We show that for every positive integer ${t \geq 2}$ there exists an integer $s$ such that every graph that contains no induced subgraph isomorphic to either the $6$-vertex path or the $(2,t)$-biclique, the complete bipartite graph $K_{2,t}$, has tree-independence number at most $s$. This result makes partial progress on a conjecture of Dallard, Krnc, Kwon, Milanič, Munaro, Štorgel, and Wiederrecht.

We are concerned with solvability of nonlinear systems involving a discrete singular $ϕ$-Laplacian operator of type \begin{equation*} u \mapsto Δ\left[ϕ(Δu(n-1))\right] \qquad (n\in \{1, \dots, T\}), \end{equation*} associated with a general two point boundary condition having the form \begin{equation*} \left(ϕ(Δu(0)),-ϕ(Δu(T))\right)\inγ(u(0),u(T+1)), \end{equation*} where $γ:\mathbb{R}^N\times\mathbb{R}^N\to2^{\mathbb{R}^N\times\mathbb{R}^N}$ is a maximal monotone operator with $0_{\mathbb{R}^N \times \mathbb{R}^N}\in γ(0_{\mathbb{R}^N \times \mathbb{R}^N})$. The mapping $ϕ$ is a potential homeomorphism from an open ball of radius $a$ centered at the origin $B_a \subset \mathbb{R}^N$ onto $\mathbb{R}^N$ and $Δ$ stands for the usual forward difference operator. When the perturbing nonlinearity in the system has not a potential structure we obtain existence of solutions by a priori estimates. Also, when the nonlinearity is of gradient type and $γ$ is a subdifferential, we provide a variational approach of the system in the frame of critical point theory for convex, lower semicontinuous perturbations of $C^1$-functionals. Then we derive the existence of solutions either as minimizers or saddle points of the corresponding energy functional.

In this kick-off presentation for the "Recent developments in QCD" session at Baryons 2025 I will tie together the recent progress made on the extraction of parton distribution functions (PDFs) in lattice QCD and the long standing efforts in solving the inverse problem in the form of spectral function reconstruction.

Let $(L, v_L) / (K, v_K)$ be a finite or purely transcendental extension of real valued fields. We construct the associated integral cotangent and log cotangent complexes in terms of a MacLane-Vaquié chain approximating $v_L$. This leads to explicit formulas for associated invariants such as the (absolute) (log) different, weight norm and Kähler norm. As a corollary of our methods we obtain strong control of the higher homology of the integral (log) cotangent complex, generalizing an important result of Gabber and Ramero to the logarithmic setting.

Background and Objective: Accurate surrogate modeling of knee joint contact mechanics is important for reconstructing stress distributions and identifying risk-relevant regions, yet the relative suitability of different modeling paradigms under practically relevant input-limited conditions remains unclear. Methods: Nine male soccer players performed 90° change-of-direction trials. Finite element simulations driven by subject-specific joint posture and reaction forces were converted into graph-structured samples. Five surrogate architectures representing local diffusion, history-context enhancement, hierarchical multi-scale modeling, explicit global interaction, and local-global hybridization were compared using three-fold cross-subject validation under full, pose-corrupted, load-corrupted, and minimal-input conditions. Performance was evaluated using full-field error, high-stress error, high-risk region overlap, and hotspot localization metrics. Results: The hybrid model achieved the best overall performance under full inputs and remained the most robust under pose- and load-corrupted conditions. Under minimal inputs, no single model dominated all metrics: the history-context model yielded lower overall and high-stress errors, the hybrid model better preserved high-risk region reconstruction, and the hierarchical model showed an advantage in hotspot localization. Conclusion: Evaluation of surrogate models for knee joint contact mechanics should shift from accuracy comparisons under ideal inputs to a comprehensive assessment of the preservation of risk-relevant information under realistic input constraints. Although the local-global hybrid model showed the best overall robustness, the optimal model under minimal-input conditions remained task-dependent.

