Pub Date : 2025-04-05DOI: 10.1016/j.disc.2025.114522
Ming-Jian Ding
In this paper, we show that several consecutive generating functions of the multinomial coefficients form an interlacing sequence. As applications, we provide a positive response to a question proposed by Fisk regarding the interlacing property for zeros of polynomials, which are generated by the central trinomial (quadrinomial) coefficients.
Furthermore, we prove that some classical polynomial sequences also possess the interlacing property. These sequences include the (weak) exceedance polynomial sequence on involutions in the symmetric group, Motzkin polynomial sequence, local h-polynomial sequences of the cluster subdivision of Cartan-Killing types A, B and D, Narayana polynomial sequences of types A and B, and others.
{"title":"Interlacing property of polynomial sequences related to multinomial coefficients","authors":"Ming-Jian Ding","doi":"10.1016/j.disc.2025.114522","DOIUrl":"10.1016/j.disc.2025.114522","url":null,"abstract":"<div><div>In this paper, we show that several consecutive generating functions of the multinomial coefficients form an interlacing sequence. As applications, we provide a positive response to a question proposed by Fisk regarding the interlacing property for zeros of polynomials, which are generated by the central trinomial (quadrinomial) coefficients.</div><div>Furthermore, we prove that some classical polynomial sequences also possess the interlacing property. These sequences include the (weak) exceedance polynomial sequence on involutions in the symmetric group, Motzkin polynomial sequence, local <em>h</em>-polynomial sequences of the cluster subdivision of Cartan-Killing types <em>A</em>, <em>B</em> and <em>D</em>, Narayana polynomial sequences of types <em>A</em> and <em>B</em>, and others.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 8","pages":"Article 114522"},"PeriodicalIF":0.7,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stochastic processes with renewal properties, or semi-Markovian processes, have emerged as powerful tools for modeling phenomena where the assumption of complete independence between temporally spaced events is unrealistic. These processes find applications across diverse disciplines, including biology, neuroscience, health sciences, social sciences, ecology, climatology, geophysics, oceanography, chemistry, physics, and finance. Investigating their statistical properties is crucial for understanding complex systems. Here we obtain a simple exact expression for the two-times correlation function, a key descriptor of renewal processes, as it determines the power spectrum and impacts the diffusion properties of systems influenced by such processes. Although results for the two-times correlation function have been derived, the exact expression has been evaluated only for some specific cases, as for systems with states notably the simplest is the dichotomous scenario. By averaging over trajectory realizations, we obtain a universal result for the two-times correlation function, independent of the jump statistics, provided the variance is finite. Under the standard assumption for reaching asymptotic stationarity, where waiting times decay as with , we show that stationarity depends solely on the first time , i.e., the time distance from the preparation time, while the time difference is inconsequential. For systems where stationarity is unattainable (), we provide a universal asymptotic form of the correlation function for large , extending previous results limited to specific time difference regimes. We examine two interpretations of renewal processes: shot noise and step noise—, relevant to physical systems such as general Continuous Time Random Walks and Lévy walks with random velocities. While this study focuses on two-times correlations, the simple methodology is generalizable to -times correlations, offering a pathway for future research into the statistical mechanics of renewal processes.
