304,686 results
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2. A Feynman–Kac approach to a paper of Chung and Feller on fluctuations in the coin-tossing game
- Author
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Sergio Grunbaum and F alberto Grunbaum
- Subjects
Discrete mathematics ,symbols.namesake ,Coin flipping ,Applied Mathematics ,General Mathematics ,symbols ,Feynman diagram ,Mathematics - Abstract
A classical result of K. L. Chung and W. Feller deals with the partial sums S k S_k arising in a fair coin-tossing game. If N n N_n is the number of “positive” terms among S 1 S_1 , S 2 S_2 , …, S n S_n then the quantity P ( N 2 n = 2 r ) P(N_{2n} = 2r) takes an elegant form. We lift the restriction on an even number of tosses and give a simple expression for P ( N 2 n + 1 = r ) P(N_{2n+1} = r) , r = 0 r = 0 , 1 1 , 2 2 , …, 2 n + 1 2n+1 . We get to this ansatz by adaptating the Feynman–Kac methodology.
- Published
- 2022
3. Comments on 'A Note on the Paper 'Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifactors''
- Author
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N. Gadhi
- Subjects
Mathematical optimization ,021103 operations research ,Control and Optimization ,Applied Mathematics ,0211 other engineering and technologies ,010103 numerical & computational mathematics ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Bilevel optimization ,Bellman equation ,Theory of computation ,0101 mathematics ,Mathematics - Abstract
Necessary optimality conditions for a bilevel optimization problem are given in the paper by Kohli (J Optim Theory Appl 152: 632–651, 2012). Recently, the same author corrected his results in the note (J Optim Theory Appl 181:706–707, 2019). In this work, we have pointed out that some of the new modifications are wrong. We correct the flaws and present an alternative proof for the main result.
- Published
- 2021
4. Social and content aware One-Class recommendation of papers in scientific social networks.
- Author
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Wang, Gang, He, XiRan, and Ishuga, Carolyne Isigi
- Subjects
INFORMATION technology ,SOCIAL networks ,SPARSE graphs ,HYBRID computers (Computer architecture) ,HYBRID power systems - Abstract
With the rapid development of information technology, scientific social networks (SSNs) have become the fastest and most convenient way for researchers to communicate with each other. Many published papers are shared via SSNs every day, resulting in the problem of information overload. How to appropriately recommend personalized and highly valuable papers for researchers is becoming more urgent. However, when recommending papers in SSNs, only a small amount of positive instances are available, leaving a vast amount of unlabelled data, in which negative instances and potential unseen positive instances are mixed together, which naturally belongs to One-Class Collaborative Filtering (OCCF) problem. Therefore, considering the extreme data imbalance and data sparsity of this OCCF problem, a hybrid approach of Social and Content aware One-class Recommendation of Papers in SSNs, termed SCORP, is proposed in this study. Unlike previous approaches recommended to address the OCCF problem, social information, which has been proved playing a significant role in performing recommendations in many domains, is applied in both the profiling of content-based filtering and the collaborative filtering to achieve superior recommendations. To verify the effectiveness of the proposed SCORP approach, a real-life dataset from CiteULike was employed. The experimental results demonstrate that the proposed approach is superior to all of the compared approaches, thus providing a more effective method for recommending papers in SSNs. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
5. Mass Balance Equations for Retention and Basis Weight in a Paper Machine
- Author
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Pradeep Kumar Juneja, Gauri Yadav, Neha Belwal, Mayank Chaturvedi, and A. K. Ray
- Subjects
Paper machine ,business.product_category ,Mass balance ,Applied mathematics ,Process control ,business ,Stock (geology) ,Mathematics - Abstract
In a paper industry, especially in thick stock wet end process, the two most important variables are retention in forming section of a paper machine and basis weight of the thick stock. Present paper attempts to understand the governing mass balance equations which may be required to deduce an appropriate process model.
- Published
- 2019
6. Remarks on a recent paper titled: 'On the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings in Banach spaces'
- Author
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Charles E. Chidume
- Subjects
Pure mathematics ,Smoothness (probability theory) ,Applied Mathematics ,lcsh:Mathematics ,Banach space ,Hilbert space ,Regular polygon ,010103 numerical & computational mathematics ,Fixed point ,lcsh:QA1-939 ,01 natural sciences ,Opial property ,010101 applied mathematics ,symbols.namesake ,Accretive ,Uniformly smooth ,Common fixed point ,symbols ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Constant (mathematics) ,Analysis ,Mathematics - Abstract
In a recently published theorem on the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings, Tang et al. (J. Inequal. Appl. 2015:305, 2015) studied a uniformly convex and 2-uniformly smooth real Banach space with the Opial property and best smoothness constant κ satisfying the condition $0 0 < κ < 1 2 , as a real Banach space more general than Hilbert spaces. A well-known example of a uniformly convex and 2-uniformly smooth real Banach space with the Opial property is $E=l_{p}$ E = l p , $2\leq p 2 ≤ p < ∞ . It is shown in this paper that, if κ is the best smoothness constant of E and satisfies the condition $0 0 < κ ≤ 1 2 , then E is necessarily $l_{2}$ l 2 , a real Hilbert space. Furthermore, some important remarks concerning the proof of this theorem are presented.
- Published
- 2021
7. Multivariate extremes and max-stable processes: discussion of the paper by Zhengjun Zhang
- Author
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R. L. Smith
- Subjects
Statistics and Probability ,Multivariate statistics ,Computational Theory and Mathematics ,Applied Mathematics ,Maximum likelihood ,Zhàng ,Context (language use) ,Statistics, Probability and Uncertainty ,Extreme value theory ,Mathematical economics ,Analysis ,Mathematics - Abstract
This discussion reviews the paper by Zhengjun Zhang in the context of broader research on multivariate extreme value theory and max-stable processes.
- Published
- 2021
8. Corrigendum to a Paper by Charak and Laine
- Author
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Kuldeep Singh Charak and Ilpo Laine
- Subjects
Discrete mathematics ,Class (set theory) ,Applied Mathematics ,General Mathematics ,Entire function ,Prime (order theory) ,Mathematics - Abstract
This is a corrigendum to our paper, “On a class of prime entire functions”, published in Acta Math. Sin., Engl. Ser., 25, 1647–1652 (2009).
