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Effective cue integration is essential for an animal's survival. The ring attractor network has emerged as a powerful framework for understanding how animals seamlessly integrate various cues. This network not only elucidates neural dynamics within the brain, especially in spatial encoding systems like the heading direction (HD) system, but also sheds light on cue integration within decision-making processes. Yet, many significant phenomena across different fields lack clear explanations. For instance, in physiology, the integration mechanism of Drosophila's compass neuron when confronted with conflicting self-motion cues and external sensory cues with varying gain control settings is not well elucidated. Similarly, in ethology, the decision-making system shows Bayesian integration (BI) under minimal cue conflicts, but shifts to a winner-take-all (WTA) mode as conflicts surpass a certain threshold. To address these gaps, we introduce a ring attractor network with asymmetrical neural connections and synaptic dynamics in this paper. A thorough series of simulations has been conducted to assess its ability to track external cues and integrate conflicting cues. The results from these simulations demonstrate that the proposed model replicates observed neural dynamics and offers a framework for modeling biologically plausible cue integration behaviors. Furthermore, our findings yield several testable predictions that could inform future neuroethological research, providing insights into the role of ring attractor dynamics in the animal brain.

Abstract Image restoration with impulse noise is an important task in image processing. Taking into account the statistical distribution of impulse noise, the ℓ1‐norm data fidelity and total variation (ℓ1TV) model has been widely used in this area. However, the ℓ1TV model usually performs worse when the noise level is high. To overcome this drawback, several nonconvex models have been proposed. In this paper, an efficient iterative algorithm is proposed to solve nonconvex models arising in impulse noise. Compared to existing algorithms, the proposed algorithm is a completely explicit algorithm in which every subproblem has a closed‐form solution. The key idea is to transform the original nonconvex models into an equivalent constrained minimization problem with two separable objective functions, where one is differentiable but nonconvex. As a consequence, the proximal linearized alternating direction method of multipliers is employed to solve it. Extensive numerical experiments are presented to demonstrate the efficiency and effectiveness of the proposed algorithm.

Looming perception, the ability to sense approaching objects, is crucial for the survival of humans and animals. After hundreds of millions of years of evolutionary development, biological entities have evolved efficient and robust looming perception visual systems. However, current artificial vision systems fall short of such capabilities. In this study, we propose a novel spiking neural network for looming perception that mimics biological vision to communicate motion information through action potentials or spikes, providing a more realistic approach than previous artificial neural networks based on sum-then-activate operations. The proposed spiking looming perception network (SLoN) comprises three core components. Neural encoding, known as phase coding, transforms video signals into spike trains, introducing the concept of phase delay to depict the spatial-temporal competition between phasic excitatory and inhibitory signals shaping looming selectivity. To align with biological substrates where visual signals are bifurcated into parallel ON/OFF channels encoding brightness increments and decrements separately to achieve specific selectivity to ON/OFF-contrast stimuli, we implement eccentric down-sampling at the entrance of ON/OFF channels, mimicking the foveal region of the mammalian receptive field with higher acuity to motion, computationally modeled with a leaky integrate-and-fire (LIF) neuronal network. The SLoN model is deliberately tested under various visual collision scenarios, ranging from synthetic to real-world stimuli. A notable achievement is that the SLoN selectively spikes for looming features concealed in visual streams against other categories of movements, including translating, receding, grating, and near misses, demonstrating robust selectivity in line with biological principles. Additionally, the efficacy of the ON/OFF channels, the phase coding with delay, and the eccentric visual processing are further investigated to demonstrate their effectiveness in looming perception. The cornerstone of this study rests upon showcasing a new paradigm for looming perception that is more biologically plausible in light of biological motion perception.

