In the present work we explore for the first time the general structure and properties of the nonperturbative quark-gluon vertex in the complex plane. Specifically, we focus on the transversely-projected quark-gluon vertex that emerges from a recently developed symmetry-preserving approach for the study of meson properties beyond the rainbow-ladder approximation. The analysis focuses on the so-called "soft-gluon" limit, which reduces the momentum-dependence of the corresponding vertex form factors to a single momentum variable. The complexification of this variable inside the defining integrals furnishes unambiguously all eight vertex form factors within a concrete domain of the complex variable, delimited by a characteristic parabola. The extent of this reliable domain is determined by the appearance of the first singularity in the integrands of the vertex integrals, where the standard Wick rotation must be duly supplemented by additional crucial contributions. This primary analytic region may be extended considerably by resorting to standard extrapolation methods, which remain valid up until the appearance of complex structures associated with the onset of physical processes. The generalization of the method to arbitrary gluon momenta, and its relevance for the determination of the quark propagator in the complex plane, are briefly discussed.

The problem of optimal dosage estimation arises in diverse scientific domains, from pharmacology and toxicology to aquaculture and environmental studies. Statistical modeling of nonlinear dose-response relationships is essential to quantify biological effects and determine response-optimal levels. This paper introduces a flexible Bayesian fractional polynomial (BFP) framework for modeling such relationships, allowing for model uncertainty quantification and robust prediction through Bayesian model averaging. Extensive simulation results demonstrate that the proposed BFP approach yields accurate estimation of optimal dose levels, outperforming benchmarks significantly. The approach is demonstrated on real data from fish nutrient requirement experiments.

The Plackett-Luce model is widely used to deal with probabilities in discrete choice settings. This paper introduces a novel two-level Plackett-Luce model combined with a multinomial logistic scheme that provides the basis for the route choice module in a smart mobility platform. For this, we develop Bayesian inference and prediction mechanisms to capture consumers' preferences for personalized route recommendations. The model is empirically tested, allowing for refinements and discussion of its applicability. We also illustrate its practical relevance through several use cases, including relevant route selection, coordinated car pooling, incentive design and synthetic data generation.

Non-collinear antiferromagnets are a class of spin-polarized antiferromagnets in which chiral spin textures give rise to Berry-curvature-driven phenomena, such as the anomalous Hall effect (AHE), without net magnetization. We investigate the properties of thin films of antiperovskite non-collinear antiferromagnetic metals Mn3NiN and Mn3GaN using pump-probe experiments. In both materials, we observe a strong dependence of pump-polarization-independent dynamics, induced by femtosecond laser pulses, on the angle between the sample normal and the direction of probe propagation. In Mn3NiN, where the presence of a sizable AHE indicates the Γ4g phase, the measured magnetooptical (MO) signals acquire an additional, strong dependence on the external magnetic field when the probe pulses are incident at nonzero angles. In contrast, in Mn3GaN, where the absence of AHE indicates the Γ5g phase, the measured signals do not depend on the magnetic field. Using probe-polarization-resolved measurements combined with full optical modeling based on Yeh's formalism, we quantitatively separate magnetic and non-magnetic contributions to the measured signals. We show that in Mn3NiN, the observed magnetic field dependence results from field-controlled redistribution of magnetic domain populations, enabled by their piezomagnetic moments and detected by a Kerr-like MO effect, while this effect is absent in Mn3GaN. Temperature-dependent measurements reveal a change from single-step to two-step quenching dynamics with increasing temperature in Mn3NiN. This behavior contrasts with the nearly temperature-independent quenching dynamics reported for the non-collinear antiferromagnetic Heusler compound Mn3Sn, but resembles the crossover from type-I to type-II demagnetization dynamics in metallic ferromagnets.

