Locally active memristor (LAM), which has an ability to amplify fluctuations, is a natural component for constructing artificial neuron circuits. This paper proposes a novel third-order neuron circuit by paralleling two LAMs and a capacitor. Firstly, two parallel LAMs are equivalently modeled as a second-order LAM to facilitate theoretical analysis. Regarding the third-order neuron, the parameter design and operating condition are obtained by calculating its small signal impedance functions poles or Jacobin matrixs eigenvalues. It is demonstrated that the neuron exhibits various neuromorphic behaviors, including periodic spiking, chaos and burst-number adaptation. Due to the two different LAMs, the proposed thirdorder system has multiple equilibrium points, leading to the generation of coexisting attractors. Interestingly, the generated chaotic attractor does not revolve around a single unstable equilibrium point, but is located between two unstable equilibrium points. Furthermore, the emergence of oscillating behaviors is dependent on the distance between the two unstable equilibrium points. Detailed theoretical and simulation analysis are presented to investigate the neuron dynamics and provide an explanation for the observed neuromorphic behaviors. Finally, physical circuit implementation of the neuron is constructed based on the memristor emulator, which also demonstrates the practicability of the proposed neuron model and the correctness of the theoretical analysis.

The symmetry-breaking phenomenon, appearing, under suitable conditions, when identical reaction cells, quiet on their own, are let interact via diffusion processes, is dubbedTuring Instability. Its local form exposes the local destabilization, which allows two multistable cells lose stability at one of its locallyasymptotically-stableoperating points. While the globalTuring Instabilityand its mechanisms have been recently explained in (Ascoli et al., 2022), its local form and an experimental demonstration of these complex effects on a physical memristive medium have not been reported yet. This paper investigates a local form ofTuring Instabilityin a two-cell array, when one of the possiblelocally asymptotically-stableandlocally-activestatic solutions loses stability, when let interact with an identical reaction cell via diffusion processes, resulting in the emergence of two different static solutions after transients fade away. In order to study its mechanisms, this paper first introduces a current-controlled Chua Corsage Memristor (CCM), and demonstrates the operating point destabilization in a single current-controlled CCM-based cell. Adding a dissipative resistor and a capacitor to the current-controlled CCM, preliminarily poised on anedge of chaosoperating point, gives birth to two unstable circuits, inducing a local quiescent bi-stability and a local oscillation, respectively. The mechanisms behind a local form ofTuring Instability, appearing in a current-controlled CCM-based two-cell array, have been elucidated, and the bifurcation, spawning symmetry-breaking effects, locally, across the cellular network, has been identified. Both numerical and experimental results confirm the correctness of the theoretical analysis.

Diffusion Probabilistic Models (DPMs) have shown remarkable potential in image generation, but their sampling efficiency is hindered by the need for numerous denoising steps. Most existing solutions accelerate the sampling process by proposing fast ODE solvers. However, the inevitable discretization errors of the ODE solvers are significantly magnified when the number of function evaluations (NFE) is fewer. In this work, we propose PFDiff, a novel training-free and orthogonal timestep-skipping strategy, which enables existing fast ODE solvers to operate with fewer NFE. Specifically, PFDiff initially utilizes score replacement from past time steps to predict a springboard. Subsequently, it employs this ``springboard" along with foresight updates inspired by Nesterov momentum to rapidly update current intermediate states. This approach effectively reduces unnecessary NFE while correcting for discretization errors inherent in first-order ODE solvers. Experimental results demonstrate that PFDiff exhibits flexible applicability across various pre-trained DPMs, particularly excelling in conditional DPMs and surpassing previous state-of-the-art training-free methods. For instance, using DDIM as a baseline, we achieved 16.46 FID (4 NFE) compared to 138.81 FID with DDIM on ImageNet 64x64 with classifier guidance, and 13.06 FID (10 NFE) on Stable Diffusion with 7.5 guidance scale. Code is available at https://github.com/onefly123/PFDiff.

