This work introduces ParamRF: a Python library for efficient, parametric modelling of radio frequency (RF) circuits. Built on top of the next-generation computational library JAX, as well as the object-oriented wrapper Equinox, the framework provides an easy-to-use, declarative modelling interface, without sacrificing performance. By representing circuits as JAX PyTrees and leveraging just-in-time compilation, models are compiled as pure functions into an optimized, algebraic graph. Since the resultant functions are JAX-native, this allows computation on CPUs, GPUs, or TPUs, providing integration with a wide range of solvers. Further, thanks to JAX's automatic differentiation, gradients with respect to both frequency and circuit parameters can be calculated for any circuit model outputs. This allows for more efficient optimization, as well as exciting new analysis opportunities. We showcase ParamRF's typical use-case of fitting a model to measured data via its built-in fitting engines, which include classical optimizers like L-BFGS and SLSQP, as well as modern Bayesian samplers such as PolyChord and BlackJAX. The result is a flexible framework for frequency-domain circuit modelling, fitting and analysis.

We show that any smooth closed immersed curve in $\mathbb R^n$ with a one-to-one convex projection onto some $2$-plane develops a Type~I singularity and becomes asymptotically circular under Curve Shortening flow in $\mathbb R^n$. As an application, we prove an analog of Huisken's conjecture for Curve Shortening flow in $\mathbb R^n$, showing that any smooth closed immersed curve in $\mathbb R^n$ can be smoothly perturbed to a closed immersed curve in $\mathbb R^{n+2}$ which shrinks to a round point under Curve Shortening flow. Our proof relies on a novel contradiction argument in which Type~{II} singularities are excluded by proving both the uniqueness and non-uniqueness of the tangent flows at the singular point.

We investigate the gluon distribution in a proton at very low $x$, both integrated and transverse momentum dependent, using the Laplace transform technique. By accounting for leading and main next-to-leading contributions, we derive compact analytical expressions for the gluon densities valid in the asymptotic limit $x \to 0$. Our results closely match those from other analytical and numerical approaches, with the main advantage being the simplicity of the expressions, which capture the essential features of more complex calculations.

For $s\in(0,1)$ and an open bounded set $Ω\subset\mathbb R^n$, we prove existence and uniqueness of absolute minimisers of the supremal functional $$E_\infty(u)=\|(-Δ)^s u\|_{L^\infty(\mathbb R^n)},$$ where $(-Δ)^s$ is the Fractional Laplacian of order $s$ and $u$ has prescribed Dirichlet data in the complement of $Ω$. We further show that the minimiser $u_\infty$ satisfies the (fractional) PDE $$ (-Δ)^s u_\infty=E_\infty(u_\infty)\,\mathrm{sgn}f_\infty \qquad\mbox{in }Ω, $$ for some analytic function $f_\infty\in L^1(Ω)$ obtained as the restriction of an $s$-harmonic measure $μ$ in $Ω$.

We point out that a simple redefinition of the regularizing parameter in regular black hole (RBH) metrics can preserve the self-similarity of the evaporation process. This implies that a RBH can evaporate completely, mirroring the behavior of its singular counterpart. Consequently, RBHs need not evolve into exotic, unverified remnant states such as horizonless compact objects or wormholes. We then provide a general framework to study dark matter (DM) production from evaporation of regular primordial black holes (RPBHs). As illustrative examples, we explicitly work out the cases of the Hayward metric and the Simpson-Visser metric. The formalism can be readily applied to other metrics. RPBH generally exhibits different Hawking temperature and horizon size compared to their singular counterpart, leading to distinct lifetime and mass evolution. We calculate the resulting modified cosmological constraints and the allowed parameter space to obtain the correct DM abundance. This intriguing scenario provides a unified resolution to both the DM problem and the black hole singularity problem, while preserving the standard self-similar evaporation process.

