Extreme Points Research Articles

A new multiscale imaging method for estimating the depth and structural index of magnetic source

The fast automatic technique for determining the source parameter is very commonly used to interpret magnetic data. A new method is proposed to estimate the magnetic source parameter based on the any order analytic signals of magnetic anomalies at different altitudes. The new method is based on the relationship between the location, depth and structural index of the source and the expressions of analytic signals, and employs the altitude z and a depth scaling factor β to establish a new multiscale imaging method called Variable Depth Mirror Imaging (VDMI), whose extreme points are related to the source parameters. Two equations are given to calculate the source depth and structural index on the basis of the vertical positions of the peaks of VDMI sections with two different β. Moreover, a series of solutions of source parameters will be obtained when a number of β are selected, which can make the results more reasonable. The method is stable and can be directly applied to noisy anomalies or high-order derivatives because it is based on magnetic anomalies of upward continuation. In addition, the method is flexible as we can select different β as desired. Moreover, the method can be applied to multisource cases, and can simultaneously estimate the depth and structural index for each source. The method was tested on noise-free and noise-corrupted synthetic magnetic anomalies. In all cases, the VDMI method effectively estimates the depths and structural indices of the sources. The VDMI method was also applied to real aeromagnetic data from the Hamrawien area, Egypt, and ground magnetic data over Neibei Farm of Heilongjiang Province, China.

A new subclass of harmonic univalent functions associated with q-calculus

The purpose of the present paper is to introduce a new subclass of harmonic univalent functions by applying q-calculus. Coefficient inequalities, extreme points, distortion bounds, covering results, convolution condition and convex combination are determined for this class. Finally, we discuss a class preserving integral operator for this class.

Gravity and Magnetic Joint Imaging Based on Gramian Constraints

Gravity and magnetic imaging produce numerical images proportional to the density and magnetization source distribution through the upward continuation of potential field data. However, the inherent ambiguity and non-uniqueness in gravity or magnetic imaging restrict the reliability of the imaging model. We develop a joint iterative imaging framework for gravity and magnetic data based on Gramian constraints. The imaging fields of gravity and magnetic field are initially calculated by the depth from extreme points method. With the recovered magnetization and density distribution, the gradient directions of the Gramian function for these model parameters are calculated and utilized to regularize the joint imaging directions for gravity and magnetic fields. The introduction of Gramian constraints achieves mutual complementarity of the gravity and magnetic data and generates density and magnetization models with more distinct boundaries and improved structural coherence. The proposed approach is tested by two synthetic examples and applied to field data from the Galinge iron deposit in Qinghai, China. The real case results are verified by information from drillholes and physical properties measurements of ore and rock samples. Joint imaging provides an alternative to joint inversion with improved resolution and reliability of imaging models compared to separate imaging through the complementarity of gravity and magnetic data.

Extremal marginals of an unbounded local completely positive and local completely contractive map

In this paper, we consider the unbounded local completely positive and local completely contractive maps on a maximal tensor product of unital locally C ∗ -algebras and discuss on extremal points of certain convex subsets in the set of such maps.

Regulation strategy and analysis of the ultra-low temperature heat and mass transfer capacity of 3He-4He mixture in the mixing chamber of dilution refrigerator

As an important method for achieving millikelvin temperatures, dilution refrigerators (DRs) have been widely utilized in the fields of low-temperature superconductivity, low-temperature measurement, and space exploration. The mixing chamber (MC) uses a 3He-4He mixture as the refrigerant and serves as the cold end of the DR. However, the current research lacks a detailed study of the effect of the structure of porous media on the MC cooling capacity. In this study, the heat and mass transfer model in the MC is established using the finite element method. The model is based on the improved two-fluid model to evaluate its cooling capacity and propose regulation strategies. The reliability of the model is verified through experiments. When the load power stabilizes at 10 μW, the steady-state temperature is 59.6 mK, and the Kapitza thermal resistance significantly affects the cooling process of the MC. Three strategies for regulating Kapitza thermal resistance are provided. First, the optimal porosity of the sintering cylinder for the porous medium is ε = 0.5. Second, the extreme point of the sintering cylinder is at a height of h = 1.75 cm, and the cooling capacity is at its minimum at this location. Third, the steady-state temperature initially increases and then decreases with an increase in the cylinder radius. This study is of great significance as it reveals the influence of a porous medium heat exchanger on the heat and mass transfer process of mixtures at ultra-low temperatures, guiding the design of DR.

