The paper addresses the problem of transforming single-output discrete-time state equations into the generalized observer form, which comprises a linear observable component and a nonlinear injection term, depending on the inputs, output, and a finite number of their known past values. The intrinsic necessary and sufficient transformability conditions are provided, under two mild assumptions, in terms of a certain vector field, defined by the system output and its past values. The first assumption requires the state transition map to be invertible with respect to the state variable, and the second requires the constructibility rank condition to be satisfied. The algorithm is presented to find the required parametrized state transformation. The generalized observer form can be applied, under mild conditions, to also jointly estimate the states and disturbances. Two examples illustrate the theory.

Longitudinal studies have known widespread use in the last years in several fields of research, as they allow to distinguish between different sources of variation. We may observe differences at the beginning of the study that stay persistent through time, and changes in the response that are due to temporal dynamics in the observed covariates. Individual-specific, time-constant, effects are often included in the linear predictor to allow for unobserved individual-specific, time constant, heterogeneity motivated by omitted individual features. The random effect approach to estimation is based on considering such effects as random variables, usually with a specific parametric distribution. This approach has been frequently criticized, as it is often employed not considering correlation between observed (i.e., covariates) and unobserved (i.e., random effects) terms. To solve this issue, we may explicitly account for correlation between observed and unobserved heterogeneity, using the so-called correlated effects approach. In this article, we show that a more general solution may be developed by estimating the random effect conditional distribution non-parametrically via a discrete probability distribution on a finite number of locations. The approach we propose is assessed via a large-scale simulation study and illustrated by the analysis of a benchmark dataset.

Human communication is generally overt: We address each other with verbal cues, use eye contact, and point for each other, all to be understood and avoid misunderstandings. What are the cognitive underpinnings and evolutionary roots of overt communication? For decades, the Gricean interpretation of overt communication was taken for granted, despite two widely recognized problems: a developmental paradox in language acquisition and a methodological barrier to identifying the presence of its signature features in nonhuman animals. We introduce a further challenge: the "signaler assumption problem." This concerns the mechanism of how signalers are supposed to establish "common ground." We avoid these problems by replacing the Gricean approach with an evolutionarily grounded version of script theory, originally developed to model procedural knowledge. Our updated version of script theory posits that individuals recognize recurring situations as belonging to basic event schemata that form larger sets of patterned social interactions. In social interactions, individuals follow a finite number of scripts and understand others as following the same scripts. If the scripts of different individuals align during a social interaction, common ground is established. It is this common ground rather than mutual higher order mentalizing that renders a predominantly overt communication system possible. We review the theoretical and empirical literature and argue that the perception of social events as hierarchically structured scripts fostered the evolution of overt communication. Script theory offers an empirically more plausible and more parsimonious evolutionary explanation of the emergence of human linguistic communication than Gricean assumptions of complex mentalizing abilities. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

ABSTRACT This paper addresses the existence and large‐time asymptotic behavior of strong solutions to the viscous liquid–gas two‐phase flow model subject to slip boundary conditions in a three‐dimensional, simply connected bounded domain with a smooth boundary consisting of finite number 2D connected components. Compared to the Cauchy problem studied in Yu [ Journal of Differential Equations 272 (2021): 732–759] and Guo et al. [ Journal of Mathematical Physics 52 (2011): 9], the main advancement lies in overcoming key difficulties involving boundary integral estimates. We establish the global existence and uniqueness of strong solutions for the system provided that the initial energy is sufficiently small. Moreover, we characterize the large‐time decay of these solutions. Notably, our analysis allows for initial densities exhibiting large oscillations and including vacuum states.

Abstract Given a finite number of samples of a continuous set-valued function $F$, mapping an interval to nonempty compact subsets of $\mathbb{R}^{d}$, $F: [a,b] \to K(\mathbb{R}^{d})$, we discuss the problem of computing good approximations of $F$. We also discuss algorithms for a direct high-order evaluation of the graph of $F$, namely, the set $Graph(F)=\{(t,y)\ | \ y\in F(t),\ t\in [a,b]\}\in K(\mathbb{R}^{d+1})$. A set-valued function can be continuous and yet have points where the topology of the image sets changes. The main challenge in set-valued function approximation is to derive high-order approximations near these points. In a previous paper, together with Q. Muzaffar, we presented an algorithm for approximating set-valued functions with one-dimensional sets ($d=1$) as images, achieving a high approximation order near points of topology change. Here, we build upon the results and algorithms for the case $d=1$, first in more detail for the important case $d=2$, and later for approximating set-valued functions and their graphs in higher dimensions.

