On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin

We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold.     

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.     

An algebraic variational multiscale–multigrid method for large-eddy simulation of turbulent variable-density flow at low Mach number

An algebraic variational multiscale–multigrid method is proposed for large-eddy simulation of turbulent variable-density flow at low Mach number. Scale-separating operators generated by level-transfer operators from plain aggregation algebraic multigrid methods enable the application of modeling terms to selected scale groups (here, the smaller of the resolved scales) in a purely algebraic way. Thus, for scale separation, no additional discretization besides the basic one is required, in contrast to earlier approaches based on geometric multigrid methods. The proposed method is thoroughly validated via three numerical test cases of increasing complexity: a Rayleigh–Taylor instability, turbulent channel flow with a heated and a cooled wall, and turbulent flow past a backward-facing step with heating. Results obtained with the algebraic variational multiscale–multigrid method are compared to results obtained with residual-based variational multiscale methods as well as reference results from direct numerical simulation, experiments and LES published elsewhere. Particularly, mean and various second-order velocity and temperature results obtained for turbulent channel flow with a heated and a cooled wall indicate the higher prediction quality achievable when adding a small-scale subgrid-viscosity term within the algebraic multigrid framework instead of residual-based terms accounting for the subgrid-scale part of the non-linear convective term.     

Insights into the photophysics,protonation and Cu2+ ion coordination behaviour of anthracene-9,10-dione-based chemosensors

Carboxylic acid–diamine-based Cu²⁺ chromogenic sensors (3 and 4) exhibited colour switching from red to blue with good sensitivity and selectivity towards Cu²⁺ among other physiologically important alkali, alkaline earth and heavy metal ions. This colour-switching phenomenon arises due to selective deprotonation of aryl amine NH by Cu²⁺. Significantly, chemosensor 3 (λ_max 492 nm) shows multiple modes of complexation towards Cu²⁺. It is very much evident from the appearance of blue colour (λ_max 615 nm) at pH >7.0 and yellow colour (λ_max 465 nm) at pH < 4.0. In addition, chemosensor 3 exhibits a unique logic gate system that involves ‘INHIBIT’ and ‘TRANSFER’ logic gates.     

Ag+与Hg2+对G-四链体DNA结构的破坏及其对构筑DNA逻辑门的应用

本工作利用圆二色光谱研究了Ag+与Hg2+对4种代表性G-四链体DNA结构的破坏作用。结果表明Ag+可能通过与碱基G螯合从而破坏G-四链体结构;Hg2+能通过形成T-Hg2+-T碱基对,及其他方式破坏G-四链体结构。含巯基(-SH)的半胱氨酸与Ag+与Hg2+可以发生较强的配位作用,从而使被Ag+与Hg2+破坏后的G-四链体DNA结构得以回复。基于此,一个新颖的Ag+/Hg2+-半胱氨酸-DNA逻辑门得以构筑。     

A bifunctional,colorimetric and fluorescent probe for recognition of Cu2+ and Hg2+ and its application in molecular logic gate

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Biocomputing Based on DNA Strand Displacement Reactions

The high sequence specificity and precise base complementary pairing principle of DNA provides a rich orthogonal molecular library for molecular programming, making it one of the most promising materials for developing bio-compatible intelligence. In recent years, DNA has been extensively studied and applied in the field of biological computing. Among them, the toehold-mediated strand displacement reaction (SDR) with properties including enzyme free, flexible design and precise control, have been extensively used to construct biological computing circuits. This review provides a systemic overview of SDR design principles and the applications. Strategies for designing DNA-only, enzymes-assisted, other molecules-involved and external stimuli-controlled SDRs are described. The recently realized computing functions and the application of DNA computing in other fields are introduced. Finally, the advantages and challenges of SDR-based computing are discussed.     

A Light‐up Logic Platform for Selective Recognition of Parallel G‐Quadruplex Structures via Disaggregation‐Induced Emission

The design of turn‐on dyes with optical signals sensitive to the formation of supramolecular structures provides fascinating and underexplored opportunities for G‐quadruplex (G4) DNA detection and characterization. Here, we show a new switching mechanism that relies on the recognition‐driven disaggregation (on‐signal) of an ultrabright coumarin‐quinazoline conjugate. The synthesized probe selectively lights‐up parallel G4 DNA structures via the disassembly of its supramolecular state, demonstrating outputs that are easily integrable into a label‐free molecular logic system. Finally, our molecule preferentially stains the G4‐rich nucleoli of cancer cells.