Differentially flat models are frequently used to design feedforward controllers for electromechanical systems. However, control performance depends on model accuracy, which makes feedback imperative. This paper presents a control scheme for electromechanical systems in which measuring or estimating the output to be controlled -- typically the position -- is not feasible. It employs an identifiable-model-based controller and predictor, coupled with an iterative loop that updates model parameters using the error between a measurable output and its prediction. Simulations on electromechanical switching devices show effective tracking of the desired position trajectory using only coil current measurements.

In this paper, we apply the Feature Space Decomposition (FSD) method developed in [LS24, GLS25, LSSW26, ALSS26] to obtain, under fairly general conditions, matching upper and lower bounds for the population excess risk of spectral methods in linear regression under the squared loss, for every covariance and every signal. This result enables us, for a given linear regression problem, to define a pre-order on the set of spectral methods according to their convergence rates, thereby characterizing which spectral algorithm is superior for that specific problem. Furthermore, this allows us to generalize the saturation effect proposed in inverse problems and to provide necessary and sufficient conditions for its occurrence. Our method also shows that, under broad conditions, any spectral algorithm cannot overcome the barrier of the information exponent in problems such as single-index learning.

The light-shining-through-a-wall experiment ALPS II at DESY in Hamburg searched for axions and similar lightweight particles in its first science campaign from February to May 2024. No evidence for the existence of such particles was found. For pseudoscalar bosons like the axion, with masses below about 0.1 meV, we achieved a limit for the di-photon coupling strength of 1.5e-9 1/GeV at a 95% confidence level. This is more than a factor of 20 improvement compared to all previous similar experiments. We also provide limits on photon interactions for scalar, vector and tensor bosons. An achievement of this first science campaign is the demonstration of stable operation and robust calibration of the complex experiment. Currently, the optical system of ALPS II is being upgraded aiming for another two orders of magnitude sensitivity increase.

The aim of this letter is to compute the evolution of some expected values, such as the field operators $a^\pm$, quadratures and atomic inversion, under supersymmetric (SUSY) partner Hamiltonians associated to the Jaynes-Cummings Hamiltonian of quantum optics. This kind of SUSY partners are characterized by having spectra which differ in a finite number of energy levels. We wish to elucidate if the partner connection has any influence on these expected values. In particular, we want also to know in which way the classical and revival times are affected by such SUSY partners.

Networked Predictive Control is widely used to mitigate the effect of delays and dropouts in Networked Control Systems, particularly when these exceed the sampling time. A key design choice of these methods is the delay bound, which determines the prediction horizon and the robustness to information loss. This work develops a systematic method to select the optimal bound by quantifying the trade-off between prediction errors and open-loop operation caused by communication losses. Simulation studies demonstrate the performance gains achieved with the optimal bound.

We construct a nontrivial three-dimensional subshift of finite type whose projective $\Z$-subdynamics, or $\Z$-trace, is 2-sparse, meaning that there are at most two nonzero symbols in any vertical column. The subshift is deterministic in the direction of the subdynamics, so it is topologically conjugate to the set of spacetime diagrams of a partial cellular automaton. We also present a variant of the subshift that is defined by Wang cubes, and one whose alphabet is binary.

In this work, we investigate synchrotron emission and the observational signatures of anisotropic non-thermal electrons during magnetic-flux eruptions in a magnetically arrested disk, using 3D GRMHD simulations. Non-thermal electrons are assumed to be accelerated from the thermal background through magnetic reconnection, with pitch-angle distributions modeled as beamed or loss-cone types, alongside an isotropic case for comparison. The results show that non-thermal emission can produce pronounced flux outbursts and localized brightening during eruptions, while the associated increase in optical depth can suppress the linear polarization fraction. Introducing pitch-angle anisotropy further reshapes the angular distribution of the intrinsic emissivity and modulates its contribution to various observable signatures. Strong field-aligned beaming in the electron distribution suppresses non-thermal emission for near-axis observers, effectively driving the image morphology toward a purely thermal limit. In contrast, moderately anisotropic models remain effective at imprinting non-thermal electron signatures on both the total intensity and polarization structure. We further quantify how eruption-driven increases in absorption depth and enhanced Faraday effects reduce the linear polarization fraction and modify the azimuthal coherence of the polarization field. Overall, our results demonstrate that incorporating anisotropic non-thermal electrons is essential for a physically self-consistent interpretation of time-variable EHT polarimetric observations.

