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PREMISE: Molecular studies based on chloroplast markers have questioned the monophyly of the fern genus Pecluma (Polypodioideae, Polypodiaceae), which has several species of Polypodium nested within it. We explored the delimitation of Pecluma and its biogeographic pattern by evaluating the phylogenetic position of four Polypodium species not sequenced thus far and integrating the first fossil evidence of Pecluma. METHODS: Using herbarium material, we applied a genome-skimming approach to obtain a phylogenetic hypothesis of Polypodioideae; assessed the combination of character states observed in the fossil from Miocene Dominican amber using a previously published phylogeny of Polypodioideae based on four plastid markers as framework; calculated divergence times; and conducted an ancestral area estimation. RESULTS: Within Polypodioideae, Pecluma was recovered as sister to Phlebodium. Three of the newly sequenced species-Polypodium otites, P. pinnatissimum, and P. ursipes-were recovered with maximum support within the Pecluma clade, whereas P. christensenii remained within Polypodium. The closest combination of character states of the fossil was found within Pecluma. Our biogeographic analyses suggest an Eocene origin of the genus in South America, with several subsequent Oligocene and Miocene colonization events to Mexico-Central America and to the West Indies. CONCLUSIONS: Although the circumscription of Pecluma is still challenging, our results elucidate the origin and age of the genus. The newly described fossil, Pecluma hispaniolae sp. nov., supports the hypothesis that the epiphytic communities of the Greater Antilles exhibit a constant generic composition since the Miocene. We propose new combinations (Pecluma otites, Pecluma pinnatissima, and Pecluma ursipes) to accommodate three species previously classified in Polypodium.

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SUMMARY: The present study aimed to investigate the utility of the proximal femur in the forensic age estimation by assessing changes in bone densities through radiographs. Using Otsu's threshold, bone density was quantified by counting all white pixel values within selected regions of interest, which include femoral head (FH), femoral neck (FN), Ward's triangle (WT), and greater trochanter (GT) from 354 left femora of Northern Thai descent. The pixel width of medullary cavity (MC) was also estimated. Furthermore, the study evaluated the performance of linear regression (LR) models for age estimation from radiographic images of proximal femora. Negative correlations were observed between FH, FN, WT, and GT pixel intensity with the age-at-death of the samples, with females exhibiting stronger correlations than males. Moreover, a positive correlation was found between age and MC width in female samples, while male MC widths did not show any relationship with increasing age. The results showed a slight difference between the LR model applied to both sexes, which integrated all variables, and the alternative configuration that only utilized relevant attributes. Both models exhibited similar performance, with a narrow range of root mean square error (RMSE) values, ranging from 12.67 to 12.71 years, and a correlation coefficient range of 0.51 to 0.52. For females, the LR model with FN and WT as selected attributes (RMSE = 11.85 years, correlation coefficient = 0.65) performed decently, while for males, the LR model with all variables showed RMSE of 12.52 years and correlation coefficient of 0.46. This study showcased the potential application of pixel intensity in predicting age.

El presente estudio tuvo como objetivo investigar la utilidad del fémur proximal en la estimación forense de la edad mediante la evaluación de cambios en las densidades óseas a través de radiografías. Utilizando el umbral de Otsu, la densidad ósea se cuantificó contando todos los valores de pixeles blancos dentro de regiones de interés seleccionadas, que incluyen la cabeza femoral (CF), el cuello femoral (CF), el triángulo de Ward (WT) y el trocánter mayor (TM) de 354 fémures izquierdos de ascendencia del norte de Tailandia. También se estimó el ancho de pixeles de la cavidad medular (CM). Además, el estudio evaluó el rendimiento de modelos de regresión lineal (RL) para la estimación de la edad a partir de imágenes radiográficas de fémur proximal. Se observaron correlaciones negativas entre la intensidad de los pixeles CF, CF, WT y TM con la edad de muerte, y las mujeres exhibieron correlaciones más fuertes que los hombres. Además, se encontró una correlación positiva entre la edad y el ancho del CM en muestras de mujeres, mientras que el ancho del CM del hombre no mostró ninguna relación con el aumento de la edad. Los resultados mostraron una ligera diferencia entre el modelo RL aplicado a ambos sexos, que integraba todas las variables, y la configuración alternativa que sólo utilizaba atributos relevantes. Ambos modelos mostraron un rendimiento similar, con un rango estrecho de valores del error cuadrático medio (RMSE), que oscilaba entre 12,67 y 12,71 años, y un rango de coeficiente de correlación de 0,51 a 0,52. Para las mujeres, el modelo RL con CF y WT como atributos seleccionados (RMSE = 11,85 años, coeficiente de correlación = 0,65) tuvo un desempeño satisfactorio, mientras que para los hombres, el modelo RL con todas las variables mostró un RMSE de 12,52 años y un coeficiente de correlación de 0,46. Este estudio mostró la posible aplicación de la intensidad de los pixeles en la predicción de la edad.

