Mathematical Model For Prediction Research Articles

Acceleration analysis and unsteady mathematical prediction of flame spread over thermal insulation layer in u-shaped building façade fires

As one of the most commonly used energy-saving methods in buildings, thermal insulation layer is widely used in building façade and it also endangers the human safety in buildings due to its combustibility. U-shaped facade is a commonly used structure in high-rise buildings since it could improve both the light and ventilation conditions indoors. This paper investigated the flame acceleration over the thermal insulation in u-shaped building facade fires. It was found that the flame spread rate over u-shaped facade had an exponential growth with time as the direction of preheating zone location is the same direction of the heat transfer from the pyrolysis zone. The air entrainment and the upward induced airflow played an important role in the acceleration. As the side wall length increased or the back wall length decreased, the flame spread rate accelerated more rapidly. Furthermore, a mathematical prediction model of the unsteady flame spread rate over u-shaped structure façade was established and validated through experiments. This study provides technical guidance for the fire safety design of building facade.

Mathematical Modeling and Optimal Stopping Theory-Based Extra Layers for 30-Day Rate Risk Prediction of Readmission to Intensive Care Units

Mathematical Modeling and Optimal Stopping Theory-Based Extra Layers for 30-Day Rate Risk Prediction of Readmission to Intensive Care Units

Iontophoresis-coupled rapidly dissolving polymeric microneedle patch of naloxone for its enhanced transdermal delivery

The transdermal delivery of naloxone for opioid overdose emergency purposes is a challenge due to its poor rate of diffusion through the layers of skin. This results in delayed delivery of an insufficient amount of the drug within minimal time as is desired to save lives. The ability of dissolving polymeric microneedles to shorten the lag time significantly has been explored and shown to have prospects in terms of the transdermal delivery of naloxone. This is an option that offers critical advantages to the ongoing opioid crisis, including ease of distribution and easy administration, with little to no need for intervention by clinicians. Nonetheless, this approach by itself needs augmentation to meet pharmacokinetic delivery attributes desired for a viable clinical alternative to existing market dosage forms. In this study, we report the success of an optimized iontophoresis-coupled naloxone loaded dissolving microneedle patch which had facilitated a 12- fold increase in average cumulative permeation and a 6-fold increase in drug flux over a conventional dissolving microneedle patch within 60 min of application (p < 0.05). This translates to a 30 % decrease in dose requirement in a mechanistically predicted microneedle patch established to be able to achieve the desired early plasma concentration time profile needed in an opioid overdose emergency. Applying a predictive mathematical model, we describe an iontophoresis-coupled microneedle patch design capable of meeting the desired pharmacokinetic profile for a viable naloxone delivery form through skin.

Statistical and mathematical preliminary interpretation of mechanical test results on sands grouted with colloidal silica

ABSTRACT Colloidal silica is a relatively new grouting low-carbon material used in soil improvement projects. A series of mechanical tests on a sand with different solid contents of the binder, i.e. 40, 30 and 20% solid content have been performed. Unconfined compressive strength at 7, 28 and 56 days, shear tests and permeability tests at 7 days were assessed. A statistical interpretation of these data has been performed and values were interpreted. A mathematical prediction model was suggested to estimate the mechanical strength of the grouted sand as the dilution grade varies. Furthermore, some considerations useful for geotechnical design on the evolution over time of the mechanical characteristics of the grouted sands have been carried out. Results show, from a statistical and mathematical view, that colloidal silica is a promising binder for ground improvement applications.