Recent measurements of the $t\bar{t}$ cross section, performed both inclusively and differentially by the ATLAS and CMS Collaborations, are reported. In particular, off-shell effects are probed in the $pp\to W^+bW^-\bar{b}$ and $pp\to e^\pmμ^\mp +b\bar{b}$ processes, and modelling aspects of the POWHEG bb4$\ell$ Monte Carlo generator are discussed. Cross section and properties measurements are also performed at the threshold: we review an indirect extraction of the top quark Yukawa coupling, as well as the recent observations by both experiments of an excess of events near the top pair production threshold that is consistent with the formation of quasi-bound states.

We present a large-scale experimental study of quantum-computing-based molecular simulation carried out on IQM's Sirius 24-qubit superconducting processor, utilizing up to 16 operational qubits. The work employs Sample-based Quantum Diagonalization (SQD) together with the Local Unitary Cluster Jastrow (LUCJ) ansatz to estimate ground-state energies for a set of benchmark molecules, including H$_2$, LiH, BeH$_2$, H$_2$O, and NH$_3$. In addition, we introduce a Linear-CNOT variant of the Unitary Coupled-Cluster Singles and Doubles (LCNot-UCCSD) ansatz within the SQD workflow, trading higher circuit depth for reduced classical preprocessing. A comparison between these ansätze is provided, clarifying their respective strengths, limitations, and suitability for near-term quantum hardware. We further explore potential energy landscapes through 1D scans for H$_2$ and HeH$^+$ using both STO-3G and 6-31G basis sets, and for LiH and BeH$_2$ in STO-3G. Extending beyond this, we demonstrate the experimental construction of a full 2D potential energy surface for the water molecule on quantum hardware, mapped over a 32 $\times$ 32 grid in bond length and bond angle. To move beyond small benchmark systems, we combine SQD(LUCJ) with Density Matrix Embedding Theory (DMET) to compute active-space energies for a set of ligand-like molecules, as well as the pharmacologically relevant amantadine system. Across all studies, the majority of quantum-computed energies agree with reference FCI results, as well as with DMET-CASCI energies for embedded systems, to within chemical accuracy for the chosen basis sets. These results demonstrate the reliability of sample-based diagonalization approaches and underscore the potential of hybrid embedding strategies for extending quantum simulations to increasingly complex molecular systems, while also highlighting their practicality on current IQM quantum hardware.

The curve shortening flow is a geometric heat equation for curves and provides an accessible setting to illustrate many important concepts from nonlinear partial differential equations, including maximum principle estimates, monotonicity formulas, Harnack inequalities and blowup analysis. All these techniques will be combined to give an exposition of Huisken's proof of Grayson's beautiful theorem that the curve shortening flow shrinks any closed embedded curve in the plane to a round point.

Recently, the Dark Energy Spectroscopic Instrument (DESI) collaboration has presented results indicating that dark energy may exhibit dynamical behavior. Calibrated gamma-ray burst (GRB) correlations can be employed to verify or reject a time-evolution of the dark energy (DE) equation of state, $ω(z)$, up to redshifts $z\sim 9$. We use the most updated catalog of GRBs fulfilling the Combo correlation and improve its calibration employing three catalogs of type Ia supernovae at redshifts $z\leq0.075$ and the Bézier interpolation of the Hubble rate, as an alternative to the cosmographic series that fails to be constraining at high redshifts. To test the evolution of $ω(z)$, we adopt a model-independent, redshift-binned DE parametrization. In both the calibration and the DE reconstruction analyses the impact of the spatial curvature on the results is explored. The calibrated Combo correlation yields a Hubble constant $H_0\sim70$ km/s/Mpc which alleviates the existing Hubble tension and is broadly consistent with current measurements, although the uncertainties prevent a high-precision measurement. Regarding the reconstruction of $ω(z)$ of DE, spatially curved scenarios are disfavored and, despite the apparent ''phantom'' behavior at $z\lesssim0.55$ due to the limited statistics caused by the shortage of nearby events, at $z>0.55$ the analysis provides statistically robust evidence in favor of the cosmological constant scenario. The Combo correlation alleviates the Hubble tension and shows no significant evidence in favor of dynamical DE. This suggests that GRBs, as distance indicators, are broadly consistent with the current cosmic distance ladder.