While powerful for generation, Diffusion Probabilistic Models (DPMs) face slow sampling challenges, for which various distillation-based methods have been proposed. However, they typically require significant additional training costs and model parameter storage, limiting their practicality. In this work, we propose **P**CA-based **A**daptive **S**earch (PAS), which optimizes existing solvers for DPMs with minimal additional costs. Specifically, we first employ PCA to obtain a few basis vectors to span the high-dimensional sampling space, which enables us to learn just a set of coordinates to correct the sampling direction; furthermore, based on the observation that the cumulative truncation error exhibits an ``S"-shape, we design an adaptive search strategy that further enhances the sampling efficiency and reduces the number of stored parameters to approximately 10. Extensive experiments demonstrate that PAS can significantly enhance existing fast solvers in a plug-and-play manner with negligible costs. E.g., on CIFAR10, PAS optimizes DDIM's FID from 15.69 to 4.37 (NFE=10) using only **12 parameters and sub-minute training** on a single A100 GPU. Code is available at https://github.com/onefly123/PAS.

Chua corsage memristor (CCM) is characterized by its local activity and can be used to construct neuron circuits. Edge of chaos is a subset of the locally active domain, which is responsible for the emergence of complexity and neuromorphic behaviors. When two identical resting “dead” CCM neurons poised on the edge of chaos are coupled through a linear passive resistor, these two neurons can be activated and a couple of oscillations appear. This phenomenon is referred to as the Smale paradox, which has not been observed from hardware circuits. The present paper addresses this issue by proposing the stability criterion of the two-port coupled system using the small-signal analysis method and then derives an emergence condition of the Smale paradox based on two coupled “dead” CCM neurons in terms of the parameter value ranges. Simulation results demonstrate the correctness of the theoretical analysis. Interestingly, anti-phase synchronization is observed after two identical neurons are coupled with a linear resistor, which is different from the traditional in-phase synchronization between resistively coupled oscillators. The resistively coupled memristive neurons are implemented by hardware based on the poor man’s circuit. The experimental results confirm the reproduction of the Smale paradox and reveal the effect of the coupling resistance on the dynamics of the system.

Inspired by recent research reported in [1], this paper investigates the bio-inspired bifurcation patterns of a simple memristive neuron on edge of chaos. The adopted memristive neuron, comprising a DC current source, a current-controlled locally active memristor, and a capacitor, successfully reproduces the bifurcation cascade patterns observed in the Hodgkin-Huxley (H-H) neuron model, including fold limit cycle bifurcation (FLCB), subcritical Hopf bifurcation (SUB-HB), and supercritical Hopf bifurcation (SUP-HB). Through attraction basin analysis and pulse-based initial state regulation, we verify the coexistence phenomenon of stable and unstable limit cycles induced by FLCB, as well as the bistable behaviors triggered by SUB-HB. Furthermore, taking resistively coupled memristive neurons as an example, we explore the influence of the dynamics of individual neurons on the bifurcation patterns of coupled networks, where two neurons have identical parameters but different initial states. The results demonstrate that the three bifurcation modes also emerge in memristive coupled networks, and their evolutionary patterns are closely related to the dynamic behaviors of individual neurons. Finally, hardware experiments successfully reproduce the bifurcation cascade phenomenon thereby validating the correctness of theoretical analysis and simulation results.

In this paper, we propose a novel inductor-free chaotic circuit by using two locally active memristors (LAMs), a capacitor, and a DC bias. These two LAMs are the current-controlled and voltage-controlled type, respectively, exhibiting S-type and N-type DC V-I (voltage-current) characteristics. Only when the two LAMs are both operated in the negative differential resistance (NDR) regions, may the periodical and chaotic dynamic behaviors appear in the proposed circuit. This may be because the local activity contributes to the generation of complexity. With different initial conditions, the coexisting attractors are observed in the circuit, which is analyzed through the equilibrium points and phase portraits. Finally, physical circuit realizations of the inductor-free chaotic circuit are presented, including the S-type and N-type memristor emulators. Both simulation and experimental results demonstrate the feasibility of the proposed chaotic circuit.

