Nonlinear Dependence Research Articles

Decomposing causality into its synergistic, unique, and redundant components

Causality lies at the heart of scientific inquiry, serving as the fundamental basis for understanding interactions among variables in physical systems. Despite its central role, current methods for causal inference face significant challenges due to nonlinear dependencies, stochastic interactions, self-causation, collider effects, and influences from exogenous factors, among others. While existing methods can effectively address some of these challenges, no single approach has successfully integrated all these aspects. Here, we address these challenges with SURD: Synergistic-Unique-Redundant Decomposition of causality. SURD quantifies causality as the increments of redundant, unique, and synergistic information gained about future events from past observations. The formulation is non-intrusive and applicable to both computational and experimental investigations, even when samples are scarce. We benchmark SURD in scenarios that pose significant challenges for causal inference and demonstrate that it offers a more reliable quantification of causality compared to previous methods.

Integrating machine learning with causal inference for enhanced system dynamics modeling: A framework for predicting complex interactions

Approaches and methods like System Dynamics Modelling (SDM) have been significant for assessing the behavior of many systems. However, classical methodologies applied in traditional approaches to SDM fail to identify nonlinear feedback and power dependencies, revealing hidden temporal casual relationships. In this paper, I present a novel approach that combines ML and causal inference methods to improve the forecast capability and semantics of system dynamics models. Incorporating ML algorithms for predictions and Causal Inference techniques for explanation, this combined strategy presents a new era for understanding the system interaction and quantifying the hidden causes within various systems. We illustrate the advantages of the suggested framework over traditional SDM and purely ML approaches by employing it to analyze a genuine circumstance for both prognosis and discovering causal relationships. Our findings indicate that such integration is effective in enhancing the comprehension of system interactions and deriving a reliable method for estimating subsequent state conditions in complex contexts. The results are relevant for various disciplines, starting with economics and ending with environmental protection sciences, where interactions and changes vary. As a result, it will give a foundation for further studies of integrating future computerized methods in the dynamical system modeling of the next generation.

Electric Response of a Negative Dielectric Anisotropy Nematic Liquid Crystal Doped with Ionic Dopant

The electrical properties measurements have been performed in a homogeneous alignment parallelepiped cell containing 4-methoxy benzylidene- 4-butylaniline (MBBA) liquid crystal doped with 0.02%wt tetrabutylammonium bromide (TBAB). The measurement of the complex permittivity was conducted in the nematic phase, covering a frequency range of 42 Hz to 5 MHz. A new relaxation mode was observed in the low-frequency region, which was not present in pure MBBA. The obtained dielectric dispersion could be fitted using the double Cole–Cole formula to determine the relaxation frequencies. The steady-state current exhibited a nonlinear dependence on the applied voltage, and hysteresis was observed in the transient current-voltage characteristic curve.

Air Pollutant Concentration Forecasting with WTMP: Wavelet Transform-Based Multilayer Perceptron

Atmospheric pollutants’ real-time changes and the internal interactions among various data make it challenging to efficiently predict concentration variations. In order to extract more information from the time series of pollutants and improve the accuracy of prediction models, we propose a type of Multilayer Perceptron model based on wavelet decomposition, named Wavelet Transform-based Multilayer Perceptron (WTMP) model. This model decomposes pollutant data through overlapping discrete wavelet transforms to extract non-stationarity and nonlinear dependencies in the time series. It combines the decomposed data with static covariate information such as data collection time and inputs them into an improved Multilayer Perceptron (MLP) model, reconstructing and outputting the prediction results. Finally, the model is validated using atmospheric pollutant data collected at a specific location in Ruian City, Zhejiang Province, China. The results indicate that the model performs well with minimal prediction errors.

