Setting Ranges in Potential Biomarkers for Type 2 Diabetes Mellitus Patients Early Detection By Sex-An Approach with Machine Learning Algorithms.

Type 2 diabetes mellitus (T2DM) is one of the most common metabolic diseases in the world and poses a significant public health challenge. Early detection and management of this metabolic disorder is crucial to prevent complications and improve outcomes. This paper aims to find core differences in male and female markers to detect T2DM by their clinic and anthropometric features, seeking out ranges in potential biomarkers identified to provide useful information as a pre-diagnostic tool whie excluding glucose-related biomarkers using machine learning (ML) models. We used a dataset containing clinical and anthropometric variables from patients diagnosed with T2DM and patients without TD2M as control. We applied feature selection with three different techniques to identify relevant biomarker models: an improved recursive feature elimination (RFE) evaluating each set from all the features to one feature with the Akaike information criterion (AIC) to find optimal outputs; Least Absolute Shrinkage and Selection Operator (LASSO) with glmnet; and Genetic Algorithms (GA) with GALGO and forward selection (FS) applied to GALGO output. We then used these for comparison with the AIC to measure the performance of each technique and collect the optimal set of global features. Then, an implementation and comparison of five different ML models was carried out to identify the most accurate and interpretable one, considering the following models: logistic regression (LR), artificial neural network (ANN), support vector machine (SVM), k-nearest neighbors (KNN), and nearest centroid (Nearcent). The models were then combined in an ensemble to provide a more robust approximation. The results showed that potential biomarkers such as systolic blood pressure (SBP) and triglycerides are together significantly associated with T2DM. This approach also identified triglycerides, cholesterol, and diastolic blood pressure as biomarkers with differences between male and female actors that have not been previously reported in the literature. The most accurate ML model was selection with RFE and random forest (RF) as the estimator improved with the AIC, which achieved an accuracy of 0.8820. In conclusion, this study demonstrates the potential of ML models in identifying potential biomarkers for early detection of T2DM, excluding glucose-related biomarkers as well as differences between male and female anthropometric and clinic profiles. These findings may help to improve early detection and management of the T2DM by accounting for differences between male and female subjects in terms of anthropometric and clinic profiles, potentially reducing healthcare costs and improving personalized patient attention. Further research is needed to validate these potential biomarkers ranges in other populations and clinical settings.

Comparison of five equations in describing the variation of leaf area distributions of Alangium chinense (Lour.) Harms.

Previous studies have validated a performance equation (PE) and its generalized version (GPE) in describing the rotated and right-shifted Lorenz curves of organ size (e.g., leaf area and fruit volume) distributions of herbaceous plants. Nevertheless, there are still two questions that have not been adequately addressed by prior work: (i) whether the PE and GPE apply to woody plant species and (ii) how do the PE and GPE perform in comparison with other Lorenz equations when fitting data. To address these deficiencies, we measured the lamina length and width of each leaf on 60 Alangium chinense saplings to compare the performance of the PE and GPE with three other Lorenz equations in quantifying the inequality of leaf area distributions across individual trees. Leaf area is shown to be the product of a proportionality coefficient (k) and leaf length and width. To determine the numerical value of k, we scanned 540 leaves to obtain the leaf area empirically. Using the estimated k, the leaf areas of 60 A. chinense saplings were calculated. Using these data, the two performance equations and three other Lorenz equations were then compared and assessed using the root-mean-square error (RMSE) and Akaike information criterion (AIC). The PE and GPE were found to be valid in describing the rotated and right-shifted Lorenz curves of the A. chinense leaf area distributions, and GPE has the lowest RMSE and AIC values. This work validates the GPE as the best model in gauging variations in leaf area of the woody species.

Bootstrap Approximation of Model Selection Probabilities for Multimodel Inference Frameworks.

