Sigmoid Function Research Articles

Modulable 3D-printed plantibody-laden platform enabling microscale affinity extraction and ratiometric front-face fluorescence detection of microcystin-LR in marine waters

A 3D-printed stereolithographic platform for selective biorecognition is designed to enable convective microscale affinity extraction of microcystin-LR (MC-LR) followed by direct solid-phase optosensing exploiting ratiometric front-face fluorescence spectroscopy. For this purpose, a recombinant monoclonal plantibody (recAb) is covalently attached to a 3D-printed structure for sorptive immunoextraction, whereupon the free and unbound primary amino moieties of the recAb are derivatized with a fluorescent probe. The fluorophore-recAb-MC-LR laden device is then accommodated in the cuvette holder of a conventional fluorometer without any instrumental modification for the recording of the solid-phase fluorescence emission. Using Rodbard’s four-parameter sigmoidal function, the 3D-printed bioselective platform features a limit of detection (LOD) of 28 ng L−1 using a sample volume of 500 mL, device-to-device reproducibility down to 12%, and relative recoveries ranging from 91 to 100% in marine waters. Printed prototypes are affordable, just 0.4 € per print and ≤ 10 € per device containing recAb. One of the main assets of the miniaturized immunoextraction device is that it performs comparably well in terms of analytical figures of merit with costly mass spectrometric-based analytical methodologies, such as HPLC–MS/MS. The device is readily applicable to high-matrix samples, such as seawater, as opposed to previous biosensing platforms, just applied to freshwater systems.Graphical abstract

Few-Shot Learning Based on Dimensionally Enhanced Attention and Logit Standardization Self-Distillation

Few-shot learning (FSL) is a challenging problem. Transfer learning methods offer a straightforward and effective solution to FSL by leveraging pre-trained models and generalizing them to new tasks. However, pre-trained models often lack the ability to highlight and emphasize salient features, a gap that attention mechanisms can fill. Unfortunately, existing attention mechanisms encounter issues such as high complexity and incomplete attention information. To address these issues, we propose a dimensionally enhanced attention (DEA) module for FSL. This DEA module introduces minimal additional computational overhead while fully attending to both channel and spatial information. Specifically, the feature map is first decomposed into 1D tensors of varying dimensions using strip pooling. Next, a multi-dimensional collaborative learning strategy is introduced, enabling cross-dimensional information interactions through 1D convolutions with adaptive kernel sizes. Finally, the feature representation is enhanced by calculating attention weights for each dimension using a sigmoid function and weighting the original input accordingly. This approach ensures comprehensive attention to different dimensions of information, effectively characterizing data in various directions. Additionally, we have found that knowledge distillation significantly improves FSL performance. To this end, we implement a logit standardization self-distillation method tailored for FSL. This method addresses the issue of exact logit matching, which arises from the shared temperature in the self-distillation process, by employing logit standardization. We present experimental results on several benchmark datasets where the proposed method yields significant performance improvements.

Construction and approximation rate for feedforward neural network operators with sigmoidal functions

It is well known that feedforward neural networks (FNNs) are universal approximators. This fact constitutes the theoretical basis for FNN learning. Constructing FNNs and estimating their errors of approximation are important and interesting, which not only theoretically verify the generalization ability of the constructed FNNs without training, but also avoid the local minimum solution in the parameters optimization process. This paper aims to construct several classes of FNNs with generalized sigmoidal function, i.e., the sigmoidal function satisfying certain asymptotic behaviours. Another main purpose of this paper is to estimate approximation rates for the constructed FNNs. Using the modulus of continuity of function as a metric, the upper bounds of approximation are estimated. In particular, the results of this paper contain the corresponding results for FNNs consisting of some classical sigmoidal functions.

Design of a sliding mode observer based on sigmoid function and its application in detecting small faults of induction motor

Design of a sliding mode observer based on sigmoid function and its application in detecting small faults of induction motor

Predicting the probability of complications during prostatectomy in pa-tients with prostate cancer using machine learning methods

