Extreme Points Research Articles

A convexity-constrained parameterization of the random effects generalized partial credit model.

An alternative closed-form expression for the marginal joint probability distribution of item scores under the random effects generalized partial credit model is presented. The closed-form expression involves a cumulant generating function and is therefore subjected to convexity constraints. As a consequence, complicated moment inequalities are taken into account in maximum likelihood estimation of the parameters of the model, so that the estimation solution is always proper. Another important favorable consequence is that the likelihood function has a single local extreme point, the global maximum. Furthermore, attention is paid to expected a posteriori person parameter estimation, generalizations of the model, and testing the goodness-of-fit of the model. Procedures proposed are demonstrated in an illustrative example.

Fractional-order stochastic gradient descent method with momentum and energy for deep neural networks

In this paper, a novel fractional-order stochastic gradient descent with momentum and energy (FOSGDME) approach is proposed. Specifically, to address the challenge of converging to a real extreme point encountered by the existing fractional gradient algorithms, a novel fractional-order stochastic gradient descent (FOSGD) method is presented by modifying the definition of the Caputo fractional-order derivative. A FOSGD with moment (FOSGDM) is established by incorporating momentum information to accelerate the convergence speed and accuracy further. In addition, to improve the robustness and accuracy, a FOSGD with moment and energy is established by further introducing energy formation. The extensive experimental results on the image classification CIFAR-10 dataset obtained with ResNet and DenseNet demonstrate that the proposed FOSGD, FOSGDM and FOSGDME algorithms are superior to the integer order optimization algorithms, and achieve state-of-the-art performance.

Smooth Dispersion Is Physically Appropriate: Assessing and Amending the D4 Dispersion Model.

The addition of dispersion corrections to density functionals is essential for accurate energy and geometry predictions. Among them, the D4 scheme is popular due to its low computational cost and high accuracy. However, due to its design, the D4 correction can occasionally lead to anomalies, such as unphysical curvature and bumps in the potential energy surface. We find these anomalies are common in the D4 model, although observable consequences are rarer than in the D3 model for reasons we explain. Nevertheless, we uncover instances of unphysical local minima and stationary points with the D4 scheme and propose two solutions that yield smoother dispersion energy as a function of nuclear position. One is trivial to implement, based on a smoother reparametrization of Gaussian weighting (D4S) to find the effective coordination number. The other replaces Gaussian weighting with soft linear interpolation (D4SL). These new approaches usually remove artificial extremum points, while maintaining accuracy.

An adversarial diverse deep ensemble approach for surrogate‐based traffic signal optimization

AbstractSurrogate‐based traffic signal optimization (TSO) is a computationally efficient alternative to simulation‐based TSO. By replacing the simulation‐based objective function, a surrogate model can quickly identify solutions by searching for extreme points on its response surface. As a popular surrogate model, the ensemble of multiple diverse deep learning models can approximate complicated systems with a strong generalizability. However, existing ensemble methods barely focus on strengthening the prediction of extreme points, which we found can be realized by further diversifying base learners in the ensemble. The study proposes an adversarial diverse ensemble (ADE) method for online TSO with limited computational resources, comprising two stages: In the offline stage, base extractors are diversified with unlabeled data by a designed adversarial diversity training algorithm; in the online stage, base predictors are trained in parallel with limited labeled data, and the ensemble then serves as the surrogate model to search for solutions iteratively for TSO. First, it is demonstrated that the prediction accuracy on extreme points, and associated solution quality, can be constantly improved with base learners’ diversity enhanced by ADE. Case studies of TSO conducted on a four‐intersection arterial further demonstrate the superior solution quality and computational efficiency of the ADE surrogate model in a wide range of traffic scenarios. Moreover, a large‐scale online TSO experiment under dynamic traffic demand proves ADE's effectiveness in practical applications.

