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2. 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
3. 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
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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.
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- 2021
4. Evolutionary dynamics of rock-paper-scissors game in the patchy network with mutations
- Author
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Tina Verma and Arvind Kumar Gupta
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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.
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- 2021
5. Remarks on two connected papers about Keller–Segel systems with nonlinear production
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Giuseppe Viglialoro, Tomomi Yokota, and Yuya Tanaka
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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.
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- 2021
6. Rényi’s divergence as a chemical similarity criterion
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N. Flores-Gallegos
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Original Paper ,Work (thermodynamics) ,Rényi’s divergence ,Rényi’s entropy ,Applied Mathematics ,Chemical similarity ,General Chemistry ,Statistical physics ,Chemical reactivity ,Expression (computer science) ,Divergence (statistics) ,Mathematics - Abstract
In this work, a new version of Rényi’s divergence is presented. The expression obtained is used as a tool to identify molecules that could share some chemical or structural properties, and a data basis set of 1641 molecules is used in this study. Our results suggest that this new form of Rényi divergence could be a useful tool that will eventually permit complementary studies in which the main goal is to obtain molecules with similar properties.
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- 2021
7. Dynamics and optimal control of a stochastic coronavirus (COVID-19) epidemic model with diffusion
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Zhouchao Wei and Yuxi Li
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Original Paper ,Stationary distribution ,Computer simulation ,Reaction–diffusion ,Turing instability ,Applied Mathematics ,Mechanical Engineering ,COVID-19 ,Aerospace Engineering ,Ocean Engineering ,Optimal control ,Nonlinear system ,symbols.namesake ,Stochastic epidemic model ,Control and Systems Engineering ,Reaction–diffusion system ,Taylor series ,symbols ,Applied mathematics ,Uniqueness ,Electrical and Electronic Engineering ,Epidemic model ,Amplitude equations ,Mathematics - Abstract
In view of the facts in the infection and propagation of COVID-19, a stochastic reaction–diffusion epidemic model is presented to analyse and control this infectious diseases. Stationary distribution and Turing instability of this model are discussed for deriving the sufficient criteria for the persistence and extinction of disease. Furthermore, the amplitude equations are derived by using Taylor series expansion and weakly nonlinear analysis, and selection of Turing patterns for this model can be determined. In addition, the optimal quarantine control problem for reducing control cost is studied, and the differences between the two models are compared. By applying the optimal control theory, the existence and uniqueness of the optimal control and the optimal solution are obtained. Finally, these results are verified and illustrated by numerical simulation.
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- 2021
8. Nonlinear analysis of a four-dimensional fractional hyper-chaotic system based on general Riemann–Liouville–Caputo fractal–fractional derivative
- Author
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Yuhang Pan
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Original Paper ,Series (mathematics) ,Applied Mathematics ,Mechanical Engineering ,General Caputo–Fabrizio ,Aerospace Engineering ,Ocean Engineering ,Fractal–Fractional Derivative (FFD) ,Function (mathematics) ,Fractal dimension ,Fractional calculus ,Nonlinear system ,Riemann–Liouville–Caputo (RLC) ,Fractal ,Control and Systems Engineering ,Attractor ,Qi Hyper-chaotic system ,Applied mathematics ,Uniqueness ,Electrical and Electronic Engineering ,Fractional-Order Hyperchaotic System ,Mathematics - Abstract
In this study, a four-dimensional fractional hyperchaotic model is analyzed based on general Riemann–Liouville–Caputo (RLC) fractal–fractional derivative (FFD). A series of new operators are constructed using three different elements, namely, the general Mittag–Leffler function, exponential decay, and power law. The operators have two parameters: One is considered as fractional order and the other as fractal dimension. The Qi hyperchaotic fractional attractor is modeled by using these operators, and the models are solved numerically using a very efficient numerical scheme. Meanwhile, the existence and uniqueness of solutions have been investigated to justify the physical adequacy of the model and the numerical scheme proposed in the resolution. The numerical simulations for some specific fractional order and fractal dimension are presented. Furthermore, these results obtained via generalized Caputo–Fabrizio and fractal–fractional derivative show some crossover effects, which is due to non-index law property. Finally, these obtained from generalized fractal–fractional derivative show very strange and new attractors with self-similarities.
