A Novel Deep Learning Approach for Forecasting Myocardial Infarction Occurrences with Time Series Patient Data.

Myocardial Infarction (MI) commonly referred to as a heart attack, results from the abrupt obstruction of blood supply to a section of the heart muscle, leading to the deterioration or death of the affected tissue due to a lack of oxygen. MI, poses a significant public health concern worldwide, particularly affecting the citizens of the Chittagong Metropolitan Area. The challenges lie in both prevention and treatment, as the emergence of MI has inflicted considerable suffering among residents. Early warning systems are crucial for managing epidemics promptly, especially given the escalating disease burden in older populations and the complexities of assessing present and future demands. The primary objective of this study is to forecast MI incidence early using a deep learning model, predicting the prevalence of heart attacks in patients. Our approach involves a novel dataset collected from daily heart attack incidence Time Series Patient Data spanning January 1, 2020, to December 31, 2021, in the Chittagong Metropolitan Area. Initially, we applied various advanced models, including Autoregressive Integrated Moving Average (ARIMA), Error-Trend-Seasonal (ETS), Trigonometric seasonality, Box-Cox transformation, ARMA errors, Trend and Seasonal (TBATS), and Long Short Time Memory (LSTM). To enhance prediction accuracy, we propose a novel Myocardial Sequence Classification (MSC)-LSTM method tailored to forecast heart attack occurrences in patients using the newly collected data from the Chittagong Metropolitan Area. Comprehensive results comparisons reveal that the novel MSC-LSTM model outperforms other applied models in terms of performance, achieving a minimum Mean Percentage Error (MPE) score of 1.6477. This research aids in predicting the likely future course of heart attack occurrences, facilitating the development of thorough plans for future preventive measures. The forecasting of MI occurrences contributes to effective resource allocation, capacity planning, policy creation, budgeting, public awareness, research identification, quality improvement, and disaster preparedness.

Enhancing hydrological modeling with transformers: a case study for 24-h streamflow prediction.

In this paper, we address the critical task of 24-h streamflow forecasting using advanced deep-learning models, with a primary focus on the transformer architecture which has seen limited application in this specific task. We compare the performance of five different models, including persistence, long short-term memory (LSTM), Seq2Seq, GRU, and transformer, across four distinct regions. The evaluation is based on three performance metrics: Nash-Sutcliffe Efficiency (NSE), Pearson's r, and normalized root mean square error (NRMSE). Additionally, we investigate the impact of two data extension methods: zero-padding and persistence, on the model's predictive capabilities. Our findings highlight the transformer's superiority in capturing complex temporal dependencies and patterns in the streamflow data, outperforming all other models in terms of both accuracy and reliability. Specifically, the transformer model demonstrated a substantial improvement in NSE scores by up to 20% compared to other models. The study's insights emphasize the significance of leveraging advanced deep learning techniques, such as the transformer, in hydrological modeling and streamflow forecasting for effective water resource management and flood prediction.

Enhancing short-term streamflow prediction in the Haihe River Basin through integrated machine learning with Lasso.

With the widespread application of machine learning in various fields, enhancing its accuracy in hydrological forecasting has become a focal point of interest for hydrologists. This study, set against the backdrop of the Haihe River Basin, focuses on daily-scale streamflow and explores the application of the Lasso feature selection method alongside three machine learning models (long short-term memory, LSTM; transformer for time series, TTS; random forest, RF) in short-term streamflow prediction. Through comparative experiments, we found that the Lasso method significantly enhances the model's performance, with a respective increase in the generalization capabilities of the three models by 21, 12, and 14%. Among the selected features, lagged streamflow and precipitation play dominant roles, with streamflow closest to the prediction date consistently being the most crucial feature. In comparison to the TTS and RF models, the LSTM model demonstrates superior performance and generalization capabilities in streamflow prediction for 1-7 days, making it more suitable for practical applications in hydrological forecasting in the Haihe River Basin and similar regions. Overall, this study deepens our understanding of feature selection and machine learning models in hydrology, providing valuable insights for hydrological simulations under the influence of complex human activities.

Simple mathematical model for predicting COVID-19 outbreaks in Japan based on epidemic waves with a cyclical trend.

