Computational analysis of a class of singular nonlinear fractional multi-order heat conduction model of the human head.

The subject of the article is devoted to the development of a matrix collocation technique based upon the combination of the fractional-order shifted Vieta-Lucas functions (FSVLFs) and the quasilinearization method (QLM) for the numerical evaluation of the fractional multi-order heat conduction model related to the human head with singularity and nonlinearity. The fractional operators are adopted in accordance with the Liouville-Caputo derivative. The quasilinearization method (QLM) is first utilized in order to defeat the inherent nonlinearity of the problem, which is converted to a family of linearized subequations. Afterward, we use the FSVLFs along with a set of collocation nodes as the zeros of these functions to reach a linear algebraic system of equations at each iteration. In the weighted [Formula: see text] norm, the convergence analysis of the FSVLFs series solution is established. We especially assert that the expansion series form of FSVLFs is convergent in the infinity norm with order [Formula: see text], where K represents the number of FSVLFs used in approximating the unknown solution. Diverse computational experiments by running the presented combined QLM-FSVLFs are conducted using various fractional orders and nonlinearity parameters. The outcomes indicate that the QLM-FSVLFs produces efficient approximate solutions to the underlying model with high-order accuracy, especially near the singular point. Furthermore, the methodology of residual error functions is employed to measure the accuracy of the proposed hybrid algorithm. Comparisons with existing numerical models show the superiority of QLM-FSVLFs, which also is straightforward in implementation.

What affects China's green finance? Evidence from cryptocurrency market, oil market, and economic policy uncertainty.

This paper discusses the dynamic long- and short-term effects of bitcoin price (BTP), crude oil price (COP), and uncertainty of economic policy (EPU) on China's green bond (CGB) market, separately. Depending on the quantile autoregressive distributed lag method, the empirical results are shown that BTP and EPU exert substantial positive and negative effects on the CGB market in the long term for most circumstances, while their effects reflect not prominent in the short term. The main contributions can be summarized as follows. Given that China is the largest bitcoin mining state and a major green bond issuer, this study first explores the linkages between them. Furthermore, both long- and short-term effects are investigated from BTP, COP, and EPU to CGB, and long-term effects are dominated in the interrelationships among variables, indicating that the CGB market is mainly driven by permanent shocks. In addition, the mentioned long-term effects are deeply discussed from time- and quantile-varying aspects. This approach considers diverse situations in the bond market and various incidents that occur at various durations of time. The results underscore the significance of market participants gaining a deeper comprehension of how BTP, COP, and EPU impact green bond within varying market conditions. Implementing specific policies, such as establishing a cohesive and efficient bond market and making careful adjustments to economic policies, can be advantageous in maintaining stability within the CGB market.

Exploring the type and strength of nonlinearity in water quality responses to nutrient loading reduction in shallow eutrophic water bodies: Insights from a large number of numerical simulations.

Reducing the load of nutrients is essential to improve water quality while water quality may not respond to the load reduction in a linear way. Despite nonlinear water quality responses being widely mentioned by studies, there is a lack of comprehensive assessment on the extent and type of nonlinear responses considering the seasonal changes. This study aimed to measure the strength of nonlinearity of theoretically possible water quality responses and explore their potential types in shallow eutrophic water bodies. Hereto, we generated 14,710 numerical water body cases that describe the water quality processes using the Environmental Fluid Dynamics Code (EFDC) and applied eight load reduction scenarios on each water body case. Inflows are simplified from Lake Dianchi. The climate conditions consider three cases: Lake Dianchi, Wissahickon Creek, and Famosa Slough. We then developed a nonlinearity strength indicator to quantify the strength and frequency of nonlinear water quality responses. Based on the quantification of nonlinearity, we clustered all the samples of water quality responses using K-Means, an unsupervised Machine Learning algorithm, to find the potential types of nonlinear water quality responses for TN (total nitrogen), TP (total phosphorus), and Chla (chlorophyll a). Results show linear or near-linear response types account for 90%, 69%, and 20% of TN, TP, and Chla samples respectively. TP and Chla could perform more types of nonlinearity. Representative nonlinear water quality responses include disproportional improvement, peak change (disappear, move forwards or afterward), and seasonal deterioration of TN after load reduction. This study would contribute to the current understanding of nonlinear water quality responses to load reduction and provide a basis to study under which conditions the nonlinear responses may emerge.

