This study investigates the non-singular bounce within the framework of Myrzakulov-type $f(R,T) = R + αT + βT^2$ gravity by adopting a Chaplygin gas equation of state. We employ two methodologies: a reconstruction scheme via a symmetric scale factor ansatz (Model I) and an autonomous dynamical system analysis (Model II). Our results indicate that the quadratic trace parameter $β$ acts as a primary physical driver; specifically, for $β< 0$, the matter-geometry coupling generates sufficient geometric repulsion to effectively violate the Null Energy Condition (NEC) at high densities without the requirement of exotic matter fields. A numerical scan of the $(β, ρ_0)$ parameter space indicates a critical density threshold required to initiate the bounce, below which the Universe follows a singular General Relativity trajectory. The models are shown to be physically viable, with the effective equation of state asymptotically approaching a de Sitter attractor ($w_{\text{eff}} \to -1$) and the squared speed of sound remaining within the stability and causality bounds ($0 \le c_s^2 \le 1$). This study shows that the $f(R,T)$ framework provides a stable, classically geometric alternative to the Big Bang singularity, consistent with both early-universe requirements and late-time accelerated expansion.

This study proposes an encrypted visual feedback control algorithm for regulating a one-dimensional stage using Ring Learning With Errors (RLWE) encryption. The proposed algorithm performs both feature extraction and controller computations directly on encrypted images, ensuring that sensitive visual data remain protected throughout the entire control process. Furthermore, an image captured by the camera is encrypted into a single ciphertext leveraging the message packing technique of RLWE encryption, thereby reducing computational cost. The effectiveness of the proposed framework is demonstrated through numerical simulations.

Digitalization has transformed modern work by increasing efficiency while also introducing new forms of strain. Technostress (TS) describes subjective, physiological, and behavioral stress responses related to digital technology use. Existing TS research has predominantly focused on neurotypical populations and rarely integrates multiple stress dimensions within a single design. This paper addresses these gaps by proposing a controlled experimental research design that systematically compares neurodivergent and neurotypical individuals under standardized digital stress conditions. The proposed design combines structured and unstructured digital tasks with a multimodal measurement approach covering subjective perceptions, physiological activation, and observable interaction behavior. By integrating neurodiversity into TS research, the paper contributes to a more differentiated understanding of digital stress and provides a methodological approach for more inclusive digital work design.

We investigate the strong decay properties of light unflavored and strange mesons within a relativistic quark-pair-creation (QPC) framework, and compare the results with those obtained in the conventional non-relativistic QPC model. Our analysis shows that, within the present theoretical and experimental uncertainties, the relativistic QPC model yields predictions for strong decay widths of comparable overall quality to those of the non-relativistic QPC model. This indicates that the non-relativistic QPC approach remains adequate for estimating decay widths in most practical applications. Nevertheless, owing to the inclusion of Lorentz boosts and Wigner rotations, the relativistic QPC model exhibits a stronger suppression of decay amplitudes in the high-energy region. This feature may be useful in studies based on unquenched quark models, where the relativistic QPC coupling could lead to more controlled meson-loop effects and mass shifts.

Be stars are rapid rotators generally produced by binary interactions. The single Be stars in the observations pose challenges to the Be star formation theory. In this paper, we propose a new pathway for the formation of single Be stars, in which the Be star is taken as the ejected companion star from a Type Ia supernova (SN Ia) explosion. Recent numerical simulations suggest that explosive oxygen burning, initiated via the convective Urca process in certain helium (He) stars near the Chandrasekhar mass limit, can set off a SN Ia. Based on this proposition, we further demonstrate that about $0.4\%$ of He star + main-sequence (MS) star binaries may evolve into single Be stars, where the MS star is spun up due to the mass accretion from the He star, and then the He star explodes as a SN Ia. We employ detailed binary evolutionary simulations and find the parameter space that would produce single Be stars via the SN Ia channel. Around $22\%$ of Be stars from the SN Ia progenitor channel exhibit peculiar tangential velocities exceeding $24\ \rm km/s$, classifying them as runaway stars. This suggests that the SN Ia channel plays a meaningful role in forming single Be stars, particularly within the runaway star population.

