Nonlinear Effects Research Articles

Modelling nonlinear moderation effects with local structural equation modelling (LSEM): A non-technical introduction.

Understanding the differential strength of effects in the presence of a third variable, known as a moderation effect, is a common research goal in many psychological and behavioural science fields. If structural equation modelling is applied to test effects of interest, the investigation of differential strength of effects will typically ask how parameters of a latent variable model are influenced by categorical or continuous moderators, such as age, socio-economic status, personality traits, etc. Traditional approaches to continuous moderators in SEMs predominantly address linear moderation effects, risking the oversight of nonlinear effects. Moreover, some approaches have methodological limitations, for example, the need to categorise moderators or to pre-specify parametric forms of moderation. This tutorial introduces local structural equation modelling (LSEM) in a non-technical way. LSEM is a nonparametric approach that allows the analysis of nonlinear moderation effects without the above-mentioned limitations. Using an empirical dataset, we demonstrate the implementation of LSEM through the R-sirt package, emphasising its versatility in both exploratory analysis of nonlinear moderation without prior knowledge and confirmatory testing of hypothesised moderation functions. The tutorial also addresses common modelling issues and extends the discussion to different application scenarios, demonstrating its flexibility.

Ultra-broadband all-optical nonlinear activation function enabled by MoTe2/optical waveguide integrated devices

All-optical nonlinear activation functions (NAFs) are crucial for enabling rapid optical neural networks (ONNs). As linear matrix computation advances in integrated ONNs, on-chip all-optical NAFs face challenges such as limited integration, high latency, substantial power consumption, and a high activation threshold. In this work, we develop an integrated nonlinear optical activator based on the butt-coupling integration of two-dimensional (2D) MoTe2 and optical waveguides (OWGs). The activator exhibits an ultra-broadband response from visible to near-infrared wavelength, a low activation threshold of 0.94 μW, a small device size (~50 µm2), an ultra-fast response rate (2.08 THz), and high-density integration. The excellent nonlinear effects and broadband response of 2D materials have been utilized to create all-optical NAFs. These activators were applied to simulate MNIST handwritten digit recognition, achieving an accuracy of 97.6%. The results underscore the potential application of this approach in ONNs. Moreover, the classification of more intricate CIFAR-10 images demonstrated a generalizable accuracy of 94.6%. The present nonlinear activator promises a general platform for three-dimensional (3D) ultra-broadband ONNs with dense integration and low activation thresholds by integrating a variety of strong nonlinear optical (NLO) materials (e.g., 2D materials) and OWGs in glass.

Ownership structure and capital structure dynamics in South African firms

Background: The ownership structure can impact capital structure decisions as owners are an influential group that govern the financial decisions of firms. Hence, the ownership structure and the categories of its owners have important implications for the capital structure of firms.Aim: This study investigates the linear and non-linear effects of different ownership types (managerial, foreign, institutional, government, and family) on the debt ratios of firms.Setting: This study includes 267 non-financial firms listed on the Johannesburg Stock Exchange (JSE) from 2004 to 2021, accounting for fluctuation in listings during this period.Method: The fixed effects model is used to estimate the impact of ownership structure on capital structure, while the Sasabuchi-Lind-Mehlum test evaluates non-linearity. Additionally, the Durbin-Wu-Hausman test is employed to detect whether endogeneity is present in this study.Results: The findings indicate that government ownership has a positive linear relation with the total debt and long-term debt ratio, while a non-linear inverse U-shaped relationship is found between institutional ownership and long-term debt, with an optimal level of 34.3%.Conclusion: The study concludes that the ownership structure is an important factor driving capital structure decisions, with government and institutional ownership directly impacting the debt ratios of firms.Contribution: This article expands the limited knowledge of the impact of ownership structure on capital structure and is the first to explore non-linear effects in the South African context. The findings offer valuable insights for boards and management that may aid them in strategically configuring ownership structures that optimise their capital structures.

Linezolid Pharmacokinetic-Anemia Modeling in Children with Rifampicin-Resistant Tuberculosis.

