Nonlinear Least-squares Regression Research Articles

Parameterized lattice strain models for REE partitioning between amphibole and silicate melt

The distribution of rare earth elements (REEs) between amphibole and silicate melt is important for understanding a wide variety of igneous and metamorphic processes in the lithosphere. In this study, we used published experimental REE and Y partitioning data between amphibole and silicate melt, the lattice strain model, and nonlinear least-squares regression method to parameterize key partitioning parameters in the lattice strain model ( D 0 , r 0 , and E ) as a function of pressure, temperature, and both amphibole and melt compositions. Two models, which give nearly identical results, are obtained in this study. In the first model, D 0 depends on temperature and amphibole composition: it positively correlates with Ti content and negative correlates with temperature and Mg, Na, and K contents in the amphibole. In the second model, D 0 depends solely on the melt composition: it positively correlates with Si content and negatively correlates with Ti and Ca contents in the melt. In both the mineral and melt composition models, r 0 negatively correlates with the ferromagnesian content in the M4 site of the amphibole, and E is a constant. The very similar coefficients in the equations for r 0 and best-fit values for E in the two models allow us to connect the two models through amphibole-melt phase equilibria. An application of our model to amphiboles in mantle xenoliths shows that observed major element compositional variations in amphibole alone can give rise to order of magnitude variations in amphibole-melt REE partition coefficients. Together with experimental data simulating fractional crystallization of arc magmas, out models suggest that: (1) REE partition coefficients between amphibole and melt can vary by an order of magnitude during arc magma crystallization due to variation in the temperature and composition of the amphibole and melt, and that (2) amphibole fractional crystallization plays a key role in depleting the middle REEs relative to heavy REEs and light REEs in arc magmas.

Preliminary Sizing Correlations for Fixed-Wing Unmanned Aerial Vehicle Characteristics

A comprehensive set of preliminary sizing correlations can be invaluable in the early design stages of any aircraft or to provide initial characteristics for multidisciplinary optimization. For unmanned aircraft, such a set of correlations is not available. The current paper provides correlations based on data for 856 fixed-wing platforms. Correlations for the main mission, mass, and geometric parameters are derived through a nonlinear least-squares regression analysis. Where needed, a distinction is made between aircraft employing different propulsion systems; and the aircraft are split into five categories: piston-, battery-, turbine-, fuel-cell-, and solar-powered aircraft. Significant trends are revealed, and a closed set of correlations is provided to generate an initial sizing, starting from mission and payload requirements.

Escitalopram plasma levels and antidepressant response

Major Depression Disorder (MDD) has a highly variable treatment response due to the large inter-individual variation in the pharmacokinetics and pharmacodynamics of drug treatments. In detail the correlation between plasma level and efficacy has been much debated. Among first-line drugs for MDD, one of the most used is escitalopram. In the present study we investigated the association between serum concentration of escitalopram (SCE) and antidepressant response (AR). 70 MDD patients treated with escitalopram monotherapy were recruited and followed for three months. Hamilton Depression Rating Scale - 21 (HAMD-21) was administrated at baseline, month 1, and month 3 to assess AR. SCE was measured at steady state. Linear regression analysis and nonlinear least-squares regression were used to estimate association between SCE and AR. We found an association between SCE and AR both at month 1 (p<0.001) and month 3 (p=0.0003), which persists also excluding 3 patients with SCE equal to 0. Interestingly, by excluding patients with SCE < 20ng/mL, i.e. with a SCE lower than the putative therapeutic threshold, these associations disappeared. The curvilinear function AR = a + (SCE-SCE2) explained a higher proportion of variance compared to the linear other models (p<0.001). Our results suggest that for escitalopram the association between SCE and AR likely follows a nearly-asymptotic function, with poor AR at sub-therapeutic SCE and stable AR response at therapeutic SCE. Thus, when a patient reaches the therapeutic SCE range, further increase of escitalopram dosage seems to be useless, although further studies are needed to confirm our findings.

