Symmetry

Research

Jump to: Review

24 pages, 1966 KiB

Open AccessArticle

A Hybrid Bayesian Machine Learning Framework for Simultaneous Job Title Classification and Salary Estimation

by Wail Zita, Sami Abou El Faouz, Mohanad Alayedi and Ebrahim E. Elsayed

Symmetry 2025, 17(8), 1261; https://doi.org/10.3390/sym17081261 - 7 Aug 2025

Viewed by 237

Abstract

In today’s fast-paced and evolving job market, salary continues to play a critical role in career decision-making. The ability to accurately classify job titles and predict corresponding salary ranges is increasingly vital for organizations seeking to attract and retain top talent. This paper [...] Read more.

In today’s fast-paced and evolving job market, salary continues to play a critical role in career decision-making. The ability to accurately classify job titles and predict corresponding salary ranges is increasingly vital for organizations seeking to attract and retain top talent. This paper proposes a novel approach, the Hybrid Bayesian Model (HBM), which combines Bayesian classification with advanced regression techniques to jointly address job title identification and salary prediction. HBM is designed to capture the inherent complexity and variability of real-world job market data. The model was evaluated against established machine learning (ML) algorithms, including Random Forests (RF), Support Vector Machines (SVM), Decision Trees (DT), and multinomial naïve Bayes classifiers. Experimental results show that HBM outperforms these benchmarks, achieving 99.80% accuracy, 99.85% precision, 100% recall, and an F1 score of 98.8%. These findings highlight the potential of hybrid ML frameworks to improve labor market analytics and support data-driven decision-making in global recruitment strategies. Consequently, the suggested HBM algorithm provides high accuracy and handles the dual tasks of job title classification and salary estimation in a symmetric way. It does this by learning from class structures and mirrored decision limits in feature space. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

► Show Figures

Figure 1

16 pages, 278 KiB

Open AccessArticle

Maximal Norms of Orthogonal Projections and Closed-Range Operators

by Salma Aljawi, Cristian Conde, Kais Feki and Shigeru Furuichi

Symmetry 2025, 17(7), 1157; https://doi.org/10.3390/sym17071157 - 19 Jul 2025

Viewed by 233

Abstract

Using the Dixmier angle between two closed subspaces of a complex Hilbert space

H

, we establish the necessary and sufficient conditions for the operator norm of the sum of two orthogonal projections,

P_{W_{1}}

and

P_{W_{2}}

, onto closed [...] Read more.

Using the Dixmier angle between two closed subspaces of a complex Hilbert space

H

, we establish the necessary and sufficient conditions for the operator norm of the sum of two orthogonal projections,

P_{W_{1}}

and

P_{W_{2}}

, onto closed subspaces

W_{1}

and

W_{2}

, to attain its maximum, namely

∥ P_{W_{1}} + P_{W_{2}} ∥ = 2 .

These conditions are expressed in terms of the geometric relationship and symmetry between the ranges of the projections. We apply these results to orthogonal projections associated with a closed-range operator via its Moore–Penrose inverse. Additionally, for any bounded operator T with closed range in

H

, we derive sufficient conditions ensuring

∥ T T^{†} + T^{†} T ∥ = 2,

where

T^{†}

denotes the Moore–Penrose inverse of T. This work highlights how symmetry between operator ranges and their algebraic structure governs norm extremality and extends a recent finite-dimensional result to the general Hilbert space setting. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

20 pages, 922 KiB

Open AccessArticle

Distributed Time Delay Models: An Alternative to Fractional Calculus-Based Models for Fractional Behavior Modeling

by Jocelyn Sabatier

Symmetry 2025, 17(7), 1101; https://doi.org/10.3390/sym17071101 - 9 Jul 2025

Viewed by 337

Abstract

This paper illustrates that distributed time delay models can exhibit fractional behaviors, addressing the limitations of fractional calculus-based models outlined in the introduction. Given the extensive results generated by these models, they present a compelling alternative to fractional models. The demonstration is done [...] Read more.