- Published
- 2020
9. Addendum to the paper 'High‐order symmetric cubature rules for tetrahedra and pyramids'
- Author
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Jan Jaśkowiec and N. Sukumar
- Subjects
Combinatorics ,Numerical Analysis ,Applied Mathematics ,General Engineering ,Tetrahedron ,Addendum ,High order ,Mathematics - Published
- 2021
10. Properties of a novel stochastic rock–paper–scissors dynamics
- Author
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Hailing Wang, Zuxiong Li, Zhusong Chu, and Jun Cheng
- Subjects
Lyapunov function ,education.field_of_study ,Stochastic modelling ,Applied Mathematics ,Dynamics (mechanics) ,Population ,01 natural sciences ,010305 fluids & plasmas ,Computational Mathematics ,symbols.namesake ,Bounded function ,0103 physical sciences ,Theory of computation ,symbols ,Applied mathematics ,010306 general physics ,education ,Mathematics - Abstract
This paper is concerned with some stochastic properties of a novel rock–paper–scissors model. Firstly, the global existence of an unique positive solution of the stochastic model is obtained. Then we demonstrate the positive solution of the model is stochastically bounded. Besides, some sufficient conditions for population to be stochastically permanent and extinct are derived with the use of some appropriate Lyapunov functions. At last, some numerical simulations are carried out to illustrate our theoretical analysis results.
- Published
- 2020
11. Ramsey, Paper, Scissors
- Author
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Jacob Fox, Xiaoyu He, and Yuval Wigderson
- Subjects
Computer Science::Computer Science and Game Theory ,Applied Mathematics ,General Mathematics ,Combinatorial game theory ,0102 computer and information sciences ,01 natural sciences ,Computer Graphics and Computer-Aided Design ,Upper and lower bounds ,Combinatorics ,010201 computation theory & mathematics ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,FOS: Mathematics ,Mathematics - Combinatorics ,Graph (abstract data type) ,Combinatorics (math.CO) ,Ramsey's theorem ,Null graph ,Software ,MathematicsofComputing_DISCRETEMATHEMATICS ,Mathematics ,Independence number - Abstract
We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph on $n$ vertices, on each turn Proposer proposes a potential edge and Decider simultaneously decides (without knowing Proposer's choice) whether to add it to the graph. Proposer cannot propose an edge which would create a triangle in the graph. The game ends when Proposer has no legal moves remaining, and Proposer wins if the final graph has independence number at least $s$. We prove a threshold phenomenon exists for this game by exhibiting randomized strategies for both players that are optimal up to constants. Namely, there exist constants $0B\sqrt{n}\log{n}$. This is a factor of $\Theta(\sqrt{\log{n}})$ larger than the lower bound coming from the off-diagonal Ramsey number $r(3,s)$.
- Published
- 2020
12. Some remarks on the paper 'Fixed point theorems for generalized contractive mappings in metric spaces'
- Author
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Ovidiu Popescu
- Subjects
Pure mathematics ,Metric space ,Applied Mathematics ,Modeling and Simulation ,Fixed-point theorem ,Geometry and Topology ,Mathematics - Abstract
In this work, we improve and correct some results in the paper by Proinov (J Fixed Point Theory Appl 22:1–27, 2020).
- Published
- 2021
13. Correcting mistakes in the paper 'A mass formula for negacyclic codes of length 2k and some good negacyclic codes over $\mathbb {Z}_{4}+u\mathbb {Z}_{4}$' [Cryptogr. Commun. (2017) 9: 241–272]
- Author
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Rama Krishna Bandi, Yuan Cao, Yonglin Cao, and Fang-Wei Fu
- Subjects
Mass formula ,Combinatorics ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Computer Networks and Communications ,Applied Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,020206 networking & telecommunications ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Mathematics - Abstract
We correct some mistakes in the paper “A mass formula for negacyclic codes of length 2k and some good negacyclic codes over $\mathbb {Z}_{4}+u\mathbb {Z}_{4}$ ” (Bandi et al. Cryptogr. Commun. 9, 241–272, 2017).
- Published
- 2020
14. Quantifying the impact of scholarly papers based on higher-order weighted citations.
- Author
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Bai, Xiaomei, Zhang, Fuli, Hou, Jie, Lee, Ivan, Kong, Xiangjie, Tolba, Amr, and Xia, Feng
- Subjects
CITATION analysis ,SCHOLARLY publishing ,BIBLIOMETRICS ,SIMULATION methods & models ,ALGORITHMS - Abstract
Quantifying the impact of a scholarly paper is of great significance, yet the effect of geographical distance of cited papers has not been explored. In this paper, we examine 30,596 papers published in Physical Review C, and identify the relationship between citations and geographical distances between author affiliations. Subsequently, a relative citation weight is applied to assess the impact of a scholarly paper. A higher-order weighted quantum PageRank algorithm is also developed to address the behavior of multiple step citation flow. Capturing the citation dynamics with higher-order dependencies reveals the actual impact of papers, including necessary self-citations that are sometimes excluded in prior studies. Quantum PageRank is utilized in this paper to help differentiating nodes whose PageRank values are identical. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
15. On the Paper 'On hyperideals of ordered semihypergroups' by ZeGu in Ital. J. Pure Appl. Math
- Author
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Niovi Kehayopulu
- Subjects
Statistics and Probability ,Numerical Analysis ,Lemma (mathematics) ,Pure mathematics ,Algebra and Number Theory ,Corollary ,Applied Mathematics ,Semiprime ,Ideal (order theory) ,Geometry and Topology ,Prime (order theory) ,Theoretical Computer Science ,Mathematics - Abstract
Giving the proper citations, it is shown that, except of Lemma 2.4 and Theorem 2.6, almost all the results of the paper in the title have been previously published for ordered hypersemigroups in Eur. J. Pure Appl. Math. and they are not new. There are also two results obtained from ordered semigroups just putting a ``$\circ$" instead of ``$\cdot$" (that isn't a correct way to work), without reference to ordered semigroups on which the results on ordered hypersemigroups are based. One of them can be obtained as corollary to a theorem in Eur. J. Pure Appl. Math. as well, and it is not new.
