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Let $K$ be a simplicial complex, and let $\Delta_i^{up}(K)$ be the $i$-th up normalized Laplacian of $K$. Horak and Jost showed that the largest eigenvalue of $\Delta_i^{up}(K)$ is at most $i+2$, and characterized the equality case by the orientable or non-orientable circuits. In this paper, by using the balancedness of signed graphs, we show that $\Delta_i^{up}(K)$ has an eigenvalue $i+2$ if and only if $K$ has an $(i+1)$-path connected component $K'$ such that the $i$-th signed incidence graph $B_i(K')$ is balanced, which implies Horak and Jost's characterization. We also characterize the multiplicity of $i+2$ as an eigenvalue of $\Delta_i^{up}(K)$, which generalizes the corresponding result in graph case. Finally we gave some classes of infinitely many simplicial complexes $K$ with $\Delta_i^{up}(K)$ having an eigenvalue $i+2$ by using wedge, Cartesian product and duplication of motifs., Comment: arXiv admin note: substantial text overlap with arXiv:2405.19078

We demonstrate for the first time that the nonlinear saturation of neoclassical tearing modes (NTMs) can be found directly using a variational principle based on Taylor relaxation, without needing to simulate the intermediate, resistivity-dependent dynamics. As in previous investigations of classical tearing mode saturation (Loizu et al. 2020; Loizu & Bonfiglio 2023), we make use of SPEC (Hudson et al. 2012), an equilibrium solver based on the variational principle of the Multi-Region relaxed MHD, featuring stepped pressure profiles and arbitrary magnetic topology. We work in slab geometry and employ a simple bootstrap current model $J_\textrm{bs} = C \nabla p$ to study the bootstrap-driven tearing modes, scanning over the asymptotic matching parameter $\Delta'$ and the bootstrap current strength. Saturated island widths produced by SPEC agree well with the predictions of an initial value resistive MHD code (Huang & Bhattacharjee 2016) while being orders of magnitude faster to calculate. Additionally, we observe good agreement with a simple analytical Modified Rutherford Equation, without requiring any fitting coefficients. The match is obtained for both linearly unstable classical tearing modes in the presence of bootstrap current, and neoclassical tearing modes, which are linearly stable but nonlinear-unstable due to the effects of the bootstrap current, Comment: Submitted to PPCF

Plasmoid instability accelerates reconnection in collisional plasmas by transforming a laminar reconnection layer into numerous plasmoids connected by secondary current sheets in two dimensions (2D) and by fostering self-generated turbulent reconnection in three dimensions (3D). In large-scale astrophysical and space systems, plasmoid instability likely initiates in the collisional regime but may transition into the collisionless regime as the fragmentation of the current sheet progresses toward kinetic scales. Hall MHD models are widely regarded as a simplified yet effective representation of the transition from collisional to collisionless reconnection. However, plasmoid instability in 2D Hall MHD simulations often leads to a single-X-line reconnection configuration, which significantly differs from fully kinetic particle-in-cell simulation results. This study shows that single-X-line reconnection is less likely to occur in 3D compared to 2D. Moreover, depending on the Lundquist number and the ratio between the system size and the kinetic scale, Hall MHD can also realize 3D self-generated turbulent reconnection. We analyze the features of the self-generated turbulent state, including the energy power spectra and the scale dependence of turbulent eddy anisotropy.