{"title":"Universal behavior of the two-times correlation functions of random processes with renewal","authors":"Marco Bianucci , Mauro Bologna , Daniele Lagomarsino-Oneto , Riccardo Mannella","doi":"10.1016/j.chaos.2025.116351","DOIUrl":"10.1016/j.chaos.2025.116351","url":null,"abstract":"<div><div>Stochastic processes with renewal properties, or semi-Markovian processes, have emerged as powerful tools for modeling phenomena where the assumption of complete independence between temporally spaced events is unrealistic. These processes find applications across diverse disciplines, including biology, neuroscience, health sciences, social sciences, ecology, climatology, geophysics, oceanography, chemistry, physics, and finance. Investigating their statistical properties is crucial for understanding complex systems. Here we obtain a simple exact expression for the two-times correlation function, a key descriptor of renewal processes, as it determines the power spectrum and impacts the diffusion properties of systems influenced by such processes. Although results for the two-times correlation function have been derived, the exact expression has been evaluated only for some specific cases, as for systems with <span><math><mi>N</mi></math></span> states notably the simplest is the dichotomous scenario. By averaging over trajectory realizations, we obtain a universal result for the two-times correlation function, independent of the jump statistics, provided the variance is finite. Under the standard assumption for reaching asymptotic stationarity, where waiting times decay as <span><math><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mi>μ</mi></mrow></msup></math></span> with <span><math><mrow><mi>μ</mi><mo>></mo><mn>2</mn></mrow></math></span>, we show that stationarity depends solely on the first time <span><math><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, i.e., the time distance from the preparation time, while the time difference <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span> is inconsequential. For systems where stationarity is unattainable (<span><math><mrow><mn>1</mn><mo><</mo><mi>μ</mi><mo><</mo><mn>2</mn></mrow></math></span>), we provide a universal asymptotic form of the correlation function for large <span><math><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, extending previous results limited to specific time difference regimes. We examine two interpretations of renewal processes: shot noise and step noise—, relevant to physical systems such as general Continuous Time Random Walks and Lévy walks with random velocities. While this study focuses on two-times correlations, the simple methodology is generalizable to <span><math><mi>n</mi></math></span>-times correlations, offering a pathway for future research into the statistical mechanics of renewal processes.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116351"},"PeriodicalIF":5.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is known that a given smooth del Pezzo surface or Fano threefold admits a choice of log Calabi–Yau compactified mirror toric Landau–Ginzburg model (with respect to certain fixed Kähler classes and Gorenstein toric degenerations). Here we consider the problem of constructing a corresponding map from a domain in the complexified Kähler cone of to a well-defined, separated moduli space of polarised manifolds endowed with a canonical metric. We prove a complete result for del Pezzos and a partial result for some special Fano threefolds. The construction uses some fundamental results in the theory of constant scalar curvature Kähler metrics. As a consequence parametrises -stable manifolds and the domain of is endowed with the pullback of a Weil–Petersson form.
{"title":"Some applications of canonical metrics to Landau–Ginzburg models","authors":"Jacopo Stoppa","doi":"10.1112/jlms.70148","DOIUrl":"https://doi.org/10.1112/jlms.70148","url":null,"abstract":"<p>It is known that a given smooth del Pezzo surface or Fano threefold <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> admits a choice of log Calabi–Yau compactified mirror toric Landau–Ginzburg model (with respect to certain fixed Kähler classes and Gorenstein toric degenerations). Here we consider the problem of constructing a corresponding map <span></span><math>\u0000 <semantics>\u0000 <mi>Θ</mi>\u0000 <annotation>$Theta$</annotation>\u0000 </semantics></math> from a domain in the complexified Kähler cone of <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> to a well-defined, separated moduli space <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathfrak {M}$</annotation>\u0000 </semantics></math> of polarised manifolds endowed with a canonical metric. We prove a complete result for del Pezzos and a partial result for some special Fano threefolds. The construction uses some fundamental results in the theory of constant scalar curvature Kähler metrics. As a consequence <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathfrak {M}$</annotation>\u0000 </semantics></math> parametrises <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-stable manifolds and the domain of <span></span><math>\u0000 <semantics>\u0000 <mi>Θ</mi>\u0000 <annotation>$Theta$</annotation>\u0000 </semantics></math> is endowed with the pullback of a Weil–Petersson form.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70148","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143778240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-05DOI: 10.1007/s10878-025-01276-5
Gabriel Gazzinelli Guimarães, Kelly Cristina Poldi, Mateus Martin
In real-life production, the cutting stock problem is often associated with additional constraints and objectives. Among the auxiliary objectives, two of the most relevant are the minimization of the number of different cutting patterns used and the minimization of the maximum number of simultaneously open stacks. The first auxiliary objective arises in manufacturing environments where the adjustment of the cutting tools when changing the cutting patterns incurs increased costs and time spent in production. The second is crucial to face scenarios where the space near the cutting machine or the number of automatic unloading stations is limited. In this paper, we address the one-dimensional cutting stock problem, considering the additional goals of minimizing the number of different cutting patterns used and the maximum number of simultaneously open stacks. We propose two Integer Linear Programming (ILP) formulations and a Constraint Programming (CP) model for the problem. Moreover, we develop new upper bounds on the frequency of the cutting patterns in a solution and address some special cases in which the problem may be simplified. All three approaches are embedded into an iterative exact framework to find efficient solutions. We perform computational experiments using two sets of instances from the literature. The proposed approaches proved effective in determining the entire Pareto front for small problem instances, and several solutions for medium-sized instances with minimum trim loss, a reduced maximum number of simultaneously open stacks, and a small number of different used cutting patterns.
