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Developing efficient electrocatalysts for CO$_2$ reduction into value-added products is crucial for the green economy. Inspired by the recent synthesis of Biphenylene (BPH), we have systematically investigated pristine, defective, and Cu-decorated BPH as an electrocatalyst for the CO$_2$ reduction reactions (CRR). Our first-principles calculations show the CO$_2$ molecules weakly interact with the pristine BPH surface while defective BPH facilitates the CO$_2$ adsorption with a binding energy ($E_b$) of -3.22 eV, indicating the detrimental process for the CRR on the surface of both systems. Furthermore, we have investigated the binding energy and kinetic stability of Cu-decorated BPH as a single-atom-catalyst (SAC). The molecular dynamics simulations confirm the kinetic stability, revealing that the Cu-atom avoids agglomeration under low metal dispersal conditions. The CO$_2$ molecule gets adsorbed horizontally on the Cu-BPH surface with $E_b$ of -0.52 eV. The CRR mechanism is investigated using two pathways beginning with two different initial intermediate states, formate ($\mathrm{^*OCOH}$) and the carboxylic ($\mathrm{^*COOH}$) pathways. The formate pathway confirms the conversion of $\mathrm{^*OCOH}$ to $\mathrm{^*HCOOH}$ with the rate-limiting potential ($U_L$) of 0.57 eV for the production of HCOOH, while for the carboxylic pathway, the conversion of $\mathrm{^*COH}$ to $\mathrm{^*CHOH}$ has $U_L$ of 0.49 eV for the production of CH$_3$OH. We have also investigated the effect of protons using charged hydrogen pseudopotential, which hints towards the possible formation of CH$_3$OH as fuel. Our findings propose Cu-BPH as an efficient single-atom catalyst for CO$_2$ conversion compared to the well-known Cu metal., Comment: 9 pages, 6 figures, 8 figures in Supplementary Information

We study a quantum oscillator interacting and back-reacting on a classical oscillator. This can be done consistently provided the quantum system decoheres, while the backreaction has a stochastic component which causes the classical system to undergo diffusion. Nonetheless the state of the quantum oscillator can remain pure conditioned on the trajectory of the classical oscillator. We solve the system using the classical-quantum path integral formulation, and investigate slow moving regimes of either the classical or quantum oscillator. Lastly, we study the correlators of this classicalquantum setup. We are able to identify the free correlators of the theory and compute the full partition function perturbatively up to second order. This serves as a toy model for a number of other systems in which one system can be treated as effectively classical, such as a scalar quantum field interacting with another field undergoing decoherence, or a system emitting radiation, one of which is treated classically.

One of the obstacles to reconciling quantum theory with general relativity, is constructing a theory which is both consistent with observation, and and gives finite answers at high energy, so that the theory holds at arbitrarily short distances. Quantum field theory achieves this through the process of renormalisation, but famously, perturbative quantum gravity fails to be renormalisable, even without coupling to matter. Recently, an alternative to quantum gravity has been proposed, in which the geometry of spacetime is taken to be classical rather than quantum, while still being coupled to quantum matter fields [1, 2]. This can be done consistently, provided the dynamics is fundamentally stochastic. Here, we find that the pure gravity theory is formally renormalisable. We do so via the path integral formulation by relating the classical-quantum action to that of quadratic gravity which is renormalisable. Because the action induces stochastic dynamics of space-time, rather than deterministic evolution of a quantum field, the classical-quantum theory is free of tachyons and negative norm ghosts. The key remaining question is whether the renormalisation prescription retains completely positive (CP) dynamics. This consideration appears to single out the scale invariant and asymptotically free theory. We give further evidence that the theory is CP, by showing that the two-point function of the scalar mode is positive. To support the use of precision accelerometers in testing the quantum nature of spacetime, we also compute the power spectral density of the acceleration. The results presented here have a number of implications for inflation, CMB data, and experiments to test the quantum nature of spacetime. They may also provide a way to compute probabilities in the regime of quantum gravity where spacetime can be treated as effectively classical., Comment: v2: PSD pole prescription fand power spectral density for the acceleration added

We analyse the geometric instability of embeddings produced by graph neural networks (GNNs). Existing methods are only applicable for small graphs and lack context in the graph domain. We propose a simple, efficient and graph-native Graph Gram Index (GGI) to measure such instability which is invariant to permutation, orthogonal transformation, translation and order of evaluation. This allows us to study the varying instability behaviour of GNN embeddings on large graphs for both node classification and link prediction.

In this paper, we explore the performance of different pruning methods in the context of the lottery ticket hypothesis. We compare the performance of L1 unstructured pruning, Fisher pruning, and random pruning on different network architectures and pruning scenarios. The experiments include an evaluation of one-shot and iterative pruning, an examination of weight movement in the network during pruning, a comparison of the pruning methods on networks of varying widths, and an analysis of the performance of the methods when the network becomes very sparse. Additionally, we propose and evaluate a new method for efficient computation of Fisher pruning, known as batched Fisher pruning., Comment: 10 pages

Driven by closed-loop automation, the Zero-Touch Network and Services Management (ZSM) framework offers invigorating features for the end-to-end management and orchestration of a sliced network. Although ZSM is considered a promising framework by 3GPP, there is a lack of concrete ZSM-based solutions for the 3GPP Network Slicing management. This article presents an architectural framework of a ZSM-based management system for 3GPP Network Slicing. The proposed framework employs recursive ZSM management domains to meet the specific management requirements of the standard 3GPP Network Slicing framework. Two deployment options are considered for the presented framework. The first option features the integration of the standard services of the 3GPP Management System within ZSM. The other one considers ZSM as a complementary system for the standard 3GPP Management System. From these deployment options, some key questions are identified on ZSM's interoperability with the existing 3GPP Network Slicing systems. Finally, for each option, the architectural and operational feasibility of the ZSM interoperation with 3GPP Network Slicing systems is shown through an example use case.