The discovery of materials with tailored properties is increasingly reliant on computational methods. However, the fragmented landscape of existing software often hinders the seamless integration of large-scale structure prediction with rigorous stability validation, particularly in high-performance computing (HPC) environments. To address this gap, we present GEWUM (General Exploration Workflow for the Utopia of Materials), a unified, open-source platform designed to automate and accelerate materials discovery. GEWUM integrates the Selective Random Structure Search (SRSS) strategy with universal Machine Learning Interatomic Potentials (uMLIPs), enabling efficient exploration of vast chemical spaces. Its core architecture features a modular design with native support for SLURM-based HPC clusters. The platform unifies the entire workflow, from random structure generation and diversity-preserving selection to thermodynamic and dynamic stability assessments, as well as advanced property calculations (e.g., elastic constants, thermal conductivity, and quasi-harmonic approximations). We demonstrate GEWUM's capabilities through three distinct case studies: (1) the prediction of low-energy polymorphs in the complex Al-Sc-N nitride system; (2) the identification of a P-62c phase of U3Si5, distinct from the known AlB2 type; and (3) the high-pressure structure prediction of ThH10 at 150 GPa. Furthermore, benchmark tests show reasonable agreement in predicting thermophysical properties. By bridging the gap between uMLIPs and automated high-throughput workflows, GEWUM serves as a valuable framework to facilitate efficient and scalable materials exploration.

AI WiFi offload is emerging as a promising approach for providing large language model (LLM) services to resource-constrained wireless devices. However, unlike conventional edge computing, LLM inference over WiFi must jointly address heterogeneous model capabilities, wireless contention, uncertain task complexity, and semantic correlation among reasoning tasks. In this paper, we investigate LLM inference offloading in a multi-user multi-edge WiFi network, where each task can be executed locally, directly offloaded to a nearby edge access point (AP), or decomposed into multiple subtasks for collaborative execution across local and edge nodes. To this end, we propose a user-edge collaborative framework with an LLM-based planner that not only performs task decomposition but also infers subtask difficulty and expected output token length, enabling more accurate estimation of execution quality and latency on heterogeneous nodes. Based on these estimates, we further design a decomposition-aware scheduling strategy that jointly optimizes subtask assignment, execution, and aggregation under communication, queuing, and computation constraints. Simulation results show that the proposed framework achieves a better latency-accuracy tradeoff than local-only and nearest-edge baselines, reducing the average latency by $20\%$ and improving the overall reward by $80\%$. Moreover, the distilled lightweight planner approaches the performance of the large teacher model while remaining more suitable for practical edge deployment.

Unconventional magnets that combine antiferromagnetic structures with ferromagnetic-like responses are essential for the development of next-generation spintronics. Their emergent properties are fundamentally dictated by the interplay between exchange-driven magnetic geometry and spin-orbit coupling, which are described by spin space group (SSG) and magnetic space group (MSG) frameworks, respectively. However, the lack of direct correspondence between these frameworks, developed in different eras, hinders the systematic tracking of symmetry evolution of these intertwined physical contributions. In this work, we introduce FINDSPINGROUP, a computational architecture that implements the recently emerged, oriented spin space group framework to unify SSG and MSG descriptions. By automating the tracking of symmetry-breaking pathways from the non-relativistic to the relativistic limit, this online platform enables the classification of magnetic phases and the derivation of symmetry-constrained tensors for phenomena such as momentum-dependent spin splitting and the anomalous Hall effect. By standardizing data exchange through the spin crystallographic information file, this architecture establishes a computational infrastructure for the high-throughput discovery and design of unconventional magnets.

Motivated by Sarnak's conjecture on Möbius orthogonality, we investigate the general problem of orthogonality for a bounded sequence to topological models of characteristic classes of measure-preserving automorphisms. Our main observation is that whenever a strong form of such orthogonality holds in a system $(X,T)$ then the orthogonality holds for all topological systems in which each ergodic measure yields an automorphism that is measure-theoretically isomorphic to one arising from an ergodic measure in $(X,T)$. This leads us to study two purely dynamical problems: the existence of universal topological models for characteristic classes of measure-preserving automorphisms and the existence of a common ergodic extension for a measurable family of ergodic automorphisms. We show that the class of automorphisms with relative discrete spectrum over the identity factor--as well as several related classes including the weakly mixing case--admit universal models. We also highlight potential applications to the orthogonality phenomena. Moreover, we show that if the set of all measure-theoretic eigenvalues of a zero entropy system $(X,T)$ is countable, then $(X,T)$ satisfies Sarnak's conjecture along a subsequence of full logarithmic density.