{"title":"Mathematical models for the one-dimensional cutting stock problem with setups and open stacks","authors":"Gabriel Gazzinelli Guimarães, Kelly Cristina Poldi, Mateus Martin","doi":"10.1007/s10878-025-01276-5","DOIUrl":"https://doi.org/10.1007/s10878-025-01276-5","url":null,"abstract":"<p>In real-life production, the cutting stock problem is often associated with additional constraints and objectives. Among the auxiliary objectives, two of the most relevant are the minimization of the number of different cutting patterns used and the minimization of the maximum number of simultaneously open stacks. The first auxiliary objective arises in manufacturing environments where the adjustment of the cutting tools when changing the cutting patterns incurs increased costs and time spent in production. The second is crucial to face scenarios where the space near the cutting machine or the number of automatic unloading stations is limited. In this paper, we address the one-dimensional cutting stock problem, considering the additional goals of minimizing the number of different cutting patterns used and the maximum number of simultaneously open stacks. We propose two Integer Linear Programming (ILP) formulations and a Constraint Programming (CP) model for the problem. Moreover, we develop new upper bounds on the frequency of the cutting patterns in a solution and address some special cases in which the problem may be simplified. All three approaches are embedded into an iterative exact framework to find efficient solutions. We perform computational experiments using two sets of instances from the literature. The proposed approaches proved effective in determining the entire Pareto front for small problem instances, and several solutions for medium-sized instances with minimum trim loss, a reduced maximum number of simultaneously open stacks, and a small number of different used cutting patterns.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"217 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143782634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-05DOI: 10.1016/j.camwa.2025.03.032
Xiaochen Chu , Xiangyu Shi , Dongyang Shi
The purpose of this article is to explore the superconvergence behavior of the first-order backward-Euler (BE) implicit/explicit fully discrete schemes for the unsteady incompressible MHD equations with low-order mixed finite element method (MFEM) by utilizing the scalar auxiliary variable (SAV) and zero-energy-contribution (ZEC) methods. Through dealing with linear terms in implicit format and nonlinear terms in explicit format, the original problem is decomposed into several subproblems, which effectively reduces the amount of calculation. Particularly, a new high-precision estimation is given, which acts as a requisite role in getting the expected results. Following this, combined with a simple, effective and economic interpolation post-processing approach, the superclose and superconvergence error estimates of the decoupled and linearized fully discrete finite element SAV-BE scheme are rigorously derived. And the derivation process is also applicable to the ZEC-BE scheme. Finally, the corresponding numerical simulations are carried out to confirm the accuracy and reliability of our theoretical findings.