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While the estimate of hospital costs concerns the past, its planning focuses on the future. However, in many low and middle-income countries, public hospitals do not have robust accounting health systems to evaluate and project their expenses. In Brazil, public hospitals are funded based on government estimates of available hospital infrastructure, historical expenditures and population needs. However, these pieces of information are not always readily available for all hospitals. To solve this challenge, we propose a flexible simulation-based optimisation algorithm that integrates this dual task: estimating and planning hospital costs. The method was applied to a network of 17 public hospitals in Brazil to produce the estimates. Setting the model parameters for population needs and future hospital infrastructure can be used as a cost-projection tool for divestment, maintenance, or investment. Results show that the method can aid health managers in hospitals' global budgeting and policymakers in improving fairness in hospitals' financing.

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In this study, a model was developed to simulate the effect of temperature ( T $T$ ) and initial substrate concentration ( S 0 ${S}_{0}$ ) on the ethanol concentration limit ( P max ${P}_{\max }$ ) using the yeast Saccharomyces cerevisiae. To achieve this, regressions were performed using data provided by other authors for P max ${P}_{\max }$ to establish a model dependent on T $T$ and S 0 ${S}_{0}$ capable of predicting results with statistical significance. After constructing the model, a response surface was generated to determine the conditions where P max ${P}_{\max }$ reaches higher values: temperatures between 28°C and 32°C and an initial substrate concentration around 200 g/L. Thus, the proposed model is consistent with the observations that increasing temperatures decrease the ethanol concentration obtained, and substrate concentrations above 200 g/L lead to a reduction in ethanol concentration even at low temperatures such as 28°C.

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This paper aims to evaluate the statistical association between exposure to air pollution and forced expiratory volume in the first second (FEV1) in both asthmatic and non-asthmatic children and teenagers, in which the response variable FEV1 was repeatedly measured on a monthly basis, characterizing a longitudinal experiment. Due to the nature of the data, an robust linear mixed model (RLMM), combined with a robust principal component analysis (RPCA), is proposed to handle the multicollinearity among the covariates and the impact of extreme observations (high levels of air contaminants) on the estimates. The Huber and Tukey loss functions are considered to obtain robust estimators of the parameters in the linear mixed model (LMM). A finite sample size investigation is conducted under the scenario where the covariates follow linear time series models with and without additive outliers (AO). The impact of the time-correlation and the outliers on the estimates of the fixed effect parameters in the LMM is investigated. In the real data analysis, the robust model strategy evidenced that RPCA exhibits three principal component (PC), mainly related to relative humidity (Hmd), particulate matter with a diameter smaller than 10 µm (PM10) and particulate matter with a diameter smaller than 2.5 µm (PM2.5).

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Early or late pubertal onset can lead to disease in adulthood, including cancer, obesity, type 2 diabetes, metabolic disorders, bone fractures, and psychopathologies. Thus, knowing the age at which puberty is attained is crucial as it can serve as a risk factor for future diseases. Pubertal development is divided into five stages of sexual maturation in boys and girls according to the standardized Tanner scale. We performed genome-wide association studies (GWAS) on the "Growth and Obesity Chilean Cohort Study" cohort composed of admixed children with mainly European and Native American ancestry. Using joint models that integrate time-to-event data with longitudinal trajectories of body mass index (BMI), we identified genetic variants associated with phenotypic transitions between pairs of Tanner stages. We identified $42$ novel significant associations, most of them in boys. The GWAS on Tanner $3\rightarrow 4$ transition in boys captured an association peak around the growth-related genes LARS2 and LIMD1 genes, the former of which causes ovarian dysfunction when mutated. The associated variants are expression and splicing Quantitative Trait Loci regulating gene expression and alternative splicing in multiple tissues. Further, higher individual Native American genetic ancestry proportions predicted a significantly earlier puberty onset in boys but not in girls. Finally, the joint models identified a longitudinal BMI parameter significantly associated with several Tanner stages' transitions, confirming the association of BMI with pubertal timing.