In the present work we revisit the problem of the dark solitary wave pinned in the discrete nonlinear Schr{ö}dinger equation. In a number of recent studies, the methodology of exponential asymptotics was attempted to be utilized in this problem, however the results were not found to be fully in agreement with associated multiprecision numerical computations. Here we resolve this conundrum by finding precise exponential asymptotics for the pinned dark solitary waves. Moreover, we reconcile the relevant result with a general theory of pinned dark solitary waves in the {\it continuum} nonlinear Schr{ö}dinger equations in the presence of external potentials.

We discuss solutions of the one dimensional scalar conservation law with the flux function $y\longmapsto G_{c,ρ}\left(y\right)=((1-ρ)c-y)\mathbb{1}_{\{y>c\}}-ρy\mathbb{1}_{\{y\leqslant c\}}$ for two specific initial conditions $u(\cdot,0)=u_0$. This equation arises as the limit of a specific conceptual hydrological model. For initial data strictly below (resp. above) the threshold level $c$, the equation reduces to a constant-speed transport equation with velocity $p$ (resp. $1$). Our goal is to understand precisely what happens when the initial condition crosses the threshold $c$, which corresponds to a generalisation of the Riemann problem, and to provide, in such cases, quasi-closed-form expressions for the corresponding solutions.

The study of highly charged ions offers a unique platform for probing the breakdown of non-relativistic theory under the influence of extreme electromagnetic environments. Here, we investigate the photoabsorption of highly charged ions within the dipole approximation using both the time-dependent Schrödinger equation (TDSE) and the time-dependent Dirac equation (TDDE), modelling the external field as an instantaneous broadband excitation. Nonrelativistic scaling relations with respect to the nuclear charge are utilized as a diagnostic tool to systematically identify and quantify relativistic contributions. Within the purely nonrelativistic TDSE framework, these scaling relations hold exactly, allowing the absorption spectra of arbitrary highly charged ions to be inferred directly from a neutral hydrogenic reference. However, as the nuclear charge increases, relativistic effects become dominant through a sizeable blue shift in the absorption cross section, due to the relativistic enhancement of the binding energy. We further evaluate semi-relativistic TDSE approximations by direct comparison with full TDDE simulations, assessing their predictive power and establishing the regimes where a full Dirac treatment is indispensable for quantitative accuracy.

Let $G$ be a linear semisimple Lie group without compact factors. We show that uniform approximate lattices $Λ$ arising as regular model sets in $G$ determine the ambient group $G$ in a strong sense. Specifically, for every non-compact Cartan subgroup $C$ of $G$, there exists $g \in G$ such that the intersection $gCg^{-1} \cap Λ^2$ is non-empty and itself forms a uniform approximate lattice, extending a classical result of Mostow for lattices. The proof relies on a Moore-type ergodicity theorem for the hull of a strong approximate lattice, proved here as a key tool. Moreover, we prove that such approximate lattices determine the $\mathbb{R}$-rank of the ambient group $G$, drawing on ideas from the work of Prasad and Raghunathan on lattices.

Urban populations exhibit fractal organization and systematic scaling regularities, yet the scaling exponents reported across cities vary substantially, challenging existing theory. Using 100~m gridded population maps for 477 urban areas spanning the Netherlands (2000--2023) and major world cities (1975--2020), we recursively coarse-grain each city and quantify how the mean and variance of inhabitants in square grid cells of side length $\ell$ scale with $\ell$. This yields two exponents, $β$ from $\langle N_\ell\rangle\sim \ell^β$ and $γ$ from $\mathrm{Var}(N_\ell)\sim \ell^γ$, where in the small-$\ell$ limit $β$ equals the planar fractal dimension of populated space. Across cities within a given year, $γ$ depends linearly on $β$. Compiling $>$10,000 exponent estimates over five decades shows that this hyperscaling relation is robust yet non-universal: its slope and intercept vary across continents and drift systematically in time, trending toward the limiting form $γ\simeq 2+β$. A mean-field (independent-cell) argument predicts a quadratic mean--variance mapping and cannot reproduce the observed $β$--$γ$ dependence, implying strong spatial correlations. We derive a correlation-aware variance decomposition in which $γ$ is controlled by a correlation dimension $D_c$; in the correlation-dominated regime $γ=2+D_c$. If large maturing cities, as are the ones selected in our dataset, evolve to effective monofractal ($D_c\simeq β$) cities, the asymptotic prediction becomes $γ\simeq 2+β$, consistent with the observed temporal drift. This interdependence links urban form and fluctuations, constrains mechanistic growth models, and implies scaling predictions for spatial indicators built from local means and variances.