Astrophysical scenarios such as binary neutron star mergers, protoneutron stars, and core-collapse supernovae involve finite temperatures and strong magnetic fields. Previous studies on the effect of magnetic fields on flavor-equilibration processes relied on the Fermi surface approximation, which is not a reliable approximation in the neutrino-transparent regime of matter in supernovae or neutron star mergers. In a recent study, we went beyond the Fermi surface approximation, performing the full phase space integral to obtain direct Urca rates in a background magnetic field. In this work, we extend these calculations to incorporate the collisional broadening (modified Urca) contribution. We use the recently developed nucleon width approximation, which naturally includes the magnetic field dependence of all contributions. We demonstrate the impact of magnetic fields on the flavor-equilibrium condition for two finite-temperature equations of state with different direct Urca thresholds. We also study the impact of magnetic fields on the bulk viscous dissipation of density oscillations relevant in postmerger scenarios.

Supernova H0pe is a multiply-imaged Type Ia supernova (SN~Ia) and the second lensed SN to yield a measurement of the Hubble constant by the time-delay cosmography method, finding $H_0 = 75.4^{+8.1}_{-5.5} \text{km s}^{-1} \text{Mpc}^{-1}$ (Pascale et. al 2025). We investigate the seven lens modeling approaches used to derive $H_0$, assessing their agreement with $Λ\text{CDM}$ constraints from SN~Ia surveys through a purely observational comparison. \textbf{We test each lens model by combining its predicted magnifications with the observed time delays to reconstruct the intrinsic SN~Ia luminosity and corresponding distance modulus.} While photometrically derived magnifications yield distance moduli in line with $Λ\text{CDM}$ expectations, our comparison reveals that lens model predictions, even the most precise ones, \textbf{consistently overestimate the magnification, with an offset $> 1$~mag}. This known bias, already appreciated by modeling teams, is independently confirmed through our analysis and highlights the value of lensed SNe as a tool to test model accuracy. If unaccounted for, such magnification biases can propagate into uncertainties in derived cosmological parameters, including $H_0$, a critical challenge for precision cosmology using strongly lensed transients.

The generalized Brillouin zones (GBZs) are integral in the analysis of non-Hermitian band structures. Conventional wisdom suggests that the GBZ should be connected, where each point can be indexed by the real part of the wavevector, similar to the Brillouin zone. Here we demonstrate rich topological features of the GBZs in generic non-Hermitian one-dimensional models. We prove and discuss a set of sufficient conditions for the model to ensure the connectivity of its GBZ. In addition, we show that the GBZ can become disconnected and have more connected components than the number of bands, which results from the point-gap features of the band structure. This novel GBZ topology is applied to further demonstrate a counterintuitive effect, where the line gap of an open-boundary spectrum with sublattice symmetry may be closed without changing its point-gap topology. Our results challenge the current understanding of bands and gaps in non-Hermitian systems and highlight the need to further investigate the topological effects associated with the GBZ including topological invariants and open-boundary braiding.

We provide exact integral formulas for hyperbolic and spherical volumes of cone-manifolds whose underlying space is the $3$-sphere and whose singular set belongs to three infinite families of two-bridge knots: $C(2n,2)$ (twist knots), $C(2n,3)$, and $C(2n,-2n)$ for any non-zero integer $n$. Our formulas express volumes as integrals of explicit rational functions involving Chebyshev polynomials of the second kind, with integration limits determined by roots of algebraic equations. This extends previous work where only implicit formulas requiring numerical approximation were known.

Differential top quark pair production cross sections are measured in the dilepton final states e$^+$e$^-$, $μ^+μ^-$, and e$^\pmμ^\mp$, as a function of kinematic variables of the two-neutrino system: the transverse momentum $p_\mathrm{T}^{νν}$ of the dineutrino system, the minimum distance in azimuthal angle between $\vec{p}_\mathrm{T}^{\,νν}$ and leptons, and in two dimensions in bins of both observables. The measurements are performed using CERN LHC proton-proton collisions at $\sqrt{s}$ = 13 TeV, recorded by the CMS detector between 2016 and 2018, corresponding to an integrated luminosity of 138 fb$^{-1}$. The measured cross sections are unfolded to the particle level using an unregularized least squares method. Results are compared with predictions by the standard model of particle physics, and found to be in agreement with theoretical calculations as well as Monte Carlo simulations.

