Small Neighborhood Research Articles

A global kernel estimator for partially linear varying coefficient additive hazards models.

We study kernel-based estimation methods for partially linear varying coefficient additive hazards models, where the effects of one type of covariates can be modified by another. Existing kernel estimation methods for varying coefficient models often use a "local" approach, where only a small local neighborhood of subjects are used for estimating the varying coefficient functions. Such a local approach, however, is generally inefficient as information about some non-varying nuisance parameter from subjects outside the neighborhood is discarded. In this paper, we develop a "global" kernel estimator that simultaneously estimates the varying coefficients over the entire domains of the functions, leveraging the non-varying nature of the nuisance parameter. We establish the consistency and asymptotic normality of the proposed estimators. The theoretical developments are substantially more challenging than those of the local methods, as the dimension of the global estimator increases with the sample size. We conduct extensive simulation studies to demonstrate the feasibility and superior performance of the proposed methods compared with existing local methods and provide an application to a motivating cancer genomic study.

Cooperative-Critic Learning-Based Secure Tracking Control for Unknown Nonlinear Systems With Multisensor Faults.

This article develops a cooperative-critic learning-based secure tracking control (CLSTC) method for unknown nonlinear systems in the presence of multisensor faults. By introducing a low-pass filter, the sensor faults are transformed into "pseudo" actuator faults, and an augmented system that integrates the system state and the filter output is constructed. To reduce design costs, a joint neural network Luenberger observer (NNLO) structure is established by using neural network and input/output data of the system to identify unknown system dynamics and sensor faults online. To achieve the optimal secure tracking control, an augmented tracking system is formed by integrating the dynamics of tracking error, reference trajectory, and filter output. Then, a novel cost function is designed for the augmented tracking system, which employs the fault estimation and the discount factor. The Hamilton-Jacobi-Bellman equation is solved to obtain the CLSTC strategy through an adaptive critic structure with cooperative tuning laws. Besides, the Lyapunov stability theorem is utilized to prove that all signals of the closed-loop system converge to a small neighborhood of the equilibrium point. Simulation results demonstrate that the proposed control method has good fault tolerance performance and is suitable for solving secure control problems of nonlinear systems with various sensor faults.

A parallel algorithm for minimum weight set cover with small neighborhood property

A parallel algorithm for minimum weight set cover with small neighborhood property

Fuzzy Adaptive Event-Triggered Consensus Control for Nonlinear Multiagent Systems With Output Constraints and DoS Attacks.

In this article, the fuzzy adaptive event-triggered consensus control issue is addressed for nonlinear multiagent systems (MASs) under output constraints and Denial of Service (DoS) attacks. First of all, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions. Then, a novel switching observer is constructed to observe the leader's state and handle DoS attacks. With the help of the exponent-dependent barrier Lyapunov functions (BLFs), the system output can be constrained within a preset region. Based on dynamic surface control (DSC) technique, the issue of computational complexity can be effectively avoided. Combining the designed switching observer and relative thresholds, a robust fuzzy adaptive event-triggered controller is developed, which ensures that the consensus output tracking errors converge to a small neighborhood of zero, and all signals in the closed-loop system keep bounded. Moreover, Zeno behavior can be avoided. Ultimately, simulation results are given to validate the feasibility and effectiveness of the proposed control strategy and theory.

METHOD OF INTEGRAL TRANSFORMATIONS IN SOLVING THE PROBLEM OF DETECTING SMALL VEHICLES IN IMAGES

The article proposes a method for forming a set of features on images based on three integral transformations: the Radon transform, the Steklov function and the Fourier transform. Using a discrete analog of these transformations, the values that form a set of features are calculated. Depending on the transformation parameters, the number of features can be changed. We selected the values of these parameters such that the number of features is 903. The use of this approach in solving the problem of detecting small-sized, and therefore poorly visible, vehicles in video images is shown. In addition, we have developed an improved version of the least squares method based on processing the obtained features using some transformations of the labels of the training set of images. The main essence of this method is to perform an affine transformation of the label value into a small neighborhood of its original value. A priori estimates show a decrease in the approximation error using the least squares method. The paper also shows a comparison of the developed approach with convolutional neural networks. This comparison allows us to say that it is not much inferior to them in such an indicator as the percentage of correct predictions. At the same time, in terms of prediction execution time, the method presented in the article works 3-4 times faster depending on the model used. In the practical part of the work, software tools from the OpenCV, Keras and Scikit-learn libraries were used.

