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.     

A cationic hydro­xo-bridged dinuclear gallium complex

The crystal structure of μ-hydro­xo-bis{[N-iso­propyl-2-(isopropyl­amino)­tropon­imino-N,N′](methyl)gallium(II)} tetrakis(pentafluorophenyl)borate (troponimine is 2,4,6-cycloheptatrien-1-imine), [Ga₂(C₁₄H₂₂N₂)₂(OH)]B(C₆H₅)₄, is discussed. The two (ⁱPr₂-ATI)GaMe (ATI is aminotroponimime) units of the dinuclear cation are linked by a bridging hydro­xo group and are both slightly twisted from planarity.     

Synthesis and magnetic properties of Gd doped EuS nanocrystals with enhanced Curie temperatures

EuS nanocrystals (NCs) were doped with Gd resulting in an enhancement of their magnetic properties. New EuS and GdS single source precursors (SSPs) were synthesized, characterized, and employed to synthesize Eu(1-x)Gd(x)S NCs by decomposition in oleylamine and trioctylphosphine at 290 °C. The doped NCs were characterized using X-ray diffraction, transmission electron microscopy, and scanning transmission electron microscopy, which support the uniform distribution of Gd dopants through electron energy loss spectroscopy (EELS) mapping. X-ray absorption spectroscopy (XAS) revealed the dopant ions in Eu(1-x)Gd(x)S NCs to be predominantly Gd(3+). NCs with a variety of doping ratios of Gd (0 ≤ x < 1) were systematically studied using vibrating sample magnetometry and the observed magnetic properties were correlated with the Gd doping levels (x) as quantified with ICP-AES. Enhancement of the Curie temperature (T(C)) was observed for samples with low Gd concentrations (x ≤ 10%) with a maximum T(C) of 29.4 K observed for NCs containing 5.3% Gd. Overall, the observed T(C), Weiss temperature (θ), and hysteretic behavior correspond directly to the doping level in Eu(1-x)Gd(x)S NCs and the trends qualitatively follow those previously reported for bulk and thin film samples.     

Gauge-Higgs unification in the left–right model

We construct a supersymmetric left–right model in four dimension with gauge-Higgs unification starting from a SU(3)_c×SU(4)_w×U(1)_B−L gauge symmetry in five dimension. The model has several interesting features, such as, the CKM mixings in the quark sector are naturally small while for the neutrino sector it is not, light neutrino masses can be generated via the seesaw mechanism in the usual way, and the model has a U(1)_R symmetry which naturally forbid dimension five proton decay operators. We also discuss the grand unification of our model in SO(12) in five dimensions.     

Novel Mechanism of Bioluminescence: Oxidative Decarboxylation of a Moiety Adjacent to the Light Emitter of Fridericia Luciferin

A novel luciferin from a bioluminescent Siberian earthworm Fridericia heliota was recently described. In this study, the Fridericia oxyluciferin was isolated and its structure elucidated. The results provide insight into a novel bioluminescence mechanism in nature. Oxidative decarboxylation of a lysine fragment of the luciferin supplies energy for light generation, while a fluorescent CompX moiety remains intact and serves as the light emitter.     

Influence of Solution Volume on the Dissolution Rate of Silicon Dioxide in Hydrofluoric Acid

Experimental data and modeling of the dissolution of various Si/SiO₂ thermal coatings in different volumes of hydrofluoric acid (HF) are reported. The rates of SiO₂‐film dissolution, measured by means of various electrochemical techniques, and alteration in HF activity depend on the thickness of the film coating. Despite the small volumes (0.6–1.2 mL) of the HF solution, an effect of SiO₂‐coating thickness on the dissolution rate was detected. To explain alterations detected in HF activity after SiO₂ dissolution, spectroscopic analyses (NMR and FTIR) of the chemical composition of the solutions were conducted. This is associated with a modification in the chemical composition of the HF solution, which results in either the formation of an oxidized species in solution or the precipitation of dissolution products. HF₂^? accumulation in the HF solution, owing to SiO₂ dissolution was identified as the source of the chemical alteration.     

Moment convergence of <Emphasis Type="Italic">Z</Emphasis>-estimators

The problem to establish the asymptotic distribution of statistical estimators as well as the moment convergence of such estimators has been recognized as an important issue in advanced theories of statistics. This problem has been deeply studied for M-estimators for a wide range of models by many authors. The purpose of this paper is to present an alternative and apparently simple theory to derive the moment convergence of Z-estimators. In the proposed approach the cases of parameters with different rate of convergence can be treated easily and smoothly and any large deviation type inequalities necessary for the same result for M-estimators do not appear in this approach. Applications to the model of i.i.d. observation, Cox’s regression model as well as some diffusion process are discussed.     

Tautomerism, structure and properties of 1,1′,1″-(2,4,6-trihydroxybenzene-1,3,5-triyl)triethanone

According to computational predictions 1,1′,1″-(2,4,6-trihydroxybenzene-1,3,5-triyl)triethanone (triacetylphloroglucinol) (TTT, form a) can exist in five tautomeric forms, among which 2,4,6-tris(1-hydroxyethylidene)-1,3,5-cyclohexanetrione (form e) exhibits thermodynamic stability comparable to that of form a. X-ray investigations reveal that the compound exists in form a in the crystalline solid phase. Analysis of the arrangement of atoms involved in the three intramolecular H-bonds, responsible for the stabilization of tautomer a by 55.4 kcal/mol, suggests that there could be fast H atom (proton) transfer within the hydrogen bonds, bringing about the transformation of a into e and vice versa. Such an effect could explain the unique behaviour and spectral properties of TTT in solutions.