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- 2021
9. Data driven regularization by projection
- Author
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Otmar Scherzer, Andrea Aspri, Yury Korolev, Korolev, Y [0000-0002-6339-652X], Scherzer, O [0000-0001-9378-7452], Apollo - University of Cambridge Repository, Korolev, Yury [0000-0002-6339-652X], and Scherzer, Otmar [0000-0001-9378-7452]
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Paper ,Variational regularization ,010103 numerical & computational mathematics ,Gram–Schmidt orthogonalization ,01 natural sciences ,Regularization (mathematics) ,Theoretical Computer Science ,Data-driven ,FOS: Mathematics ,Applied mathematics ,Mathematics - Numerical Analysis ,Gram–Schmidt process ,Schmidt orthogonalization ,Gram– ,0101 mathematics ,data driven regularization ,Mathematical Physics ,Mathematics ,Gram– ,Generality ,Training set ,Radon transform ,inverse problems ,Applied Mathematics ,47A52, 65J20, 65J22, 65F22 ,variational regularization ,regularization by projection ,Numerical Analysis (math.NA) ,Inverse problem ,Computer Science Applications ,010101 applied mathematics ,Signal Processing - Abstract
We study linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regularization by projection and variational regularization can be formulated by using the training data only and without making use of the forward operator. We study convergence and stability of the regularized solutions in view of Seidman (1980 J. Optim. Theory Appl. 30 535), who showed that regularization by projection is not convergent in general, by giving some insight on the generality of Seidman’s nonconvergence example. Moreover, we show, analytically and numerically, that regularization by projection is indeed capable of learning linear operators, such as the Radon transform.
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- 2022
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10. A Reliable Solution of Nonlinear Time Dependent Fractional Model of Ebola Virus Disease with Arbitrary Order Derivative in Liouville–Caputo Sense
- Author
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Vinod Kumar Bhardwaj and Manish Goyal
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Original Paper ,Ebola virus ,Applied Mathematics ,Fractional model ,Order (ring theory) ,Sense (electronics) ,Derivative ,medicine.disease_cause ,Fractional differential equations (FDE) ,Ebola disease model ,Computational Mathematics ,Nonlinear system ,Liouville–Caputo fractional derivative ,medicine ,Applied mathematics ,Fractional variational iteration scheme (FVIM) ,Mathematics - Abstract
In this article, the analysis of an arbitrary order Ebola virus disease model is conducted to find out its reliable solution. The fractional derivative is taken in Liouville-Caputo sense. The solution of this nonlinear model is achieved using fractional variational iteration scheme. The convergence analysis of the obtained solution is also presented which confirms that it is positive, bounded and convergent. The outcomes are discussed with figures explaining variation of susceptible, infected, recovered population and number of disease induced deaths with time. The negligible error in successive iterations of various population shows the competency of the presented scheme. The results endorse that FVIM is extremely effective, powerful and easy in usage.
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- 2021
11. Confidence intervals with higher accuracy for short and long-memory linear processes
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Masoud M Nasari and Mohamedou Ould-Haye
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Statistics and Probability ,Population mean ,05 social sciences ,Edgeworth series ,01 natural sciences ,Confidence interval ,010104 statistics & probability ,Sample size determination ,Long memory ,0502 economics and business ,Applied mathematics ,0101 mathematics ,Statistics, Probability and Uncertainty ,Real world data ,050205 econometrics ,Mathematics ,Central limit theorem - Abstract
In this paper an easy to implement method of stochastically weighing short and long-memory linear processes is introduced. The method renders asymptotically exact size confidence intervals for the population mean which are significantly more accurate than their classic counterparts for each fixed sample size n. It is illustrated both theoretically and numerically that the randomization framework of this paper produces randomized (asymptotic) pivotal quantities, for the mean, which admit central limit theorems with smaller magnitudes of error as compared to those of their leading classic counterparts. An Edgeworth expansion result for randomly weighted linear processes whose innovations do not necessarily satisfy the Cramer condition, is established. Numerical illustrations and applications to real world data are also included.