Objective. To determine the probabilities of predicting possible complications after surgery in patients with the diagnosis of prostate cancer using artificial intelligence methods. Materials and methods. Case histories of 701 patients who underwent prostatectomy were analyzed in the study. The anamnesis, findings of clinical, laboratory and instrumental study, as well as objective data of clinical observations were evaluated. The average age was 64.72. On the basis of the set of examination results, patients were selected according to the following inclusion criteria: prostate cancer patients without confirmed metastases with disease stage from T1N0M0 to T3N0M0; absence of previous and concomitant special treatment (immunotherapy or targeted therapy); informed consent to the surgery. Logistic regression, a binary classifier using a sigmoidal activation function on linear combinations of features, was used as a machine learning model. Results. It was determined that the logistic regression model based on selected parameters (prostate volume, pain syndrome, disease duration), predicts the probability of complications quite well (TPR=1). The overall accuracy of the model is: Accuracy=0.98. At the same time, it can be noticed from the agreement matrix that the trained model plays it safe and classifies some cases without complications incorrectly in 5.3% (FNR=0.053). However, the model never made an error and did not classify cases with a high risk of complications as those in which such a possibility was unlikely. Conclusions. The results obtained show that on the basis of just three parameters (prostate volume, pain syndrome, duration of the disease), it is possible to build a fairly good predictive model of the probability of complications after prostatectomy based on such machine learning method as logistic regression.

Evaluating a sigmoid dark energy model to explain the Hubble tension

AbstractIn this study, we analyze Type Ia supernovae (SNe Ia) data sourced from the Pantheon+ compilation to investigate late‐time physics effects influencing the expansion history, , at redshifts . Our focus centers on a time‐varying dark energy (DE) model that introduces a rapid transition in the equation of state, at a specific redshift, , from the baseline, , value to the present value, . The change in the equation of state is implemented as a transition in the DE density scale factor driven by a sigmoid function. The constraints obtained for the DE sigmoid phenomenological parametrization have broad applicability for dynamic DE models that invoke late‐time physics. Our analysis indicates that the sigmoid model provides a slightly better, though not statistically significant, fit to the SNe Pantheon+ data compared to the standard cold dark matter () model. The fit results, assuming a flat geometry and maintaining constant at the 2018‐Planck value of , are as follows: km s Mpc, , . The errors represent statistical uncertainties only. The available SN dataset lacks sufficient statistical power to distinguish between the baseline model and the alternative sigmoid models. A feature of interest offered by the sigmoid model is that it identifies a specific redshift, , where a potential transition in the equation of state could have occurred. The sigmoid model does not favor a DE in the phantom region (). Further constraints to the dynamic DE model have been obtained using CMB data to compute the distance to the last scattering surface. While the sigmoid DE model does not completely resolve the tension, it offers a transition mechanism that can still play a role alongside other potential solutions.

Mathematical Model of Logistic Regression for Binary Classification. Part 1. Regression Models of Data Generalization

In this article, the mathematical justification of logistic regression as an effective and simple to implement method of machine learning is performed. A review of literary sources was conducted in the direction of statistical processing, analysis and classification of data using the logistic regression method, which confirmed the popularity of this method in various subject areas. The logistic regression method was compared with the linear and probit regression methods regarding the possibility of predicting the probabilities of events. In this context, the disadvantages of linear regression and the advantages and affinity of logit and probit regression methods are noted. It is indicated that the possibility of forecasting probabilities and binary classification by the method of logistic regression is provided by the use of a sigmoid function with the property of compressive transformation of an argument with an unlimited numerical value into a limited range from 0 to 1 real value of the function. The derivation of the sigmoid function in two different ways is described: based on the model of the logarithm of the odds of events and the model of logistic population growth. Based on the method of maximum likelihood, the construction of a logarithmic loss function was demonstrated, the use of which made it possible to move from a multi-extremal nonlinear regression problem to a unimodal optimization problem. Methods of regularization of the loss function are presented to control the complexity and prevent retraining of the logistic regression model.

Research on sales strategies for target customers of electric vehicles based on gradient boosting ensemble trees

This paper focuses on the automotive industry, especially the new energy vehicle sector, which is vital for the economy and needs careful market sales decisions. It analyzes data from 1,964 potential customers, including their satisfaction and personal information. The study uses machine learning to create a math model and give sales advice. The data is first cleaned without changing its original structure, and then normalized using the Z-Score method. For any outlier values in the data, the mean of similar items is used to fill in gaps. Specifically, for 500 missing entries about the number of children (B7), the paper groups customers by age, calculates the frequency of children in each group, and uses these frequencies to fill in missing values.Using the cleaned data, the XGBoost algorithm ranks the factors influencing customer decisions. For Brand 1, the top factors are economy (a3), work experience (B10), and safety performance (a4). For Brand 2, comfort (a2), disposable income (B15), and mortgage expenses (B16) are key. For Brand 3, car loan expenses (B17), battery technology (a1), and again mortgage expenses (B16) are most important.The paper also addresses imbalanced data by using an XGBoost binary classification model. This model predicts the likelihood of buying an electric vehicle using the Sigmoid function on tree node weights. It evaluates the model using Precision, Recall, and Area Under the Receiver Operating Characteristic Curve (AUC), which works well even with imbalanced data. The Precision and Recall rates for all three brands are above 90%, with AUC over 85% for Brands 1 and 2, and over 75% for Brand 3. This shows that the model is effective and can be used in real-world situations.

