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.     

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.     

Enzyme-free and DNA-based universal platform for the construction of various logic devices based on graphene oxide and G-quadruplex

In the fields of biocomputing and biomolecular, DNA molecules are applicable to be regarded as data of logical computing platform that uses elaborate logic gates to perform a variety of tasks. Graphene oxide (GO) is a type of novel nanomaterial, which brings new research focus to materials science and biosensors due to its special selectivity and excellent quenching ability. G-quadruplex as a unique DNA structure stimulates the intelligent application of DNA assembly on the strength of its exceptional binding activity. In this paper, we report a universal logic device assisted with GO and G-quadruplex under an enzyme-free condition. Integrated with the quenching ability of GO to the TAMRA (fluorophore, Carboxytetramethylrhodamine) and the enhancement of fluorescence intensity produced by the peculiar binding of G-quadruplex to the NMM (N-methylmesoporphyrin IX), a series of basic binary logic gates (AND. OR. INHIBIT. XOR) have been designed and verified through biological experiments. Given the modularity and programmability of this strategy, two advanced logic gates (half adder and half subtractor) were realized on the basis of the same work platform. The fluorescence signals generated from different input combinations possessed satisfactory results, which provided proof of feasibility. We believe that the proposed universal logical platform that operates at the nanoscale is expected to be utilized for future applications in molecular computing as well as disease diagnosis.     

相似剩余格及其对应逻辑系统的完备性

引入了相似剩余格的概念,讨论了剩余格上相似算子和等价算子的关系,并得到了真值剩余格和相似剩余格相互转化的方法.其次,研究了相似剩余格上的相似滤子,利用相似滤子刻画了可表示的相似剩余格.最后,引入了相似剩余格对应的逻辑系统,证明了其完备性定理,并得到了其成为半线性逻辑的条件.