Large Language Models (LLMs) have revolutionized how information are collected, aggregated, and reasoned. However, this enables a novel and accessible vector of privacy intrusion: the automated and in-depth personal profiling; this engenders a chilling effect of "peepers everywhere". Existing research primarily unfolds from the training pipeline of LLM, emphasizing the exposure of Personally Identifiable Information (PII) through memorization, while privacy studies from a human-centric perspective remain underexplored. To fill this void, we empirically investigate privacy perception in the real world through the lens of human awareness and the practices of LLM-integrated platforms, revealing a significant dissonance: platforms fail to technically or policy-wise address public privacy concerns. To facilitate a systematic and quantifiable study of privacy risk, we propose the PrivacyIceberg, which categorizes real-world human privacy risks into three tiers: explicitly searched, contextually inferred, and deeply aggregated, based on the sophistication of LLM exploitation. We developed IcebergExplorer to audit privacy exposure, utilizing minimal PII as a search seed to reconstruct high-fidelity profiles, achieving over 90% factual accuracy within 10 minutes at a cost under $3, for real-world scenarios. Additionally, we identify six root causes contributing to such privacy disclosures and propose multi-stakeholder countermeasures for LLM vendors, individuals, and data publishers.

The massive Majorana field in $1+1$ dimension is employed to investigate the violation of the Bell-CHSH inequality in relativistic Quantum Field Theory. We give an explicit rapidity-space realization of the Summers-Werner modular-localization construction and reduce the vacuum Bell-CHSH correlator to a single spectral weight $h^2(ω)$ for the modular operator. The resulting analytic families approach the Tsirelson bound in the vacuum state as their spectral weight concentrates near $ω\approx0$, corresponding to the eigenvalue $λ^2 \approx 1$ of the modular operator.

Lambda quantiles, originally introduced as lambda value at risk, generalise the classical value at risk by allowing for a variable confidence level. This work presents efficient algorithms for computing lambda quantiles and demonstrates their application in portfolio optimisation. We first develop a robust algorithm, Λ-Newton-Bis, that combines Newton's method with a bisection strategy to ensure global convergence. The algorithm handles potential discontinuities and achieves local quadratic convergence under standard regularity assumptions. To address cases with multiple roots, we also propose an interval analysis approach. We then demonstrate the algorithm's computational efficiency and practical relevance within a portfolio optimization framework. To this end, we develop two alternative solution methods that incorporate the Λ-Newton-Bis procedure. Numerical experiments confirm the algorithm's convergence properties and highlight its computational advantages in optimization tasks based on lambda quantiles.

The theory of Bailey's transform provides a systematic method for deriving $q$-identities, the key factor of which is the Bailey pair. The concept of Bailey pair was first extended to bilateral version by Paule. In this paper, following Rogers' work on Fourier series, we derive two asymmetric bilateral Bailey pairs. By inserting them into the bilateral Bailey chains, we obtain several identities of Rogers-Ramanujan type, Andrews-Gordon type and also identities on false theta functions. Furthermore, based on the Bailey lattice due to Dousse, Jouhet and Konan, we get an asymmetric bilateral Bailey lemma which leads to identities on Appell-Lerch series. Moreover, by using the asymmetric bilateral Bailey lemmas due to Andrews and Warnaar, we get some identities on false theta functions and the generalized Hecke-type series.

Developers often make similar mistakes across code locations implementing related functionalities. These locations, called siblings, share similar issues and require similar fixes. Accurately identifying siblings and consistently repairing them are crucial for automated program repair. Hercules is a SOTA technique designed for sibling repair. However, it is limited by strong assumptions about sibling locations and commit-history availability, rigid AST-based sibling matching, and inflexible template-based patch generation. To address these limitations, we present SiblingRepair, a new LLM-based multi-hunk APR technique specialized for sibling repair. Starting from a suspicious location identified by spectrum-based fault localization, SiblingRepair searches for semantically related sibling candidates using token- and embedding-based code matching, without restricting discovery to failing-test coverage or commit history. It then uses an LLM to identify failure-relevant siblings and generate consistent patches through two complementary strategies: simultaneous repair, which jointly repairs siblings, and iterative repair, which progressively analyzes candidates for patch construction. SiblingRepair further preserves promising patches generated from earlier suspicious locations and combines them into generalized multi-hunk patches. We evaluate SiblingRepair on the Defects4J and GHRB benchmarks. The results show that SiblingRepair substantially outperforms SOTA multi-hunk repair techniques including Hercules. Our evaluation further demonstrates its repair efficiency, the effectiveness of its sibling detection and repair components, and limited impact of the LLM data leakage on the results. Overall, SiblingRepair advances automated sibling and general multi-hunk repair.