Multi-label feature selection based on nonlinear mapping

Feature selection is one of the important pre-processing methods for dimensionality reduction in multi-label learning tasks, which has attracted extensive attention in recent years. Most of the existing approaches transform feature data into the label space during the feature-label mapping process by assuming linear relationship between the feature and label spaces. However, the linearity assumption does not hold in most cases, especially for high-dimensional spaces. This work proposes a novel dimension reduction model for multi-label data by using nonlinear mapping (NMFS). The model introduces a point-to-point sigmoid function to describe the intrinsic relationship from data space to label space. The proposed method improves the generalization ability of feature selection by limiting the range of data transformation to the interval [0,1] which is consistent with the predicted values of the labels. The feature weight matrix is constrained by the l2,1-norm to ensure its sparsity, which forms the basis of feature selection. The variables in the NMFS model are iteratively updated using the gradient momentum optimization strategy, and a sparse weight-coefficient matrix is obtained for multi-label feature ordering. Experimental results on 14 multi-label data sets verify the effectiveness of the proposed method, and show the proposed method is superior to the most advanced multi-label feature selection methods.

Firing pattern manipulation of neuronal networks by deep unfolding‐based model predictive control

AbstractThe complexity of neuronal networks, characterized by interconnected neurons, presents significant challenges in control due to their nonlinear and intricate behaviour. This paper introduces a novel method designed to generate control inputs for neuronal networks to regulate the firing patterns of modules within the network. This methodology is built upon temporal deep unfolding‐based model predictive control, a technique rooted in the deep unfolding method commonly used in wireless signal processing. To address the unique dynamics of neurons, such as zero gradients in firing times, the method employs approximations of input currents using a sigmoid function during its development. The effectiveness of this approach is validated through extensive numerical simulations. Furthermore, control experiments were conducted by reducing the number of input neurons to identify critical features for control. Various selection techniques were utilized to pinpoint key input neurons. These experiments shed light on the importance of specific input neurons in controlling module firing within neuronal networks. Thus, this study presents a tailored methodology for managing networked neurons, extends temporal deep unfolding‐based model predictive control to nonlinear systems with reset dynamics, and demonstrates its ability to achieve desired firing patterns in neuronal networks.

DAILY DANUBE RIVER WATER LEVEL PREDICTION USING EXTREME LEARNING MACHINE APPROACH

Anticipating water levels in vast riverbeds is crucial for preventing and mitigating floods or droughts, assessing power plant capacity, and facilitating navigation management. This study introduces an innovative water level prediction model utilizing an Extreme Learning Machine developed to solve the issues of low performance of existing forecasting methods. Development of such a system is of extreme importance when talking about the largest European river – the Danube River. Experimental findings reveal the model's satisfactory performance across various accuracy metrics, complexity considerations, and calculation speed. The prediction with the highest error rate based on MAPE criteria was for Prahovo water level prediction over a 365-day period at 2.02%, whilst the most accurate predictions were for Novi Sad and Banatska Palanka over 30 days and 180 days horizons, respectively, at 0.0550%. The highest coefficient of determination (R2) was achieved with the Novi Sad data at 0.9968, whilst the lowest was observed with the Prahovo data at 0.7353. The ELM model achieved high precision by adjusting the activation functions of the hidden layer neurons, which involved using different combinations of sigmoid and radial-basis activation functions.

Smooth Logistic Real and Complex, Ordinary and Fractional Neural Network Approximations over Infinite Domains

In this work, we study the univariate quantitative smooth approximations, including both real and complex and ordinary and fractional approximations, under different functions. The approximators presented here are neural network operators activated by Richard’s curve, a parametrized form of logistic sigmoid function. All domains used are obtained from the whole real line. The neural network operators used here are of the quasi-interpolation type: basic ones, Kantorovich-type ones, and those of the quadrature type. We provide pointwise and uniform approximations with rates. We finish with their applications.

