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Second-order nonlinear processes like Sum-Frequency Generation (SFG) are essentially defined in the electric dipolar approximation. However, when dealing with the SFG responses of bulk, big nanoparticles, highly symmetric objects, or chiral species, magnetic and quadrupolar contributions play a significant role in the process too. We extend the diagrammatic theory for linear and nonlinear optics to include these terms for single objects as well as for multipartite systems in interaction. Magnetic and quadrupolar quantities are introduced in the formalism as incoming fields, interaction intermediates, and sources of optical nonlinearity. New response functions and complex nonlinear processes are defined, and their symmetry properties are analyzed. This leads to a focus on several kinds of applications involving nanoscale coupled objects, symmetric molecular systems, and chiral materials, both in line with the existing literature and opening new possibilities for original complex systems. [ABSTRACT FROM AUTHOR]

Developing fluorescence-encoded infrared (FEIR) vibrational spectroscopy for single-molecule applications requires a detailed understanding of how the molecular response and external experimental parameters manifest in the detected signals. In Paper I [L. Whaley-Mayda, A. Guha, and A. Tokmakoff, J. Chem. Phys. 159, 194201 (2023)] we introduced a nonlinear response function theory to describe vibrational dynamics, vibronic coupling, and transition dipole orientation in FEIR experiments with ultrashort pulses. In this second paper, we apply the theory to investigate the role of intermode vibrational coherence, the orientation of vibrational and electronic transition dipoles, and the effects of finite pulse durations in experimental measurements. We focus on measurements at early encoding delays—where signal sizes are largest and therefore of most value for single-molecule experiments, but where many of these phenomena are most pronounced and can complicate the appearance of data. We compare experiments on coumarin dyes with finite-pulse response function simulations to explain the time-dependent behavior of FEIR spectra. The role of the orientational response is explored by analyzing polarization-dependent experiments and their ability to resolve relative dipole angles in the molecular frame. This work serves to demonstrate the molecular information content of FEIR experiments, and develop insight and guidelines for their interpretation. [ABSTRACT FROM AUTHOR]

This article develops a neuro‐adaptive observer for state and nonlinear function estimation in systems with partially modeled process dynamics. The developed adaptive observer is shown to provide exponentially stable estimation errors in which both states and nonlinear functions converge to their true values. When the neural approximator has an approximation error with respect to the true nonlinear function, the observer can be used to provide an H∞$$ {H}_{\infty } $$ bound on the estimation error. The article does not require assumptions on the process dynamics or output equation being linear functions of neural network weights and instead assumes a reasonable affine parameter dependence in the process dynamics. A convex problem is formulated and an equivalent polytopic observer design method is developed. Finally, a hybrid estimation system that switches between a neuro‐adaptive observer for system identification and a regular nonlinear observer for state estimation is proposed. The switched operation enables parameter estimation updates whenever adequate measurements are available. The performance of the developed adaptive observer is shown through simulations for a Van der Pol oscillator and a single link robot. In the application, no manual tuning of adaptation gains is needed and estimates of both the states and the nonlinear functions converge successfully. [ABSTRACT FROM AUTHOR]

This paper proposes a fixed-time fuzzy adaptive output feedback control scheme for the robotic arm model (RAM) of steel structures. Firstly, the process of transforming RAM into a nonlinear system is elaborated. Secondly, a fuzzy observer is designed to approximate the nonlinear function and estimate the observed state of the system. Subsequently, a fixed-time adaptive controller is constructed, ensuring the system's stability within a fixed time, with the convergence time unaffected by the initial state. Finally, the effectiveness of the strategy is verified through simulation examples. [ABSTRACT FROM AUTHOR]

Given the Fourier–Legendre expansions of f and g , and mild conditions on f and g , we derive the Fourier–Legendre expansion of their product in terms of their corresponding Fourier–Legendre coefficients. We establish upper bounds on rates of convergence. We then employ these expansions to solve semi-analytically a class of nonlinear PDEs with a polynomial nonlinearity of degree 2. The obtained numerical results illustrate the efficiency and performance accuracy of this Fourier–Legendre-based solution methodology for solving a class of nonlinear PDEs. [ABSTRACT FROM AUTHOR]

The paper builds on earlier research in which a full Bayesian approach was used to derive crash modification factors (CMFs) from regression models that capture the variability in these CMFs. The approach estimates a non-linear function that reflects the logical reality that the CMF for a given change in a feature's value depends not only on the amount of the change but also on the original value. However, in developing the approach, it was necessary to amalgamate panel data over several years by averaging annual traffic volumes and modeling the summation of annual crash counts. Such aggregation could be problematic if there is significant temporal variability in traffic volumes and crash frequencies, as would be the assumption that there is no site-to-site variation in the effects of independent variables on the crash frequency. The research for this paper examined whether these limitations can materially affect the CMF estimates by using simulated data to introduce substantial temporal and spatial variability in expected crash frequencies. A non-linear model with random effects that captures this variability was developed and compared to the non-linear model with fixed effects. The results show that the parameter estimates and CMFs for freeway median width, the feature used for the case study, were almost identical for the two non-linear approaches. This suggests that the aggregation approach in the earlier research may be adequate for capturing the non-linear safety effects of roadway attributes. The finding has practical importance in the sense that the amalgamation is often necessary when traffic data are not available for each year and also in the sense that when such amalgamation is done, the extent of the temporal variability in traffic volumes and expected crash frequencies is usually unknown. Future studies should expand the investigation to datasets that exhibit temporal variations in some features, such as pavement friction. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the delayed-advanced Kaldorian business cycle model and consider how time-delay and time-advance affect economic fluctuations. Given the asymptotic stability of the original Kaldor model, we first show that an approximated Kaldor model by a Taylor series expansion can accurately describe the dynamics of the delayed Kaldor model. We also confirm that the delay has a destabilizing effect. When time-delay is replaced with time-advance, we have an advanced Kaldor model. Taking the advanced capital stock formulation, we derive the stability conditions and find that the time-advance has a stabilizing effect. Lastly, we examine these opposite-signed effects in a modified delayed-advanced model. [ABSTRACT FROM AUTHOR]