Many complex systems are organized around complementary roles and naturally described as bipartite networks. Unveiling their multiscale structure presents a fundamental challenge because coarse-graining procedures must preserve role separation, whereas standard approaches collapse it via one-mode projections. Here we introduce a Laplacian-based renormalization framework that operates directly on the bipartite architecture, enabling scale transformations while retaining role differentiation. Using controlled bipartite ensembles at criticality, we show that structural imbalance systematically reshapes organization across scales while leaving scaling properties invariant, revealing a separation between universality and geometry. Applying the coarse-graining framework to empirical bipartite networks, we uncover nontrivial multiscale hierarchies for both roles. In contrast, renormalization performed after one-mode projection -- which truncates diffusion paths to nearest neighbors -- yields qualitatively different structures. Our results identify two-mode geometry as a fundamental constraint for revealing multiscale organization in systems with role separation.

Autonomous LLM agents face a critical security risk known as workflow hijacking, where attackers subtly alter tool and skill invocations. Existing defenses rely on host-internal telemetry (such as audit logs), which can be forged if the host OS is compromised. To solve this, we introduce ClawGuard, a passive, out-of-band monitor that audits LLM-agent workflows using electromagnetic (EM) emanations. Because distinct agent skills create unique hardware usage patterns (computation, DRAM, network blocking), they emit measurable, macroscopic EM envelopes. External software-defined radios (SDRs) capture these physical signals. Using a drift-aware pipeline with 320-dimensional features, ClawGuard converts RF streams into physical evidence. Evaluated on a 7.82TB RF corpus, ClawGuard achieved an AUC of 0.9945, detecting attacks with a 100% true-positive rate and a 1.16% false-positive rate. This proves passive EM sensing is a practical, forge-resistant physical check against compromised host software.

Neural operators have achieved promising performance on partial differential equations (PDEs), but most existing models are built on fixed Eulerian coordinates. This mismatch between evolving physical structures and static coordinates creates spatial misalignment, leading to unnecessarily non-local operator mappings and reinforcing a smoothness preference near sharp transitions. Inspired by adaptive coordinate transformations in classical PDE analysis, we propose the Adaptive Coordinate Transform (ACT) block, a plug-and-play module for data-driven geometric adaptation in neural operators. ACT blocks resolve this structural limitation by learning adaptive coordinate systems within the operator learning pipeline. Specifically, given an input feature, the ACT block learns a coordinate transformation and represents the same feature under the transformed coordinates via differentiable sampling. This operation preserves the underlying signal while changing its spatial representation, equivalent to expressing the same physical quantity in different coordinate systems. By adapting the coordinate system to the data, ACT allows the network to better track evolving structures, reduce operator complexity, and dynamically focus on critical features to improve learning. We evaluate the proposed approach across diverse PDE benchmarks and multiple neural operator architectures. Experimental results demonstrate consistent and significant improvements in predictive accuracy, indicating that learning coordinate systems provides a powerful mechanism for enhancing operator learning.

Networking is central to careers in computer science, where a globally distributed and diverse community increasingly collaborates across institutional and geographic boundaries, often in hybrid and remote settings. However, access to effective networking is shaped by structural and personal factors, including geography, funding, language, identity, personality, and caregiving responsibilities. Building on prior work, this workshop focuses on women in computing to examine lived experiences of networking and the barriers they encounter. Through a community-driven discussion grounded in a factor-based framework, the workshop aims to surface overlooked challenges and foster shared understanding. Ultimately, it seeks to inform more inclusive, equitable, and accessible networking practices within the computer science community.