The Hall Effect in Single Crystals of Topological Semimetals WTe<sub>2</sub> and MoTe<sub>2</sub>

The Hall effect in single crystals of topological semimetals WTe2 and MoTe2 is studied in the temperature range from 2 to 100 K and in magnetic fields up to 9 T. It is established that the Hall resistivity of WTe2 shows a nonlinearly dependence on the magnetic field at temperatures below 100 K. At the same time, the Hall resistivity of MoTe2 depends linearly with the magnetic field at temperatures range from 2 to 25 K and a nonlinear contribution appears at 50 K. Along with the known mechanism of compensation/decompensation of electron and hole charge carriers, the nonlinear dependence of the Hall resistivity of WTe2 and MoTe2 single crystals on the magnetic field is associated with the scattering of charge carriers on the surface.

Stomatal closure as a driver of minimum leaf conductance declines at high temperature and vapor pressure deficit in Quercus.

Rising global temperatures and vapor pressure deficits (VPD) are increasing plant water demand and becoming major drivers of large-scale plant mortality. Controlling transient leaf water loss after stomatal closure (gmin) is recognized as a key trait determining how long plants survive during soil drought. Yet, substantial uncertainty remains regarding how gmin responds to elevated temperatures and VPD and the underlying mechanisms. We measured gmin in 24 Quercus species from temperate and Mediterranean climates to determine if gmin was sensitive to a coupled temperature and VPD increase. We also explored mechanistic links to phenology, climate, evolutionary history, and leaf anatomy. We found that gmin in all species exhibited a non-linear negative temperature and VPD dependence. At 25°C (VPD = 2.2 kPa), gmin varied from 1.19 to 8.09 mmol m-2 s-1 across species but converged to 0.57 ± 0.06 mmol m-2 s-1 at 45°C (VPD = 6.6 kPa). In a subset of species, the effect of temperature and VPD on gmin was reversible and linked to the degree of stomatal closure, which was greater at 45°C than at 25°C. Our results show that gmin is dependent on temperature and VPD, is highly conserved in Quercus species, and is linked to leaf anatomy and stomatal behavior.

Effects of multiple reflections on nonlinear absorption measurements.

Accurate measurement of nonlinear absorption coefficients by transmission-based techniques, such as Z-scan and its modifications, remains challenging due to high measurement errors. In this Letter, we claim that one of the reasons for that could lie in ignoring multiple reflections of light in plane-parallel samples in the presence of multi-photon excitation. Closed-form formulations for transmittance and reflectance coefficients, considering both linear and multiphoton absorption, are obtained in the geometrical optics approximation. The contributions of multiple reflections to the total transmittance are calculated for several II-VI materials reported in the literature. The results show a nonlinear dependence on incident intensity, ranging from 15.7% down to 7.9% for CdS, from 10.3% down to 5.8% for CdSe, and from 18.1% down to 9.1% for ZnSe. The dependence of the contribution of multiple reflections on the sample thickness is shown to exhibit a near exponential decay.

Geophysics-Inspired Nonlinear Stress-Strain Law for Biological Tissues and Its Applications in Compression Optical Coherence Elastography.

We propose a nonlinear stress-strain law to describe nonlinear elastic properties of biological tissues using an analogy with the derivation of nonlinear constitutive laws for cracked rocks. The derivation of such a constitutive equation has been stimulated by the recently developed experimental technique-quasistatic Compression Optical Coherence Elastography (C-OCE). C-OCE enables obtaining nonlinear stress-strain dependences relating the applied uniaxial compressive stress and the axial component of the resultant strain in the tissue. To adequately describe nonlinear stress-strain dependences obtained with C-OCE for various tissues, the central idea is that, by analogy with geophysics, nonlinear elastic response of tissues is mostly determined by the histologically confirmed presence of interstitial gaps/pores resembling cracks in rocks. For the latter, the nonlinear elastic response is mostly determined by elastic properties of narrow cracks that are highly compliant and can easily be closed by applied compressing stress. The smaller the aspect ratio of such a gap/crack, the smaller the stress required to close it. Upon reaching sufficiently high compressive stress, almost all such gaps become closed, so that with further increase in the compressive stress, the elastic response of the tissue becomes nearly linear and is determined by the Young's modulus of the host tissue. The form of such a nonlinear dependence is determined by the distribution of the cracks/gaps over closing pressures; for describing this process, an analogy with geophysics is also used. After presenting the derivation of the proposed nonlinear law, we demonstrate that it enables surprisingly good fitting of experimental stress-strain curves obtained with C-OCE for a broad range of various tissues. Unlike empirical fitting, each of the fitting parameters in the proposed law has a clear physical meaning. The linear and nonlinear elastic parameters extracted using this law have already demonstrated high diagnostic value, e.g., for differentiating various types of cancerous and noncancerous tissues.