Optimization of LiF dissolution with Al2(SO4)3 and its application to lithium extraction by fluorination of α-spodumene

Numerous Li extraction methods from minerals and e-waste have been reported in the literature. Among them, direct fluorination processes appear to be a viable alternative due to their high lithium extraction efficiencies (>90%) as LiF. However, a drawback is the low water solubility of LiF, which requires acids for its separation and to obtain other commercial lithium salts. An interesting alternative for dissolving salts with low solubility is through the formation of coordination complexes. In this case, aluminum forms highly stable soluble complexes with the F− anion, such as AlF2+, AlF2+, AlF3, AlF4−, AlF52−, AlF63−.This study proposes an acid-free LiF dissolution methodology using aluminum sulfate as a leaching agent. The LiF dissolution was modeled and optimized using Response Surface Methodology (RSM). The investigated operating parameters for LiF dissolution were the solid/liquid ratio (A), reaction temperature (B), and leaching time (C). Thus, a predictive mathematical model was successfully optimized (R2 = 0.9445). The results indicated that the S/L ratio negatively influences the dissolution of LiF, while temperature and time have a positive effect. The LiF dissolutions of 90 ± 3% were achieved with a leaching time of 31 min, a S/L ratio of 20 g/mL, and a temperature of 45 °C.

Test Method for Rapid Prediction of Steady-State Temperature of Outer Rings of Bearings under Grease Lubrication Conditions

Temperature has a great influence on the stability of bearing performance. For the study of bearing steady-state temperature, this paper proposes a test method to quickly predict the steady-state temperature of the outer ring of a bearing, which solves the problems in traditional theoretical calculations and simulation analysis methods such as the large number of calculations, complex models, and large errors. Firstly, a mathematical prediction model is established according to the bearing temperature-rise law; then, a bearing steady-state temperature detection device is designed; and finally, the prediction model parameters are solved according to the experimental results, and experimental verification is carried out. It is shown that the prediction model has high accuracy under different load and speed conditions, and the error between the predicted steady-state temperature and the tested steady-state temperature is less than 0.7 °C. This prediction method reduces the single test time of the same speed to 60 min, which greatly improves the efficiency of the temperature detection test. The steady-state temperature model has important theoretical significance in guiding the study of the limiting speed of bearings.

Radiation Dose-Volume-Response Relationships for Adverse Events in Childhood Cancer Survivors: Introduction to the Scientific Issues in PENTEC

At its very core, radiation oncology involves a trade-off between the benefits and risks of exposing tumors and normal tissue to relatively high doses of ionizing radiation. This trade-off is particularly critical in childhood cancer survivors (CCS), in whom both benefits and risks can be hugely consequential due to the long life expectancy if the primary cancer is controlled. Estimating the normal tissue-related risks of a specific radiation therapy plan in an individual patient relies on predictive mathematical modeling of empirical data on adverse events. The Pediatric Normal-Tissue Effects in the Clinic (PENTEC) collaborative network was formed to summarize and, when possible, to synthesize dose-volume-response relationships for a range of adverse events incident in CCS based on the literature. Normal-tissue clinical radiation biology in children is particularly challenging for many reasons: (1) Childhood malignancies are relatively uncommon-constituting approximately 1% of new incident cancers in the United States-and biologically heterogeneous, leading to many small series in the literature and large variability within and between series. This creates challenges in synthesizing data across series. (2) CCS are at an elevated risk for a range of adverse health events that are not specific to radiation therapy. Thus, excess relative or absolute risk compared with a reference population becomes the appropriate metric. (3) Various study designs and quantities to express risk are found in the literature, and these are summarized. (4) Adverse effects in CCS often occur 30, 50, or more years after therapy. This limits the information content of series with even very extended follow-up, and lifetime risk estimates are typically extrapolations that become dependent on the mathematical model used. (5) The long latent period means that retrospective dosimetry is required, as individual computed tomography-based radiation therapy plans gradually became available after 1980. (6) Many individual patient-level factors affect outcomes, including age at exposure, attained age, lifestyle exposures, health behaviors, other treatment modalities, dose, fractionation, and dose distribution. (7) Prospective databases with individual patient-level data and radiation dosimetry are being built and will facilitate advances in dose-volume-response modeling. We discuss these challenges and attempts to overcome them in the setting of PENTEC.

Preclinical assessment of a mathematical model for ablation zone prediction in thyroid laser ablation

Preclinical assessment of a mathematical model for ablation zone prediction in thyroid laser ablation

Machine-learning and mechanistic modeling of metastatic breast cancer after neoadjuvant treatment.

