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Results for “nonlinear analyses”

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PubMed1985

Osmotic pressure exerted by entangled polysaccharide chains.

The osmotic behavior of neutral and charged polysaccharide chains was studied utilizing membrane osmometry. Two neutral dextran fractions characterized by weight-average molecular weights of 5 X 10(5) and 2 X 10(6) daltons yielded identical osmotic pressure (pi)--mass concentration (C) relationships in the range of 0 to 8 g/dl. Furthermore, the relations were highly non-linear and departed markedly from the ideal Van't Hoff equation. For hyaluronate characterized by a weight-average molecular weight of 2 X 10(6) daltons, the pi vs C relations were dependent on the electrolyte (NaCl) concentration of the solution. In the polymer concentration range of 0.5 to 1 g/dl, increasing the ionic strength from 0.15 to 2 M NaCl caused a reduction in oncotic activity. At lower hyaluronate concentrations, oncotic activity was not altered by neutralizing the anionic sites with excess NaCl. The non-ideal behavior of the neutral and charged polysaccharide chains are compatible with recent statistical thermodynamic analyses of oncotic activity in concentrated polymer solutions. Finally, nonlinear pi vs C relationships of the matrix biopolymers provide a sensitive mechanism for volume buffering in the interstitium.

Cell Membrane Permeability↗

PubMed1995

Statistical considerations regarding the use of ratios to adjust data.

OBJECTIVE: The use of ratios to adjust data (i.e. 'index' variables) is common in obesity and related research. The rationale for the use of ratios often seems to be the desire to control or eliminate the influence of the variable in the denominator. The purpose of this paper is to gain a greater appreciation of the statistical assumptions underlying ratios and their impact on data interpretation. RESULTS: We demonstrate the limitations of the indiscriminant use of ratios to adjust data. Specifically, we show that: (1) given linearity, a zero intercept between the numerator and denominator are necessary and sufficient conditions for a ratio to remove the confounding effects of the denominator; (2) seemingly minor departures from a zero intercept can have major consequences on the ratio's ability to control for the denominator; (3) the ratio of two normally distributed variables cannot be normally distributed, and this may violate the assumptions of subsequent parametric statistical analyses; (4) the use of ratios affects the error distribution of the data which may also violate the assumptions of subsequent parametric statistical analyses; (5) the use of ratios cannot easily take nonlinear effects between the numerator and denominator into account; (6) the use of ratios can introduce spurious correlations among the ratios and other variables; (7) the use of ratios can create interpretive difficulties. We also clarify that the mean of ratios is not necessarily equivalent to the ratio of the means of the numerator and denominator. Finally, we present and discuss formulae for the reliability of ratios and residuals. CONCLUSION: Because of the above issues, we question the indiscriminant use of ratios and advocate that investigators consider regression-based approaches as alternatives.

Body Constitution↗

PubMed1999

Nonlinear analysis of blood flux in human vessels.

Laser Doppler fluxmetry (LDF) is frequently used in research on microcirculation of blood. Usually LDF time series are analysed by conventional linear methods, mainly Fourier analysis. These methods may not be optimal for the investigation of nonlinear effects of vasomotion, heartbeat or vessels. Nonlinear methods are based on a reconstruction of the system trajectory in an embedding space describing not only the measured time series but the behaviour of the whole system. The fill factor is a tool for displaying the main properties of this attractor in two dimensions and for determining diverse parameters for further analysis. A quantitative characterization of the system is possible by the distribution of correlation dimensions in the embedding space. The singular value decomposition (SVD) can be used to display and characterize individual degrees of freedom. These methods were applied to LDF time series from nine healthy controls and nine patients with Raynaud's phenomenon due to connective tissue disease. The fill factor and the SVD indicate qualitatively that in the controls vasomotion and heartbeat are the main influences on blood flow and act fairly independently of each other. In the patients there was a mixture of strong but irregular degrees of freedom. The mean and the maximal local correlation dimensions were significantly higher in the patient group. Nonlinear analysis of LDF time series provides additional information which cannot be detected using conventional approaches.

Adult↗

PubMed1996

Characterization of presystemic elimination of trichloroethylene and its nonlinear kinetics in rats.