Effect of nature of chemical crosslinker on swelling and solubility parameter of a new stimuli-responsive cationic poly(N-acryloyl-N′-propyl piperazine) hydrogel

New stimuli-responsive cationic hydrogels based on N-acryloyl-N′-propyl piperazine (AcrNPP) were prepared using two types of chemical crosslinkers, viz., N,N-methylene bisacrylamide (Mba) and 1,4-butanediol diacrylate (Bda), respectively. The solubility parameter of the hydrogels was evaluated by equilibrium swelling experiment in a series of twelve solvents with well-distributed range of solubility parameters. The hydrogels exhibited maximum equilibrium swelling ratio in 1-butanol. The experimental swelling data were analyzed by two methods, (1) non-linear curve fitting and (2) least-square regression to determine the solubility parameter of the hydrogels. The solubility parameter determined by the two methods was in the range 11.45–11.85 (cal cm−3)1/2. The solubility parameter of the hydrogel containing the hydrophilic crosslinker (Mba) was higher than the hydrogel with a hydrophobic crosslinker (Bda), in all cases. This showed that the nature of chemical crosslinker influences the swelling and thus the solubility parameter of the hydrogels. The partial solubility parameter of the hydrogels related to the cohesive energy was evaluated by plotting the equilibrium swelling data against dispersion forces, polar forces, and hydrogen bonding. It was observed that both polar forces and hydrogen bonding play an important role in the swelling of these cationic hydrogels. The solubility parameter and the related forces were also estimated theoretically using group contribution methods and compared with the experimental results.

Modelling the dynamics of total precipitation and aboveground net primary production of fescue-feather grass steppe at Askania Nova according to global climate change scenariosModelling the dynamics of total precipitation and aboveground net primary production of fescue-feather grass steppe at Askania Nova according to global climate change scenarios

This article discusses modelling of Aboveground Net Primary Production (ANPP) of steppe (arid grassland ecosystems) plant species in relation to changes in total precipitation over the previous year at the “Stara” study site, Biosphere Reserve “Askania-Nova”, Khersonregion (Ukraine). To investigate linkages between precipitation and Aboveground Net Primary Production, correlation analysis was chosen and a time series regression analysis was based on the data set for the period 1988–2012. The NPP dependence on quantity of precipitation was found to be more significant for the previous autumn-winter-spring period (AWSP) than for the previous 12 month period. A regression model of ANPP’s dependence on AWSP is proposed. This model was further validated by the authors’ samples of ANPP, collected at the “Stara” study site in 2013–2016. The regression model showed a non-linear (quadratic) dependence of net primary production of zonal and intrazonal plant coenoses and total precipitation for the autumn-winter-spring period for arid grasslands with a coefficient of determination equal to 0.54 and significance level less than 0.05. The non-linear equation for these relations, visualized by a parabola curve, was calculated using the Nonlinear Least-Squares Regression Method. The data set, based on calculated predicted values, using the calculated equation, had a similar dynamic to the historical data on ANPP, but the model could not predict critical values. For this reason, additional studies are required for critical precipitation events. Non-linear response, investigated according to regression analysis, reveals optimal zones of plant growth, depending on the total precipitation level before the vegetation peak. For research areas where the dominant species are the turf grasses Stipa ucrainica P. Smirn., S. capillata L., S. lessingiana Trin. & Rupr., Festuca valesiaca Gaudin, Koeleria cristata (L.) Pers.) the optimal precipitation rates were found to be 350–400 mm during AWSP with ANPP at 350 g/m 2 . On the basis of the regression model and current forecasts of changes in precipitation rates we made a forecast of net primary production of plant communities for four climate change scenarios (RCP2.6, RCP4.5, RCP6, and RCP8.5) described in the Fifth Assessment of Intergovernmental Panel on Climate Change (IPCC). For this purpose, bioclimate projections of 10 major climate models (The Community Climate System Model Version 4 (CCSM4), GISS-E2-R, HadGEM2-AO, HadGEM2-ES, IPSL-CM5A-LR, MIROC-ESM-CHEM, MIROC-ESM, MIROC5, MRI-CGCM3, NorESM1-M), used for preparation of the IPCC report, were analyzed and imported to the geographical information system package QGIS. QGIS modelling software was used for geoanalysis and calculation of GIS-layers for Askania-Nova and adjacent arid grasslands. The results of modelling with the 10 climate models were compared and analyzed for each of the four IPCC scenarios, depending on predicted CO 2 levels. The presented modelling results showed a trend to growth in AWSP precipitation and NPP for all scenarios up to 2040–2060. The scenarios RCP2.6, RCP4.5, RCP6 predicted the optimum precipitation zone for current plant diversity for the period of 2040–2060 and scenario RCP8.5 predicted an optimum zone peak after 2080. The study confirmed the importance of monitoring the productivity of herbaceous communities in dry steppe ecosystems ofUkraine.