Using Fourier analysis, this paper establishes near-optimal security bounds for linear correctors commonly used in True Random Number Generators (TRNGs), expressed through code weight enumerators and input bias parameters. We provide the first near-tight bias characterization in total variation, by interpolating between optimal $\ell_\infty$ and $\ell_2$ norm results. Our bounds improve security assessments by an order of magnitude over previously known (overly conservative) estimates. Across $\sim $20,000 codes, we examine fundamental trade-offs between compression efficiency, cryptographic security, and hardware complexity. Achieving 80-bit security with 10\% input bias typically requires sacrificing more than 50\% of the code rate and incurs increased hardware cost. This quantifies the inherent cost of randomness extraction in hardware TRNG implementations.

Rare and extreme events in turbulent flows play a critical role in transport, mixing and transition, yet are notoriously difficult to capture experimentally. Here we report, to our knowledge, the first direct experimental detection of an upstream-directed jet burst in a backward-facing step (BFS) flow at $Re_h=2100$, using long-duration Live Optical Flow Velocimetry (L-OFV). Continuous monitoring over 1.5 h enabled a data-driven definition of extremes as rare velocity probes excursions deep into the observed distribution's tails; in practice, large negative events ($u: Z < -6$, $v: Z < -5$ at $(x,y) = (2h,h / 2)$, where $|Z| > > 0$ stands for large deviations from the mean value) triggered the live capture of surrounding velocity fields. The recording is triggered when the probes surpass the defined threshold, using live analysis of the velocity fields. The detected event features a jet-like intrusion into the recirculation region initiated by the collapse of a merged Kelvin-Helmholtz vortex and sustained by counter-rotating vortices, and is accompanied with heavy-tailed probe statistics and simultaneous amplification of fluctuating kinetic energy and enstrophy. While a single event was recorded, underscoring its rarity, the results establish L-OFV as a viable platform for rare-event detection in separated shear layers and document a previously unreported mechanism of upstream jet bursting in BFS flow.

Particle Image Velocimetry (PIV) typically relies on cross-correlation,which makes it difficult to obtain instantaneous velocity fields that are both spatially dense and available in real time at high acquisition rates. Optical Flow Velocimetry (OFV) offers a per-pixel alternative. Here we demonstrate real-tome OFV that delivers dense velocity fields (one vector per pixel) with high effective spatial resolution at frequencies up to the kHz range. Using synthetic particle images for two benchmarks -- a Rankine vortex and a homogeneous isotropic turbulence DNS -- we show that, with suitable particle seeding, OFV can resolve strong displacement gradients down to small scales. We then achieve real-time performance through algorithmic refinements and GPU-focused optimizations, combined with practical choices of OFV parameters. With this implementation, 32 Mp fields are processed live at 90 Hz, 4 Mp fields up to 460 Hz, and 1 Mp fields up to 1400 Hz. The method is further validated experimentally on the flow past a circular cylinder, where dense instantaneous velocity fields support real-time computation of derived quantities over long durations. These capabilities enable in-experiment monitoring, recovery of low-frequency dynamics from sustained high-rate acquisition, and closed-loop-flow-control strategies based on OFV measurements while also accelerating conventional post-processing to reduce turnaround time and computational cost.

Accurate forecasts of weekly mortality are essential for public health and the insurance industry. We develop a forecasting framework that extends the Lee-Carter model with age- and region-specific seasonal effects and penalized distributed lag non-linear components that capture the delayed and non-linear effects of heat, cold, and influenza on mortality. The model accommodates overdispersed mortality rates via a negative binomial distribution. We model the temporal dynamics of the latent factors in the model using SARIMA processes and capture cross-regional dependencies through a copula-based approach. Using regional French mortality data (1990-2019), we demonstrate that the proposed framework yields well-calibrated forecast distributions and improves predictive accuracy relative to benchmark models. The results further show substantial heterogeneity in temperature- and influenza-related relative risks between ages and regions. These findings underscore the importance of incorporating exogenous drivers and dependence structures into a weekly mortality forecasting framework.