1,1,2-Trichloroethylene (TCE) is a volatile organic chemical which contaminates drinking water and food supplies and is primarily of concern because of the risk of cancer it may pose. The objectives of the present study were to evaluate the efficiency and dose dependency of presystemic elimination of TCE in rats. Cannulas were surgically implanted into male Sprague-Dawley rats (330-380 g) 24 hr before TCE dosing. TCE (0.17, 0.33, 0.71, 2, 8, 16, and 64 mg/kg) in a 5% aqueous Alkamuls emulsion was administered over 30 sec into the carotid artery, jugular vein (JV), hepatic portal vein, or the stomach. Serial arterial blood samples of 1-500 microliters were collected for up to 12 hr from the unanesthetized animals and analyzed for TCE content by headspace gas chromatography. Pharmacokinetic analyses indicated that TCE was eliminated through dose-dependent nonlinear processes. A three-compartment model with Michaelis-Menten and first-order elimination was derived to fit simultaneously the TCE blood data following JV administration. Total presystemic elimination of TCE was inversely related to dose, ranging from approximately 60 to < 1%. A dose-dependent decrease in hepatic extraction was primarily responsible for the reduction in total first-pass elimination at high doses, whereas pulmonary extraction (i.e., 5-8%) was relatively constant over the dosage range. When metabolic saturation was minimal or absent, hepatic presystemic elimination of TCE accounted for approximately 45-55% of the administered dose. These findings indicate that a substantial proportion of trace amounts of VOCs ingested in environmental media may not enter the systemic circulation nor reach extrahepatic target organs.

Administration, Oral↗

PubMed2001

The effect of mathematical modeling on critical velocity.

The purpose of this investigation was to examine the effects of mathematical modeling on critical velocity (CV) estimates and the oxygen consumption (VO2), heart rate (HR), and plasma lactate values that corresponded to the five CV estimates. Ten male subjects performed a maximal, incremental treadmill test to determine maximal VO2, and four randomly ordered treadmill runs for the estimation of CV. Two linear, two nonlinear, and one exponential mathematical models were used to estimate CV. Regression analyses were used to determine the VO2, HR, and plasma lactate values that corresponded to the five CV estimates from the relationships for VO2, HR, and plasma lactate versus running velocity from the maximal, incremental test. The nonlinear, three-component model (Nonlinear-3) resulted in a mean CV that was significantly (P < 0.05) less than the mean values derived from the other four models, and was the lowest CV estimate for each subject. The percent of maximal VO2, HR, and plasma lactate values that corresponded to the Nonlinear-3 model were 89%, 93%, and 63%, respectively. These findings indicate that CV estimates differ by as much as 20% depending upon the model used to determine the characteristics of the velocity/time relationship. Future studies are needed to determine which model provides the most valid estimate of the demarcation point between heavy and severe exercise.

Adult↗

PubMed1981

Dihydrofolate reductase hysteresis and its effect of inhibitor binding analyses.

Escherichia coli dihydrofolate reductase was shown to follow slow transient kinetics (hysteresis). Nonlinear reaction velocities were detected during the enzyme assay and required 10-15 min to reach a steady-state rate. The degree of hysteresis was influenced by the enzyme concentration and the order of substrate addition. Incubation of the enzyme with NADPH before addition of dihydrofolate resulted in slow initial velocities that increased up to 2-fold during the course of the assay. Increasing the enzyme concentration from 0.2 to 1 nM resulted in diminished hysteresis. NADPH-initiated reactions were linear at all enzyme concentrations tested. Certain drugs had profound effects on hysteresis. Pyrimethamine practically eliminated the hysteresis of dihydrofolate-started reactions, whereas trimethoprime augmented the non-linearities in the sense that hysteresis was detected in both enzyme- and NADPH-started reactions. The shape of these reaction tracings makes trimethoprim is not a slow-binding inhibitor when assayed under conditions that eliminate hysteresis. Contrary to this, sulfamethoxazole did not affect hysteresis or augment inhibition of the enzyme by trimethoprim. Sulfamethoxazole alone (at 6 mM) did not inhibit the hysteresis and allow reliable determinations of Ki values of both weak and tight binding inhibitors. For example, Ki values for pyrimethamine, trimethoprim, and methotrexate were found to be 214 nM, 1.3 nM, and 0.021 nM, respectively.

Binding Sites↗

PubMed2000

Statistical analysis of nonlinear structural equation models with continuous and polytomous data.

A general nonlinear structural equation model with mixed continuous and polytomous variables is analysed. A Bayesian approach is proposed to estimate simultaneously the thresholds, the structural parameters and the latent variables. To solve the computational difficulties involved in the posterior analysis, a hybrid Markov chain Monte Carlo method that combines the Gibbs sampler and the Metropolis-Hasting algorithm is implemented to produce the Bayesian solution. Statistical inferences, which involve estimation of parameters and their standard errors, residuals and outliers analyses, and goodness-of-fit statistics for testing the posited model, are discussed. The proposed procedure is illustrated by a simulation study and a real example.