Robust Nonlinear Regression in Enzyme Kinetic Parameters Estimation

Accurate estimation of essential enzyme kinetic parameters, such asKmandVmax, is very important in modern biology. To this date, linearization of kinetic equations is still widely established practice for determining these parameters in chemical and enzyme catalysis. Although simplicity of linear optimization is alluring, these methods have certain pitfalls due to which they more often then not result in misleading estimation of enzyme parameters. In order to obtain more accurate predictions of parameter values, the use of nonlinear least-squares fitting techniques is recommended. However, when there are outliers present in the data, these techniques become unreliable. This paper proposes the use of a robust nonlinear regression estimator based on modified Tukey’s biweight function that can provide more resilient results in the presence of outliers and/or influential observations. Real and synthetic kinetic data have been used to test our approach. Monte Carlo simulations are performed to illustrate the efficacy and the robustness of the biweight estimator in comparison with the standard linearization methods and the ordinary least-squares nonlinear regression. We then apply this method to experimental data for the tyrosinase enzyme (EC 1.14.18.1) extracted fromSolanum tuberosum,Agaricus bisporus, andPleurotus ostreatus. The results on both artificial and experimental data clearly show that the proposed robust estimator can be successfully employed to determine accurate values ofKmandVmax.

Thermogravimetric characteristics and pyrolysis kinetics of high-density-aquacultured Saccharina Japonica: Effects of water-washing

The thermogravimetric characteristics and pyrolysis kinetics of high-density-aquacultured Saccharina japonica were investigated using a thermogravimetric analyzer and micro-tubing reactor, respectively. The effect of water washing S. japonica samples on pyrolysis product distribution was studied at 360, 370 and 380°C with various residence times from 1.0 to 3.0min. The kinetic rate constants of pyrolysis for untreated and water-washed S. japonica samples were determined using nonlinear least-squares regression of experimental data assuming first-order kinetics. The predominant reaction pathway of water-washed S. japonica was liquid to gas product (k3) at each temperature, while that of untreated S. japonica was biomass to liquid product (k2) at 360 and 370°C, then liquid to gas product (k3) at 380°C. However, the k2/k1 ratio of water-washed S. japonica (1.2166–1.3247) was more than two times that of untreated S. japonica (0.5763–0.6346).