Black-hole accretion systems exhibit a characteristic coexistence of activities: broad-band X-ray variability, hot coronae, wide-angle winds, and both steady and discrete jets. This coexistence suggests a persistently time-dependent magnetic background in which noisy fluctuations and explosive release are both essential. In this paper, we connect them all to intermittent magnetic reconnection and propose a Synchronized Spin Model (SSM) in which multiple local dynamos in a rotating accretion flow are represented as interacting macro-spins. Their synchronization, partial synchronization, excursion, and reversal define a compact set of collective variables that organize both timing statistics and large-scale morphology. In this picture, multiscale magnetic reconnection sustains coronal heating, flares, intermittent outflows, and discrete jet activity, while the same synchronization dynamics produce amplitude modulation and demodulation, providing a route to $1/f$-like variability, rms--flux/Taylor-like scaling, and approximately log-normal statistics of the demodulated envelope. We further argue that, although the continuous flux distribution in black-hole systems is more naturally discussed in multiplicative or log-normal terms, broader event-catalog statistics remain useful for describing suitably defined burst hierarchies, particularly by analogy with solar and stellar flare systems. The hard/soft cycle of X-ray binaries is then interpreted as motion through magnetic state space.

We study existence and uniqueness for one-dimensional generalized stochastic differential equations with singular coefficients, including distributional drift and degenerate, possibly discontinuous, diffusion coefficients. Such singularities naturally encode changes in the dynamics at thresholds, including reflecting, skew, or sticky interface behavior. We develop two directions. We provide sufficient conditions for pathwise uniqueness, under weak existence and uniqueness in law, without assuming uniform ellipticity or continuity of the diffusion coefficient. We also investigate a pasting approach for generalized stochastic differential equations that transfers strong existence and pathwise uniqueness, as well as weak existence and uniqueness in law, from local component equations to a global solution. To the best of our knowledge, this provides the first explicit pasting theorem yielding pathwise uniqueness in the setting of generalized stochastic differential equations. As an application, we establish the first existence and uniqueness results for a class of skew sticky threshold Cox-Ingersoll-Ross-type diffusions, including the threshold Chan-Karolyi-Longstaff-Sanders process.

High-precision optical phase stabilization in quantum networks is fundamentally constrained by the strict photon-flux and duty-cycle limits required to avoid disturbing fragile quantum states. This challenge becomes especially critical when coordinating multiple independent light sources for multi-step quantum protocols. Here, we develop an integrated phase-stabilization framework that incorporates a Bayesian phase estimator to optimally extract information from sparse single-photon detection events. This approach outperforms conventional maximum-likelihood estimation and achieves the shot-noise limit under minimal photon flux. The framework enables real-time correction of combined phase noise from both nodal lasers and transmission fibers, facilitating a two-step excitation protocol for heralded entanglement generation between separate trapped-ion nodes via single-photon interference. Operating with a detected photon rate of approximately 1 MHz and a duty cycle less than or equal to 6.5%, the system maintains interferometric visibility greater than 97% over fiber links of 10 km and 100 km. This phase control yields deterministic ion-ion entanglement with parity contrast exceeding 85% at both distances, enabling device-independent quantum key distribution. Moreover, the resulting memory-memory entanglement at 10 km survives beyond the average time required to establish it -- a fundamental requirement for quantum repeaters. This work establishes a robust and scalable foundation for practical long-distance quantum networks.