{"title":"Superconvergence analysis of the decoupled and linearized mixed finite element methods for unsteady incompressible MHD equations","authors":"Xiaochen Chu , Xiangyu Shi , Dongyang Shi","doi":"10.1016/j.camwa.2025.03.032","DOIUrl":"10.1016/j.camwa.2025.03.032","url":null,"abstract":"<div><div>The purpose of this article is to explore the superconvergence behavior of the first-order backward-Euler (BE) implicit/explicit fully discrete schemes for the unsteady incompressible MHD equations with low-order mixed finite element method (MFEM) by utilizing the scalar auxiliary variable (SAV) and zero-energy-contribution (ZEC) methods. Through dealing with linear terms in implicit format and nonlinear terms in explicit format, the original problem is decomposed into several subproblems, which effectively reduces the amount of calculation. Particularly, a new high-precision estimation is given, which acts as a requisite role in getting the expected results. Following this, combined with a simple, effective and economic interpolation post-processing approach, the superclose and superconvergence error estimates of the decoupled and linearized fully discrete finite element SAV-BE scheme are rigorously derived. And the derivation process is also applicable to the ZEC-BE scheme. Finally, the corresponding numerical simulations are carried out to confirm the accuracy and reliability of our theoretical findings.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"188 ","pages":"Pages 160-182"},"PeriodicalIF":2.9,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-05DOI: 10.1016/j.chaos.2025.116310
Umut Bas, Abdullah Akkurt, Aykut Has, Huseyin Yildirim
This study explores the connections between fractional calculus, a field that has recently garnered significant research interest, and multiplicative analysis. The introduction provides a comprehensive overview of the historical development and foundational concepts of these areas. The preliminary section outlines key definitions and illustrative examples from multiplicative analysis. The research derives the multiplicative representations of the gamma and beta functions and examines their fundamental properties. Furthermore, generalizations of integrals and derivatives within the framework of multiplicative analysis are formulated, accompanied by explicit formulas for multiplicative integrals and derivatives. Finally, fractional-order multiplicative integral derivatives for selected functions are introduced and visualized through graphical representations, highlighting their practical implications.
{"title":"Multiplicative Riemann–Liouville fractional integrals and derivatives","authors":"Umut Bas, Abdullah Akkurt, Aykut Has, Huseyin Yildirim","doi":"10.1016/j.chaos.2025.116310","DOIUrl":"10.1016/j.chaos.2025.116310","url":null,"abstract":"<div><div>This study explores the connections between fractional calculus, a field that has recently garnered significant research interest, and multiplicative analysis. The introduction provides a comprehensive overview of the historical development and foundational concepts of these areas. The preliminary section outlines key definitions and illustrative examples from multiplicative analysis. The research derives the multiplicative representations of the gamma and beta functions and examines their fundamental properties. Furthermore, generalizations of integrals and derivatives within the framework of multiplicative analysis are formulated, accompanied by explicit formulas for multiplicative integrals and derivatives. Finally, fractional-order multiplicative integral derivatives for selected functions are introduced and visualized through graphical representations, highlighting their practical implications.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116310"},"PeriodicalIF":5.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gioacchino Antonelli, Marco Pozzetta, Daniele Semola
Let be a complete Riemannian manifold which is not isometric to , has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there exists a set with density 1 at infinity such that for every there is a unique isoperimetric set of volume in ; moreover, its boundary is strictly volume preserving stable. The latter result cannot be improved to uniqueness or strict stability for every large volume. Indeed, we construct a complete Riemannian surface satisfying the previous assumptions and with the following additional property: there exist arbitrarily large and diverging intervals such that isoperimetric sets with volumes exist, but they are neither unique nor do they have strictly volume preserving stable boundaries.