This work investigates the control technique for a quadrotor unmanned aerial vehicle with a slung load. By taking the advantage of the cascade property, a new hierarchical control scheme is designed that divides the control problem into three parts. For the attitude motion control of the quadrotor, the non-singularity terminal sliding mode based control law is proposed. For the translation motion control of the quadrotor, the super-twisting based control law is designed. Additional, for the swing attenuation of the slung load, a nonlinear anti-swing control design is provided. A Lyapunov stability analysis is presented to show the stability of the closed loop system, together with the fast convergence of the quadrotor's translational and attitude tracking, and exponential convergence of the slung load's swing motion. The real time experiments verifies the well performance of the proposed controller.

Autonomous mobile robots have been applied in many industries, but fast and robust trajectory tracking control remains a major challenge. This paper investigates a predefined-time trajectory tracking problem of a Mecanum-wheeled omnidirectional mobile robot (MWOMR) under the conditions of parameter uncertainties and external disturbances. First, a novel predefined-time stable system with adjustable convergence rate is proposed. Second, a predefined-time sliding mode control scheme is developed, which has better convergence performance and smaller control input. Based on Lyapunov stability theory, the effectiveness of the scheme is proven. The numerical simulation results show that the compared with traditional predefined-time control schemes, the proposed scheme has the advantages of a shorter convergence time and smaller control input.

Malignancy characterization of hepatocellular carcinoma (HCC) is of great importance in patient management and prognosis prediction. In this study, we propose an end-to-end correlated and individual feature learning framework to characterize the malignancy of HCC from Contrast-enhanced MR. From the phases of pre-contrast, arterial and portal venous, our framework simultaneously and explicitly learns both the shareable and phase-specific features that are discriminative to malignancy grades. We evaluate our method on the Contrast enhanced MR of 112 consecutive patients with 117 histologically proven HCCs. Experimental results demonstrate that arterial phase yields better results than portal vein and pre-contrast phase. Furthermore, phase specific components show better discriminant ability than the shareable components. Finally, combining the extracted shareable and individual features components has yielded significantly better performance than traditional feature fusion methods. We also conduct t-SNE analysis and feature scoring analysis to qualitatively assess the effectiveness of the proposed method for malignancy characterization.

This article proposes a new compact model and presents a circuit-theoretical analysis for a third-order memristive neuromorphic element fabricated by Kumar et al. The proposed model mainly consists of a box-shaped resistor model and a simplified piecewise-linear memristor model. Since the dynamic behavior of the box-shaped hysteresis in the quasistatic current–voltage curve is mostly unexplored, we first extract the box-shaped resistor model and construct its oscillators. The coordinate system shifting method and dynamic route analysis method are used to reveal the operating mechanism of boxshaped resistor-based oscillators. Both the theoretical analysis and simulation verification indicate that the box-shaped hysteresis characteristic facilitates the generation of neuromorphic action potentials. The proposed new compact model not only captures quasi-static characteristics but also includes dynamic behaviors, such as action potential, periodic spiking, and periodic bursting. The influences of the model parameters are further investigated to reveal the mechanism of the neuromorphic behaviors in the box-shaped hysteresis and positive differential resistance regions. Simulation results manifest the feasibility of the proposed model and the correctness of the presented analysis methods, which pave the way to the optimized design of memristive devices and the research of neuromorphic dynamics.

Locally-active memristor (LAM) is one of the promising candidates of artificial neurons, indicating it has potential applications in neuromorphic computing. Quantitative theoretical analysis on LAMs can provide benefits for designing related oscillator circuits and systems. This study begins with the aim of assessing the importance of DCV-Icharacteristic in the performance of LAMs by using small-signal analysis method. The DCV-Icurve of the LAM is specified by two parameters involving resistance (conductance) and differential resistance (differential conductance). In addition to these two static parameters, we extract a crucial dynamic parameter to describe the behavior of the LAM. Theoretical analysis demonstrates that the performance of generic current-controlled and voltage-controlled LAMs is closely associated with three crucial parameters, i.e., the above two static and one dynamic parameters. Hence, only based on these three parameters, can one derive the small-signal equivalent circuit of LAMs and determine the oscillation frequency range and condition for simple LAM-based oscillators. By applying the presented universal dynamics analysis results, we further propose a modified mathematical model with higher accuracy to mimic the quasi-static and oscillating behaviors of a real Nb2O5device, and provide some fundamental guidance for the design of LAM-based high-frequency oscillators.

