We study the ferromagnetic instability in an SU($N$) Fermi-Hubbard model on the hypercubic lattice. Combining dynamical mean-field theory with continuous-time quantum Monte Carlo simulations, we find that, in the strong-coupling regime at low temperatures, ferromagnetically ordered (FM) states develop away from the commensurate fillings. In the particle-doped SU($3$) system near one-third filling, the FM state is accompanied by a spontaneous flavor-selective Mott state, where two of the three flavors are Mott insulating while the remaining flavor is metallic. Since particles in the metallic flavor can almost freely move on the lattice without correlation effects, the ordered state is stabilized by the kinetic-energy gain of the doped particles. This is similar to the generalized Nagaoka ferromagnetism discussed in the one-hole-doped system at one-third filling. In the SU($4$) case, we find that six distinct types of FM states appear as the particle density varies. The results uncover the nature of the FM state in the SU($N$) Fermi-Hubbard systems and highlight the rich magnetic behavior enabled by enlarged internal symmetries.

The low-energy effective Hamiltonian of a cylindrical HgTe nanowire grown along the [001] crystallographic direction is constructed by using the perturbation theory. Both the anisotropic term and the bulk inversion asymmetry term of the Kane model are taken into account. Although the anisotropic term has converted the crossing between the $E_{1}$ and $H_{1}$ subbands into an anticrossing at $k_{z}R\!=\!0$, the gap-closing-and-reopening transition in the subband structure can still occur at finite wave vectors $k_{z}R\!\approx\!\pm0.24$ for critical nanowire radius $R\!\approx\!3.45$ nm. The bulk inversion asymmetry does not contribute to the low-energy effective Hamiltonian, i.e., there is no spin splitting in the $E_{1}$, $H_{1}$, and $H_{2}$ subbands for a [001] oriented cylindrical nanowire.

We reinvestigate known lower bounds for the Intersection Non-Emptiness Problem for Deterministic Finite Automata (DFA's). We first strengthen conditional time complexity lower bounds from T. Kasai and S. Iwata (1985) which showed that Intersection Non-Emptiness is not solvable more efficiently unless there exist more efficient algorithms for non-deterministic logarithmic space ($\texttt{NL}$). Next, we apply a recent breakthrough from R. Williams (2025) on the space efficient simulation of deterministic time to show an unconditional $Ω(\frac{n^2}{\log^3(n) \log\log^2(n)})$ time complexity lower bound for Intersection Non-Emptiness. Finally, we consider implications that would follow if Intersection Non-Emptiness for a fixed number of DFA's is computationally hard for a fixed polynomial time complexity class. These implications include $\texttt{PTIME} \subseteq \texttt{DSPACE}(n^c)$ for some $c \in \mathbb{N}$ and $\texttt{PSPACE} = \texttt{EXPTIME}$.

We construct analogues of Fenchel-Nielsen coordinates on an open and dense subset of the space of holonomies of branched hyperbolic structures on a closed genus-2 surface. We show that these coordinates satisfy an analogue of Wolpert's magic formula, and thus provide Darboux charts for the Goldman symplectic form. To this end, we revisit the parametrization of hyperbolic structures on a one-holed torus and describe a simple polygonal model that makes both length and twist parameters transparent. Gluing two such polygons leads to the notion of bow-tie representations of a genus-2 surface group. We prove that bow-tie representations account for most holonomies of branched hyperbolic structures, though not all: for example, Le Fils' pentagon representations form a real codimension-2 family of holonomies lying outside the bow-tie locus.

The highly anticipated 'Battle of the Water Networks' is back with a new challenge for the water community. This competition will be hosted at the 4th International Joint Conference on Water Distribution Systems Analysis and Computing and Control in the Water Industry (WDSA/CCWI 2026), taking place in Paphos, Cyprus, from May 18-21, 2026. This competition embodies the core mission of Water-Futures and the theme for WDSA/CCWI 2026: "Designing the next generation of urban water (and wastewater) systems." The objective is to design and operate a water distribution system over a long-term horizon under deep uncertainty, with interventions applied in stages. For the first time, this challenge features a staged-design approach, unobservable and unknown uncertainties, and incorporates elements of policymaking and artificial intelligence. The solutions will be assessed using a transparent and inspectable open-source evaluation framework.