Modelling methane production kinetics of complex poultry slaughterhouse wastes using sigmoidal growth functions

The kinetic evaluation of the methane potential from poultry slaughterhouse waste streams was performed using modified sigmoidal bacterial growth curve equations (Richards, logistic, Gompertz) in order to investigate their suitability to describe the degradation patterns associated with complex substrates, primarily composed of fats. The methane potential and degradation patterns under mesophilic conditions were assessed using Biochemical Methane Potential (BMP) assays. A nonlinear least-square regression analysis was performed to fit the sigmoidal functions to the cumulative methane production curves with respect to time generated from the BMP assays. In the cases modelled the Gompertz and logistic, three parameter models, sufficiently described the methane generation of the simple substrates (dissolved air flotation sludge) with no sign of acute inhibition due to high fat contents. When dealing with more complex degradation patterns of the substrates with a higher fat content (soft offals) and increased bioavailability of the organics, the three parameter models became insufficient in describing the experimental data due to features of the original growth functions, in particularly their fixed points of inflection. In such cases the fourth parameter afforded in the Richards model became critical allowing variability in the point of inflection allowing a much better fit to the experimental curves.

Temperature reconstruction from the length fluctuations of small glaciers in the eastern Alps (northeastern Italy)

In this study, a linear model computing the air temperature fluctuations from the measured glacier snout fluctuations has been applied, for the first time, to three small glaciers in the western Tauern Alps (eastern Alps) in the period 1929–2011. The considered glaciers, with areas between 0.2 and $$1.3\,\hbox {km}^2$$ , are characterized by relevant time variations of their morphology, length and slope. The model requires the knowledge of two parameters: the glacier climate sensitivity $$C_s$$ and the glacier response time $$\tau$$ , both depending on the glacier morphological characteristics and on the precipitation. Applied to the glaciers assuming $$C_s$$ and $$\tau$$ as in the original formulation, it underestimates the temperature increase of $${\approx } 1.8\,^{\circ }\hbox {C}$$ derived over the whole period from the in situ data. Given the characteristics of these small glaciers, these parameters have been recalibrated by means of a non-linear least-square regression using an independent set of glaciers. Their mean value is of about 210 m/K and 3.8 years respectively. With the recalibrated values of the new glacier climate sensitivity $$C^*_s$$ and response time $$\tau ^*$$ , the temperature fluctuations derived by the model reproduce well those obtained from the observed temperatures computed over the hydrological year, with linear correlations between 0.8 and 0.9. The increase of the modeled mean temperature over the whole period fits in with that derived from observed temperature. Considering that the length fluctuations of these small glaciers affect significantly their slope and length, we tested the impact in the model of a time dependent formulation of $$C_s$$ and $$\tau$$ : the results indicate slight improvements both in the values of the correlation between the reconstructed and the observed temperature fluctuations and in the global temperature increase. Given the above value of climate sensitivity, the large retreat of the small alpine glaciers threatens their survival within a few decades, but the morphological changes in progress may counteract the glacier disappearance.

Inverse modelling for real-time estimation of radiological consequences in the early stage of an accidental radioactivity release

A stepwise sequential assimilation algorithm is proposed based on an optimisation approach for recursive parameter estimation and tracking of radioactive plume propagation in the early stage of a radiation accident. Predictions of the radiological situation in each time step of the plume propagation are driven by an existing short-term meteorological forecast and the assimilation procedure manipulates the model parameters to match the observations incoming concurrently from the terrain. Mathematically, the task is a typical ill-posed inverse problem of estimating the parameters of the release. The proposed method is designated as a stepwise re-estimation of the source term release dynamics and an improvement of several input model parameters. It results in a more precise determination of the adversely affected areas in the terrain. The nonlinear least-squares regression methodology is applied for estimation of the unknowns. The fast and adequately accurate segmented Gaussian plume model (SGPM) is used in the first stage of direct (forward) modelling. The subsequent inverse procedure infers (re-estimates) the values of important model parameters from the actual observations. Accuracy and sensitivity of the proposed method for real-time forecasting of the accident propagation is studied. First, a twin experiment generating noiseless simulated “artificial” observations is studied to verify the minimisation algorithm. Second, the impact of the measurement noise on the re-estimated source release rate is examined. In addition, the presented method can be used as a proposal for more advanced statistical techniques using, e.g., importance sampling.