Adversarial sample attack method based on loss smoothing

Deep neural networks (DNNs) are vulnerable to adversarial examples.Although the existing momentum-based adversarial example generation method can achieve a close 100%white-box attack success rate, it is still not ideal when attacking other models, and the black- box attack success rate is low. To address this, an adversarial example attack method based on loss smoothing is proposed to improve the transferability of adversarial examples. In the iterative process of calculating the gradient at each step, the current gradient is not used directly, but the local average gradient is used to accumulate momentum, so as to suppress the local oscillation phenomenon on the loss function surface, thereby stabilizing the update direction and escaping the local extreme point. A large number of experimental results on the ImageNet dataset show that compared with the existing momentum-based method, the average black-box attack success rate of the proposed method in single model attack experiments is improved by 38.07%and 27.77%, and the average black-box attack success rate in integrated model attack experiments is improved by and.Rising32.50%and28.63%

Geometry of Kirkwood–Dirac classical states: a case study based on discrete Fourier transform

Abstract The characterization of Kirkwood-Dirac (KD) classicality or non-classicality is very important in quantum information processing. In general, the set of KD classical states with respect to two bases is not a convex polytope[J. Math. Phys. \textbf{65} 072201 (2024)], which makes us interested in finding out in which circumnstances they do form a polytope. In this paper, we focus on the characterization of KD classicality of mixed states for the case where the transition matrix between two bases is a discrete Fourier transform (DFT) matrix in Hilbert space with dimensions $p^2$ and $pq$, respectively, where $p, q$ are prime. For the two particular cases we investigate, the sets of extremal points are finite, implying that the set of KD classical states we characterize forms a convex polytope. We show that for $p^2$ dimensional system, the set $\rm{KD}_{\mathcal{A},\mathcal{B}}^+$ is a convex hull of the set $\rm {pure}({\rm {KD}_{\mathcal{A},\mathcal{B}}^+})$ based on DFT, where $\rm{KD}_{\mathcal{A},\mathcal{B}}^+$ is the set of KD classical states with respect to two bases and $\rm {pure}({\rm {KD}_{\mathcal{A},\mathcal{B}}^+})$ is the set of all the rank-one projectors of KD classical pure states with respect to two bases. In $pq$ dimensional system, we believe that this result also holds. Unfortunately, we do not completely prove it, but some meaningful conclusions are obtained about the characterization of KD classicality.

Photovoltaic Maximum Power Point Tracking Technology Based on Improved Perturbation Observation Method and Backstepping Algorithm

Photovoltaic power generation systems mainly use the maximum power tracking (MPPT) controller to adjust the voltage and current of the solar cells in the photovoltaic array, so that the photovoltaic array runs at the maximum power point (MPP) to achieve the purpose of maximum power output. At present, photovoltaic power stations mainly adopt the traditional method to track the maximum power point, but this fixed step method easily causes output power oscillation of the photovoltaic array when tracking the maximum power point, and it easily falls into the local extreme point under partial shadow conditions. In order to solve these problems, this paper proposes an improved perturbation observation method and backstepping method (IP&O-backstepping) to replace the traditional method applied to the MPPT controller to optimize the operating state of the solar cell, thereby improving the output power point of the photovoltaic array and increasing the output power of the photovoltaic array. The algorithm first uses the improved perturbation and observation (IP&O) method to search the maximum power point of the photovoltaic array and output the reference voltage. Secondly, the reference voltage is input into the backstepping algorithm for voltage tracking. Finally, the algorithm tracks the reference voltage and makes the photovoltaic array operate at the maximum power point. The simulation is carried out by using MATLAB/Simulink. The IP&O-backstepping algorithm is compared with the intelligent algorithm and the traditional method, and the results show that compared to the above algorithm, the IP&O-backstepping algorithm can not only track the maximum power point of the photovoltaic array, but also has a faster tracking speed, and the output power has almost no oscillation when the photovoltaic array runs at the maximum power point.