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- 2021
12. An algorithmic approach to small limit cycles of nonlinear differential systems: The averaging method revisited
- Author
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Bo Huang and Chee Yap
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Maple ,Algebra and Number Theory ,010102 general mathematics ,Zero (complex analysis) ,Order (ring theory) ,010103 numerical & computational mathematics ,engineering.material ,01 natural sciences ,Term (time) ,Computational Mathematics ,Nonlinear system ,Limit cycle ,engineering ,Applied mathematics ,Limit (mathematics) ,0101 mathematics ,Bifurcation ,Mathematics - Abstract
This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging method. The first algorithm allows one to transform the considered differential systems to the normal form of averaging. Here, we restricted the unperturbed term of the normal form of averaging to be identically zero. The second algorithm is used to derive the computational formulae of the averaged functions at any order. The third algorithm is based on the first two algorithms and determines the exact expressions of the averaged functions for the considered differential systems. The proposed approach is implemented in Maple and its effectiveness is shown by several examples. Moreover, we report some incorrect results in published papers on the averaging method.
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- 2023
13. A Framework for Mitigating Excessive Transportation in the Context of Manufacturing Localization
- Author
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Enes Eryarsoy, Hakki Nalcioglu, Huseyin Selcuk Kilic, Ahmet Selcuk Yalcin, Selim Zaim, Dursun Delen, and Eryarsoy E., Nalcioglu H., KILIÇ H. S., Yalcin A., Zaim S., Delen D.
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inshoring ,AHP ,Temel Bilimler (SCI) ,Mühendislik ,ENGINEERING ,Transportation ,localization ,MATHEMATICS ,Information Systems, Communication and Control Engineering ,Yapay Zeka ,Sustainable development ,Matematik ,Hesaplamalı Teori ve Matematik ,Computer Sciences ,Temel Bilimler ,Applied Mathematics ,Outsourcing ,MATHEMATICS, APPLIED ,OTOMASYON & KONTROL SİSTEMLERİ ,Computational Theory and Mathematics ,Natural Sciences (SCI) ,Physical Sciences ,Engineering and Technology ,Bilgisayar Bilimi ,fuzzy logic ,Bilgi Sistemleri, Haberleşme ve Kontrol Mühendisliği ,Control and System Engineering ,Natural Sciences ,COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE ,AUTOMATION & CONTROL SYSTEMS ,algorithms ,BİLGİSAYAR BİLİMİ, YAPAY ZEKA ,Artificial Intelligence ,reshoring ,Uygulamalı matematik ,Bilgisayar Bilimleri ,Engineering, Computing & Technology (ENG) ,offshoring ,Location awareness ,Mühendislik, Bilişim ve Teknoloji (ENG) ,COMPUTER SCIENCE ,MATEMATİK, UYGULAMALI ,Costs ,Manufacturing ,Fizik Bilimleri ,Control and Systems Engineering ,Mühendislik ve Teknoloji ,Algoritmalar ,Companies ,Kontrol ve Sistem Mühendisliği - Abstract
IEEEWhile the zeitgeist of today prescribes localization as a key to eliminate the excessive transportation for manufacturing firms, firm-level practical and workable guidelines that go beyond maxims are scant. Laden with analytical methods, this paper offers a phronetic, customizable framework based on Lean Six Sigma (LSS). The framework mimics Define-Measure-Analyze-Improve-Control (DMAIC) process. The early phases of the framework, ex-ante, prescribe the use of a variety tools and techniques from Lean Six sigma (LSS) and employ fuzzy analytic hierarchy process (FAHP) to extract the vital few root-causes that may impede localization. The latter phases suggest the use of design of experiments (DOE) to evaluate the root-causes, ex-post. The paper outlines a clear and established procedure and demonstrates each analytical phase using evidence from a two-year real-world application in steel industry.