Humans↗

PubMed2026

Comparison of classic statistical methods and machine learning approaches to classify readiness.

MOTIVATION: Predicting physical and cognitive readiness in warfighters is critical for mission success. These predictions can be improved by identifying key biomarkers using multiple omics modalities. The MASTR-E study conducted by McKetney and colleagues is one of the most comprehensive multi-omics studies of saliva samples collected from warfighters, which also applied classic linear statistical (CLS) techniques to discover key biomarkers of readiness. Aligning with McKetney et al.'s assumptions, we operationalize readiness as a binary proxy, where pre-mission samples are labeled as "ready" to reflect a rested, unstressed physiological baseline, while post-mission samples are labeled "not ready" to reflect cumulative physical and cognitive load from the mission. As such, readiness here is not a direct biological or physiological construct, but an inferred state likely dominated by stress-related physiological changes. This assumption and definition is discussed further in the Introduction and Limitations sections. Here, we apply machine learning (ML) analyses to better assess generalizability, consider hidden interactions, and identify nonlinear patterns in the data. We investigated whether ML approaches could predict readiness and identify relevant biomarkers. ML models were trained on proteomics-only or metabolomics-only datasets to classify participants as ready or not ready and important model features were considered as putative biomarkers. Training and testing datasets were curated for two objectives: (i) recognize biomolecular signatures indicative of readiness within the same donor and (ii) assess generalizability across warfighters by withholding donors for testing. RESULTS: Proteomics-based models achieved AUCs of 0.907 ± 0.034 and 0.860 ± 0.063 for Objectives 1 and 2, respectively. Metabolomics-based models achieved Objective 1 AUC of 0.994 ± 0.007 and Objective 2 AUC of 0.993 ± 0.010. Comparative analysis with existing literature validates the model's feature importances, but the identified putative biomarkers significantly differ from those discovered through CLS analyses, as only one ML-identified biomarker overlapping with those identified through CLS methods. We show that these ML models and identified features are more robust to noise and generalizable across participants than those identified using CLS methods. AVAILABILITY: The analysis pipelines are provided as Jupyter notebooks, including all code and documentation, and are available publicly on GitHub at {https://github.com/netrias/ReadinessClassification}.

Machine Learning↗

PubMed2005

Identifying ill-behaved nonlinear processes without metrics: use of symbolic dynamics.

Given ill-behaved psychological data that are unlikely to satisfy metric axioms, the use of encoding in symbolic dynamics, and hence leading into Markov analyses, is explored. Various measures of entropy are calculated. The tractability of entropic measures for categorizing the trajectories of nonlinear dynamics that may be present and chaotic is considered, with a focus on the case where there are two attractors and at least one heteroclinic orbit between them. Fast/slow dynamics are treated as a special case. The problem of identification is in other contexts the problem of diagnosis in time-varying pathologies. Some real data, selected for their psychological relevance in clinical, forensic and psychophysical processes, that are apparently edge-of chaos and nonstationary, are for comparison analysed both as metric and discrete and in symbolic encoding.

Humans↗

PubMed2000

Applications of likelihood asymptotics for nonlinear regression in herbicide bioassays.

Dose-response models are intensively used in herbicide bioassays. Despite recent advancements in the development of new herbicides, statistical analyses are commonly based on asymptotic approximations that are sometimes poor. This paper presents the use of recent results in higher order asymptotics for likelihood-based inference in nonlinear regression. The methods presented provide accurate approximation for the distribution of test statistics and for prediction limits. Analyses of the fit and measures of detection limits of the bioassays are considered, and the potential of the methods is illustrated by examples with real data.

Biological Assay↗

PubMed2004

[Nonlinear optical absorption characteristics of a novel organic material ZnTBP/CA/PhR].

The measurement of optical absorption spectrum in visible light range of a novel organic material Zn-tetrabenzoporphincrotonic acid/phenoxy resin (ZnTBP/CA/PhR) is reported in this paper. The nonlinear absorption property of the sample illuminated by lasers with different wavelengths was studied. And the absorption alteration and kinetic process of the major spectrum bands were observed. The saturation absorption (SA) and reverse saturation absorption (RSA) appeared as the input fluence increased, and re-reverse saturation absorption process of the material was demonstrated in the experiment. These properties occurred in a broad range of visible spectrum. The paper qualitatively analyses the physical mechanism during the whole course. Based on the nonlinear absorption characteristics, we showed some applications in photonics field of ZnTBP/CA/PhR.

Absorption↗

PubMed2002

Rationalization of shape and related stress distribution in posterior teeth: a finite element study using nonlinear contact analysis.