Linezolid, an important component of rifampicin- and multidrug-resistant tuberculosis (RR/MDR-TB) treatment, is associated with treatment-limiting toxicities, including anemia. Patient-level and linezolid pharmacokinetic risk factors for anemia have not been well described in children treated for RR/MDR-TB. We evaluated the pharmacokinetics of linezolid and longitudinal hemoglobin data to validate an existing population linezolid pharmacokinetic model. We assessed the impact of linezolid pharmacokinetics and the risk of developing anemia in a prospectively enrolled cohort of children. The validation of a previously published population pharmacokinetic linezolid model used nonlinear mixed effects modeling. A multivariable ordinal logistic regression model was built to predict the incidence of anemia. A total of 112 children, median age 7.2 (IQR: 2.2-16.3) years, were included from South Africa (n=87) and India (n=25). Of these, 24 children contributed new linezolid pharmacokinetic data. The population pharmacokinetic model which informs the currently recommended linezolid dosing in children (10-15 mg/kg) was validated with these additional new data. For every 1 g/dL lower baseline hemoglobin, the odds of developing grade 3 or 4 anemia increased by 2.64 (95% CI 1.98-3.62). For every 1 mg/L*h higher linezolid area under the concentration-time curve (AUC), the odds of developing a grade 3 or 4 anemia increased by 1.012 (95% CI 1.007-1.017). These data taken together, confirm currently recommended linezolid doses in children. The risk of anemia in children should be carefully considered and monitored throughout. Initiating linezolid in children with low baseline hemoglobin increases the probability of experiencing grade 3 or 4 anemia.

A glycan biomarker predicts cognitive decline in amyloid- and tau-negative patients.

Early detection of Alzheimer's disease is vital for timely treatment. Existing biomarkers for Alzheimer's disease reflect amyloid- and tau-related pathology, but it is unknown whether the disease can be detected before cerebral amyloidosis is observed. N-glycosylation has been suggested as an upstream regulator of both amyloid and tau pathology, and levels of the N-glycan structure bisecting N-acetylglucosamine (GlcNAc) correlate with tau in blood and CSF already at pre-clinical stages of the disease. Therefore, we aimed to evaluate whether bisecting GlcNAc could predict future cognitive decline in patients from a memory clinic cohort, stratified by amyloid/tau status. We included 251 patients (mean age: 65.6 ± 10.6 years, 60.6% female) in the GEDOC cohort, from the Memory Clinic at Karolinska University Hospital, Stockholm, Sweden. Patients were classified as amyloid/tau positive or negative based on CSF biomarkers. Cognitive decline, measured by longitudinal Mini-Mental State Examination scores, was followed for an average of 10.7 ± 4.1 years and modelled using non-linear mixed effects models. Additionally, bisecting GlcNAc levels were measured in hippocampus and cortex with lectin-based immunohistochemistry in 10 Alzheimer's disease and control brains. We found that CSF bisecting GlcNAc levels were elevated in tau-positive individuals compared with tau-negative individuals, but not in amyloid-positive individuals compared with amyloid-negative individuals. In the whole sample, high levels of CSF bisecting GlcNAc predicted earlier cognitive decline. Strikingly, amyloid/tau stratification showed that high CSF bisecting GlcNAc levels predicted earlier cognitive decline in amyloid-negative patients (β = 2.53 ± 0.85 years, P = 0.003) and tau-negative patients (β = 2.43 ± 1.01 years, P = 0.017), but not in amyloid- or tau-positive patients. Finally, histochemical analysis of bisecting GlcNAc showed increased levels in neurons in hippocampus and cortex of Alzheimer's disease compared with control brain (fold change = 1.44-1.49, P < 0.001). In conclusion, high CSF levels of bisecting GlcNAc reflected neuronal pathology and predicted cognitive decline in amyloid- and tau-negative individuals, suggesting that abnormal glycosylation precedes cerebral amyloidosis and tau hyper-phosphorylation in Alzheimer's disease. Bisecting GlcNAc is a promising novel early biomarker for Alzheimer's disease.

Improving Optical Transmission Performance in Multi-Channel Networks Utilizing Convolutional Neural Network-Enabled Digital Signal Processing to Mitigate Four-Wave Mixing