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- 2023
14. Some subfield codes from MDS codes
- Author
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Jinquan Luo and Can Xiang
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Class (set theory) ,Authentication ,Algebra and Number Theory ,Computer Networks and Communications ,Applied Mathematics ,Binary number ,020206 networking & telecommunications ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Microbiology ,Linear code ,Dual (category theory) ,Algebra ,Association scheme ,Finite field ,010201 computation theory & mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,Mathematics - Abstract
Subfield codes of linear codes over finite fields have recently received a lot of attention, as some of these codes are optimal and have applications in secrete sharing, authentication codes and association schemes. In this paper, a class of binary subfield codes is constructed from a special family of MDS codes, and their parameters are explicitly determined. The parameters of their dual codes are also studied. Some of the codes presented in this paper are optimal or almost optimal.
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- 2023
15. Designing tweakable enciphering schemes using public permutations
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Avijit Dutta, Debrup Chakraborty, and Samir Kundu
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Algebra and Number Theory ,Theoretical computer science ,Computer Networks and Communications ,business.industry ,Applied Mathematics ,Hash function ,020206 networking & telecommunications ,Cryptography ,0102 computer and information sciences ,02 engineering and technology ,Construct (python library) ,Random permutation ,Encryption ,Pseudorandom permutation ,01 natural sciences ,Microbiology ,Permutation ,010201 computation theory & mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,business ,Mathematics ,Block cipher - Abstract
A tweakable enciphering scheme (TES) is a length preserving (tweakable) encryption scheme that provides (tweakable) strong pseudorandom permutation security on arbitrarily long messages. TES is traditionally built using block ciphers and the security of the mode depends on the strong pseudorandom permutation security of the underlying block cipher. In this paper, we construct TESs using public random permutations. Public random permutations are being considered as a replacement of block cipher in several cryptographic schemes including AEs, MACs, etc. However, to our knowledge, a systematic study of constructing TES using public random permutations is missing. In this paper, we give a generic construction of a TES which uses a public random permutation, a length expanding public permutation based PRF and a hash function which is both almost xor universal and almost regular. Further, we propose a concrete length expanding public permutation based PRF construction. We also propose a single keyed TES using a public random permutation and an AXU and almost regular hash function.
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- 2023
16. New self-dual codes from $ 2 \times 2 $ block circulant matrices, group rings and neighbours of neighbours
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Abidin Kaya, Rhian Taylor, Adam Roberts, Joe Gildea, and Alexander Tylyshchak
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Quadratic residue ,Combinatorics ,Algebra and Number Theory ,Computer Networks and Communications ,Applied Mathematics ,Block (permutation group theory) ,Discrete Mathematics and Combinatorics ,Microbiology ,Circulant matrix ,Mathematics ,Group ring - Abstract
In this paper, we construct new self-dual codes from a construction that involves a unique combination; \begin{document}$ 2 \times 2 $\end{document} block circulant matrices, group rings and a reverse circulant matrix. There are certain conditions, specified in this paper, where this new construction yields self-dual codes. The theory is supported by the construction of self-dual codes over the rings \begin{document}$ \mathbb{F}_2 $\end{document} , \begin{document}$ \mathbb{F}_2+u \mathbb{F}_2 $\end{document} and \begin{document}$ \mathbb{F}_4+u \mathbb{F}_4 $\end{document} . Using extensions and neighbours of codes, we construct \begin{document}$ 32 $\end{document} new self-dual codes of length \begin{document}$ 68 $\end{document} . We construct 48 new best known singly-even self-dual codes of length 96.