Extreme-value analysis in nano-biological systems: applications and implications

AbstractExtreme value analysis (EVA) is a statistical method that studies the properties of extreme values of datasets, crucial for fields like engineering, meteorology, finance, insurance, and environmental science. EVA models extreme events using distributions such as Fréchet, Weibull, or Gumbel, aiding in risk prediction and management. This review explores EVA’s application to nanoscale biological systems. Traditionally, biological research focuses on average values from repeated experiments. However, EVA offers insights into molecular mechanisms by examining extreme data points. We introduce EVA’s concepts with simulations and review its use in studying motor protein movements within cells, highlighting the importance of in vivo analysis due to the complex intracellular environment. We suggest EVA as a tool for extracting motor proteins’ physical properties in vivo and discuss its potential in other biological systems. While there have been only a few applications of EVA to biological systems, it holds promise for uncovering hidden properties in extreme data, promoting its broader application in life sciences.

MedLSAM: Localize and segment anything model for 3D CT images

Recent advancements in foundation models have shown significant potential in medical image analysis. However, there is still a gap in models specifically designed for medical image localization. To address this, we introduce MedLAM, a 3D medical foundation localization model that accurately identifies any anatomical part within the body using only a few template scans. MedLAM employs two self-supervision tasks: unified anatomical mapping (UAM) and multi-scale similarity (MSS) across a comprehensive dataset of 14,012 CT scans. Furthermore, we developed MedLSAM by integrating MedLAM with the Segment Anything Model (SAM). This innovative framework requires extreme point annotations across three directions on several templates to enable MedLAM to locate the target anatomical structure in the image, with SAM performing the segmentation. It significantly reduces the amount of manual annotation required by SAM in 3D medical imaging scenarios. We conducted extensive experiments on two 3D datasets covering 38 distinct organs. Our findings are twofold: (1) MedLAM can directly localize anatomical structures using just a few template scans, achieving performance comparable to fully supervised models; (2) MedLSAM closely matches the performance of SAM and its specialized medical adaptations with manual prompts, while minimizing the need for extensive point annotations across the entire dataset. Moreover, MedLAM has the potential to be seamlessly integrated with future 3D SAM models, paving the way for enhanced segmentation performance. Our code is public at https://github.com/openmedlab/MedLSAM.

New subclass of meromorphic harmonic functions defined by symmetric q-calculus and domain of Janowski functions

In this article, by applying the convolution principle and symmetric q-calculus, we develop a new generalized symmetric q-difference operator of convolution type, which is applicable in the domain E⁎={τ:τ∈C and 0<|τ|<∞}. Utilizing this operator, we construct, analyze, and evaluate two new sets of meromorphically harmonic functions in the Janowski domain. Furthermore, we investigate the convolution properties and necessary conditions for a function F to belong to the class MSHP,R(q,q−1), examining the sufficiency conditions for F to satisfy these properties. Moreover, we examine key geometric properties of the function F in the class MSH‾P,R(q,q−1), including the distortion bound, convex combinations, the extreme point theorem, and weighted mean estimates.

Certain Subclass of Harmonic Multivalent Functions Defined by New Linear Operator

The main goal of the present paper is to introduce a new class of harmonic multivalent functions defined by a new linear operator in the open unit disc . Thus, some geometric properties have examined, including coefficient inequality, extreme points, convolution conditions, convex linear combinations, and integral transforms for the class .

Extrapolation Framework and Characteristic Analysis of Load Spectrum for Agriculture General Power Machinery

As a crucial step in food production, tillage and land preparation play a pivotal role in achieving sustainable crop production and improving the soil environment. However, accurate assessment of the load that agricultural machinery implements during the operation process has always been a vexing problem that needs urgent solutions. In this paper, an extrapolation and reconstruction framework for the time-domain load is constructed based on the probability-weighted moments (PWM) estimation and the peaks-over-threshold function, and the load spectrum is obtained for agriculture general power machinery. Firstly, the load acquisition system was developed, the traction resistance and output torque of the tractor were measured, and the collected load signals were preprocessed. Next, the mean excess function and PWM estimation are introduced to select the optimal threshold and generalized Pareto distribution (GPD) fitting parameters and the extreme load distribution that exceeds the threshold range is fitted. The extreme points in the original data are replaced by generating new extreme points that follow the GPD distribution, and the extrapolation of the load spectrum is achieved. Finally, the real extrapolated load spectrum was validated based on statistical characteristics and rainflow counting analysis, and the correlation coefficient between the fitting data and the extreme load samples was greater than 0.99. It can retain the load sequence characteristics of the original load to a great extent, truly reflecting the load state during the operation of agricultural machinery. Meanwhile, the characteristics of the load spectrum can be accurately obtained, such as extreme, mean, and amplitude values, and the real load during deep loosening and rotary tillage are accurately described. The values provide more authentic and reliable data support for the subsequent selection of optimal operating parameters, reliability design of the power transmission system, and the life assessment of the agricultural implements.

