Order-Stability in Complex Biological,Social, and AI-Systems from Quantum Information Theory

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.     

Theoretical Design of Biodegradable Phthalic Acid Ester Derivatives in Marine and Freshwater Environments

The biodegradability of phtalic acid esters in marine and freshwater environments was characterized by their binding free energy with corresponding degrading enzymes. According to comprehensive biodegradation effects weights, the binding free energy values were converted into dimensionless efficacy coefficient using ratio normalization method. Then, considering comprehensive dual biodegradation effects value and the structural parameters of PAEs in both marine and freshwater environments, a 3D-QSAR pharmacophore model was constructed, five PAE derivatives (DBP−COOH, DBP−CHO, DBP−OH, DINP−NH₂, and DINP−NO₂) were screened out based on their environmental friendliness, functionality and stability. The prediction of biodegradation effects on five PAE derivatives by biodegradation models in marine and freshwater environment increased by 15.90 %, 15.84 %, 27.21 %, 12.33 %, and 8.32 %, and 21.57 %, 15.21 %, 20.99 %, 15.10 %, and 9.74 %, respectively. By simulating the photodegradation path of the PAE derivative molecular, it was found that DBP−OH can generate ^.OH and provides free radicals for the photodegradation of microplastics in the environment.     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Application of Reynolds stress transport turbulence closure models to flows affected by Lorentz and buoyancy forces

The effect of magnetic field strength and orientation on two types of electromagnetically influenced turbulent flows was studied numerically under the Reynolds averaged Navier–Stokes (RANS) framework. Previous work (Wilson et al., 2014) used an electromagnetically extended linear eddy-viscosity model, whilst the current paper focuses on the performance of a more advanced Reynolds stress transport type model both with and without electromagnetic modifications proposed by Kenjereš et al. (2004). First, a fully-developed 2D channel flow is considered with a magnetic field imposed in either the wall-normal or streamwise direction. Both forms of the RSM gave good agreement with the DNS data for the wall-normal magnetic field across the range of Hartmann numbers with the additional electromagnetic terms providing a small, but noticeable, difference. For the streamwise magnetic field, where electromagnetic influence is only through the turbulence, the electromagnetically extended RSM performed well at moderate Hartmann numbers but returned laminar flow at the highest Hartmann number considered, contrary to the DNS. The RSM results were, however, significantly better than the previous eddy-viscosity model predictions. The second case is that of unsteady 3D Rayleigh–Bénard convection with a magnetic field imposed in either a horizontal or vertical direction. Results revealed that a significant reorganization of the flow structures is predicted to occur. For a vertically oriented magnetic field, the plume structures increase in number and become thinner and elongated along the magnetic field lines, leading to an increase in thermal mixing within the core in agreement with Hanjalić and Kenjereš (2000). With a horizontal magnetic field, the structures become two-dimensional and a striking realignment of the roll cells’ axes with the magnetic field lines occurs. The results demonstrate the capability of the Reynolds stress transport approach in modelling MHD flows that are relevant to industry and offer potential for those wishing to control levels of turbulence, heat transfer or concentration without recourse to mechanical means.     

Ligand Displacement Reaction Paths in a Diiron Hydrogenase Active Site Model Complex

The mechanism and energetics of CO, 1‐hexene, and 1‐hexyne substitution from the complexes (SBenz)₂[Fe₂(CO)₆] (SBenz=SCH₂Ph) ( 1 ‐CO), (SBenz)₂[Fe₂(CO)₅(η²‐1‐hexene)] ( 1 ‐(η²‐1‐hexene)), and (SBenz)₂[Fe₂(CO)₅(η²‐1‐hexyne)] ( 1 ‐(η²‐1‐hexyne)) were studied by using time‐resolved infrared spectroscopy. Exchange of both CO and 1‐hexyne by P(OEt)₃ and pyridine, respectively, proceeds by a bimolecular mechanism. As similar activation enthalpies are obtained for both reactions, the rate‐determining step in both cases is assumed to be the rotation of the Fe(CO)₂L (L=CO or 1‐hexyne) unit to accommodate the incoming ligand. The kinetic profile for the displacement of 1‐hexene is quite different than that for the alkyne and, in this case, both reaction channels, that is, dissociative (S_N1) and associative (S_N2), were found to be competitive. Because DFT calculations predict similar binding enthalpies of alkene and alkyne to the iron center, the results indicate that the bimolecular pathway in the case of the alkyne is lower in free energy than that of the alkene. In complexes of this type, subtle changes in the departing ligand characteristics and the nature of the mercapto bridge can influence the exchange mechanism, such that more than one reaction pathway is available for ligand substitution. The difference between this and the analogous study of (μ‐pdt)[Fe(CO)₃]₂ (pdt=S(CH₂)₃S) underscores the unique characteristics of a three‐atom S?S linker in the active site of diiron hydrogenases.     