ABSTRACT The rapid growth of online services and the global transition to digital platforms, accelerated by the COVID-19 pandemic and the emergence of AI-based services, have led to a surge in demand for high-capacity optical communication networks (OCNs). However, this transition exacerbates the issue of fiber nonlinearity, notably four-wave mixing (FWM), which can significantly impact signal integrity in long-distance OCN transmissions with multiple channels. To address this challenge, this paper presents a novel approach leveraging a convolutional neural network (CNN)-based digital signal processing (DSP) model to mitigate the nonlinear effects of FWM on signal quality. The proposed CNN model, designed with three convolutional layers and trained on a comprehensive dataset of simulated OCN transmissions, demonstrates significant improvement in reducing nonlinear distortions caused by FWM. Our method is compared with traditional compensation techniques, such as digital back-propagation and Volterra series-based equalizers, showing a reduction in power penalties by 1 dB and an enhancement in the power budget by 2 dB. Simulation results indicate that the bit error rates (BERs) remain consistently below the critical threshold of 10−9 across various transmission distances, outperforming conventional methods. The simulation analysis, conducted on a 100 km multi-channel OCN testbed, confirms the CNN equalizer’s efficacy in reducing crosstalk and improving power efficiency, with a demonstrated 15% reduction in required launch power. Moreover, the analytical models used to evaluate the CNN-based DSP model show high accuracy in predicting performance, underscoring the model’s capability to achieve high-quality transmission with lower power requirements. These findings advocate for the integration of our CNN-based DSP model into OCNs, offering a fruitful solution for managing multi-channel, long-distance, and high-data-rate optical transmissions in real-world systems.

The Role of Digital Finance in Shaping Agricultural Economic Resilience: Evidence from Machine Learning

This study offers detailed recommendations on strengthening government support without harming digital finance benefits, especially in negatively affected areas, which is critical for enhancing the inclusiveness of the digital financial landscape and reducing social disparities. This paper uses year 2011–2022 panel data from China’s 31 provinces to empirically analyze digital finance’s effects, mechanisms, and heterogeneity on agricultural economy resilience with a two-way, fixed-effect model. It further explores each feature’s impacts using machine learning methodologies like the random forest, GBRT, SHAP value method, and ALE plot. The findings show that digital finance boosted agri-economy resilience, varying by food-producing status and marketization. Among all the features analyzed, government input, urbanization level, and planting structure emerged as the most critical factors influencing agri-economy resilience. Notably, government input negatively moderated this relationship. The ALE plot revealed non-linear effects of digital finance and planting structure on agri-economy resilience.

Robust Ridge-MM Estimator in Restricted Additive Partially Regression Model

This paper, utilized the Restricted Partially Additive Regression Model to analyze air quality data in Baghdad governorate, with a focus on addressing multicollinearity issues among independent variables and outliers in the dependent variable. Through the implementation of classical estimators, ridge estimators, robust estimators, and the imposition of non-random constraints on the parametric parts of the model Through method of Robust Ridge-MM Estimator in Restricted Additive Partially Regression Model, the study aimed to assess the model's effectiveness in dealing with air pollution challenges during the summer season. Results obtained through the use of pre-built packages and algorithms in the R programming language indicated that integrating non-random constraints with robust estimators positively impacted the accuracy of estimating functions. Furthermore, certain variables, such as PM10 (airborne particles with an aerodynamic diameter of up to 10 micrometres), were found to have a significant impact on air quality This is through the parameter values. Non-linear effects were observed for some non-parametric variables. The study highlights the importance of understanding the effects of air pollutants on public health and emphasizes the urgent need for quick solutions to mitigate these negative effects. Paper type: Research paper.

Suppression of Nonlinear Chorus Wave Growth by Active Control of Gyroresonant Interactions With Electron Hole Deformation

AbstractNonlinear gyroresonant acceleration is an essential mechanism for the formation of relativistic electrons in Earth's radiation belts, yet we still have only limited knowledge of how electron motion interacts nonlinearly with plasma waves. Here we demonstrate the compelling suppression of whistler‐mode chorus emissions as a resonant wave with energetic electrons by tuning an external transmitter signal in space plasmas. Through forcible modification of electron motions via phase trapping by the external waves, the nonlinear gyroresonant current is suppressed along with the electron hole deformation. Moreover, this can decrease the population of relativistic electrons due to the lack of coherent resonant waves seen by the phase‐organized electrons. Understanding such nonlinear wave suppression effects is crucial for a potential active control of Earth's plasma environment.

Deflection of light by a compact object with electric charge and magnetic dipole in Einstein–Born–Infeld gravity

We consider the bending of light around a compact astrophysical object with both the electric field and the magnetic field in Einstein–Born–Infeld theory. From the null geodesic of a light ray passing a massive object with electric charge and magnetic dipole, the effective metric was obtained from the light cone condition reflecting the nonlinear electromagnetic effects. We found the asymptotic form of the effective metric up to the first order in gravitational constant G and Born–Infeld parameter 1/β2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1/\\beta ^2$$\\end{document} on the equatorial plane. Then we compute the bending angle of light from the geodesic equation. The result includes particular cases where only one type of field is present taking the appropriate limits.