This study considered the loading configuration of intact teeth by using finite element analyses to rationalize the clinical and biologic advantage inherent to posterior tooth shape. The biomechanical behavior of opposing molars was investigated in consideration of different loadcases simulating working, nonworking, and vertical closing micromotions starting in a position close to maximum intercuspation. The resulting stress distribution was assessed in a numerical model, reproducing 2-D buccolingual cross sections of maxillary and mandibular molars. In each case (working/nonworking/closure), the stroke was applied to the mandibular tooth in a stepping procedure (nonlinear contact analysis) until a total external force of 200 N was attained on the contact nodes. The principal stress distribution and modified Von Mises stresses were extracted from the postprocessing files. Vertical loading of the teeth did not generate harmful concentrations of stress. More challenging situations were encountered during working and nonworking micromotions, both of which generated inverted stress patterns. Supporting cusps were generally well protected during both working and nonworking cases (mostly subjected to compressive stresses). Nonsupporting cusps tended to exhibit more tensile stresses. High stress levels were found in the central groove of the maxillary molar during nonworking micromotion and at the lingual surface of enamel of the mandibular tooth during single-contact working micromotion. The occlusal load configuration as well as geometry and hard tissue arrangement had a marked influence on the stress distribution within opposing molars. Additional computations demonstrated the essential role of enamel bridges and crests to protect the crown from harmful tensile stresses.

Biomechanical Phenomena↗

PubMed1986

Density-dependent migration and human population structure in historical Massachusetts.

Studies of population structure often focus on the effects of population size and migration rates on genetic variation. Few studies, however, have investigated the relationship between these two factors. The purpose of this paper is to determine the extent to which migration (and gene flow) is density-dependent (that is, affected by population size) for populations in historical Massachusetts. Data from 4,859 marriage records were analyzed from four populations in north-central Massachusetts during the time period 1741 to 1849. These data were placed into 29 samples defined in terms of population and time cohort. Within each cohort the overall exogamy rate was computed along with three estimates of gene flow based on marital migration: local migration (k), long-distance migration (m), and effective migration rate (me). Three samples show unusually low rates that reflect the history of settlement. Regression analyses were used with the remaining samples, and they show nonlinear density-dependent migration that is unrelated to temporal trends. Migration is highest in samples with small population sizes (less than 800) and large population sizes (greater than 1,600). Migration is lowest in medium-sized populations. Two processes are suggested to explain this curvilinear relationship of migration and population size. In small populations, the lack of suitable potential mates and/or availability of settled land leads to an increase in migration into the population. As population size increases, this migration decreases. After populations reach a certain size, migration increases again, most likely reflecting the economic pull of larger populations. These patterns could act to enhance, or counter, genetic drift, depending on the direction of density dependence.

Female↗

PubMed2003

Appointments at a thyroid outpatient clinic and the lunar cycle.

INTRODUCTION: Several variables of health-related human behaviour have been analysed with regard to a possible association with lunar phases. The aim of this study was to evaluate a possible relation between the lunar cycle and the number of requests for appointments at an outpatient clinic. This variable has not been studied hitherto. METHODS: We analysed a total number of 11,413 requests for appointments at our thyroid outpatient clinic during one year. Access to this clinic is not restricted, and all patients with known or suspected thyroid disease living in the area of Vienna may ask for an appointment. During the study period, 8,852 patients requested a follow-up appointment, and 2561 patients asked for a new appointment. We analysed a possible cyclic pattern in these requests using a nonlinear regression model based on both groups of patients. RESULTS: A cosinus curve with a period of 29.531 days (the mean length of a lunar cycle) was significantly associated with the number of requests for both follow-up appointments (p = 0.007) and new appointments (p = 0.001). Requests for follow-up appointments had their highest peaks three days after the full moon, whereas requests for new appointments were most frequent five days afterwards. CONCLUSION: Our findings suggest that lunar phases may affect patients' requests for appointments at a thyroid outpatient clinic. To the best of our knowledge, this is the first study reporting a possible association between health-related behaviour and lunar phases using requests for appointments as a relevant variable. There is a need for more research into the mechanism underpinning this behaviour.

Appointments and Schedules↗

PubMed2003

Differential modulation of subcortical target and cortex during deep brain stimulation.