Advanced Analytics for Retail Inventory and Demand Forecasting

Achieving operational efficiency and enhancing customer satisfaction levels in the retail sector is directly dependent on efficient inventory management and accurate demand forecasting. The following study employs advanced analytics techniques, such as time series forecasting and machine learning, to bolster these essential functions. By leveraging on historical sales data from 45 retail stores sourced by Kaggle, this paper has constructed predictive models with the aim to optimize inventory levels and forecast demand with precision. The Seasonal AutoRegressive Integrated Moving Average with Exogenous Regressors (SARIMAX) model employed in this study adequately captures linear dependencies and seasonal patterns, while Long Short-Term Memory (LSTM) networks are responsible for the management of intricate, non-linear dependencies. The findings from this study depict the significant seasonal trends, the impact of economic factors, the impact of economic variables and the effectiveness of hybrid models in improving forecast accuracy. The integration of such advanced methodologies clearly highlights their massive potential in improving aspects such as inventory management and operational efficiency in the retail domain.

What is the impact of demand patterns on integrated online-offline and buy-online-pickup in-store (BOPS) retail in a smart supply chain management?

Retailers aim to provide in-person and remote interactions to accelerate purchases through hybrid methods, which introduce additional delivery and emissions loads but create a seamless shopping experience. The challenges of unified inventory, customer information, pricing, demand forecasting complications, and order fulfillment are met successfully in the hybrid methods. Here, a smart supply chain management that integrates traditional physical presence with cloud-based and hybrid buy-online-pickup in-store channels is optimized to meet customer demand in different demand patterns. The demand patterns considered are linear, cubic, and normalized functions of the selling price, the advertising cost, and the product lifetime. The article incorporates sustainable supply chain and omnichannel strategies to optimize supply chain performance and profitability. The paper compares the results of the proposed models with traditional supply chain models and provides some managerial insights and suggestions for online retailers. Numerical simulation reveals that nonlinear price dependence in demand provides an opportunity for higher promotional investment with a substantial rise in optimal selling price and overall profit. The shift-to-imperfect probability is seen to be the volatile component in the solution surface. The markup of the offline channel has a greater impact than buy-online-pickup in-store markup.

Tuning diagonal scale matrices for HMC

Three approaches for adaptively tuning diagonal scale matrices for HMC are discussed and compared. The common practice of scaling according to estimated marginal standard deviations is taken as a benchmark. Scaling according to the mean log-target gradient (ISG), and a scaling method targeting that the frequency of when the underlying Hamiltonian dynamics crosses the respective medians should be uniform across dimensions, are taken as alternatives. Numerical studies suggest that the ISG method leads in many cases to more efficient sampling than the benchmark, in particular in cases with strong correlations or non-linear dependencies. The ISG method is also easy to implement, computationally cheap and would be relatively simple to include in automatically tuned codes as an alternative to the benchmark practice.

Noninvasive Monitoring of Glycemia Level in Diabetic Patients by Wearable Advanced Biosensors.

