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Hypertension is one of the most prevalent cardiovascular diseases worldwide and is known to be dominated by the sympathetic nervous system (SNS). Previously, we found that targeting A Disintegrin and Metalloproteinase 17 (ADAM17) in glutamatergic neurons was able to blunt Ang-II-induced excitation of pre-autonomic neurons, and blocked DOCA-salt treatment-induced sympatho-excitation in mice, thereby alleviating their development of hypertension. However, how ADAM17 support the activation of pre-autonomic neurons remains unknown. Beyond the glutamatergic neurons, we found in the current study that microglial activation and increase of pro-inflammatory cytokine levels in the hypothalamus, induced by DOCA-salt treatment, were blunted in those mice with ADAM17 knockout in glutamatergic neurons (A17G; number of CD11b+cells per line: NT+DOCA vs. A17G+DOCA= 11±2 vs. 6±1, P= 0.0017; normalized TNFα level: NT+DOCA vs. A17G+DOCA= 1.00±0.37 vs. 0.67±0.11, P< 0.05; normalized IL-6 level: 1.00±0.32 vs. 0.59±0.20, P< 0.05). Especially, it also reversed DOCA-salt-induced downregulation of Gad67 mRNA expression (NT= 1.00±0.11, NT+DOCA= 0.66±0.12, A17G= 1.02±0.15, A17G+DOCA= 1.67±0.24 fold of change, NT vs. NT+DOCA and A17G vs. A17G+DOCA: P< 0.05), and normalized the decreased level of GABA in hypothalamus (normalized GABA levels: NT= 1.00±0.15, NT+DOCA= 0.84±0.09, A17G+DOCA= 1.09±0.17, NT vs. NT+DOCA: P< 0.05), suggesting that in addition to the effect of ADAM17 on the neuron itself, it might also regulate the SNS through altering the neuronal microenvironment. In L-NAME hypertensive model, though A17G mice showed no improvement in NOS-blockade-induced dysfunction of neuro-vascular coupling (increase of CBF induced by whisker-stimulation: NT vs. A17G= 24.34±11.20 vs. 24.87±15.78 PU%), it did exhibit improved performance in Barnes maze test (latency time: NT vs. A17G= 32.77±19.36 vs. 95.54±59.03 s, P= 0.002), suggesting that ADAM17 in glutamatergic is critical for the process of neuronal damage induced by hypoxia and ischemia, possibly through modulating the homeostasis of neuronal microenvironment.

Hypertension (HTN) has now been associated with cognitive impairment and considered as one of the risk factors for mild cognitive impairment (MCI). To investigate whether there is neuronal mechanism, HTN was induced in C57BL/6j male mice (~22 weeks) by DOCA-salt treatment (DS, 1.4mg/g+1%NaCl, 28 days), a neurogenic model. Firstly, BP was monitored by tail-cuff (sham vs. DS: SBP= 116.1±7.6 vs. 145.0±8.2 mmHg). Then, behavioral study was performed to assess the cognitive function (CFN). In whole, compared to sham, the DS mice performed worse in all 4 tasks, including object location recognition (before vs. after: NLR%= 29.34±13.73 vs. -20.81±10.70), novel object recognition (NOR%= 48.60±22.62 vs. 9.09±25.50), Barnes maze (latency T= 26.55±16.52 vs. 116.80±57.67s), and nesting (score= 4.00±0.92 vs. 2.43±1.55). Later, CBF was measured by laser doppler. The rise of CBF upon whisker-stimulation (WS) was lower in the DS mice (27.83±13.86 vs. 51.12±18.22 PU), while their basal CBF was not affected, suggesting that DS-induced MCI could be related to impairment of neuro-vascular coupling (NVC). Previously, we have showed the overactivation of brain renin-angiotensin system (RAS) in the onset of DS HTN. To identify the possible contribution from brain RAS, neuronal AT 1a R were deleted (AT1N). In AT1N mice, DS-related impairments in CFN and NVC were attenuated, as evidenced by higher nesting scores (AT1N+DS vs. NT+DS: 3.75±1.89 vs. 2.43±1.55 ), better performance in Barnes maze (61.28±54.47 vs. 116.80±57.67 s) and grater augment in CBF upon WS (41.49±10.65 vs. 27.83±13.86 PU), compared to NT. Through LTP recording in CA1 neurons using both field and whole-cell modes, we identified that activation of neuronal AT 1 R could contribute directly to the development of MCI, thereby neuronal AT 1 R was selectively knocked down in the hippocampus of NT mice (AT1hN). After DS treatment, AT1hN showed no difference in SBP compared with the sham NT (149.0±14.7 vs. 150.4±6.9 mmHg), while their CFN showed improvement in both NOR and Barnes maze (NOR%= 11.70±25.78 vs. -10.15±42.60; latency T= 71.72±47.60 vs. 113.70±65.64 s). In summary, our data suggest that neuron-expressing AT 1 R could participate in the onset of hypertension-associated MCI via both vascular and neural mechanisms.