A Pareto-optimality based black widow spider algorithm for energy efficient flexible job shop scheduling problem considering new job insertion

The utilization of flexible job shops is on the rise, driven by the decreasing life cycle of consumer products. In dynamic flexible job shops, the occurrence of disruptive events like machine breakdown, tool wear, and new job arrivals is common, emphasizing the critical need for efficient scheduling to achieve productivity and cost-effectiveness. Additionally with the growing concerns about energy consumption and global warming, the imperative to contemplate workshops with lower energy usage is becoming increasingly significant. Therefore, in this study a multi-objective dynamic flexible job shop scheduling problem (MODFJSP) with insertion of new jobs for optimization objectives: makespan, total energy consumption and schedule instability is addressed. A novel multi-objective black widow spider algorithm (MOBWSA), inspired by the mating behavior of black widow spiders, is proposed. The MOBWSA ensures an optimal balance between minimizing makespan and energy consumption through its superior evolutionary processes of procreation, mutation and cannibalism. Furthermore, a strategic on/off strategy is implemented to enhance energy efficiency. The disruptions in schedule at rescheduling stage are addressed through the proposed sigmoidal weighted instability function. To handle the multi-objective nature of the problem this work incorporates Pareto-optimality approach in combination with novel hybrid crowding distance metric. The optimization is further aided by exploitation of search space through an ensemble of local search operators. Testing and evaluation of the MOBWSA with 30 benchmark problems is conducted, and its performance for multiple metrics is compared with recently published state-of-the-art algorithms. The results establish the effectiveness and efficiency of the proposed algorithm.

Parallel Synapses with Transmission Nonlinearities Enhance Neuronal Classification Capacity.

Cortical neurons often establish multiple synaptic contacts with the same postsynaptic neuron. To avoid functional redundancy of these parallel synapses, it is crucial that each synapse exhibits distinct computational properties. Here we model the current to the soma contributed by each synapse as a sigmoidal transmission function of its presynaptic input, with learnable parameters such as amplitude, slope, and threshold. We evaluate the classification capacity of a neuron equipped with such nonlinear parallel synapses, and show that with a small number of parallel synapses per axon, it substantially exceeds that of the Perceptron. Furthermore, the number of correctly classified data points can increase superlinearly as the number of presynaptic axons grows. When training with an unrestricted number of parallel synapses, our model neuron can effectively implement an arbitrary aggregate transmission function for each axon, constrained only by monotonicity. Nevertheless, successful learning in the model neuron often requires only a small number of parallel synapses. We also apply these parallel synapses in a feedforward neural network trained to classify MNIST images, and show that they can increase the test accuracy. This demonstrates that multiple nonlinear synapses per input axon can substantially enhance a neuron's computational power.

Application of Artificial Intelligence to the Alert of Explosions in Colombian Underground Mines

The use of Artificial Intelligence (AI), particularly of Artificial Neural Networks (ANN), in alerting possible scenarios of methane explosions in Colombian underground mines is illustrated by the analysis of an explosion that killed twelve miners. A combination of geological analysis, a detailed characterization of samples of coal dust and scene evidence, and an analysis with physical modeling tools supported the hypothesis of the existence of an initial methane explosion ignited by an unprotected tool that was followed by a coal dust explosion. The fact that one victim had a portable methane detector at the moment of the methane explosion suggested that the ubiquitous use of these systems in Colombian mines could be used to alert regulatory agencies of a possible methane explosion. This fact was illustrated with the generation of a database of possible readouts of methane concentration based on the recreation of the mine atmosphere before the explosion with Computational Fluid Dynamics (CFD). This database was used to train and test an ANN that included an input layer with two nodes, two hidden layers, each with eight nodes, and an output layer with one node. The inner layers applied a rectified linear unit activation function and the output layer a Sigmoid function. The performance of the ANN algorithm was considered acceptable as it correctly predicted the need for an explosion alert in 971.9 per thousand cases and illustrated how AI can process data that is currently discarded but that can be of importance to alert about methane explosions.

Investigating the effect of using aluminum oxide nanofluid and twisted tapes with different twisted pitches on the heat transfer efficiency and using perceptron artificial neural networks in data prediction

This study investigates the effect of aluminum oxide nanofluid with 1% and 2% volume fractions (VFs) in four different tubes with identical bending and the uniform, low-high-low, low-high, and high-low-high longitudinal states with twist ratios of 0, 2 and 4. These tubes are affected by a constant thermal flux of 10000 W/m2 and Reynolds numbers of 2000-10000. For the numerical solution of these equations, the finite difference method on the basis of the control volume and the SIMPLEC algorithm and the K-ε-RNG method were applied for the turbulent flow modeling. The determined Nusselt number from the numerical methods were evaluated applying the perceptron neural network. The most optimal increase in the Nusselt number was in the twisted tube with twist ratio of 4 in the Reynolds number of 10,000 and VF of 1% and 2% nanofluid with increasing trend of length from low to high. The most optimal increase in Nusselt number compared to base fluid was about 25%. The sum of squared error and the relative error data obtained from the hyperbolic tangent function for the training and test data were 0.080-1.331 and 0.113-0.675, and from the sigmoid function for the training and test data were 0.093-0.392 and 0.097-0.147.