Fundamental quantum transition time scales are accessible through the spin polarization of photoelectrons coming from initially spin-degenerate states for solid-state materials . In this work we investigate the modification of this time scale in the vicinity of a Fano resonance in photoemission from a solid. We employ spin- and angle-resolved photoemission spectroscopy (SARPES) to study the valence band of 1T-TiSe$_2$ and 1T-TiTe$_2$, with an excitation photon energy coinciding with the Ti 3p-3d autoionization state. The energy derivative of the measured spin polarization, which is in the off-resonance case proportional to the transition time, reveals a sign reversal and significant magnitude decrease compared to off-resonance measurements. We show that this effect goes beyond conventional semi-analytical models used to translate spin polarization to the EWS time delay. At the Fano resonance, the underlying interference assumption of the model breaks down, and additional information about resonance strength is needed to extract the transition time delays.

In this work, we consider wave propagation in materials characterized by nonlinear properties or damage. To accelerate the simulations of the resulting high-dimensional problems, we apply model order reduction methods. Depending on the knowledge of the underlying equations and the availability of their discrete operators, intrusive methods (here projection-based approaches based on proper orthogonal decomposition (POD)) or non-instrusive methods (here data-driven approaches including dynamic mode decomposition (DMD) and operator inference (OpInf)) can be used. We recall the theoretical foundations of the methods and apply them to the problem of wave propagation. In three different numerical examples, we evaluate the performance of the reduction techniques.

Recently, a new framework for studying generic $2 \to 3$ hard exclusive reactions, referred to as single-diffractive hard exclusive processes, has been introduced to provide a cleaner separation of the underlying physical mechanisms. In this work, we expand this formalism to the case of exclusive real-photon electroproduction off a nucleon, $e(\ell) + N(p) \to e(\ell') + N(p') + γ(q')$, which represents the classical channel for accessing generalized parton distributions (GPDs) in nucleons and nuclei. This extension enables a more systematic and physically transparent formulation of the reaction dynamics, paving the way for improved extractions of GPDs from experimental data as compared to existing approaches.

We present the characterization of macrolensing properties of the gravitationally lensed system PKS 1830-211, utilizing data from the Fermi Large Area Telescope. While at gamma-rays we can not spatially resolve the lensed images, a macrolensing-induced time pattern is expected in the blazar's lightcurve, resulting from the delay between variable gamma-ray components originating from its two brightest lensed images. Compared to our previous study, here we employ high-quality lightcurves coupled with prolonged outburst activity, and improved time-series techniques. Analyzing six independent data segments, we identified a delay of 20.26 +/- 0.62 days (statistical and stochastic uncertainty), with a chance detection probability at the 2.5 x $10^{-5}$ level (post-trial). We also present a novel approach to the magnification ratio estimate based on a comparison with simulated data. Our work suggests that the gamma-ray flux ratio between the two main lens components is $μ_γ \lesssim$ 1.8. We do not observe convincing evidence of microlensing effects, as previously claimed. The measured gamma-ray time delay is in 2-sigma tension with radio-based estimates, suggesting either distinct emission sites, underestimated radio uncertainties, or gamma-ray production in a region opaque to radio. Our study highlights the potential of well sampled lightcurves and advanced time-series techniques to distinguish true lensing-induced delays from stochastic variability. When combined with improved radio constraints and refined lens models, PKS 1830-211 and similar sources constitute promising systems for time-delay cosmography, offering new insights into both jet structure and cosmological parameters.

The nature of the compact objects within the supposed "lower mass gap" remains uncertain. Observations of GW190814 and GW230529 highlight the challenges gravitational waves face in distinguishing neutron stars from black holes. Interpreting these systems is especially difficult because classifications depend simultaneously on measurement noise, compact binary population models, and equation of state (EOS) constraints on the maximum neutron star mass. We analyze 66 confident events from GWTC-3 to quantify how the probability of a component being a neutron star, P(NS), varies across the population. The effects are substantial, the dominant drivers of classification are the pairing preferences of neutron stars with other compact objects, and the neutron star spin distributions. The data reveals that P(NS) varies between 1% - 67% for GW230529's primary and between 51% - 100% for GW190425's primary. By contrast, P(NS) for GW190814's secondary varies by <10%, demonstrating robustness from its high signal-to-noise ratio and small mass ratio. Analysis using EOS information tends to affect P(NS) through the inferred maximum neutron star mass rather than the maximum spin. As it stands, P(NS) remains sensitive to numerous population parameters, limiting its reliability and potentially leading to ambiguous classifications of future GW events.