A popular quantitative approach to evaluating player performance in sports involves comparing an observed outcome to the expected outcome ignoring player involvement, which is estimated using statistical or machine learning methods. In soccer, for instance, goals above expectation (GAX) of a player measure how often shots of this player led to a goal compared to the model-derived expected outcome of the shots. Typically, sports data analysts rely on flexible machine learning models, which are capable of handling complex nonlinear effects and feature interactions, but fail to provide valid statistical inference due to finite-sample bias and slow convergence rates. In this paper, we close this gap by presenting a framework for player evaluation with metrics derived from differences in actual and expected outcomes using flexible machine learning algorithms, which nonetheless allows for valid frequentist inference. We first show that the commonly used metrics are directly related to Rao's score test in parametric regression models for the expected outcome. Motivated by this finding and recent developments in double machine learning, we then propose the use of residualized versions of the original metrics. For GAX, the residualization step corresponds to an additional regression predicting whether a given player would take the shot under the circumstances described by the features. We further relate metrics in the proposed framework to player-specific effect estimates in interpretable semiparametric regression models, allowing us to infer directional effects, e.g., to determine players that have a positive impact on the outcome. Our primary use case are GAX in soccer. We further apply our framework to evaluate goal-stopping ability of goalkeepers, shooting skill in basketball, quarterback passing skill in American football, and injury-proneness of soccer players.

Recent observations of large-scale statistical isotropy violations have prompted the adoption of anisotropic cosmological models that account for inherent directional curvature. Studies of these anisotropic spacetimes have shown how they can explain the evolutionary dynamics and light propagation in the universe. Here, we consider one such interesting set of spacetimes that preserve homogeneity but place no constraint on isotropy during the inflationary epoch, to examine whether we can address the possibility of anisotropic inflation in the universe. Researchers have proposed inflationary models in which a vector field coupled to the inflaton is found to violate the cosmic no-hair theorem for the anisotropic Bianchi type I spacetime, due to the existence of a stable anisotropically inflationary fixed point. Lately, this study has been extended to axisymmetric spacetimes of Bianchi type II, III, and the Kantowski-Sachs metric, and it has been inferred that the entire family of spacetimes is attracted to the anisotropic Bianchi I fixed point. By constructing inflationary models where the spatial slices are anisotropic Thurston 3-geometries, we demonstrate that the intrinsic eccentricity of the background geometry induces an isotropy-violating vector field. This field, through its coupling to the inflaton, triggers a secondary phase of anisotropic inflation. We perform dynamical stability and phase-space analyses to assess the feasibility of anisotropic inflation. The results for the considered set of Thurston geometries showed the presence of a unique, stable inflationary fixed point that converges, similar to those in Bianchi spacetimes, thereby indicating the cosmological viability of inflation with anisotropic hair.

Scientific research needs a system that better values rigorous, reusable contributions. Although open knowledge and FAIR (findable, accessible, interoperable, and reusable) principles, along with coalitions and infrastructures, are accelerating reform, evaluation still often defaults to standardized metrics such as the h-index and journal impact factor. This misalignment still incentivizes quantity over quality, undermining integrity and reproducibility, and making it harder for communities to learn from and build on existing work. In this perspective, we bring together a global community of researchers, funding institutions, industrial partners, and publishers from 14 different countries across the 5 continents to advance ongoing debates on open science and research evaluation. Our contribution to the research practice is to offer an integrative conceptual framework, an open knowledge system, that links knowledge production, validation, assessment, and reuse into a single ecosystem view, and to translate into practical recommendations across key stakeholder roles (researchers, institutions/evaluators, funders, and publishers). By shifting attention from papers and bibliometrics toward reusable knowledge contributions and their validation, the framework highlights concrete levers for cultural change (what to share, when/how to validate, how to support reuse, and what to reward) and offers a practical lens that stakeholders can use to diagnose misaligned incentives and to design reforms that make high-quality, cumulative contributions visible and valued.