Most statistical modeling applications involve the consideration of a candidate collection of models based on various sets of explanatory variables. The candidate models may also differ in terms of the structural formulations for the systematic component and the posited probability distributions for the random component. A common practice is to use an information criterion to select a model from the collection that provides an optimal balance between fidelity to the data and parsimony. The analyst then typically proceeds as if the chosen model was the only model ever considered. However, such a practice fails to account for the variability inherent in the model selection process, which can lead to inappropriate inferential results and conclusions. In recent years, inferential methods have been proposed for multimodel frameworks that attempt to provide an appropriate accounting of modeling uncertainty. In the frequentist paradigm, such methods should ideally involve model selection probabilities, i.e., the relative frequencies of selection for each candidate model based on repeated sampling. Model selection probabilities can be conveniently approximated through bootstrapping. When the Akaike information criterion is employed, Akaike weights are also commonly used as a surrogate for selection probabilities. In this work, we show that the conventional bootstrap approach for approximating model selection probabilities is impacted by bias. We propose a simple correction to adjust for this bias. We also argue that Akaike weights do not provide adequate approximations for selection probabilities, although they do provide a crude gauge of model plausibility.

Measuring complexity for hierarchical models using effective degrees of freedom.

Hierarchical models can express ecological dynamics using a combination of fixed and random effects, and measurement of their complexity (effective degrees of freedom, EDF) requires estimating how much random effects are shrunk toward a shared mean. Estimating EDF is helpful to (1) penalize complexity during model selection and (2) to improve understanding of model behavior. I applied the conditional Akaike Information Criterion (cAIC) to estimate EDF from the finite-difference approximation to the gradient of model predictions with respect to each datum. I confirmed that this has similar behavior to widely used Bayesian criteria, and I illustrated ecological applications using three case studies. The first compared model parsimony with or without time-varying parameters when predicting density-dependent survival, where cAIC favors time-varying demographic parameters more than conventional Akaike Information Criterion. The second estimates EDF in a phylogenetic structural equation model, and identifies a larger EDF when predicting longevity than mortality rates in fishes. The third compares EDF for a species distribution model fitted for 20 bird species and identifies those species requiring more model complexity. These highlight the ecological and statistical insight from comparing EDF among experimental units, models, and data partitions, using an approach that can be broadly adopted for nonlinear ecological models.

Multimodel Approaches Are Not the Best Way to Understand Multifactorial Systems.

Information-theoretic (IT) and multi-model averaging (MMA) statistical approaches are widely used but suboptimal tools for pursuing a multifactorial approach (also known as the method of multiple working hypotheses) in ecology. (1) Conceptually, IT encourages ecologists to perform tests on sets of artificially simplified models. (2) MMA improves on IT model selection by implementing a simple form of shrinkage estimation (a way to make accurate predictions from a model with many parameters relative to the amount of data, by "shrinking" parameter estimates toward zero). However, other shrinkage estimators such as penalized regression or Bayesian hierarchical models with regularizing priors are more computationally efficient and better supported theoretically. (3) In general, the procedures for extracting confidence intervals from MMA are overconfident, providing overly narrow intervals. If researchers want to use limited data sets to accurately estimate the strength of multiple competing ecological processes along with reliable confidence intervals, the current best approach is to use full (maximal) statistical models (possibly with Bayesian priors) after making principled, a priori decisions about model complexity.

Optimizing spatio-temporal correlation structures for modeling food security in Africa: a simulation-based investigation.