As closed-loop materials discovery systems scale to produce millions of candidate compounds, the credibility of the novelty they reward becomes a critical concern. Novelty is commonly assessed against databases of ordered crystal structures, in which atomic sites are fully occupied. Yet, a predicted ordered structure may simply correspond to a particular ordering of a known disordered phase, whose sites are occupied by multiple species in the statistical average structure; we refer to such a structure as an ordered child of a disordered parent. Here, we introduce order-(dis)order family trees, a symmetry-based framework that organizes ordered and disordered structures through group-subgroup relations and enables novelty to be explicitly evaluated. We develop a high-throughput family matching procedure, to identify possible disordered parents and symmetry-related ordered relatives for a given ordered structure. As validation, we test our framework on synthesis-facing case studies (A-Lab), where it correctly recovers existing disordered parents for the targeted ordered structures. Extending this family-tree-based benchmark to experimental structure databases (ICSD), computational datasets (MP-20, Alex-MP-20, and GNoME), and crystal generative models further reveals that many ordered structures that appear novel as individual entries are, in fact, better understood as members of experimentally known order-(dis)order family trees. We also show that this is particularly evident in symmetry-agnostic all-atom generative models, which more frequently produce ordered structures derived from known disordered parents, whereas symmetry-constrained models are 2-4x less prone to this behavior. Our results establish order-(dis)order family trees as a key requirement for achieving genuine novelty in data-driven materials discovery.

The estimation of stellar atmospheric parameters for large-scale samples, particularly metal-poor stars, is a cornerstone of Galactic archaeology. In this work, we optimized a photometric filter design tailored to measuring stellar metallicities for very metal-poor stars with [Fe/H]$< -1$.The optimal configurations consist of a central wavelength $λ_{\rm c}$ = 3960 Angstrom with a bandwidth $Δλ$ = 80 Angstrom for giant stars, and $λ_{\rm c} $= 3920 Angstrom with $Δλ$ = 80 Angstrom for dwarf stars. By applying these optimized filters to synthetic photometry derived from Gaia XP spectra, we inferred metallicities for both populations. Both internal and external validations demonstrate high precision across a wide metallicity range: 0.18-0.19 dex for $-2 \le \rm [Fe/H] \le -1$, 0.23-0.33 dex for $-3 \le \rm [Fe/H] \le -2$, and approximately 0.39 dex for the most metal-poor regime, successfully extending down to $\rm [Fe/H] \approx -4$ for giant stars, $\rm [Fe/H] \approx -3.3$ for dwarf stars. Finally, we present a catalog of approximately 14.5 million metal-poor stars with robust $\rm [Fe/H]$ measurements, along with more than ten thousand red giant ultra metal-poor candidates with $\rm [Fe/H] < -4.0$, providing a valuable resource for exploring the early formation and chemical evolution of the Milky Way.

Dynamic room acoustic simulation aims to render the acoustic effects of an environment in real time while accounting for potentially moving sources and receivers. In this context, the efficient synthesis of the long-term room response, also known as late reverberation, remains challenging because of the intricate relationship between room geometry and acoustic behavior. This paper introduces Taylor-SWFT, an efficient implementation of key results from Statistical Wave Field Theory (SWFT) for the geometry-aware dynamic synthesis of late reverberation. The method is evaluated on the Benchmark for Room Acoustical Simulation (BRAS) and achieves competitive performance compared with classical approaches, while substantially reducing computational cost.

Distributed stochastic optimization enables multi-agent collaboration in applications such as distributed learning and sensor networks, but also raises critical privacy concerns due to the involvement of sensitive data. While existing privacy-preserving approaches often face limitations in balancing accuracy with efficiency, we propose a novel distributed stochastic gradient descent algorithm that integrates Paillier homomorphic encryption with heterogeneous and time-varying random stepsizes. The proposed algorithm provides inherent privacy protection against both internal honest-but-curious agents and external eavesdroppers, without relying on any trusted neighbors. Furthermore, we incorporate an attenuation factor to effectively mitigate quantization error induced by the encryption process, ensuring almost sure convergence to the optimal solution while maintaining privacy preservation. Numerical simulations demonstrate the effectiveness and efficiency of the proposed approach.

