Quantifier-free epistemic term-modal logic with assignment operator

In standard epistemic logic, the names and the existence of agents are usually assumed to be common knowledge implicitly. This is unreasonable for various applications in computer science and philosophy. Inspired by term-modal logic and assignment operators in dynamic logic, we introduce a lightweight modal predicate logic where names can be non-rigid, and the existence of agents can be uncertain. The language can handle various de dicto/de re distinctions in a natural way. We characterize the expressive power of our language, obtain complete axiomatisations of the logics over several classes of varying-domain/constant-domain epistemic models, and show their (un)decidability.     

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.     

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.     

Resonant-interaction-induced Rydberg antiblockade and its applications

Different from the conventional Rydberg antiblockade (RAB) regime that either requires weak Rydberg-Rydberg interaction (RRI), or compensates the RRI-induced energy shift by introducing off-resonant interactions, we show that RAB regime can be achieved by resonantly driving the transitions between ground state and Rydberg state under strong RRI. The Rabi frequencies are of small amplitude and time-dependent harmonic oscillation, which plays a critical role for the presented RAB. The proposed unconventional RAB regime is used to construct high-fidelity controlled-Z (CZ) gate and controlled-not (CNOT) gate in one step. Each atom requires single external driving. And the atomic addressability is not required for the presented unconventional RAB, which would simplify experimental complexity and reduce resource consumption.     

Hyperbranched Hybridization Chain Reaction for Triggered Signal Amplification and Concatenated Logic Circuits

A hyper‐branched hybridization chain reaction (HB‐HCR) is presented herein, which consists of only six species that can metastably coexist until the introduction of an initiator DNA to trigger a cascade of hybridization events, leading to the self‐sustained assembly of hyper‐branched and nicked double‐stranded DNA structures. The system can readily achieve ultrasensitive detection of target DNA. Moreover, the HB‐HCR principle is successfully applied to construct three‐input concatenated logic circuits with excellent specificity and extended to design a security‐mimicking keypad lock system. Significantly, the HB‐HCR‐based keypad lock can alarm immediately if the “password” is incorrect. Overall, the proposed HB‐HCR with high amplification efficiency is simple, homogeneous, fast, robust, and low‐cost, and holds great promise in the development of biosensing, in the programmable assembly of DNA architectures, and in molecular logic operations.     

A Molecular Platform for Multistate Near‐Infrared Electrochromism and Flip‐Flop,Flip‐Flap‐Flop,and Ternary Memory

A diruthenium complex with a redox‐active amine bridge has been designed, synthesized, and studied by single‐crystal X‐ray analysis and DFT and TDDFT calculations. It shows three well‐separated redox processes with exclusive near‐infrared (NIR) absorbance at each redox state. The electropolymerized film of a related vinyl‐functionalized complex displays multistate NIR electrochromism with low operational potential, good contrast ratio, and long retention time. Flip‐flop, flip‐flap‐flop, and ternary memories have been realized by using the obtained film (ca. 15–20 nm thick) with three electrochemical inputs and three NIR optical outputs that each displays three levels of signal intensity.     

Channel temporal correlation-based optimization method for imperfect underwater acoustic channel state information

The rapid time variations and large channel estimation errors in underwater acoustic (UWA) channels mean that transmitters for adaptive resource allocation quickly become outdated and provide inaccurate channel state information (CSI). This results in poor resource allocation efficiency. To address this issue, this paper proposes an optimization approach for imperfect CSI based on a Gauss–Markov model and the per-subcarrier channel temporal correlation (PSCTC) factor. The proposed scheme is applicable to downlink UWA orthogonal frequency division multiple access systems. The proposed PSCTC factors are measured, and their long-term stability is verified using data recorded in real-world sea tests. Simulation and experimental results show that the optimized CSI effectively mitigates the effects of the temporal variability of UWA channels. It demonstrates that the resource allocation scheme using optimized CSI achieves a higher effective throughput and a lower bit error rate than both imperfect CSI and the CSI predicted by the recursive least-squares (RLS) algorithm.