Field-effect at electrical contacts to two-dimensional materials.

The inferior electrical contact to two-dimensional (2D) materials is a critical challenge for their application in post-silicon very large-scale integrated circuits. Electrical contacts were generally related to their resistive effect, quantified as contact resistance. With a systematic investigation, this work demonstrates a capacitive metal-insulator-semiconductor (MIS) field-effect at the electrical contacts to 2D materials: The field-effect depletes or accumulates charge carriers, redistributes the voltage potential, and gives rise to abnormal current saturation and nonlinearity. On one hand, the current saturation hinders the devices' driving ability, which can be eliminated with carefully engineered contact configurations. On the other hand, by introducing the nonlinearity to monolithic analog artificial neural network circuits, the circuits' perception ability can be significantly enhanced, as evidenced using a coronavirus disease 2019 (COVID-19) critical illness prediction model. This work provides a comprehension of the field-effect at the electrical contacts to 2D materials, which is fundamental to the design, simulation, and fabrication of electronics based on 2D materials. ELECTRONIC SUPPLEMENTARY MATERIAL: Supplementary material (results of the simulation and SEM) is available in the online version of this article at 10.1007/s12274-021-3670-y.

Conversion of amplitude modulation to phase modulation in the human cochlea.

When an amplitude modulated signal with a constant-frequency carrier is fed into a generic nonlinear amplifier, the phase of the carrier of the output signal is also modulated. This phenomenon is referred to as amplitude-modulation-to-phase-modulation (AM-to-PM) conversion and regarded as an unwanted signal distortion in the field of electro-communication engineering. Herein, we offer evidence that AM-to-PM conversion also occurs in the human cochlea and that listeners can use the PM information effectively to process the AM of sounds. We recorded otoacoustic emissions (OAEs) evoked by AM signals. The results showed that the OAE phase was modulated at the same rate as the stimulus modulation. The magnitude of the AM-induced PM of the OAE peaked generally around the stimulus level corresponding to the compression point of individual cochlear input-output functions, as estimated using a psychoacoustic method. A computational cochlear model incorporating a nonlinear active process replicates the abovementioned key features of the AM-induced PM observed in OAEs. These results indicate that AM-induced PM occurring at the cochlear partition can be estimated by measuring OAEs. Psychophysical experiments further revealed that, for individuals with higher sensitivity to PM, the PM magnitude is correlated with AM-detection performance. This result implies that the AM-induced PM information cannot be a dominant cue for AM detection, but listeners with higher sensitivity may partly rely on the AM-induced PM cue.

Ca2+ channel dynamics explain the nonlinear neuroplasticity induction by cathodal transcranial direct current stimulation over the primary motor cortex.

Transcranial direct current stimulation (tDCS) induces polarity-dependent neuroplasticity: with conventional protocols, anodal tDCS results in excitability enhancement while cathodal stimulation reduces excitability. However, partially non-linear responses are observed with increased stimulation intensity and/or duration. Cathodal tDCS with 2 mA for 20 min reverses the excitability-diminishing plasticity induced by stimulation with 1 mA into excitation, while cathodal tDCS with 3 mA again results in excitability diminution. Since tDCS generates NMDA receptor-dependent neuroplasticity, such non-linearity could be explained by different levels of calcium concentration changes, which have been demonstrated in animal models to control for the directionality of plasticity. In this study, we tested the calcium dependency of non-linear cortical plasticity induced by cathodal tDCS in human subjects in a placebo controlled, double-blind and randomized design. The calcium channel blocker flunarizine was applied in low (2.5 mg), medium (5 mg) or high (10 mg) dosages before 20 min cathodal motor cortex tDCS with 3 mA in 12 young healthy subjects. After-effects of stimulation were monitored with TMS-induced motor evoked potentials (MEPs) until 2 h after stimulation. The results show that motor cortical excitability-diminishing after-effects of stimulation were unchanged, diminished, or converted to excitability enhancement with low, medium and high dosages of flunarizine. These results suggest a calcium-dependency of the directionality of tDCS-induced neuroplasticity, which may have relevant implications for future basic and clinical research.