$E_G$ is a summary statistic that combines cosmological observables to achieve a test of gravity that is relatively model-independent. Here, we consider the power of a measurement of $E_G$ using galaxy-galaxy lensing and galaxy clustering with sources from the Rubin Observatory's Legacy Survey of Space and Time (LSST), and lenses from the Dark Energy Spectroscopic Instrument (DESI). We first update the theoretical framework for the covariance of $E_G$ to accommodate this Stage IV scenario. We then demonstrate that $E_G$ offers in principle a model-agnostic test of gravity using only linear-scale information, with the caveat that a careful treatment of galaxy bias is required. We finally address the persistent issue of $E_G$'s theoretical dependence on the measured value of $Ω_{\rm M}^0$. We propose a framework that takes advantage of the posterior predictive test to consistently incorporate uncertainty on $Ω_{\rm M}^0$ in tests of gravity with $E_G$, which should be of general use beyond the LSST+DESI scenario. Our forecasting study using this method shows that the prior information available for $Ω_{\rm M}^0$ is instrumental in determining the power of $E_G$ in the LSST+DESI context. For the full survey dataset, with priors on $Ω_{\rm M}^0$ from existing CMB data, we find that for some modified gravity scenarios considered, we are likely to be able to reject the GR null hypothesis.

Drug synergy is profoundly influenced by cellular context, as variations in protein interaction landscapes and pathway activities across cell types reshape how drugs act in combination. Most existing models overlook this heterogeneity, relying on static or bulk-level protein-protein interaction (PPI) networks that ignore cell-specific molecular wiring. The availability of large-scale transcriptomic data now enables the reconstruction of cell-line-resolved interactomes, offering a new foundation for contextualized drug synergy modeling. Here we present SynCell, a Contextualized Drug Synergy framework that integrates drug-protein, protein-protein, and protein-cell line relations within a unified graph architecture. SynCell leverages cell-line-specific PPI networks to embed the molecular context in which drugs act, and employs graph convolutional learning to model how pharmacological effects propagate through cell-specific signaling networks. This formulation treats synergy prediction as a cell-line-contextualized drug-drug interaction problem. Across the large-scale DrugCombDB benchmark, SynCell consistently outperforms state-of-the-art baselines - including DeepSynergy, HypergraphSynergy, HERMES, BAITSAO, DTF, and NHP - particularly in predicting synergies involving unseen drugs or novel cell lines. When benchmarked against these seven methods, SynCell demonstrates substantial gains in generalization and biological interpretability, confirming that contextualizing PPIs with cell-line resolution is indispensable for accurate synergy prediction.

We investigate the problem of detecting dependencies between the components of a high-dimensional vector. Our approach advances the existing literature in two important respects. First, we consider the problem under privacy constraints. Second, instead of testing whether the coordinates are pairwise independent, we are interested in determining whether certain pairwise associations between the components (such as all pairwise Kendall's $τ$ coefficients) do not exceed a given threshold in absolute value. Considering hypotheses of this form is motivated by the observation that in the high-dimensional regime, it is rare and perhaps impossible to have a null hypothesis that can be modeled exactly by assuming that all pairwise associations are precisely equal to zero. The formulation of the null hypothesis as a composite hypothesis makes the problem of constructing tests already non-standard in the non-private setting. Additionally, under privacy constraints, state of the art procedures rely on permutation approaches that are rendered invalid under a composite null. We propose a novel bootstrap based methodology that is especially powerful in sparse settings, develop theoretical guarantees under mild assumptions and show that the proposed method enjoys good finite sample properties even in the high privacy regime. Additionally, we present applications in medical data that showcase the applicability of our methodology.

The previously proposed modification of the standard (flat) inflationary $ΛCDM$ model in which the inflaton field(s) and ``dark energy" are replaced by the vacum in expanding Friedmann-Lemaître-Robertson-Walker Universe is studied. The expanding joint vacuum of the all ingrediences of matter, including Standard Model particles and a dark matter sector, is treated as a thermal equilibrium state at temporal Gibbons-Hawking temperature, proportional to the Hubble parameter, and chemical potentials equal to particle masses. This theory provides not only the new mechanism of inflation and its graceful exit, but also explains acceleration of expansion for the late Universe. The formalism can be combined with the anomalous quantum gravity effects leading to a viable baryogenesis mechanism and certain bounds on dark matter particle masses and lifetimes.