In this work, we introduce amortizing perpetual options (AmPOs), a fungible variant of continuous-installment options suitable for exchange-based trading. Traditional installment options lapse when holders cease their payments, destroying fungibility across units of notional. AmPOs replace explicit installment payments and the need for lapsing logic with an implicit payment scheme via the decay of the claimable notional. This amortization ensures all units evolve identically, preserving fungibility. We demonstrate that AmPO valuation can be reduced to an equivalent vanilla perpetual American option on a dividend-paying asset. This enables analytical expressions for the exercise boundaries and risk-neutral valuations for calls and puts. These formulas and relations allow us to derive the Greeks and study comparative statics with respect to the amortization rate. Illustrative numerical case studies demonstrate how the amortization rate shapes option behavior and reveal the resulting tradeoffs in the effective volatility sensitivity.

Deriving constitutive models (CMs) from numerical data has been an attractive approach as a systematic CM building method. One recent study is Rheo-SINDy, which extended the sparse identification of nonlinear dynamics (SINDy) method to rheology. Although the Rheo-SINDy framework discovered an approximate CM from numerical data under shear flow, its versatility has not been investigated. To clarify its applicability to other types of flows, this study applied Rheo-SINDy to numerically generated data under extensional flow conditions. As baseline tests for extensional flow, we considered two problems: (i) whether the Rheo-SINDy framework can reproduce the famous Giesekus model from data generated by that model, and (ii) whether it can derive an approximate CM from data generated by a dumbbell model with a finite extensible nonlinear elastic (FENE) spring. For problem (i), we confirmed that Rheo-SINDy can identify the exact expression of the Giesekus model under extensional flow. For problem (ii), the Rheo-SINDy framework discovered a relatively simple expression of the approximate CM by manually designing the library matrix based on rheological knowledge. The identified approximate CM can reasonably predict extensional rheological properties of the FENE dumbbell model, including an extrapolation region. These findings demonstrate the fundamental validity of using Rheo-SINDy under extensional flow.

Determining the optimal selling price is a challenge in revenue management, especially in markets characterized by nonlinear and price-sensitive demand. While traditional models, such as linear, power, and exponential demand functions, offer analytical convenience, they often fail to capture realistic purchase dynamics, leading to suboptimal pricing. The logit demand function addresses these limitations through its bounded, S-shaped curve, offering a more realistic representation of consumer behavior. Despite its advantages, most existing literature relies on heuristic approaches, such as pricing at the inflection point, which prioritizes maximum price sensitivity but does not guarantee maximum revenue. This study proposes a novel, exact pricing algorithm that analytically derives the revenue-maximizing price under the logit demand function using the Lambert W function. By providing a closed-form solution, the approach eliminates reliance on heuristic iterative methods and corrects the common practice of considering the inflection point price as market price. In fact, we demonstrate that the optimal price is consistently lower than the inflection-point price under reasonable assumptions, leading to lower prices for consumers and higher revenue for sellers. Numerical experiments illustrate the proposed algorithm and examine the changes in the optimality gap as demand function parameters vary. Results indicate that the optimal price is consistently lower than the inflection-point price, with an average 20% price reduction accompanied by a 15% increase in revenue.

We develop a discrete spectral framework for Dirichlet $L$-functions that reveals a combinatorial structure underlying their special values and connects this to their zeros. Our approach approximates the classical Dirichlet series by finite spectral sums $L_n(s,χ)$ associated with cyclic graphs $\mathbb{Z}/n\mathbb{Z}$ and studies their asymptotics as $n\rightarrow \infty$. Combining a refined Euler Maclaurin expansion with a structural polynomiality property, we show that at integer arguments the asymptotic expansions terminate and yield exact identities. This asymptotic to exact principle produces new infinite families of relations among special values of Dirichlet $L$-functions and recovers, by a different mechanism, formulas previously obtained by Xie, Zhao and Zhao. An interesting feature of our method is that $ζ(2n)$ and the corresponding special values for all Dirichlet $L$-functions thereby admit a finite combinatorial interpretation in terms of rooted spanning forests on any fixed cyclic graph. Concerning zeros, the same framework leads to some remarks about real zeros and a reformulation of the Generalized Riemann Hypothesis in the case of odd primitive characters in terms of an asymptotic functional equation relating $ξ_n(1-s,\overlineχ)$ to $ξ_n(s,χ)$ of the completed discrete functions. This establishes the remaining case of the one dimensional picture obtained in earlier works.