On the motion of a dynamically symmetric satellite in one case of multiple parametric resonance

The paper studies the motions of a dynamically symmetric satellite (rigid body) relative to the center of mass in the central Newtonian gravitational field on a weakly elliptical orbit in the neighborhood of its stationary rotation (cylindrical precession). We consider the values of the parameters for which, in the limiting case of a circular orbit, one of the frequencies of small linear oscillations is equal to unity and the other is equal to zero, and the rank of the coefficient matrix of the linearized equations of the perturbed motion is equal to two, as well as a small neighborhood of this resonant point in the three-dimensional space of parameters. The resonant periodic motions of the satellite, analytical in fractional powers of a small parameter (the eccentricity of the orbit of the satellite's center of mass), are constructed. A rigorous nonlinear analysis of their stability is carried out. The methods of KAM theory are used to describe two- and three-frequency conditionally periodic motions of a satellite, with frequencies of different orders in a small parameter. A number of general theoretical issues concerning the considered multiple parametric resonance in Hamiltonian systems with two degrees of freedom that are close to autonomous and periodic in time are discussed. Several qualitatively different variants of parametric resonance regions are constructed. It is shown that in the general case the nature of nonlinear resonant oscillations of the system is determined by the first approximation system in a small parameter.

Dynamics of a thin film of fluid spreading over a lubricated substrate

We examine the gravity-driven flow of a thin film of viscous fluid spreading over a rigid plate that is lubricated by another viscous fluid. We model the flow over such a ‘soft’ substrate by applying the principles of lubrication theory, assuming that vertical shear provides the dominant resistance to the flow. We do so in axisymmetric and two-dimensional geometries in settings in which the flow is self-similar. Different flow regimes arise, depending on the values of four key dimensionless parameters. As the viscosity ratio varies, the behaviour of the intruding layer ranges from that of a thin coating film, which exerts negligible traction on the underlying layer, to a very viscous gravity current spreading over a low-viscosity, near-rigid layer. As the density difference between the two layers approaches zero, the nose of the intruding layer steepens, approaching a shock front in the equal-density limit. We characterise a frontal stress singularity, which forms near the nose of the intruding layer, by performing an asymptotic analysis in a small neighbourhood of the front. We find from our asymptotic analysis that unlike single-layer viscous gravity currents, which exhibit a cube-root frontal singularity, the nose of a viscous gravity current propagating over another viscous fluid instead exhibits a square-root singularity, to leading order. We also find that large differences in the densities between the two fluids give rise to flows similar to that of thin films of a single viscous fluid spreading over a rigid, yet mobile, substrate.

Finite‐Time Decentralized Adaptive Fuzzy Control for Non‐Triangular Form Large‐Scale Time‐Delay Systems With Full State Constraints

ABSTRACTThis paper is concerned with the problem of finite‐time decentralized adaptive fuzzy fault tolerant control for a class of non‐triangular form large‐scale time delay systems with full state constraints. By using the fuzzy logic systems and domination approach, the unknown nonlinear functions are approximated and the non‐triangular form structure is tackled, respectively. The time‐varying barrier Lyapunov function (TBLF) is used to ensure that the full state constraints are satisfied. Based on the proposed TBLF and backstepping technique, an adaptive fuzzy fault‐tolerant control protocol is presented. It can assure that the errors converge to a small neighborhood of the origin in a finite time, the signals of the whole closed‐loop systems are bounded and the full state constraints are satisfied. Simulation example is presented to further demonstrate the effectiveness of the proposed approach.