We investigate dense-matter equations of state (EOSs) within a Bayesian framework, with particular emphasis on whether recent small-radius compact-star candidates can be accommodated in a twin-star scenario. For the hadronic sector, we adopt a meta-modeling EOS constrained by the NICER mass--radius measurements of PSR J0030$+$0451, PSR J0437$-$4715, PSR J0614$-$3329, and the massive pulsar PSR J0740$+$6620. The hadronic inference indicates that PSR J0614$-$3329 favors a somewhat softer EOS than the other two \(\sim1.4\,M_\odot\) pulsars, while the \(\sim2\,M_\odot\) constraint prevents the EOS from becoming too soft. We then introduce a strong first-order phase transition through a constant-speed-of-sound quark-matter segment. Using HESS J1731$-$347 and XTE J1814$-$338 to constrain the phase-transition parameters, we find a preferred transition density of \(n_\mathrm{t}\sim2.7\text{--}2.8\,n_0\), a sizable energy-density jump of \(600\text{--}700\) MeV, and a relatively large post-transition sound speed of \(c_s^2/c^2\sim0.85\). Such a phase transition generates a disconnected hybrid branch with radii of about \(6\text{--}7\) km at masses around \(1.2\text{--}1.4\,M_\odot\), and strongly suppresses the dimensionless tidal deformability relative to the purely hadronic branch. This pronounced change in tidal deformability is a characteristic signature of the twin-star mechanism and may provide an important observational tool for identifying phase transitions in neutron-star matter in future multimessenger measurements. These results show that small-radius compact stars can provide direct constraints on both the strength of a first-order phase transition and the stiffness of the post-transition phase in dense matter.

Extended finite state machines (EFSMs) model stateful systems with internal data variables and have numerous applications in software engineering. A major advantage of this type of model lies in its ability to model both the data flow and the data-dependent control behaviour. In the absence of such models, it is desirable to reverse-engineer them by observing the system's behaviour. However, existing approaches generally require the ability to reset the system during inference, or can only handle situations where the control flow depends exclusively on the input parameters, and not on the values of the stored data. In this work, we present a black-box active learning algorithm that infers EFSMs with guards and registers, and which significantly relaxes the assumptions that have to be made about the system in comparison to previous attempts.

We present a formal proof of the Sands-Sauer-Woodrow (SSW) theorem using the Rocq proof assistant and the MathComp/SSReflect library. The SSW theorem states that in a directed graph whose edges are colored with two colors and that contains no monochromatic infinite outward path, there exists an independent set S of vertices such that every vertex outside S can reach S by a monochromatic path. We formalize the graph using two binary relations Eb and Er , representing the blue and red edges respectively, and we develop a dedicated library for binary relations represented as classical sets. Beyond formalizing the original SSW theorem, we establish a strictly stronger version in which the assumption ''no monochromatic infinite outward path'' is replaced by the weaker condition that the asymmetric parts of the transitive closures of Eb and Er admit no infinite outward paths. The original SSW theorem is then recovered as a corollary via a lemma showing that an infinite path for the asymmetric part of the transitive closure of a relation implies an infinite path for the relation.

We show in this article the improvements which can be obtained in the description of the luminescence properties of Pr3+ doped materials by using an extension of the Judd-Ofelt theory in order to relax some strong selection rules and approximations of the standard formalism and to better account for the influence of the 4f5d excited electronic configuration. The demonstration is made by re-examining the case of Pr3+:YAG, a well known luminescent and laser crystal with a very low energy 4f5d absorption band. Our extension thus provides a better agreement between calculated and measured absorption intensities, especially for the hypersensitive 3 H4 $\rightarrow$ 3 P2 transition. A comparison is made with the results obtained in the case of Pr3+:ZBLAN, a laser fluoride glass with much higher 4f5d absorption levels. Our investigation also gives the opportunity, in the case of Pr3+:YAG, to provide more complete and more reliable absorption and emission data than reported in the past literature and to exploit these data to better address the question of laser operation at various emission wavelengths. It is thus demonstrated that laser operation should be possible with improved laser performance at 488 nm, 616 nm and 744 nm, as it was already achieved in the past, but also at 566 nm and 931 nm by using appropriate laser cavities and laser mirrors.

Parametric insurance contracts translate index measurements to compensation for policyholders' losses using predefined payment schemes. These need to be designed carefully to keep basis risk, i.e. the disparity between payouts and true damages, small. Previous research has motivated the use of conditional expectiles as payment schemes, whose compensation is impacted by the policyholder's potentially unknown attitude towards basis risk. To alleviate this model uncertainty and to investigate the impact of (hidden) influencing factors, we characterize existence and uniqueness of the optimal basis risk weighting in a utility-maximization framework through a set of boundary conditions. In the absence of an optimal solution, we provide comparisons to the utility of no insurance and full indemnity coverage. We establish a link between location-scale distributions and separability of conditional expectiles' derivatives, thus improving the understanding of these statistical functionals. A simulation study on parametric hurricane insurance visualizes our results, investigates the influence of premium loading and risk aversion on the optimal weighting, and comments on the challenge of (spatial) loss dependence.

