the cycloaddition and exchange reactions widespread in organic chemistry.

Covalently Bonded Fullerene Nano-Aggregates (C60)n: Digitalizing Their Energy–Topology–Symmetry

Fullerene dimers and oligomers are attractive molecular objects with an intermediate position between the molecules and nanostructures. Due to the size, computationally assessing their structures and molecular properties is challenging, as it currently requires high-cost quantum chemical techniques. In this work, we have jointly studied energies, topological (Wiener indices and roundness), and information theoretic (information entropy) descriptors, and have obtained regularities in triad ‘energy–topology–symmetry’. We have found that the topological indices are convenient to indicating the most and least reactive atoms of the fullerene dimer structures, whereas information entropy is more suitable to evaluate odd–even effects on the symmetry of (C60)n. Quantum chemically assessed stabilities of selected C120 structures, as well as linear and zigzag (C60)n, are discussed.

Information Entropy in Chemistry: An Overview

Basic applications of the information entropy concept to chemical objects are reviewed. These applications deal with quantifying chemical and electronic structures of molecules, signal processing, structural studies on crystals, and molecular ensembles. Recent advances in the mentioned areas make information entropy a central concept in interdisciplinary studies on digitalizing chemical reactions, chemico-information synthesis, crystal engineering, as well as digitally rethinking basic notions of structural chemistry in terms of informatics.

Classification of isentropic molecules in terms of Shannon entropy

Shannon entropy is widely used as a descriptor of molecular structure. Isentropicity of the molecules in terms of Shannon approach emerges in specific problems of physical and organic chemistry. In the present work, we consider the main classes of isentropic molecules, exemplify them, and provide their hierarchy.

Adaptive-Cognitive Kalman Filter and Neural Network for an Upgraded Nondispersive Thermopile Device to Detect and Analyze Fusarium Spores

Noises such as thermal noise, background noise or burst noise can reduce the reliability and confidence of measurement devices. In this work, a recursive and adaptive Kalman filter is proposed to detect and process burst noise or outliers and thermal noise, which are popular in electrical and electronic devices. The Kalman filter and neural network are used to preprocess data of three detectors of a nondispersive thermopile device, which is used to detect and quantify Fusarium spores. The detectors are broadband (1 µm to 20 µm), λ 1 (6.09 ± 0.06 µm) and λ 2 (9.49 ± 0.44 µm) thermopiles. Additionally, an artificial neural network (NN) is applied to process background noise effects. The adaptive and cognitive Kalman Filter helps to improve the training time of the neural network and the absolute error of the thermopile data. Without applying the Kalman filter for λ 1 thermopile, it took 12 min 09 s to train the NN and reach the absolute error of 2.7453 × 104 (n. u.). With the Kalman filter, it took 46 s to train the NN to reach the absolute error of 1.4374 × 104 (n. u.) for λ 1 thermopile. Similarly, to the λ 2 (9.49 ± 0.44 µm) thermopile, the training improved from 9 min 13 s to 1 min and the absolute error of 2.3999 × 105 (n. u.) to the absolute error of 1.76485 × 105 (n. u.) respectively. The three-thermopile system has proven that it can improve the reliability in detection of Fusarium spores by adding the broadband thermopile. The method developed in this work can be employed for devices that encounter similar noise problems.