Journal Description
Axioms
Axioms
is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published monthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT), International Fuzzy Systems Association (IFSA) and Union of Slovak Mathematicians and Physicists (JSMF) are affiliated with Axioms and their members receive discounts on the article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High visibility: indexed within SCIE (Web of Science), dblp, and other databases.
- Journal Rank: JCR - Q2 (Mathematics, Applied)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 21.8 days after submission; acceptance to publication is undertaken in 2.8 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Companion journal: Logics.
Impact Factor:
2.0 (2022);
5-Year Impact Factor:
1.9 (2022)
Latest Articles
Product States of Infinite Tensor Product of JC-Algebras
Axioms 2024, 13(3), 205; https://doi.org/10.3390/axioms13030205 (registering DOI) - 18 Mar 2024
Abstract
The objective of our study is to generalize the results on product states of the tensor product of two JC-algebras to infinite tensor product JC-algebras. Also, we characterize the tracial product state of the tensor product of two JC-algebras, and the tracial product
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The objective of our study is to generalize the results on product states of the tensor product of two JC-algebras to infinite tensor product JC-algebras. Also, we characterize the tracial product state of the tensor product of two JC-algebras, and the tracial product state of infinite tensor products of JC-algebras.
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(This article belongs to the Special Issue Yang-Baxter Equations, Nonassociative Structures and Applications—In Memoriam, Stefan Papadima)
Open AccessArticle
Generating Geometric Patterns Using Complex Polynomials and Iterative Schemes
by
Asifa Tassaddiq, Amna Kalsoom, Maliha Rashid, Kainat Sehr and Dalal Khalid Almutairi
Axioms 2024, 13(3), 204; https://doi.org/10.3390/axioms13030204 - 18 Mar 2024
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Iterative procedures have been proved as a milestone in the generation of fractals. This paper presents a novel approach for generating and visualizing fractals, specifically Mandelbrot and Julia sets, by utilizing complex polynomials of the form
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Iterative procedures have been proved as a milestone in the generation of fractals. This paper presents a novel approach for generating and visualizing fractals, specifically Mandelbrot and Julia sets, by utilizing complex polynomials of the form , where . It establishes escape criteria that play a vital role in generating these sets and provides escape time results using different iterative schemes. In addition, the study includes the visualization of graphical images of Julia and Mandelbrot sets, revealing distinct patterns. Furthermore, the study also explores the impact of parameters on the deviation of dynamics, color, and appearance of fractals.
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Open AccessArticle
3F4 Hypergeometric Functions as a Sum of a Product of 2F3 Functions
by
Jack C. Straton
Axioms 2024, 13(3), 203; https://doi.org/10.3390/axioms13030203 - 18 Mar 2024
Abstract
This paper shows that certain hypergeometric functions can be expanded in sums of pair products of functions, which reduce in special cases to functions expanded in sums of pair products of
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This paper shows that certain hypergeometric functions can be expanded in sums of pair products of functions, which reduce in special cases to functions expanded in sums of pair products of functions. This expands the class of hypergeometric functions having summation theorems beyond those expressible as pair-products of generalized Whittaker functions, functions, and functions into the realm of functions where for both the summand and terms in the series. In addition to its intrinsic value, this result has a specific application in calculating the response of the atoms to laser stimulation in the Strong Field Approximation.
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(This article belongs to the Special Issue Advances in Generalized Hypergeometric Functions, Integral Transforms and Number Theory)
Open AccessArticle
On the Two-Variable Analogue Matrix of Bessel Polynomials and Their Properties
by
Ahmed Bakhet, Shahid Hussain, Mohamed Niyaz, Mohammed Zakarya and Ghada AlNemer
Axioms 2024, 13(3), 202; https://doi.org/10.3390/axioms13030202 - 17 Mar 2024
Abstract
In this paper, we explore a study focused on a two-variable extension of matrix Bessel polynomials. We initiate the discussion by introducing the matrix Bessel polynomials involving two variables and derive specific differential formulas and recurrence relations associated with them. Additionally, we present
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In this paper, we explore a study focused on a two-variable extension of matrix Bessel polynomials. We initiate the discussion by introducing the matrix Bessel polynomials involving two variables and derive specific differential formulas and recurrence relations associated with them. Additionally, we present a segment detailing integral formulas for the extended matrix Bessel polynomials. Lastly, we introduce the Laplace–Carson transform for the two-variable matrix Bessel polynomial analogue.