- Published
- 2019
16. Physics driven behavioural clustering of free-falling paper shapes
- Author
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Fumiya Iida, Toby Howison, Josie Hughes, Fabio Giardina, Howison, Toby [0000-0001-8548-5550], Iida, Fumiya [0000-0001-9246-7190], and Apollo - University of Cambridge Repository
- Subjects
Inertia ,Physiology ,Physical system ,Social Sciences ,computer.software_genre ,Systems Science ,01 natural sciences ,010305 fluids & plasmas ,Physical Phenomena ,Physical phenomena ,Medicine and Health Sciences ,Psychology ,Cluster Analysis ,Moment of Inertia ,Multidisciplinary ,Applied Mathematics ,Simulation and Modeling ,theoretical model ,article ,Classical Mechanics ,Dynamical Systems ,Variety (cybernetics) ,Free falling ,machine learning ,Physical Sciences ,Medicine ,physics ,Algorithms ,Research Article ,Paper ,Computer and Information Sciences ,Reynolds Number ,Science ,Fluid Mechanics ,Research and Analysis Methods ,Machine learning ,Continuum Mechanics ,Motion ,Machine Learning Algorithms ,Artificial Intelligence ,0103 physical sciences ,010306 general physics ,Set (psychology) ,Cluster analysis ,Behavior ,Biological Locomotion ,business.industry ,Biology and Life Sciences ,Fluid Dynamics ,Models, Theoretical ,Nonlinear Dynamics ,Artificial intelligence ,business ,computer ,Mathematics - Abstract
Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour. © 2019 Howison et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
- Published
- 2019
17. Some comments on Chen Xu, Mengmei Xi, Xuejun Wang and Hao Xia's paper 'L^r convergence for weighted sums of extended negatively dependent random variables'
- Author
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da Silva and João Lita
- Subjects
Discrete mathematics ,L(R) ,Chen ,biology ,Convergence of random variables ,Applied Mathematics ,General Mathematics ,Dependent random variables ,Convergence (routing) ,biology.organism_classification ,Mathematics - Abstract
This work is a contribution to the Project UIDB/04035/2020, funded by FCT - Fundacao para a Ciencia e a Tecnologia, Portugal.
- Published
- 2020
18. Measurement of some properties of pulp and paper made from date palm midribs and wheat straw by soda-AQ pulping process
- Author
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Mohamed A. Abdel-Aal, Salim Hiziroglu, Hamad A. Al-Mefarrej, N. D. Shetta, Ibrahim M. Aref, and Ramadan A. Nasser
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biology ,Applied Mathematics ,Pulp (paper) ,Raw material ,Juniperus procera ,Straw ,engineering.material ,Condensed Matter Physics ,biology.organism_classification ,Pulp and paper industry ,chemistry.chemical_compound ,Cedar wood ,chemistry ,Phoenix dactylifera ,engineering ,Lignin ,Hemicellulose ,Electrical and Electronic Engineering ,Instrumentation ,Mathematics - Abstract
The objective of this study was to characterize the properties of pulp and paper manufactured from two agricultural residues namely, wheat straw (Triticum aestivum L. em Thell.) and date palm midribs (Phoenix dactylifera L.) widely available in Saudi Arabia by employing soda-anthraquinone (AQ) pulping process. Specimens from cedar wood (Juniperus procera Hochst. ex Endl.) wood was also used as control samples. Chemical and the morphological characteristics of all three types of raw materials in addition to basic properties of hand sheets made from such resources were evaluated. The results indicated that wheat straw had the highest hemicellulose and ash values of 35% and 7% and the lowest lignin content value of 18%, respectively. The fibre length of the both palm fronds and wheat straw was lower than that of 2.2 mm which was found for J. procera. Overall strength properties of the handsheet made from two agricultural raw materials were significantly lower than those made from J. procera pulp. Wheat straw handsheets also had higher strength properties than those made from date palm midribs with an exception of their tear index. Based on the results of this study it appears that both types of raw materials, date palm midribs and wheat straw could have a potential to manufacture pulp and paper with accepted properties so that such underutilized species can be converted into value-added products.
- Published
- 2015
19. Numerical Solution of Differential and Differential–Algebraic Equations. Selected Papers from NUMDIFF-15
- Author
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Jens Lang, Jason Frank, Helmut Podhaisky, Elena Celledoni, Rüdiger Weiner, and Martin Arnold
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Computational Mathematics ,Applied Mathematics ,Applied mathematics ,Differential algebraic equation ,Differential (mathematics) ,Mathematics - Published
- 2021
20. Special issue: Selected papers of CMMSE
- Author
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Jorge Eduardo Macías-Díaz, Raquel Garcia-Rubio, and Jesús Vigo-Aguiar
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Computational Mathematics ,Applied Mathematics ,Mathematics education ,Mathematics - Published
- 2019
21. Comments on the paper 'A conservative linear difference scheme for the 2D regularized long-wave equation', by Xiaofeng Wang, Weizhong Dai and Shuangbing Guo [Applied Mathematics and Computation, 342 (2019) 55-70]
- Author
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Asma Rouatbi and Khaled Omrani
- Subjects
0209 industrial biotechnology ,Applied Mathematics ,Computation ,020206 networking & telecommunications ,02 engineering and technology ,Wave equation ,Computational Mathematics ,020901 industrial engineering & automation ,Norm (mathematics) ,Scheme (mathematics) ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Mathematics - Abstract
In the above article, a second-order convergence in the maximum norm of the two-dimensional regularized long-wave equation is proved. However, due to a wrong inequality in Lemma 3.3 used in X. Wang et al.[1], there are some fundamental errors in this paper, in particular the proof of Theorem 3.3 and the convergence Theorem are no longer correct. The present brief paper contains clarifying comments.
- Published
- 2021
22. Evolutionary dynamics of rock-paper-scissors game in the patchy network with mutations
- Author
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Tina Verma and Arvind Kumar Gupta
- Subjects
Hopf bifurcation ,education.field_of_study ,General Mathematics ,Applied Mathematics ,Population ,Evolutionary game theory ,Biodiversity ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Metapopulation ,symbols.namesake ,Transcritical bifurcation ,Evolutionary biology ,Mutation (genetic algorithm) ,symbols ,education ,Evolutionary dynamics ,Mathematics - Abstract
Connectivity is the safety network for biodiversity conservation because connected habitats are more effective for saving the species and ecological functions. The nature of coupling for connectivity also plays an important role in the co-existence of species in cyclic-dominance. The rock-paper-scissors game is one of the paradigmatic mathematical model in evolutionary game theory to understand the mechanism of biodiversity in cyclic-dominance. In this paper, the metapopulation model for rock-paper-scissors with mutations is presented in which the total population is divided into patches and the patches form a network of complete graph. The migration among patches is allowed through simple random walk. The replicator-mutator equations are used with the migration term. When migration is allowed then the population of the patches will synchronized and attain stable state through Hopf bifurcation. Apart form this, two phases are observed when the strategies of one of the species mutate to other two species: co-existence of all the species phase and existence of one kind of species phase. The transition from one phase to another phase is taking place due to transcritical bifurcation. The dynamics of the population of species of rock, paper, scissors is studied in the environment of homogeneous and heterogeneous mutation. Numerical simulations have been performed when mutation is allowed in all the patches (homogeneous mutation) and some of the patches (heterogeneous mutation). It has been observed that when the number of patches is increased in the case of heterogeneous mutation then the population of any of the species will not extinct and all the species will co-exist.