Output feedback control for non-strict feedback nonlinear systems: an adaptive fuzzy backstepping scheme

The adaptive fuzzy tracking control design issue is considered in this paper for a class of non-strict feedback nonlinear systems subject to external disturbances. A fuzzy high-gain state observer is constructed to reconstruct the unmeasurable states of the system by leveraging the universal approximation property of fuzzy logic systems for arbitrary unknown nonlinear functions. Within the framework of backstepping control design and in conjunction with adaptive techniques, an adaptive fuzzy control approach is presented. Subsequently, to work out the inherent ‘complexity explosion’ problem of the proposed control approach, dynamic surface control technique is introduced, leading to a simplified adaptive fuzzy output feedback control scheme. Stability analysis shows that the two proposed control schemes can ensure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded, meanwhile the system tracking error can converge to a small neighborhood around the origin. Ultimately, a numerical simulation example is provided to validate the feasibility of the proposed control scheme.

Predefined-time event-triggered adaptive neural practical tracking control for flexible-joint robot

This paper researches the predefined-time event-triggered adaptive neural practical tracking control problem for flexible-joint robot system. An improved predefined-time command filter is utilized to get rid of the “explosion of complexity” problem, and the filter errors can be eliminated by an improved error compensation mechanism. Moreover, as an effective approximation tool, radial basis function neural networks are exploited to tackle the nonlinear terms existing in flexible-joint robot system. Finally, the communication burden of the system is reduced by using event-triggered technology, and an advanced adaptive predefined-time event-triggered controller is designed. The actual controller in the control scheme is updated only when it meets the conditions of the event-triggered mechanism. For flexible-joint robot system, the resulting control scheme makes the tracking error approach to a small neighborhood of zero, and all signals of the closed-loop system remain bounded within the predefined time. The effectiveness of the proposed controller is directly illustrated by the simulation results.

Geographic variation of recorded neurodevelopmental disorders in children and adults

INTRODUCTION. While diagnosis rates of autism spectrum disorders (ASD) and attention deficit hyperactivity disorder (ADHD) vary within countries at a large-scale municipal level, small neighbourhood geographic variation remains understudied. In this nationwide study, we describe the rates of ASD and ADHD diagnoses in children and adults by geographical data zones of approximately 2,500 residents across Denmark. METHODS. We included a population of children born from 1993 through 2020 and an adult population born from 1977 through 2003. We followed children from their first birthday and adults from their 18th birthday to either diagnosis, death, emigration or 31 December 2021, whichever came first. Data were analysed using multilevel log-linear Poisson regression adjusting for age and sex. Data zones, a data-driven approach to define small geographical neighbourhoods, were used as the unit for spatial analyses. We present incidence rates in data zones and median incidence rate ratios (MRRs) as estimates of the variation in rates of the disorders between data zones. RESULTS. ASD and ADHD diagnoses among children showed considerable variations between data zones (ASD: MRR = 1.44; 95% confidence interval (CI): 1.42-1.47, ADHD: MRR = 1.38; 95% CI: 1.36-1.40), suggesting that the incidence can be 44% and 38% higher in high incidence zones than in others. Similar variations were observed for diagnoses among adults (ASD: MRR = 1.44; 95% CI: 1.40-1.48, ADHD: MRR = 1.44; 95% CI: 1.41-1.46). CONCLUSIONS. The large variations might reflect differential treatment seeking, referral practice and diagnostic procedures across Denmark. FUNDING. This study received funding from BERTHA – the Danish Big Data Centre for Environment and Health, and the Novo Nordisk Foundation Challenge Programme (grant NNF17OC0027864). TRIAL REGISTRATION. Not relevant.

Fuzzy Adaptive Event-Triggered Consensus Control for Nonlinear Multiagent Systems Under Jointly Connected Switching Networks.