In an approval-based committee election, the task is to select a committee of up to $k$ candidates from a set of $m$ candidates based on the preferences of $n$ voters, each of whom approves a subset of the candidates. A central open question is whether there always exists a committee in the core, a stability notion capturing proportional representation. We prove core non-emptiness for all approval-based committee elections with at most five voters. The proof is based on affine monoid methods and shows that, for $n\le5$, every fractional committee admits a deterministic rounding to an integral committee that preserves each voter's utility up to floors. We extend our argument to the weighted voter setting, which implies core existence for instances with up to five distinct approval sets. In all these cases, a core committee can be computed in polynomial time. We show that our technique cannot be extended as-is: our rounding method breaks down for $n=6$, and for $n=3$ when applied to more general models with additive valuations or non-unit candidate costs.

Recently we have proposed a new auxiliary-field formulation for self-dual nonlinear electrodynamics (NLED) which makes use of two building blocks: (i) a seed self-dual theory $L(F_{μν};g)$, where $F_{μν}$ is the electromagnetic field strength and $g$ a duality-invariant coupling constant; and (ii) a scalar potential $W(ψ)$. Our formulation is based on the Lagrangian $ \mathfrak{L}(F_{μν};ψ) = L(F_{μν};ψ) + W(ψ)$, where $ψ$ is an auxiliary scalar field. Integrating out $ψ$, using its equation of motion, one obtains a $\mathsf{U}(1)$ duality-invariant NLED. Different self-dual NLEDs are derived by choosing different potentials $W(ψ)$. In the case that the seed Lagrangian defines the Born-Infeld theory, in this paper we demonstrate that the resulting models for self-dual NLED are causal and provide a general solution of the self-duality equation. We also elaborate on the procedure to relate our formulation to that developed by Russo and Townsend.

Carbon Atomic Wires (CAWs) are finite linear chains of sp-hybridized carbon atoms. Here the electrochemical reduction of CAWs in the form of polyynes (i.e. with alternated single-triple bonds) is reported. Upon applying a reducing potential to a solution containing polydispersed hydrogen-capped polyynes, the formation of a black precipitate was observed. Electronic absorption spectroscopy confirmed the irreversible reaction of the carbon chains while excluding degradation or side reactions. Subsequent analyses revealed that the precipitate consisted of amorphous carbon nanoparticles with tunable diameters. This control over particle size is attributed to the modulation of growth kinetics through restricted mass transport toward the solid-liquid interface. Raman spectroscopy showed that the resulting material exhibits an amorphous sp-sp2 character, with a retained sp fraction exceeding 60%. Smaller nanoparticles displayed reduced disorder within the sp2 domains and a broader distribution of sp-chain lengths preserved in the amorphous matrix. Additional experiments on size-selected polyynes suggest that this synthesis method allows to better preserve the starting chain length in the final structure. Unlike previously reported amorphous sp-sp2 carbon networks, the nanoparticles produced in this study show remarkable stability under ambient conditions, retaining their sp character for times in excess of six months. These findings pave the way for future applications, particularly as further diameter tuning may enable access to the quantum-dot regime.