- Published
- 2021
23. Learning regularization parameters of inverse problems via deep neural networks:Paper
- Author
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Julianne Chung, Matthias Chung, and Babak Maboudi Afkham
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,Bilevel optimization ,010103 numerical & computational mathematics ,01 natural sciences ,Regularization (mathematics) ,Theoretical Computer Science ,Machine Learning (cs.LG) ,Bayes' theorem ,Design objective ,Deep neural networks ,Regularization ,FOS: Mathematics ,Mathematics - Numerical Analysis ,0101 mathematics ,Representation (mathematics) ,Mathematical Physics ,Mathematics ,Applied Mathematics ,Supervised learning ,Deep learning ,Numerical Analysis (math.NA) ,Inverse problem ,Computer Science Applications ,010101 applied mathematics ,Optimal experimental design ,Signal Processing ,Minification ,Algorithm ,Hyperparameter selection - Abstract
In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the mapping from observation data to regularization parameters. Once the network is trained, regularization parameters for newly obtained data can be computed by efficient forward propagation of the DNN. We show that a wide variety of regularization functionals, forward models, and noise models may be considered. The network-obtained regularization parameters can be computed more efficiently and may even lead to more accurate solutions compared to existing regularization parameter selection methods. We emphasize that the key advantage of using DNNs for learning regularization parameters, compared to previous works on learning via optimal experimental design or empirical Bayes risk minimization, is greater generalizability. That is, rather than computing one set of parameters that is optimal with respect to one particular design objective, DNN-computed regularization parameters are tailored to the specific features or properties of the newly observed data. Thus, our approach may better handle cases where the observation is not a close representation of the training set. Furthermore, we avoid the need for expensive and challenging bilevel optimization methods as utilized in other existing training approaches. Numerical results demonstrate the potential of using DNNs to learn regularization parameters., 27 pages, 16 figures
- Published
- 2021
24. On the paper 'On an identity for the zeros of Bessel functions' by Baricz et al
- Author
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N. Anghel
- Subjects
Pure mathematics ,Applied Mathematics ,Entire function ,010102 general mathematics ,Order (ring theory) ,Riemann–Stieltjes integral ,Type (model theory) ,01 natural sciences ,symbols.namesake ,Identity (mathematics) ,0103 physical sciences ,symbols ,0101 mathematics ,010306 general physics ,Analysis ,Bessel function ,Mathematics - Abstract
In this note we offer some criticism on the paper “On an identity for zeros of Bessel functions” by Baricz et al. [3] . The paper gives identities of type Stieltjes–Calogero for the sums of reciprocals of differences of fourth powers of zeros of Bessel functions. Although interesting in principle, by containing one too many sums of similar complexity the identities fail to convey the true spirit of the work of Stieltjes and Calogero. We rectify this by providing what we think is the correct type of identity for the above-said sums, in the general setup of entire functions of order
- Published
- 2018
25. Metapopulation model of rock-scissors-paper game with subpopulation-specific victory rates stabilized by heterogeneity
- Author
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Genki Ichinose, Takashi Nagatani, and Kei-ichi Tainaka
- Subjects
0301 basic medicine ,Statistics and Probability ,General Immunology and Microbiology ,Applied Mathematics ,Victory ,Metapopulation ,General Medicine ,Models, Theoretical ,Random walk ,01 natural sciences ,General Biochemistry, Genetics and Molecular Biology ,Graph ,Combinatorics ,03 medical and health sciences ,030104 developmental biology ,Game Theory ,Homogeneous ,Modeling and Simulation ,0103 physical sciences ,Neutral stability ,Computer Simulation ,010306 general physics ,General Agricultural and Biological Sciences ,Mathematics - Abstract
Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species.
- Published
- 2018
26. Pride and Passion: Remarks on Thomas L. Saaty’s Final Papers
- Author
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Barış Kiremitci and Eyüp Çetin
- Subjects
Statistics and Probability ,Numerical Analysis ,Pride ,Algebra and Number Theory ,business.industry ,Applied Mathematics ,media_common.quotation_subject ,Analytic network process ,Life satisfaction ,Analytic hierarchy process ,Passion ,Theoretical Computer Science ,Management ,Analytics ,Publishing ,Honor ,Geometry and Topology ,business ,media_common ,Mathematics - Abstract
Thomas L. Saaty, a world-renowned scholar and our beloved Advisory Editor, passed away on August 14, 2017 at the age of 91.  He has made many fundamental contributions to operations research, analytics, business and mathematics. Despite his heavy illness for 14 months, as passionate about science, he has also enthusiastically published his research. We review his final works published in 2017 and 2018. We are also honored to reveal and publish his final statements on neural firing and synthesis in making comparisons & life satisfaction, respectively, in his final two papers; the previous one submitted by him just before his passing and the other one submitted by his co-authors after his death to European Journal of Pure and Applied Mathematics (EJPAM).We just would like to remember and honor Saaty’s memory by publishing his final papers at EJPAM and this humble remarks dedicated to the memory of Thomas L. Saaty on the occasion of the first anniversary of his passing, August 14, 2018.
- Published
- 2018
27. A note on the paper 'A novel approach of graphical rectangular b-metric spaces with an application to the vibrations of a vertical heavy hanging cable'
- Author
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Fei He, Ning Lu, and Shu-Fang Li
- Subjects
Algebra ,Vibration ,Metric space ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Applied Mathematics ,Modeling and Simulation ,Fixed-point theorem ,Geometry and Topology ,Fundamental lemma ,Mathematical proof ,Counterexample ,Mathematics - Abstract
In this work, a counterexample is given to refute a result in the paper by Younis et al. (J Fixed Point Theory Appl 21:1–33, 2019). Furthermore, applying this counterexample, we give negative answers to some of the open problems in their paper. Recently, Baradol et al. give a new theorem to rectify the result of Younis et al. However, we find that there are some gaps in the proofs of their results. Finally, we introduce a fundamental lemma and fill these gaps.