BACKGROUND: Several models have been used to predict outbreaks during the COVID-19 pandemic, with limited success. We developed a simple mathematical model to accurately predict future epidemic waves. METHODS: We used data from the Ministry of Health, Labour and Welfare of Japan for newly confirmed COVID-19 cases. COVID-19 case data were summarized as weekly data, and epidemic waves were visualized and identified. The periodicity of COVID-19 in each prefecture of Japan was confirmed using time-series analysis and the autocorrelation coefficient, which was used to investigate the longer-term pattern of COVID-19 cases. Outcomes using the autocorrelation coefficient were visualized via a correlogram to capture the periodicity of the data. An algorithm for a simple prediction model of the seventh COVID-19 wave in Japan comprised three steps. Step 1: machine learning techniques were used to depict the regression lines for each epidemic wave, denoting the "rising trend line"; Step 2: an exponential function with good fit was identified from data of rising straight lines up to the sixth wave, and the timing of the rise of the seventh wave and speed of its spread were calculated; Step 3: a logistic function was created using the values calculated in Step 2 as coefficients to predict the seventh wave. The accuracy of the model in predicting the seventh wave was confirmed using data up to the sixth wave. RESULTS: Up to March 31, 2023, the correlation coefficient value was approximately 0.5, indicating significant periodicity. The spread of COVID-19 in Japan was repeated in a cycle of approximately 140 days. Although there was a slight lag in the starting and peak times in our predicted seventh wave compared with the actual epidemic, our developed prediction model had a fairly high degree of accuracy. CONCLUSION: Our newly developed prediction model based on the rising trend line could predict COVID-19 outbreaks up to a few months in advance with high accuracy. The findings of the present study warrant further investigation regarding application to emerging infectious diseases other than COVID-19 in which the epidemic wave has high periodicity.

Short-term prediction of PM2.5 concentration by hybrid neural network based on sequence decomposition.

Accurate forecasting of PM2.5 concentrations serves as a critical tool for mitigating air pollution. This study introduces a novel hybrid prediction model, termed MIC-CEEMDAN-CNN-BiGRU, for short-term forecasting of PM2.5 concentrations using a 24-hour historical data window. Utilizing the Maximal Information Coefficient (MIC) for feature selection, the model integrates Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Convolutional Neural Network (CNN), and Bidirectional Recurrent Gated Neural Network (BiGRU) to optimize predictive accuracy. We used 2016 PM2.5 monitoring data from Beijing, China as the empirical basis of this study and compared the model with several deep learning frameworks. RNN, LSTM, GRU, and other hybrid models based on GRU, respectively. The experimental results show that the prediction results of the hybrid model proposed in this question are more accurate than those of other models, and the R2 of the hybrid model proposed in this paper improves the R2 by nearly 5 percentage points compared with that of the single model; reduces the MAE by nearly 5 percentage points; and reduces the RMSE by nearly 11 percentage points. The results show that the hybrid prediction model proposed in this study is more accurate than other models in predicting PM2.5.

Forecasting the spread of COVID-19 based on policy, vaccination, and Omicron data.

The COVID-19 pandemic caused by the novel SARS-COV-2 virus poses a great risk to the world. During the COVID-19 pandemic, observing and forecasting several important indicators of the epidemic (like new confirmed cases, new cases in intensive care unit, and new deaths for each day) helped prepare the appropriate response (e.g., creating additional intensive care unit beds, and implementing strict interventions). Various predictive models and predictor variables have been used to forecast these indicators. However, the impact of prediction models and predictor variables on forecasting performance has not been systematically well analyzed. Here, we compared the forecasting performance using a linear mixed model in terms of prediction models (mathematical, statistical, and AI/machine learning models) and predictor variables (vaccination rate, stringency index, and Omicron variant rate) for seven selected countries with the highest vaccination rates. We decided on our best models based on the Bayesian Information Criterion (BIC) and analyzed the significance of each predictor. Simple models were preferred. The selection of the best prediction models and the use of Omicron variant rate were considered essential in improving prediction accuracies. For the test data period before Omicron variant emergence, the selection of the best models was the most significant factor in improving prediction accuracy. For the test period after Omicron emergence, Omicron variant rate use was considered essential in deciding forecasting accuracy. For prediction models, ARIMA, lightGBM, and TSGLM generally performed well in both test periods. Linear mixed models with country as a random effect has proven that the choice of prediction models and the use of Omicron data was significant in determining forecasting accuracies for the highly vaccinated countries. Relatively simple models, fit with either prediction model or Omicron data, produced best results in enhancing forecasting accuracies with test data.