Locally repairable codes with availability have become essential components in modern large-scale distributed cloud storage systems and numerous other applications. In this paper, we focus on the construction of locally repairable codes with one or two recovering sets via elliptic function fields. Prior pioneering work by Li et al. (IEEE Trans. Inf. Theory, vol. 65, no. 1, 2019) and Ma and Xing (J. Comb. Theory Ser. A., vol. 193, 2023) employed maximal supersingular elliptic curves to obtain several optimal (classical) locally repairable codes. In contrast, we consider ordinary elliptic curves with many rational points. This approach yields several new families of \(q\)-ary optimal locally repairable codes with length \(O(q+2\sqrt{q})\) and flexible locality. Consequently, our work broadens the selection of curves available for the construction of optimal locally repairable codes. Furthermore, we present a general framework for constructing locally repairable codes with two recovering sets via automorphism groups of elliptic function fields. To realize this framework, we devise a novel construction for determining the functions \(e_i\) in the construction of locally repairable codes. By employing both supersingular and ordinary elliptic curves, we obtain several families of locally repairable codes with two recovering sets. In particular, we construct a family of \(q^2\)-ary locally repairable codes with two recovering sets, achieving length \(O(q^2+2q)\) and Singleton-defect \(O\!\left(\frac{2\ell}{q^2+2q-8\ell}\right)\), where \(\ell \mid\mid q + 2\) with \(4\ell < q\).

This paper introduces a novel method to approximate limit cycles of nonlinear ODEs by use of switching affine dynamics in order to ease data-based modeling and analysis. Previous approaches to approximating limit cycles by switching systems have been largely confined to simple partitions into two-regions or low-dimensional (often planar) settings. In contrast, this study utilizes more general partitions in higher-dimensional state spaces, augmented by external signals, to develop a synthesis scheme that guarantees a globally stable limit cycle. The synthesis task is formulated and solved based on constrained numerical optimization. Starting from sampled data of the nonlinear dynamics, the method minimizes the error between the data and the limit cycle generated by the switching affine model, while employing stability constraints to ensure global stability. Based on the obtained model, the paper tackles the problem of reference tracking for switching affine systems with periodic behavior. While the approximation scheme is based on a common Lyapunov function, the reference tracking approach uses multiple Lyapunov functions to achieve less conservative convergence results. The principle and effectiveness of the proposed methods are illustrated through a set of examples.

Analog quantum simulators emulate complex many-body dynamics through native continuous-time evolution under hardware-defined interactions. Yet once a platform is specified, its interaction structure is largely fixed by the underlying hardware, restricting the Hamiltonians that can be realized and limiting programmability. Here we introduce universal analog quantum simulation (UAQS), a hybrid framework that systematically expands the range of accessible quantum evolutions within a given analog platform. UAQS employs optimized continuous-time control fields to engineer target dynamics directly, avoiding decomposition into discrete gate sequences. By preserving native analog evolution while extending the set of achievable Hamiltonians, UAQS transforms fixed-interaction analog devices into programmable simulators. Numerical studies on representative architectures, including superconducting circuits and Rydberg-atom arrays, show that UAQS accurately reproduces non-trivial many-body dynamics beyond the intrinsic interaction structure of the hardware. These results establish UAQS as a practical route toward programmable analog quantum simulation.

We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with intervention policies triggered by safety levels, notably in insurance surplus management with dividend payments and capital injections. These features place the problem outside the scope of classical stochastic maximum principle (SMP) results, which rely on global smoothness assumptions. We establish both necessary and sufficient optimality conditions for this class of control problems. Our approach combines a Sobolev-type representation of the first variation process with smooth approximations and Ekeland's variational principle. As application, we study an optimal premium adjustment and reserve management policies for an insurance whose surplus is modelled by threshold-based dividend and capital injection policies.

Given a Lipschitz conductor $K$ in the smooth compact Riemannian $2\le n$-manifold $(M,g)$, such a half generic heat dispersion law $$ {\rm H^d}_{p,\varPhi,\varPsi}(K,M)=2^{-1} {\rm H^d}_{Δ_p,\varPhi,\varPsi}(K,M) $$ is not only newly-established via Theorem 1.1 but also deeply-explored through not only Proposition 3.1 (a comparison law for the generic heat dispersion) but also Proposition 3.2 (a recycling law for the quasilinear Laplace-Robin eigenvalue).