Species coexistence through simultaneous fluctuation-dependent mechanisms.

Understanding the origins and maintenance of biodiversity remains one of biology's grand challenges. From theory and observational evidence, we know that variability in environmental conditions through time is likely critical to the coexistence of competing species. Nevertheless, experimental tests of fluctuation-driven coexistence are rare and have typically focused on just one of two potential mechanisms, the temporal storage effect, to the neglect of the theoretically equally plausible mechanism known as relative nonlinearity of competition. We combined experiments and simulations in a system of nectar yeasts to quantify the relative contribution of the two mechanisms to coexistence. Resource competition models parameterized from single-species assays predicted the outcomes of mixed-culture competition experiments with 83% accuracy. Model simulations revealed that both mechanisms have measurable effects on coexistence and that relative nonlinearity can be equal or greater in magnitude to the temporal storage effect. In addition, we show that their effect on coexistence can be both antagonistic and complementary. These results falsify the common assumption that relative nonlinearity is of negligible importance, and in doing so reveal the importance of testing coexistence mechanisms in combination.

Scaling Effect on Silicon Nitride Memristor with Highly Doped Si Substrate.

A feasible approach is reported to reduce the switching current and increase the nonlinearity in a complementary metal-oxide-semiconductor (CMOS)-compatible Ti/SiNx /p+ -Si memristor by simply reducing the cell size down to sub-100 nm. Even though the switching voltages gradually increase with decreasing device size, the reset current is reduced because of the reduced current overshoot effect. The scaled devices (sub-100 nm) exhibit gradual reset switching driven by the electric field, whereas that of the large devices (≥1 µm) is driven by Joule heating. For the scaled cell (60 nm), the current levels are tunable by adjusting the reset stop voltage for multilevel cells. It is revealed that the nonlinearity in the low-resistance state is attributed to Fowler-Nordheim tunneling dominating in the high-voltage regime (≥1 V) for the scaled cells. The experimental findings demonstrate that the scaled metal-nitride-silicon memristor device paves the way to realize CMOS-compatible high-density crosspoint array applications.

Nanomaterials application for heavy metals recovery from polluted water: The combination of nano zero-valent iron and carbon nanotubes. Competitive adsorption non-linear modeling.

Carbon Nanotubes (CNTs) and nano Zero-Valent Iron (nZVI) particles, as well as two nanocomposites based on these novel nanomaterials, were employed as nano-adsorbents for the removal of hexavalent chromium, selenium and cobalt, from aqueous solutions. Nanomaterials characterization included the determination of their point of zero charge and particle size distribution. CNTs were further analyzed using scanning electron microscopy, thermogravimetric analysis and Raman spectroscopy to determine their morphology and structural properties. Batch experiments were carried out to investigate the removal efficiency and the possible competitive interactions among metal ions. Adsorption was found to be the main removal mechanism, except for Cr(VI) treatment by nZVI, where reduction was the predominant mechanism. The removal efficiency was estimated in decreasing order as CNTs-nZVI > nZVI > CNTs > CNTs-nZVI* independently upon the tested heavy metal. In the case of competitive adsorption, Cr(VI) exhibited the highest affinity for every adsorbent. The preferable Cr(VI) removal was also observed using binary systems of the tested metals by means of the CNTs-nZVI nanocomposite. Single species adsorption was better described by the non-linear Sips model, whilst competitive adsorption followed the modified Langmuir model. The CNTs-nZVI nanocomposite was tested for its reusability, and showed high adsorption efficiency (the qmax values decreased less than 50% with respect to the first use) even after three cycles of use.

The development of a fast method for recording Schroeder-phase masking functions.