We report on the possibility of noninvasive diabetes monitoring through continuous analysis of sweat. The prediction of the blood glucose level in diabetic patients is possible on the basis of their sweat glucose content due to the positive correlation discovered. The ratio between the blood glucose and sweat glucose concentrations for a certain diabetic subject is stable within weeks, excluding requirements for frequent blood probing. The glucose variations in sweat display allometric (non-linear) dependence on those in blood, allowing more precise blood glucose estimation. Selective (avoiding false-positive responses) and sensitive (sweat glucose is on average 30-50 times lower) detection is possible with biosensors based on the glucose oxidase enzyme coupled with a Prussian Blue transducer. Reliable glucose detection in just secreted sweat would allow noninvasive monitoring of the glycemia level in diabetic patients.

Spatiotemporal Modeling of Mitochondrial Network Architecture

In many cell types, mitochondria undergo extensive fusion and fission to form dynamic, responsive network structures that contribute to a number of homeostatic, metabolic, and signaling functions. The relationship between the dynamic interactions of individual mitochondrial units and the cell-scale network architecture remains an open area of study. In this work, we use coarse-grained simulations and approximate analytic models to establish how the network morphology is governed by local mechanical and kinetic parameters. The transition between fragmented structures and extensive networks is controlled by local fusion-to-fission ratios, network density, and geometric constraints. Similar fusion rate constants are found to account for the very different structures formed by mammalian networks (poised at the percolation transition) and well-connected budding yeast networks. Over a broad parameter range, the simulated network structures can be described by effective mean-field association constants that exhibit a nonlinear dependence on the microscopic nonequilibrium fusion, fission, and transport rates. Intermediate fusion rate constants are shown to result in the highest rates of network remodeling, with mammalian mitochondrial networks situated in a regime of high turnover. This spatially resolved modeling and simulation framework helps elucidate the emergence of cellular scale network structures, and allows for the quantitative extraction of microscopic kinetic parameters from past and future experimental data. Published by the American Physical Society 2024

The (un)known issue with using rose bengal as a standard of singlet oxygen photoproduction.

Rose bengal (RB) is a widely used photosensitizer for determining quantum yields of singlet oxygen generation. While it is known to aggregate in polar environments at concentrations above 2 μM, the relationship between RB concentration and singlet oxygen photogeneration remains unclear. This study investigates the shift from monomeric to dimeric RB with increasing concentration and its impact on singlet oxygen generation in D2O-based solutions and DMPC liposomes. Absorbance maxima for RB were observed at 514 nm (dimer) and 549 nm (monomer), with ionic environments influencing aggregation rates. Singlet oxygen phosphorescence showed non-linear dependency above 2 μM, indicating the effects of aggregation. Results suggest that RB concentrations should be kept at 1 μM or lower in photochemical studies to avoid aggregation-related discrepancies in singlet oxygen yield determination. These findings highlight the importance of considering RB aggregation in photochemical research and medical applications.

Comparison of Lab vs. Backcalculated Moduli of Virgin Aggregate and Recycled Aggregate Base Layers

The resilient modulus (MR) and the backcalculated modulus from the FWD testing (EFWD) of the unbound layers are critical inputs in the analysis/design of pavements. Several studies have tried to develop a conversion factor between these two parameters, while the nonlinear stress dependency of unbound materials and the pavement strain response are mostly missing from the literature. This study aims to compare the laboratory-measured MR of recycled aggregate base (RAB) materials and a virgin aggregate base using field-based EFWD and tries to establish pavement’s responses to loading using vertical strains from both the MR and EFWD values of the respective materials as comparability parameters between the two. For this purpose, a control virgin aggregate (VA, limestone) and three types of RAB materials were selected to construct four test sections. The test sections were modeled in layered elastic- and finite-element-based pavement response models to calculate the vertical strains at the mid-depth of the base and top of the subgrade layers. A comparison of the lab-calculated vertical strains using MR with actual vertical strains in the field from EFWD showed that there was no relationship between the two stiffness parameters in all tested RABs. The vertical strains, based on the lab MR, undermined the stiffness of the recycled aggregates in the field. In contrast, the values of EFWD based on the vertical strains remained close to the MR strains of limestone (VA) throughout the testing period, establishing an EFWD vs. MR relationship (MR = 0.87 EFWD). The results also show that fine RCA was a better-performing material over three years. This research not only explores how the hydration process in RABs limits the development of MR-EFWD correlations but also underscores the need to consider real-world conditions when assessing their performance.