Nonlinear dynamics and effects of fast-ion driven instabilities in HL-2A NBI heating high-βN H-mode plasmas

High-performance plasmas had been obtained with hybrid scenarios on HL-2A in past several years, and the quality factor G=H89βN/q952 is around 0.3-0.4. In these high-βN H-mode plasmas with βN>2.5 and H98>1.2 Chen et al. (2022) [24], there are multiple energetic-ion driven instabilities, such as toroidal Alfvén eigenmode (TAE) and beta-induced Alfvén eigenmode (BAE), and there are complex magnetohydrodynamic (MHD) dynamics, e.g. nonlinear mode-mode and mode-particle interactions. The TAE amplitude increases explosively, and the frequency is fast chirping in the range of f=90−150 kHz. The TAE toroidal mode-number is n=3−4, and they localize in outer plasma region. The BAE amplitude also increases explosively, and the BAE frequency is fast chirping in the range of f=50−90 kHz. The toroidal mode-number of dominant BAEs is n=2, and these modes localize at q=2 rational surface where there is a large radius internal transport barrier (ITB). Generally, the energetic-ion fraction is low in outer plasma region. It indicates that thermal ions at large radius ITB location possibly provide additional drive and destabilize the BAE in company with energetic-ions. These TAEs/BAEs occur regularly in high-βN region and before large type-I ELM burst. To further illuminate the characteristics of these Alfvénic modes, the 2D and radial mode structures had been calculated by using a well-benchmarked general Alfvénic mode eigenvalue code (MAS). The experimental results suggest that these Alfvénic modes may have important effects on the pedestal transport and ELM-onset.

Optimization of Ultrasound-Assisted Enzymatic Extraction Conditions on Yield, DPPH Antioxidant Activity, and Gel Strength of Agar from Gracilaria fisheri

ABSTRACT This study investigated the effect of ultrasound-assisted enzymatic extraction (UAEE) conditions: solid-to-water ratio (1:50–1:100), ultrasonic power (296–506 W), and temperature (40–60°C) on key criteria (responses) of Gracilaria fisheri agar. Response surface methodology resulted in accurate quadratic models for predicting responses. Non-linear (quadratic and interaction) effects of UAEE conditions significantly (p < 0.05) influenced the responses. Optimal conditions (solid-to-water ratio of 1:98, ultrasonic power of 506 W, and temperature of 60°C) produced 32.02% agar yield, 58.05% DPPH antioxidant activity, and 83.48 g/cm2 gel strength, aligning with predictions. This research establishes an efficient agar extraction method with controllable qualities from red seaweed.

Dynamic tunability of NIR absorption in a plasmonic grating through nonlinear kerr-effect of graphene-oxide and photothermal phase transition of GSST

In this paper, we present an in-depth examination of the absorption dynamics of a silver plasmonic grating incorporating Kerr-type nonlinear graphene-oxide (GO) nanoslits and a Ge2Sb2Se4Te1 (GSST) phase-change material, both in linear and nonlinear regimes. Linear absorption approaches unity at the resonant wavelength when GSST is amorphous. Upon exposure to a nanosecond Gaussian pulse laser irradiation with appropriate fluences, the amorphous GSST partially crystallizes through a thermoplasmonic-induced process, resulting in a significant reduction of the linear on-resonance absorption in the form of a step-like curve. Additionally, the weak off-resonance linear absorption of the system can be enhanced owing to the non-uniform phase-transition within the GSST. Transitioning to a nonlinear regime, considering the third-order nonlinearity of GO nanoslits, reveals distinct absorption behaviors. Temporal analysis reveals that at the on-resonance wavelength, the unit absorption decreases with increasing laser intensity, reaching a minimum at the pulse peak due to the Kerr nonlinearity in the GO. Intriguingly, the absorption exhibits a U-shaped curve at lower fluences, while at higher fluences, it stabilizes at a lower value post-pulse peak where the amorphous GSST undergoes a thermally driven partially crystallization phase transformation. In the off-resonance mode, the weak absorption enhances dramatically by increasing the fluence, tracing an imperfect parabolic trajectory that reaches nearly unit at the trailing edge of the pulse, attributed to the Kerr nonlinearity within the GO nanoslits. By further increasing the laser fluence, the photothermal response of the GSST emerges as the dominant factor, diminishing the unity absorption observed at the trailing edge of the pulse. These findings underscore the dynamic responsiveness of the proposed grating to pulsed laser illumination, driven by the nonlinear Kerr effect and GSST reconfigurability, offering promising opportunities for developing active optical switching devices.