This paper considers constrained stochastic nonsmooth minimax optimization problem of the form $\min_{\mathbf{x}\in\mathcal{X}}\max_{\mathbf{y}\in\mathcal{Y}}f\left(\mathbf{x},\mathbf{y}\right)=\mathbb{E}[F(\mathbf{x},\mathbf{y};\mathbfξ)]$, where the objective $f(\mathbf{x},\mathbf{y})$ is concave in $\mathbf{y}$ but possibly nonconvex in $\mathbf{x}$, the stochastic component $F(\mathbf{x},\mathbf{y};\mathbfξ)$ indexed by random variable $\mathbfξ$ is mean-squared Lipschitz continuous, and the feasible sets $\mathcal X$ and $\mathcal Y$ are convex and compact. We introduce the notion of $(η_x,η_y,δ,ε)$-Goldstein saddle stationary point (GSSP) to characterize the convergence for solving constrained nonsmooth minimax problems. We then develop projected gradient-free descent ascent methods for finding $(η_x,η_y,δ,ε)$-GSSPs of the objective function $f(\mathbf{x},\mathbf{y})$ with non-asymptotic convergence rates. We further propose nested-loop projected gradient-free descent ascent methods to establish the non-asymptotic convergence for finding $(η,δ,ε)$-generalized Goldstein stationary points (GGSP) [Liu et al., 2024] of the primal function $Φ(\mathbf{x})\triangleq\max_{\mathbf{y}\in\mathcal{Y}}{f}\left(\mathbf{x},\mathbf{y}\right)$. It is worth noting that our algorithm designs and theoretical analyses do not require additional assumptions such as the weak convexity used in prior works on nonsmooth minimax optimization [Lin et al., 2025, Boţ and Böhm, 2023].

Zeroth-order (ZO) optimization is indispensable for complex non-convex tasks where explicit gradients are computationally prohibitive or strictly inaccessible. For deploying ZO methods over distributed heterogeneous networks, the gradient tracking technique is often employed to eliminate structural data biases. However, the inherent variance of derivative-free estimators is also amplified. To overcome this problem, we propose Zeroth-Order Momentum Gradient Tracking (ZO-MGT), which integrates momentum-based variance reduction with dynamic gradient tracking. Specifically, ZO-MGT that requires exactly two function queries per iteration can avoid costly batch sampling and prevent variance explosion, while eliminating structural biases. Moreover, by utilizing Rademacher perturbations, it preserves optimal query efficiency and enables bitwise hardware acceleration. We theoretically analyze the convergence of ZO-MGT and establish an $\mathcal{O}(1/T)$ convergence rate. Furthermore, we prove that a large momentum factor can aggressively suppress the heterogeneity-induced bias floor at a remarkable quadratic rate of $\mathcal{O}((1-β)^2)$. Numerical experiments under extreme data heterogeneity verify that ZO-MGT can effectively overcome traditional tracking failures with accelerated convergence guarantees, while achieving significantly tighter consensus.

Let $X$ be a smooth complex projective curve. We prove that there exists a surjective commutative forgetful diagram from the chain of $\mathbb{C}^{*}$-flips of the moduli spaces of $\mathcal{O}_{X}$-twisted rank 2 constrained framed Hitchin pairs on $X$ to the chain of $\mathbb{C}^{*}$-flips of the moduli spaces of rank 2 framed modules on $X$.

We study some geometric properties of the excursion set of a slope field alpha associated to a smooth, planar, centered, Gaussian field f. That, is we consider the set of all points such that the value of alpha is at most l where l is a real parameter called the level. We restrict our attention to the levels l that are supercritical. We show that for almost such l, in the sense of the Lebesgue measure, then with high probability the chemical distance between two points connected in the excursion set at level l is comparable to the usual Euclidean distance between those two points. This result is in the spirit of the Antal Pisztora theorem for Bernoulli percolation. However, many new difficulties arise such as the fact that alpha is a continuous field (not differentiable everywhere) with long range correlations and whose law is still not well understood.