Using Support Vector Machines to Classify Road Surface Conditions to Promote Safe Driving.

Accurate detection of road surface conditions in adverse winter weather is essential for traffic safety. To promote safe driving and efficient road management, this study presents an accurate and generalizable data-driven learning model for the estimation of road surface conditions. The machine model was a support vector machine (SVM), which has been successfully applied in diverse fields, and kernel functions (linear, Gaussian, second-order polynomial) with a soft margin classification technique were also adopted. Two learner designs (one-vs-one, one-vs-all) extended their application to multi-class classification. In addition to this non-probabilistic classifier, this study calculated the posterior probability of belonging to each group by applying the sigmoid function to the classification scores obtained by the trained SVM. The results indicate that the classification errors of all the classifiers, excluding the one-vs-all linear learners, were below 3%, thereby accurately classifying road surface conditions, and that the generalization performance of all the one-vs-one learners was within an error rate of 4%. The results also showed that the posterior probabilities can analyze certain atmospheric and road surface conditions that correspond to a high probability of hazardous road surface conditions. Therefore, this study demonstrates the potential of data-driven learning models in classifying road surface conditions accurately.

Adaptive chaotic dynamic learning-based gazelle optimization algorithm for feature selection problems

Feature Selection (FS) is considered a crucial procedure for eliminating unnecessary features from datasets. FS is considered a challenging problem that is difficult to solve efficiently due to its combinatorial nature. As the problem size increases, so does the computation time. Recently, researchers have been focusing on metaheuristic FS algorithms. Therefore, this paper introduces an adaptive chaotic dynamic gazelle optimization algorithm (ACD-GOA) with enhanced elite Strategy for FS problems. The ACD-GOA is a novel enhanced version of the recently published GOA, incorporating multiple improved strategies to enhance its search capabilities and convergence speed. The initialization phase and iteration initialization adopt the dynamic opposition learning strategy to avoid premature convergence. Additionally, several enhancement strategies are employed to improve the efficiency of the standard GOA. Adaptive inertia weight and sigmoid function are used to enhance search efficiency. Furthermore, enhanced elite and exchanging information strategies are implemented to maintain population diversity and avoid local solutions, respectively. Experimental evaluations are conducted using various functions, including the twelve CEC2022 standard functions and fourteen FS benchmark datasets. The performance of ACD-GOA is compared with several other metaheuristic algorithms. Statistical tests such as Friedman and Wilcoxon signed-rank tests are used to analyze the experimental data. The experimental results highlight the proposed algorithm’s exceptional capacity to overcome problems associated with local minima and expedite the convergence process. The suggested algorithm has been extensively compared to state-of-the-art algorithms, demonstrating significant breakthroughs. The reported accuracy of the proposed algorithm ranges from 0.78 to 1.00 with K-NN classifier.

Single-Frequency Lasers’ Linewidths Elegantly Characterized with Sigmoid Functions of Observation Time

Single-Frequency Lasers’ Linewidths Elegantly Characterized with Sigmoid Functions of Observation Time

A physics-informed machine learning model for the prediction of drop breakup in two-phase flows

Predictive simulations of two-phase flows are highly sought after because of their widespread applications in propulsion, energy, agriculture, and medicine. One crucial goal for many of these simulations is the accurate and efficient prediction of the size distribution and number density of atomized drops. The multi-scale nature of these flows makes it practically impossible to capture all scales within a single simulation. In particular, the breakup processes producing the smallest drops through secondary breakup often necessitate resolutions far below the Kolmogorov scale. Consequently, models must be employed for secondary breakup. Existing physics-based and stochastic breakup models are not universal and fail to account for the local and instantaneous flow field and drop geometry. We present a physics-informed machine learning model for predicting the statistics of daughter drops generated during the breakup of under-resolved drops. By training on high-fidelity simulations, the model can predict breakup outcomes from severely under-resolved input fields. This is made possible by a careful choice of quantities of interest and by taking inspiration from the discrete nature of breakup events to encode the temporal evolution via a mixture of sigmoid functions. We showcase proof-of-concept results from the canonical settings of 3D Taylor–Green vortex flows and homogeneous isotropic turbulence. Compared to results generated by low-resolution simulations (i.e., without a model) and baseline state-of-the-art models, our approach achieves superior accuracy in predicting drop size distribution and critical quantities of interest, such as surface area. This work paves the path towards the development of embedded machine learning models for the prediction of primary and secondary breakup.