Early warning of systemic risk in stock market based on EEMD-LSTM.

With the increasing importance of the stock market, it is of great practical significance to accurately describe the systemic risk of the stock market and conduct more accurate early warning research on it. However, the existing research on the systemic risk of the stock market lacks multi-dimensional factors, and there is still room for improvement in the forecasting model. Therefore, to further measure the systemic risk profile of the Chinese stock market, establish a risk early warning system suitable for the Chinese stock market, and improve the risk management awareness of investors and regulators. This paper proposes a combination model of EEMD-LSTM, which can describe the complex nonlinear interaction. Firstly, 35 stock market systemic risk indicators are selected from the perspectives of macroeconomic operation, market cross-contagion and the stock market itself to build a comprehensive indicator system that conforms to the reality of China. Furthermore, based on TEI@I complex system methodology, an EEMD-LSTM model is proposed. The EEMD method is adopted to decompose the composite index sequence into intrinsic mode function components (IMF) of different scales and one trend term. Then the LSTM algorithm is used to predicted and model the decomposed sub-sequences. Finally, the forecast result of the composite index is obtained through integration. The empirical results show that the stock market systemic risk index constructed in this paper can effectively identify important risk events within the sample period. In addition, compared with the benchmark model, the EEMD-LSTM model constructed in this paper shows a stronger early warning ability for systemic financial risks in the stock market.

Uncertainty reduction for precipitation prediction in North America.

Large differences in projected future annual precipitation increases in North America exists across 27 CMIP6 models under four emission scenarios. These differences partly arise from weak representations of land-atmosphere interactions. Here we demonstrate an emergent constraint relationship between annual growth rates of future precipitation and growth rates of historical temperature. The original CMIP6 projections show 0.49% (SSP126), 0.98% (SSP245), 1.45% (SSP370) and 1.92% (SSP585) increases in precipitation per decade. Combining observed warming trends, the constrained results show that the best estimates of future precipitation increases are more likely to reach 0.40-0.48%, 0.83-0.93%, 1.29-1.45% and 1.70-1.87% respectively, implying an overestimated future precipitation increases across North America. The constrained results also are narrow the corresponding uncertainties (standard deviations) by 13.8-31.1%. The overestimated precipitation growth rates also reveal an overvalued annual growth rates in temperature (6.0-13.2% or 0.12-0.37°C) and in total evaporation (4.8-14.5%) by the original models' predictions. These findings highlight the important role of temperature for accurate climate predictions, which is important as temperature from current climate models' simulations often still have systematic errors.

High-frequency enhanced VaR: A robust univariate realized volatility model for diverse portfolios and market conditions.

In the field of financial risk management, the accuracy of portfolio Value-at-Risk (VaR) forecasts is of critical importance to both practitioners and academics. This study pioneers a comprehensive evaluation of a univariate model that leverages high-frequency intraday data to improve portfolio VaR forecasts, providing a novel contrast to both univariate and multivariate models based on daily data. Existing research has used such high-frequency-based univariate models for index portfolios, it has not adequately studied their robustness for portfolios with diverse risk profiles, particularly under changing market conditions, such as during crises. Our research fills this gap by proposing a refined univariate long-memory realized volatility model that incorporates realized variance and covariance metrics, eliminating the necessity for a parametric covariance matrix. This model captures the long-run dependencies inherent in the volatility process and provides a flexible alternative that can be paired with appropriate return innovation distributions for VaR estimation. Empirical analyses show that our methodology significantly outperforms traditional univariate and multivariate Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models in terms of forecasting accuracy while maintaining computational simplicity and ease of implementation. In particular, the inclusion of high-frequency data in univariate volatility models not only improves forecasting accuracy but also streamlines the complexity of portfolio risk assessment. This research extends the discourse between academic research and financial practice, highlighting the transformative impact of high-frequency data on risk management strategies within the financial sector.

Long-term water demand forecasting using artificial intelligence models in the Tuojiang River basin, China.