Radiation forces and torques enable the manipulation of objects with acoustic and electromagnetic waves. Yet, harnessing them in complex scattering media remains a formidable challenge, especially when multiple objects must be controlled under competing objectives. Here, we demonstrate that sound or light can be shaped to tailor momentum transfer to multiple objects simultaneously in a complex scattering medium. For a single object, our theory yields the maximal achievable force or torque; for multiple objects, it produces Pareto-optimal actuation and exact bounds on the simultaneous realization of incompatible objectives. This opens new applications for wave tweezers, enabling selective and precise manipulation of objects within complex media, ranging from the handling of cells, organoids, or microrobots, to targeted drug delivery in biological media.

We study energy-conserving Hamiltonian Boundary Value Methods (HBVMs) for Hamiltonian systems, which arise in applications where long-term preservation of energy and symplecticity is essential. HBVMs are multi-stage schemes whose stage equations reformulate as matrix equations with a low-rank right-hand side. For linear systems, we exploit this structure directly via Krylov projection solvers. For nonlinear systems, we leverage it within simplified Newton iterations and as a preconditioner in a Newton--Krylov framework, combined with adaptive time-stepping for robust convergence. Numerical experiments on semi-discretized wave equations demonstrate the efficiency and robustness of the proposed approach.

The correct identification of charged hadrons plays a crucial role in flavor-physics measurements. The final detector configurations at the proposed Future Circular Collider are yet to be determined and this study aims to contribute to this discussion by benchmarking the particle-identification (PID) performance of the proposed CLD and IDEA detectors using fully simulated events. At present, neither detector proposal includes dedicated PID systems, relying instead on information from the tracking subsystems. We estimate the expected level of contamination due to misidentified charged hadrons for $b$-flavor tagging, rare $b\to s$ transitions, and $s$-jet tagging. The PID information provided by silicon trackers, namely time-of-flight and energy-deposit measurements, leads to significant background suppression with high signal efficiency for the low-momentum hadrons considered for same-side $b$-flavor tagging. In order to improve the contamination in rare decays where momenta are in the medium range, only good timing resolution of 30ps and below can yield an improvement of one order of magnitude below the level achieved by kinematic criteria alone. Light-quark jet-flavor tagging requires identification of particles with very large momentum, which is not possible using only time-of-flight or energy-deposit information in silicon. Access to the number of clusters in a drift-chamber setup, as proposed for the IDEA detector however, results in strong background suppression in every case. This suppression can be further improved in some scenarios by time-of-flight resolution of 30-50ps or better. The PID quality generally exhibits only a small dependence on the cluster-counting efficiency. Whether dedicated PID detectors could further enhance flavor-physics sensitivity should be the subject of future study.

In this work, we prove a critical version of a Hardy-Rellich type inequality. We show that for $N\geq 1$ there exists a constant $C_N>0$ such that \[ \int_{\mathbb R^N}\left|\nabla\left(\frac{u(x)}{|x|}\right)\right|^N\,\mathrm{d}x\leq C_N\int_{\mathbb R^N}\left|Δu(x)\right|^N\,\mathrm{d}x, \] for any $u\in C^\infty_c(\mathbb R^N\setminus\left\{0\right\})$.

Spaceborne gravitational wave observatories, exemplified by the Laser Interferometer Space Antenna (LISA) mission, are designed to remove laser noise and clock noise from interferometric phase measurements in postprocessing. The planned observatories will utilize electro-optic modulators (EOMs) to encode the onboard clock timing onto the beam phase. Recent research has demonstrated the advantage of introducing an optical frequency comb (OFC) in the metrology system with the modified framework of time-delay interferometry (TDI): the removal of the EOM and the simultaneous suppression of the stochastic jitter of the laser and the clock in the observation band. In this paper, we explore an alternative approach with the OFC-based metrology system. We report that after proper treatment, it is possible to use the measured carrier-carrier heterodyne frequencies to monitor the time derivative of the pseudoranges, which represent the physical light travel time and the clock difference. This approach does not require changing the existing TDI framework, as previous OFC based efforts did. Furthermore, this approach naturally captures not only stochastic jitter but also clock offsets and slow drifts. We also present the experimental demonstration of our scheme using two separate systems to model two spacecraft. Using this novel approach, we synchronize the two independent phase measurement systems with an accuracy better than 0.47 ns, while the stochastic jitter in the observation band is suppressed down to the setup sensitivity around the LISA performance levels at 15 pm/sqrt(Hz).