Multimodal medical imaging plays a crucial role in the diagnosis and characterization of lesions. However, challenges remain in lesion characterization based on multimodal feature fusion. First, current fusion methods have not thoroughly studied the relative importance of characterization modals. In addition, multimodal feature fusion cannot provide the contribution of different modal information to inform critical decision-making. In this study, we propose an adaptive multimodal fusion method with an attention-guided deep supervision net for grading hepatocellular carcinoma (HCC). Specifically, our proposed framework comprises two modules: attention-based adaptive feature fusion and attention-guided deep supervision net. The former uses the attention mechanism at the feature fusion level to generate weights for adaptive feature concatenation and balances the importance of features among various modals. The latter uses the weight generated by the attention mechanism as the weight coefficient of each loss to balance the contribution of the corresponding modal to the total loss function. The experimental results of grading clinical HCC with contrast-enhanced MR demonstrated the effectiveness of the proposed method. A significant performance improvement was achieved compared with existing fusion methods. In addition, the weight coefficient of attention in multimodal fusion has demonstrated great significance in clinical interpretation.

Neuromorphic computing can solve computationally hard problems with energy efficiencies unattainable for von Neumann architectures. A locally-active memristor, which possesses the capability to amplify infinitesimal fluctuations in energy and can be used to generate neuromorphic behaviors, is a natural candidate for constructing an electronic equivalent of biological neurons. This paper identifies some unknown neuromorphic dynamics of the Chua corsage memristor (CCM), and shows that the CCM, when biased at the edge of chaos domain, can exhibit rich dynamics of biological neurons. Using Chua’s theories of local activity and edge of chaos, we demonstrate that under the destabilizing of the input voltage and the circuit parameters (inductance or capacitance), two CCM-based circuits can produce thirteen types of neuromorphic behaviors either on, or near the edge of chaos domain via supercritical or subcritical Hopf bifurcation. In addition, we give the conditions to test the edge of chaos of the CCM and the CCM-based circuit only by using the poles and the zero of their admittance functions.

Memristors have great application in many fields such as neural networks, non-volatile memory and nonlinear circuits by virtue of the nanoscale and non-volatile characteristics. Multi-valued devices possess significant meaning in digital logic circuit, chaos control and synapse networks. In this paper, the concept of multi-valued memristors is proposed, and the ternary flux-controlled memristor is taken as an example investigated concretely. Moreover, the specific ternary mathematical model is given and a series of numerical analyses have been studied. After that, a ternary flux-controlled memristor emulator is realized by off-the-shelf circuit components, both Multisim simulations and hardware experiments are performed to verify its effectiveness and the results shows that the theoretical analysis based on the mathematical model is in good agreement with the simulation and experimental results, which laid the theoretical foundation for the construction of multi-valued digital logic and other multi-valued applications.

Preoperative knowledge of the malignancy of hepatocellular carcinoma (HCC) based on medical images plays a significant role in deciding therapy strategies and patient management in clinical prac-tice. Deep learning with Convolutional Neural Network (CNN) has shown high diagnostic performance for lesion characterization with medical images. However, it is very challenging to train robust deep learning system for lesion characterization, especially for HCC, because there are often limited samples in clinical practice. In this work, we propose an efficient end-to-end framework that flexibly combines Conditional Adversarial network (CAN) and CNN to characterize the malignancy of HCC. Specifically, we introduce a similarity discriminative network to make the CAN efficiently generate more discrepant samples and devise hybrid loss functions to embed the proposed similarity discriminative network to the end-to-end framework with CAN and CNN. Experimental results of 115 clinical HCCs with pathologically confirmed malignancy demonstrate that the proposed end-to-end framework with similarity discriminative network can significantly improve the performance of deep feature based malignancy characterization of HCC and remarkably reduce the risk of overfitting with limited samples for the deep learning model in clinical practice.