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Breast cancer is the most common malignant neoplasm and the leading cause of cancer mortality among women globally. Current prediction models based on risk factors are inefficient in specific populations, so an appropriate and calibrated breast cancer prediction model for Cuban women is essential. This article proposes a conceptual model for breast cancer risk estimation for Cuban women using machine learning algorithms and risk factors. The model has three main components: knowledge representation, risk estimation modeling, and risk predictor evaluation. Nine of the most common machine learning algorithms were used to generate risk predictors using the proposed model. Two data sources served as case studies: the first comprised data collected from Cuban women, and the second included data from US Hispanic women obtained from the Breast Cancer Surveillance Consortium dataset. The results show that the model effectively estimates breast cancer risk and could be a valuable tool for early detection of breast cancer and identification of patients at risk. According to the first experiment results, the best predictor of breast cancer risk for the Cuban female population corresponds to the Random Forest algorithm with a weighted score of 5.981, a training accuracy of 0.996 and a training AUC of 0.997. In a second experiment, it was demonstrated that the risk predictors generated by the proposed model using data from Cuban women obtained better AUC and accuracy values compared to the predictors generated by using the US Hispanic population, potentially generalizable to other Hispanic populations. Implementing this model could be an economically viable alternative to reduce the mortality rate of this type of cancer in Latin American countries such as Cuba.

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This study aimed to evaluate the reliability of an age estimation method based on the pulp/tooth area ratio by assessing intra- and inter-examiner agreement across five observers at different intervals. Using the same X-ray device and technical parameters, 96 digital periapical X-ray images of upper and lower canines were obtained from 28 deceased people in Central America, whose age at death ranged from 19 to 49 years. Excellent and good agreement of results were achieved, and there were no statistically significant differences. The R2 value for upper teeth (54.0%) was higher than the R2 value for lower teeth (45.7%). The highest intraclass correlation coefficient value was 0.995 (0.993-0.997) and the lowest 0.798 (0.545-0.895). Inter-examiner agreement was high with values of 0.975 (0.965-0.983) and 0.927 (0.879-0.955). This method is adequate for assessing age in missing and unidentified people, including victims of mass disasters.

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Aquaculture requires precise non-invasive methods for biomass estimation. This research validates a novel computer vision methodology that uses a signature function-based feature extraction algorithm combining statistical morphological analysis of the size and shape of fish and machine learning to improve the accuracy of biomass estimation in fishponds and is specifically applied to tilapia (Oreochromis niloticus). These features that are automatically extracted from images are put to the test against previously manually extracted features by comparing the results when applied to three common machine learning methods under two different lighting conditions. The dataset for this analysis encompasses 129 tilapia samples. The results give promising outcomes since the multilayer perceptron model shows robust performance, consistently demonstrating superior accuracy across different features and lighting conditions. The interpretable nature of the model, rooted in the statistical features of the signature function, could provide insights into the morphological and allometric changes at different developmental stages. A comparative analysis against existing literature underscores the competitiveness of the proposed methodology, pointing to advancements in precision, interpretability, and species versatility. This research contributes significantly to the field, accelerating the quest for non-invasive fish biometrics that can be generalized across various aquaculture species in different stages of development. In combination with detection, tracking, and posture recognition, deep learning methodologies such as the one provided in the latest studies could generate a powerful method for real-time fish morphology development, biomass estimation, and welfare monitoring, which are crucial for the effective management of fish farms.

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SUMMARY: The study aims to demonstrate the success of deep learning methods in sex prediction using hyoid bone. The images of people aged 15-94 years who underwent neck Computed Tomography (CT) were retrospectively scanned in the study. The neck CT images of the individuals were cleaned using the RadiAnt DICOM Viewer (version 2023.1) program, leaving only the hyoid bone. A total of 7 images in the anterior, posterior, superior, inferior, right, left, and right-anterior-upward directions were obtained from a patient's cut hyoid bone image. 2170 images were obtained from 310 hyoid bones of males, and 1820 images from 260 hyoid bones of females. 3990 images were completed to 5000 images by data enrichment. The dataset was divided into 80 % for training, 10 % for testing, and another 10 % for validation. It was compared with deep learning models DenseNet121, ResNet152, and VGG19. An accuracy rate of 87 % was achieved in the ResNet152 model and 80.2 % in the VGG19 model. The highest rate among the classified models was 89 % in the DenseNet121 model. This model had a specificity of 0.87, a sensitivity of 0.90, an F1 score of 0.89 in women, a specificity of 0.90, a sensitivity of 0.87, and an F1 score of 0.88 in men. It was observed that sex could be predicted from the hyoid bone using deep learning methods DenseNet121, ResNet152, and VGG19. Thus, a method that had not been tried on this bone before was used. This study also brings us one step closer to strengthening and perfecting the use of technologies, which will reduce the subjectivity of the methods and support the expert in the decision-making process of sex prediction.