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- 2023
17. How to go viral: A COVID-19 model with endogenously time-varying parameters
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Christian Matthes, Paul Ho, and Thomas A. Lubik
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Economics and Econometrics ,medicine.medical_specialty ,Coronavirus disease 2019 (COVID-19) ,Parameterized complexity ,Biology ,01 natural sciences ,Article ,010104 statistics & probability ,0502 economics and business ,Pandemic ,Epidemiology ,Statistics ,medicine ,Positive test ,0101 mathematics ,Mathematics ,050205 econometrics ,Bayes estimator ,Social distance ,Applied Mathematics ,Mortality rate ,05 social sciences ,Percentage point ,Bayesian estimation ,Regression ,Time-varying parameters ,Panel - Abstract
This paper estimates a panel model with endogenously time-varying parameters for COVID-19 cases and deaths in U.S. states. The functional form for infections incorporates important features of epidemiological models but is flexibly parameterized to capture different trajectories of the pandemic. Daily deaths are modeled as a spike-and-slab regression on lagged cases. The paper's Bayesian estimation reveals that social distancing and testing have significant effects on the parameters. For example, a 10 percentage point increase in the positive test rate is associated with a 2 percentage point increase in the death rate among reported cases. The model forecasts perform well, even relative to models from epidemiology and statistics.
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- 2023
18. The weight recursions for the 2-rotation symmetric quartic Boolean functions
- Author
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Thomas W. Cusick and Younhwan Cheon
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Sequence ,Monomial ,Algebra and Number Theory ,Computer Networks and Communications ,Applied Mathematics ,020206 networking & telecommunications ,0102 computer and information sciences ,02 engineering and technology ,Function (mathematics) ,01 natural sciences ,Microbiology ,Combinatorics ,010201 computation theory & mathematics ,Quartic function ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,Invariant (mathematics) ,Boolean function ,Hamming weight ,Rotation (mathematics) ,Mathematics - Abstract
A Boolean function in \begin{document}$ n $\end{document} variables is 2-rotation symmetric if it is invariant under even powers of \begin{document}$ \rho(x_1, \ldots, x_n) = (x_2, \ldots, x_n, x_1) $\end{document} , but not under the first power (ordinary rotation symmetry); we call such a function a 2-function. A 2-function is called monomial rotation symmetric (MRS) if it is generated by applying powers of \begin{document}$ \rho^2 $\end{document} to a single monomial. If the quartic MRS 2-function in \begin{document}$ 2n $\end{document} variables has a monomial \begin{document}$ x_1 x_q x_r x_s $\end{document} , then we use the notation \begin{document}$ {2-}(1,q,r,s)_{2n} $\end{document} for the function. A detailed theory of equivalence of quartic MRS 2-functions in \begin{document}$ 2n $\end{document} variables was given in a \begin{document}$ 2020 $\end{document} paper by Cusick, Cheon and Dougan. This theory divides naturally into two classes, called \begin{document}$ mf1 $\end{document} and \begin{document}$ mf2 $\end{document} in the paper. After describing the equivalence classes, the second major problem is giving details of the linear recursions that the Hamming weights for any sequence of functions \begin{document}$ {2-}(1,q,r,s)_{2n} $\end{document} (with \begin{document}$ q say), \begin{document}$ n = s, s+1, \ldots $\end{document} can be shown to satisfy. This problem was solved for the \begin{document}$ mf1 $\end{document} case only in the \begin{document}$ 2020 $\end{document} paper. Using new ideas about "short" functions, Cusick and Cheon found formulas for the \begin{document}$ mf2 $\end{document} weights in a \begin{document}$ 2021 $\end{document} sequel to the \begin{document}$ 2020 $\end{document} paper. In this paper the actual recursions for the weights in the \begin{document}$ mf2 $\end{document} case are determined.
