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Neuromodulation plays a critical role in the normal physiological functions of organisms. With advancements in science and technology, neuromodulation has expanded into various fields. For instance, in the field of engineering, in vitro-cultured neural networks are utilized to perform closed-loop control for achieving complex functionalities. Conducting pioneering theoretical research using mathematical models is particularly essential for enhancing efficiency and reducing costs. This study focuses on examining the relationship between input and output in order to establish a groundwork for more advanced closed-loop regulation applications in engineering. Using a constructed neural network model, Poisson, square wave and direct current (DC) stimulation are applied. The results show that the network’s firing rate increases with the frequency or amplitude of these stimulations. And the network’s firing rate could reach to a stable state after the stimulation is applied for 0.8s and return to initial states when the stimulus is removed for 1s. To ascertain if the system exhibits a memory effect from the previous stimulus, we conduct independent and continuous stimulation schemes. Comparing the firing rate of neuronal networks under these two stimulation schemes reveals a memory effect of the system on the previous stimulus, which is independent of network properties and stimulus types. Finally, by applying square wave stimulation to the in vitro cultured neural network, we have confirmed that cultured neural network actually can reach to a steady state and have memory effects on the previous stimulus. Our research results have important theoretical significance and reference value for designing the closed-loop regulation strategy of in vitro cultured neuronal networks.

Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high dimensions with partial knowledge of the states. In this paper, we propose a new framework based on a well-designed cost functional, the minimization of which transforms the determination of both the unknown parameters and the unknown state evolution into parameter learning. This method can be conveniently used to reconstruct structures and dynamics of complex networks, even in the presence of noisy disturbances or for intricate parameter dependence. As a demonstration, we successfully apply it to the reconstruction of different dynamics on complex networks such as coupled Lorenz oscillators, neuronal networks, phase oscillators and gene regulation, from only a partial measurement of the node behavior. The simplicity and efficiency of the new framework makes it a powerful alternative to recover system dynamics even in high dimensions, which expects diverse applications in real-world reconstruction.

With the continuous operation of check dams, the silting elevation of the whole dam gradually increases. When the silting height is close to the elevation of the broad-crested weir, it will result in a large change in the hydraulic characteristics of the original flow pattern. For subsequent reinforcement work, it is necessary to know how excessive sediment deposition affects the overflow from the broad-crested weir into the spillway. However, few studies about discharge coefficients are available in the case of spillways with sediment. In this paper, the hydraulic characteristics and discharge coefficient of a broad-crested weir whose width is 270 mm are investigated with physical experiments under different siltation heights and discharges. The research shows that: (1) With the increase in siltation height, the water level on the weir decreases and the drop of the flow becomes smaller. The overall flow pattern tends to the open-channel flow pattern. (2) In the same siltation height condition, the water surface profile along the broad-crested weir rises with the increase in discharge, and the surface velocity of the water in front of the weir increases with the increase in discharge. However, in the same discharge condition, the water surface profile along the broad-crested weir decreases with the increase in siltation height, and the surface velocity of the water in front of the weir gradually increases, which reflects that the increase in siltation height improves the overflow capacity of the broad-crested weir. (3) The present empirical formulas for the discharge coefficient have large errors when there is sediment accumulation. Therefore, a new formula for the discharge coefficient with sediment deposition is obtained using experimental data and its maximum relative error is 4.02%, which can provide a theoretical basis for risk elimination and reinforcement work on check dams in the Loess Plateau.

We describe a colorimetric method for the determination of Hg(II) that is based on the aggregation of silver nanoparticles (AgNPs) in the presence of Hg(II) and lysine. If Hg(II) ions are added to unmodified AgNPs, they will deposit on the surface where they will be reduced to Hg(0) by NaBH 4 to form a shell around the AgNPs. Upon addition of lysine to the Hg(II)-capped AgNPs, the aggregation of the AgNPs will be induced because the two amino groups of lysine have a high affinity for Hg(II). Aggregation results in a color change from orange to yellowish. The effect was exploited to design a colorimetric assay for Hg(II) that has a 1 nM detection limit. Graphical Abstract A simple, fast, and sensitive, colorimetric probe for the detection of Hg 2+ is designed.