El estudio tuvo como objetivo demostrar el éxito de los métodos de aprendizaje profundo en la predicción del sexo utilizando el hueso hioides. En el estudio se escanearon retrospectivamente las imágenes de personas de entre 15 y 94 años que se sometieron a una tomografía computarizada (TC) de cuello. Las imágenes de TC del cuello de los individuos se limpiaron utilizando el programa RadiAnt DICOM Viewer (versión 2023.1), dejando solo el hueso hioides. Se obtuvieron un total de 7 imágenes en las direcciones anterior, posterior, superior, inferior, derecha, izquierda y derecha-anterior-superior a partir de una imagen seccionada del hueso hioides de un paciente. Se obtuvieron 2170 imágenes de 310 huesos hioides de hombres y 1820 imágenes de 260 huesos hioides de mujeres. Se completaron 3990 imágenes a 5000 imágenes mediante enriquecimiento de datos. El conjunto de datos se dividió en un 80 % para entrenamiento, un 10 % para pruebas y otro 10 % para validación. Se comparó con los modelos de aprendizaje profundo DenseNet121, ResNet152 y VGG19. Se logró una tasa de precisión del 87 % en el modelo ResNet152 y del 80,2 % en el modelo VGG19. La tasa más alta entre los modelos clasificados fue del 89 % en el modelo DenseNet121. Este modelo tenía una especificidad de 0,87, una sensibilidad de 0,90, una puntuación F1 de 0,89 en mujeres, una especificidad de 0,90, una sensibilidad de 0,87 y una puntuación F1 de 0,88 en hombres. Se observó que se podía predecir el sexo a partir del hueso hioides utilizando los métodos de aprendizaje profundo DenseNet121, ResNet152 y VGG19. De esta manera, se utilizó un método que no se había probado antes en este hueso. Este estudio también nos acerca un paso más al fortalecimiento y perfeccionamiento del uso de tecnologías, que reducirán la subjetividad de los métodos y apoyarán al experto en el proceso de toma de decisiones de predicción del sexo.

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Cefepime and piperacillin/tazobactam are antimicrobials recommended by IDSA/ATS guidelines for the empirical management of patients admitted to the intensive care unit (ICU) with community-acquired pneumonia (CAP). Concerns have been raised about which should be used in clinical practice. This study aims to compare the effect of cefepime and piperacillin/tazobactam in critically ill CAP patients through a targeted maximum likelihood estimation (TMLE). A total of 2026 ICU-admitted patients with CAP were included. Among them, (47%) presented respiratory failure, and (27%) developed septic shock. A total of (68%) received cefepime and (32%) piperacillin/tazobactam-based treatment. After running the TMLE, we found that cefepime and piperacillin/tazobactam-based treatments have comparable 28-day, hospital, and ICU mortality. Additionally, age, PTT, serum potassium and temperature were associated with preferring cefepime over piperacillin/tazobactam (OR 1.14 95% CI [1.01-1.27], p = 0.03), (OR 1.14 95% CI [1.03-1.26], p = 0.009), (OR 1.1 95% CI [1.01-1.22], p = 0.039) and (OR 1.13 95% CI [1.03-1.24], p = 0.014)]. Our study found a similar mortality rate among ICU-admitted CAP patients treated with cefepime and piperacillin/tazobactam. Clinicians may consider factors such as availability and safety profiles when making treatment decisions.

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We introduce the bivariate unit-log-symmetric model based on the bivariate log-symmetric distribution (BLS) defined in Vila et al. [25] as a flexible family of bivariate distributions over the unit square. We then study its mathematical properties such as stochastic representations, quantiles, conditional distributions, independence of the marginal distributions and marginal moments. Maximum likelihood estimation method is discussed and examined through Monte Carlo simulation. Finally, the proposed model is used to analyze some soccer data sets.

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In the present work, both direct and inverse problems are considered for a Fisher-type fractional diffusion equation, which is proposed to describe the phenomenon of cell migration. For the direct problem, a solution is given via the Fourier method and the Laplace transform. On the other hand, we solved the inverse problem from a Bayesian statistical framework using a set of data that are the result of a cell migration experiment on a wound closure assay. We estimated the parameters of the mathematical model via Markov Chain Monte Carlo methods.