Importance: We introduce a novel Retrieval Augmented Generation (RAG)-Large Language Model (LLM) framework as a Clinical Decision Support Systems (CDSS) to support safe medication prescription. Objective: To evaluate the efficacy of LLM-based CDSS in correctly identifying medication errors in different patient case vignettes from diverse medical and surgical sub-disciplines, against a human expert panel derived ground truth. We compared performance for under 2 different CDSS practical healthcare integration modalities: LLM-based CDSS alone (fully autonomous mode) vs junior pharmacist + LLM-based CDSS (co-pilot, assistive mode). Design, Setting, and Participants: Utilizing a RAG model with state-of-the-art medically-related LLMs (GPT-4, Gemini Pro 1.0 and Med-PaLM 2), this study used 61 prescribing error scenarios embedded into 23 complex clinical vignettes across 12 different medical and surgical specialties. A multidisciplinary expert panel assessed these cases for Drug-Related Problems (DRPs) using the PCNE classification and graded severity / potential for harm using revised NCC MERP medication error index. We compared. Results RAG-LLM performed better compared to LLM alone. When employed in a co-pilot mode, accuracy, recall, and F1 scores were optimized, indicating effectiveness in identifying moderate to severe DRPs. The accuracy of DRP detection with RAG-LLM improved in several categories but at the expense of lower precision. Conclusions This study established that a RAG-LLM based CDSS significantly boosts the accuracy of medication error identification when used alongside junior pharmacists (co-pilot), with notable improvements in detecting severe DRPs. This study also illuminates the comparative performance of current state-of-the-art LLMs in RAG-based CDSS systems.

Purpose: Large Language Models (LLMs) hold significant promise for medical applications. Retrieval Augmented Generation (RAG) emerges as a promising approach for customizing domain knowledge in LLMs. This case study presents the development and evaluation of an LLM-RAG pipeline tailored for healthcare, focusing specifically on preoperative medicine. Methods: We developed an LLM-RAG model using 35 preoperative guidelines and tested it against human-generated responses, with a total of 1260 responses evaluated. The RAG process involved converting clinical documents into text using Python-based frameworks like LangChain and Llamaindex, and processing these texts into chunks for embedding and retrieval. Vector storage techniques and selected embedding models to optimize data retrieval, using Pinecone for vector storage with a dimensionality of 1536 and cosine similarity for loss metrics. Human-generated answers, provided by junior doctors, were used as a comparison. Results: The LLM-RAG model generated answers within an average of 15-20 seconds, significantly faster than the 10 minutes typically required by humans. Among the basic LLMs, GPT4.0 exhibited the best accuracy of 80.1%. This accuracy was further increased to 91.4% when the model was enhanced with RAG. Compared to the human-generated instructions, which had an accuracy of 86.3%, the performance of the GPT4.0 RAG model demonstrated non-inferiority (p=0.610). Conclusions: In this case study, we demonstrated a LLM-RAG model for healthcare implementation. The pipeline shows the advantages of grounded knowledge, upgradability, and scalability as important aspects of healthcare LLM deployment., Comment: NA

In this paper, by the representation theory of symmetric group, we give a decomposition of the Laplace operator (in matrix form) of a covering simplicial complex into the direct sum of some matrices, including the Laplace operator of the underlying simplicial complex. So, the spectrum of a covering simplicial complex can be expressed into a union of the spectrum of the underlying simplicial complex and the spectra of some other matrices, which implies a result of Horak and Jost. In particular, we show that the spectrum of a $2$-fold covering simplicial complex is the union the that of the underlying simplicial complex and that of an incidence-signed simplicial complex, which is an analog of Bilu and Linial's result on graphs. Finally we show that the dimension of the cohomology group of a covering simplicial complex is greater than or equal to that of the underlying simplicial complex.

Additive manufacturing (AM) technology is undergoing rapid development and emerging as an advanced technique that can fabricate complex near-net shaped and light-weight metallic parts with acceptable strength and fatigue performance. A number of studies have indicated that the strength or other mechanical properties of AM metals are comparable or even superior to that of conventionally manufactured metals, but the fatigue performance is still a thorny problem that may hinder the replacement of currently used metallic components by AM counterparts when the cyclic loading and thus fatigue failure dominates. This article reviews the state-of-art published data on the fatigue properties of AM metals, principally including $S$--$N$ data and fatigue crack growth data. The AM techniques utilized to generate samples in this review include powder bed fusion (e.g., EBM, SLM, DMLS) and directed energy deposition (e.g., LENS, WAAM). Further, the fatigue properties of AM metallic materials that involve titanium alloys, aluminum alloys, stainless steel, nickel-based alloys, magnesium alloys, and high entropy alloys, are systematically overviewed. In addition, summary figures or tables for the published data on fatigue properties are presented for the above metals, the AM techniques, and the influencing factors (manufacturing parameters, e.g., built orientation, processing parameter, and post-processing). The effects of build direction, particle, geometry, manufacturing parameters, post-processing, and heat-treatment on fatigue properties, when available, are provided and discussed. The fatigue performance and main factors affecting the fatigue behavior of AM metals are finally compared and critically analyzed, thus potentially providing valuable guidance for improving the fatigue performance of AM metals., Comment: 201 pages, 154 figures