We address the nonlinear properties of the double-Morse potential as a resource for single-mode quantum states due to its double-well structure and anharmonicity. We obtain analytical expressions for the ground-state wavefunction and the corresponding ground-state energy, using the inverse barrier-width parameter $α$ as the primary control parameter. We then assess non-Gaussianity and nonclassicality as quantitative signatures of nonlinearity and quantumness, and we find that both increase monotonically with $α$. Furthermore, we analyze the metrological performance of the model for estimating the inverse barrier-width parameter $α$. By evaluating the corresponding Fisher information, we show that position measurements are optimal and can saturate the Cramér-Rao bound. In particular, the estimation of $α$ is most precise in the shallow-well regime, where the quantum Fisher information is largest. For deep wells, enhanced sensitivity is instead obtained for the reparameterized control variable $A=2e^{-αx_0}$, provided that $x_0$ is independently calibrated. These results establish the double-Morse potential as a controllable source of non-Gaussianity and nonclassicality, with a metrological behavior that depends on the chosen estimation parameter. We highlight possible applications of this model in quantum sensing, continuous-variable quantum information, and quantum simulation.

Motivated by recent theoretical predictions of a square-shaped skyrmion lattice (S-SkL) in centrosymmetric tetragonal Ce-based magnets [Yan Zha and Satoru Hayami, Phys. Rev. B 111, 165155 (2025)], we perform a comprehensive theoretical investigation into the role of multiorbital effects and momentum-based frustrated exchange interactions in stabilizing such topologically nontrivial magnetic textures. By employing self-consistent mean-field calculations over a broad range of model parameters, we demonstrate that the cooperative interplay among interorbital coupling, frustrated exchange interactions at higher-harmonic wave vectors, and crystal-field-induced anisotropy is crucial for the stabilization of the S-SkL. Furthermore, the competition between the easy-plane intraorbital anisotropy and the easy-axis interorbital anisotropy leads to a significant enhancement of the S-SkL stability region. We also identify a rich variety of multi-$Q$ states, including a topologically nontrivial S-SkL state with a slight breaking of fourfold rotational symmetry (S-SkL$'$), magnetic bubble lattices (MBLs), and double-$Q$ phases with a local/net scalar chirality. Our findings elucidate the microscopic mechanism responsible for the emergence of S-SkLs in prototypical Ce-based magnets and provide a route toward realizing skyrmion lattices in a broader class of $f$-electron materials beyond conventional Gd- and Eu-based systems lacking orbital angular momentum.

We develop a Clark theory for commuting compressed shift operators on model spaces $K_ϕ$ associated with inner functions $ϕ$ on the bidisk, which exhibits both similarities and marked differences compared to the classical one-variable version. We first identify the adjoint of the embedding operator $J_α \colon K_ϕ\to L^2(σ_α)$ as a weighted Cauchy transform of the Clark measure $σ_α$. Under natural assumptions, which generically include the case when $ϕ$ is rational inner, we obtain commuting unitaries on $K_ϕ$ that are (often infinite-dimensional) perturbations of the compressed shift operators $K_ϕ$. We prove that these unitaries are unitarily equivalent to multiplication by the coordinate functions on $L^2(σ_α)$ and then establish a number of related properties and simplified results in special cases. Finally, we show that the Taylor joint spectrum of these Clark unitaries coincides with level sets of $ϕ$ when $ϕ$ is a rational inner function.