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BACKGROUND & AIMS: In children with Cerebral palsy (CP) bone deformities create a difficulty in the collection of height measures by direct methods. Body segments are an alternative to study for anthropometric evaluation in children with CP. Motor compromise affects growth in these children. To our knowledge, no equations have been developed to estimate height that consider the level of involvement of children with CP. The aim was to develop equations to estimate height using segmental measures for children with cerebral palsy (CP). METHODS: This was a cross-sectional study. The sample consisted of children and adolescents with CP of both sexes from 2 to 19 years old from five cities in Argentina. Children whose height and knee-heel height (KH) could be measured were included. Height, KH, and clinical covariables were collected. Linear regression models with height as the dependent variable and KH as predictors adjusted for significant covariates were developed and compared for R2, adjusted R2, and the root mean square of the error. RESULTS: 242 children and adolescents (mean age 9 ± 4 years) with a confirmed diagnosis of CP were included. The interaction between height and other variables such KH, sex, GMFCS, and age was analyzed. Two equations were developed to estimate height according to GMFCS level (GMFCS Level I-III: H = 1.5 × KH(cm) + 2.28 × age(years) + 51; GMFCS Level IV-V: H = 2.13 × KH (cm)+ 0.91 × age(years) + 37). The concordance correlation coefficient between estimated and observed height was 0.95 (95%CI [0.94; 0.96]). CONCLUSION: Height in children and adolescents with CP can be predicted using KH, GMFCS, and age. The equations and software can estimate height when this cannot be obtained directly.

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OBJECTIVES: To estimate the incremental medical cost of diabetes mellitus using information from administrative databases in Colombia. METHODS: We carried out a retrospective cohort study with administrative health databases from Colombian population affiliated in the contributory health insurance scheme. We used an operative definition to select the cohort with diabetes. Incremental cost and cost ratio of diabetes were estimated using an inverse probability weighting of treatment approach to find the causal effect of having the disease. Weights were calculated by a propensity score method using a Random Forest model. The flexibility of this machine learning algorithm allows to have a better specification and bias reduction. Additionally, we reported incremental costs and cost ratios with confidence intervals using bootstrapping and analyzed costs by age groups and complications associated with diabetes. RESULTS: The estimated prevalence of diabetes was 2834 per 100 000 cases, in 2018. The group with diabetes was comprised 634 015 people and the control group 1 524 808. The calculated annual direct medical cost was $860, for which the incremental cost was $493 and the cost ratio 2.34. The incremental annual cost for some type of complication ranges from $1239 to $2043, renal complication being the most expensive. Incremental cost by age groups ranges from $347 to $878, being higher in younger people. CONCLUSIONS: Although the cost of diabetes in Colombia ranges among the global averages and is similar to other Latin-American countries, a greater incremental cost was found in patients with renal, circulatory, and neurologic complications.

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Colonoscopy is the choice procedure to diagnose, screening, and treat the colon and rectum cancer, from early detection of small precancerous lesions (polyps), to confirmation of malign masses. However, the high variability of the organ appearance and the complex shape of both the colon wall and structures of interest make this exploration difficult. Learned visuospatial and perceptual abilities mitigate technical limitations in clinical practice by proper estimation of the intestinal depth. This work introduces a novel methodology to estimate colon depth maps in single frames from monocular colonoscopy videos. The generated depth map is inferred from the shading variation of the colon wall with respect to the light source, as learned from a realistic synthetic database. Briefly, a classic convolutional neural network architecture is trained from scratch to estimate the depth map, improving sharp depth estimations in haustral folds and polyps by a custom loss function that minimizes the estimation error in edges and curvatures. The network was trained by a custom synthetic colonoscopy database herein constructed and released, composed of 248400 frames (47 videos), with depth annotations at the level of pixels. This collection comprehends 5 subsets of videos with progressively higher levels of visual complexity. Evaluation of the depth estimation with the synthetic database reached a threshold accuracy of 95.65%, and a mean-RMSE of 0.451cm, while a qualitative assessment with a real database showed consistent depth estimations, visually evaluated by the expert gastroenterologist coauthoring this paper. Finally, the method achieved competitive performance with respect to another state-of-the-art method using a public synthetic database and comparable results in a set of images with other five state-of-the-art methods. Additionally, three-dimensional reconstructions demonstrated useful approximations of the gastrointestinal tract geometry. Code for reproducing the reported results and the dataset are available at https://github.com/Cimalab-unal/ColonDepthEstimation.