Accurate forecasts of water demand are a crucial factor in the strategic planning and judicious use of finite water resources within a region, underpinning sustainable socio-economic development. This study aims to compare the applicability of various artificial intelligence models for long-term water demand forecasting across different water use sectors. We utilized the Tuojiang River basin in Sichuan Province as our case study, comparing the performance of five artificial intelligence models: Genetic Algorithm optimized Back Propagation Neural Network (GA-BP), Extreme Learning Machine (ELM), Gaussian Process Regression (GPR), Support Vector Regression (SVR), and Random Forest (RF). These models were employed to predict water demand in the agricultural, industrial, domestic, and ecological sectors using actual water demand data and relevant influential factors from 2005 to 2020. Model performance was evaluated based on the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE), with the most effective model used for 2025 water demand projections for each sector within the study area. Our findings reveal that the GPR model demonstrated superior results in predicting water demand for the agricultural, domestic, and ecological sectors, attaining R2 values of 0.9811, 0.9338, and 0.9142 for the respective test sets. Also, the GA-BP model performed optimally in predicting industrial water demand, with an R2 of 0.8580. The identified optimal prediction model provides a useful tool for future long-term water demand forecasting, promoting sustainable water resource management.

Static graph approximations of dynamic contact networks for epidemic forecasting.

Epidemic modeling is essential in understanding the spread of infectious diseases like COVID-19 and devising effective intervention strategies to control them. Recently, network-based disease models have integrated traditional compartment-based modeling with real-world contact graphs and shown promising results. However, in an ongoing epidemic, future contact network patterns are not observed yet. To address this, we use aggregated static networks to approximate future contacts for disease modeling. The standard method in the literature concatenates all edges from a dynamic graph into one collapsed graph, called the full static graph. However, the full static graph often leads to severe overestimation of key epidemic characteristics. Therefore, we propose two novel static network approximation methods, DegMST and EdgeMST, designed to preserve the sparsity of real world contact network while remaining connected. DegMST and EdgeMST use the frequency of temporal edges and the node degrees respectively to preserve sparsity. Our analysis show that our models more closely resemble the network characteristics of the dynamic graph compared to the full static ones. Moreover, our analysis on seven real-world contact networks suggests EdgeMST yield more accurate estimations of disease dynamics for epidemic forecasting when compared to the standard full static method.

Dynamic hierarchical state space forecasting.

In this paper, we aim to both borrow information from existing units and incorporate the target unit's history data in time series forecasting. We consider a situation when we have time series data from multiple units that share similar patterns when aligned in terms of an internal time. The internal time is defined as an index according to evolving features of interest. When mapped back to the calendar time, these time series can span different time intervals that can include the future calendar time of the targeted unit, over which we can borrow the information from other units in forecasting the targeted unit. We first build a hierarchical state space model for the multiple time series data in terms of the internal time, where the shared components capture the similarities among different units while allowing for unit-specific deviations. A conditional state space model is then constructed to incorporate the information of existing units as the prior information in forecasting the targeted unit. By running the Kalman filtering based on the conditional state space model on the targeted unit, we incorporate both the information from the other units and the history of the targeted unit. The forecasts are then transformed from internal time back into calendar time for ease of interpretation. A simulation study is conducted to evaluate the finite sample performance. Forecasting state-level new COVID-19 cases in United States is used for illustration.

Machine learning in epidemiology: Neural networks forecasting of monkeypox cases.

This study integrates advanced machine learning techniques, namely Artificial Neural Networks, Long Short-Term Memory, and Gated Recurrent Unit models, to forecast monkeypox outbreaks in Canada, Spain, the USA, and Portugal. The research focuses on the effectiveness of these models in predicting the spread and severity of cases using data from June 3 to December 31, 2022, and evaluates them against test data from January 1 to February 7, 2023. The study highlights the potential of neural networks in epidemiology, especially concerning recent monkeypox outbreaks. It provides a comparative analysis of the models, emphasizing their capabilities in public health strategies. The research identifies optimal model configurations and underscores the efficiency of the Levenberg-Marquardt algorithm in training. The findings suggest that ANN models, particularly those with optimized Root Mean Squared Error, Mean Absolute Percentage Error, and the Coefficient of Determination values, are effective in infectious disease forecasting and can significantly enhance public health responses.