Parallelizing Nonlinear Least-Squares Regression with Application to Analyses of Microalgae

ABSTRACTNonlinear least-squares regression is a valuable tool for gaining chemical insights into complex systems. Yet, the success of nonlinear regression as measured by residual sum of squares (RSS), correlation, and reproducibility of fit parameters strongly depends on the availability of a good initial solution. Without such, iterative algorithms quickly become trapped in an unfavorable local RSS-minimum. For determining an initial solution, a high-dimensional parameter space needs to be screened, a process that is very time-consuming but can be parallelized. Another advantage of parallelization is equally important: After determining initial solutions, the used processors can be tasked to each optimize an initial guess. Even if several of these optimizations become stuck in a shallow local RSS-minimum, other processors continue and improve the regression outcome. A software package for parallel processing-based constrained nonlinear regression (RegressionLab) has been developed, implemented, and tested on a variety of hardware configurations. As proof-of-principle, microalgae to environment interactions have been studied by infrared attenuated total reflection spectroscopy. Additionally, light microscopy has been used to monitor cell production. It is shown that spectroscopic data sets with 10,000 s of data points and >1000 nonlinear model parameters as well as imaging data with 100,000s of data points and >2000 nonlinear model parameters may now be investigated by constrained nonlinear regression. Acceleration factors of up to 8.1 have been obtained which is of high practical relevance when computations take weeks on single-processor machines. Solely using parallel processing, the RSS values may be improved up to a factor of 5.5.

Thermogravimetric characteristics of α-cellulose and decomposition kinetics in a micro-tubing reactor

The pyrolysis characteristics and kinetics of α-cellulose were investigated using thermogravimetric analyzer (TGA) and micro tubing reactor, respectively. Most of the α-cellulose decomposed between 250 and 400 °C at heating rate of 5–20 °C/min. The apparent activation energy was observed in the range of 263.02 kJ mol−1 to 306.21 kJ mol−1 at the conversion of 10-80%. The kinetic parameters were determined by nonlinear least-squares regression of the experimental data, assuming first-order kinetics. It was found from the kinetic rate constants that the predominant reaction pathway was A(α-cellulose) to B(bio-oil) rather than A(α-cellulose) to C(gas; C1-C4) and/or to B(bio-oil) to C(gas; C1-C4) at temperatures of 340-360 °C.

Tree Morphologic Plasticity Explains Deviation from Metabolic Scaling Theory in Semi-Arid Conifer Forests, Southwestern USA.

A significant concern about Metabolic Scaling Theory (MST) in real forests relates to consistent differences between the values of power law scaling exponents of tree primary size measures used to estimate mass and those predicted by MST. Here we consider why observed scaling exponents for diameter and height relationships deviate from MST predictions across three semi-arid conifer forests in relation to: (1) tree condition and physical form, (2) the level of inter-tree competition (e.g. open vs closed stand structure), (3) increasing tree age, and (4) differences in site productivity. Scaling exponent values derived from non-linear least-squares regression for trees in excellent condition (n = 381) were above the MST prediction at the 95% confidence level, while the exponent for trees in good condition were no different than MST (n = 926). Trees that were in fair or poor condition, characterized as diseased, leaning, or sparsely crowned had exponent values below MST predictions (n = 2,058), as did recently dead standing trees (n = 375). Exponent value of the mean-tree model that disregarded tree condition (n = 3,740) was consistent with other studies that reject MST scaling. Ostensibly, as stand density and competition increase trees exhibited greater morphological plasticity whereby the majority had characteristically fair or poor growth forms. Fitting by least-squares regression biases the mean-tree model scaling exponent toward values that are below MST idealized predictions. For 368 trees from Arizona with known establishment dates, increasing age had no significant impact on expected scaling. We further suggest height to diameter ratios below MST relate to vertical truncation caused by limitation in plant water availability. Even with environmentally imposed height limitation, proportionality between height and diameter scaling exponents were consistent with the predictions of MST.