Various lines of evidence, including the occurrence of bitumen and fluid inclusions, show that oil charge once took place in the Kela-2 gas field, Kuqa foreland basin, Northwest China. However, the scale of the ancient oil reservoir remains unclear, as does the process by which the reservoir evolved into the present dry gas field. Here, using data from analyses of fluid inclusions, petrography, laser Raman spectroscopy, and quantitative fluorescence, the hydrocarbon accumulation history of the Kela-2 gas field is reconstructed. The results show that the gas field underwent three periods of hydrocarbon charging and one period of adjustment. The first oil charging occurred at about 12 Ma, as recorded by the first group of oil inclusions containing 0–8 vol.% gas with yellowish-brown fluorescence. The second charging involved mature oil charging at about 4 Ma, recorded by the second group of oil inclusions containing 15–25 vol.% gas with blue-white fluorescence. According to quantitative grain fluorescence (QGF) and rock pyrolysis analysis, an ancient oil reservoir existed with an oil-column height of about 350 m, and the paleo oil–water contact was lower than the present gas–water contact. Under intense thrusting from 3 Ma, the ancient oil reservoir was destroyed, with oil escaping through the Kashangtuokai thrust fault, which broke the salt layer, as this layer at that time lay in the brittle deformation domain. The inferred destruction of the ancient oil reservoir is supported by the numerous oil and gas shows at the surface and in shallow layers near the Kashangtuokai fault, as well as the anomalous development of authigenic kaolinite in the gas reservoir, which was enhanced by an open or semiopen system caused by the fault breaking through the salt layer. Subsequently, with increasing burial depth to more than 3000 m, the fault that had cut through the salt layer annealed because the salt layer then lay within the ductile deformation domain. The higher overpressure that occurred during the third gas charging at about 2 Ma reflected the annealing of the fault in the salt layer, favoring late gas accumulation and preservation. The evolution of the Kela-2 gas field provides an important case study for understanding the role of the salt layer crossing the brittle–plastic transition and the dynamic evolution of the salt caprock in salt-containing foreland basins.

Nonlinear dynamics is a rapidly developing subject across all disciplines involving spatial or temporal evolution. The reconstruction of equations of motion for a nonlinear system from observed time series has been a hot topic for a long time. Nevertheless, in practice only partial information is available for many systems which are very likely contaminated with noise. Here, based on the invariance of the evolution equation of an autonomous system during time translation, a globally valid local approximation of the trajectory is determined, which could be reliably used for the reconstruction of the vector fields with unknown parameters or functional forms, or even with partial observations. Moreover, the noise interference with nonlinearity is computed to the leading order, which together with the global consideration bestows exceptional robustness and extra accuracy to the technique. The new scheme asks only for the solutions of linear equations and thus is very efficient, which is nicely demonstrated in the Lorenz equation in different conditions, while an FitzHugh–Nagumo (FHN) neural network model is used to show its strength in high dimensions.

Benefiting from ultrafast temporal resolution, broadband spectral bandwidth, as well as high peak power, passively mode-locked fibre lasers have attracted growing interest and exhibited great potential from fundamental sciences to industrial and military applications. As a nonlinear system containing complex interactions from gain, loss, nonlinearity, dispersion, etc., ultrafast fibre lasers deliver not only conventional single soliton but also soliton bunching with different types. In analogy to molecules consisting of several atoms in chemistry, soliton molecules (in other words, bound solitons) in fibre lasers are of vital importance for in-depth understanding of the nonlinear interaction mechanism and further exploration for high-capacity fibre-optic communications. In this Review, we summarize the state-of-the-art advances on soliton molecules in ultrafast fibre lasers. A variety of soliton molecules with different numbers of soliton, phase-differences and pulse separations were experimentally observed owing to the flexibility of parameters such as mode-locking techniques and dispersion control. Numerical simulations clearly unravel how different nonlinear interactions contribute to formation of soliton molecules. Analysis of the stability and the underlying physical mechanisms of bound solitons bring important insights to this field. For a complete view of nonlinear optical phenomena in fibre lasers, other dissipative states such as vibrating soliton pairs, soliton rains, rogue waves and coexisting dissipative solitons are also discussed. With development of advanced real-time detection techniques, the internal motion of different pulsing states is anticipated to be characterized, rendering fibre lasers a versatile platform for nonlinear complex dynamics and various practical applications.