This paper illustrates that distributed time delay models can exhibit fractional behaviors, addressing the limitations of fractional calculus-based models outlined in the introduction. Given the extensive results generated by these models, they present a compelling alternative to fractional models. The demonstration is done both in discrete time and in continuous time. The two cases yield fractional behavior within a defined time/frequency range. To conclude and using two examples, the article highlights that modeling fractional behaviors using distributed delay systems allows for coherent physical interpretations, which a fractional model representation struggles to achieve. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

► Show Figures

Figure 1

25 pages, 2709 KiB

Open AccessArticle

Dynamics of a Modified Lotka–Volterra Commensalism System Incorporating Allee Effect and Symmetric Non-Selective Harvest

by Kan Fang, Yiqin Wang, Fengde Chen and Xiaoying Chen

Symmetry 2025, 17(6), 852; https://doi.org/10.3390/sym17060852 - 30 May 2025

Viewed by 487

Abstract

This study investigates a modified Lotka–Volterra commensalism system that incorporates the weak Allee effect in prey and symmetric (equal harvesting effort for both species) non-selective harvesting, addressing a critical gap in ecological modeling. Unlike previous work, we rigorously examine how the interaction between [...] Read more.

This study investigates a modified Lotka–Volterra commensalism system that incorporates the weak Allee effect in prey and symmetric (equal harvesting effort for both species) non-selective harvesting, addressing a critical gap in ecological modeling. Unlike previous work, we rigorously examine how the interaction between the Allee effect and harvesting disrupts system stability, giving rise to novel bifurcation phenomena and population collapse thresholds. Using eigenvalue analysis and the Dulac–Bendixson criterion, we derive sufficient conditions for the existence and stability of equilibria. We find that harvesting destabilizes the system by inducing two saddle-node bifurcations. Notably, prey abundance can increase with greater Allee intensity under controlled harvesting—a rare and counterintuitive ecological outcome. Moreover, exceeding a critical harvesting threshold drives both species to extinction, while controlled harvesting allows sustainable coexistence. Numerical simulations support these analytical findings and identify critical parameter ranges for species coexistence. These results contribute to theoretical ecology and offer insights for designing sustainable harvesting strategies that balance exploitation with conservation. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

► Show Figures

Figure 1

15 pages, 277 KiB

Open AccessArticle

Harmonic Functions with Montel’s Normalization

by Jacek Dziok

Symmetry 2025, 17(5), 720; https://doi.org/10.3390/sym17050720 - 8 May 2025

Viewed by 215

Abstract

In the Geometric Theory of Analytic Functions, classes of functions with several normalizations are considered. We consider the symmetric idea for harmonic functions. Classes of harmonic functions f with normalization

f (0) = f_{\bar{z}}^{'} (0) = 0,

[...] Read more.

In the Geometric Theory of Analytic Functions, classes of functions with several normalizations are considered. We consider the symmetric idea for harmonic functions. Classes of harmonic functions f with normalization

f (0) = f_{\bar{z}}^{'} (0) = 0,

f_{z}^{'} (0) = 1

are usually considered in the geometric theory of harmonic functions. The normalization is called the classical normalization. We can obtain some interesting results by using Montel’s normalization

f (0) = f_{\bar{z}}^{'} (0) = 0,

f_{z}^{'} (ρ) - f_{\bar{z}}^{'} (ρ) = 1

, where

ρ \in [0, 1) .

In the paper, we consider the class of harmonic functions with Montel’s normalization associated with the generalized hypergeometric function. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

17 pages, 13197 KiB

Open AccessArticle

Dual Graph Laplacian RPCA Method for Face Recognition Based on Anchor Points

by Shu-Ting Zhuang, Qing-Wen Wang and Jiang-Feng Chen

Symmetry 2025, 17(5), 691; https://doi.org/10.3390/sym17050691 - 30 Apr 2025

Viewed by 370

Abstract

High-dimensional data often contain noise and undancy, which can significantly undermine the performance of machine learning. To address this challenge, we propose an advanced robust principal component analysis (RPCA) model that integrates bidirectional graph Laplacian constraints along with the anchor point technique. This [...] Read more.