Bio-inspired models based on the lobula giant movement detector (LGMD) in the locust’s visual brain have received extensive attention and application for collision perception in various scenarios. These models offer advantages such as low power consumption and high computational efficiency in visual processing. However, current LGMD-based computational models, typically organized as four-layered neural networks, often encounter challenges related to noisy signals, particularly in complex dynamic environments. Biological studies have unveiled the intrinsic stochastic nature of synaptic transmission, which can aid neural computation in mitigating noise. In alignment with these biological findings, this paper introduces a probabilistic LGMD (Prob-LGMD) model that incorporates a probability into the synaptic connections between multiple layers, thereby capturing the uncertainty in signal transmission, interaction, and integration among neurons. Comparative testing of the proposed Prob-LGMD model and two conventional LGMD models was conducted using a range of visual stimuli, including indoor structured scenes and complex outdoor scenes, all subject to artificial noise. Additionally, the model’s performance was compared to standard engineering noise-filtering methods. The results clearly demonstrate that the proposed model outperforms all comparative methods, exhibiting a significant improvement in noise tolerance. This study showcases a straightforward yet effective approach to enhance collision perception in noisy environments.

IntroductionLobular giant motion detector (LGMD) neurons, renowned for their distinctive response to looming stimuli, inspire the development of visual neural network models for collision prediction. However, the existing LGMD-based models could not yet incorporate the invaluable feature of depth distance and still suffer from the following two primary drawbacks. Firstly, they struggle to effectively distinguish the three fundamental motion patterns of approaching, receding, and translating, in contrast to the natural abilities of LGMD neurons. Secondly, due to their reliance on a general determination process employing an activation function and fixed threshold for output, these models exhibit dramatic fluctuations in prediction effectiveness across different scenarios.MethodsTo address these issues, we propose a novel LGMD-based model with a binocular structure (Bi-LGMD). The depth distance of the moving object is extracted by calculating the binocular disparity facilitating a clear differentiation of the motion patterns, after obtaining the moving object's contour through the basic components of the LGMD network. In addition, we introduce a self-adaptive warning depth-distance, enhancing the model's robustness in various motion scenarios.ResultsThe effectiveness of the proposed model is verified using computer-simulated and real-world videos.DiscussionFurthermore, the experimental results demonstrate that the proposed model is robust to contrast and noise.

Prey-predator interactions play a pivotal role in elucidating the evolution and adaptation of various organism’s traits. Numerous approaches have been employed to study the dynamics of prey-predator interaction systems, with agent-based methodologies gaining popularity. However, existing agent-based models are limited in their ability to handle multi-modal interactions, which are believed to be crucial for understanding living organisms. Conversely, prevailing prey-predator integration studies often rely on mathematical models and computer simulations, neglecting real-world constraints and noise. These elusive attributes, challenging to model, can lead to emergent behaviors and embodied intelligence. To bridge these gaps, our study designs and implements a prey-predator interaction scenario that incorporates visual and olfactory sensory cues not only in computer simulations but also in a real multi-robot system. Observed emergent spatial-temporal dynamics demonstrate successful transitioning of investigating prey-predator interactions from virtual simulations to the tangible world. It highlights the potential of multi-robotics approaches for studying prey-predator interactions and lays the groundwork for future investigations involving multi-modal sensory processing while considering real-world constraints.

In this paper, we propose a directionally selective fractional-order lobular giant motion detector (LGMD) visual neural network. Unlike most collision-sensing network models based on LGMDs, our model can not only sense collision threats but also obtain the motion direction of the collision object. Firstly, this paper simulates the membrane potential response of neurons using the fractional-order differential operator to generate reliable collision response spikes. Then, a new correlation mechanism is proposed to obtain the motion direction of objects. Specifically, this paper performs correlation operation on the signals extracted from two pixels, utilizing the temporal delay of the signals to obtain their position relationship. In this way, the response characteristics of direction-selective neurons can be characterized. Finally, ON/OFF visual channels are introduced to encode increases and decreases in brightness, respectively, thereby modeling the bipolar response of special neurons. Extensive experimental results show that the proposed visual neural system conforms to the response characteristics of biological LGMD and direction-selective neurons, and that the performance of the system is stable and reliable.