- Published
- 2020
28. A Note on the Paper 'Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps'
- Author
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Farid Bozorgnia and Allahkaram Shafie
- Subjects
Discrete mathematics ,021103 operations research ,Control and Optimization ,Applied Mathematics ,0211 other engineering and technologies ,Regular polygon ,010103 numerical & computational mathematics ,02 engineering and technology ,Management Science and Operations Research ,Mathematical proof ,01 natural sciences ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Vector optimization ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Metrization theorem ,Theory of computation ,FOS: Mathematics ,0101 mathematics ,Mathematics ,Vector space ,Counterexample - Abstract
In this work, some counterexamples are given to refute some results reported in the paper by Guo and Li [8] (J Optim Theory Appl 162,(2014), 821-844). We correct the faulty in some of their theorems and we present alternative proofs. Moreover, we extend the definition of approximately pseudo-dissipative in the setting of metrizable topological vector spaces.
- Published
- 2019
29. Metapopulation dynamics in the rock-paper-scissors game with mutation: Effects of time-varying migration paths
- Author
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Kei-ichi Tainaka, Genki Ichinose, and Takashi Nagatani
- Subjects
0301 basic medicine ,Statistics and Probability ,Mutation rate ,Phase transition ,Population Dynamics ,Population ,Metapopulation ,General Biochemistry, Genetics and Molecular Biology ,03 medical and health sciences ,0302 clinical medicine ,Game Theory ,Mutation Rate ,Animals ,Quantitative Biology::Populations and Evolution ,Statistical physics ,Diffusion (business) ,education ,Mathematics ,Chronobiology Phenomena ,education.field_of_study ,General Immunology and Microbiology ,Applied Mathematics ,General Medicine ,Models, Theoretical ,Random walk ,030104 developmental biology ,Modeling and Simulation ,Mutation (genetic algorithm) ,Path (graph theory) ,Animal Migration ,General Agricultural and Biological Sciences ,030217 neurology & neurosurgery - Abstract
Migration paths of animals are rarely the same. The paths may change according to seasonal and circadian rhythms. We study the effect of temporal migration on population dynamics of rock-paper-scissors (RPS) games with mutation by using the metapopulation dynamic model with two patches. Via mutation, an individual R changes to S with rate μ. All agents move by random walk between two patches and the RPS game is performed in each patch. The migration path between two patches is switched on or off periodically. The dynamics are represented by the reaction-diffusion equations with time-dependent diffusion coefficients in diffusively coupled reactors. We obtain the solutions of time-dependent reaction-diffusion equations numerically and analytically. The time-varying migration path induces complex behavior for the RPS dynamics, depending on the frequency of the periodical path. We find that the phase transitions occur by varying mutation rate μ. The phase transition depends highly on the frequency.
- Published
- 2019
30. Critical perspectives on provable security: Fifteen years of 'another look' papers
- Author
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Neal Koblitz and Alfred Menezes
- Subjects
Provable security ,Algebra and Number Theory ,Computer Networks and Communications ,business.industry ,Applied Mathematics ,020206 networking & telecommunications ,Subject (documents) ,Cryptography ,0102 computer and information sciences ,02 engineering and technology ,Computer security ,computer.software_genre ,Mathematical proof ,01 natural sciences ,Microbiology ,010201 computation theory & mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,business ,computer ,Mathematics - Abstract
We give an overview of our critiques of "proofs" of security and a guide to our papers on the subject that have appeared over the past decade and a half. We also provide numerous additional examples and a few updates and errata.
- Published
- 2019
31. The contribution of cause-effect link to representing the core of scientific paper—The role of Semantic Link Network.
- Author
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Cao, Mengyun, Sun, Xiaoping, and Zhuge, Hai
- Subjects
COMPLEXITY (Philosophy) ,CAUSATION (Philosophy) ,SEMANTICS ,RESEARCH ,PHILOSOPHY - Abstract
The Semantic Link Network is a general semantic model for modeling the structure and the evolution of complex systems. Various semantic links play different roles in rendering the semantics of complex system. One of the basic semantic links represents cause-effect relation, which plays an important role in representation and understanding. This paper verifies the role of the Semantic Link Network in representing the core of text by investigating the contribution of cause-effect link to representing the core of scientific papers. Research carries out with the following steps: (1) Two propositions on the contribution of cause-effect link in rendering the core of paper are proposed and verified through a statistical survey, which shows that the sentences on cause-effect links cover about 65% of key words within each paper on average. (2) An algorithm based on syntactic patterns is designed for automatically extracting cause-effect link from scientific papers, which recalls about 70% of manually annotated cause-effect links on average, indicating that the result adapts to the scale of data sets. (3) The effects of cause-effect link on four schemes of incorporating cause-effect link into the existing instances of the Semantic Link Network for enhancing the summarization of scientific papers are investigated. The experiments show that the quality of the summaries is significantly improved, which verifies the role of semantic links. The significance of this research lies in two aspects: (1) it verifies that the Semantic Link Network connects the important concepts to render the core of text; and, (2) it provides an evidence for realizing content services such as summarization, recommendation and question answering based on the Semantic Link Network, and it can inspire relevant research on content computing. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
32. A Generalized Zero-Forcing Precoder with Successive Dirty-Paper Coding in MISO Broadcast Channels
- Author
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Sha Hu and Fredrik Rusek
- Subjects
Discrete mathematics ,FOS: Computer and information sciences ,Computer Science - Information Theory ,Applied Mathematics ,Information Theory (cs.IT) ,020206 networking & telecommunications ,020302 automobile design & engineering ,02 engineering and technology ,Maximization ,Main diagonal ,Computer Science Applications ,symbols.namesake ,0203 mechanical engineering ,Broadcast channels ,Lagrange multiplier ,0202 electrical engineering, electronic engineering, information engineering ,Zero Forcing Equalizer ,symbols ,Dirty paper coding ,Electrical and Electronic Engineering ,Mathematics ,Coding (social sciences) ,Communication channel - Abstract