The choice between conservative and non-conservative formulations is a fundamental dilemma in CFD. While non-conservative forms offer intuitive modeling in primitive variables, they typically produce erroneous shock speeds. This paper critically analyzes these formulations, contrasting classical failures against the capabilities of Physics-Informed Neural Networks (PINNs). Using the Adaptive Weight and Viscosity (PINNs-AWV) architecture, we evaluate cases ranging from shallow water equations to unsteady 1D and 2D Euler equations. Results reveal a significant dichotomy: while PINNs-AWV restores physical fidelity in scalar and steady systems, standard non-conservative PINNs fail in unsteady systems like the Sod shock tube. We demonstrate this failure stems from non-vanishing source terms introduced by viscous regularization, which violate the Rankine--Hugoniot jump conditions. To resolve this, we implement a path-integral framework based on Dal Maso--LeFloch--Murat (DLM) theory. By incorporating path-consistent losses in PINNs (PI-PINN) and using path-conservative numerical schemes, we successfully recover correct shock speeds within non-conservative frameworks. Our results prove the path-integral approach provides a rigorous mathematical bridge for physical accuracy in both classical and machine learning solvers, enabling primitive-variable formulations in transient, high-speed simulations.

Modern analytical workloads increasingly combine relational data with array-valued attributes. While columnar database systems efficiently process such workloads, their ability to optimize queries that interleave relational operators with array manipulations remains limited. This paper introduces A3D-RA, an extended relational algebra supporting array-valued attributes, together with a comprehensive framework for algebraic reasoning and optimization. We formalize its data model and semantics, develop a complete set of equivalence-preserving transformation rules capturing pairwise interactions between relational and array operators, and propose a plan enumeration strategy with an optimality guarantee that remains polynomial in all non-join operators. We design A3D-RA as a modular, backend-independent optimization layer that can be instantiated over existing analytical database systems. Experimental results across three high-performance engines on a real-world workload show consistent performance gains enabled by the proposed algebraic optimization layer.

This paper addresses the design of an impulsive controller for a continuous scalar time-invariant linear plant that constitutes the simplest conceivable model of chemical kinetics. The model is ubiquitous in process control as well as pharmacometrics and readily generalizes to systems of Wiener structure. Given the impulsive nature of the feedback, the control problem formulation is particularly suited to discrete dosing applications in engineering and medicine, where both doses and inter-dose intervals are manipulated. Since the feedback controller acts at discrete time instants and employs both amplitude and frequency modulation, whereas the plant is continuous, the closed-loop system exhibits hybrid dynamics featuring complex nonlinear phenomena. The problem of confining the plant output to a predefined corridor of values is considered. The method at the heart of the proposed approach is to design a stable periodic solution, called a 1-cycle, whose one-dimensional orbit coincides with the predefined corridor. Conditions ensuring local and global attractivity of the 1-cycle are established. As a numerical illustration of the proposed approach, the problem of intravenous paracetamol dosing is considered.