Schroeder-phase masking complexes have been used in many psychophysical experiments to examine the phase curvature of cochlear filtering at characteristic frequencies, and other aspects of cochlear nonlinearity. In a normal nonlinear cochlea, changing the "scalar factor" of the Schroeder-phase masker from -1 through 0 to +1 results in a marked difference in the measured masked thresholds, whereas this difference is reduced in ears with damaged outer hair cells. Despite the valuable information it may give, one disadvantage of the Schroeder-phase masking procedure is the length of the test - using the conventional three-alternative forced-choice technique to measure a masking function takes around 45 min for one combination of probe frequency and intensity. As an alternative, we have developed a fast method of recording these functions which uses a Békésy tracking procedure. Testing at 500 Hz in normal hearing participants, we demonstrate that our fast method: i) shows good agreement with the conventional method; ii) shows high test-retest reliability; and iii) shortens the testing time to 8 min.

Forward-masking recovery and the assumptions of the temporal masking curve method of inferring cochlear compression.

The temporal masking curve (TMC) method is a behavioral technique for inferring human cochlear compression. The method relies on the assumptions that in the absence of compression, forward-masking recovery is independent of masker level and probe frequency. The present study aimed at testing the validity of these assumptions. Masking recovery was investigated for eight listeners with sensorineural hearing loss carefully selected to have absent or nearly absent distortion product otoacoustic emissions. It is assumed that for these listeners basilar membrane responses are linear, hence that masking recovery is independent of basilar membrane compression. TMCs for probe frequencies of 0.5, 1, 2, 4, and 6 kHz were available for these listeners from a previous study. The dataset included TMCs for masker frequencies equal to the probe frequencies plus reference TMCs measured using a high-frequency probe and a low, off-frequency masker. All of the TMCs were fitted using linear regression, and the resulting slope and intercept values were taken as indicative of masking recovery and masker level, respectively. Results for on-frequency TMCs suggest that forward-masking recovery is generally independent of probe frequency and of masker level and hence that it would be reasonable to use a reference TMC for a high-frequency probe to infer cochlear compression at lower frequencies. Results further show, however, that reference TMCs were sometimes shallower than corresponding on-frequency TMCs for identical probe frequencies, hence that compression could be overestimated in these cases. We discuss possible reasons for this result and the conditions when it might occur.

Frequency response areas in the inferior colliculus: nonlinearity and binaural interaction.

The tuning, binaural properties, and encoding characteristics of neurons in the central nucleus of the inferior colliculus (CNIC) were investigated to shed light on nonlinearities in the responses of these neurons. Results were analyzed for three types of neurons (I, O, and V) in the CNIC of decerebrate cats. Rate responses to binaural stimuli were characterized using a 1st- plus 2nd-order spectral integration model. Parameters of the model were derived using broadband stimuli with random spectral shapes (RSS). This method revealed four characteristics of CNIC neurons: (1) Tuning curves derived from broadband stimuli have fixed (i. e., level tolerant) bandwidths across a 50-60 dB range of sound levels; (2) 1st-order contralateral weights (particularly for type I and O neurons) were usually larger in magnitude than corresponding ipsilateral weights; (3) contralateral weights were more important than ipsilateral weights when using the model to predict responses to untrained noise stimuli; and (4) 2nd-order weight functions demonstrate frequency selectivity different from that of 1st-order weight functions. Furthermore, while the inclusion of 2nd-order terms in the model usually improved response predictions related to untrained RSS stimuli, they had limited impact on predictions related to other forms of filtered broadband noise [e. g., virtual-space stimuli (VS)]. The accuracy of the predictions varied considerably by response type. Predictions were most accurate for I neurons, and less accurate for O and V neurons, except at the lowest stimulus levels. These differences in prediction performance support the idea that type I, O, and V neurons encode different aspects of the stimulus: while type I neurons are most capable of producing linear representations of spectral shape, type O and V neurons may encode spectral features or temporal stimulus properties in a manner not easily explained with the low-order model. Supported by NIH grant DC00115.