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- 2023
19. General biconvex functions and bivariational inequalities
- Author
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Khalida Inayat Noor and Muhammad Aslam Noor
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Control and Optimization ,Algebra and Number Theory ,Operator (computer programming) ,Iterative method ,Applied Mathematics ,Convergence (routing) ,Variational inequality ,Banach space ,Applied mathematics ,Function (mathematics) ,Affine transformation ,Parallelogram ,Mathematics - Abstract
In this paper, we define and introduce some new concepts of the higher order strongly general biconvex functions involving the arbitrary bifunction and a function. Some new relationships among various concepts of higher order strongly general biconvex functions have been established. It is shown that the new parallelogram laws for Banach spaces can be obtained as applications of higher order strongly affine general biconvex functions, which is itself an novel application. It is proved that the optimality conditions of the higher order strongly general biconvex functions are characterized by a class of variational inequalities, which is called the higher order strongly general bivariational inequality. Auxiliary principle technique is used to suggest an implicit method for solving strongly general bivariational inequalities. Convergence analysis of the proposed method is investigated using the pseudo-monotonicity of the operator. Some special cases also discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results.
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- 2023
20. Some results on lightweight stream ciphers Fountain v1 & Lizard
- Author
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Dibyendu Roy, Ravi Anand, and Santanu Sarkar
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Discrete mathematics ,Algebra and Number Theory ,Selection (relational algebra) ,Computer Networks and Communications ,Applied Mathematics ,Initialization ,020206 networking & telecommunications ,Context (language use) ,Cube (algebra) ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Microbiology ,Cipher ,010201 computation theory & mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,Fountain ,Stream cipher ,Distinguishing attack ,Mathematics - Abstract
In this paper, we propose cryptanalytic results on two lightweight stream ciphers: Fountain v1 and Lizard. The main results of this paper are the followings: \begin{document}$ - $\end{document} We propose a zero-sum distinguisher on reduced round Fountain v1. In this context, we study the non-randomness of the cipher with a careful selection of cube variables. Our obtained cube provides a zero-sum on Fountain v1 till \begin{document}$ 188 $\end{document} initialization rounds and significant non-randomness till \begin{document}$ 189 $\end{document} rounds. This results in a distinguishing attack on Fountain v1 with \begin{document}$ 189 $\end{document} initialization rounds. \begin{document}$ - $\end{document} Further, we find that the same cipher has a weakness against conditional Time-Memory-Data-Tradeoff (TMDTO). We show that TMDTO attack using sampling resistance has online complexity \begin{document}$ 2^{110} $\end{document} and offline complexity \begin{document}$ 2^{146} $\end{document} . \begin{document}$ - $\end{document} Finally, we revisit the Time-Memory-Data-Tradeoff attack on Lizard by Maitra et al. (IEEE Transactions on Computers, 2018) and provide our observations on their work. We show that instead of choosing any random string, some particular strings would provide better results in their proposed attack technique.
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- 2023
21. A new construction of weightwise perfectly balanced Boolean functions
- Author
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Sihong Su and Rui Zhang
- Subjects
Discrete mathematics ,Class (set theory) ,Algebra and Number Theory ,Degree (graph theory) ,Computer Networks and Communications ,Computer Science::Information Retrieval ,Applied Mathematics ,020206 networking & telecommunications ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Microbiology ,Nonlinear system ,Integer ,010201 computation theory & mathematics ,Algebraic immunity ,Quartic function ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,Algebraic number ,Boolean function ,Mathematics - Abstract
In this paper, we first introduce a class of quartic Boolean functions. And then, the construction of weightwise perfectly balanced Boolean functions on \begin{document}$ 2^m $\end{document} variables are given by modifying the support of the quartic functions, where \begin{document}$ m $\end{document} is a positive integer. The algebraic degree, the weightwise nonlinearity, and the algebraic immunity of the newly constructed weightwise perfectly balanced functions are discussed at the end of this paper.
