Boolean delay equations: A simple way of looking at complex systems

Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the classification of ordinary or partial differential equations. Solutions to certain conservative BDEs exhibit growth of complexity in time; such BDEs can be seen therefore as metaphors for biological evolution or human history. Dissipative BDEs are structurally stable and exhibit multiple equilibria and limit cycles, as well as more complex, fractal solution sets, such as Devil’s staircases and “fractal sunbursts.” All known solutions of dissipative BDEs have stationary variance. BDE systems of this type, both free and forced, have been used as highly idealized models of climate change on interannual, interdecadal and paleoclimatic time scales. BDEs are also being used as flexible, highly efficient models of colliding cascades of loading and failure in earthquake modeling and prediction, as well as in genetics. In this paper we review the theory of systems of BDEs and illustrate their applications to climatic and solid-earth problems. The former have used small systems of BDEs, while the latter have used large hierarchical networks of BDEs. We moreover introduce BDEs with an infinite number of variables distributed in space (“partial BDEs”) and discuss connections with other types of discrete dynamical systems, including cellular automata and Boolean networks. This research-and-review paper concludes with a set of open questions.     

An unusual reaction of cyclopropenylphosphonium bromide with sodium polyphosphides – A novel approach to sodium 3,4,5-triphenyl-1,2-diphosphacyclopentadienide

1,2,3-Triphenylcyclopropenylphosphonium bromide reacts with sodium polyphosphides to give sodium 3,4,5-triphenyl-1,2-diphosphacyclopentadienide in high yield.     

Noise in a Small Genetic Circuit that Undergoes Bifurcation

Based on the consideration of Boolean dynamics, it has been hypothesized that cell types may correspond to alternative attractors of a gene regulatory network. Recent stochastic Boolean network analysis, however, raised the important question concerning the stability of such attractors. In this paper a detailed numerical analysis is performed within the framework of Langevin dynamics. While the present results confirm that the noise is indeed an important dynamical element, the cell type as represented by attractors can still be a viable hypothesis. It is found that the stability of an attractor depends on the strength of noise related to the distance of the system to the bifurcation point and it can be exponentially stable depending on biological parameters.     

New 1,3,5-triphenyl-2-pyrazoline-containing 3-hydroxychromones as highly solvatofluorochromic ratiometric polarity probes

Two novel 1,3,5-triphenyl-2-pyrazoline moiety containing derivatives of 3-hydroxychromone were synthesized and studied by ¹H NMR, absorption and fluorescence spectroscopy. The prospects of practical application of these compounds exhibiting high solvatofluorochromism into analytical chemistry and biophysics as effective ratiometric polarity probes were discussed proceeding from the data on their fluorescent properties.     

Palladium(II)–rare-earth metal(III) paddlewheel carboxylate complexes: Easy total acetate to pivalate metathesis

Bis-paddlewheel heterobimetallic complexes in which palladium(II) is connected to the rare-earth metals(III) [Pd(μ-OOCMe)₄Ln(OH₂)(μ,η²-OOCMe)]₂ × 2HOOCMe (Ln = Nd, Sm, Eu, Yb and Tm) by four acetate bridges were synthesised by the reaction of Pd₃(μ-OOCMe)₆ with the Ln^III acetates. The tetraacetate-bridged complexes were unexpectedly found to be readily transformed by the stoichiometric amount of pivalic acid into the mono-paddlewheel tetrapivalate-bridged analogues in which the paddlewheel structure [Pd(μ-OOCR)₄Ln] maintains as established by X-ray crystallography. The role of the intra- and intermolecular H-bonding in these complexes is discussed.     

Extended Lattice Boltzmann Model

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.     

Are there reliable DFT approaches for 13C NMR chemical shift predictions of fullerene C60 derivatives?

The relationships between experimental and theoretical ¹³C NMR chemical shifts of a pristine fullerene C₆₀, monoadducts from [2 + n] cycloaddition (n = 1–3), and one [2 + 1] bis‐adduct are systematically analyzed for the first time by using diverse quantum‐chemical levels of theory. These levels involved B3LYP, B3PW91, B97‐2, mPW1PW91, PBE1PBE, and X3LYP hybrid functionals combined with 3‐21G, 6‐31G, 6‐31G(d), 6‐31G(d,p), 6‐31G(d,2p), LanL2DZ, and SDDAll basis sets. X3LYP/6‐31G approach is determined to have the lowest deviations from the ¹³C NMR experimental data compared to the other methods for all the fullerene compounds (mean absolute error value is 0.856 ppm and root mean squared error value is 1.197 ppm). The highest deviations are characteristic for α (sp² C2/C5/C8/C10) and β (sp² C6/C7/C11/C12) carbon atoms relative to a functionalization site and for those (sp³ C1/C9) directly attached with a side fragment in the [2 + n] monoadducts (n = 1–3). A probable reason of such deviation is that the approaches do not take into account a contribution of paramagnetic ring currents to ¹³C NMR chemical shifts. The results will be useful in design of novel fullerene derivatives and in performing unambiguous ¹³C NMR chemical shift assignments with modern quantum chemistry calculations.     

MyD88-dependent and independent pathways of Toll-Like Receptors are engaged in biological activity of Triptolide in ligand-stimulated macrophages

Background  

Triptolide is a diterpene triepoxide from the Chinese medicinal plant Tripterygium wilfordii Hook F., with known anti-inflammatory, immunosuppressive and anti-cancer properties.