This paper presents a novel neural model of insect’s visual perception paradigm to address a challenging problem on detection of looming motion, particularly in extremely low-contrast, and highly variable natural scenes. Current looming detection models are greatly affected by visual contrast between moving target and cluttered background lacking robust and low-cost solutions. Considering the anatomical and physiological homology between preliminary visual systems of different insect species, this gap can be significantly reduced by coordinating motion and contrast neural processing mechanisms. The proposed model draws lessons from research progress in insect neuroscience, articulates a neural network hierarchy based upon ON/OFF channels encoding motion and contrast signals in four parallel pathways. Specifically, the two ON/OFF motion pathways react to successively expanding ON–ON and OFF–OFF edges through spatial–temporal interactions between polarity excitations and inhibitions. To formulate contrast neural computation, the instantaneous feedback normalization of preliminary motion received at starting cells of ON/OFF channels works effectively to suppress time-varying signals delivered into the ON/OFF motion pathways. Besides, another two ON/OFF contrast pathways are dedicated to neutralize high-contrast polarity optic flows when converging with motion signals. To corroborate the proposed method, we carried out systematic experiments with thousands of looming-square motions at varied grey scales, embedded in different natural moving backgrounds. The model response achieves remarkably lower variance and peaks more smoothly to looming motions in different natural scenarios, a significant enhancement upon previous works. Such robustness can be maintained against extremely low-contrast looming motion against cluttered backgrounds. The results demonstrate a parsimonious solution to stabilize looming detection against high input variability, analogous to insect’s capability.

In this paper, a general optimization formulation is proposed for the subspace segmentation by low rank representation via the sparse-prompting quasi-rank function. We prove that, with the clean data from independent linear subspaces, the optimal solution to our optimization formulation not only is the lowest rank but also forms a block-diagonal matrix, which implies that it is reasonable to use any sparse-prompting quasi-rank function as the measure of the low rank in subspace clustering. With the data contaminated by Gaussian noise and/or gross errors, the alternating direction method of multipliers is applied to solving it and every sub-optimization problem has a closed-form optimal solution when the band restricted thresholding operator induced by its corresponding sparse-prompting function has an analytic expression, in which the gross errors part is replaced with the sparse-prompting matrix function. Finally, taking a specific sparse-prompting function, the fraction function, we conduct a series of simulations on different databases to get the performance of our algorithm tested, and experimental results show that our algorithm can obtain lower clustering error rate and higher value of evaluation indicators ACC, NMI and ARI than other state-of-the-art subspace clustering algorithms on different databases.

Building an efficient and reliable small target motion detection visual system is challenging for artificial intelligence robotics because a small target only occupies few pixels and hardly displays visual features in images. Biological visual systems that have evolved over millions of years could be ideal templates for designing artificial visual systems. Insects benefit from a class of specialized neurons, called small target motion detectors (STMDs), which endow them with an excellent ability to detect small moving targets against a cluttered dynamic environment. Some bio-inspired models featured in feed-forward information processing architectures have been proposed to imitate the functions of the STMD neurons. However, feedback, a crucial mechanism for visual system regulation, has not been investigated deeply in the STMD-based neural circuits and its roles in small target motion detection remain unclear. In this paper, we propose a time-delay feedback STMD model for small target motion detection in complex backgrounds. The main contributions of this study are as follows. First, a feedback pathway is designed by transmitting information from output-layer neurons to lower-layer interneurons in the STMD pathway and the role of the feedback is analyzed from the view of mathematical analysis. Second, to estimate the feedback constant, the existence and uniqueness of solutions for nonlinear dynamical systems formed by feedback loop are analyzed via Schauder's fixed point theorem and contraction mapping theorem. Finally, an iterative algorithm is designed to solve the nonlinear problem and the performance of the proposed model is tested by experiments. Experimental results demonstrate that the feedback is able to weaken background false positives while maintaining a minor effect on small targets. It outperforms existing STMD-based models regarding the accuracy of fast-moving small target detection in visual clutter. The proposed feedback approach could inspire the relevant modeling of robust motion perception robotics visual systems.