A Combined Quasi-Newton-Type Method Using 4th-Order Directional Derivatives for Solving Degenerate Problems of Unconstrained Optimization

Introduction. Methods of unconstrained optimization play a significant role in machine learning [1–6]. When solving practical problems in machine learning, such as tuning nonlinear regression models, the extremum point of the chosen optimality criterion is often degenerate, which significantly complicates its search. Therefore, degenerate problems are the most challenging in optimization. Known numerical methods for solving the general unconstrained optimization problem, up to the second order, have very low convergence rates when solving degenerate problems [7, 8]. This is explained by the fact that for a significant improvement in convergence rate in this case, it is necessary to use higher-order derivatives in the method than the second order [10]. The purpose of the paper is to develop an efficient quasi-Newton method for solving degenerate unconstrained optimization problems, the idea of which (unlike regularization) involves dividing the entire space into the sum of two orthogonal subspaces. This idea was introduced in [23]. The space division at each iteration of the method is based on the spectral decomposition of the matrix approximating the Hessian of the objective function using the BFGS formula [3]. Each subspace exhibits its own behavior of the objective function, and therefore, an appropriate minimization method is applied on it. Results. A combined quasi-Newton method is presented for solving degenerate unconstrained optimization problems, based on orthogonal decomposition of the Hessian approximation matrix and division of the entire space into the sum of two orthogonal subspaces. On one subspace (the kernel of the Hessian approximation matrix), a method is applied where derivatives in the direction of the 4th order are computed, while on the orthogonal complement to it, a quasi-Newtonian method is applied. A separate one-dimensional search is applied on each of these subspaces to determine the step multiplier in the respective direction. The effectiveness of the presented combined method is confirmed by numerical experiments conducted on widely accepted test functions for unconstrained optimization problems. The proposed method allows obtaining fairly accurate solutions to test tasks in case of degeneracy of the minimum point with significantly lower computational costs for gradient calculations compared to optimization procedures of well-known mathematical packages. Conclusions. The idea of dividing the entire space into the sum of two (or possibly more) orthogonal subspaces when solving complex optimization problems is quite promising in terms of applying a combination of different numerical methods on separate subspaces. In the future, it is planned to conduct theoretical research on the convergence rate of the presented combined method in solving degenerate unconstrained optimization problems. Keywords: unconstrained optimization, quasi-Newton methods, degenerate minimum point, spectral matrix decomposition, Machine Learning.

Multi-step prediction of ship heave motion using transformer-enhanced multi-scale CNN

To achieve precise multi-step heave motion prediction for active compensation control in marine equipment, an innovative approach that integrates an attention-fused multi-scale CNN with a Transformer encoder is introduced in this study. The dual-path CNN and point-wise convolution-enhanced Transformer encoder are designed to capture local features across various scales and the global characteristics of heave motion signals, respectively. Furthermore, a novel optimization objective which combines a slope factor-optimized Huber loss function with a maximum square distance loss function is proposed to better approximate the original signals at extreme points. The proposed model is trained and tested on simulated data under multiple sea conditions. In typical active compensation scenarios (Hs=3.5m), the proposed model demonstrates superior performance compared to baseline methods, achieving an RMSE of 0.0083 m, an MAE of 0.0066 m, and the upper whisker of the box plot for the prediction error is less than 0.02 m. These outcomes effectively satisfy the accuracy requirements for active compensation systems. The generalization test on real-ship collected data demonstrates excellent performance after fine-tuning. Additionally, the model is considered suitable for deployment in real-world applications due to its memory efficiency and fast inference speed.