Large Language Models (LLMs) are increasingly deployed on edge devices with Neural Processing Units (NPUs), yet the decode phase remains memory-intensive, limiting performance. Processing-in-Memory (PIM) offers a promising solution, but co-executing NPU-PIM systems face challenges such as data layout mismatches, bandwidth loss, and redundant storage. To address these issues, we propose UMDAM, a unified memory-affinity data layout and DRAM address mapping scheme tailored for NPU-PIM co-execution. UMDAM employs a column-major, tile-based layout and a configurable DRAM mapping strategy to ensure compatibility with NPU computation while maximizing PIM efficiency -- without introducing extra memory overhead or bandwidth loss. Comprehensive evaluations on OPT models demonstrate that UMDAM reduces time-to-first-token (TTFT) by up to 3.0x and time-to-last-token (TTLT) by 2.18x, significantly improving end-to-end LLM inference efficiency on edge devices.

The high redshift merger rate and mass distribution of black hole binaries provide a direct probe to distinguish astrophysical black holes (ABHs) and primordial black holes (PBHs), which can be studied using the Stochastic Gravitational-Wave Background (SGWB). The conventional analyses solely based on the power spectrum are limited in constraining the properties of the underlying source population under the assumption of a non-sporadic Gaussian distribution. However, recent studies have shown that SGWB is expected to be sporadic and non-Gaussian in nature, which gives rise to non-zero \textit{spectral correlation} that depends on the high redshift merger rate and mass distribution of the compact objects. In this work, we present the first spectral covariance analysis of the SGWB using data from the LIGO--Virgo--KAGRA collaboration during the third and the first part of the fourth observing runs. Our analysis indicates that the current spectral correlation is consistent with non-stationary noise, yielding no detection and providing only upper bounds over the frequency range of 20 Hz to 100 Hz. This upper bound on the spectral correlation translates into a mass-distribution-dependent upper bound on the merger rate of PBHs. This provides a stringent upper bound on the PBH merger rate at high redshift and hence puts constraints on the PBH formation scenarios. In the future, detection of this signal will provide a new avenue to probe the high-redshift black hole population using gravitational waves.

Infinite-layer nickelates are among the most promising cuprate-akin superconductors, although relevant differences from copper oxides have been reported. Here, we present momentum- and polarization-resolved RIXS measurements on chemically undoped, superconducting PrNiO2, and compare its magnetic and orbital excitations with those of the reference infinite layer cuprate CaCuO2. In PrNiO2, the in-plane magnetic exchange integrals are smaller than in CaCuO2, whereas the out-of-plane values are similar, indicating that both materials support a three-dimensional antiferromagnetic order. Orbital excitations, associated to the transitions within 3d states of the metal, are well reproduced within a single-ion model and display similar characteristics, except for the Ni-dxy peak which, besides lying at significantly lower energy, shows an opposite dispersion to that of Cu-dxy. This is interpreted as a consequence of orbital superexchange coupling between nearest neighbor sites, which drives the orbiton propagation. Our observations demonstrate that infinite layer cuprates and nickelates share most of the spin and orbital properties, despite their markedly different charge-transfer energy Delta.

Tin-based halide perovskites have emerged as promising lead-free alternatives for optoelectronic applications, yet their structural stability and phase behavior at finite temperatures remain challenging to predict. Here, we assess the predictive capabilities of the foundational machine learning model MACE-MP-0 - trained on a broad chemical space and applied without system-specific fine-tuning - for the temperature-dependent behavior of CsSnBr3 and Cs2SnBr6. Molecular Dynamics simulations in the NpT ensemble were performed from 100 K to 500 K, and thermodynamic and structural descriptors including enthalpy, specific heat, radial distribution functions, translational order, bond angle distributions, and vibrational spectra were analyzed. Our results show that CsSnBr3 undergoes a low-temperature orthorhombic-to-cubic phase transition, evidenced by both the evolution of lattice parameters and subtle anomalies in enthalpy and specific heat, although the experimentally observed intermediate tetragonal phase is not captured. In contrast, Cs2SnBr6 remains cubic and maintains a more rigid octahedral framework across the entire temperature range. Overall, MACE-MP-0 qualitatively reproduces key thermal and structural features of these materials, highlighting its usefulness as a first step for studying new materials. For cases where capturing more subtle phase behavior is required, system-specific fine-tuning with Density Functional Theory data should be considered.