Clinical trials involving systemic neoadjuvant treatments in breast cancer aim to shrink tumors before surgery while simultaneously allowing for controlled evaluation of biomarkers, toxicity, and suppression of distant (occult) metastatic disease. Yet neoadjuvant clinical trials are rarely preceded by preclinical testing involving neoadjuvant treatment, surgery, and post-surgery monitoring of the disease. Here we used a mouse model of spontaneous metastasis occurring after surgical removal of orthotopically implanted primary tumors to develop a predictive mathematical model of neoadjuvant treatment response to sunitinib, a receptor tyrosine kinase inhibitor (RTKI). Treatment outcomes were used to validate a novel mathematical kinetics-pharmacodynamics model predictive of perioperative disease progression. Longitudinal measurements of presurgical primary tumor size and postsurgical metastatic burden were compiled using 128 mice receiving variable neoadjuvant treatment doses and schedules (released publicly at https://zenodo.org/records/10607753). A non-linear mixed-effects modeling approach quantified inter-animal variabilities in metastatic dynamics and survival, and machine-learning algorithms were applied to investigate the significance of several biomarkers at resection as predictors of individual kinetics. Biomarkers included circulating tumor- and immune-based cells (circulating tumor cells and myeloid-derived suppressor cells) as well as immunohistochemical tumor proteins (CD31 and Ki67). Our computational simulations show that neoadjuvant RTKI treatment inhibits primary tumor growth but has little efficacy in preventing (micro)-metastatic disease progression after surgery and treatment cessation. Machine learning algorithms that included support vector machines, random forests, and artificial neural networks, confirmed a lack of definitive biomarkers, which shows the value of preclinical modeling studies to identify potential failures that should be avoided clinically.

Characterisation of the surface growth of Mucor circinelloides in cheese agar media using predictive mathematical models

The main objective of this work was to characterise the mycelial growth of Mucor circinelloides, one of the fungal contaminants that appear frequently in the artisan cheese production environment. The study uses primary Baranyi and Huang models to compare their parameters and predict M. circinelloides on cheese-based medium (CBA) under diverse environmental conditions (temperature range from 6 to 37 °C and 0 and 1 % NaCl concentration). However, the Baranyi model consistently estimated longer lag phases and higher surface growth rates (sgr) than the Huang model; both models showed adequate best-fit performance (exactly with the mean coefficient of determination R2 = (0.993 ± 0.020 × 10−1). The groups of primary growth parameters were analysed against temperature using the cardinal model (CM) with the following main outputs. The optimal surface growth rates (sgropt) on CBA were 6.8 and 6.5 mm/d calculated with the Baranyi and Huang models, respectively. They were reduced by approximately 46 % on the surface of the agar medium when 1 % NaCl was added. Topt was estimated in a very narrow range of 32.1–32.5 °C from both primary sgr data sets (0 % and 1 % NaCl). Similarly, Tmax values of 37.2 °C and 37.3 °C were estimated for the Baranyi and Huang models, respectively; however, they decreased at 2 °C in CBA with 1 % NaCl (Tmax = 35.1 °C). The application of CM for sgr provided an estimation of the parameter Tmin with negative values that are considered only as a theoretical output. The results provide insight into the modelling and prediction of fungi growth as a function of time and salt concentration, including the times to detect visible mycelial growth of Mucor circinelloides. The mere quantification of this phenomenon can be useful for practice. Adjusting the frequency of the cheese surface washing step with a salt solution at the early stage of ripening properly can prevent the growth of not only fast fungal growers.