We consider the numerical solution of high-frequency scattering problems modeled by the Helmholtz equation with a bounded obstacle. Although the analysis of this problem dates back at least 50 years, over the past decade or so, tools and techniques from $\textit{semiclassical analysis}$ have provided a new perspective and been used to settle several long-standing open problems in this area. Semiclassical analysis works in phase space (i.e., position and frequency) and describes rigorously the extent to which solutions of high-frequency PDEs are dictated by the properties of the corresponding geometric-optic rays. The goals of the article are to (i) give a introduction to semiclassical analysis aimed at non-experts and (ii) showcase some of the numerical-analysis results about finite-element methods, boundary-element methods, and domain-decomposition methods obtained using semiclassical techniques.

We investigate the behavior of the Schmidt gap, the von Neumann entanglement entropy, and the non-stabiliserness in proximity to the classical phase transition of the one-dimensional long-range transverse-field Ising model (LRTFIM). Leveraging the time-dependent variational principle (TDVP) within a tensor-network formulation, we simulate thermal states through their purified tensor-network representations. Our results show that these observables, typically regarded as hallmarks of quantum criticality, exhibit pronounced and coherent signatures even at a classical thermal transition, highlighting the emergence of quantum complexity as the system nears thermal criticality.

The increasing depth of quantum circuits presents a major limitation for the execution of quantum algorithms, as the limited coherence time of physical qubits leads to noise that manifests as errors during computation. In this work, we focus on CNOT ladder circuits, which find applications in several quantum computing tasks, including the preparation of GHZ states, the implementation of fan-out and long-range CNOT gates, fermionic simulations, and the construction of ansatz circuits for variational quantum computing. The linearly increasing depth of a CNOT ladder circuit can be exchanged for constant CNOT depth at the expense of wider circuits that rely on mid-circuit measurements and classically controlled operations. Our error analysis shows that the choice between these two constructions depends on the relative difference between CNOT and idling error rates. Overall, the technique developed in this work enables low-depth implementations of circuits that are ubiquitous in quantum computing algorithms.

The manipulation of magnetization in ferromagnetic metals (FMs) through orbital torque (OT) has emerged as a promising route for energy-efficient magnetic devices without relying on heavy metals. While Ti and Cu are among the most extensively studied light nonmagnetic metals (NMs) for OT devices, theoretical calculations of the resulting torque have remained limited. Here, we present a systematic and quantitative theoretical study of current-induced torques in Ti/FM and Cu/FM (FM = Co, Ni) bilayers using realistic tight-binding models derived from \textit{ab initio} electronic structures. We find that the torque in Ti/FM is larger for Ni than for Co, but this trend does not necessarily hold in Cu/FM, revealing that the FM dependence of OT is not universal but varies with the orbital current source. Moreover, the dependence of OT on NM thickness clearly indicates its NM bulk origin in both Ti- and Cu-based systems. Notwithstanding, the quantitative characteristics of OT cannot be explained by a simplified picture based on the individual bulk properties of the NM or FM layers. These results provide microscopic insight and practical guidance for designing light-metal-based orbitronic devices.

We study superconformal indices of four-dimensional $SU(N)$ gauge theories with $\mathcal{N}=1,2,4$ supersymmetry. The usual representation of a gauge theory index involves multiple contour integrals and reflects the BPS spectrum at zero Yang-Mills coupling. To find an alternative, closed form expression, it is natural to attempt an evaluation of the integrals through residues. However, the presence of non-isolated essential singularities prevents a straightforward evaluation. We show how this difficulty can be resolved by fixing the residual Weyl symmetry of the integral. This allows us to evaluate the residue sums for superconformal indices of $SU(2)$ gauge theories in terms of basic and elliptic hypergeometric series. For the Macdonald index of the $\mathcal{N}=4$ $SU(2)$ super Yang--Mills theory, we show how known transformation formulas for basic hypergeometric series can be used to simplify the residue sum. We observe that the simplified form encodes features of the BPS spectrum at non-zero coupling and suggests the absence of fortuitous or non-graviton operators in the Macdonald sector. Furthermore, we evaluate the residue sums for the Macdonald and full superconformal indices of a general class of $SU(2)$ gauge theories. In the process, we find various applications to the theory of basic and elliptic hypergeometric integrals, including a convergent residue sum for Spiridonov's elliptic beta integral. Finally, we discuss the generalization of our method to higher rank gauge groups and evaluate the $\mathcal{N}=4$ $SU(3)$ Macdonald index in closed form.