{"title":"Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature","authors":"Gioacchino Antonelli, Marco Pozzetta, Daniele Semola","doi":"10.1002/cpa.22252","DOIUrl":"https://doi.org/10.1002/cpa.22252","url":null,"abstract":"Let be a complete Riemannian manifold which is not isometric to , has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there exists a set with density 1 at infinity such that for every there is a unique isoperimetric set of volume in ; moreover, its boundary is strictly volume preserving stable. The latter result cannot be improved to uniqueness or strict stability for every large volume. Indeed, we construct a complete Riemannian surface satisfying the previous assumptions and with the following additional property: there exist arbitrarily large and diverging intervals such that isoperimetric sets with volumes exist, but they are neither unique nor do they have strictly volume preserving stable boundaries.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"73 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143782633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-05DOI: 10.1016/j.disc.2025.114511
Yifang Hao , Shuchao Li , Yuantian Yu
<div><div>The binding number <span><math><mi>b</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of a graph <em>G</em> is the minimum value of <span><math><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo><mo>|</mo><mo>/</mo><mo>|</mo><mi>S</mi><mo>|</mo></math></span> taken over all non-empty subsets <em>S</em> of <span><math><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> such that <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo><mo>≠</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. The bipartite binding number <span><math><msup><mrow><mi>b</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of a bipartite graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math></span> is defined to be <span><math><mi>min</mi><mo></mo><mo>{</mo><mo>|</mo><mi>X</mi><mo>|</mo><mo>,</mo><mo>|</mo><mi>Y</mi><mo>|</mo><mo>}</mo></math></span> if <span><math><mi>G</mi><mo>=</mo><msub><mrow><mi>K</mi></mrow><mrow><mo>|</mo><mi>X</mi><mo>|</mo><mo>,</mo><mo>|</mo><mi>Y</mi><mo>|</mo></mrow></msub></math></span> and<span><span><span><math><mi>min</mi><mo></mo><mrow><mo>{</mo><munder><mi>min</mi><mrow><mtable><mtr><mtd><mo>∅</mo><mo>≠</mo><mi>S</mi><mo>⊆</mo><mi>X</mi></mtd></mtr><mtr><mtd><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo><mo>⊊</mo><mi>Y</mi></mtd></mtr></mtable></mrow></munder><mo></mo><mfrac><mrow><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo><mo>|</mo></mrow><mrow><mo>|</mo><mi>S</mi><mo>|</mo></mrow></mfrac><mo>,</mo><mspace></mspace><munder><mi>min</mi><mrow><mtable><mtr><mtd><mo>∅</mo><mo>≠</mo><mi>T</mi><mo>⊆</mo><mi>Y</mi></mtd></mtr><mtr><mtd><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>T</mi><mo>)</mo><mo>⊊</mo><mi>X</mi></mtd></mtr></mtable></mrow></munder><mo></mo><mfrac><mrow><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>T</mi><mo>)</mo><mo>|</mo></mrow><mrow><mo>|</mo><mi>T</mi><mo>|</mo></mrow></mfrac><mo>}</mo></mrow></math></span></span></span> otherwise. Fan and Lin <span><span>[9]</span></span> investigated <span><math><mi>b</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> from spectral perspectives, and provided tight sufficient conditions in terms of the spectral radius of a graph <em>G</em> to guarantee <span><math><mi>b</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>⩾</mo><mi>r</mi></math></span>, where <em>r</em> is a positive integer. The study of the existence of <em>k</em>-factors in graphs is a classic problem in graph theory. Fan and Lin <span><span>[9]</span></span> also provided the spectral radius conditions for 1-binding graphs to contain a perfect matching and a 2-factor, respectively. In this paper, we consider the bipartite analogues of those results obtained in <span><span>[9]</sp
{"title":"Bipartite binding number, k-factor and spectral radius of bipartite graphs","authors":"Yifang Hao , Shuchao Li , Yuantian Yu","doi":"10.1016/j.disc.2025.114511","DOIUrl":"10.1016/j.disc.2025.114511","url":null,"abstract":"<div><div>The binding number <span><math><mi>b</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of a graph <em>G</em> is the minimum value of <span><math><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo><mo>|</mo><mo>/</mo><mo>|</mo><mi>S</mi><mo>|</mo></math></span> taken over all non-empty subsets <em>S</em> of <span><math><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> such that <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo><mo>≠</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. The bipartite binding number <span><math><msup><mrow><mi>b</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of a bipartite graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math></span> is defined to be <span><math><mi>min</mi><mo></mo><mo>{</mo><mo>|</mo><mi>X</mi><mo>|</mo><mo>,</mo><mo>|</mo><mi>Y</mi><mo>|</mo><mo>}</mo></math></span> if <span><math><mi>G</mi><mo>=</mo><msub><mrow><mi>K</mi></mrow><mrow><mo>|</mo><mi>X</mi><mo>|</mo><mo>,</mo><mo>|</mo><mi>Y</mi><mo>|</mo></mrow></msub></math></span> and<span><span><span><math><mi>min</mi><mo></mo><mrow><mo>{</mo><munder><mi>min</mi><mrow><mtable><mtr><mtd><mo>∅</mo><mo>≠</mo><mi>S</mi><mo>⊆</mo><mi>X</mi></mtd></mtr><mtr><mtd><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo><mo>⊊</mo><mi>Y</mi></mtd></mtr></mtable></mrow></munder><mo></mo><mfrac><mrow><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo><mo>|</mo></mrow><mrow><mo>|</mo><mi>S</mi><mo>|</mo></mrow></mfrac><mo>,</mo><mspace></mspace><munder><mi>min</mi><mrow><mtable><mtr><mtd><mo>∅</mo><mo>≠</mo><mi>T</mi><mo>⊆</mo><mi>Y</mi></mtd></mtr><mtr><mtd><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>T</mi><mo>)</mo><mo>⊊</mo><mi>X</mi></mtd></mtr></mtable></mrow></munder><mo></mo><mfrac><mrow><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>T</mi><mo>)</mo><mo>|</mo></mrow><mrow><mo>|</mo><mi>T</mi><mo>|</mo></mrow></mfrac><mo>}</mo></mrow></math></span></span></span> otherwise. Fan and Lin <span><span>[9]</span></span> investigated <span><math><mi>b</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> from spectral perspectives, and provided tight sufficient conditions in terms of the spectral radius of a graph <em>G</em> to guarantee <span><math><mi>b</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>⩾</mo><mi>r</mi></math></span>, where <em>r</em> is a positive integer. The study of the existence of <em>k</em>-factors in graphs is a classic problem in graph theory. Fan and Lin <span><span>[9]</span></span> also provided the spectral radius conditions for 1-binding graphs to contain a perfect matching and a 2-factor, respectively. In this paper, we consider the bipartite analogues of those results obtained in <span><span>[9]</sp","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 8","pages":"Article 114511"},"PeriodicalIF":0.7,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-05DOI: 10.1016/j.chaos.2025.116401
Ateke Goshvarpour
Purpose
Schizophrenia diagnosis remains challenging due to the reliance on subjective clinical assessments and the lack of robust, objective biomarkers. Current neuroimaging methods are often expensive, time-consuming, and may lack specificity, highlighting the need for the development of scalable and accurate diagnostic tools. This study investigates the feasibility of using electroencephalogram (EEG) frequency waves as biomarkers for the detection of schizophrenia, employing a quantum-based feature extraction methodology. The primary objective of this research is to develop an advanced detection methodology that integrates quantum-based feature extraction with sophisticated channel and feature selection techniques. This approach aims to enhance the accuracy and reliability of schizophrenia diagnosis by identifying the most informative EEG channels and features for classification purposes.
Methods
First, EEG frequency bands are extracted using the wavelet packet decomposition technique. Next, three channel selection algorithms prioritize channels based on the highest variance, power, and lowest coefficient of variation. The methodology involves applying discrete quantum analysis for feature extraction, followed by the extraction of statistical measures to create a comprehensive feature set. Feature selection is performed using Minimum Redundancy Maximum Relevance (mRMR) and ReliefF to retain the most relevant and non-redundant features. These features are then analyzed using various classification models, including AdaBoost, Support Vector Machine (SVM), Decision Tree (DT), and K-Nearest Neighbors (KNN).
Results
The findings of the study underscore the superior performance of the mRMR method when combined with variance and coefficient of variation-based channel selection techniques, particularly in the β and θ frequency bands. The KNN classifier achieves 100 % accuracy, sensitivity, and F1 score for the δ, θ, SMR, and β waves under optimal conditions. The mRMR method attains an average accuracy of 92.80 % for δ waves, 95.20 % for θ waves, 92.59 % for SMR waves, and 94.26 % for β waves when used in conjunction with coefficient of variation-based channel selection. In contrast, the ReliefF method demonstrates suboptimal performance in higher frequency bands, such as the γ wave, achieving an average accuracy of only 51.55 % when paired with variance-based channel selection.
Conclusion
The proposed methodology presents a promising approach to improving the accuracy and reliability of schizophrenia diagnosis.
