Nonlocal Feedback Research Articles

Behavior-induced phase transitions with far from equilibrium patterning in a SIS epidemic model: Global vs non-local feedback

Here, we explore the phase transitions triggered by the implementation of social distancing in a basic spatiotemporal model of a qualitative SIS-type infectious disease. We consider human decisions made based on spatiotemporal information regarding the disease spread. This information can be either local, nonlocal with a finite range, or global in scope.We show that nonlocal and global feedbacks, while resulting in the same spatially homogeneous equilibria, lead to a dynamic behavior that is fundamentally distinct from what is observed when decisions are made based on local information.Various phenomena arise due to the nonlocal nature of the feedback: (i) Instabilization of Otherwise Stable Homogeneous Equilibria; (ii) Nucleation/Invasion Phenomena; (iii) Onset of Standard and Generalized Traveling Waves, which can incur in wave-pinning; iv) in case of Global Information Feedback, onset of locally stable Far From Equilibrium Patterns that coexist with a locally stable disease-elimination equilibrium. Thus, the nonlocal nature of the human behavior-related feedback introduces a rich array of dynamic behaviors and patterns in the system.

Qualitative Study on ψ−Caputo fractional differential inclusion with non-local conditions and feedback control

Qualitative Study on ψ−Caputo fractional differential inclusion with non-local conditions and feedback control

Stabilization of the Viscoelastic Wave Equation with Variable Coefficients and a Delay Term in Nonlocal Boundary Feedback

Stabilization of the Viscoelastic Wave Equation with Variable Coefficients and a Delay Term in Nonlocal Boundary Feedback

How to Grow a Flat Leaf.

Growing a flat lamina such as a leaf is almost impossible without some feedback to stabilize long wavelength modes that are easy to trigger since they are energetically cheap. Here we combine the physics of thin elastic plates with feedback control theory to explore how a leaf can remain flat while growing. We investigate both in-plane (metric) and out-of-plane (curvature) growth variation and account for both local and nonlocal feedback laws. We show that a linearized feedback theory that accounts for both spatially nonlocal and temporally delayed effects suffices to suppress long wavelength fluctuations effectively and explains recently observed statistical features of growth in tobacco leaves. Our work provides a framework for understanding the regulation of the shape of leaves and other leaflike laminar objects.

A Dynamic Fusion of Local and Non-Local Features-Based Feedback Network on Super-Resolution

Many Symmetry blocks were proposed in the Single Image Super-Resolution (SISR) task. The Attention-based block is powerful but costly on non-local features, while the Convolutional-based block is good at efficiently handling the local features. However, assembling two different Symmetry blocks will generate an Asymmetry block, making the classic Symmetry-block-based Super-Resolution (SR) architecture fail to deal with these Asymmetry blocks. In this paper, we proposed a new Dynamic fusion of Local and Non-local features-based Feedback Network (DLNFN) for SR, which focus on optimizing the traditional Symmetry-block-based SR architecture to hold two Symmetry blocks in parallel, making two Symmetry-blocks working on what they do best. (1) We introduce the Convolutional-based block for the local features and Attention-based network block for non-local features and propose the Delivery–Adjust–Fusion framework to hold these blocks. (2) we propose a Dynamic Weight block (DW block) which can generate different weight values to fuse the outputs on different feedback iterations. (3) We introduce the MAConv layer to optimize the In block, which is critical for our two blocks-based feedback algorithm. Experiments show our proposed DLNFN can take full advantage of two different blocks and outperform other state-of-the-art algorithms.

A Local and Non-Local Features Based Feedback Network on Super-Resolution.

Recent advances in Single Image Super-Resolution (SISR) achieved a powerful reconstruction performance. The CNN-based network (both sequential-based and feedback-based) performs well in local features, while the self-attention-based network performs well in non-local features. However, single block cannot always perform well due to the realistic images always with multiple kinds of features. In order to take full advantage of different blocks on different features. We have chosen three different blocks cooperating to extract different kinds of features. Addressing this problem, in this paper, we propose a new Local and non-local features-based feedback network for SR (LNFSR): (1) The traditional deep convolutional network block is used to extract the local non-feedbackable information directly and non-local non-feedbackable information (needs to cooperate with other blocks). (2) The dense skip-based feedback block is use to extract local feedbackable information. (3) The non-local self-attention block is used to extract non-local feedbackable information and the based LR feature information. We also introduced the feature up-fusion-delivery blocks to help the features be delivered to the right block at the end of each iteration. Experiments show our proposed LNFSR can extract different kinds of feature maps by different blocks and outperform other state-of-the-art algorithms.