In this paper, we consider precoder designs for multiuser multiple-input-single-output (MISO) broadcasting channels. Instead of using a traditional linear zero-forcing (ZF) precoder, we propose a generalized ZF (GZF) precoder in conjunction with successive dirty-paper coding (DPC) for data-transmissions, namely, the GZF-DP precoder, where the suffix \lq{}DP\rq{} stands for \lq{}dirty-paper\rq{}. The GZF-DP precoder is designed to generate a band-shaped and lower-triangular effective channel $\vec{F}$ such that only the entries along the main diagonal and the $\nu$ first lower-diagonals can take non-zero values. Utilizing the successive DPC, the known non-causal inter-user interferences from the other (up to) $\nu$ users are canceled through successive encoding. We analyze optimal GZF-DP precoder designs both for sum-rate and minimum user-rate maximizations. Utilizing Lagrange multipliers, the optimal precoders for both cases are solved in closed-forms in relation to optimal power allocations. For the sum-rate maximization, the optimal power allocation can be found through water-filling, but with modified water-levels depending on the parameter $\nu$. While for the minimum user-rate maximization that measures the quality of the service (QoS), the optimal power allocation is directly solved in closed-form which also depends on $\nu$. Moreover, we propose two low-complexity user-ordering algorithms for the GZF-DP precoder designs for both maximizations, respectively. We show through numerical results that, the proposed GZF-DP precoder with a small $\nu$ ($\leq\!3$) renders significant rate increments compared to the previous precoder designs such as the linear ZF and user-grouping based DPC (UG-DP) precoders., Comment: 31 pages, 13 figures, submitted to IEEE Transactions on Wireless Communications in Aug. 2016
- Published
- 2017
- Full Text
- View/download PDF
33. Call for Papers: T.C. Machine-Learning Mathematical Structures
- Author
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Rafał Abłamowicz
- Subjects
business.industry ,Applied Mathematics ,Artificial intelligence ,Mathematical structure ,business ,Mathematics - Published
- 2021
34. Bifurcation analysis of the rock–paper–scissors game with discrete-time logit dynamics
- Author
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Yosuke Umezuki
- Subjects
Computer Science::Computer Science and Game Theory ,Sociology and Political Science ,05 social sciences ,General Social Sciences ,01 natural sciences ,010305 fluids & plasmas ,symbols.namesake ,Bifurcation theory ,Discrete time and continuous time ,Nash equilibrium ,Best response ,0502 economics and business ,0103 physical sciences ,Attractor ,symbols ,Applied mathematics ,050207 economics ,Statistics, Probability and Uncertainty ,Invariant (mathematics) ,General Psychology ,Bifurcation ,Saddle ,Mathematics - Abstract
In this study, we investigate a discrete-time version of logit dynamics, as applied to the rock–paper–scissors (RPS) game. First, we show that around the Nash equilibrium point, an attracting closed invariant curve appears due to the Neimark–Sacker bifurcation. Next, near the resonance point, we find a period-three attracting cycle, which can be thought of as a counterpart to the cyclically stable set in the RPS game with best response dynamics. Moreover, we show that the cycle can coexist with an attracting closed invariant curve, a period-three saddle cycle, and the attracting or repelling Nash equilibrium point. Finally, we use the codimension-two bifurcation theory to specify the set of heteroclinic bifurcations that destroy the coexistence of the attractors.
- Published
- 2018
35. Comments on Paper 'On the Relation Between Two Approaches to Necessary Optimality Conditions in Problems with State Constraints'
- Author
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Dmitry Karamzin
- Subjects
0209 industrial biotechnology ,021103 operations research ,Control and Optimization ,Relation (database) ,Applied Mathematics ,0211 other engineering and technologies ,Subject (philosophy) ,02 engineering and technology ,State (functional analysis) ,Management Science and Operations Research ,Optimal control ,020901 industrial engineering & automation ,Maximum principle ,Theory of computation ,Mathematical economics ,Mathematics - Abstract
This Forum Note concerns the question of necessary optimality conditions in optimal control problems subject to state constraints. Some critical remarks about a recently published paper are made.
- Published
- 2018
36. Paper folding and trigonometric ratios
- Author
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Arsalan Wares
- Subjects
Mathematical logic ,Applied Mathematics ,010102 general mathematics ,05 social sciences ,050301 education ,Folding (DSP implementation) ,01 natural sciences ,Education ,Algebra ,Mathematics (miscellaneous) ,Concept learning ,0101 mathematics ,Trigonometry ,Mathematics instruction ,0503 education ,Mathematics - Abstract
The purpose of this note is to discuss how paper folding can be used to find the exact trigonometric ratios of the following four angles: 22.5°, 67.5°, 27°, and 63°.
- Published
- 2018
37. Physics driven behavioural clustering of free-falling paper shapes.
- Author
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Howison, Toby, Hughes, Josie, Giardina, Fabio, and Iida, Fumiya
- Subjects
- *
PHYSICS , *SET functions , *MACHINE learning , *PHENOMENOLOGICAL theory (Physics) , *CONTINUUM mechanics - Abstract
Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
38. Extension of Kalman Filtering to Semilinear PDE Systems-Application to Pulp and Paper
- Author
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Ivan Francisco Yupanqui Tello, Alain Vande Wouver, and Daniel Coutinho
- Subjects
Spatial variable ,0209 industrial biotechnology ,Observer (quantum physics) ,02 engineering and technology ,Kalman filter ,Chemical reactor ,Nonlinear system ,020901 industrial engineering & automation ,Distributed parameter system ,0202 electrical engineering, electronic engineering, information engineering ,Riccati equation ,Pulp bleaching ,Applied mathematics ,020201 artificial intelligence & image processing ,Mathematics - Abstract
This paper deals with the observer design of nonlinear tubular chemical reactor models. The analysis is performed on a linearized version of the model around a steady-state profile, in which some coefficients are a function of the spatial variable. The study starts from a general model of chemical tubular reactors that will serve as a benchmark model for the formulation in the infinite dimensional Hilbert state space. The optimal output injection operator associated to the proposed observer is computed via the solution of the infinite-dimensional Riccati equation in the space variable. The performance of the observer is illustrated through numerical experiments of an industrial pulp bleaching tubular reactor model.