We perform dynamical analysis on a stochastic Rosenzweig-MacArthur model driven by {\alpha}-stable L\'evy motion. We analyze the existence of the equilibrium points, and provide a clear illustration of their stability. It is shown that the nonlinear model has at most three equilibrium points. If the coexistence equilibrium exists, it is asymptotically stable attracting all nearby trajectories. The phase portraits are drawn to gain useful insights into the dynamical underpinnings of prey-predator interaction. Specifically, we present a transcritical bifurcation curve at which system bifurcates. The stationary probability density is characterized by the non-local Fokker-Planck equation and confirmed by some numerical simulations. By applying Monte Carlo method and using statistical data, we plot a substantial number of simulated trajectories for stochastic system as parameter varies. For initial conditions that are arbitrarily close to the origin, parameter changes in noise terms can lead to significantly different future paths or trajectories with variations, which reflect chaotic behaviour in mutualistically interacting two-species prey-predator system subject to stochastic influence.

In this work, we mainly characterize stochastic bifurcations and tipping phenomena of insect outbreak dynamical systems driven by α-stable Lévy processes. In one-dimensional insect outbreak model, we find the fixed points representing refuge and outbreak from the bifurcation curves, and carry out a sensitivity analysis with respect to small changes in the model parameters, the stability index and the noise intensity. We perform the numerical simulations of dynamical trajectories using Monte Carlo methods, which contribute to looking at stochastic hysteresis phenomenon. As for two-dimensional insect outbreak system, we identify the global stability properties of fixed points and express the probability density function by the stationary solution of the nonlocal Fokker-Planck equation. Through numerical modelling, the phase portrait makes it possible to detect critical transitions among the stable states. It is then worth describing stochastic bifurcation associated with tipping points induced by noise through a careful examination of the dynamical paths of the insect outbreak system with external forcing. The results give new insight into the sensitivity of ecosystems to realistic environmental changes represented by stochastic perturbations.

This work is devoted to investigating stochastic turbulence for the fluid flow in one-dimensional viscous Burgers equation perturbed by Lévy space-time white noise with the periodic boundary condition. We rigorously discuss the regularity of solutions and their statistical quantities in this stochastic dynamical system. The quantities include moment estimate, structure function and energy spectrum of the turbulent velocity field. Furthermore, we provide qualitative and quantitative properties of the stochastic Burgers equation when the kinematic viscosity [Formula: see text] tends towards zero. The inviscid limit describes the strong stochastic turbulence.

Hypertension is one of the most prevalent cardiovascular disorders worldwide, affecting 1.13 billion people, or 14% of the global population. Hypertension is the single biggest risk factor for cerebrovascular dysfunction. According to the American Heart Association, high blood pressure (BP), especially in middle-aged individuals (~ 40 to 60 years old), is associated with an increased risk of dementia, later in life. Alzheimer's disease and cerebrovascular disease are the two leading causes of dementia, accounting for around 80% of the total cases and usually combining mixed pathologies from both. Little is known regarding how hypertension affects cognitive function, so the impact of its treatment on cognitive impairment has been difficult to assess. The brain renin-angiotensin system (RAS) is essential for BP regulation and overactivity of this system has been established to precede the development and maintenance of hypertension. Angiotensin II (Ang-II), the main peptide within this system, induces vasoconstriction and impairs neuro-vascular coupling by acting on brain Ang-II type 1 receptors (AT

Internet of Things (IoT) security becomes of great importance, as IoT is the foundation for many emerging services. To safeguard IoT security, cryptosystems at upper layer relying on sophisticated key management alone can face many challenges due to the massive deployment of resource constrained machine-type communication (MTC) devices. Physical layer (PHY) security can complement and enhance IoT security, by exploiting the characteristics of the bottom layer. In PHY security, channel state information (CSI) estimated through reverse pilot training is essential for the sender to select appropriate beamforming/precoder, which however is also vulnerable to adversaries. An adversary can actively launch pilot contamination attacks to affect the channel estimation and improve its signal reception quality. In this paper, we propose a relay-aided vectorized (RAV) secure transmission scheme, to safeguard the downlink communication in IoT networks under potential pilot contamination attacks. The proposed scheme does not distinguish the pilot sequences sent from an adversary and the receiver; and the sender utilizes what it receives to estimate the CSI for beamforming/precoder design. Then, a set of data symbols are presuperposed using a random complex matrix to form signal vectors to send. Through cooperation with a relay, the signal vectors can be recovered by the intended receiver whereas the adversary or the relay cannot, as proved through security analysis. The simulation results also demonstrate that the bit error rate (BER) of the adversary is 0.5 regardless of its channel quality, indicating perfect secrecy is achieved.

