What if Ω ≠ 2q?

We discuss various possible scenarios where 2q, where stands for the density parameter andq for the deceleration parameter. We further estimate the corrections necessary when a variable cosmological constant is considered in the theory.     

A Family of Fitness Landscapes Modeled through Gene Regulatory Networks

Fitness landscapes are a powerful metaphor for understanding the evolution of biological systems. These landscapes describe how genotypes are connected to each other through mutation and related through fitness. Empirical studies of fitness landscapes have increasingly revealed conserved topographical features across diverse taxa, e.g., the accessibility of genotypes and “ruggedness”. As a result, theoretical studies are needed to investigate how evolution proceeds on fitness landscapes with such conserved features. Here, we develop and study a model of evolution on fitness landscapes using the lens of Gene Regulatory Networks (GRNs), where the regulatory products are computed from multiple genes and collectively treated as phenotypes. With the assumption that regulation is a binary process, we prove the existence of empirically observed, topographical features such as accessibility and connectivity. We further show that these results hold across arbitrary fitness functions and that a trade-off between accessibility and ruggedness need not exist. Then, using graph theory and a coarse-graining approach, we deduce a mesoscopic structure underlying GRN fitness landscapes where the information necessary to predict a population’s evolutionary trajectory is retained with minimal complexity. Using this coarse-graining, we develop a bottom-up algorithm to construct such mesoscopic backbones, which does not require computing the genotype network and is therefore far more efficient than brute-force approaches. Altogether, this work provides mathematical results of high-dimensional fitness landscapes and a path toward connecting theory to empirical studies.     

Gaussian Amplitude Amplification for Quantum Pathfinding

We study an oracle operation, along with its circuit design, which combined with the Grover diffusion operator boosts the probability of finding the minimum or maximum solutions on a weighted directed graph. We focus on the geometry of sequentially connected bipartite graphs, which naturally gives rise to solution spaces describable by Gaussian distributions. We then demonstrate how an oracle that encodes these distributions can be used to solve for the optimal path via amplitude amplification. And finally, we explore the degree to which this algorithm is capable of solving cases that are generated using randomized weights, as well as a theoretical application for solving the Traveling Salesman problem.     

Propargylation of aromatic compounds using Ce(OTf)3 as catalyst

Ce(OTf)₃ was successfully employed as catalyst for the activation of the hydroxyl group in the Friedel–Crafts reaction of aromatic compounds with propargylic alcohols in nitromethane. The products were obtained in good to excellent yields.     

One Way Traffic: Base-to-Backbone Hole Transfer in Nucleoside Phosphorodithioate

The directionality of the hole-transfer processes between DNA backbone and base was investigated by using phosphorodithioate [P(S⁻)=S] components. ESR spectroscopy in homogeneous frozen aqueous solutions and pulse radiolysis in aqueous solution at ambient temperature confirmed initial formation of G^.+-P(S⁻)=S. The ionization potential of G-P(S⁻)=S was calculated to be slightly lower than that of guanine in 5′-dGMP. Subsequent thermally activated hole transfer from G^.+ to P(S⁻)=S led to dithiyl radical (P-2S^.) formation on the μs timescale. In parallel, ESR spectroscopy, pulse radiolysis, and density functional theory (DFT) calculations confirmed P-2S^. formation in an abasic phosphorodithioate model compound. ESR investigations at low temperatures and higher G-P(S⁻)=S concentrations showed a bimolecular conversion of P-2S^. to the σ²-σ*¹-bonded dimer anion radical [-P-2S 2S-P-]⁻ [ΔG (150 K, DFT)=−7.2 kcal mol⁻¹]. However, [-P-2S 2S-P-]⁻ formation was not observed by pulse radiolysis [ΔG° (298 K, DFT)=−1.4 kcal mol⁻¹]. Neither P-2S^. nor [-P-2S 2S-P-]⁻ oxidized guanine base; only base-to-backbone hole transfer occurs in phosphorodithioate.     

ON THE PHOSPHORUS-31 CHEMICAL SHIFTS OF SUBSTITUTED TRIARYLPHOSPHINES

Abstract

The ³¹P chemical shifts of eleven (4-ZC₆H₄)₃P compounds show a slight correlation with the Hammet [sgrave]para constant of Z. The unusually large upfield chemical shifts of (2-ZC₆H₄)₃P compounds are attributed to an extreme “gamma” effect caused by the restricted conformations due to the steric influence of the ortho substituents. Chemical shifts are given for about thirty triarylphosphines, and group contributions to phosphine chemical shifts are listed for twenty-one aryl groups.     

A New Synthesis of Vinylidene Bis-phosphine Sulfides

Abstract

1,1-Bis(diphenylphosphino)ethene, 1a, was originally prepared by Colquhoun and McFarlane¹ by the reaction of lithium diphenylphosphide and vinylidene chloride. Subsequently, Schmidbaur et al.,² reported further novel chemistry of 1a and its derivatives such as 1b and 1c.     

Iron(III) Chloride–Promoted Direct Conversion of Aryl/Alkyl Cyanides to Esters

Aryl/alkyl cyanides were quickly converted into the corresponding esters in the presence of iron(III) chloride in refluxing alcohols with very good yields.     

NaOH/Et3N-Promoted Stereoselective One-Pot Synthesis of α-Diazo Oxime Ethers via Diazo Transfer Reaction

For the first time, we have observed a combined effect of two bases NaOH/Et₃N to promote the diazo transfer reaction of β-oximino esters. This unusual synergistic effect has been employed to obtain α-diazo oxime ethers directly from β-keto esters by one-pot process. This method is simple and cost-effective and the reagents are readily available.