This article studies the fuzzy adaptive event-triggered (ET) consensus control issue of nonlinear multiagent systems (NMASs) under jointly connected switching networks. Since the leader and its high-order derivatives are unknown under jointly connected switching networks, a novel distributed ET reference generator equipped with an ET mechanism is constructed to estimate them. Meanwhile, the continuous information transmission among agents is avoided and the network channel utilization is optimized. Subsequently, fuzzy logic systems (FLSs) are employed to approximate unknown dynamics, and a fuzzy adaptive ET consensus control algorithm only using intermittent communication is designed by backstepping control methodology. It is demonstrated that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), with the tracking errors converging to a small neighborhood around zero. Finally, we apply the developed fuzzy adaptive ET consensus control algorithm to unmanned surface vehicles (USVs), and the simulation results verify the effectiveness of the proposed ET consensus control algorithm.

Adaptive Neural Control of Constrained MIMO Nonlinear Systems With Asymmetric Input Saturation and Dead Zone.

In this article, the adaptive neural control is studied for multiple-input-multiple-output (MIMO) nonlinear systems with asymmetric input saturation, dead zone, and full state-function constraints. A suitable transformation is introduced to overcome the dead zone and saturation nonlinearity, and radial basis function (RBF) neural networks (NNs) are used to approximate the unknown nonlinear functions. What is more, we apply the Nussbaum function and time-varying barrier Lyapunov function (BLF) to deal with the unknown control gains and full state-function constraints, respectively. Based on the backstepping method, a universal adaptive neural control scheme is presented such that not only the state-function constraints of the closed-loop system cannot be violated and all signals of the closed-loop systems are bounded, but also the tracking error converges to a small neighborhood containing the origin. The effectiveness of the proposed control scheme is verified by an application to the mass-spring-damper system and a numerical example.

Hidden-like Attractors in a Class of Discontinuous Dynamical Systems

In continuous dynamical systems, a hidden attractor occurs when its basin of attraction does not connect with small neighborhoods of equilibria. This research aims to investigate the presence of hidden-like attractors in a class of discontinuous systems that lack equilibria. The nature of non-smoothness in Filippov systems is critical for producing a wide variety of interesting dynamical behaviors and abrupt transient responses to dynamic processes. To show the effects of non-smoothness on dynamic behaviors, we provide a simple discontinuous system made of linear subsystems with no equilibria. The explicit closed-form solutions for each subsystem have been derived, and the generalized Poincaré maps have been established. Our results show that the periodic orbit can be completely established within a sliding region. We then carry out a mathematical investigation of hidden-like attractors that exhibit sliding-mode characteristics, particularly those associated with grazing-sliding behaviors. The proposed system evolves by adding a nonlinear function to one of the vector fields while still preserving the condition that equilibrium points do not exist in the whole system. The results of the linear system are useful for investigating the hidden-like attractors of flow behavior across a sliding surface in a nonlinear system using numerical simulation. The discontinuous behaviors are depicted as motion in a phase space governed by various hidden attractors, such as period doubling, period-m segments, and chaotic behavior, with varying interactions with the sliding mode.

Combinatorial chance-constrained economic optimization of distributed energy resources

The transformation of the energy system towards sustainable energy sources is characterized by an increase in weather dependent distributed energy resources (DER). This adds a layer of uncertainty in energy generation on top of already uncertain load distribution. At the same time, many households are fitted with renewable generation units and storage systems. The increased intermittent generation in the distribution grid leads to new challenges for the commitment and economic dispatch of DER. The main challenge addressed in this work is to decide which available resources to select for a given task. To solve this, we introduce Stochastic Resource Optimization (SRO), a general purpose, combinatorial, chance-constrained optimization model for the short-term economic selection of stochastic DER. It incorporates correlations between stochastic resources are using copula theory. The contributions of this paper are twofold: First, we validate the applicability of the SRO formulation on a simplified congestion management use-case in a small neighbourhood grid comprised of prosumer households. Second, we provide an analysis of the performance of different solving algorithms for SRO problems and their run-times. Our results show that a fast metaheuristic algorithm can provide high quality solutions in acceptable time on the evaluated problem sets.

