The Scope and Generality of Bell’s Theorem

I present what might seem to be a local, deterministic model of the EPR-Bohm experiment, inspired by recent work by Joy Christian, that appears at first blush to be in tension with Bell-type theorems. I argue that the model ultimately fails to do what a hidden variable theory needs to do, but that it is interesting nonetheless because the way it fails helps clarify the scope and generality of Bell-type theorems. I formulate and prove a minor proposition that makes explicit how Bell-type theorems rule out models of the sort I describe here.     

Synthesis of Oligonucleotides Containing Trans Mitomycin C DNA Adducts at N6 of Adenine and N2 of Guanine

Mitomycin C, (MC), an antitumor drug, is a DNA alkylating agent currently used in the clinics. Inert in its native form, MC is reduced to reactive mitosenes, which undergo nucleophilic attack by guanine or adenine bases in DNA to form monoadducts as well as interstrand crosslinks (ICLs). Although ICLs are considered the most cytotoxic lesions, the role of each individual adduct in the drug's cytotoxicity is still not fully understood. Synthetic routes have been developed to access modified oligonucleotides containing dG MC-monoadducts and dG-MC-dG ICL at a single position of their base sequences to investigate the biological effects of these adducts. However, until now, oligonucleotides containing monoadducts formed by MC at the adenine base had not been available, thus preventing the examination of the role played by these lesions in the toxicity of MC. Here, we present a route to access these substrates. Structural proof of the adducted oligonucleotides were provided by enzymatic digestion to nucleosides and high-resolution mass spectral analysis. Additionally, parent oligonucleotides containing a dG monoadduct and a dG-MC-dG ICL were also produced. The stability and physical properties of all substrates were compared via CD spectroscopy and UV melting temperature studies. Finally, virtual models were created to explore the conformational space and structural features of these MC-DNA complexes.     

Mechanochemical Formation,Solution Rearrangements,and Catalytic Behavior of a Polymorphic Ca/K Allyl Complex

Without solvents present, the often far-from-equilibrium environment in a mechanochemically driven synthesis can generate high-energy, non-stoichiometric products not observed from the same ratio of reagents used in solution. Ball milling 2 equiv. K[A’] (A’=[1,3-(SiMe₃)₂C₃H₃]⁻) with CaI₂ yields a non-stoichiometric calciate, K[CaA’₃], which initially forms a structure ( 1 ) likely containing a mixture of pi- and sigma-bound allyl ligands. Dissolved in arenes, the compound rearranges over the course of several days to a structure ( 2 ) with only η³-bound allyl ligands, and that can be crystallized as a coordination polymer. If dissolved in alkanes, however, the rearrangement of 1 to 2 occurs within minutes. The structures of 1 and 2 have been modeled with DFT calculations, and 2 initiates the anionic polymerization of methyl methacrylate and isoprene; for the latter, under the mildest conditions yet reported for a heavy Group 2 species (one-atm pressure and room temperature).     

A Molecular Circuit Regenerator to Implement Iterative Strand Displacement Operations

The predictable chemistry of Watson–Crick base-pairing imparts a unique structural programmability to DNA, enabling the facile design of molecular reactions that perform computations. However, many of the current architectures limit devices to a single operational cycle. Herein, we introduce the design of the “regenerator”, a device based on coupled enthalpic and entropic reactions that permits the regeneration of molecular circuit components.     

Saturation of Berge hypergraphs

Given a graph $F$, a hypergraph is a Berge- $F$ if it can be obtained by expanding each edge in $F$ to a hyperedge containing it. A hypergraph $H$ is Berge-$F$-saturated if $H$ does not contain a subhypergraph that is a Berge-$F$, but for any edge $e\in E\left(\overline{H}\right)$, $H+e$ does. The $k$-uniform saturation number of Berge-$F$ is the minimum number of edges in a $k$-uniform Berge-$F$-saturated hypergraph on $n$ vertices. For $k=2$ this definition coincides with the classical definition of saturation for graphs. In this paper we study the saturation numbers for Berge triangles, paths, cycles, stars and matchings in $k$-uniform hypergraphs.