Feedback-stabilized dynamical steady states in the Bose-Hubbard model

The implementation of a combination of continuous weak measurement and classical feedback provides a powerful tool for controlling the evolution of quantum systems. In this work, we investigate the potential of this approach from three perspectives. First, we consider a double-well system in the classical large-atom-number limit, deriving the exact equations of motion in the presence of feedback. Second, we consider the same system in the limit of small atom number, revealing the effect that quantum fluctuations have on the feedback scheme. Finally, we explore the behavior of modest sized Hubbard chains using exact numerics, demonstrating the near-deterministic preparation of number states, a tradeoff between local and non-local feedback for state preparation, and evidence of a feedback-driven symmetry-breaking phase transition.

Metric inertia for eddy densities of nonlocal matter-space

ABSTRACT Monistic thermomechanics of eddy mater-space with metric stresses of Maxwellian type and inelastic metric waves can be developed for purely kinetic densities of the nonlocal mass-energy integral. Pseudo-Riemannian 4-geometry uses locally warped time to preserve the Euclidean sublight transport of nonlocally correlated densities with instantaneous metric connections and coherent conservation of local 4-currents everywhere. The kinematic viscosity of geometrised energy-momentum densities and their geodesic self-pushes by correlated metric stresses quantitatively clarify the adaptive all-unity of continuous kinetic energy, including material ether or variable rest-energy. The metric self-organisation of matter-space+time implies a nonlocal feedback of correlated eddy densities and their tensor response to the vector density of external forces. Such tensor inertial responses of correlated metric stresses reveal the nonlocal nature of turbulence and predict adaptive auto-modes or thermal waves of Euclidean material space due to the modified geodesic equation with viscose autowaves and the inverse Cavendish constant. The proposed nonlocal alternative to Euler/Navier-Stokes hydrodynamics can distinguish between Cartesian and Newtonian worldviews in conceptual laboratory probes of new macroscopic mechanics for metric self-organisations of thermokinetic energies of viscose material space without negative gravitational energies.

Spatially varying multifeedback for robust signaling

AbstractElaborate regulatory feedback processes are thought to make biological development robust, that is, resistant to changes induced by sustained genetic or environmental perturbations. How this might be accomplished is still not completely understood, especially when models of some known feedback processes have been shown, some analytically and others by numerical simulations, to be ineffective in promoting robust signaling. By working with nonlocal feedback processes, combinations of two of these ineffective feedback processes were found to ensure robustness as measured by a well‐defined robustness index for the Dpp–Tkv (decapentaplegic–thickvein) signaling in the wing imaginal disc of Drosophila fruit flies. In this paper, we show that there are also spatially varying multifeedback combinations of individually ineffective components that are similarly successful. The analysis of these Hill function type multifeedback models are found to be much more challenging mathematically as the relevant boundary‐value problem remains nonlinear even for systems in a steady state of low receptor occupancy.

Electrodiffusion with Calcium-Activated Potassium Channels in Dendritic Spine.

We investigate calcium signaling feedback through calcium-activated potassium channels of a dendritic spine by applying the immersed boundary method with electrodiffusion. We simulate the stochastic gating of such ion channels and the resulting spatial distribution of concentration, current, and membrane voltage within the dendritic spine. In this simulation, the permeability to ionic flow across the membrane is regulated by the amplitude of chemical potential barriers. With spatially localized ion channels, chemical potential barriers are locally and stochastically regulated. This regulation represents the ion channel gating with multiple subunits, the open and closed states governed by a continuous-time Markov process. The model simulation recapitulates an inhibitory action on voltage-sensitive calcium channels by the calcium-activated potassium channels in a stochastic manner as a non-local feedback loop. The model predicts amplified calcium influx with more closely placed channel complexes, proposing a potential mechanism of differential calcium handling by channel distributions. This work provides a foundation for future computer simulation studies of dendritic spine motility and structural plasticity.