{"title":"Quantum-inspired feature extraction model from EEG frequency waves for enhanced schizophrenia detection","authors":"Ateke Goshvarpour","doi":"10.1016/j.chaos.2025.116401","DOIUrl":"10.1016/j.chaos.2025.116401","url":null,"abstract":"<div><h3>Purpose</h3><div>Schizophrenia diagnosis remains challenging due to the reliance on subjective clinical assessments and the lack of robust, objective biomarkers. Current neuroimaging methods are often expensive, time-consuming, and may lack specificity, highlighting the need for the development of scalable and accurate diagnostic tools. This study investigates the feasibility of using electroencephalogram (EEG) frequency waves as biomarkers for the detection of schizophrenia, employing a quantum-based feature extraction methodology. The primary objective of this research is to develop an advanced detection methodology that integrates quantum-based feature extraction with sophisticated channel and feature selection techniques. This approach aims to enhance the accuracy and reliability of schizophrenia diagnosis by identifying the most informative EEG channels and features for classification purposes.</div></div><div><h3>Methods</h3><div>First, EEG frequency bands are extracted using the wavelet packet decomposition technique. Next, three channel selection algorithms prioritize channels based on the highest variance, power, and lowest coefficient of variation. The methodology involves applying discrete quantum analysis for feature extraction, followed by the extraction of statistical measures to create a comprehensive feature set. Feature selection is performed using Minimum Redundancy Maximum Relevance (mRMR) and ReliefF to retain the most relevant and non-redundant features. These features are then analyzed using various classification models, including AdaBoost, Support Vector Machine (SVM), Decision Tree (DT), and K-Nearest Neighbors (KNN).</div></div><div><h3>Results</h3><div>The findings of the study underscore the superior performance of the mRMR method when combined with variance and coefficient of variation-based channel selection techniques, particularly in the β and θ frequency bands. The KNN classifier achieves 100 % accuracy, sensitivity, and F1 score for the δ, θ, SMR, and β waves under optimal conditions. The mRMR method attains an average accuracy of 92.80 % for δ waves, 95.20 % for θ waves, 92.59 % for SMR waves, and 94.26 % for β waves when used in conjunction with coefficient of variation-based channel selection. In contrast, the ReliefF method demonstrates suboptimal performance in higher frequency bands, such as the γ wave, achieving an average accuracy of only 51.55 % when paired with variance-based channel selection.</div></div><div><h3>Conclusion</h3><div>The proposed methodology presents a promising approach to improving the accuracy and reliability of schizophrenia diagnosis.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116401"},"PeriodicalIF":5.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-05DOI: 10.1007/s00245-025-10254-6
Wenqiang Zhao, Xia Liu
In this article, a class of non-local stochastic lattice models with fractional powers of the discrete p-Laplacian, incorporating time-varying-distributed delay as well as multiplicative noises at each node, are propounded. First, by utilizing an existence theorem of solutions for infinite ordinary differential equations, we prove the well-posedness of the stochastic equations, whose solution operator admits an NRDS. Besides, the tempered random attractor is constructed for this NRDS. Finally, with the identical conditions, we prove that the solution is jointly continuous in initial time and initial data, and eventually, a family of invariant sample Borel probability measures supported in the random attractors are established in a Banach space (not a Hilbert space) for the corresponding NRDS.
{"title":"Invariant Sample Measures for Non-autonomous Stochastic Non-local Discrete p-Laplacian Equations with Time Varying Delay and Multiplicative Noises","authors":"Wenqiang Zhao, Xia Liu","doi":"10.1007/s00245-025-10254-6","DOIUrl":"10.1007/s00245-025-10254-6","url":null,"abstract":"<div><p>In this article, a class of <i>non-local</i> stochastic lattice models with fractional powers of the discrete <i>p</i>-Laplacian, incorporating time-varying-distributed delay as well as multiplicative noises at each node, are propounded. First, by utilizing an existence theorem of solutions for infinite ordinary differential equations, we prove the well-posedness of the stochastic equations, whose solution operator admits an NRDS. Besides, the tempered random attractor is constructed for this NRDS. Finally, with the identical conditions, we prove that the solution is jointly continuous in initial time and initial data, and eventually, a family of invariant sample Borel probability measures supported in the random attractors are established in a Banach space (not a Hilbert space) for the corresponding NRDS.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143778001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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