PHResponsive Nanoemulsions With different Energetic Covalent Surfactant

We also show that the GLT model works seamlessly with the susceptible-infected or susceptible-infected-recovered model. One can easily combine them to model a hybrid spreading process in which simple contagion accumulates the critical mass for the complex contagion that leads to the global cascades. Overall, the GLT model we proposed can be a useful tool to study complex contagion, especially when studying the time evolution of the spreading.In this paper, we study the dynamics and control of a Caputo fractional difference form of the Duffing map. We use phase plots, bifurcation diagrams, and Lyapunov exponents to establish the existence of chaos over a wide range of fractional orders and examine the nature of the dynamics. Also, we present the 0-1 test to detect chaos and C0 complexity, which is an alternative nonlinear statistical measure that can quantify the regularity of a time series. In addition, we measure the approximate entropy to see the performance of our numerical results. Through phase plots and bifurcation diagrams, it is shown that the proposed fractional map exhibits a range of different dynamical behaviors including chaos and coexisting attractors. A one-dimensional feedback stabilization controller is proposed. The asymptotic convergence of the proposed controller is established by means of the stability theory of linear fractional order discrete-time systems. Simulation results have been carried out to illustrate the findings of the study.Consider any network of n identical Kuramoto oscillators in which each oscillator is coupled bidirectionally with unit strength to at least μ(n-1) other oscillators. Then, there is a critical value of μ above which the system is guaranteed to converge to the in-phase synchronous state for almost all initial conditions. The precise value of μ remains unknown. In 2018, Ling, Xu, and Bandeira proved that if each oscillator is coupled to at least 79.29% of all the others, global synchrony is ensured. In 2019, Lu and Steinerberger improved this bound to 78.89%. Here, we find clues that the critical connectivity may be exactly 75%. Our methods yield a slight improvement on the best known lower bound on the critical connectivity from 68.18% to 68.28%. We also consider the opposite end of the connectivity spectrum, where the networks are sparse rather than dense. In this regime, we ask how few edges one needs to add to a ring of n oscillators to turn it into a globally synchronizing network. We prove a partial result all the twisted states in a ring of size n=2m can be destabilized by adding just O(nlog2⁡n) edges. To finish the proof, one needs to rule out all other candidate attractors. We have done this for n≤8 but the problem remains open for larger n. Thus, even for systems as simple as Kuramoto oscillators, much remains to be learned about dense networks that do not globally synchronize and sparse ones that do.We study the coarse-grained distribution of a Hamiltonian system on the space partition determined by the initial measurement inaccuracies. Using methods of coding theory, introduced by Shannon and further researchers, Kolmogorov treated the stationary case for a discretized time, when the microscopic system is initially uniformly distributed. Following his work, we consider the non-stationary mesoscopic process induced by the Hamiltonian evolution from an inhomogeneous initial distribution. In general, this process has an infinite memory, but we show that its memory fades out with time with any finite accuracy a, it can be approximated by a process with a memory limited to the n past events, n depending only on a. As a result, under suitable hypotheses, the mesoscopic process obeys an approximate Markov equation on groups of n successive states. More roughly, one obtains an ordinary Markov system by introducing a time coarse-graining on n successive elementary time steps. So, in a generic case, the system eventually tends to equilibrium for any initial mesoscopic distribution.We systematically study the percolation phase transition at the change of concentration of the chaotic defects (pores) in an extended system where the disordered defects additionally have a variable random radius, using the methods of a neural network (NN). Two important parameters appear in such a material the average value and the variance of the random pore radius, which leads to significant change in the properties of the phase transition compared with conventional percolation. To train a network, we use the spatial structure of a disordered environment (feature class), and the output (label class) indicates the state of the percolation transition. We found high accuracy of the transition prediction (except the narrow threshold area) by the trained network already in the two-dimensional case. We have also employed such a technique for the extended three-dimensional (3D) percolation system. Our simulations showed the high accuracy of prediction in the percolation transition in 3D case too. The considered approach opens up interesting perspectives for using NN to identify the phase transitions in real percolating nanomaterials with a complex cluster structure.Motor fluctuations and dyskinesias are severe complications of Parkinson's disease (PD), especially evident at its advanced stage, under long-term levodopa therapy. Despite their strong clinical prevalence, the neural origin of these motor symptoms is still a subject of intense debate. In this work, a non-linear deterministic neurocomputational model of the basal ganglia (BG), inspired by biology, is used to provide more insights into possible neural mechanisms at the basis of motor complications in PD. In particular, the model is used to simulate the finger tapping task. The model describes the main neural pathways involved in the BG to select actions [the direct or Go, the indirect or NoGo, and the hyperdirect pathways via the action of the sub-thalamic nucleus (STN)]. A sensitivity analysis is performed on some crucial model