We present a length-structured matrix model for fish populations in which the probability that a fish grows into the next length class is a decreasing nonlinear function of the total biomass of the population. We present mathematical results classifying the dynamics that this density-dependent model predicts. We illustrate these results with numerical simulations for an invasive white perch population and show how the mathematical results can be used to predict the persistence and/or boundedness of the population as well as an equilibrium structure that is dominated by small fish. We illustrate the results with management recommendations for an invasive white perch population.

This work is concerned with the dynamics of a class of slow–fast stochastic dynamical systems driven by non-Gaussian stable Lévy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, and then we eliminate the fast variables to reduce the dimensions of these stochastic dynamical systems. It is shown that as the scale parameter tends to zero, the slow manifolds converge to critical manifolds in distribution, which helps to investigate long time dynamics. The approximations of slow manifolds with error estimate in distribution are also established. Furthermore, we corroborate these results by three examples from biological sciences.

Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bifurcation are commonly used. In contrast, stochastic bifurcation techniques are infrequently employed. Here we establish stochastic P-bifurcation behavior of (i) a growth model with state-dependent birth rate and constant death rate, and (ii) a logistic growth model with state-dependent carrying capacity, both of which are driven by multiplicative symmetric stable Levy noise. Transcritical bifurcation occurs in the deterministic counterpart of the first model, while saddle-node bifurcation takes place in the logistic growth model. We focus on the impact of the variations of the growth rate, the per capita daily adult mortality rate, the stability index, and the noise intensity on the stationary probability density functions of the associated non-local Fokker-Planck equation. In the first model, the bifurcation parameter is the ratio of the population birth rate to the population death rate. In the second model, the bifurcation parameter corresponds to the sensitivity of carrying capacity to change in the size of the population near equilibrium. In each case, we show that as the value of the bifurcation parameter increases, the shape of the steady-state probability density function changes and that both stochastic models exhibit stochastic P-bifurcation. The unimodal density functions become more peaked around deterministic equilibrium points as the stability index increases. While an increase in any one of the other parameters has an effect on the stationary probability density function. That means the geometry of the density function changes from unimodal to flat, and its peak appears in the middle of the domain, which means a transition occurs., Comment: 17 pages, 19 figures

This work focuses on stochastic bifurcation for a slow–fast dynamical system driven by non-Gaussian α-stable Lévy noise. We prove the main result for the stochastic equilibrium states for the original system and the reduced system based on the random slow manifold. Then, it is verified that the slow reduced system bears the stochastic bifurcation phenomenon inherited from the original system. Furthermore, we investigate the number and stability type of stochastic equilibrium states for dynamical systems through numerical simulations, and it is illustrated that the slow reduced system captures the stochastic bifurcation of the original system.

The pilot contamination attack is one kind of active eavesdropping activities conducted by a malicious user during the channel training phase. In the existing physical layer transmission against such attack, it is usually assumed that the transmitters may obtain prior knowledge to identify the legitimate users first, then design secure scheme based on the corrected main channel information. However, sometimes it is likely that the prior knowledge is not available, which makes it more difficult to design the transmitting scheme. Motivated by this, we propose a novel transmission against the pilot contamination attack. In our scheme, it is assumed that ideal prior knowledge of the main channel state information (CSI) is not available. Additionally, an extra assistant node is introduced to the well-known Wyner eavesdropping model. Both the uncorrected main CSI and the CSI at the assistant node are used to design the random scrambling scheme at the transmitter, which means there is no need to differentiate between eavesdroppers and legitimate users. Furthermore, we discuss the receiving performance of legitimate users cooperated with the assistant node. Numerical results shows that the legitimate users could achieve pleasant receiving performance while eavesdroppers could hardly obtain acceptable recovery of the original signal.

This work aims at understanding the slow dynamics of a nonlocal fast-slow stochastic evolutionary system with stable Levy noise. Slow manifolds along with the exponential tracking property for a nonlocal fast-slow stochastic evolutionary system with stable Levy noise are constructed, and two examples with numerical simulations are presented to illustrate the results.

We consider a non-autonomous predator–prey model, with prey subject to the disease and Lévy noise. We show the existence of global positive solution and stochastic boundedness. Then, we examine the asymptotic properties of the solution. Finally, we offer sufficient conditions for persistence and extinction.

The problem of how to double the volume of a cube, also known as the Delian problem, has intrigued mathematicians for millennia. The great variety of solutions discovered over the centuries have used diverse tools, mathematical and otherwise. Recently, in 1936, Margherita Piazollo Beloch discovered a simple and elegant solution to this question. It uses a single piece of paper and a handful of folds. The solution has renewed interest in geometrical constructability problems, in particular those that incorporate origami. And ultimately, it's given rise to the field of origami mathematics. Faculty Sponsor: Shenglan Yuan