Coherent control and braiding of anyons remain central challenges in realizing topologically protected quantum operations. We propose a Ramsey interferometry protocol to directly access the geometric phases associated with anyons in fractional Chern insulators. Our approach employs impurities with individually addressable internal states that bind to the anyons, allowing their adiabatic motion and exchange under full spatial control. By combining Ramsey and spin-echo sequences using one and two impurities, the protocol gives independent access to the Aharonov-Bohm and exchange contributions to the total geometric phase, thereby providing an unambiguous probe of anyonic statistics. Our scheme can potentially be implemented in cold-atom quantum simulators as well as in van der Waals heterostructures. Complementary finite-size simulations in non-interacting Chern insulators quantify the system sizes required to faithfully extract geometric phases, highlighting the role of edge effects. Our results establish impurity-based interferometry as a feasible route toward direct anyon braiding experiments in quantum simulators and lay the groundwork for future explorations of non-Abelian braiding and topological quantum control.

Mobility-on-demand systems like ride-hailing have transformed urban transportation, but they have also exacerbated socio-economic inequalities in access to these services, also due to surge pricing strategies. Although several fairness-aware frameworks have been proposed in smart mobility, they often overlook the temporal and situational variability of user urgency that shapes real-world transportation demands. This paper introduces a non-monetary, Karma-based mechanism that models endogenous urgency, allowing user time-sensitivity to evolve in response to system conditions as well as external factors. We develop a theoretical framework maintaining the efficiency and fairness guarantees of classical Karma economies, while accommodating this realistic user behavior modeling. Applied to a simplified simulated mobility-on-demand scenario, we provide a proof-of-concept illustration of the proposed framework, showing that it exhibits promising behavior in terms of system efficiency and equitable resource allocation, while acknowledging that a full treatment of realistic MoD complexity remains an important direction for future work.

Beamforming with desired directivity patterns using compact microphone arrays is essential in many audio applications. Directivity patterns achievable using traditional beamformers depend on the number of microphones and the array aperture. Generally, their effectiveness degrades for compact arrays. To overcome these limitations, we propose a neural directional filtering (NDF) approach that leverages deep neural networks to enable sound capture with a predefined directivity pattern. The NDF computes a single-channel complex mask from the microphone array signals, which is then applied to a reference microphone to produce an output that approximates a virtual directional microphone with the desired directivity pattern. We introduce training strategies and propose data-dependent metrics to evaluate the directivity pattern and directivity factor. We show that the proposed method: i) achieves a frequency-invariant directivity pattern even above the spatial aliasing frequency, ii) can approximate diverse and higher-order patterns, iii) can steer the pattern in different directions, and iv) generalizes to unseen conditions. Lastly, experimental comparisons demonstrate superior performance over conventional beamforming and parametric approaches.

We establish quantitative stability results for classical distortion minimization problems in the theory of quasiconformal mappings. We consider the mean distortion functional and prove sharp stability estimates for the minimization problems regarding the linear stretch and spiral stretch maps, which arise as extremals in the class of mappins with finite distortion under appropriate boundary conditions. More precisely, we show that if a mapping has mean distortion close to the minimal value in the appropriate function class, then it must be quantitatively close, in certain Lebesgue norms.

Synchrony patterns characterize network states in which nodes organize into clusters based on their synchronized dynamics. The synchronized clusters may further exhibit either active or inactive states. The simultaneous invariance of active and inactive clusters of synchronized nodes poses a dynamical constraint because fluctuations from active clusters must cancel out for a desired cluster to be inactive. By exploiting permutation symmetries in the network structure and choosing dynamics on top such that internal dynamics and coupling functions are odd functions in the phase space, we demonstrate that this combination of structure and dynamics exhibits stable invariant patterns composed of coexisting active and inactive clusters. The symmetries in a network generate active clusters that are in antisynchrony with each other, resulting in the cancellation of fluctuations for clusters connected with these antisynchronous clusters. We use full network symmetries to obtain synchronized clusters, while quotient network symmetries are used to find coexisting active-inactive states of clusters. We show that as the coupling between nodes changes, active clusters lose their activity at different coupling values, and the network transitions from one activity pattern to another. Numerical simulations are presented for networks of Van der Pol and Stuart-Landau oscillators. Finally, we extend the master stability framework to these patterns and provide stability conditions for their existence.