Effect of Oral Frailty on Postoperative Infection in Patients Undergoing Abdominal Visceral Surgery.

To assess effects of the oral frailty index-8 (OFI-8) on the incidence of postoperative infection. This retrospective study included patients aged ≥ 65 years who underwent elective abdominal visceral surgery under general anaesthesia. Oral frailty was assessed using OFI-8 (total score, 0-11), with higher scores indicating poorer oral health. The primary outcome measure was incidence of postoperative infection. The association between incidence of postoperative infection and OFI-8 score was evaluated using multiple logistic regression analysis adjusted for clinically relevant preoperative and intraoperative covariates. Data of 791 patients (mean age, 74 years; mean OFI-8 score, 3.4) were analysed. The OFI-8 score had a linear association (P for nonlinear effect on postoperative infection = 0.43) with a composite postoperative infection at a rate of 14.2% (95% confidence interval: 11.8-16.7). The adjusted odds ratio of the OFI-8 score for the primary outcome was 1.10 (95% confidence interval: 1.00-1.21), indicating that patients with higher OFI-8 scores tended to have postoperative infections. This study's findings suggest that patients with higher OFI-8 scores were more likely to develop postoperative infection after undergoing elective abdominal visceral surgery.

Quantification of nonlinear effect in seismic signal using Holo-Hilbert spectral analysis

Affected by excitation conditions, absorption, and attenuation of stratum and receiving instruments, the seismic signal is non-stationary and nonlinear. Time-frequency spectral analysis methods are effective and widely used in describing the time-varying features of seismic signals. However, these methods are all based on additive expansions, and cannot represent the nonlinearity of signal, which is achieved through a multiplicative process. Therefore, the information provided by the time-frequency spectrum is incomplete. To show the nonlinearity of seismic signal, that is, the modulation effect of low-frequency components on high-frequency components, the Holo-Hilbert spectral analysis method is introduced in this paper. Holo-Hilbert spectral analysis (HHSA) contains nested empirical mode decomposition and Hilbert transform to achieve a full informational spectrum represented by two frequency dimensions. In the Holo-Hilbert spectrum, one dimension represents frequency-modulated (FM) frequency, which characterizes the non-stationarity of the signal, and the other dimension represents the amplitude-modulated (AM) frequency, which indicates the nonlinear effect in the signal. Synthetic and field data examples verify the feasibility of HHSA in characterizing the cross-frequency interaction of non-stationary seismic signals as a potential tool to detect reservoirs.

The importance of including both sexes in preclinical sleep studies and analyses

A significant effort in biomedical sciences has been made to examine relationships between sex and the mechanisms underlying various disease states and behaviors, including sleep. Here, we investigated biological sex differences in sleep using male and female C57BL/6J mice (n = 267). Physiological parameters were recorded for 48-h using non-invasive piezoelectric cages to determine total sleep, non-rapid eye movement (NREM) sleep, rapid eye movement (REM)-like sleep, and wakefulness (WAKE). We fit hierarchical generalized linear mixed models with nonlinear time effects and found substantial sex differences in sleep. Female mice slept less overall, with less NREM sleep compared to males. Females also exhibited more REM-like sleep and WAKE and had shorter NREM sleep bout lengths. We also conducted a simulation exercise where we simulated a hypothetical treatment that altered the sleep of female mice, but not male mice. In models that included an appropriate sex by treatment interaction, a female-specific treatment response was accurately estimated when sample sizes were equal but was not detected when sample sizes were unequal, and females were underrepresented. Failure to include both sexes in experimental designs or appropriately account for sex during analysis could lead to inaccurate translational recommendations in pre-clinical sleep studies.

Nonlinear effect of absorption on the ringdown of a spinning black hole

Nonlinear effect of absorption on the ringdown of a spinning black hole

Evaluating Models of the Ageing BOLD Response.