We present a receding-horizon optimal control for nonlinear continuous-time systems subject to state constraints. The cost is a quadratic finite-horizon integral. The key enabling technique is a new constrained approximate dynamic programming (C-ADP) approach for finite-horizon nonlinear optimal control with constraints that are affine in the control. The C-ADP approach is intuitive because it uses a quadratic approximation of the cost-to-go function at each backward step. This method yields a sequence of analytic closed-form optimal control functions, which have identical structure and where parameters are obtained from 2 Riccati-like difference equations. This C-ADP method is well suited for real-time implementation. Thus, we use the C-ADP approach in combination with control barrier functions to obtain a continuous-time receding-horizon optimal control that is farsighted in the sense that it optimizes the integral cost subject to state constraints along the entire prediction horizon. Lastly, receding-horizon C-ADP control is demonstrated in simulation of a nonholonomic ground robot subject to velocity and no-collision constraints. We compare performance with 3 other approaches.

Cloud infrastructure supports the efficient operation of data pipelines regarding requirements like cost, speed, and resource utilization. We present an integrated view of optimization opportunities for cloud-based data pipelines by conducting a systematic review of existing literature on optimization approaches to cloud infrastructure performance for data pipelines. Our study contributes a theory of optimization goals like minimizing cost, reducing execution time, and cost-makespan trade-offs, consisting of dimensions such as single vs. multi-cloud, batch vs. stream processing, etc. We highlight gaps in primary research, including the underexploration of multi-tenant environments and lack of industry evaluation, and suggest directions for future research.

The fast frequency support (FFS) towards frequency trajectory optimization provides a system view for the frequency regulation of wind farms (WFs). However, the existing frequency trajectory optimization-based FFS generally relies on the accurate governor dynamics model of synchronous generators (SGs), which aggrandizes the difficulty of controller implementation. In this paper, a proportional-integral (PI) based FFS of WFs is designed for tracking the optimal frequency trajectory, which gets rid of the dependence on the governor model. Firstly, the prototypical PI-based FFS of WFs is proposed and its feasibility for tracking the optimal frequency trajectory is analyzed and demonstrated. Then, based on the "frequency-RoCoF" form of the optimal frequency trajectory, a more practical PI controller is constructed, avoiding the time dependence of the prototypical PI controller. Besides, an adaptive gain associated with PI parameters is designed for multi-WF coordination. Finally, the validity of the proposed method is verified in both the single-WF system and the multi-WF system.

Antiperovskite derivatives have recently emerged as promising lead-free alternatives to halide perovskites for optoelectronic applications. Here, using a comprehensive first-principles calculations including density functional perturbation theory and many-body perturbation theory (involving GW and Bethe-Salpeter equation (BSE)), we investigate the stability, excitonic, polaronic, and optoelectronic properties of cubic Ba$_3$MA$_3$ (M = P, As, Sb, Bi; A = Cl, Br, I). These compounds are found to be dynamically and thermodynamically stable direct-gap semiconductors with G$_0$W$_0$@PBE+SOC band gaps spanning 1.23-2.17 eV. BSE calculations reveal moderate exciton binding energies (0.254-0.352 eV) and intermediate-radius excitons, while Fröhlich polaron analysis indicates intermediate carrier-phonon coupling and mobilities up to $\sim$ 75 cm$^{2}$V$^{-1}$s$^{-1}$. The resulting spectroscopic limited maximum efficiencies reach $\sim$ 19-32%, surpassing several lead-based perovskites. Our results establish Ba-based antiperovskite derivatives as a robust, eco-friendly platform for next-generation optoelectronic devices.

We introduce a residence-time approach (RTA) for determining position-dependent diffusivities from biased molecular dynamics simulations. The method is formulated for trajectory segments in which the effective drift along the transport coordinate is negligible, as realized here using adaptive biasing force simulations. In this regime, local diffusivities are obtained directly from mean first-exit times out of finite spatial intervals. Unlike conventional fluctuation-based approaches, the RTA does not require dedicated harmonically restrained simulations or numerical integration of noisy time-correlation functions. We assess the method for oxygen diffusion across a hexadecane slab, water permeation across a lipid bilayer, and permeation of water and selected volatile organic compounds through a model skin-barrier membrane. In the slab system, the RTA reproduces independently determined bulk diffusivities within statistical uncertainty. In the membrane systems, the inferred diffusivity profiles are supported by propagator-level validation. These results establish the RTA as a practical approach for extracting position-dependent diffusivities from biased molecular simulations.