parameters (the dopamine level, the strength of the STN mechanism, and the strength of competition among different actions in the motor cortex) at different levels of synapses, reflecting major or minor motor training. Depending on model parameters, results show that the model can reproduce a variety of clinically relevant motor patterns, including normokinesia, bradykinesia, several attempts before movement, freezing, repetition, and also irregular fluctuations. Oxaliplatin Motor symptoms are, especially, evident at low or high dopamine levels, with excessive strength of the STN and with weak competition among alternative actions. Moreover, these symptoms worsen if the synapses are subject to insufficient learning. The model may help improve the comprehension of motor complications in PD and, ultimately, may contribute to the treatment design.The introduction of the multiscale entropy (MSE) method was a milestone in the field of complex physiological signal analysis. However, since MSE is inapplicable for short signals, several variants of MSE have been proposed. One of the most important variants of MSE is the modified multiscale entropy (MMSE), even though it can still produce biased estimates due to the hard similarity criteria of sample entropy. Taking the advantages of MMSE and the concept of fuzzy entropy, we propose the modified multiscale fuzzy entropy (MMFE). We evaluated the robustness of MMSE and MMFE using segmented stochastic noises and actual heart rate variability series and compared it with the classical MSE results obtained with the full signals. Results show that MMFE is much more robust than MMSE for short physiological time series, resembling MSE for series as shorter as 400 samples. We also show the existence of an exponential relationship between the MMFE fuzzy parameter and the signal size. We suggest the use of this relationship to choose the optimal MMFE parameter as part of the method.Excessive neuronal synchrony is a hallmark of several neurological disorders, e.g., Parkinson's disease. An established treatment for medically refractory Parkinson's disease is high-frequency deep brain stimulation. However, it provides only acute relief, and symptoms return shortly after cessation of stimulation. A theory-based approach called coordinated reset (CR) has shown great promise in achieving long-lasting effects. During CR stimulation, phase-shifted stimuli are delivered to multiple stimulation sites to counteract neuronal synchrony. Computational studies in plastic neuronal networks reported that synaptic weights reduce during stimulation, which may cause sustained structural changes leading to stabilized desynchronized activity even after stimulation ceases. Corresponding long-lasting effects were found in recent preclinical and clinical studies. We study long-lasting desynchronization by CR stimulation in excitatory recurrent neuronal networks of integrate-and-fire neurons with spike-timing-dependent plasticity (STDP). We focus on the impact of the stimulation frequency and the number of stimulation sites on long-lasting effects. We compare theoretical predictions to simulations of plastic neuronal networks. Our results are important regarding CR calibration for two reasons. We reveal that long-lasting effects become most pronounced when stimulation parameters are adjusted to the characteristics of STDP-rather than to neuronal frequency characteristics. This is in contrast to previous studies where the CR frequency was adjusted to the dominant neuronal rhythm. In addition, we reveal a nonlinear dependence of long-lasting effects on the number of stimulation sites and the CR frequency. Intriguingly, optimal long-lasting desynchronization does not require larger numbers of stimulation sites.Nonlinear pulse propagation is a major feature in continuously extended excitable systems. The persistence of this phenomenon in coupled excitable systems is expected. Here, we investigate theoretically the propagation of nonlinear pulses in a 1D array of evanescently coupled excitable semiconductor lasers. We show that the propagation of pulses is characterized by a hopping dynamics. The average pulse speed and bifurcation diagram are characterized as a function of the coupling strength between the lasers. Several instabilities are analyzed such as the onset and disappearance of pulse propagation and a spontaneous breaking of the translation symmetry. The pulse propagation modes evidenced are specific to the discrete nature of the 1D array of excitable lasers.This paper is devoted to the study of an averaging principle for fractional stochastic differential equations in Rn with Lévy motion, using an integral transform method. We obtain a time-averaged effective equation under suitable assumptions. Furthermore, we show that the solutions of the averaged equation approach the solutions of the original equation. Our results provide a better understanding for effective approximation of fractional dynamical systems with non-Gaussian Lévy noise.The coronavirus 2019 (COVID-19) respiratory disease is caused by the novel coronavirus SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), which uses the enzyme ACE2 to enter human cells. This disease is characterized by important damage at a multi-organ level, partially due to the abundant expression of ACE2 in practically all human tissues. However, not every organ in which ACE2 is abundant is affected by SARS-CoV-2, which suggests the existence of other multi-organ routes for transmitting the perturbations produced by the virus. We consider here diffusive processes through the protein-protein interaction (PPI) network of proteins targeted by SARS-CoV-2 as an alternative route. We found a subdiffusive regime that allows the propagation of virus perturbations through the PPI network at a significant rate. By following the main subdiffusive routes across the PPI network, we identify proteins mainly expressed in the heart, cerebral cortex, thymus, testis, lymph node, kidney, among others of the organs reported to be affected by COVID-19.