Challenges of COVID-19 Case Forecasting in the US, 2020-2021.

During the COVID-19 pandemic, forecasting COVID-19 trends to support planning and response was a priority for scientists and decision makers alike. In the United States, COVID-19 forecasting was coordinated by a large group of universities, companies, and government entities led by the Centers for Disease Control and Prevention and the US COVID-19 Forecast Hub (https://covid19forecasthub.org). We evaluated approximately 9.7 million forecasts of weekly state-level COVID-19 cases for predictions 1-4 weeks into the future submitted by 24 teams from August 2020 to December 2021. We assessed coverage of central prediction intervals and weighted interval scores (WIS), adjusting for missing forecasts relative to a baseline forecast, and used a Gaussian generalized estimating equation (GEE) model to evaluate differences in skill across epidemic phases that were defined by the effective reproduction number. Overall, we found high variation in skill across individual models, with ensemble-based forecasts outperforming other approaches. Forecast skill relative to the baseline was generally higher for larger jurisdictions (e.g., states compared to counties). Over time, forecasts generally performed worst in periods of rapid changes in reported cases (either in increasing or decreasing epidemic phases) with 95% prediction interval coverage dropping below 50% during the growth phases of the winter 2020, Delta, and Omicron waves. Ideally, case forecasts could serve as a leading indicator of changes in transmission dynamics. However, while most COVID-19 case forecasts outperformed a naïve baseline model, even the most accurate case forecasts were unreliable in key phases. Further research could improve forecasts of leading indicators, like COVID-19 cases, by leveraging additional real-time data, addressing performance across phases, improving the characterization of forecast confidence, and ensuring that forecasts were coherent across spatial scales. In the meantime, it is critical for forecast users to appreciate current limitations and use a broad set of indicators to inform pandemic-related decision making.

Spatio-temporal characterization of earthquake sequence parameters and forecasting of strong aftershocks in Xinjiang based on the ETAS model.

In this paper, the Integrated Nested Laplace Algorithm (INLA) is applied to the Epidemic Type Aftershock Sequence (ETAS) model, and the parameters of the ETAS model are obtained for the earthquake sequences active in different regions of Xinjiang. By analyzing the characteristics of the model parameters over time, the changes in each earthquake sequence are studied in more detail. The estimated values of the ETAS model parameters are used as inputs to forecast strong aftershocks in the next period. We find that there are significant differences in the aftershock triggering capacity and aftershock attenuation capacity of earthquake sequences in different seismic regions of Xinjiang. With different cutoff dates set, we observe the characteristics of the earthquake sequence parameters changing with time after the mainshock occurs, and the model parameters of the Ms7.3 earthquake sequence in Hotan region change significantly with time within 15 days after the earthquake. Compared with the MCMC algorithm, the ETAS model fitted with the INLA algorithm can forecast the number of earthquakes in the early period after the occurrence of strong aftershocks more effectively and can forecast the sudden occurrence time of earthquakes more accurately.

Advanced forecasting of COVID-19 epidemic: Leveraging ensemble models, advanced optimization, and decomposition techniques.

In the global effort to address the outbreak of the new coronavirus pneumonia (COVID-19) pandemic, accurate forecasting of epidemic patterns has become crucial for implementing successful interventions aimed at preventing and controlling the spread of the disease. The correct prediction of the course of COVID-19 outbreaks is a complex and challenging task, mainly because of the significant volatility in the data series related to COVID-19. Previous studies have been limited by the exclusive use of individual forecasting techniques in epidemic modeling, disregarding the integration of diverse prediction procedures. The lack of attention to detail in this situation can yield worse-than-ideal results. Consequently, this study introduces a novel ensemble framework that integrates three machine learning methods (kernel ridge regression (KRidge), Deep random vector functional link (dRVFL), and ridge regression) within a linear relationship (L-KRidge-dRVFL-Ridge). The optimization of this framework is accomplished through a distinctive approach, specifically adaptive differential evolution and particle swarm optimization (A-DEPSO). Moreover, an effective decomposition method, known as time-varying filter empirical mode decomposition (TVF-EMD), is employed to decompose the input variables. A feature selection technique, specifically using the light gradient boosting machine (LGBM), is also implemented to extract the most influential input variables. The daily datasets of COVID-19 collected from two countries, namely Italy and Poland, were used as the experimental examples. Additionally, all models are implemented to forecast COVID-19 at two-time horizons: 10- and 14-day ahead (t+10 and t+14). According to the results, the proposed model can yield higher correlation coefficient (R) for both case studies: Italy (t+10 = 0.965, t+14 = 0.961) and Poland (t+10 = 0.952, t+14 = 0.940) than the other models. The experimental results demonstrate that the model suggested in this paper has outstanding results in various kinds of complex epidemic prediction situations. The proposed ensemble model demonstrates exceptional accuracy and resilience, outperforming all similar models in terms of efficacy.