In this paper we investigate Ramanujan hypergraphs by using hypergraph coverings. We first show that the spectrum of a $k$-fold covering $\bar{H}$ of a connected hypergraph $H$ contains the spectrum of $H$, and that it is the union of the spectrum of $H$ and the spectrum of an incidence-signed hypergraph with $H$ as underlying hypergraph if $k=2$, which generalizes Bilu-Linial result on graph coverings. We give a lower bound for the second largest eigenvalue of a $d$-regular hypergraph by universal cover, which generalizes Alon-Boppana bound on $d$-regular graphs and Feng-Li bound on $(d,r)$-regular hypergraphs. By using interlacing family of polynomials, we prove that every $(d,r)$-regular hypergraph has a right-sided Ramanujan $2$-covering, and has a left-sided Ramanujan $2$-covering if the roots of the matching polynomial of its incident graph satisfy some condition. By Ramanujan $2$-coverings, we prove the existence of some families of infinite many left-sided or right-sided $(d,r)$-regular Ramanujan hypergraphs under certain conditions on $d$ and $r$.

Origami-inspired robots with multiple advantages, such as being lightweight, requiring less assembly, and exhibiting exceptional deformability, have received substantial and sustained attention. However, the existing origami-inspired robots are usually of limited functionalities and developing feature-rich robots is very challenging. Here, we report an origami-wheeled robot (OriWheelBot) with variable width and outstanding sand walking versatility. The OriWheelBot's ability to adjust wheel width over obstacles is achieved by origami wheels made of Miura origami. An improved version, called iOriWheelBot, is also developed to automatically judge the width of the obstacles. Three actions, namely direct pass, variable width pass, and direct return, will be carried out depending on the width of the channel between the obstacles. We have identified two motion mechanisms, i.e., sand-digging and sand-pushing, with the latter being more conducive to walking on the sand. We have systematically examined numerous sand walking characteristics, including carrying loads, climbing a slope, walking on a slope, and navigating sand pits, small rocks, and sand traps. The OriWheelBot can change its width by 40%, has a loading-carrying ratio of 66.7% on flat sand and can climb a 17-degree sand incline. The OriWheelBot can be useful for planetary subsurface exploration and disaster area rescue., Comment: 23 papes, 7 figures

The extraordinary properties of a heterostructure by stacking atom-thick van der Waals (vdW) magnets have been extensively studied. However, the magnetocaloric effect (MCE) of heterostructures that are based on monolayer magnets remains to be explored. Herein, we deliberate MCE of vdW heterostructure composed of a monolayer CrI$_3$ and metal atomic layers (Ag, Hf, Au, and Pb). It is revealed that heterostructure engineering by introducing metal substrate can improve MCE of CrI$_3$, particularly boosting relative cooling power to 471.72 $\mu$Jm$^{-2}$ and adiabatic temperature change to 2.1 K at 5 T for CrI$_3$/Hf. This improved MCE is ascribed to the enhancement of magnetic moment and intralayer exchange coupling in CrI$_3$ due to the CrI$_3$/metal heterointerface induced charge transfer. Electric field is further found to tune MCE of CrI$_3$ in heterostructures and could shift the peak temperature by around 10 K in CrI$_3$/Hf, thus manipulating the working temperature window of MCE. The discovered electric-field and substrate regulated MCE in CrI$_3$/metal heterostructure opens new avenues for low-dimensional magnetic refrigeration.