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Glioblastoma Multiforme is a brain tumor distinguished by its aggressiveness. We suggested that this aggressiveness leads single-cell RNA-sequence data (scRNA-seq) to span a representative portion of the cancer attractors domain. This conjecture allowed us to interpret the scRNA-seq heterogeneity as reflecting a representative trajectory within the attractor's domain. We considered factors such as genomic instability to characterize the cancer dynamics through stochastic fixed points. The fixed points were derived from centroids obtained through various clustering methods to verify our method sensitivity. This methodological foundation is based upon sample and time average equivalence, assigning an interpretative value to the data cluster centroids and supporting parameters estimation. We used stochastic simulations to reproduce the dynamics, and our results showed an alignment between experimental and simulated dataset centroids. We also computed the Waddington landscape, which provided a visual framework for validating the centroids and standard deviations as characterizations of cancer attractors. Additionally, we examined the stability and transitions between attractors and revealed a potential interplay between subtypes. These transitions might be related to cancer recurrence and progression, connecting the molecular mechanisms of cancer heterogeneity with statistical properties of gene expression dynamics. Our work advances the modeling of gene expression dynamics and paves the way for personalized therapeutic interventions.

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Chile had a violent military coup (1973-1990) that resulted in 3,000 victims declared detained, missing or killed; many are still missing and unidentified. Currently, the Human Rights Unit of the Forensic Medical Service in Chile applies globally recognised forensic anthropological approaches, but many of these methods have not been validated in a Chilean sample. As current research has demonstrated population-specificity with extant methods, the present study aims to validate sex estimation methods in a Chilean population and thereafter establish population-specific equations. A sample of 265 os coxae of known age and sex of adult Chileans from the Santiago Subactual Osteology Collection were analysed. Visual assessment and scoring of the pelvic traits were performed in accordance with the Phenice (1969) and Klales et al. (2012) methods. The accuracy of Phenice (1969) in the Chilean sample was 96.98%, with a sex bias of 7.68%. Klales et al. (2012) achieved 87.17% accuracy with a sex bias of -15.39%. Although both methods showed acceptable classification accuracy, the associated sex bias values are unacceptable in forensic practice. Therefore, six univariate and eight multivariate predictive models were formulated for the Chilean population. The most accurate univariate model was the ventral arc at 96.6%, with a sex bias of 5.2%. Classification accuracy using all traits was 97.0%, with a sex bias of 7.7%. This study provides Chilean practitioners a population-specific morphoscopic standard with associated classification probabilities acceptable to accomplish legal admissibility requirements in human rights and criminal cases specific to the second half of the 20th century.

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This research focuses on the development of a state observer for performing indirect measurements of the main variables involved in the soybean oil transesterification reaction with a guishe biochar-based heterogeneous catalyst; the studied reaction takes place in a batch reactor. The mathematical model required for the observer design includes the triglycerides' conversion rate, and the reaction temperature. Since these variables are represented by nonlinear differential equations, the model is linearized around an operation point; after that, the pole placement and linear quadratic regulator (LQR) methods are considered for calculating the observer gain vector L(x). Then, the estimation of the conversion rate and the reaction temperature provided by the observer are used to indirectly measure other variables such as esters, alcohol, and byproducts. The observer performance is evaluated with three error indexes considering initial condition variations up to 30%. With both methods, a fast convergence (less than 3 h in the worst case) of the observer is remarked.

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This paper presents a novel method for load torque estimation in three-phase induction motors using air gap flux measurement and the conversion of this type of time-domain signal into grayscale images for further processing as inputs for an inception-type convolutional neural network. The magnetic flux was measured employing a Hall effect sensor installed inside the machine, near the stator slots, and above the stator windings. In this case, the sensor was able to measure a resultant magnetic flux density, having both rotor and stator magnetic flux contributions. The present methodology does not require motor parameters for torque prediction. The proposed approach successfully estimated load torque using three optimizers across almost the entire motor load operational range, spanning from 1.5% to 93.9% of the rated load. Four model configurations achieved a mean absolute percentage error (MAPE) less than or equal to 3.7%. Specifically, two models for a 40 × 50 pixel image achieved MAPE of 3.7% and 3%, one model for a 40 × 25 pixel image achieved a MAPE of 3.5%, and one model for a 50 × 80 pixel image achieved a MAPE of 3.3%. This research has been experimentally validated with a 7.5 kW squirrel cage induction machine.