Identification of the Payne effect in a viscoelastic material coupling Bayesian identification and digital twin

The Payne or Fletcher-Gent effect is a particular behavior occurring in viscoelastic materials containing fillers. It induces a nonlinear dependency of the viscoelastic storage modulus on the amplitude of the applied strain. This amplitude dependency must be taken into account in engineering applications as it does change the elastodynamic behavior of the overall structure integrating the material. A methodology is developed in the proposed work to identify this nonlinear effect. The approach first starts with the identification by Bayesian inference of the frequency and damping properties of a viscoelastic sample. The input data are obtained from a modified Oberst test, conducted for different displacement load amplitudes. A digital twin of the experimental set-up is then used to evaluate the stiffness behavior, and in particular the Young's modulus of the material, at the measured frequencies, and to deduce the strain level within the sample. This work shows that the Payne effect, which leads to the decrease with the amplitude of the Young's modulus, can thus be estimated in terms of mean and standard deviation by combining experiments and numerical simulations.

Effect of CaCO3, SrCO3 and BaCO3 additions on the microstructure and electrical characteristics of SnO2-based varistor ceramics

The ceramic varistors SnO2–Co3O4–Nb2O5–Cr2O3 with the addition of CaCO3, SrCO3 or BaCO3 were sintered at temperatures 1250 and 1350°C, then their structures and electrical properties were studied. In all samples, the SnO2 cassiterite phase with a rutile-type structure and the Co2SnO4 phase with a spinel-type structure were observed. All materials exhibited a highly nonlinear dependence of the current density on the electric field with the nonlinearity coefficient 24–50. When alkaline earth metal carbonates were added, the grain size of all samples decreased and the electric field E1 increased. The addition of CaCO3 lead to the decrease of the low-field electrical conductivity of varistors. The lowest low-field conductivities 4·10-13 and 6·10-13 Ω-1 cm-1 were found in the samples with CaCO3 addition baked at 1250 and 1350°C, respectively. The observed effect is due to the increase of the potential barrier height at the SnO2 grain boundaries by 7 and 13%, respectively, and the decrease of the grain size by 26 and 28% compared to SnO2-based varistor ceramics without CaCO3 addition.

Structure and dynamics of the near-surface water layer under conditions of natural convection

A series of laboratory and numerical experiments have been performed to study the process of the surface water cooling. The process of the submergence of an ensemble of jets (a thermal-like structure) or a negative buoyancy flux was recorded using digital cameras (∼2 and 10 Hz). Quantitative estimates of the structure and dynamical features of the initial phase of the submergence of a density front of the ensemble of jets were obtained. These estimates were compared with the previous results of the study of individual thermals. It was found that the deepening velocity is characterized by the nonlinear dependence from the submergence depth in time of both the thermals and the density front of the ensemble. The numerical calculations also showed nonlinearity in this dependence. The process of submergence of the density front was divided into three stages, which were described for the first time. The deepening velocity of the density front of the ensemble of jets was ∼0.15 cm/s. The results are qualitatively consistent with the theoretical estimates of the evolution of the free convection. The observed laboratory flows have the laminar nature of convective movements (Reynolds numbers ranging from 3 to 60). A geometric model was proposed to describe linear quantity of both the thermal and jet. It was shown that the effects of turbulence on the seawater measurements were caused externally and not related to the process of the surface water cooling. Thus, it is assumed that either thermal or saline turbulence dominates over free convection conditions. This conclusion has an important role in the study of the heat exchange process in ocean models.

