It is a challenging problem to establish safe and simple therapeutic methods for various complicated diseases of the nervous system, particularly dynamical diseases such as epilepsy, Alzheimer's disease, and Parkinson's disease. From the viewpoint of nonlinear dynamical systems, a dynamical disease can be considered to be caused by a bifurcation induced by a change in the values of one or more regulating parameter. Therefore, the theory of bifurcation control may have potential applications in the diagnosis and therapy of dynamical diseases. In this study, we employ a washout filter-aided dynamic feedback controller to control the onset of Hopf bifurcation in the Hodgkin-Huxley (HH) model. Specifically, by the control scheme, we can move the Hopf bifurcation to a desired point irrespective of whether the corresponding steady state is stable or unstable. In other words, we are able to advance or delay the Hopf bifurcation, so as to prevent it from occurring in a certain range of the externally applied current. Moreover, we can control the criticality of the bifurcation and regulate the oscillation amplitude of the bifurcated limit cycle. In the controller, there are only two terms: the linear term and the nonlinear cubic term. We show that while the former determines the location of the Hopf bifurcation, the latter regulates the criticality of the Hopf bifurcation. According to the conditions of the occurrence of Hopf bifurcation and the bifurcation stability coefficient, we can analytically deduce the linear term and the nonlinear cubic term, respectively. In addition, we also show that mixed-mode oscillations (MMOs), featuring slow action potential generation, which are frequently observed in both experiments and models of chemical and biological systems, appear in the controlled HH model. It is well known that slow firing rates in single neuron models could be achieved only by type-I neurons. However, the controlled HH model is still classified as a type-II neuron, as is the original HH model. We explain that the occurrence of MMOs can be related to the presence of the canard explosion where a small oscillation grows through a sequence of canard cycles to a relaxation oscillation as the control parameter moves through an interval of exponentially small width.
The transmission properties of an integrate-and-fire neuron model that transmits coherent subthreshold spike trains in a shot noise environment are investigated by numerical simulation. For very weak coherent couplings, it is shown that the input-output signal-to-noise ratio (SNR) gain is easier to exceed unity; while for stronger coherent couplings it is difficult to observe the SNR gain larger than unity at the optimal noise intensity. These observations are different from those acquired in the case of continuous noise. Our analysis further suggests that the larger SNR gain in the very weak coherent coupling case should be due to the noise-induced resonance. It is also shown that there is more possibility of the SNR gain above unity for slower periodic spike trains transmitted by the model. The results may be useful in understanding the performance of real noisy neurons acting as signal-processing elements.
This paper proposes an approach to changing the types of neuronal excitability via bifurcation control. A washout filter-aided dynamic feedback controller is introduced to bifurcation dynamics of a two-dimensional Hindmarsh-Rose type model neuron, which shows a saddle-node on invariant circle (SNIC) bifurcation from quiescence to periodic spiking and then exhibits type-I excitability. At first, a Hopf bifurcation is created at a desired parameter value before the SNIC bifurcation occurs, and then the criticality of the created Hopf bifurcation is regulated by choosing appropriate values of the controller parameters. In this manner, the model neuron starts to show type-II excitability. Therefore the type of neuronal excitability is transformed from type-I excitability to type-II excitability for the model neuron via the washout filter-aided dynamic feedback controller. In such a controller, the linear control gain is determined by the two basic critical conditions for the Hopf bifurcation, i.e., the eigenvalue assignment and the transversality condition. We apply the center manifold and normal form theory to deduce a closed-form analytic expression for the bifurcation stability coefficient, which is a function with respect to the nonlinear control gain. A suitable nonlinear control gain is chosen to make the bifurcation stability coefficient negative, and thus the criticality of the created Hopf bifurcation can be changed from subcritical to supercritical. In addition, the amplitude of the corresponding periodic solution can be also regulated by the nonlinear control gain.
To defend against quantum computer attacks, the National Institute of Standards and Technology (NIST) has been exploring post-quantum cryptography (PQC). Now, NIST has standardised only two PQC algorithms, one of which is the Leighton-Micali signature (LMS). However, the performance of LMS limits its practical application. In this paper, we propose a parallel LMS implementation on multiple nodes. Considering different application scenarios, we provide two parallel schemes: algorithmic parallelism and data parallelism. The main part of our work is the two-tier parallel structure for the LMS tree. Targeting the x86/64 multiple nodes, our work introduces vectorization to present the three-tier parallel structure. We also design communication optimization, including the selection of communication primitives and the creation of communicators for multi-node running. Experimental evidence shows that our code effectively reduces the latency, and is 19.04× faster than the fastest implementation on the same platform when running key pair generation for LMS SHA256 M32 H20(20).
Yttria‐stabilized zirconia (YSZ) powder with surface Ni plating has promising application in many fields due to its large surface area, low density and excellent high temperature performance. In this study, YSZ/Ni double‐shell powder was fabricated via electroless deposition method, and an active surface kinetic model was developed to tune the surface area and nuclei loading quantitatively. A novel concept, active surface ratio (ASR, the ratio of active deposition surface area to projected area of ceramic powder), is proposed to intrinsically correlate deposition rate with nuclei topology on ceramic surface. The intrinsic relationship between microstructure of metallized ceramic surface and deposition duration was clarified. The active surface kinetic model reveals the correlation between the ASR and instantaneous deposition rate and provides necessary theoretical basis for effective control of ceramic surface modification process by electroless deposition.
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