This study investigates the impact of spatio- temporal correlation using four spatio-temporal models: Spatio-Temporal Poisson Linear Trend Model (SPLTM), Poisson Temporal Model (TMS), Spatio-Temporal Poisson Anova Model (SPAM), and Spatio-Temporal Poisson Separable Model (STSM) concerning food security and nutrition in Africa. Evaluating model goodness of fit using the Watanabe Akaike Information Criterion (WAIC) and assessing bias through root mean square error and mean absolute error values revealed a consistent monotonic pattern. SPLTM consistently demonstrates a propensity for overestimating food security, while TMS exhibits a diverse bias profile, shifting between overestimation and underestimation based on varying correlation settings. SPAM emerges as a beacon of reliability, showcasing minimal bias and WAIC across diverse scenarios, while STSM consistently underestimates food security, particularly in regions marked by low to moderate spatio-temporal correlation. SPAM consistently outperforms other models, making it a top choice for modeling food security and nutrition dynamics in Africa. This research highlights the impact of spatial and temporal correlations on food security and nutrition patterns and provides guidance for model selection and refinement. Researchers are encouraged to meticulously evaluate the biases and goodness of fit characteristics of models, ensuring their alignment with the specific attributes of their data and research goals. This knowledge empowers researchers to select models that offer reliability and consistency, enhancing the applicability of their findings.

Comparison of four performance models in quantifying the inequality of leaf and fruit size distribution.

The inequality in leaf and fruit size distribution per plant can be quantified using the Gini index, which is linked to the Lorenz curve depicting the cumulative proportion of leaf (or fruit) size against the cumulative proportion of the number of leaves (or fruits). Prior researches have predominantly employed empirical models-specifically the original performance equation (PE-1) and its generalized counterpart (GPE-1)-to fit rotated and right-shifted Lorenz curves. Notably, another potential performance equation (PE-2), capable of generating similar curves to PE-1, has been overlooked and not systematically compared with PE-1 and GPE-1. Furthermore, PE-2 has been extended into a generalized version (GPE-2). In the present study, we conducted a comparative analysis of these four performance equations, evaluating their applicability in describing Lorenz curves related to plant organ (leaf and fruit) size. Leaf area was measured on 240 culms of dwarf bamboo (Shibataea chinensis Nakai), and fruit volume was measured on 31 field muskmelon plants (Cucumis melo L. var. agrestis Naud.). Across both datasets, the root-mean-square errors of all four performance models were consistently smaller than 0.05. Paired t-tests indicated that GPE-1 exhibited the lowest root-mean-square error and Akaike information criterion value among the four performance equations. However, PE-2 gave the best close-to-linear behavior based on relative curvature measures. This study presents a valuable tool for assessing the inequality of plant organ size distribution.

Development of a community severance index for urban areas in the United States: A case study in New York City.

BACKGROUND AND AIMS: Traffic-related exposures, such as air pollution and noise, have a detrimental impact on human health, especially in urban areas. However, there remains a critical research and knowledge gap in understanding the impact of community severance, a measure of the physical separation imposed by road infrastructure and motorized road traffic, limiting access to goods, services, or social connections, breaking down the social fabric and potentially also adversely impacting health. We aimed to robustly quantify a community severance metric in urban settings exemplified by its characterization in New York City (NYC). METHODS: We used geospatial location data and dimensionality reduction techniques to capture NYC community severance variation. We employed principal component pursuit, a pattern recognition algorithm, combined with factor analysis as a novel method to estimate the Community Severance Index. We used public data for the year 2019 at census block group (CBG) level on road infrastructure, road traffic activity, and pedestrian infrastructure. As a demonstrative application of the Community Severance Index, we investigated the association between community severance and traffic collisions, as a proxy for road safety, in 2019 in NYC at CBG level. RESULTS: Our data revealed one multidimensional factor related to community severance explaining 74% of the data variation. In adjusted analyses, traffic collisions in general, and specifically those involving pedestrians or cyclists, were nonlinearly associated with an increasing level of Community Severance Index in NYC. CONCLUSION: We developed a high spatial-resolution Community Severance Index for NYC using data available nationwide, making it feasible for replication in other cities across the United States. Our findings suggest that increases in the Community Severance Index across CBG may be linked to increases in traffic collisions in NYC. The Community Severance Index, which provides a novel traffic-related exposure, may be used to inform equitable urban policies that mitigate health risks and enhance well-being.