Non-Reciprocal Supratransmission in Mechanical Lattices with Non-Local Feedback Control Interactions

We numerically investigate the supratransmission phenomenon in an active nonlinear system modeled by the 1D/2D discrete sine-Gordon equation with non-local feedback. While, at a given frequency, the typical passive system exhibits a single amplitude threshold marking the onset of the phenomenon, we show that the inclusion of non-local feedback manifests additional thresholds that depend upon the specific boundary from which supratransmission is stimulated, realizing asymmetric (i.e., non-reciprocal) dynamics. The results illustrate a new means of controlling nonlinear wave propagation and energy transport for, e.g., signal amplification and mechanical logic.

Decay estimates for a degenerate wave equation with a dynamic fractional feedback acting on the degenerate boundary

In this paper, we consider a one-dimensional weakly degenerate wave equation with a dynamic nonlocal boundary feedback of fractional type acting at a degenerate point. First We show well-posedness by using the semigroup theory. Next, we show that our system is not uniformly stable by spectral analysis. Hence, we look for a polynomial decay rate for a smooth initial data by using a result due Borichev and Tomilov which reduces the problem of estimating the rate of energy decay to finding a growth bound for the resolvent of the generator associated with the semigroup. This analysis proves that the degeneracy affect the energy decay rates.

Survival criterion for a population subject to selection and mutations; Application to temporally piecewise constant environments

We study a parabolic Lotka–Volterra type equation that describes the evolution of a population structured by a phenotypic trait, under the effects of mutations and competition for resources modelled by a nonlocal feedback. The limit of small mutations is characterized by a Hamilton–Jacobi equation with constraint that describes the concentration of the population on some traits. This result was already established in Barles and Perthame (2008); Barles et al. (2009); Lorz et al. (2011) in a time-homogeneous environment, when the asymptotic persistence of the population was ensured by assumptions on either the growth rate or the initial data. Here, we relax these assumptions to extend the study to situations where the population may go extinct at the limit. For that purpose, we provide conditions on the initial data for the asymptotic fate of the population. Finally, we show how this study for a time-homogeneous environment allows to consider temporally piecewise constant environments.

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

We investigate non-Hermitian elastic lattices characterized by non-local feedback interactions. In one-dimensional lattices, proportional feedback produces non-reciprocity associated with complex dispersion relations characterized by gain and loss in opposite propagation directions. For non-local controls, such non-reciprocity occurs over multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional wave amplification. Moreover, the combination of skin effect in two directions produces modes that are localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and suggest new possibilities for the design of meta materials with novel functionalities related to selective wave filtering, amplification and localization. The considered non-local lattices also provide a platform for the investigation of topological phases of non-Hermitian systems.

Regulatory feedback on receptor and non-receptor synthesis for robust signaling.

Elaborate regulatory feedback processes are thought to make biological development robust, that is, resistant to changes induced by genetic or environmental perturbations. How this might be done is still not completely understood. Previous numerical simulations on reaction-diffusion models of Dpp gradients in Drosophila wing imaginal disc have showed that feedback (of the Hill function type) on (signaling) receptors and/or non-(signaling) receptors are of limited effectiveness in promoting robustness. Spatial nonuniformity of the feedback processes has also been shown theoretically to lead to serious shape distortion and a principal cause for ineffectiveness. Through mathematical modeling and analysis, the present article shows that spatially uniform nonlocal feedback mechanisms typically modify gradient shape through a shape parameter (that does not change with location). This in turn enables us to uncover new multi-feedback instrument for effective promotion of robust signaling gradients.

An Optimal Control Problem of Nonlocal Pyragas Feedback Controllers for Convective FitzHugh--Nagumo Equations with Time-Delay

We study an optimal control problem governed by a class of Pyragas-type nonlocal feedback controllers with time-delay for the convective FitzHugh--Nagumo equation. An optimal control problem is constrained by a coupled nonlinear system of parabolic partial differential equations. Well-posedness of the feedback control system and the differentiability of the control-to-state mapping are proved. Further, the main goal of the paper is to establish existence results for the distributed optimal kernels in the controllers. In particular, we take kernels as control functions, and we show that optimal kernels are the solution to the optimal control problem. Furthermore, we also derive the first-order necessary optimality conditions.