Toward Functional Type III [Fe]‐Hydrogenase Biomimics for H2 Activation: Insights from Computation

The chemistry of [Fe]‐hydrogenase has attracted significant interest due to its ability to activate molecular hydrogen. The intriguing properties of this enzyme have prompted the synthesis of numerous small molecule mimics aimed at activating H₂. Despite considerable effort, a majority of these compounds remain nonfunctional for hydrogenation reactions. By using a recently synthesized model as an entry point, seven biomimetic complexes have been examined through DFT computations to probe the influence of ligand environment on the ability of a mimic to bind and split H₂. One mimic, featuring a bidentate diphosphine group incorporating an internal nitrogen base, was found to have particularly attractive energetics, prompting a study of the role played by the proton/hydride acceptor necessary to complete the catalytic cycle. Computations revealed an experimentally accessible energetic pathway involving a benzaldehyde proton/hydride acceptor and the most promising catalyst.     

The ASBM-SA turbulence closure: Taking advantage of structure-based modeling in current engineering CFD codes

Structure-based turbulence models (SBM) carry information about the turbulence structure that is needed for the prediction of complex non-equilibrium flows. SBM have been successfully used to predict a number of canonical flows, yet their adoption rate in engineering practice has been relatively low, mainly because of their departure from standard closure formulations, which hinders easy implementation in existing codes. Here, we demonstrate the coupling between the Algebraic Structure-Based Model (ASBM) and the one-equation Spalart–Allmaras (SA) model, which provides an easy route to bringing structure information in engineering turbulence closures. As the ASBM requires correct predictions of two turbulence scales, which are not taken into account in the SA model, Bradshaw relations and numerical optimizations are used to provide the turbulent kinetic energy and dissipation rate. Attention is paid to the robustness and accuracy of the hybrid model, showing encouraging results for a number of simple test cases. An ASBM module in Fortran-90 is provided along with the present paper in order to facilitate the testing of the model by interested readers.     

Self‐Assembly and Compartmentalization of Nanozymes in Mesoporous Silica‐Based Nanoreactors

Herein, to mimic complex natural system, polyelectrolyte multilayer (PEM)‐coated mesoporous silica nanoreactors were used to compartmentalize two different artificial enzymes. PEMs coated on the surface of mesoporous silica could serve as a permeable membrane to control the flow of molecules. When assembling hemin on the surface of mesoporous silica, the hemin‐based mesoporous silica system possessed remarkable peroxidase‐like activity, especially at physiological pH, and could be recycled more easily than traditional graphene–hemin nanocompounds. The hope is that these new findings may pave the way for exploring novel nanoreactors to achieve compartmentalization of nanozymes and applying artificial cascade catalytic systems to mimic cell organelles or important biochemical transformations     

Integrable boundary conditions for the B_2 model

New integrable B_2 model with off-diagonal boundary reflections is proposed. The general solutions of the reflection matrix for the B_2 model are obtained by using the fusion technique. Wefind that the reflection matrix has 7 free boundary parameters, which are used to describe the degree of freedom of boundary couplings, without breaking the integrability of the system. The new quantization conditions will induce the novel structure of the energy spectrum and the boundary states. The corresponding boundary effects can be studied based on the results in this paper. Meanwhile, the reflection matrix of high rank models associated with Bnalgebra can also be obtained by using the method suggested in this paper.     

Determination of structure parameters in strong-field ionization models of atoms

The Ammosov–Delone–Krainov (ADK) and Perelomov–Popov–Terent’ev (PPT) ionization models were widely used in strong-field physics and attosecond science due to their many attractive advantages such as simpler analytical formula, less computational demands, and satisfied accuracy of ionization rate. Based on the density-functional theory, we systematically determine accurate structure parameters of 25 atoms, 24 positive ions and 13 negative ions and tabulate for future applications. The wave function with correct asymptotic behavior is obtained by solving the time-independent Schrödinger equation with B-spline basis sets and the accurate structure parameters are extracted from this wave function in the asymptotic region. The accuracies of structure parameters are carefully examined by comparing the ionization probabilities (or yields) calculated by PPT and ADK models with those of solving the three-dimensional time-dependent Schrödinger equation and the experimental data.