Full article
(This article belongs to the Special Issue Research in Special Functions)
Open AccessArticle
Approximate and Parametric Solutions to SIR Epidemic Model
by
Lazhar Bougoffa, Smail Bougouffa and Ammar Khanfer
Axioms 2024, 13(3), 201; https://doi.org/10.3390/axioms13030201 (registering DOI) - 16 Mar 2024
Abstract
This article provides a detailed exploration of the SIR epidemic model, starting with its meticulous formulation. The study employs a novel approach called the upper and lower bounds technique to approximate the solution to the SIR model, providing insights into the dynamic interplay
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This article provides a detailed exploration of the SIR epidemic model, starting with its meticulous formulation. The study employs a novel approach called the upper and lower bounds technique to approximate the solution to the SIR model, providing insights into the dynamic interplay between susceptible S, infected I, and recovered R populations. A new parametric solution to this model has been presented. Applying the Adomian decomposition method (ADM) allows for the attaining of highly accurate approximate solutions in the context of the SIR epidemic model. To validate the accuracy and robustness of the proposed approach, a numerical exploration is conducted, considering a diverse range of experimental parameters. This numerical analysis provides valuable insights into the sensitivity and responsiveness of the SIR epidemic model under varying conditions, contributing to the broader understanding of infectious disease dynamics. The interplay between theoretical formulation and numerical exploration establishes a comprehensive framework for studying the SIR model, with implications for refining our ability to predict and manage the spread of infectious diseases.
Full article
(This article belongs to the Special Issue Infinite Dynamical System and Differential Equations)
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Open AccessArticle
Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty
by
Xinya Li, Yan Sun, Jinfeng Qi and Danzhu Wang
Axioms 2024, 13(3), 200; https://doi.org/10.3390/axioms13030200 - 16 Mar 2024
Abstract
This study investigates a green multimodal routing problem with soft time window. The objective of routing is to minimize the total costs of accomplishing the multimodal transportation of a batch of goods. To improve the feasibility of optimization, this study formulates the routing
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This study investigates a green multimodal routing problem with soft time window. The objective of routing is to minimize the total costs of accomplishing the multimodal transportation of a batch of goods. To improve the feasibility of optimization, this study formulates the routing problem in an uncertain environment where the capacities and carbon emission factors of the travel process and the transfer process in the multimodal network are considered fuzzy. Taking triangular fuzzy numbers to describe the uncertainty, this study proposes a fuzzy nonlinear programming model to deal with the specific routing problem. To make the problem solvable, this study adopts the fuzzy chance-constrained programming approach based on the possibility measure to remove the fuzziness of the proposed model. Furthermore, we use linear inequality constraints to reformulate the nonlinear equality constraints represented by the continuous piecewise linear functions and realize the linearization of the nonlinear programming model to improve the computational efficiency of problem solving. After model processing, we can utilize mathematical programming software to run exact solution algorithms to solve the specific routing problem. A numerical experiment is given to show the feasibility of the proposed model. The sensitivity analysis of the numerical experiment further clarifies how improving the confidence level of the chance constraints to enhance the possibility that the multimodal route planned in advance satisfies the real-time capacity constraint in the actual transportation, i.e., the reliability of the routing, increases both the total costs and carbon emissions of the route. The numerical experiment also finds that charging carbon emissions is not absolutely effective in emissions reduction. In this condition, bi-objective analysis indicates the conflicting relationship between lowering transportation activity costs and reducing carbon emissions in routing optimization. The sensitivity of the Pareto solutions concerning the confidence level reveals that reliability, economy, and environmental sustainability are in conflict with each other. Based on the findings of this study, the customer and the multimodal transport operator can organize efficient multimodal transportation, balancing the above objectives using the proposed model.
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(This article belongs to the Special Issue Dynamic Optimization, Optimal Control and Machine Learning)
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On Proximity Spaces Constructed on Rough Sets
by
Jong Il Baek, S. E. Abbas, Kul Hur and Ismail Ibedou
Axioms 2024, 13(3), 199; https://doi.org/10.3390/axioms13030199 - 15 Mar 2024
Abstract
Based on equivalence relation R on X, equivalence class of a point and equivalence class of a subset represent the neighborhoods of x and A, respectively. These neighborhoods play the main role in defining separation
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Based on equivalence relation R on X, equivalence class of a point and equivalence class of a subset represent the neighborhoods of x and A, respectively. These neighborhoods play the main role in defining separation axioms, metric spaces, proximity relations and uniformity structures on an approximation space depending on the lower approximation and the upper approximation of rough sets. The properties and the possible implications of these definitions are studied. The generated approximation topology on X is equivalent to the generated topologies associated with metric d, proximity and uniformity on X. Separated metric spaces, separated proximity spaces and separated uniform spaces are defined and it is proven that both are associating exactly discrete topology on X.
Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Its Applications)
Open AccessArticle
Fuzzy Decision-Making and Resource Management Model of Performance Evaluation Indices
by
Kuen-Suan Chen, Tsung-Hua Hsieh, Chia-Pao Chang, Kai-Chao Yao and Tsun-Hung Huang
Axioms 2024, 13(3), 198; https://doi.org/10.3390/axioms13030198 - 15 Mar 2024
Abstract
The Performance Evaluation Matrix (PEM) is an excellent decision-making tool for assessment and resource management. Satisfaction Index and Importance Index are two important evaluation indicators of construction and PEM. Managers can decide whether the service item needs to be improved based on the
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The Performance Evaluation Matrix (PEM) is an excellent decision-making tool for assessment and resource management. Satisfaction Index and Importance Index are two important evaluation indicators of construction and PEM. Managers can decide whether the service item needs to be improved based on the Satisfaction Index of the service item. When resources are limited, managers can determine the priority of improving the service item based on the Importance Index. In order to avoid the risk of misjudgment caused by sample errors and meet the needs of enterprises’ rapid decision-making, this study proposed a fuzzy test built on the confidence intervals of the above two key indicators to decide whether essential service items should be improved and determine the priority of improvement. Since the fuzzy test was relatively complex, this study further came up with fuzzy evaluation values and fuzzy evaluation critical values of service items following fuzzy testing rules. Besides, evaluation rules were established to facilitate industrial applications. This approach can be completed with any common word processing software, so it is relatively convenient in application and easy to manage. Finally, an application example was presented in this paper to explain the applicability of the proposed approach.
Full article
(This article belongs to the Special Issue Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications)
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Open AccessArticle
Optimal Construction for Decoding 2D Convolutional Codes over an Erasure Channel
by
Raquel Pinto, Marcos Spreafico and Carlos Vela
Axioms 2024, 13(3), 197; https://doi.org/10.3390/axioms13030197 - 15 Mar 2024
Abstract
In general, the problem of building optimal convolutional codes under a certain criteria is hard, especially when size field restrictions are applied. In this paper, we confront the challenge of constructing an optimal 2D convolutional code when communicating over an erasure channel. We
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In general, the problem of building optimal convolutional codes under a certain criteria is hard, especially when size field restrictions are applied. In this paper, we confront the challenge of constructing an optimal 2D convolutional code when communicating over an erasure channel. We propose a general construction method for these codes. Specifically, we provide an optimal construction where the decoding method presented in the bibliography is considered.
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(This article belongs to the Special Issue Advances in Linear Algebra with Applications)
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Open AccessArticle
New Summation and Integral Representations for 2-Variable (p,q)-Hermite Polynomials
by
Nusrat Raza, Mohammed Fadel and Wei-Shih Du
Axioms 2024, 13(3), 196; https://doi.org/10.3390/axioms13030196 - 15 Mar 2024
Abstract
In this paper, we introduce and study new features for 2-variable -Hermite polynomials, such as the -diffusion equation, -differential formula and integral representations. In addition, we establish some
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In this paper, we introduce and study new features for 2-variable -Hermite polynomials, such as the -diffusion equation, -differential formula and integral representations. In addition, we establish some summation models and their -derivatives. Certain parting remarks and nontrivial examples are also provided.
Full article
(This article belongs to the Special Issue New Theory and Applications of Nonlinear Analysis, Fractional Calculus and Optimization)
Open AccessArticle
Some Chen Inequalities for Submanifolds in Trans-Sasakian Manifolds Admitting a Semi-Symmetric Non-Metric Connection
by
Mohammed Mohammed, Fortuné Massamba, Ion Mihai, Abd Elmotaleb A. M. A. Elamin and M. Saif Aldien
Axioms 2024, 13(3), 195; https://doi.org/10.3390/axioms13030195 - 15 Mar 2024
Abstract
In the present article, we study submanifolds tangent to the Reeb vector field in trans-Sasakian manifolds. We prove Chen’s first inequality and the Chen–Ricci inequality, respectively, for such submanifolds in trans-Sasakian manifolds which admit a semi-symmetric non-metric connection. Moreover, a generalized Euler inequality
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In the present article, we study submanifolds tangent to the Reeb vector field in trans-Sasakian manifolds. We prove Chen’s first inequality and the Chen–Ricci inequality, respectively, for such submanifolds in trans-Sasakian manifolds which admit a semi-symmetric non-metric connection. Moreover, a generalized Euler inequality for special contact slant submanifolds in trans-Sasakian manifolds endowed with a semi-symmetric non-metric connection is obtained.