We develop a Markovian traffic equilibrium model for ride-hailing in which vehicles, whether empty or hired, make sequential order-acceptance and link-choice decisions over a traffic network to maximize total discounted return in an infinite-horizon semi-Markov decision process. The model endogenizes both competition among empty vehicles for passenger demand and traffic congestion arising from road usage at the link level. We characterize equilibrium as the solution to a fixed-point system, establish its existence, and develop relaxed fixed-point iteration algorithms for equilibrium computation, with convergence results for specialized network structures. Computational experiments on realistic networks demonstrate the model's practical value for transportation planning. Ablation analyses reveal that ignoring either traffic congestion or drivers' forward-looking behavior can lead to potentially substantial biases in policy evaluation.

Let Y be a compact Riemann surface, phi:Y -> CP^1 a meromorphic function, and Gamma in Y a ribbon graph avoiding the critical points of phi. Then phi(Gamma) is an immersed graph in CP^1. Conversely, given an immersion im:Theta to bCP^1 of an abstract multigraph Theta without vertices of valence 1 or 2, we describe a construction of a compact Riemann surface Y and a meromorphic function phi_{im}:Y in CP^1 such that phi_{im}(Gamma)=im(Theta). We investigate the relation between the topology of Y and the combinatorics of Gamma. In particular, for a surface of genus g we construct spanning ribbon graphs whose underlying abstract graphs have arbitrary prescribed graph genus g' smaller or equal g, including the planar case. As a consequence, the number of self-intersections of ϕ(Gamma) cannot, in general, be controlled solely by the genus of Y. We establish general lower bounds for the number of self-intersections and formulate several open problems, with emphasis on planar ribbon graphs.

Formation of nonequilibrium counterparts of supersolids, simultaneously characterized with spontaneous superfluid and crystalline order, was recently reported in incoherently pumped polariton condensates. We investigate collective excitation spectra of this phase and explicitly demonstrate the emergence of gapless Nambu-Goldstone modes due to spontaneously broken continuous phase and translation symmetries. For the recent implementation of the polariton nonequilibrium supersolidity in semiconductor metasurfaces [D. Trypogeorgos et al., Nature 639, 337 (2025)], we demonstrate the key role of attractive polariton interactions, mediated by the excitonic reservoir, for stability of the supersolid phase. Performing a thorough numerical investigation, we identify the conditions for existence of the diagonal and off-diagonal long-range order in negative-mass nonequilibrium supersolids.

Magnetic quantum sensors based on trapped ions utilize properties of quantum mechanics which have optimized precision and beat current limits in sensor technology. Trapped ions are highly sensitive in a large span of signal ranging from DC or static B-field to the radiofrequency range in 100s of MHz and can attain the sensitivity in the range of pT to sub pT . They are tuneable to frequencies of interest and can be used as a lock-in frequency detector. This modelling and simulation based study presents an innovative design of Surface Paul Traps, enabling the use of trapped ions as ultra-sensitive sensors for magnetic field detection and precise measurement of magnetic field gradients at a sub-millimeter spatial resolution. The novel design features multiple trapping regions, allowing for the mapping of magnetic fields across various ion-trapping zones. The study demonstrates groundbreaking advancements in ion manipulation and confinement through innovative chip architecture.

We present a Monte Carlo study of the fractal geometry of clusters formed by discrete-time simple random walks (sRW) of $L^2$ steps on a periodic square $L\times L$ lattice. We verify with high precision that the asymptotic behavior of the cluster mass follows $M/L^2 \simeq (\ln L)^{-1} [\fracπ{2}+b (\ln L)^{-2}]$, with $b\approx -(π/2)^{-2}$, demonstrating marginal ``logarithmic fractals". We further determine the fractal dimension of the hull to be $d_{\rm hull}=1.333\,29(14)=4/3$, in excellent agreement with the prediction of Schramm-Loewner evolution ($\rm SLE_{8/3}$) for the Brownian frontier universality class. More importantly, we analyze the chemical distance $S$ spanning the cluster and obtain strong evidence that it asymptotically scales as $S\sim L(\ln L)^{1/4}$, lying exactly on the theoretical upper bound for the chemical distance for level-set percolation clusters on the two-dimensional Gaussian free field. Our numerical results show that the sRW cluster exhibits a conformally invariant external frontier and contains highly efficient asymptotically linear connective paths.