Seroprevalence and renal carriage of pathogenic Leptospira in livestock in Cotonou, Benin.

BACKGROUND: Leptospirosis is a zoonotic disease. It is particularly prevalent in tropical countries and has major consequences for human and animal health. In Benin, the disease's epidemiology remains poorly understood, especially in livestock, for which data are lacking. OBJECTIVES: To characterise Leptospira seroprevalence and locally circulating serogroups in livestock from Cotonou and to estimate the prevalence of Leptospira renal carriage in cattle. METHODS: We conducted a cross-sectional study in February 2020 during which livestock were sampled at an abattoir and in an impoverished city district. We analysed blood samples from 279 livestock animals (i.e. cattle, sheep, goats and pigs) using the microscopic agglutination test. Additionally, samples of renal tissue from 100 cattle underwent 16s rRNA (rrs) real-time PCR analysis. RESULTS: For the 131 cattle, 85 sheep, and 50 goats tested, seroprevalence was 18% (95% confidence interval [CI] [12%, 26%]), 9% (95% CI [4%, 17%] and 2% (95% CI [0%, 9%]), respectively, and most of the seropositive animals were associated with 1:100 titres. All 13 pigs were seronegative. Leptospira DNA was found in the renal tissue of 10% (95% CI [5%, 18%]) of the cattle tested (n = 100). Leptospira borgpetersenii was the main species present (n = 7), but Leptospira interrogans (n = 2) and Leptospira kirschneri (n = 1) were also detected. Various serogroups (Canicola, Grippotyphosa, Sejroe, Icterohaemorrhagiae, Pomona, Pyrogenes, Australis and Autumnalis) were detected using microscopic agglutination test without a clear predominance of any of them. CONCLUSIONS: These results suggest that abattoir workers and people living in close contact with livestock in poor urban areas are exposed to the risk of Leptospira infection.

Fit of biokinetic data in molecular radiotherapy: a machine learning approach.

BACKGROUND: In literature are reported different analytical methods (AM) to choose the proper fit model and to fit data of the time-activity curve (TAC). On the other hand, Machine Learning algorithms (ML) are increasingly used for both classification and regression tasks. The aim of this work was to investigate the possibility of employing ML both to classify the most appropriate fit model and to predict the area under the curve (τ). METHODS: Two different ML systems have been developed for classifying the fit model and to predict the biokinetic parameters. The two systems were trained and tested with synthetic TACs simulating a whole-body Fraction Injected Activity for patients affected by metastatic Differentiated Thyroid Carcinoma, administered with [131I]I-NaI. Test performances, defined as classification accuracy (CA) and percentage difference between the actual and the estimated area under the curve (Δτ), were compared with those obtained using AM varying the number of points (N) of the TACs. A comparison between AM and ML were performed using data of 20 real patients. RESULTS: As N varies, CA remains constant for ML (about 98%), while it improves for F-test (from 62 to 92%) and AICc (from 50 to 92%), as N increases. With AM, [Formula: see text] can reach down to - 67%, while using ML [Formula: see text] ranges within ± 25%. Using real TACs, there is a good agreement between τ obtained with ML system and AM. CONCLUSIONS: The employing of ML systems may be feasible, having both a better classification and a better estimation of biokinetic parameters.

Fuzzy multicomponent stress-strength reliability in presence of partially accelerated life testing under generalized progressive hybrid censoring scheme subject to inverse Weibull model.