Towards Efforts to Equalize Income in Africa: The Role of Tourism Development

ABSTRACT A vast literature has investigated the nexus between tourism and income inequality in developing and developed countries. Unfortunately, the literature on the impact of tourism on income inequality in Africa is sparse. Hence, this study examines the influence of tourism on income inequality in 30 African countries over the period 1996–2020. In addition to international tourism arrivals and international tourism receipts which have been widely used by previous studies, this study uses a plethora of tourism indicators, namely business tourism spending, leisure tourism spending, internal travel and tourism consumption, domestic tourism spending, and visitor exports. Moreover, unlike previous studies that have extensively used the Gini index with its inadequacy as a measurement of income inequality; this study uses the Atkinson index and Palma ratio to capture extreme points of the inequality distribution. The empirical evidence is based on the panel-corrected standard error (PCSE) estimation technique. The results reveal that tourism contributes to the equalization of income in Africa, contingent on the type of tourism. Policy implications are discussed.

Optimizing Variational Problems through Weighted Fractional Derivatives

In this article, we explore a variety of problems within the domain of calculus of variations, specifically in the context of fractional calculus. The fractional derivative we consider incorporates the notion of weighted fractional derivatives along with derivatives with respect to another function. Besides the fractional operators, the Lagrange function depends on extremal points. We examine the fundamental problem, providing the fractional Euler–Lagrange equation and the associated transversality conditions. Both the isoperimetric and Herglotz problems are also explored. Finally, we conclude with an analysis of the variational problem, incorporating fractional derivatives of any positive real order.

Identification of the continuum field structure at multiple scale levels.

For continuum fields such as turbulence, analyses of the field structure offer insights into their kinematic and dynamic properties. To ensure the analyses are quantitative rather than merely illustrative, two conditions are essential: space-filling and structure quantification. A pertinent example is the dissipation element (DE) structure, which is however susceptible to noisy interference, rendering it inefficient for extracting the large-scale features of the field. In this study, the multi-level DE structure is proposed based on the multi-level extremal point concept. At a given scale level, the entire field can be decomposed into the corresponding space-filling and non-overlapping DEs, each characterized by its length scale l and the scalar difference Δϕ between its two extremal points. We will first elaborate on the fundamental principles of this method. Results from an artificially constructed two-scale field indicate that the decomposed units adequately represent the geometry of the original field. In examining the fractal Brownian motion, a structure function equivalent ⟨Δϕ|l⟩ and an energy spectrum equivalent are introduced. The scaling relation derived from ⟨Δϕ|l⟩ corresponds with the Hurst number. Furthermore, the multi-level DE structure distinctly reveals the two different inertial ranges in two-dimensional turbulence. Overall, this novel structure identification approach holds significant potential for complex analyses concerning the field geometry.

Dissecting Bayes: Using influence measures to test normative use of probability density information derived from a sample test.

Bayesian decision theory (BDT) is frequently used to model normative performance in perceptual, motor, and cognitive decision tasks where the possible outcomes of actions are associated with rewards or penalties. The resulting normative models specify how decision makers should encode and combine information about uncertainty and value-step by step-in order to maximize their expected reward. When prior, likelihood, and posterior are probabilities, the Bayesian computation requires only simple arithmetic operations: addition, etc. We focus on visual cognitive tasks where Bayesian computations are carried out not on probabilities but on (1) probability density functions and (2) these probability density functions are derived from samples. We break the BDT model into a series of computations and test human ability to carry out each of these computations in isolation. We test three necessary properties of normative use of pdf information derived from a sample-accuracy, additivity and influence. Influence measures allow us to assess how much weight each point in the sample is assigned in making decisions and allow us to compare normative use (weighting) of samples to actual, point by point. We find that human decision makers violate accuracy and additivity systematically but that the cost of failure in accuracy or additivity would be minor in common decision tasks. However, a comparison of measured influence for each sample point with normative influence measures demonstrates that the individual's use of sample information is markedly different from the predictions of BDT. We will show that the normative BDT model takes into account the geometric symmetries of the pdf while the human decision maker does not. An alternative model basing decisions on a single extreme sample point provided a better account for participants' data than the normative BDT model.

The extremal point process of branching Brownian motion in Rd

The extremal point process of branching Brownian motion in Rd

Convergence Analysis of Novel Fractional-Order Backpropagation Neural Networks With Regularization Terms.

