γ-variable first-order logic of uniform attachment random graphs

We study logical limit laws for uniform attachment random graphs. In this random graph model, vertices and edges are introduced recursively: at time $n+1$, the vertex $n+1$ is introduced together with m edges joining the new vertex with m different vertices chosen uniformly at random from $1,\dots ,n$. We prove that this random graph obeys convergence law for first-order sentences with at most $m?2$ variables.     

Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.     

Versatile and Homogeneous DNA Tetraplex Platform for Constructing Label-Free Logic Devices: From Design to Application

The design of DNA-based logic circuits has become an active research field in DNA nanotechnology and holds great potential in intelligent bioanalysis. To date, although many DNA-based logic systems have been realized, the implementation of advanced logic functions is still challenging, especially with simple and homogeneous compositions. Herein, by integrating two DNA tetraplex structures (G-quadruplex and i-motif), a completely label-free logic platform with high scalability was established, with which a series of advanced functions were realized, including arithmetic (adders and subtractors) and nonarithmetic ones (majority and dual-transfer gates). Furthermore, the platform was also applied as an intelligent biosensor to coanalyze two cancer-related micro-RNAs with high sensitivities and specificities. Considering the excellent versatility, expandability, and biocompatibility, the platform may promote the development of DNA computing and hold great potential in multiparameter sensing and medical diagnosis.     

Ambident Reactivity of Imidazolium Cations as Evidence of the Dynamic Nature of N-Heterocyclic Carbene-Mediated Organocatalysis

This work reveals ambident nucleophilic reactivity of imidazolium cations towards carbonyl compounds at the C2 or C4 carbene centers depending on the steric properties of the substrates and reaction conditions. Such an adaptive behavior indicates the dynamic nature of organocatalysis proceeding via a covalent interaction of imidazolium carbenes with carbonyl substrates and can be explained by generation of the H-bonded ditopic carbanionic carbenes.     

Alkane Shape- and Size-Recognized Selective Vapor Sorption in “Channel-Like” Crystals Based on Thiacalixarene Assemblies

Alkanes composed of C−C and C−H show a low electric polarization, and therefore, there is only very weak interaction between alkanes and adsorbents. Thus, it is difficult to separate a specific alkane from a mixture of alkanes by adsorption. Here, two activated “channel-like” crystals generated from brominated thiacalix[4]arene propyl ethers, which adopt 1,3-alternate and partial cone conformations, recognize specific alkane vapors depending on alkane-shape and -size, sorting in three-type alkane guests such as linear, branched, and cyclic alkanes. Two activated crystals, which are prepared by removal of solvent upon heating under reduced pressure, incorporate branched and/or cyclic alkane vapors by a unique “gate-opening” mechanism via a crystal transformation in the process. Linear alkane vapors do not trigger gate opening and are not taken up by the activated crystals. The shape and size molecular-recognition properties of the activated crystals promises considerable usefulness for the separation of linear, branched, and cyclic alkanes.     

Scalable Total Syntheses and Structure–Activity Relationships of Haouamines A,B, and Their Derivatives as Stable Formate Salts

Haouamines A, B, and their derivatives were synthesized via Suzuki–Miyaura coupling and three key cyclization reactions as follows: the newly developed palladium(0)-catalyzed arylative cyclization of phenylalanine-derived alkyne–aldehydes with 2-bromoarylboronic acid (an “anti-Wacker”-type cyclization); BF₃ ⋅ OEt₂-promoted Friedel–Crafts-type cyclization of symmetrical electron-rich aromatic rings adjacent to a tertiary allylic alcohol leading to the indeno-tetrahydropyridine skeleton; and (cyanomethyl)trimethylphosphonium iodide-mediated macrocyclization of amino alcohols to afford aza-paracyclophane precursors. The palladium-catalyzed reduction of mono- and di-triflate intermediates in the later stages enabled the alteration of both the position and number of hydroxyl groups on the C-ring. The instability of haouamine B was dramatically improved by salt formation with formic acid. An unambiguous evaluation of the cytotoxicity of the prepared haouamine derivative formates with and without hydroxyl groups at different positions on the C-ring indicated that the catechol structure in haouamine B produced weak cytotoxicity.     

Existential monadic second order logic of undirected graphs: The Le Bars conjecture is false

In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that $\mathsf{P}(G_n??)$ does not converge as $n\to \infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\{1,\dots ,n\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture.