Fractional Kinetics in Kac–Zwanzig Heat Bath Models

We study a variant of the Kac–Zwanzig model of a particle in a heat bath. The heat bath consists of n particles which interact with a distinguished particle via springs and have random initial data. As n → ∞ the trajectories of the distinguished particle weakly converge to the solution of a stochastic integro-differential equation—a generalized Langevin equation (GLE) with power-law memory kernel and driven by 1/f ^α -noise. The limiting process exhibits fractional sub-diffusive behaviour. We further consider the approximation of non-Markovian processes by higher-dimensional Markovian processes via the introduction of auxiliary variables and use this method to approximate the limiting GLE. In contrast, we show the inadequacy of a so-called fractional Fokker–Planck equation in the present context. All results are supported by direct numerical experiments.     

Recent Trends in Multiclass Analysis of Emerging Endocrine Disrupting Contaminants (EDCs) in Drinking Water

Ingestion of water is a major route of human exposure to environmental contaminants. There have been numerous studies exploring the different compounds present in drinking water, with recent attention drawn to a new class of emerging contaminants: endocrine-disrupting compounds (EDCs). EDCs encompass a broad range of physio-chemically diverse compounds; from naturally occurring to manmade. Environmentally, EDCs are found as mixtures containing multiple classes at trace amounts. Human exposure to EDCs, even at low concentrations, is known to lead to adverse health effects. Therefore, the ability to evaluate EDC contamination with a high degree of sensitivity and accuracy is of the utmost importance. This review includes (i) discussion on the perceived and actual risks associated with EDC exposure (ii) regulatory actions that look to limit EDC contamination (iii) analytical methods, including sample preparation, instrumentation and bioassays that have been advanced and employed for multiclass EDC identification and quantitation.     

Deoxygenation of Aromatic Ketones Using Transfer Hydrogenolysis with Raney Nickel in 2-Propanol

Aryl ketones are readily deoxygenated to their corresponding aryl alkanes upon treatment with Raney nickel catalyst in boiling 2-propanol.

Aerobic Iron‐Based Cross‐Dehydrogenative Coupling Enables Efficient Diversity‐Oriented Synthesis of Coumestrol‐Based Selective Estrogen Receptor Modulators

An iron‐based cross‐dehydrogenative coupling (CDC) approach was applied for the diversity‐oriented synthesis of coumestrol‐based selective estrogen receptor modulators (SERMs), representing the first application of CDC chemistry in natural product synthesis. The first stage of the two‐step synthesis of coumestrol involved a modified aerobic oxidative cross‐coupling between ethyl 2‐(2,4‐dimethoxybenzoyl)acetate and 3‐methoxyphenol, with FeCl₃ (10 mol %) as the catalyst. The benzofuran coupling product was then subjected to sequential deprotection and lactonization steps, affording the natural product in 59 % overall yield. Based on this new methodology other coumestrol analogues were prepared, and their effects on the proliferation of the estrogen receptor (ER)‐dependent MCF‐7 and of the ER‐independent MDA‐MB‐231 breast cancer cells were tested. As a result, new types of estrogen receptor ligands having an acetamide group instead of the 9‐hydroxyl group of coumestrol were discovered. Both 9‐acetamido‐coumestrol and 8‐acetamidocoumestrol were found more active than the natural product against estrogen‐dependent MCF‐7 breast cancer cells, with IC₅₀ values of 30 and 9 nM , respectively.     

Electrical properties study of multi-walled carbon nanotubes/hybrid-glass nanocomposites

Electrical properties of multi-walled carbon nanotubes (MWNTs)/hybrid-glass nanocomposites prepared by the fast-sol–gel reaction were investigated in light of percolation theory. A good correlation was found between the experimental results and the theory. We obtained a percolation threshold ? _c  = 0.22 wt%, and a critical exponent of t = 1.73. These values are reported for the first time for a silica-based system. The highest conductivity measured on the MWNT/hybrid-glass nanocomposites was σ ≈ 10^?3(Ω cm)^?1 for 2 wt% carbon nanotube (CNT) loading. The electrical conductivity was at least 12 orders of magnitude higher than that of pure silica. Electrostatic force microscopy and conductive-mode atomic force microscopy studies demonstrated conductivity at the micro-level, which was attributed to the CNT dispersed in the matrix. It appears that the dispersion in our MWNT/hybrid-glass system yields a particularly low percolation threshold compared with that of a MWNT/silica-glass system. Materials with electrical conductivities described in this work can be exploited for anti-static coating.     

Divergent and Overlapping Roles for Selected Phytochemicals in the Regulation of Pathological Cardiac Hypertrophy

Plant-based foods, like fruits, vegetables, whole grains, legumes, nuts, seeds and other foodstuffs, have been deemed as heart healthy. The chemicals within these plant-based foods, i.e., phytochemicals, are credited with protecting the heart. However, the mechanistic actions of phytochemicals, which prevent clinical endpoints, such as pathological cardiac hypertrophy, are still being elucidated. We sought to characterize the overlapping and divergent mechanisms by which 18 selected phytochemicals prevent phenylephrine- and phorbol 12-myristate 13-acetate-mediated cardiomyocyte enlargement. Of the tested 18 compounds, six attenuated PE- and PMA-mediated enlargement of neonatal rat ventricular myocytes. Cell viability assays showed that apigenin, baicalein, berberine hydrochloride, emodin, luteolin and quercetin dihydrate did not reduce cell size through cytotoxicity. Four of the six phytochemicals, apigenin, baicalein, berberine hydrochloride and emodin, robustly inhibited stress-induced hypertrophy and were analyzed further against intracellular signaling and genome-wide changes in mRNA expression. The four phytochemicals differentially regulated mitogen-activated protein kinases and protein kinase D. RNA-sequencing further showed divergence in gene regulation, while pathway analysis demonstrated overlap in the regulation of inflammatory pathways. Combined, this study provided a comprehensive analysis of cardioprotective phytochemicals. These data highlight two defining observations: (1) that these compounds predominantly target divergent gene pathways within cardiac myocytes and (2) that regulation of overlapping signaling and gene pathways may be of particular importance for the anti-hypertrophic actions of these phytochemicals. Despite these new findings, future works investigating rodent models of heart failure are still needed to understand the roles for these compounds in the heart.     

The Elekes–Szabó Theorem in four dimensions

Let F ∈ C[x, y, s, t] be an irreducible constant-degree polynomial, and let A,B,C,D ? C be finite sets of size n. We show that F vanishes on at most O(n^8/3) points of the Cartesian product A × B × C × D, unless F has a special group-related form. A similar statement holds for A,B,C,D of unequal sizes, with a suitably modified bound on the number of zeros. This is a four-dimensional extension of our recent improved analysis of the original Elekes–Szabó theorem in three dimensions. We give three applications: an expansion bound for three-variable real polynomials that do not have a special form, a bound on the number of coplanar quadruples on a space curve that is neither planar nor quartic, and a bound on the number of four-point circles on a plane curve that has degree at least five.