Hexagonal optical lattices, emulating graphene and hexagonal boron nitride (h-BN) structures, provide a versatile platform for exploring strongly correlated quantum matter. Using continuous-space exact diagonalization and quantum Monte Carlo simulations, we investigate the phase diagrams of ultracold bosons in honeycomb and h-BN lattices. For the honeycomb lattice, we find significant deviations from the standard Bose-Hubbard model even for strong lattice amplitudes. We observe suppressed Mott insulator lobes and the absence of higher-order insulating phases, attributed to strong density-assisted tunneling effects. In the h-BN case, a rich phase diagram emerges, featuring multiple Mott lobes with various sublattice occupations, driven by the interplay of lattice asymmetry, interactions, and particle filling. Our results highlight the necessity of continuous-space treatments for capturing the full complexity of bosonic quantum phases in hexagonal geometries, paving the way for experimental realizations with ultracold atoms and further theoretical work.

Weekly healthcare activity data are typically non-negative counts with temporal dependence and occasional system-wide disruptions, settings in which Gaussian time-series models may be inadequate. Solid organ transplant (SOT) activity provides a representative case study of a count process affected by a large external shock. We analyse weekly SOT counts in the USA and Italy from 2014 to October 2024, stratified by donor type (deceased vs living) and organ (kidney and liver). We fit Poisson and negative-binomial count time-series models incorporating short-term dynamics, calendar effects (holiday weeks), and pre-specified pandemic-period level and/or slope indicators. Candidate specifications are screened within a pre-defined portfolio and selected using BIC within each training window. Forecasting performance is evaluated with an expanding-window design at horizons $h\in\{4,8,12\}$ weeks. Alongside RMSE, we report empirical coverage of nominal $95\%$ predictive intervals and interval widths to summarise calibration and forecast uncertainty. Across strata, selected models capture substantial pandemic-period deviations and varying post-period trajectories. Deceased-donor series are broadly consistent with a return towards pre-pandemic baselines in both countries, whereas the US living-donor series shows a more gradual convergence in this application. Within the explored model class and validation protocol, auxiliary covariates representing COVID burden and mortality add limited incremental predictive contribution beyond autoregressive and calendar components. Our analysis shows that donation time series represent an unconditional phenomenon, with auxiliary variables having a statistically negligible impact on donations, thus allowing a focus on more practical aspects related to ongoing challenges in the post-pandemic era, such as hospital overloads and changes in public perception.

We propose a variational method for constructing the eigenvalues and generalized eigenvalues for an arbitrary $N\times N$ complex matrix. The quantum part of our algorithm is based on encoding the matrix elements into the pure state of a quantum system and expressing the loss function with optimization parameters in terms of certain probability amplitudes in the superposition state. The principal step of this algorithm is the measurement of the ancilla state that removes all extra terms from the above superposition and allows to probabilistically construct the required loss function along with its derivatives with respect to the optimization parameters. These output data are used to find the new values of optimization parameters for the next iteration of the loss function in the gradient optimization method. The depth and size of the circuit for this algorithm are, respectively, $O(N^2 \log N)$ and $O(\log N)$.

We prove the normal subgroup property for every group that acts properly and cocompactly on a two-dimensional Euclidean building: every normal subgroup has finite index or is contained in the finite kernel of the action. As a consequence, the non-residually finite lattices constructed by Titz Mite and the second author are virtually simple. They are the first known simple lattices on irreducible Euclidean buildings.

We show that, for an $SU(2)$ gauge field (the reasoning extends trivially to $SU(N)$), spontaneous symmetry breaking changes the field cohomology. This defines a new field with cohomological properties characteristic of matter fields. Consequently, the construction of a renormalizable unitary gauge fixing, following Morse's problem of functional extremization, leads to the Gribov condition being automatically solved on-shell. This result occurs because a specific combination of fields is cohomologically matter-like and therefore free of the Gribov problem.