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- 2023
22. Application of Caputo–Fabrizio operator to suppress the Aedes Aegypti mosquitoes via Wolbachia: An LMI approach
- Author
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Jinde Cao, Jehad Alzabut, Ovidiu Bagdasar, Michal Niezabitowski, Ramachandran Raja, and J. Dianavinnarasi
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Numerical Analysis ,education.field_of_study ,General Computer Science ,Applied Mathematics ,Population ,Linear matrix inequality ,010103 numerical & computational mathematics ,02 engineering and technology ,01 natural sciences ,Theoretical Computer Science ,Fractional calculus ,Operator (computer programming) ,Exponential stability ,Modeling and Simulation ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Order operator ,020201 artificial intelligence & image processing ,Uniqueness ,0101 mathematics ,Logistic function ,education ,Mathematics - Abstract
The aim of this paper is to establish the stability results based on the approach of Linear Matrix Inequality (LMI) for the addressed mathematical model using Caputo–Fabrizio operator (CF operator). Firstly, we extend some existing results of Caputo fractional derivative in the literature to a new fractional order operator without using singular kernel which was introduced by Caputo and Fabrizio. Secondly, we have created a mathematical model to increase Cytoplasmic Incompatibility (CI) in Aedes Aegypti mosquitoes by releasing Wolbachia infected mosquitoes. By this, we can suppress the population density of A.Aegypti mosquitoes and can control most common mosquito-borne diseases such as Dengue, Zika fever, Chikungunya, Yellow fever and so on. Our main aim in this paper is to examine the behaviours of Caputo–Fabrizio operator over the logistic growth equation of a population system then, prove the existence and uniqueness of the solution for the considered mathematical model using CF operator. Also, we check the α -exponential stability results for the system via linear matrix inequality technique. Finally a numerical example is provided to check the behaviour of the CF operator on the population system by incorporating the real world data available in the known literature.
- Published
- 2022
23. New delay-dependent conditions for finite-time extended dissipativity based non-fragile feedback control for neural networks with mixed interval time-varying delays
- Author
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Thongchai Botmart, Wajaree Weera, Suphachai Charoensin, and Chantapish Zamart
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Numerical Analysis ,General Computer Science ,Artificial neural network ,Applied Mathematics ,Feedback control ,Multiple integral ,Stability (learning theory) ,Process (computing) ,Interval (mathematics) ,Theoretical Computer Science ,Control theory ,Modeling and Simulation ,Finite time ,MATLAB ,computer ,Mathematics ,computer.programming_language - Abstract
This paper studies the delay-dependent conditions for finite-time extended dissipativity based non-fragile feedback control for neural networks with mixed interval time-varying delays. By applying Jensen’s inequality, an extended Jensen’s double integral inequality, and a free matrix form inequality to the Lyapunov–Krasovskii functional (LKF), delay-dependent conditions are derived and solved by the Matlab control toolbox in terms of linear matrix inequalities (LMIs). By stability criteria, this paper is less conservative than the other works. In addition, we demonstrate the advantage of our obtained methods by five numerical examples. One practical example shows a real-world approach: the quadruple-tank process system (QTPS).
- Published
- 2022
24. The new soliton solutions for long and short-wave interaction system
- Author
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Mohammad Bagher Ghaemi, Javad Vahidi, Sayyed Masood Zekavatmand, Hadi Rezazadeh, and Mühendislik ve Doğa Bilimleri Fakültesi
- Subjects
Maple software ,Environmental Engineering ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Applied mathematics ,Ocean Engineering ,Extended Rational Sine-Cosine Method ,Soliton ,Type (model theory) ,Oceanography ,System of linear equations ,Extended Rational Sinh-Cosh Method ,Mathematics - Abstract
The goal of this paper is to discover modern soliton solutions to long and short-wave interaction system by procedures called extended rational sine-cosine and rational sinh-cosh methods. We assume that the equation has a hypothetical soliton solutions. By reorganizing the resulting equations, we obtain a system of equations. Using Maple software, we get unknown coefficients in the system and writing them in the original equation, we obtain new solition solutions of the equation. The results show that the soliton solutions generated by the method for the long and short-wave interaction system are bright, kink type, bright periodic and dark solutions. We provided 3-D figures to illustrate the solutions. Computational results indicate that the method employed in this paper is superior than some other methods used in the literature to solve the same system equations.