Full article
(This article belongs to the Special Issue Differential Geometry and Its Application II)
Open AccessArticle
The Generalized 3-Connectivity of Exchanged Folded Hypercubes
by
Wantao Ning and Hao Li
Axioms 2024, 13(3), 194; https://doi.org/10.3390/axioms13030194 - 14 Mar 2024
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For denotes the maximum number k of edge disjoint trees in G, such that for any and . For an integer , the generalized r-connectivity of G is defined as . In fact, is the traditional connectivity of G. Hence, the generalized r-connectivity is an extension of traditional connectivity. The exchanged folded hypercube , in which and are positive integers, is a variant of the hypercube. In this paper, we find that with .
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Open AccessArticle
Ratio-Covarieties of Numerical Semigroups
by
María Ángeles Moreno-Frías and José Carlos Rosales
Axioms 2024, 13(3), 193; https://doi.org/10.3390/axioms13030193 - 14 Mar 2024
Abstract
In this work, we will introduce the concept of ratio-covariety, as a family of numerical semigroups that has a minimum, denoted by is closed under intersection, and if and
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In this work, we will introduce the concept of ratio-covariety, as a family of numerical semigroups that has a minimum, denoted by is closed under intersection, and if and , then where denotes the ratio of The notion of ratio-covariety will allow us to: (1) describe an algorithmic procedure to compute ; (2) prove the existence of the smallest element of that contains a set of positive integers; and (3) talk about the smallest ratio-covariety that contains a finite set of numerical semigroups. In addition, in this paper we will apply the previous results to the study of the ratio-covariety
Full article
(This article belongs to the Special Issue The Pythagorean Heritage: From Number Theory and Combinatorics to Artificial Intelligence)
Open AccessArticle
Moduli of Continuity in Metric Models and Extension of Livability Indices
by
Roger Arnau, Jose M. Calabuig, Álvaro González and Enrique A. Sánchez Pérez
Axioms 2024, 13(3), 192; https://doi.org/10.3390/axioms13030192 - 14 Mar 2024
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Index spaces serve as valuable metric models for studying properties relevant to various applications, such as social science or economics. These properties are represented by real Lipschitz functions that describe the degree of association with each element within the underlying metric space. After
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Index spaces serve as valuable metric models for studying properties relevant to various applications, such as social science or economics. These properties are represented by real Lipschitz functions that describe the degree of association with each element within the underlying metric space. After determining the index value within a given sample subset, the classic McShane and Whitney formulas allow a Lipschitz regression procedure to be performed to extend the index values over the entire metric space. To improve the adaptability of the metric model to specific scenarios, this paper introduces the concept of a composition metric, which involves composing a metric with an increasing, positive and subadditive function . The results presented here extend well-established results for Lipschitz indices on metric spaces to composition metrics. In addition, we establish the corresponding approximation properties that facilitate the use of this functional structure. To illustrate the power and simplicity of this mathematical framework, we provide a concrete application involving the modeling of livability indices in North American cities.
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Open AccessArticle
On Blow-Up Solutions for the Fourth-Order Nonlinear Schrödinger Equation with Mixed Dispersions
by
Huiling Niu, Abdoulaye Ali Youssouf and Binhua Feng
Axioms 2024, 13(3), 191; https://doi.org/10.3390/axioms13030191 - 13 Mar 2024
Abstract
In this paper, we consider blow-up solutions for the fourth-order nonlinear Schrödinger equation with mixed dispersions. We study the dynamical properties of blow-up solutions for this equation, including the -concentration and limiting profiles, which extend and improve the existing
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In this paper, we consider blow-up solutions for the fourth-order nonlinear Schrödinger equation with mixed dispersions. We study the dynamical properties of blow-up solutions for this equation, including the -concentration and limiting profiles, which extend and improve the existing results in the literature.
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Open AccessArticle
New Simplified High-Order Schemes for Solving SDEs with Markovian Switching Driven by Pure Jumps
by
Yang Li, Yingmei Xu, Qianhai Xu and Yu Zhang
Axioms 2024, 13(3), 190; https://doi.org/10.3390/axioms13030190 - 13 Mar 2024
Abstract
New high-order weak schemes are proposed and simplified to solve stochastic differential equations with Markovian switching driven by pure jumps (PJ-SDEwMs). Using Malliavin calculus theory, it is rigorously proven that the new numerical schemes can achieve a high-order convergence rate. Some numerical experiments
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New high-order weak schemes are proposed and simplified to solve stochastic differential equations with Markovian switching driven by pure jumps (PJ-SDEwMs). Using Malliavin calculus theory, it is rigorously proven that the new numerical schemes can achieve a high-order convergence rate. Some numerical experiments are provided to show the efficiency and accuracy.