It typically takes a lot of time to monitor life-testing experiments on a product or material. Units can be tested under harsher conditions than usual, known as accelerated life tests to shorten the testing period. This study's goal is to investigate the issue of partially accelerated life testing that use generalized progressive hybrid censored samples to estimate the stress-strength reliability in the multicomponent case. Also, the fuzziness of the model is considered that gives more sensitive and accurate analyses about the underlying system. Maximum likelihood estimation method under the inverse Weibull distribution and using the generalized progressively hybrid censoring scheme is introduced to obtain an estimator for the fuzzy multicomponent stress-strength reliability. Also, an asymptotic confidence interval is deduced to examine the reliability of the fuzzy multicomponent stress-strength. Simulation study is conducted using maximum likelihood estimates and confidence intervals for the fuzzy multicomponent stress-strength reliability for different values of the parameters and different schemes. A real data application representing the data for the failure times for a certain software model is introduced to obtain the fuzzy multicomponent stress-strength reliability for different schemes.•The fuzzy multicomponent stress-strength reliability is investigated under partially accelerated life testing and the generalized progressively hybrid censored scheme.•An algorithm is introduced to simulate data for the censoring scheme.•A real data application is presented to obtain the fuzzy multicomponent stress-strength reliability at different schemes.

A Selective Review on Information Criteria in Multiple Change Point Detection.

Change points indicate significant shifts in the statistical properties in data streams at some time points. Detecting change points efficiently and effectively are essential for us to understand the underlying data-generating mechanism in modern data streams with versatile parameter-varying patterns. However, it becomes a highly challenging problem to locate multiple change points in the noisy data. Although the Bayesian information criterion has been proven to be an effective way of selecting multiple change points in an asymptotical sense, its finite sample performance could be deficient. In this article, we have reviewed a list of information criterion-based methods for multiple change point detection, including Akaike information criterion, Bayesian information criterion, minimum description length, and their variants, with the emphasis on their practical applications. Simulation studies are conducted to investigate the actual performance of different information criteria in detecting multiple change points with possible model mis-specification for the practitioners. A case study on the SCADA signals of wind turbines is conducted to demonstrate the actual change point detection power of different information criteria. Finally, some key challenges in the development and application of multiple change point detection are presented for future research work.

Automatic detection of myocardial ischaemia using generalisable spatio-temporal hierarchical Bayesian modelling of DCE-MRI.

Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) can be used as a non-invasive method for the assessment of myocardial perfusion. The acquired images can be utilised to analyse the spatial extent and severity of myocardial ischaemia (regions with impaired microvascular blood flow). In the present paper, we propose a novel generalisable spatio-temporal hierarchical Bayesian model (GST-HBM) to automate the detection of ischaemic lesions and improve the in silico prediction accuracy by systematically integrating spatio-temporal context information. We present a computational inference procedure with an adequate trade-off between accuracy and computational efficiency, whereby model parameters are sampled from the posterior distribution with Gibbs sampling, while lower-level hyperparameters are selected using model selection strategies based on the Watanabe Akaike information criterion (WAIC). We have assessed our method on both synthetic (in silico) data with known gold-standard and 12 sets of clinical first-pass myocardial perfusion DCE-MRI datasets. We have also carried out a comparative performance evaluation with four established alternative methods: Gaussian mixture model (GMM), opening and closing operations based on Gaussian mixture model (GMMC&Omax), Markov random field constrained Gaussian mixture model (GMM-MRF) and model-based hierarchical Bayesian model (M-HBM). Our results show that the proposed GST-HBM method achieves much higher in silico prediction accuracy than the established alternative methods. Furthermore, this method appears to provide a more robust delineation of ischaemic lesions in datasets affected by spatially variant noise.

Estimation of In Vitro True Digestibility and Fiber Degradation from Feedstuff Fiber Composition When Incubated in Equine Fecal Inoculum.