Let $f$ be a transcendental entire function with hyper-order strictly less than 1 and having a Borel exceptional small function. If $f$ and $Δ^n f$, or $f'$ and $f(z+1)$, share a function CM, then the exact form of $f$ is determined, which improves the previous results given by Lü et al. [Results Math. 74, article number 30 (2019)] and Liu et al. [Bull. Korean Math. Soc. 51, 1453-1467 (2014)]. As an application, the relationship between $f$ and $Δ^n f$ is established under the condition that they share a finite set, which partially resolves Liu's question raised in [J. Math. Anal. Appl. 359, 384-393 (2009)]. Furthermore, several examples are presented to demonstrate these results.

The rapid advancement of AI workloads and domain-specific architectures has led to increasingly diverse processor microarchitectures, whose design exploration requires fast and accurate performance validation. However, traditional workflows defer validation process until RTL design and SoC integration are complete, significantly prolonging development and iteration cycle. In this work, we present FASE framework, FPGA-Assisted Syscall Emulation, the first work for adapt syscall emulation on FPGA platforms, enabling complex multi-thread benchmarks to directly run on the processor design without integrating SoC or target OS for early-stage performance validation. FASE introduces three key innovations to address three critical challenges for adapting FPGA-based syscall emulation: (1) only a minimal CPU interface is exposed, with other hardware components untouched, addressing the lack of a unified hardware interface in FPGA systems; (2) a Host-Target Protocol (HTP) is proposed to minimize cross-device data traffic, mitigating the low-bandwidth and high-latency communication between FPGA and host; and (3) a host-side runtime is proposed to remotely handle Linux-style system calls, addressing the challenge of cross-device syscall delegation. Experiments ware conducted on Xilinx FPGA with open-sourced RISC-V SMP processor Rocket. With single-thread CoreMark, FASE introduces less than 1% performance error and achieves over 2000x higher efficiency compared to Proxy Kernel due to FPGA acceleration. With complex OpenMP benchmarks, FASE demonstrates over 96% performance validation accuracy for most single-thread workloads and over 91.5% for most multi-thread workloads compared to full SoC validation, significantly reducing development complexity and time-to-feedback. All components of FASE framework are released as open-source.

The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure theory, and therefore any operational characterization of the notion of probability is still missing in quantum mechanics. In our former works [K. Tadaki, arXiv:1804.10174], based on the toolkit of algorithmic randomness, we presented a refinement of the Born rule, called the principle of typicality, for specifying the property of results of measurements in an operational way. The Wigner's friend paradox is a Gedankenexperiment regarding when and where the reduction of the state vector occurs in a chain of the measurements by several observers where the state of the consciousness of each observer is measured by the subsequent observer. In this paper, we extend the framework of the principle of typicality so that it can be applicable to the situation where apparatuses perform measurements over other apparatuses. We then make an analysis of the Wigner's friend paradox within this extended framework of quantum mechanics based on the principle of typicality. We draw common sense conclusions about it. Deutsch's thought experiment is a variant of the Wigner's friend paradox, which can, in principle, verify the effect of the consciousness of observer on the reduction of the state vector. We make an analysis of it comprehensively within the extended framework. We then make a prediction which is testable in principle. In our extended framework, we can analyze still more complicated situations. As such an example, we introduce a combination of the above two, called the Wigner-Deutsch collaboration, and perform a thorough analysis of it.

Multidimensional factor models with moderations on all model parameters have so far been limited to single-factor and two-factor models. This does not align well with existing psychological measures, which are commonly intended to assess 3-5 dimensions of a latent construct. In this paper, I introduce a multidimensional MNLFA model that permits the moderation of item intercepts, loadings, residual variances, factor means, variances, and correlations across three or more latent factors. I describe efforts to implement the model using Bayesian methods through Stan and penalized maximum likelihood approaches to stabilize estimation and detect partial measurement non-invariance while preserving model interpretability. Closed-form analytic gradients of the likelihood, eliminating the need for costly numerical or MCMC-based approximations. We conclude by discussing the theoretical implications of penalization for measurement invariance, computational considerations, and future directions for extending the framework to categorical indicators, longitudinal data, and applied research contexts.