Neural activity cannot be directly observed using fMRI; rather it must be inferred from the hemodynamic responses that neural activity causes. Solving this inverse problem is made possible through the use of forward models, which generate predicted hemodynamic responses given hypothesised underlying neural activity. Commonly-used hemodynamic models were developed to explain data from healthy young participants; however, studies of ageing and dementia are increasingly shifting the focus toward elderly populations. We evaluated the validity of a range of hemodynamic models across the healthy adult lifespan: from basis sets for the linear convolution models commonly used to analyse fMRI studies, to more advanced models including nonlinear fitting of a parameterised hemodynamic response function (HRF) and nonlinear fitting of a biophysical generative model (hemodynamic modelling, HDM). Using an exceptionally large sample of participants, and a sensorimotor task optimized for detecting the shape of the BOLD response to brief stimulation, we first characterised the effects of age on descriptive features of the response (e.g., peak amplitude and latency). We then compared these to features from more complex nonlinear models, fit to four regions of interest engaged by the task, namely left auditory cortex, bilateral visual cortex, left (contralateral) motor cortex and right (ipsilateral) motor cortex. Finally, we validated the extent to which parameter estimates from these models have predictive validity, in terms of how well they predict age in cross-validated multiple regression. We conclude that age-related differences in the BOLD response can be captured effectively by models with three free parameters. Furthermore, we show that biophysical models like the HDM have predictive validity comparable to more common models, while additionally providing insights into underlying mechanisms, which go beyond descriptive features like peak amplitude or latency, and include estimation of nonlinear effects. Here, the HDM revealed that most of the effects of age on the BOLD response could be explained by an increased rate of vasoactive signal decay and decreased transit rate of blood, rather than changes in neural activity per se. However, in the absence of other types of neural/hemodynamic data, unique interpretation of HDM parameters is difficult from fMRI data alone, and some brain regions in some tasks (e.g., ipsilateral motor cortex) can show responses that are more difficult to capture using current models.

All-optical simultaneous OR and AND optical logic gates based on nonlinear photonic crystal ring resonator

Abstract An all-optical simultaneous OR and AND logic gates using the nonlinear Kerr effect and ring resonator based on a two-dimensional photonic crystal are proposed in this paper. The proposed structure has a resonant wavelength of 1551.3 nm and a power consumption (1 kW/μm2). The proposed structure is suitable for all-optical photonic integrations because of its simplicity and small size (23 μm x 30.4 μm). Moreover, the structure executes two logic operations without requiring an additional spare/control signal through a single structure, making fabrication easy. The total footprint of the photonic crystal ring resonator structure measures approximately 699 μm². A very high contrast ratio of 26.10 dB and 25.34 dB is obtained for the OR and AND logic gates, with response times equal to 2 ps and 0.67 ps, respectively. In addition, the calculated bit rates for OR and AND logic gates are approximately 0.5 and 1.5 Tbps, respectively. Using the Rsoft CAD commercial software, the FullWAVE and BandSOLVE module of the software is used for numerical and theoretical investigation of the structure.

Driven-dissipative phases and dynamics in non-Markovian nonlinear photonics

Interactions between photons (nonlinearities) enable a powerful form of control over the state of light. This control has enabled technologies such as light sources at new wavelengths, ultra-short optical pulses, frequency-comb metrology systems, even quantum light sources. Common to a wide variety of nonlinear optical technologies is an equilibrium between an energy source, such as an external laser, and dissipation, such as radiation loss or absorption. In the vast majority of these systems, the coupling between the system and the outside world (which leads to loss) is well described as “Markovian,” meaning that the outside world has no memory of its past state. In this work, we introduce a class of driven-dissipative systems in which a nonlinear cavity experiences non-Markovian coupling to the outside world. In the classical regime, we show that these non-Markovian cavities can have extremely low thresholds for nonlinear effects, as well as self-pulsing instabilities at THz rates, and rich phase diagrams with alternating regions of stability and instability. In the quantum regime, we show how these systems, when implemented on state-of-the-art platforms, can enable generation of strongly squeezed cavity states with intensity fluctuations that can be more than 15 dB below the classical limit, in contrast to the Markovian driven-dissipative cavity, in which the limit is 3 dB. In the regime of few-photon nonlinearity, such non-Markovian cavities can enable a deterministic protocol to generate Fock states of high order, which are long-desired, but still elusive at optical frequencies. We expect that exploiting non-Markovian couplings in nonlinear optics should in the future lead to even richer possibilities than those discussed here for both classical and quantum light manipulations.