Nonlinear activation functions play a crucial role in artificial neural networks. However, digital implementations of sigmoidal functions, the commonly used activation functions, are facing challenges related to energy consumption and area requirements. To address these issues, we develop a proof-of-concept computing system that utilizes magnetic tunnel junctions as the key element for implementing sigmoidal activation functions. Using this system, we train a neural network for speech separation. When compared to state-of-the-art digital implementations, our scalable circuit has the potential to consume up to 383 times less energy and occupy 7354 times smaller area. These results pave the way for more efficient computing systems in the future. [ABSTRACT FROM AUTHOR]

In this paper, based on linear matrix inequality technique, a simple controller and a compensatory controller are designed. It can track arbitrary fixed points and any periodic orbits. In addition, a synchronization control method via Chebyshev neural network with external disturbances is proposed. An adaptive controller is given. The Chebyshev neural network is used to approximate the uncertain nonlinear function and the adaptive law is used to adjust the corresponding parameters in the system. Taking a 4D memristive chaotic system as examples, the results are in consistent with the simulations. From a framework and control theoretical point of view, the proposed synchronization approach via compensation controller and Chebyshev neural network is firstly presented. From an application point of view, the proposed scheme can simplify the complexity of controller design. It is promising in many applications for mem-systems as secure communications and neural networks. [ABSTRACT FROM AUTHOR]

Background: Time-varying exposures like pet ownership pose challenges for identifying critical windows due to multicollinearity when modeled simultaneously. The Distributed Lag Model (DLM) estimates critical windows for time-varying exposures, which are mainly continuous variables. However, applying complex functions such as high-order splines and nonlinear functions within DLMs may not be suitable for situations with limited time points or binary exposure, such as in questionnaire surveys. Objectives: (1) We examined the estimation performance of a simple DLM with fractional polynomial function for time-varying binary exposures through simulation experiments. (2) We evaluated the impact of pet ownership on childhood wheezing onset and estimate critical windows. Methods: (1) We compared logistic regression including time-varying exposure in separate models, in one model simultaneously, and using DLM. For evaluation, we employed bias, empirical standard error (EmpSE), and mean squared error (MSE). (2) The Japan Environment and Children's Study (JECS) is a prospective birth cohort study of approximately 100,000 parent-child pairs, registered across Japan from 2011 to 2014. We applied DLM to the JECS data up to age 3. The estimated odds ratios (OR) were considered to be within critical windows when they were significant at the 5% level. Results: (1) DLM and the separate model exhibited lower bias compared to the simultaneously model. Additionally, both DLM and the simultaneously model demonstrated lower EmpSEs than the separate model. In all scenarios, DLM had lower MSEs than the other methods. Specifically, where critical windows is clearly present and exposure correlation is high, DLM showed MSEs about 1/2 to 1/200 of those of other models. (2) Application of DLM to the JECS data showed that, unlike other models, a significant exposure effect was observed only between the ages of 0 and 6 months. During that periods, the highest ORs were 1.07 (95% confidence interval, 1.01 to 1.14) , observed between the ages of 2 and 5 months. Conclusions: (1) A simple DLM improves the accuracy of exposure effect and critical windows estimation. (2) 0–6 months may be the critical windows for the effect of pet ownership on the wheezing onset at 3 years. [ABSTRACT FROM AUTHOR]

Summary: The problem of interval observer design for systems described by nonlinear models with uncertainties is considered. The problem is solved based on special mathematical technique (the algebra of functions) which allows obtaining solution for systems containing non‐smooth nonlinearities. The relations to design interval observer insensitive or having minimal sensitivity to the disturbance and estimating the prescribed nonlinear function of the state vector of the original system are derived. Theoretical results are illustrated by example. [ABSTRACT FROM AUTHOR]

Summary: This article considers the problem of designing distributed event‐triggered states and unknown disturbances observers for a class of nonlinear interconnected systems where the local state vectors are affected by unknown delays and the nonlinear function satisfying the Lipschitz condition. Distributed observers are designed based on the local input vector and both the local and remote output vectors. Different from previously distributed observers for interconnected systems where the local and remote output vectors are updated continuously, the one in this article uses only information on the local and remote output vectors updating at triggering instants of proposed event‐triggered mechanisms. This indicates that the proposed method in this article is better than the existing ones in saving communication resources while still keeping an acceptable estimation performance. Sufficient conditions for the existence of the proposed distributed observers are established and are formed in a convex optimization problem which can be easily solved by using the MATLAB LMI Control Toolbox. Finally, a numerical example is given to confirm the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: Nonlinear systems widely exist in real‐word applications and the research for these systems has enjoyed a long and fruitful history, including the system identification community. However, the modeling for nonlinear systems is often quite challenging and still remains many unresolved questions. This article considers the online identification issue of Hammerstein systems, whose nonlinear static function is modeled by a B‐spline network. First, the identification model of the studied system is constructed using the bilinear parameter decomposition model. Second, the online recursive algorithms are proposed to find the estimates using the moving data window and the particle swarm optimization procedure, and show that these estimates converge to their true values with a low computational burden. Numerical examples are also given to test the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article addresses the attitude manoeuvre control without unwinding based on variable gain (i.e. adaptive) super-twisting algorithm (STA) and the modified Rodrigues parameters (MRPs). First, a selection logic for the MRP set and its shadow set is designed in order to construct an attitude control system model for rigid spacecraft. Second, a nonlinear sliding function is presented, and on the sliding phase, finite-time convergence and anti-unwinding performance are guaranteed. As a result, a first-order sliding mode controller is created to ensure finite-time convergence and anti-unwinding performance on the reaching phase. To alleviate the chattering and improve convergence speed, an adaptive STA is presented, and the finite-time convergence and anti-unwinding performance are guaranteed on the reaching phase. Furthermore, the adaptive gains are designed based on dual-layer adaptive law, which allows the gains to be increased and decreased as appropriate. It is further demonstrated that when the controller gains are time-varying according to adaptive law, the convergence property and anti-unwinding performance are guaranteed. Numerical simulations are carried out to illustrate the closed-loop system's performance under the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper discusses pseudospectra and stability radii for structured nonlinear matrix functions, such as Hermitian, skew‐Hermitian, H‐even, H‐odd, complex symmetric, and complex skew‐symmetric. To compute pseudospectra and stability radii, eigenvalue backward error is required. Hence, we initially present the structured eigenvalue backward error. Subsequently, we compute the structured pseudospectra using the obtained results for the eigenvalue backward error of a class of structured nonlinear matrix functions. Finally, we discuss the stability radii of the above‐structured problems arising in different applications. The paper also generalizes the results on the eigenvalue backward error of matrix polynomials in the literature for the above structures. [ABSTRACT FROM AUTHOR]