We reproduce the consistently-seen experimental voltage versus pressure (V-P) dependence of DC magnetron sputtering (DCMS) with 2D-RZ particle-in-cell (PIC) simulation. Informed by PIC simulation, we develop a steady-state, 1D-axial fluid model of the sheath and presheath that also reproduces this V-P dependence. The V-P dependence is the relationship between the steady-state voltage needed to maintain a constant discharge current and the neutral gas pressure. V-P dependence is fundamental to device performance, but has not previously been reproduced with simulation or satisfactorily explained. In this work, we compare the V-P curve of our simulated device and fluid model with past experiments and then present a theoretical explanation for this V-P dependence. We find that the decrease in voltage with increasing pressure is not due to electron recapture at the cathode. Rather, the constant current dictates a constant global ionization rate, so the voltage decrease compensates for the increase in neutral gas density by lowering the energy of the plasma electrons, which decreases their ionization probability. The PIC simulations also reveal that the presheath and bulk plasma are unaffected by the electron reflection coefficient at the cathode; the only effect of increasing reflection is a reduction in the sheath voltage and width. In addition to the potential structure, we explore how pressure affects the plasma density, particle drifts, and particle energy distributions.

"Macrorealism" posits that a system possesses definite properties at all times and that we can discover these properties, in principle, without disturbing the system's subsequent behaviour. The Leggett-Garg inequalities are derived under these assumptions and are readily violated by standard quantum mechanics, thereby providing a scheme to test whether demonstrably macroscopic systems can exhibit quantum coherence. Unfortunately, Leggett-Garg tests suffer from the difficult to avoid clumsiness loophole - the difficulty of proving that sequential measurements have not inadvertently disturbed the system. The recently uncovered Tsirelson inequality is derived from the simple dynamical assumption of uniform precession, obeyed by many classical systems, and requires only single-time measurements. However, Tsirelson inequality violations could be explained by a macrorealistic system that merely breaks the dynamical assumption, rather than genuine quantum behaviour. By carrying out a quantum-mechanical analysis of the Tsirelson inequality in the harmonic oscillator, we develop a protocol to rule out this possibility by assessing generalised conditions of uniform precession. We show that various measures of uniform precession, some of which are related to Leggett-Garg quantities, are satisfied well enough that the presence of quantum-mechanical interference terms must be implied. We derive several incidental mathematical results relating to violating states of Tsirelson's inequality, concerning dwell time, crossing number and probability currents, and also consider a group theoretic analysis of the Tsirelson operator.

Parametric instabilities are a known feature of periodically driven dynamic systems; at particular frequencies and amplitudes of the driving modulation, the system's quasi-periodic response undergoes a frequency lock-in, leading to a periodically unstable response. Here, we demonstrate an analogous phenomenon in a purely static context. We show that the buckling patterns of an elastic beam resting on a modulated Winkler foundation display the same kind of frequency lock-in observed in dynamic systems. Through simulations and experiments, we reveal that compressed elastic strips with modulated height alternate between predictable quasi-periodic and periodic buckling modes. Our findings uncover previously unexplored analogies between structural and dynamic instabilities, highlighting how even simple elastic structures can give rise to rich and intriguing behaviors.

We investigate finite-energy solutions to Kazdan-Warner type equations in 2-dimensional integer lattice graph $$ - Δu= \varepsilon e^{κu} +βδ_0\quad {\rm in}\ \mathbb{Z}^2,$$ where $\varepsilon=\pm1$, $κ>0$ and $β\in\mathbb{R}$. When $\varepsilon=1$, we prove the existence of a continuous family of finite-energy solutions for some parameter $κ$. This provides a partial resolution of the open problem on the existence of finite-energy solutions to the Liouville equation. When $\varepsilon=-1$ and $β>\frac{4π}κ$, we prove that the set of finite-energy solutions exhibits a layer structure. Moreover, we derive the extremal solution in this case.

A principal contracts with an agent through an informed delegate. Although the principal cannot directly mediate the interaction, she can restrict the menus of contracts the delegate may offer. We characterize the outcomes implementable through delegated contracting: they are exactly those achievable by a centralized Bayesian mechanism that is dominant-strategy incentive compatible and ex-post individually rational for the agent. We use this result to identify the optimal contractual restrictions in several settings. First, an organization that procures through a budget-indulgent agency should grant full flexibility below an expected spending cap. Second, unlike centralized mechanisms, delegated contracting can never dissolve partnerships efficiently, highlighting a limit to delegated authority. Finally, a seller can entrust sales to an intermediary without revenue loss by combining a resale price agreement with a buyback policy.