Engulfing behavior of vapor bubbles in downward facing heated surface boiling

Boiling of the coolant at the hot surface provides relatively better cooling by absorbing latent heat along with convection heat transfer as compared to heat transfer under single-phase conditions. In boiling, the orientation of heated surface also plays a crucial role. Downward facing boiling is complex than upward facing boiling, as the detachment of the bubble inhibited due to the heater surface orientation. Consequently, the bubble residence time and interaction with other bubbles are different in such boiling conditions. Our experiments on a large downward facing flat surface (100 × 400 mm2) revealed unexplored boiling phenomena. The boiling process is dominated by a complex engulfing phenomenon, which is rarely reported in the past. The engulfing phenomena have been captured using high-speed photography, wherein, at low heat fluxes, it is observed that larger bubbles engulf small bubbles by opening their mouth and swallowing the small bubbles. However, at higher heat fluxes, this phenomenon disappears. A larger vapor blanket is formed due to engulfing of bubbles, which may lead to departure from nucleate boiling. This engulfing behavior depends on the heat flux and subcooling. With the increase in heat flux, it is found that the rate of vapor engulfing increases. We have attempted to explain the science behind such engulfing phenomenon based on the capillary pressure difference. These results are consistent at various subcooling. This research provides new insights into nucleate boiling and may help in developing advanced mathematical models for accurate heat transfer prediction on downward facing nucleate boiling.

Quantifying cell cycle regulation by tissue crowding

The spatiotemporal coordination and regulation of cell proliferation is fundamental in many aspects of development and tissue maintenance. Cells have the ability to adapt their division rates in response to mechanical constraints, yet we do not fully understand how cell proliferation regulation impacts cell migration phenomena. Here, we present a minimal continuum model of cell migration with cell cycle dynamics, which includes density-dependent effects and hence can account for cell proliferation regulation. By combining minimal mathematical modeling, Bayesian inference, and recent experimental data, we quantify the impact of tissue crowding across different cell cycle stages in epithelial tissue expansion experiments. Our model suggests that cells sense local density and adapt cell cycle progression in response, during G1 and the combined S/G2/M phases, providing an explicit relationship between each cell-cycle-stage duration and local tissue density, which is consistent with several experimental observations. Finally, we compare our mathematical model’s predictions to different experiments studying cell cycle regulation and present a quantitative analysis on the impact of density-dependent regulation on cell migration patterns. Our work presents a systematic approach for investigating and analyzing cell cycle data, providing mechanistic insights into how individual cells regulate proliferation, based on population-based experimental measurements.

Establishment of a Reference Evapotranspiration Forecasting Model Based on Machine Learning

Water scarcity is a global problem. Deficit irrigation (DI) reduces evapotranspiration, improving water efficiency in agriculture. Reference evapotranspiration (ET0) is an important factor in determining DI. ET0 forecasting predicts field water consumption and enables proactive irrigation decisions, offering guidance for water resource management. However, implementation of ET0 forecasting faces challenges due to complex calculations and extensive meteorological data requirements. This project aims to develop a machine learning system for ET0 forecasting. The project involves studying ET0 methods and identifying required meteorological parameters. Historical meteorological data and weather forecasts were obtained from meteorological websites and analyzed for accuracy after preprocessing. A machine learning-based model was created to forecast reference crop evapotranspiration. The model’s input parameters were selected through path analysis before it was optimized using Bayesian optimization to reduce overfitting and improve accuracy. Three forecasting models were developed: one based on historical meteorological data, one based on weather forecasts, and one that corrects the weather forecasts. All three models achieved good accuracy, with root mean square errors ranging from 0.52 to 0.81 mm/day. Among them, the model based on weather forecast had the highest accuracy; the RMSE six days before the forecast period was between 0.52 and 0.75 mm/day, and the RMSE on the seventh day of the forecast period was 1.12 mm/day. In summary, this project has established a mathematical model of ET0 prediction based on machine learning, which can achieve more accurate predictions for within a few days.

Advanced Detection of Failed LEDs in a Short Circuit for Automotive Lighting Applications.

This paper addresses the issue of LED short-circuit fault detection in signaling and lighting systems in the automotive industry. The conventional diagnostic method commonly implemented in newer vehicles relies on measuring the voltage drop across different LED branches and comparing it with threshold values indicating faults caused by open circuits or LED short circuits. With this algorithm, detecting cases of a few LEDs short-circuited within a branch, particularly a single malfunctioning LED, is particularly challenging. In this work, two easily implementable algorithms are proposed to address this issue within the vehicle's control unit. One is based on a mathematical prediction model, while the other utilizes a neural network. The results obtained offer a 100% LED short-circuit fault detection rate in the majority of analyzed cases, representing a significant improvement over the conventional method, even in scenarios involving a single malfunctioning LED within a branch. Additionally, the neural network-based model can accurately predict the number of failed LEDs.