Recently there have been renewed interests in high order neural networks (HONNs) for its powerful mapping capability. Ridge polynomial neural network (RPNN) is an important kind of HONNs, which always occupies a key position as an efficient instrument in the tasks of classification or regression. In order to make the convergence speed faster and the network generalization ability stronger, we introduce a regularization model for RPNN with Group Lasso penalty, which deals with the structural sparse problem at the group level in this paper. Nevertheless, there are two main obstacles for introducing the Group Lasso penalty, one is numerical oscillation and the other is convergence analysis challenge. In doing so, we adopt smoothing function to approximate the Group Lasso penalty to overcome these drawbacks. Meanwhile, strong and weak convergence theorems, and monotonicity theorems are provided for this novel algorithm. We also demonstrate the efficiency of our proposed algorithm by numerical experiments, and compare it to the no regularizer, $L_{2}$ regularizer, $L_{1/2}$ regularizer, smoothing $L_{1/2}$ regularizer, and the Group Lasso regularizer, and also the relevant theoretical analysis has been verified.

Accurate and timely perception of collision in highly variable environments is still a challenging problem for artificial visual systems. As a source of inspiration, the lobula giant movement detectors (LGMDs) in locust's visual pathways have been studied intensively, and modelled as quick collision detectors against challenges from various scenarios including vehicles and robots. However, the state-of-the-art LGMD models have not achieved acceptable robustness to deal with more challenging scenarios like the various vehicle driving scenes, due to the lack of adaptive signal processing mechanisms. To address this problem, we propose an improved neuronal system model, called LGMD+, that is featured by novel modelling of spatiotemporal inhibition dynamics with biological plausibilities including 1) lateral inhibitions with global biases defined by a variant of Gaussian distribution, spatially, and 2) an adaptive feed-forward inhibition mediation pathway, temporally. Accordingly, the LGMD+ performs more effectively to detect merely approaching objects threatening head-on collision risks by appropriately suppressing motion distractors caused by vibrations, near-miss or approaching stimuli with deviations from the centre view. Through evolutionary learning with a systematic dataset of various crash and non-collision driving scenarios, the LGMD+ shows improved robustness outperforming the previous related methods. After evolution, its computational simplicity, flexibility and robustness have also been well demonstrated by real-time experiments of autonomous micro-mobile robots.

The perception of different visual motion cues is crucial for autonomous mobile robots to react to or interact with the dynamic visual world. It is still a great challenge for a micro mobile robot to cope with dynamic environments due to the restricted computational resources and the limited functionalities of its visual systems. In this study, we propose a compound visual neural system to automatically extract and fuse different visual motion cues in real-time using the extremely constrained computation power of micro mobile robots. The proposed visual system contains multiple bio-inspired visual motion perceptive neurons each with a unique role, for example to extract collision visual cues, darker collision cue and directional motion cues. In the embedded system, these multiple visual neurons share a similar presynaptic network to minimise the consumption of computation resources. In the postsynaptic part of the system, visual cues pass results to corresponding action neurons using lateral inhibition mechanism. The translational motion cues, which are identified by comparing pairs of directional cues, are given the highest priority, followed by the darker colliding cues and approaching cues. Systematic experiments with both virtual visual stimuli and real-world scenarios have been carried out to validate the system's functionality and reliability. The proposed methods have demonstrated that (1) with extremely limited computation power, it is still possible for a micro mobile robot to extract multiple visual motion cues robustly in a complex dynamic environment; (2) the cues extracted can be fused with a lateral inhibited postsynaptic network, thus enabling the micro robots to respond effectively with different actions, accordingly to different states, in real-time. The proposed embedded visual system has been modularised and can be easily implemented in other autonomous mobile platforms for real-time applications. The system could also be used by neurophysiologists to test new hypotheses pertaining to biological visual neural systems.