We study the degree of band flatness and anisotropic quantum geometry in magic-angle twisted bilayer graphene by varying the twist angle and the lattice relaxation through optical conductivity. We show that the degree of band flatness and its quantum geometry can be revealed through optical absorption and its resulting optical bounds, which are based on the trace condition in quantum geometry. More specifically, the narrow and isolated peak of optical absorption in the low-energy region provides information about the bandwidth between two flat bands. When this value is smaller than the electron interaction, it serves as a critical condition for the emergence of flat band superconductivity. Furthermore, optical absorption also provides the gap value between the flat band and the dispersive band, and when this gap is larger than the electron interaction, it facilitates the realization of fractional Chern insulating phases. We show that the narrow and isolated peak of optical bound near zero energy decreases as lattice relaxation increases. Meanwhile, we demonstrate that the imaginary part of generalized optical Hall conductivity reveals the vanishing of the negative part of Berry curvature, which is enforced by the refined trace-determinant inequality. Accordingly, we show that the total amount of the negative part and component of the Berry curvature approaches zero in the single ideal flat-band case. In contrast, when considering all occupied bands, the total amount of the negative component is slightly different from zero. Finally, we demonstrate that the condition of vanishing of flat band velocities and the emergent chiral symmetry are sufficient for the saturation of the trace condition, which pertains to the isotropic case.

Exploiting quantum features allows for estimating external parameters with precisions well beyond the capacity of classical sensors, a phenomenon known as quantum-enhanced precision. Quantum criticality has been identified as a resource for achieving such enhancements with respect to the probe size. However, they demand complex probe preparation and measurement and the achievable enhancement is ultimately restricted to narrow parameter regimes. On the other hand, non-equilibrium probes harness dynamics, enabling quantum-enhanced precision with respect to time over a wide range of parameters through simple probe initialization. Here, we unify these approaches through a Stark-Wannier localization platform, where competition between a linear gradient field and particle tunneling enables quantum-enhanced sensitivity across an extended parameter regime. The probe is implemented on a 9-qubit superconducting quantum device, in both single- and double-excitation subspaces, where we explore its performance in the extended phase, the critical point and the localized phase. Despite employing only computational-basis measurements we have been able to achieve near-Heisenberg-limited precision by combining outcomes at distinct evolution times. In addition, we demonstrate that the performance of the probe in the entire extended phase is significantly outperforming the performance in the localized regime. Our results highlight Stark-Wannier systems as versatile platforms for quantum sensing, where the combination of criticality and non-equilibrium dynamics enhances precision over a wide range of parameters without stringent measurement requirements.

A scalar ultralight dark matter (ULDM) candidate would induce oscillatory motion of freely falling test masses via its coupling to Standard Model fields. Such oscillations would create an observable Doppler shift of light exchanged between the test masses, and in particular would be visible in space-based gravitational waves (GW) detectors, such as LISA. While this kind of detection has been proposed multiple times in the recent years, we numerically investigate if it is possible to extract a scalar ULDM signal in a space-based GW detector, and in particular how to differentiate such a signal from a GW signal. Using one year of realistic orbits for the LISA spacecrafts and Bayesian methods, we find that LISA will indeed be able to discriminate between the two signals.

For the $1+1$ dimensional damped stochastic Klein-Gordon equation, we show that random singularities associated with the law of the iterated logarithm exist and propogate in the same way as the stochastic wave equation. This provides evidence for possible connections to microlocal analysis, ie. the exact regularity and singularities described in this paper should admit wavefront set type descriptions whose propagation is determined by the highest order terms of the linear operator. Despite the results being exactly the same as those of the wave equation, our proofs are significantly different than the proofs for the wave equation. Miraculously, proving our results for the critically damped equation implies them for the general equation, which significantly simplifies the problem. Even after this simplification, many important parts of the proof are significantly different than (and we think are more intuitive from the PDE viewpoint compared to) existing proofs for the wave equation.