- Published
- 2020
39. Response to 'Comments on the paper by B. E. <scp>Grossman‐Ponemon</scp> , L. M. Keer, and A. J. Lew ‘A method to compute mixed‐mode stress intensity factors for nonplanar cracks in three dimensions’ ( Int. J. Numer. Methods Eng ., 2020)'
- Author
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Adrian J. Lew and Benjamin E. Grossman-Ponemon
- Subjects
Numerical Analysis ,Grossman ,Applied Mathematics ,INT ,General Engineering ,Mixed mode ,Stress intensity factor ,Mathematics ,Mathematical physics - Published
- 2021
40. Ten Simple Rules for writing algorithmic bioinformatics conference papers
- Author
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Paul Medvedev
- Subjects
0301 basic medicine ,Computer and Information Sciences ,Computer science ,QH301-705.5 ,Bioinformatics ,Writing ,Gene Identification and Analysis ,Genetic Networks ,Research and Analysis Methods ,Field (computer science) ,03 medical and health sciences ,Cellular and Molecular Neuroscience ,Database and Informatics Methods ,Clustering Algorithms ,0302 clinical medicine ,Computer software ,Genetics ,Humans ,Prototypes ,Biology (General) ,Molecular Biology ,Ecology, Evolution, Behavior and Systematics ,Simple (philosophy) ,Publishing ,Ecology ,Information Dissemination ,Software Tools ,Applied Mathematics ,Simulation and Modeling ,Computational Biology ,Software Engineering ,Biology and Life Sciences ,Congresses as Topic ,030104 developmental biology ,Editorial ,Technology Development ,Computational Theory and Mathematics ,Modeling and Simulation ,Physical Sciences ,Engineering and Technology ,Sequence Analysis ,Sequence Alignment ,030217 neurology & neurosurgery ,Algorithms ,Mathematics ,Network Analysis - Abstract
Author summary Conferences are great venues for disseminating algorithmic bioinformatics results, but they unfortunately do not offer an opportunity to make major revisions in the way that journals do. As a result, it is not possible for authors to fix mistakes that might be easily correctable but nevertheless can cause the paper to be rejected. As a reviewer, I wish that I had the opportunity to tell the authors, “Hey, you forgot to do this really important thing, without which it is hard to accept the paper, but if you could go back and fix it, you might have a great paper for the conference.” This lack of a back and forth can be especially problematic for first-time submitters or those from outside the field, e.g., biologists. In this article, I outline Ten Simple Rules to follow when writing an algorithmic bioinformatics conference paper to avoid having it rejected.
- Published
- 2020
41. (CMMSE paper) A finite‐difference model for indoctrination dynamics
- Author
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María G. Medina-Guevara, Héctor Vargas-Rodríguez, and Pedro B. Espinoza-Padilla
- Subjects
Agent-based model ,Finite difference model ,Opinion dynamics ,General Mathematics ,Dynamics (mechanics) ,Indoctrination ,General Engineering ,Applied mathematics ,Mathematics - Published
- 2018
42. Comment on the paper 'Heat and mass transfer in unsteady MHD slip flow of Casson fluid over a moving wedge embedded in a porous medium in the presence of chemical reaction: Numerical solutions using Keller‐Box method, Imran Ullah, Ilyas Khan, Sharidan Shafie, Numerical Methods for Partial Differential Equations , November 2017, https://doi.org/10.1002/num.22221'
- Author
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Asterios Pantokratoras
- Subjects
Numerical Analysis ,business.product_category ,Applied Mathematics ,010103 numerical & computational mathematics ,Mechanics ,01 natural sciences ,Chemical reaction ,Wedge (mechanical device) ,010101 applied mathematics ,Computational Mathematics ,Ullah ,Mass transfer ,Slip flow ,Casson fluid ,0101 mathematics ,Magnetohydrodynamics ,business ,Porous medium ,Analysis ,Mathematics - Published
- 2018
43. Comments on the paper: Bilinear form and exact solutions for a new extended (2 + 1)-dimensional Boussinesq equation by Ping Cui [Results Phys 22 (2021) 103919]
- Author
-
Lazhar Bougoffa
- Subjects
010302 applied physics ,Ping (video games) ,Exact solution ,Physics ,QC1-999 ,One-dimensional space ,Hirota bilinear form ,General Physics and Astronomy ,02 engineering and technology ,Bilinear form ,021001 nanoscience & nanotechnology ,01 natural sciences ,Extended (2 + 1)-dimensional Boussinesq equation ,Exact solutions in general relativity ,0103 physical sciences ,Applied mathematics ,0210 nano-technology ,Bilinear Bell polynomial ,Mathematics - Abstract
The purpose of this comment paper is to show that the results of the paper (Cui, 2021) are incorrect.
- Published
- 2021
44. Corrigendum to the paper: A way to model stochastic perturbations in population dynamics models with bounded realizations. Commun Nonlinear Sci Numer Simulat, 77 (2019), 239–257
- Author
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Javier López-de-la-Cruz, Alain Rapaport, Renato Colucci, and Tomás Caraballo
- Subjects
Numerical Analysis ,education.field_of_study ,Stochastic process ,Applied Mathematics ,Dynamics (mechanics) ,Population ,Process (computing) ,Random perturbation ,01 natural sciences ,010305 fluids & plasmas ,Nonlinear system ,Modeling and Simulation ,Bounded function ,0103 physical sciences ,Applied mathematics ,010306 general physics ,education ,Mathematics - Abstract
In this corrigendum we correct an error in our paper [T. Caraballo, R. Colucci, J. Lopez-de-la-Cruz and A. Rapaport. A way to model stochastic perturbations in population dynamics models with bounded realizations, Commun Nonlinear Sci Numer Simulat, 77(2019) 239–257]. We present a correct way to model real noisy perturbations by considering a slightly different stochastic process based, as in the original paper, on the Ornstein-Uhlenbeck process. Namely, we correct the formulae that generates the noisy realizations to ensure the boundedness property to be satisfied with probability one (which turns out not to be true in our original paper even though it was observed in all the simulations).
- Published
- 2021
45. Remarks on two connected papers about Keller–Segel systems with nonlinear production
- Author
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Giuseppe Viglialoro, Tomomi Yokota, and Yuya Tanaka
- Subjects
010101 applied mathematics ,Nonlinear system ,Sublinear function ,Applied Mathematics ,Signal production ,010102 general mathematics ,Applied mathematics ,Production (computer science) ,Nonlinear diffusion ,0101 mathematics ,01 natural sciences ,Analysis ,Mathematics - Abstract
These notes aim to provide a deeper insight on the specifics of two articles dealing with chemotaxis models with nonlinear production. More precisely, we are referring to the papers “Boundedness of solutions to a quasilinear parabolic–parabolic chemotaxis model with nonlinear signal production” by Tao et al. (2019) [2] and “Boundedness for a fully parabolic Keller–Segel model with sublinear segregation and superlinear aggregation” by Frassu and Viglialoro (2021) [1] . These works, independently published in these last years, present results leaving open room for further improvement. Indeed, in the first a gap in the proof of the main claim appears, whereas the cornerstone assumption in the second is not sharp. In these pages we give a more complete picture to the relative underlying comprehension.