Josephson parametric devices are widely used in superconducting quantum computing research but suffer from an inherent gain-bandwidth trade-off. This limitation is partly overcome by coupling the device to its input/output transmission line via a bandpass filter, leading to wider bandwidth at undiminished gain. Here we perform a non-perturbative circuit analysis in terms of dressed transmission-line modes for representative resonant coupling circuits, going beyond the weak-coupling treatment. The strong frequency dependence of the resulting coupling coefficients implies that the Markov approximation commonly employed in cQED analysis is inadequate. By retaining the full frequency dependence of the coupling, we arrive at a non-Markovian form of the quantum Langevin equation with the frequency-dependent complex-valued self-energy of the coupling in place of a single damping parameter. We also consistently generalize the input-output relations and unitarity conditions. Using the exact self-energies of elementary filter networks -- a series- and parallel-LC circuit and a simple representative bandpass filter consisting of their combination -- we calculate the generalized parametric gain factors. Compared with their Markovian counterpart, these gain profiles are strongly modified. We find bandwidth broadening not only in the established parameter regime, where the self-energy of the coupling is in resonance with the device and its real part has unity slope, but also within off-resonant parameter regimes where the real part of the self-energy is large. Our results offer insight for the bandwidth engineering of Josephson parametric devices using simple coupling networks.

An ongoing challenge in animal ecology is developing movement models that account for the autocorrelation, and often temporal irregularity, in telemetry data. Continuous-time Langevin diffusion models have been proposed to model temporally autocorrelated and irregularly sampled data. However, current estimation techniques obtain increasingly biased parameter estimates as the time between observations increases. In this paper, we propose using Brownian bridges in an importance sampling scheme to improve the likelihood approximation of the Langevin diffusion model. In a series of simulation studies, we showed that our approach effectively removed the bias under various scenarios. We found that the precision of the estimated habitat coefficients increased for data spanning a longer duration at a lower frequency than for shorter, more frequently sampled tracks. This suggests that the model may be well suited for modelling tracking data sampled at a coarser resolution, as is common in datasets collected with older generations of animal tags. We illustrated the application of our model using tracking data from Steller sea lions, \textit{Eumetopias jubatus}. We found that the coefficient estimates converged to values significantly different than those estimated in previous studies, suggesting that bias in conventional estimation methods may meaningfully affect ecological conclusions about habitat preference. Together, these improvements broaden the applicability of Langevin diffusion models, thereby improving ecological insight into habitat selection.

We begin our journey by recalling the fundamentals of Probability Theory that underlie one of its most significant applications to real-world problems: Parametric Estimation. Throughout the text, we systematically develop this theme by presenting and discussing the main tools it encompasses (concentration inequalities, limit theorems, confidence intervals, maximum likelihood, least squares, and hypothesis testing) always with an eye toward both their theoretical underpinnings and practical relevance. While our approach follows the broad contours of conventional expositions, we depart from tradition by consistently exploring the geometric aspects of probability, particularly the invariance properties of normally distributed random vectors. This geometric perspective is taken further in an extended appendix, where we introduce the rudiments of Brownian motion and the corresponding stochastic calculus, culminating in Itô's celebrated change-of-variables formula. To highlight its scope and elegance, we present some of its most striking applications: the sharp Gaussian concentration inequality (a central example of the "concentration of measure phenomenon"), the Feynman-Kac formula (used to derive a path integral representation for the Laplacian heat kernel), and, as a concluding delicacy, the Black-Scholes strategy in Finance.

We study a minimal change to an observation-driven Bayesian Dirichlet ARMA (B--DARMA) for compositional time series: replace the raw additive log-ratio (ALR) residual in the moving-average block with a centered innovation that subtracts the Dirichlet conditional ALR mean, available in closed form via digamma identities. We prove a recursion-level first-order equivalence (in $1/ϕ$) between the centered specification and a digamma-link DARMA at fixed parameters, under explicit interior and lag-stability conditions. The result clarifies why the two specifications should be predictively indistinguishable in the high-precision regime but does not by itself govern the geometry of the Bayesian posteriors that re-estimation produces. On weekly Federal Reserve H.8 bank-asset shares (October~2015 through October~2025, $T=522$ weeks), predictive performance is statistically indistinguishable across $104$ rolling weekly origins on every accuracy metric examined, while Hamiltonian Monte Carlo divergent transitions are approximately an order of magnitude more frequent under the raw specification, driven by isolated rolling fits at which the raw posterior exhibits localized pathologies. A four-reference sensitivity analysis confirms that predictive equivalence is reference-invariant and that the geometric advantage of centering is preserved across references but varies with the prevalence of pathological raw fits, from a substantial reduction at the loans reference to parity at the cash reference. The practical implication is operational rather than predictive: centering avoids the catastrophic raw-MA divergence spikes that occur at isolated rolling origins, which matters for production workflows in which posterior simulation feeds downstream stress tests. The adjustment is analytic and plug-in, and requires only a local change to the MA innovation calculation.