In-plane electrical conductivity of PEDOT:PSS/Halloysite composite thin films

PEDOT:PSS has found numerous applications in the field of advanced materials, especially in the development of organic electronics. Embedding nanoparticles into the polymer matrix has emerged as an effective strategy to modify the properties of PEDOT:PSS and develop advanced functional composites. Over the past decade, Halloysite nanotubes (HNT) have garnered significant interest and utility as nanofillers and/or templates due to their unique physical-chemical properties, small size, relatively low cost, and large availability. Interestingly, pairing PEDOT:PSS with non-conductive HNT has been demonstrated to enhance the charge transport properties of the composite film. Our discoveries show how the HNT can act as scaffolding for PEDOT:PSS by improving the local ordering of PEDOT chains and enabling the formation of conductive pathways. Consequently, the mechanism responsible for the observed changes in conductivity and the correlation between PEDOT:PSS and insulating nanofillers (HNT) could be different to that previously proposed. Hence, in this work it was observed that PEDOT:PSS/HNT composite films exhibited a non-linear conductivity dependence as a function of the HNT loading. From thermogravimetric analysis, infrared and UV-Vis-NIR spectroscopies, as well as impedance spectroscopy, a more complex interaction between the polymer chains and the nanotubes is revealed. Our study includes the modification of the interaction between the PEDOT chains and the nanofillers by using the secondary doping effect and functionalization of the nanotubes, which confirms our findings. These results represent a significant progress toward a deeper understanding of the emergence of a conductive polymer network on the nanofiller surface, leading to improvements in the electrical conductivity in the composite material.

Data-driven reduced order surrogate modeling for coronary in-stent restenosis

Background:The intricate process of coronary in-stent restenosis (ISR) involves the interplay between different mediators, including platelet-derived growth factor, transforming growth factor-β, extracellular matrix, smooth muscle cells, endothelial cells, and drug elution from the stent. Modeling such complex multiphysics phenomena demands extensive computational resources and time. Methods:This paper proposes a novel non-intrusive data-driven reduced order modeling approach for the underlying multiphysics time-dependent parametrized problem. In the offline phase, a 3D convolutional autoencoder, comprising an encoder and decoder, is trained to achieve dimensionality reduction. The encoder condenses the full-order solution into a lower-dimensional latent space, while the decoder facilitates the reconstruction of the full solution from the latent space. To deal with the 5D input datasets (3D geometry + time series + multiple output channels), two ingredients are explored. The first approach incorporates time as an additional parameter and applies 3D convolution on individual time steps, encoding a distinct latent variable for each parameter instance within each time step. The second approach reshapes the 3D geometry into a 2D plane along a less interactive axis and stacks all time steps in the third direction for each parameter instance. This rearrangement generates a larger and complete dataset for one parameter instance, resulting in a singular latent variable across the entire discrete time-series. In both approaches, the multiple outputs are considered automatically in the convolutions. Moreover, Gaussian process regression is applied to establish correlations between the latent variable and the input parameter. Results:The constitutive model reveals a significant acceleration in neointimal growth between 30−60 days post percutaneous coronary intervention (PCI). The surrogate models applying both approaches exhibit high accuracy in pointwise error, with the first approach showcasing smaller errors across the entire evaluation period for all outputs. The parameter study on drug dosage against ISR rates provides noteworthy insights of neointimal growth, where the nonlinear dependence of ISR rates on the peak drug flux exhibits intriguing periodic patterns. Applying the trained model, the rate of ISR is effectively evaluated, and the optimal parameter range for drug dosage is identified. Conclusion:The demonstrated non-intrusive reduced order surrogate model proves to be a powerful tool for predicting ISR outcomes. Moreover, the proposed method lays the foundation for real-time simulations and optimization of PCI parameters.