Comprehensive approaches to combat AMR empower discovery research efforts Antonio Ruzzini shares how enduring efforts to uncover AMR determinants in agrifood will enhance our understanding and management of the ongoing AMR crisis. The World Organisation for Animal Health (WOAH) and its List of Antimicrobial Agents of Veterinary Importance remind us that we possess a finite number of antibiotics to combat bacterial infections. The antimicrobial resistance (AMR) crisis is defined by the emergence of pathogens with genetic determinants that protect them from these essential therapies. Thousands of genetic determinants are known. How many AMR genes (ARGs) we have left to discover, what might evolve, and what might become prominent are unknowns.

This paper concentrates on the large-scale composite optimization problems, whose objective function is the aggregation of a finite number of nonconvex smooth functions and a nonconvex nonsmooth regularization term. While the existing proximal-like incremental aggregated gradient (PLIAG) algorithm performs well in solving large-scale optimization problems, it requires computing the proximal operators of the sum of two functions, which typically results in the absence of a closed-form solution or even hard to solve. Motivated by the Douglas-Rachford splitting method, we propose a implementing proximal incremental aggregated Douglas-Rachford splitting method, named as the Prox2-IAG method, which computes the proximal operators of the two functions respectively. The Prox2-IAG method includes many existing algorithms as special cases, such as the Douglas-Rachford method, the incremental aggregated gradient method and the incremental aggregated proximal method. Under the Kurdyka-Łojasiewicz property, we present the global convergence of the sequence generated by the Prox2-IAG method. Additionally, the convergence rate is established under the KL framework. Experiments are conducted on sparse logistic regression problem to demonstrate the efficiency of the Prox2-IAG algorithm.

In this work, we introduce an ansatz for continuous matrix-product operators for quantum field theory. We show that (1) they admit a closed-form expression in terms of finite number of matrix-valued functions without reference to any lattice parameter; (2) they are obtained as a suitable continuum limit of matrix-product operators; and (3) they preserve the entanglement area law directly in the continuum, and in particular they map a continuous matrix-product state (cMPS) to another cMPS. As an application, we use this ansatz to construct several families of continuous matrix-product unitaries beyond quantum cellular automata.

Kinetic theory offers a promising alternative to conventional turbulence modelling by providing a mesoscopic perspective that naturally captures non-equilibrium physics such as non-Newtonian effects. In this work, we present an extension and theoretical analysis of the kinetic model for incompressible turbulent flows developed by Chen et al. ( Atmosphere , 2023, vol. 14(7), p. 1109), constructed for unbounded flows. The first extension is to reselect a relaxation time such that the turbulent transport coefficients are obtained consistently and better align with well-established turbulence theory. The Chapman–Enskog (CE) analysis of the kinetic model reproduces the linear eddy-viscosity and gradient diffusion models for Reynolds stress and turbulent kinetic energy flux at the first order, and yields nonlinear eddy-viscosity and closure models at the second order. In particular, a previously unreported CE solution for turbulent kinetic energy flux is obtained. The second extension is to enable the model for wall-bounded turbulent flows with preserved near-wall asymptotic behaviours. This involves developing a low-Reynolds-number model incorporating wall damping effects and viscous diffusion, with boundary conditions enabling both viscous sublayer resolution and wall function application. Comprehensive validation against experimental and direct numerical simulation data for turbulent Couette flow demonstrates excellent agreement in predicting mean velocity profiles, skin friction coefficients and Reynolds shear-stress distributions, although the near-wall-normal stress anisotropy is underestimated. The results show that averaged turbulent flow behaves similarly to rarefied-gas flow at finite Knudsen number, capturing non-Newtonian effects beyond linear eddy-viscosity models. This kinetic model provides a physics-based foundation for turbulence modelling with reduced empirical dependence.

Abstract We consider the problem of minimizing a smooth and convex function over the n -dimensional spectrahedron — the set of real symmetric $$n\times n$$ n × n positive semidefinite matrices with unit trace, which underlies numerous applications in statistics, machine learning and additional domains. Standard first-order methods often require high-rank matrix computations which are prohibitive when the dimension n is large. The well-known Frank-Wolfe method on the other hand, only requires efficient rank-one matrix computations, however suffers from worst-case slow convergence, even under conditions that enable linear convergence rates for standard methods. In this work we present the first Frank-Wolfe-based algorithm that only applies efficient rank-one matrix computations and, assuming quadratic growth and strict complementarity conditions, is guaranteed, after a finite number of iterations, to converge linearly, in expectation, and independently of the ambient dimension.