A Hinge Moment Alleviation Control Strategy for Morphing Tail Aircraft Based on a Data-Driven Method

Morphing airplane technology is currently a focal point of research. For morphing airplanes, besides effective morphing strategies and control schemes, the hinge moment at the root of the vertical tail during morphing is a critical factor influencing flight safety. To prevent failure in tail morphing due to excessive hinge moments, this paper analyzes the hinge moment characteristics of the variable vertical tail structure in high-speed flight, based on a flying wing model from the China Aerodynamics Research and Development Center. The proposed adaptive morphing tail hinge moment reduction (AMTHR) method is model-free, utilizing real-time data to dynamically adjust the rudder and reduce hinge moments without requiring prior knowledge of system dynamics. This method utilizes the concept of extremum-seeking control by introducing periodic perturbations to the system and adjusting the control input based on their impact on the output. This approach drives the output toward an extremum point, enabling real-time reduction of the vertical tail hinge moment. Finally, the simulation analysis is carried out under the conditions of no wind and gust disturbance, and the effect of this method on the load reduction of the tail hinge moment is verified.

Developing an experiment-based strong machine learning model for performance prediction and full analysis of Maisotsenko dewpoint evaporative air cooler

Among all direct and indirect water-based evaporative air coolers, Maisotsenko indirect evaporative cooler (MIEC) is the only one which can supply sub wet-bulb air temperature while adding no moisture to the product air. For any given MIEC, four thermal/fluid parameters including dry channel flow rate, wet-to-dry-side air flow ratio, ambient air temperature and ambient relative humidity impact the performance of the MIEC. Sub-wet bulb supply temperature while having maximum cooling capacity happen only for a specific range of the mentioned thermal/fluid parameters. For any ambient condition and dry side air flow, a magic value of air-flow-ratio can maximize the cooling capacity of the cooler. Thousands of data is required to provide a simultaneous multi-aspect analysis of each parameter (while other parameters vary as well) to identify all possible curve behaviors and secrets of this technology. That is why, for the first time in this research, a strong machine learning (ML) model, is developed for MIEC cooler using 625 validated analytical/experimental-based training data (full factorial design). This model is employed to generate around 3600 unseen data to fully clarify the impact of each parameter (on supply temperature, total cooling capacity, useful cooling capacity and wet-bulb effectiveness) while other parameters are variable too. This strategy makes it possible to see all hidden extremum or peak point where the performance of the cooler is maximized or minimized. Interesting results are found in this research. For any ambient condition, there is an extremum point of the air flow ratio at which the total cooling capacity is maximized. The results indicate that as the dry side air flow increases, this extremum value decreases. For instance, under an ambient condition of 18 °C and 9 % relative humidity, the extremum point of the air flow ratio is 0.45 when the dry side air flow is 0.8 L/s and 0.25 when the dry side air flow is 4.8 L/s. In real-world commercial cooler, this can be simply happened by appropriate re-adjusting the dry and wet side fan speeds.

The Thermal Activation of Serpentinite from the Zhitikarinsky Deposit (Kazakhstan).

Changes in the phase composition of serpentinite from the Zhitikarinsky deposit (Kazakhstan) were studied during heat treatment in the temperature range of 105-800 °C in order to determine the phase that leads to an increase in the reactivity of serpentinite during interactions with acids. In accordance with this, the task was set to consider the influence of temperatures (105 °C, 600 °C, 660 °C, 725 °C, 750 °C and 800 °C), selected according to the extreme points of the main transformations from its derivatogram, on changes in the phase composition. The effects of heat treatment on the phase composition and reactivity of serpentinite during interactions with sulfuric acid were studied and discussed using the diffraction patterns of serpentinite heat treated at selected temperatures for 1 h and using methods of thermodynamic evaluation of the possible reactions in the temperature range of 350-750 °C, as well as establishing the nature of their interaction with sulfuric acid under identical conditions. It has been shown that, in the range of 600-750 °C, the crystal lattice of the structural composition of serpentinite is completely destroyed with the formation of not only magnesium silicates but possibly also magnesium oxide, which leads to the thermal activation of serpentinite in relation to interactions with acids and the improvement of the technological process of extracting magnesium from it. The greatest increase in reactivity was found in serpentinite samples heat treated at temperatures of 725 °C and 750 °C, which can be recommended for the thermal activation of serpentinite before using acid methods to improve the technological performance of the process of extracting magnesium from serpentinite.