Controlling Fluorescence Wavelength in the Synthesis of TGA-Capped CdTe Quantum Dots

Quantum dots (QDs) are semiconductor materials, with a size range between 1–10 nm, showcasing unique size-dependent physical and chemical properties. Such properties have potentiated their use in areas like medical imaging and biosensing. Herein, we present an open-air approach for synthesis of QDs, reducing the need for controllable atmospheric conditions. Furthermore, we present a predictive mathematical model for maximum emission wavelength (λmax) control. Through a straightforward microwave-based aqueous synthesis of TGA-CdTe QDs, we investigated the influence of time, temperature, and Te:Cd and TGA:Cd molar ratios on λmax, using a chemometric experimental design approach. CdTe-QDs were characterized by UV-Vis and fluorescence spectroscopies. Additionally, Fourier-Transform Infrared spectroscopy, X-ray photoelectron spectroscopy, Transmission Electron Microscopy, and Energy Dispersive X-ray were conducted. Stable QDs with fluorescence ranging from green to red (527.6 nm to 629.2 nm) were obtained. A statistical analysis of the results revealed that time and temperature were the most significant factors influencing λmax. After fine-tuning the variables, a mathematical model with 97.7% of prediction accurately forecasted experimental conditions for synthesizing TGA-CdTe QDs at predefined λmax. Stability tests demonstrated that the QDs retained their optical characteristics for over a month at 4 °C, facilitating diverse applications.

Predictive Models of Life Span in Old Female Mice Based on Immune, Redox, and Behavioral Parameters.

The development of mathematical models capable of predicting the lifespan of animals is growing. However, there are no studies that compare the predictive power of different sets of parameters depending on the age of the animals. The aim of the present study is to test whether mathematical models for life span prediction developed in adult female mice based on immune, redox, and behavioral parameters can predict life span in old animals and to develop new models in old mice. For this purpose, 29 variables, including parameters of immune function, redox state, and behavioral ones, were evaluated in old female Swiss mice (80 ± 4 weeks). Life span was registered when they died naturally. Firstly, we observed that the models developed in adults were not able to accurately predict the life span of old mice. Therefore, the immunity (adjusted R2 = 73.6%), redox (adjusted R2 = 46.5%), immunity-redox (adjusted R2 = 96.4%), and behavioral (adjusted R2 = 67.9%) models were developed in old age. Finally, the models were validated in another batch of mice. The developed models in old mice show certain similarities to those in adults but include different immune, redox, and behavioral markers, which highlights the importance of age in the prediction of life span.

Modelling the weld cladding process to predict weld clad position and shape error

Wire arc additive manufacturing (WAAM) is one of the most productive metal additive manufacturing methods. One of its most promising applications holds in the manufacturing of difficult-to-cut materials where production costs can be reduced with minimizing the time of machining and total tool costs. To develop a correct WAAM, technological processes for manufacturing complex-shaped components welding torch path corrections and welding power corrections have to be made especially in critical sections such as corners and sharp edges. A predictive mathematical model of the material cladding during the WAAM process has been developed for the purposes of generating an optimal toolpath of the WAAM clads. This predictive mathematical model is simplified to reflect the important physical phenomena in the weld pool but also to optimize computing time. In this paper, the principle of the mathematical model is described, and its functionality is verified by the welding experiments with five different welding power settings. For the initial calibration of the model parameters single straight-line weld clads with 5 different welding power settings (wire feeds) ranging from 5.0 to 8.6 m/min were investigated. 3D scans of these welded samples are used for the verification. With the calibrated simulation model, it was possible to predict the precise shape with a maximum deviation circa 0.20 mm. The start portions of the weld clads seem more complex having the deviation circa 0.30 mm. These are valuable results as the WAAM technology is generally considered to be reasonably rough.