Efficient stability analysis of fluid flows using complex mapping techniques

Global linear stability analysis of open flows leads to difficulties associated to boundary conditions, leading to either spurious wave reflections (in compressible cases) or to non-local feedback due to the elliptic nature of the pressure equation (in incompressible cases). A novel approach is introduced to address both these problems. The approach consists of solving the problem using a complex mapping of the spatial coordinates, in a way that can be directly applicable in an existing code without any additional auxiliary variable. The efficiency of the method is first demonstrated for a simple 1D equation modeling incompressible Navier–Stokes, and for a linear acoustics problem. The application to full linearized Navier–Stokes equation is then discussed. A criterion on how to select the parameters of the mapping function is derived by analyzing the effect of the mapping on plane wave solutions. Finally, the method is demonstrated for three application cases, including an incompressible jet, a compressible hole-tone configuration and the flow past an airfoil. The examples allow to show that the method allows to suppress the artificial modes which otherwise dominate the spectrum and can possibly hide the physical modes. Finally, it is shown that the method is still efficient for small truncated domains, even in cases where the computational domain is comparable to the dominant wavelength.

Control of spiral drift by using feedback signals from a circular measuring domain in oscillatory media

In this paper, a non-local feedback is used to force spiral waves in the oscillatory system modeled by the complex Ginzburg-Landau equation, where the feedback signal is derived from a circular measuring domain. It is found that the spiral tip could be driven to follow an attractor after a period of drift. The existence of multiple types of attractors, which include a point attractor at the measuring center and a set of circular attractors concentric with the measuring domain, is illustrated. Which to be chosen depends on the direction of the spiral initial drift and the distance between the initial tip position and the measuring center. Here the diameter of the circular attractor has a periodic change with the size of the measuring domain, but is not affected by the movement of the measuring domain. Correlation between the tip drift and the feedback signal is analyzed, and the modulus function of the feedback signal will has a constant value after the spiral tip arrives at the attractors. If the feedback signal is generated from the measuring domain far away from the position of the initial spiral tip, the spiral breakup can be caused by the feedback control, and it fist occurs near the boundary and then invades inward until the area of the remaining spiral is small enough. The effect of the feedback gain, the delay time and the scaling parameter is also considered.

Mechanoregulation of Bone Remodeling and Healing as Inspiration for Self-Repair in Materials

The material bone has attracted the attention of material scientists due to its fracture resistance and ability to self-repair. A mechanoregulated exchange of damaged bone using newly synthesized material avoids the accumulation of fatigue damage. This remodeling process is also the basis for structural adaptation to common loading conditions, thereby reducing the probability of material failure. In the case of fracture, an initial step of tissue formation is followed by a mechanobiological controlled restoration of the pre-fracture state. The present perspective focuses on these mechanobiological aspects of bone remodeling and healing. Specifically, the role of the control function is considered, which describes mechanoregulation as a link between mechanical stimulation and the local response of the material through changes in structure or material properties. Mechanical forces propagate over large distances leading to a complex non-local feedback between mechanical stimulation and material response. To better understand such phenomena, computer models are often employed. As expected from control theory, negative and positive feedback loops lead to entirely different time evolutions, corresponding to stable and unstable states of the material system. After some background information about bone remodeling and healing, we describe a few representative models, the corresponding control functions, and their consequences. The results are then discussed with respect to the potential design of synthetic materials with specific self-repair properties.

Numerical algorithms for solving the optimal control problem of simple bioreactors

The modified nonlocal feedback controller is used to control the production of drugs in a simple bioreactor. This bioreactor is based on the enzymatic conversion of substrate into the required product. The dynamics of this device is described by a system of two nonstationary nonlinear diffusion–convection–reaction equations. The analysis of the influence of the convection transport is one the aims of this paper. The control loop is defined using the relation, which shows how the amount of the drug produced in the bioreactor and delivered into a human body depends on the substrate concentration specified on the external boundary of the bioreactor. The system of PDEs is solved by using the finite volume and finite difference methods, the control loop parameters are defined from the analysis of stationary linearized equations. The second aim of this paper is to solve the inverse problem and to determine optimal boundary conditions. These results enable us to estimate the potential accuracy of the proposed devices.