THE HISTORIOGRAPHY OF UKRAINIAN PHILOSOPHY AND THE STUDIES IN HISTORIOGRAPHY OF PHILOSOPHY IN UKRAINE

Drawing on recent publications on studies in historiography of philosophy in French-, English-, and German-speaking philosophy, the author clarifies the subject matter and tasks of studies in historiography of philosophy as a historico-philosophical approach, in particular, counting among such subjects the images of philosophy's past constructed by histories of philosophy, as well as the historiographical attitudes of historians of philosophy and the contexts and factors that determine these historiographical attitudes. The article analyses the conceptions and implementations of three projects of studies in historiography of philosophy that have taken place in Ukraine in recent decades: the project of “History of Historico-philosophical Science”, led by Yu. Kushakov in the 1980s and 2000s and dedicated to the study of historico-philosophical conceptions of German and Russian philosophers of the 19th and early 20th; S. Rudenko's study of post-Soviet methodological approaches to the history of Ukrainian philosophy (2012); and the Ukrainian part of the bilateral project “Philosophy in the system of national culture: comparative analysis of historico-philosophical studies in Belarus and Ukraine” (2011-2012), led by V. Yevarousky and S. Yosypenko. Based on the results of the latter project and on his more recent research, the author outlines the socio-political, general philosophical and institutional context in which the historiography of Ukrainian philosophy was formed and functioned during the 20th century; analyses the images of the history of Ukrainian philosophy created by D. Tschižewskij and V. Horskyi, which embody two extreme points in the development of the historiography of Ukrainian philosophy in the 20th century; and points out the changes in the general philosophical and institutional context of historico-philosophical research in independent Ukraine and the consequences of these changes for the further development of the historiography of Ukrainian philosophy.

Extremal Polynomials and Sets of Minimal Capacity

Extremal Polynomials and Sets of Minimal Capacity

Structural Design and Horizontal Wave Force Estimation of a Wall-Climbing Robot for the Underwater Cleaning of Jackets

Currently, divers face significant safety risks when cleaning marine organisms from the steel structures of offshore underwater platform jackets. Consequently, utilizing robots instead of divers to carry out underwater biofouling removal operations will be an important development direction for the underwater maintenance of offshore platforms in the future. In this study, a wall-climbing robot was designed to clean marine organisms from the underwater surface of a platform jacket leg. The overall structure of the underwater cleaning wall-climbing robot is introduced, including the cleaning actuator and the variable curvature-adapted connecting rod mechanism. The corresponding relationship between the variable curvature-adapted connecting rod mechanism and the jacket leg is analyzed in detail. The variable curvature-adapted connecting rod mechanism was optimized using a genetic algorithm to ensure that the underwater cleaning wall-climbing robot can adapt to a minimum diameter of 1 m for the jacket leg. By drawing on Airy wave theory and random wave theory, the Airy wave parameters for waves were analyzed under different sea conditions, considering practical application scenarios. By using Fluent software 2022, a 2D numerical wave tank was constructed to simulate waves under various sea conditions, and the wave surface shapes for different sea states were determined. By building on the Morison equation, a method for calculating the horizontal wave forces on the underwater cleaning wall-climbing robot using the equivalent area and equivalent volume is proposed. By using the two aforementioned methods, the horizontal wave forces on the underwater cleaning wall-climbing robot under specific sea states were determined. The horizontal wave forces of the underwater cleaning wall-climbing robot under different sea conditions were analyzed and simulated in a 3D numerical wave tank. By comparing the theoretical analysis results with the numerical simulation results, where the maximum difference at the extreme points is approximately 11%, the feasibility of the proposed horizontal wave force estimation method was verified.