This article studies approximations to the set of trajectories, attainable sets and integral funnel of a control system described by an ordinary differential equation. It is assumed that the equation is nonlinear with respect to the phase state vector and affine with respect to the control vector. The system includes control functions, some of which satisfy the \(L_p\) \((p\in (1,\infty))\) norm constraint, while the others satisfy the \(L_{\infty}\) norm constraint. Step by step, the set of admissible control functions is replaced by a set consisting of a finite number of piecewise-constant control functions that generate a finite number of trajectories. Error evaluations are provided for the Hausdorff distances between the set of trajectories, attainable sets, integral funnel, and their approximations, which depend on discretization parameters. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/27/abstr.html

We study randomized quasi-Monte Carlo (RQMC) estimation of a multivariate integral where one of the variables takes only a finite number of values. This problem arises when the variable of integration is drawn from a mixture distribution as is common in importance sampling and also arises in some recent work on transport maps. We find that when integration error decreases at an RQMC rate that it is then important to oversample the smallest mixture components instead of using a proportional allocation; this can even improve the rate of convergence. The optimal allocations depend on the possibly unknown convergence rate. Designing the sample with an incorrect assumption on the rate still attains that convergence rate, with an inferior implied constant. The penalty for using a pessimistic rate is typically higher than for using an optimistic one. We also find that for the most accurate RQMC sampling methods, it is advantageous to arrange that our n = 2 m randomized Sobol’ points split into subsample sizes that are also powers of 2.

BackgroundTotal generalized variation (TGV) based CT iterative reconstruction algorithm has the ability to effectively suppress the staircase effects caused by the piecewise constant assumption of total variation regularization. By unrolling the model-based iterative reconstruction to networks, the deep unrolling approach can further improve image quality within a finite number of iterations by data-driven training. However, most deep unrolling approaches focus on unrolling the data fidelity term into deep neural networks, which limit the performance of the deep unrolling approach.ObjectiveTo address this issue, we unrolled both the data fidelity term and the TGV term to construct a novel low-dose CT reconstruction network, called TGV based deep unrolling approach (TGV-DU).MethodsThe Chambolle-Pock algorithm was employed to solve the TGV based CT iterative reconstruction problem to obtain a single-loop CT iterative reconstruction algorithm, which is easy to be unrolled to neural networks. In the proposed algorithm, the parameterized mapping that updates primal variables and dual variables across successive iterations was implemented by convolutional neural networks and was dynamically learned from big data.ResultsTo validate the effectiveness of our proposed algorithm, we perform the experiment on the "Low-Does CT Image and Projection Data" dataset. The results show that the proposed TGV-DU outperforms other state-of-the-art methods quantitatively and qualitatively.ConclusionsExperiments show that our proposed algorithm can effectively alleviate the piecewise smoothness while preserve more structural details.

This short note modifies a reconstruction method by the author Garde (2020), for reconstructing piecewise constant conductivities in the Calderón problem (electrical impedance tomography). In the former paper, a layering assumption and the local Neumann-to-Dirichlet map were needed since the piecewise constant partition also was assumed unknown. Here I show how to modify the method in case the partition is known, for general piecewise constant conductivities and only a finite number of partial boundary measurements. Moreover, no lower/upper bounds on the unknown conductivity are needed.

This article proposes an accelerated learning control framework for point-to-point (P2P) tracking systems subject to stochastic noise, with a focus on reducing input energy. A novel stochastic accelerated method with a fixed penalty factor is established, resulting in substantial performance advancements for the overall iteration process. In this method, we introduce a two-loop structure. A historical term is designed and appropriately incorporated into the input update to improve the convergence process of the inner loop, and a Lagrange multiplier is updated in the outer loop to ensure the input sequence to converge to a limit that is closest to the initial input, achieving the effect of energy reduction. Additionally, practical implementation of the proposed framework is addressed by terminating the inner loop within a finite number of iterations according to a given accuracy. In this scenario, two types of Lagrange multiplier updating are conducted to handle the noise's impact. Numerical simulations are provided to validate the theoretical results.

In this article, a hybrid intelligent optimization method is proposed for the dynamic optimization of path-constrained switched systems with free switching sequences. This method combines improved particle swarm optimization and differential evolution (IPSO-DE) method with a gradient-based dynamic optimization method, which can simultaneously obtain the global optimal solution, i.e., optimal control input, optimal switching instants, and optimal switching sequences. First, control vector parameterization (CVP), switching time parameterization (STP), and switching sequence smoothing techniques are employed to transform the original problem into a continuous finite-dimensional dynamic one. Second, the path constraints are discretized into a finite number of point constraints, and the IPSO-DE algorithm is proposed to search for the global optimal solution of the continuous dynamic problem with discretized constraints. Then, the obtained optimal solution serves as the initial point to calculate the gradients of the objective function with respect to control input, switching instants, and switching sequences. Third, the gradient-based deterministic method is applied to obtain the global optimal solution that satisfies the first-order optimality condition. Fourth, the finite termination of the hybrid intelligent optimization method is proven. Finally, the effectiveness of the proposed method is verified through three numerical examples.