Neutral detergent fiber (NDF) and acid detergent fiber (ADF) composition have been shown to predict in vitro true digestibility (IVTD), in vitro NDF digestibility (IVNDFD), and in vitro ADF digestibility (IVADFD) in ruminants. This study's objective was to estimate in vitro digestibility measures within the DaisyII incubator using equine fecal inoculum from feedstuff NDF and ADF composition. Analyzed feedstuffs included alfalfa hay (Medicago sativa), Coastal Bermudagrass hay, soybean meal, rice bran, hempseed meal, and Bluebonnet® Equilene® Pellets. Data were analyzed using Akaike's information criterion (AIC) within the R Statistical Program©. The highest ranked model for IVTD was the interaction of NDF and ADF: 10003.32 - 0.2904 × NDF - 0.4220 × ADF - 0.0010 × NDF × ADF (Adjusted R2 = 0.959 and AICc = 474.97). Sample IVNDFD was moderately predicted by ADF: 855.15 - 1.5183 × ADF (Adjusted R2 = 0.749 and AICc = 560.82). Feedstuff ADF produced the highest ranked model for IVNDFD: 881.91 - 1.5952 × ADF (Adj. R2 = 0.835 and AICc = 541.33). These results indicate the effectiveness of using feedstuff NDF and ADF composition to predict IVTD, IVNDFD, and IVADFD within equine fecal inoculum. The findings of this study provide better understanding of feedstuff digestibility using equine fecal inoculum, but more research is warranted for validation of the models and the potential impact in vivo.

[The Validity of the Poisson Distribution to Analyze Microbial Colony Counts on Agar Plates for Food Samples].

Microbial colony counts of food samples in microbiological examinations are one of the most important items. The probability distributions for the colony counts per agar plate at the dilution of counting had not been intensively studied so far. Recently we analyzed the colony counts of food samples with several probability distributions using the Pearson's chi-square value by the "traditional" statistics as the index of fit [Fujikawa and Tsubaki, Food Hyg.Saf.Sc., 60, 88-95 (2019)]. As a result, the selected probability distributions depended on the samples. In this study we newly selected a probability distribution, namely a statistical model, suitable for the above data with the method of maximum likelihood from the probabilistic point of view. The Akaike's Information Criterion (AIC) was used as the index of fit. Consequently, the Poisson model were better than the negative binomial model for all of four food samples. The Poisson model was also better than the binomial for three of four microbial culture samples. With Baysian Information Criterion (BIC), the Poisson model was also better than these two models for all the samples. These results suggested that the Poisson distribution would be the best model to estimate the colony counts of food samples. The present study would be the first report on the statistical model selection for the colony counts of food samples with AIC and BIC.

Comparing DIC and WAIC for multilevel models with missing data.

In Bayesian statistics, the most widely used criteria of Bayesian model assessment and comparison are Deviance Information Criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC). We use a multilevel mediation model as an illustrative example to compare different types of DIC and WAIC. More specifically, we aim to compare the performance of conditional and marginal DICs and WAICs, and investigate their performance with missing data. We focus on two versions of DIC ([Formula: see text] and [Formula: see text]) and one version of WAIC. In addition, we explore whether it is necessary to include the nuisance models of incomplete exogenous variables in likelihood. Based on the simulation results, whether [Formula: see text] is better than [Formula: see text] and WAIC and whether we should include the nuisance models of exogenous variables in likelihood functions depend on whether we use marginal or conditional likelihoods. Overall, we find that the marginal likelihood based-[Formula: see text] that excludes the likelihood of covariate models generally had the highest true model selection rates.

Model selection in multivariate adaptive regressions splines (MARS) using alternative information criteria.