Fatigue properties of additively manufactured (AM) materials depend on many factors such as AM processing parameter, microstructure, residual stress, surface roughness, porosities, post-treatments, etc. Their evaluation inevitably requires these factors combined as many as possible, thus resulting in low efficiency and high cost. In recent years, their assessment by leveraging the power of machine learning (ML) has gained increasing attentions. Here, we present a comprehensive overview on the state-of-the-art progress of applying ML strategies to predict fatigue properties of AM materials, as well as their dependence on AM processing and post-processing parameters such as laser power, scanning speed, layer height, hatch distance, built direction, post-heat temperature, etc. A few attempts in employing feedforward neural network (FNN), convolutional neural network (CNN), adaptive network-based fuzzy system (ANFS), support vector machine (SVM) and random forest (RF) to predict fatigue life and RF to predict fatigue crack growth rate are summarized. The ML models for predicting AM materials' fatigue properties are found intrinsically similar to the commonly used ones, but are modified to involve AM features. Finally, an outlook for challenges (i.e., small dataset, multifarious features, overfitting, low interpretability, unable extension from AM material data to structure life) and potential solutions for the ML prediction of AM materials' fatigue properties is provided.

The advancement of two-dimensional polar metals tends to be limited by the incompatibility between electric polarity and metallicity as well as dimension reduction. Here, we report polar and metallic Janus monolayers of MoSi$_2$N$_4$ family by breaking the out-of-plane (OOP) structural symmetry through Z (P/As) substitution of N. Despite the semiconducting nature of MoSi$_2$X$_4$ (X=N/P/As), four Janus MoSi$_2$N$_{x}$Z$_{4-x}$ monolayers are found to be polar metals owing to the weak coupling between the conducting electrons and electric polarity. The metallicity is originated from the Z substitution induced delocalization of occupied electrons in Mo-d orbitals. The OOP electric polarizations around 10$-$203 pC/m are determined by the asymmetric OOP charge distribution due to the non-centrosymmetric Janus structure. The corresponding OOP piezoelectricity is further revealed as high as 39$-$153 pC/m and 0.10$-$0.31 pm/V for piezoelectric strain and stress coefficients, respectively. The results demonstrate polar metallicity and high OOP piezoelectricity in Janus MoSi$_2$N$_{x}$Z$_{4-x}$ monolayers and open new vistas for exploiting unusual coexisting properties in monolayers derived from MoSi$_2$N$_4$ family.

Implicit neural representation has recently shown a promising ability in representing images with arbitrary resolutions. In this paper, we present a Local Implicit Transformer (LIT), which integrates the attention mechanism and frequency encoding technique into a local implicit image function. We design a cross-scale local attention block to effectively aggregate local features. To further improve representative power, we propose a Cascaded LIT (CLIT) that exploits multi-scale features, along with a cumulative training strategy that gradually increases the upsampling scales during training. We have conducted extensive experiments to validate the effectiveness of these components and analyze various training strategies. The qualitative and quantitative results demonstrate that LIT and CLIT achieve favorable results and outperform the prior works in arbitrary super-resolution tasks.

Two-dimensional magnets could potentially revolutionize information technology, but their potential application to cooling technology and magnetocaloric effect (MCE) in a material down to the monolayer limit remain unexplored. Herein, we reveal through multiscale calculations the existence of giant MCE and its strain tunability in monolayer magnets such as CrX$_3$ (X=F, Cl, Br, I), CrAX (A=O, S, Se; X=F, Cl, Br, I), and Fe$_3$GeTe$_2$. The maximum adiabatic temperature change ($\Delta T_\text{ad}^\text{max}$), maximum isothermal magnetic entropy change, and specific cooling power in monolayer CrF$_3$ are found as high as 11 K, 35 $\mu$Jm$^{-2}$K$^{-1}$, and 3.5 nWcm$^{-2}$ under a magnetic field of 5 T, respectively. A 2% biaxial and 5% $a$-axis uniaxial compressive strain can remarkably increase $\Delta T_\text{ad}^\text{max}$ of CrCl$_3$ and CrOF by 230% and 37% (up to 15.3 and 6.0 K), respectively. It is found that large net magnetic moment per unit area favors improved MCE. These findings advocate the giant-MCE monolayer magnets, opening new opportunities for magnetic cooling at nanoscale.

Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces and a continuous rotational transform. These currents have two components: a surface current (Dirac $\delta$-function in flux surface labeling) that prevents the formation of magnetic islands and an algebraically divergent Pfirsch--Schl\"uter current density when a pressure gradient is present across the rational surface. At flux surfaces adjacent to the rational surface, the traditional treatment gives the Pfirsch--Schl\"uter current density scaling as $J\sim1/\Delta\iota$, where $\Delta\iota$ is the difference of the rotational transform relative to the rational surface. If the distance $s$ between flux surfaces is proportional to $\Delta\iota$, the scaling relation $J\sim1/\Delta\iota\sim1/s$ will lead to a paradox that the Pfirsch--Schl\"uter current is not integrable. In this work, we investigate this issue by considering the pressure-gradient-driven singular current in the Hahm\textendash Kulsrud\textendash Taylor problem, which is a prototype for singular currents arising from resonant magnetic perturbations. We show that not only the Pfirsch--Schl\"uter current density but also the diamagnetic current density are divergent as $\sim1/\Delta\iota$. However, due to the formation of a Dirac $\delta$-function current sheet at the rational surface, the neighboring flux surfaces are strongly packed with $s\sim(\Delta\iota)^{2}$. Consequently, the singular current density $J\sim1/\sqrt{s}$, making the total current finite, thus resolving the paradox., Comment: Minor corrections of typos

Modelling elastocaloric effect (eCE) is crucial for the design of environmentally friendly and energy-efficient eCE based solid-state cooling devices. Here, a thermodynamically consistent non-isothermal phase-field model (PFM) coupling martensitic transformation with mechanics and heat transfer is developed and applied for simulating eCE. The model is derived from a thermodynamic framework which invokes the microforce theory and Coleman--Noll procedure. To avoid the numerical issue related to the non-differentiable energy barrier function across the transition point, the austenite-martensite transition energy barrier in PFM is constructed as a smooth function of temperature. Both the indirect method using isothermal PFM with Maxwell relations and the direct method using non-isothermal PFM are applied to calculate the elastocaloric properties. The former is capable of calculating both isothermal entropy change and adiabatic temperature change ($\Delta T_{\text{ad}}$), but induces high computation cost. The latter is computationally efficient, but only yields $\Delta T_{\text{ad}}$. In a model Mn-22Cu alloy, the maximum $\Delta T_{\text{ad}}$ ($\Delta T_{\text{ad}}^{\text{max}}$) under a compressive stress of 100 MPa is calculated as 9.5 and 8.5 K in single crystal (3.5 and 3.8 K in polycrystal) from the indirect and direct method, respectively. It is found that the discrepancy of $\Delta T_{\text{ad}}^{\text{max}}$ by indirect and direct method is within 10% at stress less than 150 MPa, confirming the feasibility of both methods in evaluating eCE at low stress. The results demonstrate the developed PFM herein, combined with both indirect and direct method for eCE calculations, as a practicable toolkit for the computational design of elastocaloric devices., Comment: 26 pages, 10 figures

This paper introduces the first results of observations with the Ultra-Long-Wavelength (ULW) -- Low Frequency Interferometer and Spectrometer (LFIS) on board the selenocentric satellite Longjiang-2. We present a brief description of the satellite and focus on the LFIS payload. The in-orbit commissioning confirmed a reliable operational status of the instrumentation. We also present results of a transition observation, which offers unique measurements on several novel aspects. We estimate the RFI suppression required for such a radio astronomy instrumentation at the Moon distances from Earth to be of the order of 80 dB. We analyse a method of separating Earth- and satellite-originated radio frequency interference (RFI). It is found that the RFI level at frequencies lower than a few MHz is smaller than the receiver noise floor., Comment: Accepted for publication in Experimental Astronomy; 22 pages, 11 figures