This paper provides a new sliding mode control (SMC) approach, by which both the nominal and robust stability associated with a trajectory tracking problem for an uncertain robot manipulator are achieved. More precisely, the new control law consists of linear and nonlinear functions of tracking errors, in which the former is for the nominal stability and the latter is to ensure the robust stability of the resulting closed‐loop systems. The nonlinear function can be interpreted as an extended version of conventional SMC approach, and the reaching phase corresponding to a pregiven sliding surface is shown to be completed in a finite time; the tracking errors arrive at the sliding surface in a finite time and do not deviate from it after the arrival. In the sliding phase, the tracking errors are also ensured to converge to the origin. Finally, some simulation results are given to demonstrate both the theoretical validity and practical effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

The efficiency and dynamic response of air compressors are crucial for stability and lifespan of hydrogen fuel cells. A predictive control scheme with surge‐ and choke‐constrained awareness is proposed to ensure safe and efficient operation of air compressors in this study. The proposed scheme consists of an efficiency enhancement model predictive control (EE‐MPC), and an improved active disturbance rejection control (IADRC). Surge‐ and choke‐constrained awareness is achieved by comparing predicted air flow with surge and choke limitations. Simultaneously, the EE‐MPC is constrained with oxygen excess ratio (OER) and obtains optimal solution by searching active set. The reference flow and supply manifold pressure trajectories for IADRC are generated by EE‐MPC. A designed piecewise differentiable nonlinear smoothing function is embedded in IADRC. The disturbances are estimated for coordinating flow and pressure control. Under China heavy‐duty commercial vehicle test cycle for bus conditions, root‐mean‐squared errors (RMSEs) of flow and pressure are 3.27 g s−1 and 1.88 × 103 Pa, respectively, and the mean efficiency can be enhanced by 13.4% compared to the MPC with fixed OER. Finally, a controller hardware‐in‐the‐loop test is conducted, with flow and pressure RMSEs of 2.48 g s−1 and 4.28 × 103 Pa between the test and simulation, respectively. [ABSTRACT FROM AUTHOR]

The study delves into higher-order networks, extending beyond pairwise connections, using modulated laser models, and employing simplicial complexes to model non-pairwise interactions. Two coupling scenarios, linear and nonlinear diffusive functions, are explored. Our results demonstrate that the linear diffusive coupling leads to synchronization, further enhanced with multi-node interactions, and a tendency for forming synchronous clusters before complete synchrony. In contrast, nonlinear diffusive coupling results in a cluster synchronization state with oscillation death and periodic solutions, along with observed chimera and solitary states. In this scenario, the network fails to achieve complete synchrony. Regardless of the coupling function, the network exhibits different solutions within each synchronization pattern, showcasing the potential for multistability—the coexistence of stable solutions across various collective dynamics. [ABSTRACT FROM AUTHOR]

The classical PID (proportional‐integral‐derivative) control is the most basic and widely used control algorithm in engineering systems by far. Whether PID control can effectively deal with coupled multiagent uncertain nonlinear dynamics is well worth investigating. In this article, a class of PID controlled multiagent stochastic systems with coupled uncertain dynamics is considered, where the control input is nonaffine. Each agent has its own regulation objective, and only has access to its own regulation error information for PID feedback. First, a PID parameter set will be constructed explicitly based on some prior knowledge about the nonlinear functions, such that the overall multiagent system can be stabilized globally in the mean square sense, as long as the PID parameters are chosen from the constructed set. Moreover, the regulation error will be proven to have an upper bound proportional to the noise intensity along the reference signal. Furthermore, it will be shown that the regulation error of each agent can be arbitrarily small by choosing the PID parameters suitably large. Finally, the theoretical results will be verified by simulations. [ABSTRACT FROM AUTHOR]

The current investigation address a novel generalized elasto‐thermodiffusion model for a thermoelastic porous half‐space incorporating the nonlocal stress theory proposed by Eringen. Modeling of the problem is performed by adopting Moore‐Gibson‐Thompson (MGT) thermoelasticity theory defined in an integral form of a common derivative on a slipping interval, well known as the memory‐dependent derivative. The bounding plane of the medium is subjected to time‐dependent thermal and chemical shocks and there is no change in the volume fraction field. Laplace transform and the Fourier transform techniques have been adopted to represent the analytical solutions in the transformed domain. The distributions of the physical fields such as the temperature, stress, chemical potential, mass concentration and the volume fraction field were found in the real space‐time domain adopting suitable numerical scheme based on the Fourier series expansion. According to the discussion of the computational results and the respective graphical representations, the prominent role of different parameters such as the effect of nonlocality, effect of void and thermodiffusion is analyzed. Moreover, the superiority of a nonlinear kernel function compared to a linear form is also reported. [ABSTRACT FROM AUTHOR]