In situ carbonate U-Pb dating is gaining popularity, and it has great potential for application in petroleum geology. However, the low U content (<10 µg/g) and high common Pb content of carbonate minerals, along with the uneven distribution of U and Pb and the lack of matrix-matched reference material make carbonate U-Pb dating inaccurate and less successful, which limits the widespread application in geosciences. This study evaluated the limitations of in situ carbonate U-Pb dating and proposed a method to rationally determine the laser ablation parameters of samples by improving the experimental approach based on the laser ablation sector field inductively coupled plasma mass spectrometry (LA-SF-ICP-MS). By setting a different spot size and laser frequency for the reference material and unknown samples in the same session based on the U content of the sample, the ablation craters of the reference material and unknown samples were given the same depth/width ratio, avoiding systematic offset caused by differences in down-hole element fractionation and reducing the consume of reference material. Depending on the heterogeneous distribution of U and Pb contents in carbonate minerals, the method of grid screening and setting ablation spots during screening were used to quickly select domains with high U and low common Pb, which improves the efficiency of setting laser spots and the success rate of dating, as well as reduces the experimental time and economic cost. The accuracy and success rate of carbonate U-Pb dating were effectively improved by improving the experimental method, and the technique was applied to two carbonate samples with low U and high common Pb contents that were difficult to date by traditional methods. The two samples are the saddle dolomite in the central Sichuan Basin and the calcite cement in the sandstone reservoir of the Cretaceous Qingshuihe Formation in the South Junggar Basin. The robust ages have been obtained, which constrains the timing of the diagenetic and hydrocarbon accumulation process in the studied area.

Although flavonoid compounds exhibit various pharmacological activities, their clinical applications are restricted by low oral bioavailability owing to their poor solubility. Nanocrystals (NCs) represent an excellent strategy for enhancing the oral bioavailability of flavonoids. Hydroxyethyl starch (HES), a biomaterial compound used as a plasma expander, could be an ideal stabilizer material for preparing flavonoid NCs. HES was used to stabilize flavonoid nanocrystals (NCs), using luteolin (LUT) as a model drug. After full characterization, the freeze-drying and storage stability, solubility, intestinal absorption, pharmacokinetics, and in vivo anti-hyperuricemic effect of the optimized HES-stabilized LUT NCs (LUT-HES NCs) were investigated. Uniformed LUT-HES NCs were prepared with mean particle size of 191.1±16.8 nm, zeta potential of about -23 mV, drug encapsulation efficiency of 98.52 ± 1.01%, and drug loading of 49.26 ± 0.50%. The freeze-dried LUT-HES NCs powder showed good re-dispersibility and storage stability for 9 months. Notably, compared with the coarse drug, LUT-HES NCs exhibited improved saturation solubility (7.49 times), increased drug dissolution rate, enhanced Caco-2 cellular uptake (2.78 times) and oral bioavailability (Fr=355.7%). Pharmacodynamic studies showed that LUT-HES NCs remarkably lowered serum uric acid levels by 69.93% and ameliorated renal damage in hyperuricemic mice. HES is a potential stabilizer for poorly soluble flavonoid NCs and provides a promising strategy for the clinical application of these compounds. LUT-HES NCs may be an alternative or complementary strategy for hyperuricemia treatment.

Luteolin is a natural flavonoid, which exists in many plants, including onions, broccoli, carrots, peppers, celery, olive oil, and mint. Luteolin is a dietary flavonoid with potent uric acid‐lowering and antioxidant bioactivities. To date, the mechanism by which luteolin alleviates hyperuricemia nephropathy (HN) still needs to be better defined. This study aims to evaluate the therapeutic efficacy of luteolin in a preclinical mouse model and in vitro. Luteolin was administered in the HN mice induced by the combination of potassium oxonate and hypoxanthine to evaluate the potential renoprotective effects in vivo. The NRK‐52E cells were stimulated with adenosine for in vitro evaluation. Hematoxylin and eosin staining, biochemical analysis, immunoblotting, immunofluorescence, and immunohistochemistry were performed for the histopathologic and mechanistic investigations. The results suggest that luteolin attenuated tubular dilation and epithelial atrophy in the renal tissue of HN mice. Further, luteolin improved biochemical indicators concerning renal functions and oxidative stress in vivo. Mechanistically, luteolin reduced the renal expressions of KIM‐1 and caspase‐3. Luteolin activated renal SIRT1/6 cascade and its downstream Nrf2‐mediated antioxidant pathway. Furthermore, luteolin elevated the renal expressions of ATP‐binding cassette subfamily G isoform 2 protein (ABCG2) and organic anion/cation transporters. In addition, livers of luteolin‐treated HN mice exhibited robust inhibition of xanthine oxidase. Together, our study shows that luteolin alleviates renal injury in the HN mice by activating urate excretion and Nrf2/HO‐1/NQO1 antioxidant pathways and inhibiting liver xanthine oxidase activity. Thus, luteolin may be a potential agent for the treatment of HN. This study provides mechanistic insights into how luteolin suppresses renal injury caused by hyperuricemic nephropathy (HN). Luteolin intervention significantly improved renal injury in HN mice. Through in vivo and in vitro experiments, we found that luteolin can significantly activate uric acid excretion and Nrf2/HO1/NQO1 antioxidant pathway and inhibit the activity of xanthine oxidase in the liver.