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(This article belongs to the Special Issue Differential Equations and Inverse Problems)
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Translational Regular Variability and the Index Function
by
Danica Fatić, Dragan Djurčić and Ljubiša D. R. Kočinac
Axioms 2024, 13(3), 189; https://doi.org/10.3390/axioms13030189 - 13 Mar 2024
Abstract
This paper deals with translational regular and rapid variations. By using a new method of proving the Galambos–Bojanić-Seneta type theorems, we prove two theorems of this type for translationally regularly varying and translationally rapidly varying functions and sequences, important objects in the asymptotic
[...] Read more.
This paper deals with translational regular and rapid variations. By using a new method of proving the Galambos–Bojanić-Seneta type theorems, we prove two theorems of this type for translationally regularly varying and translationally rapidly varying functions and sequences, important objects in the asymptotic analysis of divergent processes. Also, we introduce and study the index functions for translationally regularly varying functions and sequences. For example, we prove that the index function of a translationally regularly varying function is also in the same class of functions.
Full article
(This article belongs to the Section Mathematical Analysis)
Open AccessArticle
ℤ2 × ℤ2 Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks
by
Zhongtian Dong, Marçal Comajoan Cara, Gopal Ramesh Dahale, Roy T. Forestano, Sergei Gleyzer, Daniel Justice, Kyoungchul Kong, Tom Magorsch, Konstantin T. Matchev, Katia Matcheva and Eyup B. Unlu
Axioms 2024, 13(3), 188; https://doi.org/10.3390/axioms13030188 - 13 Mar 2024
Abstract
This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three
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This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three two-dimensional toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training dataset. Our results show that the EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.
Full article
(This article belongs to the Special Issue Computational Aspects of Machine Learning and Quantum Computing)
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Hybrid Quantum Vision Transformers for Event Classification in High Energy Physics
by
Eyup B. Unlu, Marçal Comajoan Cara, Gopal Ramesh Dahale, Zhongtian Dong, Roy T. Forestano, Sergei Gleyzer, Daniel Justice, Kyoungchul Kong, Tom Magorsch, Konstantin T. Matchev and Katia Matcheva
Axioms 2024, 13(3), 187; https://doi.org/10.3390/axioms13030187 - 13 Mar 2024
Abstract
Models based on vision transformer architectures are considered state-of-the-art when it comes to image classification tasks. However, they require extensive computational resources both for training and deployment. The problem is exacerbated as the amount and complexity of the data increases. Quantum-based vision transformer
[...] Read more.
Models based on vision transformer architectures are considered state-of-the-art when it comes to image classification tasks. However, they require extensive computational resources both for training and deployment. The problem is exacerbated as the amount and complexity of the data increases. Quantum-based vision transformer models could potentially alleviate this issue by reducing the training and operating time while maintaining the same predictive power. Although current quantum computers are not yet able to perform high-dimensional tasks, they do offer one of the most efficient solutions for the future. In this work, we construct several variations of a quantum hybrid vision transformer for a classification problem in high-energy physics (distinguishing photons and electrons in the electromagnetic calorimeter). We test them against classical vision transformer architectures. Our findings indicate that the hybrid models can achieve comparable performance to their classical analogs with a similar number of parameters.
Full article
(This article belongs to the Special Issue Computational Aspects of Machine Learning and Quantum Computing)
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Regularization of the Boundary Equilibrium Bifurcation in Filippov System with Rich Discontinuity Boundaries
by
Nanbin Cao, Yue Zhang and Xia Liu
Axioms 2024, 13(3), 186; https://doi.org/10.3390/axioms13030186 - 12 Mar 2024
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This paper studies a particular type of planar Filippov system that consists of two discontinuity boundaries separating the phase plane into three disjoint regions with different dynamics. This type of system has wide applications in various subjects. As an illustration, a plant disease
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This paper studies a particular type of planar Filippov system that consists of two discontinuity boundaries separating the phase plane into three disjoint regions with different dynamics. This type of system has wide applications in various subjects. As an illustration, a plant disease model and an avian-only model are presented, and their bifurcation scenarios are investigated. By means of the regularization approach, the blowing up method, and the singular perturbation theory, we provide a different way to analyze the dynamics of this type of Filippov system. In particular, the boundary equilibrium bifurcations of such systems are studied. As a consequence, the nonsmooth fold bifurcation becomes a saddle-node bifurcation, while the persistence bifurcation disappears after regularization.
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