The non-convex α ⁢ ∥ ⋅ ∥ ℓ 1 − β ⁢ ∥ ⋅ ∥ ℓ 2 ( α ≥ β ≥ 0 ) regularization is a new approach for sparse recovery. A minimizer of the α ⁢ ∥ ⋅ ∥ ℓ 1 − β ⁢ ∥ ⋅ ∥ ℓ 2 regularized function can be computed by applying the ST-( α ⁢ ℓ 1 − β ⁢ ℓ 2 ) algorithm which is similar to the classical iterative soft thresholding algorithm (ISTA). Unfortunately, It is known that ISTA converges quite slowly, and a faster alternative to ISTA is the projected gradient (PG) method. Nevertheless, the current applicability of the PG method is limited to linear inverse problems. In this paper, we extend the PG method based on a surrogate function approach to nonlinear inverse problems with the α ⁢ ∥ ⋅ ∥ ℓ 1 − β ⁢ ∥ ⋅ ∥ ℓ 2 ( α ≥ β ≥ 0 ) regularization in the finite-dimensional space R n . It is shown that the presented algorithm converges subsequentially to a stationary point of a constrained Tikhonov-type functional for sparsity regularization. Numerical experiments are given in the context of a nonlinear compressive sensing problem to illustrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

A biomechanical model often requires parameter estimation and selection in a known but complicated nonlinear function. Motivated by observing that the data from a head-neck position tracking system, one of biomechanical models, show multiplicative time-dependent errors, we develop a modified penalized weighted least squares estimator. The proposed method can be also applied to a model with possible non-zero mean time-dependent additive errors. Asymptotic properties of the proposed estimator are investigated under mild conditions on a weight matrix and the error process. A simulation study demonstrates that the proposed estimation works well in both parameter estimation and selection with time-dependent error. The analysis and comparison with an existing method for head-neck position tracking data show better performance of the proposed method in terms of the variance accounted for. [ABSTRACT FROM AUTHOR]

To solve the difficulties in threshold selection and poor performance under low signal‐to‐noise ratio (SNR) conditions in existing spectrum sensing algorithms, a graph‐based spectrum sensing algorithm using nonlinear function regulation was proposed. The idea was to add a specific nonlinear transformation between the normalisation and quantization steps of the existing signal‐to‐graph converter (SGC). If the autocorrelation function of the observed signal selected as the input fed to SGC, the nonlinear function has the ability to adjust the uniformity of its probability distribution, increasing the probability of the observed signal being transformed into a complete graph under the alternative hypothesis, whereas remaining a noncomplete graph under the null hypothesis. Thus transformed the graph‐based spectrum sensing into a complete graph‐detection problem. Based on the theory of dispersive ordering, a theoretical analysis of the mechanism by which nonlinear transformations affect graph connectivity was conducted. The simulation results showed that the detection performance of the proposed algorithm was superior to that of existing graph‐based spectrum sensing algorithms. When SNR was −7 dB, the detection probability of the proposed algorithm exceeded 95%. Moreover, among the existing graph‐based spectrum sensing algorithms, the proposed algorithm exhibited the lowest computational complexity apart from the block range‐based method. [ABSTRACT FROM AUTHOR]

In psychophysics and psychometrics, an integral method to the discipline involves charting how a person's response pattern changes according to a continuum of stimuli. For instance, in hearing science, Visual Analog Scaling tasks are experiments in which listeners hear sounds across a speech continuum and give a numeric rating between 0 and 100 conveying whether the sound they heard was more like word "a" or more like word "b" (i.e. each participant is giving a continuous categorization response). By taking all the continuous categorization responses across the speech continuum, a parametric curve model can be fit to the data and used to analyze any individual's response pattern by speech continuum. Standard statistical modeling techniques are not able to accommodate all of the specific requirements needed to analyze these data. Thus, Bayesian hierarchical modeling techniques are employed to accommodate group-level non-linear curves, individual-specific non-linear curves, continuum-level random effects, and a subject-specific variance that is predicted by other model parameters. In this paper, a Bayesian hierarchical model is constructed to model the data from a Visual Analog Scaling task study of mono-lingual and bi-lingual participants. Any nonlinear curve function could be used and we demonstrate the technique using the 4-parameter logistic function. Overall, the model was found to fit particularly well to the data from the study and results suggested that the magnitude of the slope was what most defined the differences in response patterns between continua. [ABSTRACT FROM AUTHOR]