The wireless sensor network (WSN), a communication system widely used in the Internet of Things, usually collects physical data in a natural environment and monitors abnormal events. Because of the redundancy of natural data, a compressed-sensing-based model offers energy-efficient data processing to overcome the energy shortages and uneven consumption problems of a WSN. However, the convex relaxation method, which is widely used for a compressed-sensing-based WSN, is not sufficient for reducing data processing energy consumption. In addition, when abnormal events occur, the redundancy of the original data is destroyed, which makes the traditional compressed sensing methods ineffective. In this paper, we use a non-convex fraction function as the surrogate function of the ℓ0-norm, which achieves lower energy consumption of the sensor nodes. Moreover, considering abnormal event monitoring in a WSN, we propose a new data construction model and apply an alternate direction iterative thresholding algorithm, which avoids extra measurements, unlike previous algorithms. The results showed that our models and algorithms reduced the WSN’s energy consumption during abnormal events.

In this paper, we introduce a two-step inertial primal-dual algorithm (TSIPD) for solving the minimizations of the sum a smooth function with Lipschitzian gradient and two non-smooth convex functions with linear operators. This is a complete splitting approach, in the sense that non-smooth functions are treated separately by their proximity operators. In order to prove the convergence of the TSIPD, we transform the problem into a fixed point equation with good performance, and prove the convergence of the algorithm base on the fixed point theory. This work brings together and significantly extends several classical splitting schemes, like the primal-dual method (PD3O) proposed by Yan, and the recent three-operator splitting scheme proposed by Davis and Yin. The validity of the proposed method is demonstrated on an image denoising problem. Numerical results show that our iterative algorithm (TSIPD) has better performance than the original one (PD3O).

Abstract The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry some strongly nonlinear structures, and the linear model is no longer suitable. Compared with the compressed sensing under the linear circumstance, this nonlinear compressed sensing is much more difficult, in fact also NP-hard, combinatorial problem, because of the discrete and discontinuous nature of the ℓ0 $\ell _{0}$-norm and the nonlinearity. In order to get a convenience for sparse signal recovery, we set the nonlinear models have a smooth quasi-linear nature in this paper, and study a non-convex fraction function ρa $\rho_{a}$ in this quasi-linear compressed sensing. We propose an iterative fraction thresholding algorithm to solve the regularization problem (QPaλ) $(QP_{a}^{\lambda})$ for all a>0 $a>0$. With the change of parameter a>0 $a>0$, our algorithm could get a promising result, which is one of the advantages for our algorithm compared with some state-of-art algorithms. Numerical experiments show that our method performs much better than some state-of-the-art methods.

Abstract The joint sparse recovery problem is a generalization of the single measurement vector problem widely studied in compressed sensing. It aims to recover a set of jointly sparse vectors, i.e., those that have nonzero entries concentrated at a common location. Meanwhile l p $l_{p}$ -minimization subject to matrixes is widely used in a large number of algorithms designed for this problem, i.e., l 2 , p $l_{2,p}$ -minimization min X ∈ R n × r ∥ X ∥ 2 , p s.t. A X = B . $$\begin{aligned} \min_{X \in\mathbb {R}^{n\times r}} \Vert X \Vert _{2,p}\quad \text{s.t. }AX=B. \end{aligned}$$ Therefore the main contribution in this paper is two theoretical results about this technique. The first one is proving that in every multiple system of linear equations there exists a constant p ∗ $p^{\ast}$ such that the original unique sparse solution also can be recovered from a minimization in l p $l_{p}$ quasi-norm subject to matrixes whenever 0 < p < p ∗ $0< p

