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.     

Optimal time delays in a class of reaction-diffusion equations

ABSTRACT

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays.     

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。     

Fuzzy-PID分级控制变水量空调系统温度的研究

针对变水量空调系统温度控制的时变、大滞后、非线性特点,结合模糊控制和PID控制,设计了基于模糊规则切换的Fuzzy-PID分级控制器,并在Matlab/Simulink软件上进行了仿真。仿真结果表明,控制器同时具有模糊控制超调量小、鲁棒性好和PID控制精度高、响应速度快的优点。     

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.     

Actuating Shape Memory Polymer for Thermoresponsive Soft Robotic Gripper and Programmable Materials

For soft robotics and programmable metamaterials, novel approaches are required enabling the design of highly integrated thermoresponsive actuating systems. In the concept presented here, the necessary functional component was obtained by polymer syntheses. First, poly(1,10-decylene adipate) diol (PDA) with a number average molecular weight M_n of 3290 g·mol⁻¹ was synthesized from 1,10-decanediol and adipic acid. Afterward, the PDA was brought to reaction with 4,4′-diphenylmethane diisocyanate and 1,4-butanediol. The resulting polyester urethane (PEU) was processed to the filament, and samples were additively manufactured by fused-filament fabrication. After thermomechanical treatment, the PEU reliably actuated under stress-free conditions by expanding on cooling and shrinking on heating with a maximum thermoreversible strain of 16.1%. Actuation stabilized at 12.2%, as verified in a measurement comprising 100 heating-cooling cycles. By adding an actuator element to a gripper system, a hen’s egg could be picked up, safely transported and deposited. Finally, one actuator element each was built into two types of unit cells for programmable materials, thus enabling the design of temperature-dependent behavior. The approaches are expected to open up new opportunities, e.g., in the fields of soft robotics and shape morphing.