Summary: An impedance control scheme is proposed for a Stewart‐structure‐based wheel‐legged robotic system to strengthen the dynamic attitude adjustment stability in wheel motion. The wheel‐leg, which is driven by electrical cylinders in the Stewart structure, is analyzed in kinematics and dynamics. The rotation in the axial direction of every electric cylinder is calculated to improve the accuracy of the kinematic model. To fulfill the impedance demands, a passive structure with 6 degrees of freedom (DOF) is modeled. The mass of the mechanism has a coupling effect on the impedance model for each DOF, which is a nonlinear function. As motion decoupling in the workspace has been completed for the Stewart structure, an impedance control strategy with inner‐loop position tracking is employed. An extended state observer (ESO) is designed to estimate the disturbances arising from the nonlinear coupling effects. Based on the ESO observation outputs, an active disturbance rejection control that explicitly handles the workspace limit is designed with guaranteed practical stability. By reducing force interaction and body vibration, the wheel‐legged robotic system keeps wheel motion stability on uneven roads. Multiple comparative experimental results are presented to validate the stability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Integrating wind power plants into the electricity grid poses challenges due to the intermittent nature of wind energy generation. Energy storage systems (ESSs) have shown promise in mitigating the intermittent variability associated with wind power. This paper presents a distributionally robust optimization (DRO) model for sizing energy storage systems to dispatch wind power plants. The variable wind power is formulated as a moment-based ambiguity set. Dispatchability is described by the expected value of the insufficient power of wind power relative to the dispatch command, which is a sum of nonlinear functions and is taken as the optimal index. A deterministic semi-definite positive model is derived to solve the problem effectively. Numerical studies are conducted to demonstrate the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, the distributed containment control schemes are presented for a class of nonlinear heterogeneous high‐order fully actuated multi‐agent systems. First, for each follower, the reference trajectory generator is constructed by using the output information of the neighbor agents. Then, the distributed containment controllers are designed for the system with known nonlinear system function matrices and control gain matrices. Further, since the existence of modeling errors and other uncertain factors, the obtained system model is often not accurate enough, that is, the system function matrix and control gain matrix are actually unknown nonlinear matrices. To tackle these obstacles, we employ the radial basis function neural network method to approximate the unknown nonlinear system function matrices and skillfully construct the controllers combined with the adaptive technology to eliminate the effects of the unknown control gain matrices. The developed control strategies can guarantee that the containment control can be realized and the containment errors can be adjusted to arbitrary precision. In the end, the simulation results on the electromechanical system and robotic system demonstrate the availability and effectiveness of the provided schemes. [ABSTRACT FROM AUTHOR]

Summary: This article addresses the issue of bipartite containment tracking for nonlinear strict feedback multi‐agent systems (MASs) with disturbances and measurement uncertainties. To provides a better performance against strong disturbance, a coordination transformation is applied such that all the nonlinear functions, controller disturbances and measurement uncertainties are lumped into a single disturbance signal in the last state equation. Then, the lumped disturbance is compensated through a novel disturbance rebuilding method. Moreover, in order to get better control performance, state constraints are also considered through a nonlinear transformation function (NTF). Different from traditional methods dealing with the state constraint problems, the NTF method can avoid using any discontinuous Lyapunov function. Finally, an adaptive finite‐time distributed controller is established via the disturbance estimates, backstepping technique and fuzzy logic system (FLS). The performance of the controller is illustrated by a simulation example in which the bipartite containment formation of followers is realized in a practical finite time. [ABSTRACT FROM AUTHOR]

Deep feedforward and recurrent neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. Here we argue that these details are crucial in order to understand how real neural circuits operate. Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. The computation of the resulting networks can be understood as the difference of two convex functions and is thereby capable of approximating arbitrary non-linear input-output mappings. We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation. [ABSTRACT FROM AUTHOR]

Activation functions are used to extract meaningful relationships from real-world problems with the help of deep learning models. Thus, the development of activation functions which affect deep learning models' performances is of great interest to researchers. In the literature, mostly, nonlinear activation functions are preferred since linear activation functions limit the learning performances of the deep learning models. Non-linear activation functions can be classified as fixed-parameter and trainable activation functions based on whether the activation function parameter is fixed (i.e., user-given) or modified during the training process of deep learning models. The parameters of the fixed-parameter activation functions should be specified before the deep learning model training process. However, it takes too much time to determine appropriate function parameter values and can cause the slow convergence of the deep learning model. In contrast, trainable activation functions whose parameters are updated in each iteration of deep learning models training process achieve faster and better convergence by obtaining the most suitable parameter values for the datasets and deep learning architectures. This study proposes parametric RSigELU (P+RSigELU) trainable activation functions, such as P+RSigELU Single (P+RSigELUS) and P+RSigELU Double (P+RSigELUD), to improve the performance of fixed-parameter activation function of RSigELU. The performances of the proposed trainable activation functions were evaluated on the benchmark datasets of MNIST, CIFAR-10, and CIFAR-100 datasets. Results show that the proposed activation functions outperforms PReLU, PELU, ALISA, P+FELU, PSigmoid, and GELU activation functions found in the literature. To access the codes of the activation function; https://github.com/serhatklc/P-RsigELU-Activation-Function. [ABSTRACT FROM AUTHOR]

It is well known that unknown modeling errors cannot be avoided in practice. Such unmeasured uncertainties are usually denoted as unknown nonlinear functions that exist in every channel of the system equation. This paper aims to develop an output feedback adaptive control scheme by constructing state estimation filters to address such unknown modeling errors. In the controller design, these uncertainties caused by modeling errors will be accumulated to the last step for compensation. Unknown parameters existing in the upper bound functions of unknown nonlinear functions and system parameters are estimated synchronously based on tuning function approaches. It is shown that the designed output feedback controller can ensure the stability and tracking performance of the closed‐loop system, and the transient performance in terms of a truncated norm is also established. [ABSTRACT FROM AUTHOR]

Background: In last two decades, the use of high-throughput sequencing technologies has accelerated the pace of discovery of proteins. However, due to the time and resource limitations of rigorous experimental functional characterization, the functions of a vast majority of them remain unknown. As a result, computational methods offering accurate, fast and large-scale assignment of functions to new and previously unannotated proteins are sought after. Leveraging the underlying associations between the multiplicity of features that describe proteins could reveal functional insights into the diverse roles of proteins and improve performance on the automatic function prediction task. Results: We present GO-LTR, a multi-view multi-label prediction model that relies on a high-order tensor approximation of model weights combined with non-linear activation functions. The model is capable of learning high-order relationships between multiple input views representing the proteins and predicting high-dimensional multi-label output consisting of protein functional categories. We demonstrate the competitiveness of our method on various performance measures. Experiments show that GO-LTR learns polynomial combinations between different protein features, resulting in improved performance. Additional investigations establish GO-LTR's practical potential in assigning functions to proteins under diverse challenging scenarios: very low sequence similarity to previously observed sequences, rarely observed and highly specific terms in the gene ontology. Implementation: The code and data used for training GO-LTR is available at https://github.com/aalto-ics-kepaco/GO-LTR-prediction. [ABSTRACT FROM AUTHOR]