Abstract In signal processing theory, l 0 $l_{0}$ -minimization is an important mathematical model. Unfortunately, l 0 $l_{0}$ -minimization is actually NP-hard. The most widely studied approach to this NP-hard problem is based on solving l p $l_{p}$ -minimization ( 0 < p ≤ 1 $0< p\leq1$ ). In this paper, we present an analytic expression of p ∗ ( A , b ) $p^{\ast}(A,b)$ , which is formulated by the dimension of the matrix A ∈ R m × n $A\in\mathbb{R}^{m\times n}$ , the eigenvalue of the matrix A T A $A^{T}A$ , and the vector b ∈ R m $b\in\mathbb{R}^{m}$ , such that every k-sparse vector x ∈ R n $x\in\mathbb{R}^{n}$ can be exactly recovered via l p $l_{p}$ -minimization whenever 0 < p < p ∗ ( A , b ) $0< p< p^{\ast}(A,b)$ , that is, l p $l_{p}$ -minimization is equivalent to l 0 $l_{0}$ -minimization whenever 0 < p < p ∗ ( A , b ) $0< p< p^{\ast}(A,b)$ . The superiority of our results is that the analytic expression and each its part can be easily calculated. Finally, we give two examples to confirm the validity of our conclusions.

In this study, the authors address a two‐dimensional (2D) shape registration problem on data with anisotropic‐scale deformation and noise. First, the model is formulated under the iterative closest point (ICP) framework, which is one of the most popular methods for shape registration. To overcome the effect of noise, the expectation maximisation algorithm is used to improve the model. Then, the structure of Lie groups is adopted to parameterise the proposed model, which provides a unified framework to deal with the shape registration problems. Such representation makes it possible to introduce some suitable constraints to the model, which improves the robustness of the algorithm. Thereby, the 2D shape registration problem is turned to an optimisation problem on the matrix Lie group. Furthermore, a sequence of quadratic programming is designed to approximate the solution for the model. Finally, several comparative experiments are carried out to validate that the authors’ algorithm performs well in terms of robustness, especially in the presence of outliers.

In this article, we study the existence of mild solutions for fractional semilinear differential equations with nonlocal conditions in separable Banach spaces. The result is obtained by using the Hausdorff measure of noncompactness and the Schauder fixed point theorem.

The paper discusses the relationship between the null space property (NSP) and the lq-minimization in compressed sensing. Several versions of the null space property, that is, the lq stable NSP, the lq robust NSP, and the lq,p robust NSP for 0

This paper researches global asymptotic stability of impulsive cellular neural networks with proportional delays and partially Lipschitz activation functions. Firstly, by means of the transformation vi(t)=ui(et), the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Secondly, we provide novel criteria for the uniqueness and exponential stability of the equilibrium point of the latter by relative nonlinear measure and prove that the exponential stability of equilibrium point of the latter implies the asymptotic stability of one of the former. We furthermore obtain a sufficient condition to the uniqueness and global asymptotic stability of the equilibrium point of the former. Our method does not require conventional assumptions on global Lipschitz continuity, boundedness, and monotonicity of activation functions. Our results are generalizations and improvements of some existing ones. Finally, an example and its simulations are provided to illustrate the correctness of our analysis.

This paper is devoted to providing a novel method to global exponential stability of impulsive delayed differential equations. By utilizing relative nonlinear measure method, several global exponential stability criteria are presented for the impulsive delayed differential equations. Compared with the Razumikhin technique and Lyapunov function method, our method is less conservative and gives a convergence rate, and one of our stability criteria is more flexible by incorporating an adjustable matrix. An example and its simulation are provided to illustrate that our method is efficient and our results are new and correct.

The existence and uniqueness of the solutions to the Dirichlet boundary value problem in the Banach spaces is discussed by using the fixed point theory of condensing mapping, doing precise computation of measure of noncompactness, and calculating the spectral radius of linear operator.

The purpose of this paper is to establish improved bounds for restricted isometry constants δk. Our results, to some extent, improve and extend the well-known bound (δk