- Published
- 2021
46. Allowable delay sets for the stability analysis of linear time-varying delay systems using a delay-dependent reciprocally convex lemma * *This paper was supported by the ANR Project SCIDiS, contract number
- Author
-
Alexandre Seuret and Frédéric Gouaisbaut
- Subjects
0209 industrial biotechnology ,Linear system ,Stability (learning theory) ,02 engineering and technology ,Function (mathematics) ,Upper and lower bounds ,Stability conditions ,020901 industrial engineering & automation ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,Convex combination ,Constant (mathematics) ,Time complexity ,Mathematics - Abstract
This paper addresses the stability analysis of linear systems subject to a time-varying delay. The contribution of this paper is twofolds. First, we aim at presenting a new matrix inequality, which can be seen as an improved version of the reciprocally convex combination, which provides a more accurate delay-dependent lower bound. When gathering this new inequality with the Wirtinger-based integral inequality, efficient stability conditions expressed in terms of LMI are designed and show a clear reduction of the conservatism with a reasonable associated computational cost. The second original contribution of this paper consists in noting that stability conditions issued from the Wirtinger-based integral inequality depends in an affine manner on the bounds of the delay function and also on its derivative. This allows to refine the definition of allowable delay set and to relax usual convex on the delay function. As a result of this new characterization, the LMI conditions allows obtaining stability regions for slow time-varying delay systems which are very closed to the constant delay case.
- Published
- 2017
47. Kinetic approach to the collective dynamics of the rock-paper-scissors binary game
- Author
-
Francesco Salvarani, Nastassia Pouradier Duteil, Sorbonne Université (SU), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Dipartimento di matematica F. Casorati, Università degli Studi di Pavia = University of Pavia (UNIPV), Pôle Universitaire Léonard de Vinci (PULV), Work supported by the ANR projects Kimega (ANR-14-ACHN-0030-01, MFG ANR-16-CE40-0015-01) and by the Italian Ministry of Education, University and Research (Dipartimenti di Eccellenzaprogram 2018-2022, Dipartimento di Matematica ’F. Casorati’, Universita degli Studi di Pavia)., ANR-14-ACHN-0030,Kimega,Modélisation cinétique de jeux à champs moyen(2014), ANR-16-CE40-0015,MFG,Jeux Champs Moyen(2016), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Università degli Studi di Pavia, Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), and Università di Pavia
- Subjects
Domain of a function ,0209 industrial biotechnology ,Variables ,Applied Mathematics ,media_common.quotation_subject ,Binary number ,020206 networking & telecommunications ,Rigorous proof ,02 engineering and technology ,16. Peace & justice ,Kinetic energy ,Computational Mathematics ,020901 industrial engineering & automation ,Compact space ,Mathematics - Analysis of PDEs ,0202 electrical engineering, electronic engineering, information engineering ,FOS: Mathematics ,Applied mathematics ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Uniqueness ,Collective dynamics ,media_common ,Mathematics ,Analysis of PDEs (math.AP) - Abstract
International audience; This article studies the kinetic dynamics of the rock-paper-scissors binary game. We first prove existence and uniqueness of the solution of the kinetic equation and subsequently we prove the rigorous derivation of the quasi-invariant limit for two meaningful choices of the domain of definition of the independent variables. We notice that the domain of definition of the problem plays a crucial role and heavily influences the behavior of the solution. The rigorous proof of the relaxation limit does not need the use of entropy estimates for ensuring compactness.
- Published
- 2020
48. Mistakes can stabilise the dynamics of rock-paper-scissors games
- Author
-
Krishnendu Chatterjee, Maria Kleshnina, Jerzy A. Filar, and Sabrina Streipert
- Subjects
Evolutionary Genetics ,0301 basic medicine ,Computer science ,Population Dynamics ,Social Sciences ,Stable equilibrium ,Cognition ,0302 clinical medicine ,Psychology ,050207 economics ,Biology (General) ,Strategy execution ,0303 health sciences ,Animal Behavior ,Ecology ,Applied Mathematics ,05 social sciences ,Biological Evolution ,Computational Theory and Mathematics ,Dynamics (music) ,Modeling and Simulation ,Physical Sciences ,Probability distribution ,Mathematical economics ,Game theory ,Research Article ,QH301-705.5 ,Decision Making ,Microbiology ,03 medical and health sciences ,Cellular and Molecular Neuroscience ,Game Theory ,0502 economics and business ,Genetics ,Humans ,Animal behavior ,Evolutionary dynamics ,Molecular Biology ,Ecology, Evolution, Behavior and Systematics ,030304 developmental biology ,Behavior ,Evolutionary Biology ,Population Biology ,Cognitive Psychology ,Biology and Life Sciences ,Probability Theory ,Probability Distribution ,Organismal Evolution ,030104 developmental biology ,Microbial Evolution ,Cognitive Science ,Zoology ,Mathematics ,030217 neurology & neurosurgery ,Neuroscience - Abstract
A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium., Author summary A game of rock-paper-scissors is more than just a children’s game. This type of interactions is often used to describe competition among animals or humans. A special feature of such an interaction is that none of the pure strategies dominates, resulting in a cyclic pattern. However, in wild communities such interactions are rarely observed by biologists. Our results suggest that this lack of cyclicity may stem from imperfectness of interacting individuals. In other words, we show analytically that heterogeneity in behavioural patterns may break a cyclic relationship and lead to a stable equilibrium in pure or mixed strategies.
- Published
- 2021
49. A comment about the paper On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation
- Author
-
Fábio Natali and Renan H. Martins
- Subjects
Camassa–Holm equation ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Orbital stability ,Space (mathematics) ,01 natural sciences ,Instability ,010101 applied mathematics ,Mathematics - Analysis of PDEs ,Traveling wave ,0101 mathematics ,Analysis ,Energy (signal processing) ,Mathematics - Abstract
We discuss the recent paper by A. Dar\'os and L.K. Arruda (On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation, J. Diff. Equat., 266 (2019), 1946-1968). Our intention is to correct some imperfections left by the authors and present the orbital stability of periodic snoidal waves in the energy space., Comment: 10 pages and 2 figures
- Published
- 2019
50. Comments on the paper 'Asymptotic behavior for a fourth-order parabolic equation involving the Hessian. Z. Angew. Math. Phys., (2018) 69: 147'
- Author
-
Jun Zhou and Hang Ding
- Subjects
Hessian matrix ,symbols.namesake ,Fourth order ,Applied Mathematics ,General Mathematics ,symbols ,General Physics and Astronomy ,Applied mathematics ,Finite time ,Mathematics ,Energy functional ,Blowing up - Abstract
In this note, we make two revisions of the paper [2]. The first one is the asymptotic behavior of the energy functional as $$t\rightarrow T$$ (see [2, Theorem 1.6]), where T is the blow-up time. The second one is the equivalent conditions for the solutions blowing up in finite time or existing globally (see [2, Theorem 1.8]).
- Published
- 2019
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