The combination of electrical deep brain stimulation (DBS) with functional imaging offers a unique model for tracing brain circuitry and for testing the modulatory potential of electrical stimulation on a neuronal network in vivo. We therefore applied parametric positron emission tomography (PET) analyses that allow characterization of rCBF responses as linear and nonlinear functions of the experimentally modulated stimulus (variable stimulator setting). In patients with electrodes in the thalamic ventrointermediate nucleus (VIM) for the treatment of essential tremor (ET) here we show that variations in voltage and frequency of thalamic stimulation have differential effects in a thalamo-cortical circuitry. Increasing stimulation amplitude was associated with a linear raise in rCBF at the thalamic stimulation site, but with a nonlinear rCBF response in the primary sensorimotor cortex (M1/S1). The reverse pattern in rCBF changes was observed with increasing stimulation frequency. These results indicate close connectivity between the stimulated nucleus (VIM) and primary sensorimotor cortex. Likewise, stimulation parameter-specific modulation occurs at this simple interface between an electrical and a cerebral system and suggests that the scope of DBS extends beyond an ablation-like on-off effect: DBS could rather allow a gradual tuning of activity within a neuronal circuit.

Aged↗

PubMed2000

Comparison of computational analysis with clinical measurement of stresses on below-knee residual limb in a prosthetic socket.

Interface pressures and shear stresses between a below-knee residual limb and prosthetic socket predicted using finite element analyses were compared with experimental measurements. A three-dimensional nonlinear finite element model, based on actual residual geometry and incorporating PTB socket rectification and interfacial friction/slip conditions, was developed to predict the stress distribution. A system for measuring pressures and bi-axial shear stresses was used to measure the stresses in the PTB socket of a trans-tibial amputee. The FE-predicted results indicated that the peak pressure of 226 kPa occurred at the patellar tendon area and the peak shear stress of 50 kPa at the anterolateral tibia area. Quantitatively, FE-predicted pressures were 11%, on average, lower than those measured by triaxial transducers placed at all the measurement sites. Because friction/slip conditions between the residual limb and socket liner were taken into consideration by using interface elements in the FE model, the directions and magnitudes of shear stresses match well between the FE prediction and clinical measurements. The results suggest that the nonlinear mechanical properties of soft tissues and dynamic effects during gait should be addressed in future work.

Amputation Stumps↗

PubMed2001

Measurement of the affinity of melittin for zwitterionic and anionic membranes using immobilized lipid biosensors.

The binding of melittin to zwitterionic dimyristyphosphatidylcholine (DMPC) and anionic dimyristylphosphatidylglycerol (DMPG) was analysed using two different immobilized model membrane systems. The first system used surface plasmon resonance (SPR), which monitors the real-time binding of peptides to an immobilized hybrid bilayer. SPR experiments reflected a stronger binding of melittin for DMPG than for DMPC, while kinetic analysis suggested the existence of at least two distinct binding steps. The second lipid biosensor system involved an immobilized phospholipid monolayer covalently attached to a microporous silica surface. The binding of melittin to the immobilized monolayer was then monitored using dynamic elution chromatography with varied methanol concentrations to analyse the binding of melittin to DMPC and DMPG. The nonlinear binding behaviour observed for melittin with the phosphatidylcholine (PC) and phosphatidylglycerol (PG) monolayers compared with the linear retention plots and Gaussian peak shapes observed for the control molecule demonstrated that melittin undergoes significant conformational and orientational changes upon binding to the immobilized PC and PG ligands. The dependence of log k' on per cent methanol also demonstrated a bimodal interaction whereby hydrophobic forces predominated at higher temperatures and methanol concentrations, while other forces, presumably electrostatic in nature, also made a contribution to the affinity of the peptides for the lipid monolayer, particularly at lower temperatures. The complementary use of these two lipid biosensors thus allows the role of hydrophobic and electrostatic forces in peptide-membrane interactions to be studied.

Anions↗

PubMed2006

Variation within and among species in gene expression: raw material for evolution.

Heritable variation in regulatory or coding regions is the raw material for evolutionary processes. The advent of microarrays has recently promoted examination of the extent of variation in gene expression within and among taxa and examination of the evolutionary processes affecting variation. This review examines these issues. We find: (i) microarray-based measures of gene expression are precise given appropriate experimental design; (ii) there is large inter-individual variation, which is composed of a minor nongenetic component and a large heritable component; (iii) variation among populations and species appears to be affected primarily by neutral drift and stabilizing selection, and to a lesser degree by directional selection; and (iv) neutral evolutionary divergence in gene expression becomes nonlinear with greater divergence times due to functional constraint. Evolutionary analyses of gene expression reviewed here provide unique insights into partitioning of regulatory variation in nature. However, common limitations of these studies include the tendency to assume a linear relationship between expression divergence and species divergence, and failure to test explicit hypotheses that involve the ecological context of evolutionary divergence.

Animals↗