The discovery of two-dimensional (2D) layered MoSi$_2$N$_4$ and WSi$_2$N$_4$ without knowing their 3D parents by chemical vapor deposition in 2020 has stimulated extensive studies of 2D MA$_2$Z$_4$ system due to its structural complexity and diversity as well as versatile and intriguing properties. Here, a comprehensive overview on the state-of-the-art progress of this 2D MA$_2$Z$_4$ family is presented. Starting by describing the unique sandwich structural characteristics of the emerging monolayer MA$_2$Z$_4$, we summarize and anatomize their versatile properties including mechanics, piezoelectricity, thermal transport, electronics, optics/optoelectronics, and magnetism. The property tunability via strain engineering, surface functionalization and layered strategy is also elaborated. Theoretical and experimental attempts or advances in applying 2D MA$_2$Z$_4$ to transistors, photocatalysts, batteries and gas sensors are then reviewed to show its prospective applications over a vast territory. We further discuss new opportunities and suggest prospects for this emerging 2D family. The overview is anticipated to guide the further understanding and exploration on 2D MA$_2$Z$_4$., Comment: 29 pages, 21 figures

Sintering, as a thermal process at elevated temperature below the melting point, is widely used to bond contacting particles into engineering products such as ceramics, metals, polymers, and cemented carbides. Modelling and simulation as important complement to experiments are essential for understanding the sintering mechanisms and for the optimization and design of sintering process. We share in this article a state-to-the-art review on the major methods and models for the simulation of sintering process at various length scales. It starts with molecular dynamics simulations deciphering atomistic diffusion process, and then moves to microstructure-level approaches such as discrete element method, Monte--Carlo method, and phase-field models, which can reveal subtle mechanisms like grain coalescence, grain rotation, densification, grain coarsening, etc. Phenomenological/empirical models on the macroscopic scales for estimating densification, porosity and average grain size are also summarized. The features, merits, drawbacks, and applicability of these models and simulation technologies are expounded. In particular, the latest progress on the modelling and simulation of selective and direct-metal laser sintering based additive manufacturing is also reviewed. Finally, a summary and concluding remarks on the challenges and opportunities are given for the modelling and simulations of sintering process.

Magnetohydrodynamic turbulence regulates the transfer of energy from large to small scales in many astrophysical systems, including the solar atmosphere. We perform three-dimensional magnetohydrodynamic simulations with unprecedentedly large magnetic Reynolds number to reveal how rapid reconnection of magnetic field lines changes the classical paradigm of the turbulent energy cascade. By breaking elongated current sheets into chains of small magnetic flux ropes (or plasmoids), magnetic reconnection leads to a new range of turbulent energy cascade, where the rate of energy transfer is controlled by the growth rate of the plasmoids. As a consequence, the turbulent energy spectra steepen and attain a spectral index of -2.2 that is accompanied by changes in the anisotropy of turbulence eddies. The omnipresence of plasmoids and their consequences on, e.g., solar coronal heating, can be further explored with current and future spacecraft and telescopes., Comment: 32 pages, 8 figures, the world's largest 3D MHD turbulence simulation using a fifth-order scheme

Over the past decade, Boozer has argued that three-dimensional (3D) magnetic reconnection fundamentally differs from two-dimensional (2D) reconnection due to the fact that the separation between any pair of neighboring field lines almost always increases exponentially over distance in a 3D magnetic field. According to Boozer, this feature makes 3D field-line mapping chaotic and exponentially sensitive to small non-ideal effects; consequently, 3D reconnection can occur without intense current sheets. We test Boozer's theory via ideal and resistive reduced magnetohydrodynamic simulations of the Boozer-Elder coronal loop model driven by sub-Alfvenic footpoint motions [A. H. Boozer and T. Elder, Physics of Plasmas 28, 062303 (2021)]. Our simulation results significantly differ from their predictions. The ideal simulation shows that Boozer and Elder under-predict the intensity of current density due to missing terms in their reduced model equations. Furthermore, resistive simulations of varying Lundquist numbers show that the maximal current density scales linearly rather than logarithmically with the Lundquist number., Comment: 14 pages, 9 figures. Accepted for publication in Physics of Plasmas