Nonlinear least squares regression for single image scanning electron microscope signal-to-noise ratio estimation.

A new method based on nonlinear least squares regression (NLLSR) is formulated to estimate signal-to-noise ratio (SNR) of scanning electron microscope (SEM) images. The estimation of SNR value based on NLLSR method is compared with the three existing methods of nearest neighbourhood, first-order interpolation and the combination of both nearest neighbourhood and first-order interpolation. Samples of SEM images with different textures, contrasts and edges were used to test the performance of NLLSR method in estimating the SNR values of the SEM images. It is shown that the NLLSR method is able to produce better estimation accuracy as compared to the other three existing methods. According to the SNR results obtained from the experiment, the NLLSR method is able to produce approximately less than 1% of SNR error difference as compared to the other three existing methods.

Evaluation of a Hyaluronic Acid-Based Biomaterial to Enhance Wound Healing in the Equine Distal Limb

The objective of this study was to evaluate the ability of a cross-linked hyaluronic acid-based biomaterial (CMHA) to promote healing in an equine distal limb wound model. Three 6.25 cm2 full thickness skin wounds were surgically created on the dorsomedial metacarpus and metatarsus of each of four limbs of eight normal adult horses under general anesthesia. Three days after surgery, wounds were photographed and one of four treatments was applied to all three wounds on a single limb: control (no CMHA), single application of CMHA gel, multiple applications of CMHA gel, and multiple applications of CMHA film. Wounds were assessed for quality of repair tissue and photographed for image analysis at bandage changes every 4 days throughout the 47-day study. Exuberant granulation tissue was excised as needed and weighed. Size of granulating wounds was analyzed by repeated measures analysis of covariance and rate of wound healing assessed using a logistic decay model fitted to the data by nonlinear least-squares regression. Significance was set at P < .05. No adverse effects of CMHA were noted. There was a significant day by treatment interaction; however, overall, there were no significant differences among treatment groups (P = .09). Wounds treated with CMHA films decreased to half their original size significantly faster, were significantly smaller on day 31, and healed with higher quality, less fragile epithelium than wounds in other treatment groups. Treatment of distal limb wounds in horses may benefit from use of CMHA films to improve healing.

NMR study and computational assays of meclofenamic Na salt and β-cyclodextrin inclusion complex

Complexation in solution between meclofenamate sodium (MCF) and β-cyclodextrin was studied using one- and two-dimensional 1H NMR spectroscopy and molecular docking coupled with ab initio calculations. The large variation of chemical shifts from protons located inside the hydrophobic cavity of β-cyclodextrin, provided clear evidence of inclusion complexation. The stoichiometry of the inclusion complex was determined to be 1:1, using the method of continuous variation. To ascertain the solution geometry of the host–guest complex a ROESY experiment was carried out. The results suggested a preferential binding of the dichlorophenyl moiety of the guest molecule within the β-cyclodextrin cavity, conformation which also sustained by the theoretical computational investigations. The association constant of the inclusion complex was determined using 1H NMR titration method in solution followed by a non-linear least-square regression implemented in CONSTEQ, a software developed in our group. After a preliminary molecular docking investigation, the most probable conformation was subjected to ab initio calculations using SIESTA software package, to characterize more precisely the stabilization energy of the 1:1 inclusion complex.

Chemometric Modeling of Microalgal Nutrient Sequestration as a Function of Their Chemical Environment