Demand forecasting for platelet usage: From univariate time series to multivariable models.

Platelet products are both expensive and have very short shelf lives. As usage rates for platelets are highly variable, the effective management of platelet demand and supply is very important yet challenging. The primary goal of this paper is to present an efficient forecasting model for platelet demand at Canadian Blood Services (CBS). To accomplish this goal, five different demand forecasting methods, ARIMA (Auto Regressive Integrated Moving Average), Prophet, lasso regression (least absolute shrinkage and selection operator), random forest, and LSTM (Long Short-Term Memory) networks are utilized and evaluated via a rolling window method. We use a large clinical dataset for a centralized blood distribution centre for four hospitals in Hamilton, Ontario, spanning from 2010 to 2018 and consisting of daily platelet transfusions along with information such as the product specifications, the recipients' characteristics, and the recipients' laboratory test results. This study is the first to utilize different methods from statistical time series models to data-driven regression and machine learning techniques for platelet transfusion using clinical predictors and with different amounts of data. We find that the multivariable approaches have the highest accuracy in general, however, if sufficient data are available, a simpler time series approach appears to be sufficient. We also comment on the approach to choose predictors for the multivariable models.

Improving species distribution forecasts by measuring and communicating uncertainty: An invasive species case study.

Forecasting invasion risk under future climate conditions is critical for the effective management of invasive species, and species distribution models (SDMs) are key tools for doing so. However, SDM-based forecasts are uncertain, especially when correlative statistical models extrapolate to nonanalog environmental domains, such as future climate conditions. Different assumptions about the functional form of the temperature-suitability relationship can impact predicted habitat suitability under novel conditions. Hence, methods to understand the sources of uncertainty are critical when applying SDMs. Here, we use high-resolution predictions of lake water temperatures to project changes in habitat suitability under future climate conditions for an invasive macrophyte (Myriophyllym spicatum). Future suitability was predicted using five global circulation models and three statistical models that assumed different species-temperature functional responses. The suitability of lakes for M. spicatum was overall predicted to increase under future climate conditions, but the magnitude and direction of change in suitability varied greatly among lakes. Variability was most pronounced for lakes under nonanalog temperature conditions, indicating that predictions for these lakes remained highly uncertain. Integrating predictions from SDMs that differ in their species-environment response function, while explicitly quantifying uncertainty across analog and nonanalog domains, can provide a more robust and useful approach to forecasting invasive species distribution under climate change.

Causality-driven multivariate stock movement forecasting.

Our study aims to investigate the interdependence between international stock markets and sentiments from financial news in stock forecasting. We adopt the Temporal Fusion Transformers (TFT) to incorporate intra and inter-market correlations and the interaction between the information flow, i.e. causality, of financial news sentiment and the dynamics of the stock market. The current study distinguishes itself from existing research by adopting Dynamic Transfer Entropy (DTE) to establish an accurate information flow propagation between stock and sentiments. DTE has the advantage of providing time series that mine information flow propagation paths between certain parts of the time series, highlighting marginal events such as spikes or sudden jumps, which are crucial in financial time series. The proposed methodological approach involves the following elements: a FinBERT-based textual analysis of financial news articles to extract sentiment time series, the use of the Transfer Entropy and corresponding heat maps to analyze the net information flows, the calculation of the DTE time series, which are considered as co-occurring covariates of stock Price, and TFT-based stock forecasting. The Dow Jones Industrial Average index of 13 countries, along with daily financial news data obtained through the New York Times API, are used to demonstrate the validity and superiority of the proposed DTE-based causality method along with TFT for accurate stock Price and Return forecasting compared to state-of-the-art time series forecasting methods.