Fractional-order derivatives have the potential to improve the performance of backpropagation (BP) neural networks. Several studies have found that the fractional-order gradient learning methods may not converge to real extreme points. The truncation and the modification of the fractional-order derivative are applied to guarantee convergence to the real extreme point. Nonetheless, the real convergence ability is based on the assumption that the algorithm is convergent, which limits the practicality of the algorithm. In this article, a novel truncated fractional-order BP neural network (TFO-BPNN) and a novel hybrid TFO-BPNN (HTFO-BPNN) are designed to solve the above problem. First, to avoid overfitting, a squared regularization term is introduced into the fractional-order BP neural network. Second, a novel dual cross-entropy cost function is proposed and employed as a loss function for the two neural networks. The penalty parameter helps to adjust the effect of the penalty term and further alleviates the gradient vanishing problem. In terms of convergence, the convergence ability of the two proposed neural networks is first proved. Then, the convergence ability to the real extreme point is further analyzed theoretically. Finally, the simulation results effectively illustrate the feasibility, high accuracy, and good generalization ability of the proposed neural networks. Comparative studies among the proposed neural networks and some related methods further substantiate the superiority of the TFO-BPNN and the HTFO-BPNN.

Simulation of acquisition shifts in T2 weighted fluid-attenuated inversion recovery magnetic resonance images to stress test artificial intelligence segmentation networks.

To provide a simulation framework for routine neuroimaging test data, which allows for "stress testing" of deep segmentation networks against acquisition shifts that commonly occur in clinical practice for T2 weighted (T2w) fluid-attenuated inversion recovery magnetic resonance imaging protocols. The approach simulates "acquisition shift derivatives" of MR images based on MR signal equations. Experiments comprise the validation of the simulated images by real MR scans and example stress tests on state-of-the-art multiple sclerosis lesion segmentation networks to explore a generic model function to describe the F1 score in dependence of the contrast-affecting sequence parameters echo time (TE) and inversion time (TI). The differences between real and simulated images range up to 19% in gray and white matter for extreme parameter settings. For the segmentation networks under test, the F1 score dependency on TE and TI can be well described by quadratic model functions (). The coefficients of the model functions indicate that changes of TE have more influence on the model performance than TI. We show that these deviations are in the range of values as may be caused by erroneous or individual differences in relaxation times as described by literature. The coefficients of the F1 model function allow for a quantitative comparison of the influences of TE and TI. Limitations arise mainly from tissues with a low baseline signal (like cerebrospinal fluid) and when the protocol contains contrast-affecting measures that cannot be modeled due to missing information in the DICOM header.

Some properties of subclass of multivalent functions associated with a generalized differential operator

In this paper, the new subclass Sb,λ,δ,pn(α)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {S}^n_{b,\\lambda ,\\delta ,p} ({\\alpha })$$\\end{document} of a linear differential operator’s Nλ,δ,pnf(ζ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}_{\\lambda ,\\delta ,p}^{n}f(\\zeta )$$\\end{document} associated with multivalent analytical function has been introduced. Further, the coefficient inequalities, extreme points for the extremal function, sharpness of the growth and distortion bounds, partial sums, starlikeness, and convexity of the subclass is investigated.

Research on fastDTW and isolation forest-based lightweight gesture authentication

This study explores the use of the accelerometer and gyroscope sensors in an Android mobile phone to capture data during user gesture performance. The recorded data is then processed and analyzed to extract feature values. The authentication of the user's identity may be achieved by this method, which is characterized by minimal constraints. This study initially compares the user's gesture to the template gesture using FastDTW. After that, an adaptive weighted vote determines the closest gesture template. This checks if the user is doing the template category correctly. The second stage extracts effective feature values from authentic user gestures. These feature values include efficient time-frequency domain feature values and the data extreme point spacing-to-length ratio. After that, authentic gestures are used to build the Isolation Forest to verify the user. This approach suggests a reduction in FRR, FAR, and an increase in accuracy, while using a smaller amount of data.

Magnetic and GPR Data Modelling via Multiscale Methods in San Pietro in Crapolla Abbey, Massa Lubrense (Naples)

ABSTRACTWe performed magnetic and GPR measurements to image the buried ruins of the Middle Age abbey San Pietro in Crapolla, on the Sorrento‐Amalfi Coast (Massa Lubrense, Southern Italy). The site represents an important religious location, which is nowadays partially buried along the cliff. An integrated study was necessary to map the buried structures and address the archaeological excavation. For this reason, we carried out the surveys on two main grids in order to reconstruct the structures of the abbey and of its related church. The magnetic data were filtered through the discrete wavelet transform (DWT) and then transformed to total gradient maps. The obtained maps were interpreted with depth from extreme points (DEXP) imaging method to assess the horizontal and depth positions of the top. The GPR data were processed and time‐depth converted. Results from the integrated interpretation of these data suggest the possible presence of different vaulted rooms and an elongated structure at 0.3‐m depth from ground surface. This latter is interpretable in terms of perimetral and internal walls of the abbey and its church. These outcomes were crucial to successfully address archaeological excavations, which targeted one of the modelled areas and unearthed a wall at the predicted depths.