Mathematical modeling of the creation process and aging of polymer composite materials

Based on the analysis of the literature on the possibility of using neural networks to create new materials with high functional properties, the article considers a solution to the problem of determining the operational stability of polymeric composite materials by creating physical and chemically sound mathematical prediction models. Epoxy resins of the UP-637 and EA brands with an isophorone diamine hardener were chosen as the matrix of the model composite material, and oligobutadiene rubber of the SKN-10 KTR brand was chosen as the modifier. It justifies directions of work necessary for development of new materials creation methodology with optimal characteristics, building a model for changing the properties of materials at variation of composition and implementation of full-scale mathematical modeling of physical and chemical processes of polymer composite materials aging at changing level and time of climatic factors influence. Verification of the obtained dependence of service characteristics on the composition of the material and the level of influencing climatic factors was carried out on the basis of data from full-scale tests in a temperate climate. The proposed methodology for modelling the properties of polymer composite materials will reduce the development time of new materials and allow creation of polymer composites based on epoxy resin containing fillers of various natures (carbon, mineral and polymer) with high performance parameters.

Effect of climate and wood type on elastic modulus of heat-treated wood and its optimization by the Taguchi method

Wood, as the oldest building material, provides some of the basic needs of human beings, including shelter and protection. Wood is used in exterior cladding, carrier systems, joinery, ceiling-floor coverings, windows, doors, and furniture production. When wooden material is exposed to external weather conditions, due to its hygroscopic structure, its physical and mechanical properties deteriorate from exposure to moisture, temperature, and biological organisms. The bending modulus of elasticity of Scots pine (Pinus sylvestris L.), oak (Quercus petraea L.), and chestnut (Castanea sativa M.) wood that was tannin-impregnated and heat-treated at 160 °C, was investigated using Taguchi L9 (33). The sequence was optimized. After heat treatment, the carrier elements were subjected to artificial climate conditions. In the optimization of the data obtained, it was understood that the highest impact factor was the tree type. In contrast, the climate on the elastic modulus was the lowest impact factor. In Taguchi analysis, a mathematical prediction model was created using actual and predicted data using the S/N ratio’s biggest-best equation. The R2 of the model can be predicted with an accuracy rate of 98.6%.

Diagnostic and prognostic markers of morphofunctional heart state impairment and long-term persistence of heart failure in patients with myocarditis

The problem of myocarditis, has gained special relevance in recent years, therefore, the search for new diagnostic and prognostic markers of the disease unfavorable course is expedient for the timely appointment of optimal drug therapy, strengthening of regimen measures and adequate monitoring of the patient’s clinical condition. The purpose of the study: to establish laboratory and instrumental markers of morphofunctional heart state impairment and to develop a mathematical model for early prediction of long-term heart failure persistence in patients with myocarditis. We included 80 patients with acute myocarditis with a severe course and reduced left ventricular ejection fraction (LVEF) – ≤40 %. Assessment of laboratory and instrumental indicators was carried out in the 1st month from the onset of symptoms, after 6 and after 12 months of observation. All patients underwent for immunological studies, 24-hour ECG monitoring, echocardiography with speckle-tracking and cardiac magnetic resonance imaging. After 12 months of follow-up frequency of adverse cardiovascular events (ACE) was assessed. Statistical processing included Student’s t-test for comparison of mean values, binary logistic regression and ROC analysis, discriminant analysis. A set of morphofunctional instrumental indicators determined during the 1st month from the onset of myocarditis, which can serve as predictors of cardiovascular events during the next 12 months, was established: left ventricular ejection fraction ≤30 %; indicator of longitudinal global strain ≤7.0 %; the presence of paroxysms of non-sustained ventricular tachycardia; the presence of inflammatory changes in ≥6 segments and delayed contrast enhancement in ≥5 segments of the left ventricle. A mathematical model has been created, with the help of which it is possible to predict the adverse course of the disease with long-term (at least 12 months) persistence of heart failure already within the 1st month from the onset of myocarditis.