ABSTRACTRecent technical advances have significantly enhanced the value of museum specimens for molecular research, with metagenomic and metabarcoding approaches expanding further the utility of museum collections. However, given the finite number of specimens, there is a critical need to move past destructive DNA extraction approaches and to explore non‐destructive techniques. In this proof‐of‐concept study, we evaluated the feasibility of extracting historical eDNA from the ethanol preservative used to store museum specimens. We compared a variety of extraction methods (centrifugation, evaporation, filtration, and precipitation) using ten replicate samples per treatment for statistical analyses. To assess potential differences in preservative‐derived eDNA recovery across different filter‐feeding taxonomic groups, we included a bryozoan, a demosponge, and a glass sponge. Comparative analyses with tissue biopsies revealed that 10 mL ethanol filtration performed equal to or, in some instances, outperformed tissue biopsies for all three specimens when examining the historical eDNA of Antarctic fish using a 16S rRNA metabarcoding approach, both for the number of species detected (α‐diversity) and community characterisation (β‐diversity). This initial study demonstrates the potential of ethanol preservative as a valuable, non‐destructive source of historical eDNA from museum‐stored filter‐feeding specimens. These findings highlight the viability of non‐destructive sampling for molecular research on museum collections, preserving specimen integrity while enabling biodiversity assessments. Further refinement of non‐destructive eDNA extraction could expand its applicability across taxa, collection types, and preservation methods, ensuring the long‐term sustainability of museum‐based genomic, metagenomic, and metabarcoding research.

An underrecognized clinical condition that may afflict high level cyclists is external iliac artery endofibrosis (EIAE). EIAE is an intermittent claudication vascular condition that results from intimal narrowing most often of the external iliac artery (EIA). Symptoms are reported as thigh pain and loss of power that occur during high intensity efforts. EIAE is theorized to be a result of the mechanical and hemodynamic stress within the EIA heightened by psoas muscle hypertrophy in conjunction with the repetitive and extreme hip flexion coupled with high cardiac output. A combination of clinical tests (e.g. ankle-brachial index) in concert with imaging and vascular studies (e.g. duplex ultrasound) is necessary to arrive at an accurate diagnosis. The mean time from symptom onset to diagnosis is 3 years. Conservative interventions, which consist of bike hardware adjustments and/or posture modifications while riding, are generally not acceptable for a competitive cyclist. Surgical interventions take the form of percutaneous/endoscopic (e.g. balloon angioplasty, stent insertion) or open procedures (e.g. arterial release, endarterectomy, artery reconstruction) to restore arterial flow. Long-term outcomes following percutaneous procedures have followed a finite number of patients to date and are not recommended as a primary intervention for EIAE. Outcomes following open surgical procedures are strong with most riders being able to return to preinjury levels of competition. Greater awareness of EIAE among the scientific and medical community who work with cyclists is needed to improve the efficiency and overall management of EIAE.

In this paper, we investigate a two-species competition model in a landscape consisting of a finite number of adjacent patches. For the two-patch scenario, by treating edge behavior at the interface as a strategy, it has been shown that there exists an ideal free distribution (IFD) strategy, which is a globally evolutionarily stable strategy. Specifically, when the resident species follows the IFD strategy and the mutant species does not, the mutant species is unable to invade the resident population. Building on this foundation, our work focuses on exploring the dynamics of the system when neither species can adopt the IFD strategy. We demonstrate that if the strategies of both species either exceed or fall below the IFD strategy, the mutant species can outcompete and eliminate the resident species, provided that its strategy is closer to the IFD strategy and its diffusion rates are equal to or slower than those of the resident species. Furthermore, if the strategies of the two species lie on opposite sides of the IFD strategy, the two species can coexist. This result is further extended to the case of an arbitrary but finite number of patches.

The calculation of neutron kinetics functionals, including the effective fraction of delayed neutrons ( β eff ) and the prompt neutron generation time (Λ), by the Monte Carlo method is known to be challenging due to the complexities involved in calculating the adjoint function. In the context of the Monte Carlo method, it is optimal to represent the importance function as the asymptotic number of descendants of a neutron placed at a given point in phase space. In practice, it is possible to consider only a finite number of generations. This limitation forms the basis of the Iterated Fission Probability (IFP) method. However, this approach is associated with several disadvantages, including the convergence of the adjoint source through a given number of generations, the appearance of statistical noise, and high memory consumption. In this paper, we present a methodology for calculating the multigroup importance function using the matrix method implemented in the MCU code. The computational model is partitioned into a finite number of tally objects and energy groups. During the modeling process, the elements of the fission matrix are tallied, and the neutron importance function for each energy group of each object is calculated at the post-processing stage. The methodology was validated by calculating β eff and Λ for 6 ICSBEP Handbook experiments. The one- and 14-group approximation of the importance function yielded almost identical results, with a negligible difference (less than 1%), due to the minor change in importance in the energy range where most neutrons are generated.