Highly accurate computation of chronopotentiograms for a charge transfer followed by homogeneous dimerization or disproportionation reactions

A theoretical model of constant current chronopotentiometry is considered, for a reversible charge transfer followed by an irreversible homogeneous dimerization or disproportionation reactions at a planar electrode. The model is expressed by a system of two partial differential reaction–diffusion equations, one or both being nonlinear. This system decomposes into two independent initial boundary value problems, which allows one to obtain semi-analytical series solutions of the model. Detailed derivations and analysis of the series are presented. Highly accurate numerical reference solutions are also obtained. Hybrid algorithms are devised for computing electrode potential-time responses. The algorithms combine the series solution for small time, with asymptotic approximants for large time, and fitted polynomials for intermediate time. The algorithms are efficient and highly accurate: the relative error modulus does not exceed ca. 10−19−10−18, except for the small neighbourhoods of the transition time, and of the time where the potential response passes through zero. A set of C++ routines for these calculations is made available.

Adaptive neural control for a class of random nonlinear Markov jump multi-agent systems with full state constraints

This paper proposes a consensus control protocol based on the adaptive backstepping technique for a class of random Markov jump multi-agent systems (MASs) with full state constraints. Each agent is described by the high-order random nonlinear uncertain system driven by random differential equations, where the random noise is the second-order stationary stochastic process. First, a distributed tracking controller is designed for Markov jump MASs, effectively handling the interaction and coupling terms between agents. Second, an appropriate tan-type barrier Lyapunov function is selected to keep the agents’ states from the violation of constraint boundaries, and the unknown nonlinear terms with Markov jump parameters are approximated by neural networks (NNs) theory. Moreover, to address the differential explosion problem, the extended state observer (ESO) is first introduced instead of employing NNs approximation or command filtering techniques. Finally, the exponentially noise-to-state stability in mean square is proved rigorously through the Lyapunov method, which guarantees all signals of the closed-loop system are bounded in probability and the tracking error converges to a small neighborhood around zero. Simulations are given to demonstrate the feasibility of theoretical results.

A small neighborhood fabric recommender system based on user historical behavior and preference

In the current landscape, textile companies need rapid, precise, and personalized assistance, especially as digitalization and information, such as e-commerce and websites, are developing rapidly. Textile enterprises can mine user preferences to make personalized recommendations of appropriate textile fabrics; this is not only in keeping with current trends, but more importantly, can control production costs and improve user satisfaction. To support the transformation of textile enterprises to a small-batch and multi-variety business model, this paper proposes a fabric recommendation system; specifically, a fabric recommender system based on user historical behavior and preference is proposed. The proposed method is mainly based on the integration of preference, user activity, and rating; firstly, according to the fabric products purchased by the user, the features of the fabric are mined using a neural network to obtain the user’s preferences; secondly, neighbors with similar user behaviors are found according to similarity in users’ activity; and finally, understanding of the fabric is enhanced through a matrix based on the fabric ratings of the user. A focus on recommendation algorithm parameterization, including selection, thresholding, and neighborhood optimization, elevates the recommendation quality. A user–fabric dataset was used for experimental verification, and included the user’s purchase score of the fabric and the image of the fabric. Comparative analyses demonstrate superior precision with fewer neighborhoods, achieving a score of up to 0.93. Our research provides insights into user behavior and personalization, guiding future recommender system design and optimization.

Fixed-Time Event-Triggered Control of Nonholonomic Mobile Robots with Uncertain Dynamics and Preassigned Transient Performance

In this paper, a novel adaptive control scheme is proposed for the path-following problem of a nonholonomic mobile robot with uncertain dynamics based on barrier functions. To optimize communication resources, we integrate an event-triggered mechanism that avoids Zeno behavior and ensures that the tracking error of the closed-loop system converges to a small neighborhood around zero within a fixed time, while consistently satisfying predefined transient performance requirements. Extensive simulation studies demonstrate the effectiveness of the proposed approach and validate the theoretical results.

On an abrasion-motivated fractal model

Abstract In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providing a formal description of the successive chippings, we show that the net of edges converge to a compact limit set under mild assumptions. Furthermore, we study the upper box-counting dimension and the Hausdorff dimension of the limiting object of the net of edges after infinitely many chipping.