The article addresses the qualitative analysis of the two dynamical systems simulating circular gene network functioning. The equations of a three-dimensional dynamical system contain some monotonically decreasing smooth functions that describe negative feedback. A six-dimensional dynamical system consists of three equations with monotonically decreasing smooth functions and three equations with monotonically increasing smooth functions that characterize negative and positive feedbacks. In both models the process of degradation is described by smooth nonlinear functions. We construct invariants domains in order to localize cycles for both systems, show that each of the two systems has a unique stationary point in the invariant domain, and find the conditions for this point to be hyperbolic. The main result is the proof of existence of a cycle in the invariant subdomain from which the trajectories cannot pass to other subdomains obtained by discretization of the phase portrait. The cycles of three- and six-dimensional systems bound the two-dimensional invariant surfaces including the trajectories of the systems. [ABSTRACT FROM AUTHOR]

This article explores an analysis via the Noether symmetry approach to investigate an extended teleparallel F (T , X , ϕ) gravity model in the context of a Friedmann–Robertson–Walker spacetime. The model incorporates the torsion scalar T, scalar field ϕ and the kinetic term X of the scalar field. This approach allows us to select physically interesting models by restricting arbitrariness in the F (T , X , ϕ) function. Thus we focus on two types of the function F (T , X , ϕ) , namely models involving the generalized teleparallel dark energy and the nonlinear function of the kinetic term and analyze the Noether symmetry properties and demonstrate the presence of non-vanishing Noether vectors. In the first model, by specifically considering the X 4 Noether symmetry, representing a scaling symmetry, we simplify the field equations and introduce a cyclic variable to enable a more workable formulation. Furthermore, we present a comprehensive graphical analysis, showcasing the time evolution of the scale factor and the scalar field by using the solutions obtained through these new variables. Additionally, we examine some fundamental cosmological parameters. For the second model, which includes the nonlinear form of the kinetic term, Noether symmetry results in obtaining simple power-law solutions for the dynamic variables. Our findings clearly show that the considered models represent an accelerating expansion of the Universe, which is consistent with observations. This study highlights the efficacy of the Noether symmetry approach in defining the functional form of F (T , X , ϕ) and obtaining precise cosmological solutions. The analytical solutions and graphical analysis offer valuable insights into the dynamic behavior of the models, contributing to understanding the evolving nature of the Universe. [ABSTRACT FROM AUTHOR]

Electromagnetic actuation can support many fields of technology, such as robotics or biomedical applications. In this context, fully understanding the system behavior and proposing a low-cost package for feedback control is challenging. Modeling the electromagnetic force is particularly tricky because it is a nonlinear function of the actuated object's position and coil's current. Measuring in real time the position of the actuated object with the precision required for accurate motion control is also nontrivial. In this study, we propose a novel, cost-effective electromagnetic set-up to achieve position control via visual feedback. We actuated vertically and under different experimental conditions a 10 mm diameter steel ball hanging on a low-stiffness spring, demonstrating good tracking performance (the position error remained within ±0.5 mm, with a negligible phase delay in the best scenarios). The experimental results confirm the feasibility of the proposed set-up, which is characterized by minimum complexity and realized with off-the-shelf and cost-effective components. For these reasons, such a contribution helps to understand and apply electromagnetic actuation even further. [ABSTRACT FROM AUTHOR]

Mixed quantum classical (MQC)-initial value representation (IVR) is a recently introduced semiclassical framework that allows for selective quantization of the modes of a complex system. In the quantum limit, MQC reproduces the semiclassical Double Herman–Kluk IVR results, accurately capturing nuclear quantum coherences and conserving zero-point energy. However, in the classical limit, although MQC mimics the Husimi-IVR for real-time correlation functions with linear operators, it is significantly less accurate for non-linear correlation functions with errors even at time zero. Here, we identify the origin of this discrepancy in the MQC formulation and propose a modification. We analytically show that the modified MQC approach is exact for all correlation functions at time zero, and in a study of zero-point energy (ZPE) flow, we numerically demonstrate that it correctly obtains the quantum and classical limits as a function of time. Interestingly, although classical-limit MQC simulations show the expected, unphysical ZPE leakage, we find that it is possible to predict and even modify the direction of ZPE flow through selective quantization of the system, with the quantum-limit modes accepting energy but preserving the minimum quantum mechanically required energy. [ABSTRACT FROM AUTHOR]

In this paper we focus on the space of C 2 quartic splines on uniform criss-cross triangulations and we propose a method based on weighted essentially non-oscillatory techniques and obtained by modifying classical spline quasi-interpolants in order to approximate piecewise smooth functions avoiding Gibbs phenomenon near discontinuities and, at the same time, maintaining the high-order accuracy in smooth regions. We analyse the convergence properties of the proposed quasi-interpolants and we provide some numerical and graphical tests confirming the theoretical results. [ABSTRACT FROM AUTHOR]