Multivariate Adaptive Regression Splines (MARS) is a useful non-parametric regression analysis method that can be used for model selection in high-dimensional data. Since MARS can identify and model complex, non-linear relationships between the dependent variable and independent variables without requiring any assumptions, it has advantage over simple linear regression techniques. Also, for simplifying the model building process and preventing overfitting, MARS can select automatically the variables to be included in the model, which is useful for datasets with many variables. While MARS is a flexible non-parametric regression method, generalized cross validation (GCV) technique is used within the MARS framework to avoid overfitting and to select the best model. GCV criterion is widely used and can be effective in many situations, however it has some criticism. These criticism are the arbitrary value of the smoothing parameter used in the algorithm of the GCV criterion and the models obtained using this criterion are high-dimensional. In this paper, it is aimed to obtain the barest model that best explains the relationship between the dependent variable and independent variables by using alternative information criteria (Akaike information criterion (AIC), Schwarz Bayesian criterion (SBC) and information complexity criterion (ICOMP(IFIM)PEU)) instead of the use of smoothing parameters in order to put an end to the criticism. To achieve this goal, a simulation study was first conducted with a data set composed of variables that do and do not contribute to the dependent variable to test the success of the information criteria. As a consequence of this simulation work, when variables (which do not contribute to the dependent variable) are not included in the regression model, it demonstrates the success of the criteria in model selection. As a real data set, the reasons for loan defaults were investigated between the years 2005-2019 by utilizing data from 18 banks operating in Türkiye. The results obtained reveal the success of ICOMP(IFIM)PEU criterion in model selection.

Exploring the potential of Diplosphaera mucosa VSPA for the treatment of petroleum effluent with simultaneous lipid production.

The discovery of unexplored, robust microalgal strains will assist in treating highly polluted industrial effluent, including petroleum effluent. In the current analysis, a newly isolated microalgal strain, Diplosphaera mucosa VSPA, was used to treat petroleum effluent in a lab-scale raceway bioreactor. Its treatment efficiency was compared with a well-known species, Chlorella pyrenoidosa. The D. mucosa VSPA strain proliferated in petroleum effluent at a high growth rate, with final biomass, and lipid concentrations reaching 6.93 g/L and 2.72 g/L, respectively. Treatment efficiency was calculated based on the final removal efficiency of ammonium nitrogen, phosphate phosphorus, and chemical oxygen demand, which was more than 90%. Control experiments suggested that the maximum removal of pollutants from petroleum effluent was due to microalgae growth. Some growth models, including the Gompertz, Logistic, Stannard, Richard, and Schnute, were used to simulate the experimental data, verifying the results. Good fitting of all models was obtained, with the R2 value reaching more than 0.90. The development of a suitable model can help in decreasing the efforts required for the scale-up of the process.

Using long-term data from a whole ecosystem warming experiment to identify best spring and autumn phenology models.

Predicting vegetation phenology in response to changing environmental factors is key in understanding feedbacks between the biosphere and the climate system. Experimental approaches extending the temperature range beyond historic climate variability provide a unique opportunity to identify model structures that are best suited to predicting phenological changes under future climate scenarios. Here, we model spring and autumn phenological transition dates obtained from digital repeat photography in a boreal Picea-Sphagnum bog in response to a gradient of whole ecosystem warming manipulations of up to +9°C, using five years of observational data. In spring, seven equally best-performing models for Larix utilized the accumulation of growing degree days as a common driver for temperature forcing. For Picea, the best two models were sequential models requiring winter chilling before spring forcing temperature is accumulated. In shrub, parallel models with chilling and forcing requirements occurring simultaneously were identified as the best models. Autumn models were substantially improved when a CO2 parameter was included. Overall, the combination of experimental manipulations and multiple years of observations combined with variation in weather provided the framework to rule out a large number of candidate models and to identify best spring and autumn models for each plant functional type.

Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling.

Chaotic time series are widely present in practice, but due to their characteristics-such as internal randomness, nonlinearity, and long-term unpredictability-it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool for chaotic time series modeling. Focusing on chaotic time series modeling, this paper presents a generalized degree of freedom approximation method of MLP. We then obtain its Akachi information criterion, which is designed as the loss function for training, hence developing an overall framework for chaotic time series analysis, including phase space reconstruction, model training, and model selection. To verify the effectiveness of the proposed method, it is applied to two artificial chaotic time series and two real-world chaotic time series. The numerical results show that the proposed optimized method is effective to obtain the best model from a group of candidates. Moreover, the optimized models perform very well in multi-step prediction tasks.