High-dimensional data often contain noise and undancy, which can significantly undermine the performance of machine learning. To address this challenge, we propose an advanced robust principal component analysis (RPCA) model that integrates bidirectional graph Laplacian constraints along with the anchor point technique. This approach constructs two graphs from both the sample and feature perspectives for a more comprehensive capture of the underlying data structure. Moreover, the anchor point technique serves to substantially reduce computational complexity, making the model more efficient and scalable. Comprehensive evaluations on both GTdatabase and VGG Face2 dataset confirm that anchor-based methods maintain competitive accuracy with standard graph Laplacian approaches (within 0.5–2.0% difference) while achieving significant computational speedups of 5.7–27.1% and 12.9–14.6% respectively. The consistent performance across datasets, from controlled laboratory conditions to challenging real-world scenarios, demonstrates the robustness and scalability of the proposed anchor technique. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

► Show Figures

Figure 1

15 pages, 335 KiB

Open AccessArticle

On the Secant Non-Defectivity of Integral Hypersurfaces of Projective Spaces of at Most Five Dimensions

by Edoardo Ballico

Symmetry 2025, 17(3), 454; https://doi.org/10.3390/sym17030454 - 18 Mar 2025

Viewed by 235

Abstract

Let

X \subset P^{n}

, where

3 \leq n \leq 5

, be an irreducible hypersurface of degree

d \geq 2

. Fix an integer

t \geq 3

. If

n = 5

, assume

t \geq 4

and [...] Read more.

Let

X \subset P^{n}

, where

3 \leq n \leq 5

, be an irreducible hypersurface of degree

d \geq 2

. Fix an integer

t \geq 3

. If

n = 5

, assume

t \geq 4

and

(t, d) \neq (4, 2)

. Using the Differential Horace Lemma, we prove that

O_{X} (t)

is not secant defective. For a fixed X, our proof uses induction on the integer t. The key points of our method are that for a fixed X, we only need the case of general linear hyperplane sections of X in lower-dimension projective spaces and that we do not use induction on d, allowing an interested reader to tackle a specific X for

n > 5

. We discuss (as open questions) possible extensions of some weaker forms of the theorem to the case where

n > 5

. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

Review

Jump to: Research

81 pages, 2075 KiB

Open AccessReview

A Comprehensive Review on Solving the System of Equations AX = C and XB = D

by Qing-Wen Wang, Zi-Han Gao and Jia-Le Gao

Symmetry 2025, 17(4), 625; https://doi.org/10.3390/sym17040625 - 21 Apr 2025

Cited by 3 | Viewed by 418

Abstract

This survey provides a review of the theoretical research on the classic system of matrix equations

A X = C

and

X B = D

, which has wide-ranging applications across fields such as control theory, optimization, image processing, and robotics. The paper [...] Read more.

This survey provides a review of the theoretical research on the classic system of matrix equations

A X = C

and

X B = D

, which has wide-ranging applications across fields such as control theory, optimization, image processing, and robotics. The paper discusses various solution methods for the system, focusing on specialized approaches, including generalized inverse methods, matrix decomposition techniques, and solutions in the forms of Hermitian, extreme rank, reflexive, and conjugate solutions. Additionally, specialized solving methods for specific algebraic structures, such as Hilbert spaces, Hilbert

C^{*}

-modules, and quaternions, are presented. The paper explores the existence conditions and explicit expressions for these solutions, along with examples of their application in color images. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Mathematics: Feature Papers 2025

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (8 papers)

Research

Review

Further Information

Guidelines

MDPI Initiatives

Follow MDPI