Teleoperation of manipulators has allowed extending the human skills to several areas, where the commands generated by a human operator on the leader robot are followed by a remote robot. For this purpose, position-position tracking requires a mapping given the mismatch between robot workspaces. This paper compares a pair of functions for mapping the haptic device commands to handle a remote robot, considering non-identical workspaces and a classic P+d control scheme. As part of the theoretical analysis, a Lyapunov-Krasovskii-based stability analysis is developed in steps, allowing us for determining the boundedness of velocities and coordination errors. Subsequently, the performance of the teleoperation system is compared using two mapping functions. To achieve a fair comparison of results, a test protocol is developed, where different levels of haptic device damping, time delays, and workspace scales are used to evaluate the time to complete the task and the average coordination errors. Based on the results, the mapping function influences the calculation of force feedback, stability of the system, and performance metrics. During a pick-and-place task, a reduction in coordination error is observed when the linear function is chosen, while the time to complete the task is lower when a non-linear function is considered. [ABSTRACT FROM AUTHOR]

This research uses the Sinc Collocation method to numerically examine the Degasperis–Procesi and Benjamin–Bona–Mahony equations, achieving a high level of precision and accuracy on computational grounds with a variety of mesh points. The proposed technique involves global collocation using Sinc bases function (SBF) as an activation function. Initially, the time derivative discretization has been performed through finite difference scheme and the remaining spatial derivatives are approximated by θ -weighted scheme to minimize the complexity in numerical computations. The main contribution of research is in modifying the proposed scheme to overcome the complexity involved in the whole process of finding solutions with a cardinal expansion of Sinc functions in nonlinear and singular systems. The solutions of Degasperis–Procesi and Benjamin–Bona–Mahony stiff nonlinear systems are illustrated numerically and graphically and the validation and verification of the obtained results are examined through stability analysis by calculating the spectral radius by bounding the value of θ. A comparative study is presented with some of the well-known numerical techniques, which assured the accuracy and reliability of our technique. [ABSTRACT FROM AUTHOR]

• Practical fracture limit surfaces (FLSs) considering data flexibility. • A profile function for nonlinear fracture data variations in strain-based FLS. • Stress-based FLS considering evolution of stress anisotropy in the Lagrangian frame. • Both models were validated by experimental data set. • The model effectively represents the flexibility of fracture data. Ductile fracture limits have been extensively studied from the perspectives of material science and mechanics. While these studies have provided scientifically significant insights into ductile fracture limits, the influence of the evolution of anisotropy observed in actual experimental data suggests a need to account for diversity in the experimental data. To address this, it may be possible to further develop the model by investigating more influences from the field of materials science. However, from an engineering perspective, it can be effective to represent the diversity of acquired experimental data as practical functions for use, rather than solely focusing on the material science aspect. This paper presents mathematical formulations representing the strain- and stress-based fracture limit surfaces of ductile materials, to consider diverse data set for the evolution of anisotropy, under plane-stress conditions within the framework of the Lagrangian formulation. The model introduces a strain-based fracture limit surface (FLS), which has an additional anisotropic profile function based on the commonly used two-dimensional strain-based fracture limit curve (FLC). The anisotropic profile function is capable of capturing the evolving anisotropic profile based on the deformation mode and principal loading direction to represent more flexible shapes. With this function, a three-dimensional strain-based FLS, which can present the variation in fracture strains in the space of the deformation mode and principal loading direction, can be constructed. Then, the proposed model transformed this strain-based FLS into a stress-based FLS by converting the presented state vector in the former into the corresponding vector in the latter in the Lagrangian formulation. To achieve this, this study developed a formulation that considers the nonlinear evolution of stress anisotropy independent of the strain anisotropy during stress evolution. The two proposed models were validated by experimental results on a dual-phase steel. These models provide flexible fracture limit functions for ductile materials under varying stress and strain conditions in engineering applications. [ABSTRACT FROM AUTHOR]

Hybrid neural network models are effective in analyzing time-series data by combining the strengths of neural networks and differential equation models. Although most studies have focused on linear hybrid models, few have examined nonlinear problems. This work explores the potential of a hybrid nonlinear epidemic neural network in predicting the correct infection function of an epidemic model. We design a novel loss function by combining bifurcation theory and mean-squared error loss to ensure the trainability of the hybrid model. Additionally, we identify unique existence conditions that support ordinary differential equations for estimating the correct infection function. Moreover, numerical experiments using the Runge–Kutta method confirm our proposed model's soundness both on our synthetic data and the real COVID-19 data. [ABSTRACT FROM AUTHOR]

Gryllus bimaculatus (Orthoptera: Gryllidae) is widely considered an excellent nutrient source for food and feed. Despite its economic importance, there is limited information on the impact of temperature on the bionomics of this cricket to guide its effective and sustainable mass production in its geographical range. The biological parameters of G. bimaculatus were investigated at eight different temperatures ranging from 20–40˚C. The Insect Life-Cycle Modelling (ILCYM) program was used to fit linear and non-linear functions to the data to describe the influence of temperature on life history parameters and its farmability under the current and projected climate for 2050. Our results revealed that G. bimaculatus was able to complete its lifecycle in the temperature range of 20°C to 37°C with a maximum finite rate of population increase (= 1.14) at 35°C. The developmental time of G. bimaculatus decreased with increasing temperature. The least developmental time and mortality were attained at 32°C. The highest wet length and mass of G. bimaculatus occurred at 32°C. The lowest temperature threshold for G. bimaculatus egg and nymph development was approximated using linear regression functions to be at 15.9°C and 16.2°C with a temperature constant of 108.7 and 555.6 degree days. The maximum fecundity (2301.98 eggs per female), net reproductive rate (988.42 daughters/ generation), and intrinsic rate of natural increase (0.134 days) were recorded at 32°C and the shortest doubling of 5.2 days was observed at 35°C. Based on our findings G. bimaculatus can be farmed in countries with temperatures ranging between 20 and 37°C around the globe. These findings will help the cricket farmers understand and project the cricket population dynamics around the world as influenced by temperature, and as such, will contribute to more efficient farming. [ABSTRACT FROM AUTHOR]