We investigate current fluctuations in open quantum systems beyond the weak-coupling and Markovian regimes, focusing on a coherently driven qubit strongly coupled to a structured bosonic environment. By combining full counting statistics with the reaction coordinate mapping, we develop a framework that enables the calculation of steady-state current fluctuations and their temporal correlations in the strong-coupling regime. Our analysis reveals that, unlike in weak coupling, both the average current and its fluctuations exhibit nonmonotonic dependence on the system-environment interaction strength. Notably, we identify a regime where current noise is suppressed below the classical thermodynamic uncertainty bound, coinciding with enhanced anticorrelations in quantum jump trajectories and faster system relaxation. We further show that these features are linked to nonclassical properties of the reaction coordinate mode, such as non-Gaussianity and quantum coherence. Our results provide new insights and design principles for controlling current fluctuations in quantum devices operating beyond the standard weak-coupling paradigm.

We consider the following nonlocal Brézis-Nirenberg type critical Choquard problem involving the Grushin operator \begin{equation*} \left\{ \begin{aligned} -Δ_γ& u =λu + \left(\displaystyle\int_Ω\frac{|u(w)|^{2^*_{γ,μ}}}{d(z-w)^μ}dw\right) |u|^{2^*_{γ,μ}-2}u \quad &&\text{in} \ Ω, u &= 0 \quad &&\text{on} \, \partial Ω, \end{aligned} \right. \end{equation*} where $Ω$ is an open bounded domain in $\mathbb{R}^N$, $N \geq 3$, with $Ω\cap \{ x=0\} \neq \emptyset$, and $λ>0$ is a parameter. Here, $Δ_γ$ represents the Grushin operator, defined as \[ Δ_γu(z) = Δ_x u(z) +(1+γ)^2 |x|^{2γ} Δ_y u(z), \quad γ\geq 0, \] where $z=(x,y)\in Ω\subset \mathbb{R}^m\times \mathbb{R}^n$, $m+n=N \geq 3$ and $2^*_{γ,μ}= \frac{2N_γ-μ}{N_γ-2}$ is the Sobolev critical exponent in the Hardy-Littlewood context with $N_γ= m+(1+γ)n$ is the homogeneous dimension associated to the Grushin operator and $0<μ<N_γ$. The homogeneous norm related to the Grushin operator is denoted by $d(\cdot)$. In this article, we prove the existence of bifurcation from any eigenvalue $λ^*$ of $-Δ_γ$ under Dirichlet boundary conditions. Furthermore, we show that in a suitable left neighborhood of $λ^*$, the number of nontrivial solutions to the problem is at least twice the multiplicity of $λ^*$.

Resonant Inelastic X-Ray Scattering (RIXS) is a well-established tool for probing excitations in a wide range of materials. The measured spectra strongly depend on the scattering geometry, via its influence on the polarization of the incoming and outgoing light. By employing a tensor representation of the 4-point response function that governs the RIXS intensity, we disentangle the experimental geometry from the intrinsic material properties. In dipole-dipole RIXS processes and low-symmetry crystals, up to 81 linearly independent fundamental spectra can be measured as a function of light polarization. However, for crystals or molecules with symmetry, the number of independent fundamental spectra that define the RIXS tensor is significantly reduced. This work presents a systematic framework for determining the number of fundamental spectra and expressing the RIXS tensor in terms of these fundamental components. Given a specific experimental geometry, the measured spectrum can be represented as a linear combination of these fundamental spectra. To validate our approach, we performed calculations for different point group symmetries, both with and without an applied magnetic field. Within the same framework, we derived expressions for powder spectra in momentum-independent processes and spectra obtained using Bragg spectrometers. This formalism provides a valuable toolkit for optimizing experiment planning, data interpretation, and RIXS simulation.