Improvement of Z-Weighted Function Based on Fifth-Order Nonlinear Multi-Order Weighted Method for Shock Capturing of Hyperbolic Conservation Laws.

Based on a 5-point stencil and three 3-point stencils, a nonlinear multi-order weighted method adaptive to 5-3-3-3 stencils for shock capturing is presented in this paper. The form of the weighting function is the same as JS (Jiang-Shu) weighting; however, the smoothness indicator of the 5-point stencil adopts a special design with a higher-order leading term similar to the τ in Z weighting. The design maintains that the nonlinear weights satisfy sufficient conditions for the scheme to avoid degradation even near extreme points. By adjusting the linear weights to a specific value and using the τ in Z weighting, the method can be degraded to Z weighting. Analysis of linear weights shows that they do not affect the accuracy in the smooth region, and they can also adjust the resolution and discontinuity-capturing capability. Numerical tests of different hyperbolic conservation laws are conducted to test the performance of the newly designed nonlinear weights based on the weighted compact nonlinear scheme. The numerical results show that there are no obvious oscillations near the discontinuity, and the resolution of both the discontinuity and smooth regions is better than that of Z weights.

Co-occurrence order-preserving pattern mining with keypoint alignment for time series

Recently, order-preserving pattern (OPP) mining has been proposed to discover some patterns, which can be seen as trend changes in time series. Although existing OPP mining algorithms have achieved satisfactory performance, they discover all frequent patterns. However, in some cases, users focus on a particular trend and its associated trends. To efficiently discover trend information related to a specific prefix pattern, this paper addresses the issue of co-occurrence OPP mining (COP) and proposes an algorithm named COP-Miner to discover COPs from historical time series. COP-Miner consists of three parts: extracting keypoints, preparation stage, and iteratively calculating supports and mining frequent COPs. Extracting keypoints is used to obtain local extreme points of patterns and time series. The preparation stage is designed to prepare for the first round of mining, which contains four steps: obtaining the suffix OPP of the keypoint sub-time series, calculating the occurrences of the suffix OPP, verifying the occurrences of the keypoint sub-time series, and calculating the occurrences of all fusion patterns of the keypoint sub-time series. To further improve the efficiency of support calculation, we propose a support calculation method with an ending strategy that uses the occurrences of prefix and suffix patterns to calculate the occurrences of superpatterns. Experimental results indicate that COP-Miner outperforms the other competing algorithms in running time and scalability. Moreover, COPs with keypoint alignment yield better prediction performance.

Some properties of a class of holomorphic functions associated with tangent function

Abstract In this study, we define new class of holomorphic functions associated with tangent function. Furthermore, we examine the differential subordination implementation results related to Janowski and tangent functions. Also, we investigate some extreme point theorem and partial sums results, necessary and sufficient conditions, convex combination, closure theorem, growth and distortion bounds, and radii of close-to-starlikeness and starlikeness for this newly defined functions class of holomorphic functions.

What Are and What Are Not Extrema Points? Examining Definitions and Examples

AbstractThis paper reports on five secondary school mathematics prospective teachers’ conceptions of extreme point. The analysis of the data addressed students’ definitions, examples, and evaluation of given examples, with special attention to the related domain. Written assignments and individual interviews uncover salient, erroneous concept images regarding what is and what is not an extreme point. Participants viewed extrema points as points that necessarily satisfy f′ = 0 or as points that are always at a “change in monoticity” of the function. The topic “extreme points” is both an aim and a mean to address broader issues related to mathematical definitions, examples, and nonexamples. We conclude with possible next-step ideas.

Homicide in Global Extremes: Exploring the Feasibility of EHM-Based Analysis in Finland and South Africa

Homicide remains a major cause of death globally. The global risk differentials are a persistent public health challenge. Africa’s homicide rate of 13 victims per 100,000 people is markedly higher than the European average (2.2 per 100,000 people). To understand the causes of such large differences, homicide research needs to move from country-level rates to disaggregated analyses in which homicide is broken down by victim, offender, and incident characteristics. We conducted a pilot study in which the European Homicide Monitor (EHM) coding manual is applied to a South African research location and compared to an extreme point in the Global North, Finnish urban areas. We find differential patterns in the two locations. The high-rate context of South Africa manifests a younger offender and victim age structure, a higher share of criminal and revenge motives and the use of firearms, and incidents in public places. In contrast, the comparatively low-rate Finnish context shows a higher relative share of intimate partner violence and familial incidents taking place in private places. The role of alcohol and drugs appears more salient in Finnish urban homicide, a finding calling for replication. We conclude by discussing the methodological challenges revealed by the pilot comparison.