In studies of infectious disease prevention, the level of protective efficacy of medicinal products such as vaccines and prophylactic drugs tends to vary over time. Many products require administration of multiple doses at scheduled times, as opposed to one‐off or continual intervention. Accurate information on the trajectory of the level of protective efficacy over time facilitates informed clinical recommendations and implementation strategies, for example, with respect to the timing of administration of the doses. Based on concepts from pharmacokinetic and pharmacodynamic modeling, we propose a non‐linear function for modeling the trajectory after each dose. The cumulative effect of multiple doses of the products is captured by an additive series of the function. The model has the advantages of parsimony and interpretability, while remaining flexible in capturing features of the trajectories. We incorporate this series into the Andersen‐Gill model for analysis of recurrent event time data and compare it with alternative parametric and non‐parametric functions. We use data on clinical malaria disease episodes from a trial of four doses of an anti‐malarial drug combination for chemoprevention to illustrate, and evaluate the performance of the methods using simulation. The proposed method out‐performed the alternatives in the analysis of real data in terms of Akaike and Bayesian Information Criterion. It also accurately captured the features of the protective efficacy trajectory such as the area under curve in simulations. The proposed method has strong potential to enhance the evaluation of disease prevention measures and improve their implementation strategies. [ABSTRACT FROM AUTHOR]

An adaptive event‐triggered control issue based on command filter and dynamic surface control is studied for switched nonlinear systems with full state time‐varying constraints in this article. To handle state constraints, the nonlinear mapping conversion technique is used. Radial basis function neural networks (RBFNNs) are utilized to approximate unknown nonlinear continuous functions. Adaptive control algorithm is designed based on command filtered backstepping technology. Novel even triggered control is constructed for two different cases in the switching interval. Furthermore, all signals in the switched system are proved to be semi‐globally uniformly ultimate bounded (SGUUB) by the aid of dynamic surface control method under arbitrary switching. Meanwhile, all states do not violate the preset constraints and Zeno phenomenon is avoided. The validity of the presented approach is confirmed through a numerical simulation result. [ABSTRACT FROM AUTHOR]

This article is concerned with event‐triggered adaptive tracking control design of strict‐feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event‐triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed‐loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Feedback‐controlled chemical reaction networks (FCRNs) are indispensable for various biological processes, such as cellular mechanisms, patterns, and signaling pathways. Through the intricate interplay of many feedback loops (FLs), FCRNs maintain a stable internal cellular environment. Currently, creating minimalistic synthetic cells is the long‐term objective of systems chemistry, which is motivated by such natural integrity. The design, kinetic optimization, and analysis of FCRNs to exhibit functions akin to those of a cell still pose significant challenges. Indeed, reaching synthetic homeostasis is essential for engineering synthetic cell components. However, maintaining homeostasis in artificial systems against various agitations is a difficult task. Several biological events can provide us with guidelines for a conceptual understanding of homeostasis, which can be further applicable in designing artificial synthetic systems. In this regard, we organize our review with artificial homeostasis systems driven by FCRNs at different length scales, including homogeneous, compartmentalized, and soft material systems. First, we stretch a quick overview of FCRNs in different molecular and supramolecular systems, which are the essential toolbox for engineering different nonlinear functions and homeostatic systems. Moreover, the existing history of synthetic homeostasis in chemical and material systems and their advanced functions with self‐correcting, and regulating properties are also emphasized. [ABSTRACT FROM AUTHOR]

Surface ozone (O3) is the primary air pollutant threatening global vegetation. It typically reduces photosynthetic rate and stomatal conductance, leading to changes in carbon, water, and energy cycles, vegetation structure and composition, and climate. Several parameterization schemes have been developed to integrate the photosynthetic and stomatal responses to O3 exposure in regional and global process-based models to simulate time- and space-varying O3 plant damage and its cascading dynamic influence. However, these schemes are calibrated based on limited observations and often fail to reproduce the response relationships in observations, impeding accurate assessments of the role of O3 plant damage in the Earth system. This study proposes a new parameterization scheme to utilize the extensive observations from O3 fumigation experiments to inform large-scale modeling. It is built on 4210 paired data points of photosynthetic and stomatal responses compiled from peer-reviewed literature, over six times larger than those employed in earlier schemes. Functions of phytotoxic O3 dose (POD) are found to accurately reproduce the statistically significant linear or nonlinear relationships observed between POD and either relative leaf photosynthetic rate or relative stomatal conductance for needleleaf trees, broadleaf trees, shrubs, grasses, and crops. These eliminate the practice in earlier schemes of setting response functions as constants and applying the response function from one vegetation type to another. It outperforms the old scheme in the Community Land Model (CLM) which skillfully reproduces the observed response for crop photosynthetic rate only. The nonlinear response functions we developed depict decreasing plant sensitivity with increases in POD, enabling models to implicitly capture the variability in plant ozone tolerance and the shift among plant species for both intra- and inter-PFT within a vegetation type observed in the real world. Then, the new scheme is incorporated into the Community Earth System Model version 2.2 (CESM2.2), specifically its land component CLM5, to quantify the global impacts of present-day O3 plant damage by comparing the simulations with and without O3 plant damage. Results show that O3 exposure reduces the global leaf photosynthetic rate by 8.5 % and stomatal conductance by 7.4 %, around half the estimates using the old scheme. Furthermore, the new scheme improves global GPP simulations, decreasing RMSE by 11.1 % relative to simulations without O3 plant damage and by 11.7 % compared against the old scheme. These results underscore the importance of including O3 plant damage in large-scale process-based models and the effectiveness of the new scheme in global assessing and projecting the role of O3 plant damage in the Earth system. [ABSTRACT FROM AUTHOR]