The UK Cyber Security and Resilience (CS&R) Bill represents the most significant reform of UK cyber legislation since the Network and Information Systems (NIS) Regulations 2018. While existing analysis has addressed the Bill's regulatory requirements, there is a critical gap in guidance on the architectural implications for organisations that must achieve and demonstrate compliance. This paper argues that the CS&R Bill's provisions (expanded scope to managed service providers (MSPs), data centres, and critical suppliers; mandatory 24/72-hour dual incident reporting; supply chain security duties; and Secretary of State powers of direction-), collectively constitute an architectural forcing function that renders perimeter-centric and point-solution security postures structurally non-compliant. We present a systematic mapping of the Bill's key provisions to specific architectural requirements, demonstrate that Zero Trust Architecture (ZTA) provides the most coherent technical foundation for meeting these obligations, and propose a reference architecture and maturity-based adoption pathway for CISOs and security architects. The paper further addresses the cross-regulatory challenge facing UK financial services firms operating under simultaneous CS&R, DORA, and NIS2 obligations, and maps the architectural framework against the NCSC Cyber Assessment Framework v4.0. This work extends a companion practitioner guide to the Bill by translating regulatory analysis into actionable architectural strategy. Keywords: Cyber Security and Resilience Bill, Zero Trust Architecture, Security Architecture, Critical National Infrastructure, NIS Regulations, DORA, Supply Chain Security, NCSC CAF v4.0

We prove that king chasing problem in Chinese Chess is NP-hard when generalized to $n\times n$ boards. `King chasing' is a frequently-used strategy in Chinese Chess, which means that the player has to continuously check the opponent in every move until finally checkmating the opponent's king. The problem is to determine which player has a winning strategy in generalized Chinese Chess, under the constraints of king chasing. Obviously, it is a sub-problem of generalized Chinese Chess problem. We prove that king chasing problem in Chinese Chess is NP-hard by reducing from the classic NP-complete problem 3-SAT.

We conducted a large-scale resume audit of 36,880 applications to 9,220 job advertisements for new college graduates across the United States. Firms express task preferences through job-advertisement text, which we link to occupation-level task measures from O*NET and the American Community Survey. We develop a model in which discrimination increases with evaluative discretion, defined as the share of hiring decisions driven by subjective rather than verifiable assessment. Callback gaps vary systematically with the task content of jobs. In management occupations, callbacks are 28 to 43 percent lower for Black men, Black women, White women, and Hispanic men than for otherwise identical White men. Broad occupation categories conceal important variation in task demands. When jobs are grouped by task intensity, discrimination concentrates in positions combining high analytical and interpersonal demands with low routine content. Decomposing task content into subjective-evaluation and objective-precision components, we find that subjective evaluation widens callback gaps while objective precision compresses them. Customer contact amplifies this divergence, widening gaps in non-routine jobs but not in routine jobs. Randomly assigned resume credentials that increase callbacks on average reduce gaps in low-discretion jobs but not in high-discretion jobs. Early-career exclusion from high-return task bundles may entrench long-run demographic gaps in employment outcomes.

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields with residual characteristic $p\neq2$, and $\ell$ be a prime number different from $p$. We classify those $\ell$-modular cuspidal irreducible representations of ${\rm GL}_n(F)$ which are ${\rm GL}_n(F_0)$-distinguished, that is, which carry a non-zero ${\rm GL}_n(F_0)$-invariant linear form. In the case when $\ell\neq2$, an $\ell$-modular cuspidal representation of ${\rm GL}_n(F)$ is ${\rm GL}_n(F_0)$-distinguished if and only if it lifts to a ${\rm GL}_n(F_0)$-distinguished cuspidal $\ell$-adic representation, whereas when $\ell=2$, it is ${\rm GL}_n(F_0)$-distinguished if and only if it is conjugate-self-dual.