ABSTRACTMarine microalgae sequester large quantities of inorganic compounds by way of photosynthesis. Therefore, phytoplankton has a considerable environmental impact as it contributes to counter-balancing anthropogenic releases of CO2. However, open questions remain regarding interactions between microalgae and their environment in particular the inorganic compounds which cells consume as nutrients. On the other hand, Michaelis–Menten (MM) kinetics links environmental chemistry and microbiology as it concurrently explains the cells’ uptake of nutrients and utilization for cell production. Thereby, cells modify the chemical composition of their growing environment, which in turn is hypothesized to impact the cells’ sequestration capabilities. However, the system of ordinary differential equations (ODEs) that represents MM cannot be solved without further considerations, as it contains unknown physiological parameters. These parameters though are of central interest, as they describe the cells’ compound uptake in a certain chemical environment. Innovations in chemometrics are presented that derive values for these parameters as a function of the cells’ nutrient availability. For this purpose, the MM ODE system has been merged into nonlinear least-square regression in lieu of a fit function. By this approach, it is demonstrated that microalgae’s nutrient uptake is indeed driven by chemical conditions in their growing environment. These results are also indicative that the chemical conditions in a microscopic vicinity of the cells are relevant rather than nutrient concentrations on a culture level. These proof-of-principle results underline that for an accurate assessment of such chemically active samples, it is necessary to consider both the cells and their chemical environment.

Improved Least-Square Prony Analysis Technique for Parameter Evaluation of Lightning ImpulseVoltage and Current

This paper represents a fast curve-fitting technique for evaluation of either lightning impulse voltage or the current base curve. The technique based on least-square Prony analysis employs the double integration of the recorded waveform for waveform evaluation. The undesirable effect of noise exiting in Prony analysis technique is mitigated. The base curve formula is written in the complex form of the double exponential function. A decomposition technique is utilized for determination of the base curves of full lightning impulse voltages with oscillations and of lightning impulse currents. To verify the performance of the proposed method, the base curves reconstituted from the developed method were compared with the curves reconstructed from a nonlinear least-square regression prescribed in the standard. The execution time of the proposed method is much shorter than that of the conventional method because it does not need the iteration process. With noise immunity characteristics and avoidance of recorded waveform distortion, the results from the proposed technique based on the normal implementation are remarkably accurate. The results of this study indicated that the proposed method is the powerful one to apply for lightning impulse voltage and current base curve evaluation.

Experimental and analytical investigation of water diffusion process in nano-carbon/alumina/silica filled epoxy nanocomposites

This study discusses the water absorption behavior of three different types of nanocomposites. Silica, carbon and alumina nanoparticles are used as fillers incorporated in epoxy resin with different contents of 0.5, 1.5, and 3 wt%. A new nonlinear least-squares regression approach in conjunction with a gradient optimization was developed using symbolic manipulator MAPLE software to find the best fit. The equilibrium moisture content of the nanocomposites is measured as a function of time and the analytical modelling is successfully conducted. Results indicate that the addition of nanoparticles generally lower moisture content in contrast to neat epoxy. Compositions of 1.5 and 3 wt% alumina as well as silica nanocomposites however show a different behaviour. Diffusion coefficients for different types of nanocomposites were computed using Fickian and Langmuir models of diffusion. The least and highest diffusion coefficients correspond to the addition of silica 0.5 wt% and alumina 3 wt%, respectively.

Goodness of fit to a mathematical model for Drosophila sleep behavior is reduced in hyposomnolent mutants.

The conserved nature of sleep in Drosophila has allowed the fruit fly to emerge in the last decade as a powerful model organism in which to study sleep. Recent sleep studies in Drosophila have focused on the discovery and characterization of hyposomnolent mutants. One common feature of these animals is a change in sleep architecture: sleep bout count tends to be greater, and sleep bout length lower, in hyposomnolent mutants. I propose a mathematical model, produced by least-squares nonlinear regression to fit the form Y = aX∧b, which can explain sleep behavior in the healthy animal as well as previously-reported changes in total sleep and sleep architecture in hyposomnolent mutants. This model, fit to sleep data, yields coefficient of determination R squared, which describes goodness of fit. R squared is lower, as compared to control, in hyposomnolent mutants insomniac and fumin. My findings raise the possibility that low R squared is a feature of all hyposomnolent mutants, not just insomniac and fumin. If this were the case, R squared could emerge as a novel means by which sleep researchers might assess sleep dysfunction.