Existing backdoor attacks on Large Language Model-based agents remain stateless, executing fixed behaviors confined to a single session. We propose a stateful agent backdoor that extends the attack lifecycle across multiple sessions under permission isolation. The attack maintains state through persistent components, enabling autonomous, incremental execution across sessions following a one-time trigger injection. Formally, we model the attack as a Mealy machine and derive a decomposition framework that enables independent per-transition data construction. We instantiate this framework with a primary attack and two extensibility variants. The primary instantiation achieves an attack success rate of 80\%--95\% across four models, with per-transition analysis demonstrating the effectiveness of the decomposition. Extensibility variants with alternative topologies and persistent components demonstrate consistent effectiveness. Code and data are available at https://anonymous.4open.science/r/stateful_agent_backdoor-E89F.

Legal disputes unfold through sequences of filings in which parties update their positions and may settle at any stage. Most computational studies of legal prediction, however, focus on adjudicated outcomes and treat cases as static objects observed only at the end of litigation. Here we develop a temporally structured framework for predicting outcomes in civil litigation using 835,190 court filings between 1996 and 2022. We represent each case as a sequence of documents and model litigation as a three-outcome process: plaintiff win, plaintiff loss, or settlement. Documents are encoded using structured legal features, text embeddings, and information about judges and law firms, and a classifier estimates outcome probabilities at each stage of the case. The model achieves class-specific AUC values between 0.74 and 0.81, and reaches up to 97% accuracy for high-confidence plaintiff-win predictions. To study heterogeneity in predictability, we define case complexity as the entropy of the predicted outcome distribution. Richer factual and relational information improves prediction primarily in low-complexity cases, whereas its marginal contribution declines as complexity increases, suggesting that some disputes remain difficult not because information is missing, but because outcomes are less determinate. Consistent with this interpretation, complexity increases over the course of litigation, indicating that additional filings can amplify uncertainty rather than resolve it. Settlement rates follow an inverted U-shape with respect to complexity, peaking at intermediate levels of predictive uncertainty and declining at both low and high levels of complexity. These findings suggest that predictive uncertainty is not merely model error, but an empirical signal of legal complexity, litigation dynamics, and the conditions under which disputes are resolved through adjudication or settlement.

Josephson scanning tunneling microscopy (JSTM) has emerged as an important technique for probing the superconducting order parameter at the atomic scale. However, the Josephson current in JSTM may behave quite differently when the coupling strength varies. Here, we push the junction to the deep point-contact regime, reaching a normal-state junction resistance of only 0.15 $h/2e^2 \simeq 2~{\rm k}Ω$. We demonstrate, using kagome superconductors, that the zero-bias conductance, a key characteristic of the Josephson current, deviates strongly from the quadratic dependence on the normal-state conductance upon entering the deep point-contact regime. Furthermore, we observe a striking saturation of the zero-bias conductance, which we show arises from the series resistance in the circuit. This also serves as a cautious reminder when interpreting zero-bias conductance saturation or quantization in studies of exotic physics such as that of Majorana zero modes if the tip-sample junction resistance is extremely small. Finally, we identify an optimum regime where JSTM can be used as an atomic-scale probe for studying pair-density wave states in materials with low superconducting transition temperature, such as AV3Sb5 kagome superconductors.

The LCDM model has been presented with a number of cosmic tensions in the face of precision cosmological data, suggesting the presence of a dynamical dark energy component. In this context, we investigate the cosmology arising from a generalisation of Brans-Dicke theory, with a non-minimally coupled scalar field characterising deviations from standard general relativity, and having a non-canonical kinetic term. By reformulating the field equations into an autonomous set of dynamical equations, we use the methods of dynamical systems to investigate the equilibrium states of the system and their stability for a set of widely-used potentials, namely the constant, power-law, and exponential potentials, with the flow visualized using bounded phase portraits. Furthermore, we investigate the physical meaning of the critical points, and we find viable solutions that can reproduce the characteristics of the $Λ$CDM model at background level for each of the three potentials. Furthermore, in each case, we observe that the dynamical behaviour differs noticeably from that observed in other scalar-tensor models due to the non-minimal coupling and non-canonical field, despite using similarly defined dynamical variables.