When a slightly faulty transformer closes without load, the current waveform presents the coexistence of inrush and fault current. At this time, the inrush blocking module will block the relay, which may delay the removal of the slight fault and lead to more serious faults. To address this problem, this paper proposes a data-aided power transformer differential protection without inrush blocking module. The key to eliminating the negative influence of inrush current is to extract the fundamental component from the non-inrush part of the current waveform, which corresponds to the unsaturation period of the transformer core. Firstly, a data-aided module, namely an Attention module embedded Fully Convolutional Network (A-FCN), is built to distinguish the inrush and non-inrush parts of the current waveform. Then, a physical model of the current waveform is built for the non-inrush part, and the fundamental component is extracted by the nonlinear least square (NLS) algorithm. The proposed method can avoid the block of differential protections when inrush current occurs, which improves the sensitivity and rapidity of the relay, especially in the case of a weak internal fault hidden in inrush current. Finally, simulation and experimental data verify the effectiveness and generalization of the proposed method.

We derive generic properties of nonequilibrium phase transitions in all-to-all Ising models placed in contact with two thermal reservoirs, in which parameters (temperatures, interactions and field parameters) assume arbitrary values depending on the contact with each thermal bath. The presence of different kinds of external parameters leads to remarkably different sort of phase transitions. While continuous, discontinuous and even tricritical points are presented when external parameters are symmetric (e.g. the case of energetic barriers or different couplings between the system and thermal baths), the tricriticality is absent when external parameters are antisymmetric (e.g. the case of magnetic fields or biased drivings) implying that solely critical or discontinuous are possible. In such latter case, the probability distribution acquires the Boltzmann-Gibbs like form, irrespectively the model parameters when the switching between thermal reservoirs is sufficiently fast. Our work sheds light about the differences between equilibrium and nonequilibrium ingredients and theirs consequences upon phase transitions.

Existing sub-/super-synchronous (SSO) suppression methods for the direct-drive permanent magnet synchronous generators (D-PMSG) integrated power systems are mainly achieved by external devices or sub-synchronous resonance damping controller (SSRDC) at the converters, facing challenges of considerable control costs, complex parameters tuning, or inadaptability to various operating conditions. To address these problems, this paper proposes an adaptive SSRDC based on the phase-locked loop (PLL) for D-PMSG integrated power systems. Firstly, the PLL parameter is found critical to SSO suppression by a comprehensive sensitivity analysis on the dominant poles of the impedance closed-loop transfer function. Motivated by this finding, this paper then designs a PLL-based SSRDC, which features a simple structure, easy parameter tuning, and flexible adaptability to various operating modes. The simplicity in structure is guaranteed by the avoidance of phase compensation. Benefiting from the simple structure, only one key parameter needs to be tuned. Moreover, two principles of parameter tuning are proposed to enhance the efficiency, robustness, and adaptability of the proposed SSRDC. The controller-hardware-in-the-loop (CHIL) tests verify the validity of the proposed SSRDC under various operating conditions. Finally, some concerns about this method such as frequency estimation, computational efficiency and potential impacts on PLL are thoroughly analyzed and clarified.

Thin-film lithium niobate (TFLN) has emerged as a versatile integrated photonics platform, combining strong electro-optic and nonlinear effects. Among TFLN devices, ring resonators play a central role in filtering, modulation, and nonlinear optical processes. However, intrinsic loss, which ultimately limits ring performance, is most often summarized by single-valued metrics, and its statistical variability across resonances has received limited attention. Here, we show that intrinsic loss rates in monolithic TFLN ring resonators follow a statistical distribution, comprising a baseline loss and a tail arising from discrete loss events. This behavior is revealed by characterizing 2233 resonances, using an adiabatic waveguide-ring coupling architecture that selectively excites the fundamental mode and yields clean spectra in the ultra-high-Qi regime. We find the most probable intrinsic loss rate ki = 2 pi x 10.4 MHz, indicating operation in a low-loss regime comparable to state-of-the-art thick silicon nitride platforms.