We address the design of a model predictive control (MPC) scheme for large-scale linear systems using reduced-order models (ROMs). Our approach uses a ROM, leverages tools from robust control, and integrates them into an MPC framework to achieve computational tractability with robust constraint satisfaction. Our key contribution is a method to obtain guaranteed bounds on the predicted outputs of the full-order system by predicting a (scalar) error-bounding system alongside the ROM. This bound is then used to formulate a robust ROM-based MPC that guarantees constraint satisfaction and robust performance. Our method is developed step-by-step by (i) analysing the error, (ii) bounding the peak-to-peak gain, an (iii) using filtered signals. We demonstrate our method on a 100-dimensional mass-spring-damper system, achieving over four orders of magnitude reduction in conservatism relative to existing approaches.

Let $γ$-$\mathsf{GapSVP}_p$ be the decision version of the shortest vector problem in the $\ell_p$-norm with approximation factor $γ$, let $n$ be the lattice rank and $0<\varepsilon\leq 1$. We prove that there is no algorithm that solves $(2-\varepsilon)$-$\mathsf{GapSVP}_p$ uniformly for all $p\in\mathbb{N}$ in time\[ 2^{2^{o(p)}}\cdot 2^{o(n)},\] unless the Exponential Time Hypothesis is false. The proof is based on a deterministic Karp reduction from a constrained variant of the subset-sum problem to $\mathsf{GapSVP}_p$ for fixed $p$. While most hardness results for the shortest vector problem in finite norms rely on randomized reductions, our method is entirely deterministic. As a consequence, we also obtain a deterministic Karp reduction from the standard subset-sum problem to $(2-\varepsilon)$-$\mathsf{GapSVP}_{\infty}$.

The current work investigates the structural properties of neutron stars in the presence of a strong magnetic field within the framework of f(R,T) modified gravity, where the matter-geometry coupling leads to deviations from general relativity at high matter densities. We present here the mass-radius sequences, as well as the mass and pressure distributions for various values of the modified gravity parameter and the central magnetic field. The modified Tolman-Oppenheimer- Volkoff equations are numerically solved using isotropic equations of state, specifically the APR, FPS, and SLy models. Comparing the corresponding results in the context of general relativity suggests that more negative values of the modified gravity parameter result in higher maximum gravitational masses. In contrast, strong central magnetic fields of up to 1018 Gauss cause only a slight decrease in maximum mass without disrupting spherical symmetry. Our findings are in agreement with the observed data from GW170817, PSR and NICER.

We observe and model spin currents arising from chirality and effective spin-exchange interactions in a weakly interacting $^6$Li Fermi gas. Chirality is introduced by a static displacement between the center of the trapped atoms and the center of an applied magnetic bowl, which produces left- or right-handed spatially varying spin rotation. Spin current is directly observed via oscillations in the centers of mass of the spin-up and spin-down components, which appear to bounce off of or pass through one another, depending on the degree of handedness and s-wave scattering length. We show that this behavior obeys a driven oscillator equation with an effective spin-dependent driving force. Our measurements demonstrate chirality-induced spin selectivity via the direction of the current flow, extending CISS phenomena to Fermi gases.

The Krasnosel'ski\uı--Mann and Halpern iterations are classical schemes for approximating fixed points of nonexpansive mappings in Banach spaces, and have been widely studied in more general frameworks such as $CAT(κ)$ and, more generally, geodesic spaces. Convergence results and convergence rate estimates in these nonlinear settings are already well established. The contribution of this paper is twofold: first, we extend to complete $CAT(0)$ spaces proof techniques originally developed in the linear setting of Banach and Hilbert spaces, thereby recovering the same asymptotic regularity bounds; second, we introduce a Halpern--type optimizer for hyperbolic optimization as a nonlinear counterpart of the Euclidean HalpernSGD scheme.

In this paper, we propose a sample-based moving horizon estimation (MHE) scheme for general nonlinear systems to estimate the current system state using irregularly and/or infrequently available measurements. The cost function of the MHE optimization problem is suitably designed to accommodate these irregular output sequences. We also establish that, under a suitable sample-based detectability condition known as sample-based incremental input/output-to-state stability (i-IOSS), the proposed sample-based MHE achieves robust global exponential stability (RGES). Additionally, for the case of linear systems, we draw connections between sample-based observability and sample-based i-IOSS. This demonstrates that previously established conditions for linear systems to be sample-based observable can be utilized to verify or design sampling strategies that satisfy the conditions to guarantee RGES of the sample-based MHE. Finally, the effectiveness of the proposed sample-based MHE is illustrated through a simulation example.