- Published
- 2022
25. Vertex partitioning problems on graphs with bounded tree width
- Author
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Subrahmanyam Kalyanasundaram, Anjeneya Swami Kare, and N. R. Aravind
- Subjects
Matching (graph theory) ,Applied Mathematics ,0211 other engineering and technologies ,Induced subgraph ,Parameterized complexity ,021107 urban & regional planning ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Vertex (geometry) ,Combinatorics ,Treewidth ,010201 computation theory & mathematics ,Bounded function ,Discrete Mathematics and Combinatorics ,Partition (number theory) ,Time complexity ,MathematicsofComputing_DISCRETEMATHEMATICS ,Mathematics - Abstract
In an undirected graph, a matching cut is a partition of vertices into two sets such that the edges across the sets induce a matching. The Matching Cut problem is the problem of deciding whether a given graph has a matching cut. Let H be a fixed undirected graph. A vertex coloring of an undirected input graph G is said to be an H - Free Coloring if none of the color classes contain H as an induced subgraph. The H - Free Chromatic Number of G is the minimum number of colors required for an H - Free Coloring of G . Both The Matching Cut problem and the H - Free Coloring problem can be expressed using a monadic second-order logic (MSOL) formula and hence is solvable in linear time for graphs with bounded tree-width. However, this approach leads to a running time of f ( | | φ | | , t ) n O ( 1 ) , where | | φ | | is the length of the MSOL formula, t is the tree-width of the graph and n is the number of vertices of the graph. The dependency of f ( | | φ | | , t ) on | | φ | | can be as bad as a tower of exponentials. In this paper, we provide explicit combinatorial FPT algorithms for Matching Cut problem and H - Free Coloring problem, parameterized by the tree-width of G . The single exponential FPT algorithm for the Matching Cut problem answers an open question posed by Kratsch and Le (2016). The techniques used in the paper are also used to provide an FPT algorithm for a variant of H -free coloring, where H is forbidden as a subgraph (not necessarily induced) in the color classes of G .
- Published
- 2022
26. Oriented diameter of star graphs
- Author
-
K. S. Ajish Kumar, K. S. Sudeep, and Deepak Rajendraprasad
- Subjects
FOS: Computer and information sciences ,Star network ,Discrete Mathematics (cs.DM) ,0211 other engineering and technologies ,0102 computer and information sciences ,02 engineering and technology ,Orientation (graph theory) ,Star (graph theory) ,05C20, 05C12 ,Network topology ,01 natural sciences ,Upper and lower bounds ,Prime (order theory) ,Combinatorics ,Permutation ,FOS: Mathematics ,Mathematics - Combinatorics ,Discrete Mathematics and Combinatorics ,Mathematics ,Applied Mathematics ,021107 urban & regional planning ,Computer Science - Distributed, Parallel, and Cluster Computing ,010201 computation theory & mathematics ,Distributed, Parallel, and Cluster Computing (cs.DC) ,Combinatorics (math.CO) ,Hypercube ,Computer Science - Discrete Mathematics - Abstract
An {\em orientation} of an undirected graph $G$ is an assignment of exactly one direction to each edge of $G$. Converting two-way traffic networks to one-way traffic networks and bidirectional communication networks to unidirectional communication networks are practical instances of graph orientations. In these contexts minimising the diameter of the resulting oriented graph is of prime interest. The $n$-star network topology was proposed as an alternative to the hypercube network topology for multiprocessor systems by Akers and Krishnamurthy [IEEE Trans. on Computers (1989)]. The $n$-star graph $S_n$ consists of $n!$ vertices, each labelled with a distinct permutation of $[n]$. Two vertices are adjacent if their labels differ exactly in the first and one other position. $S_n$ is an $(n-1)$-regular, vertex-transitive graph with diameter $\lfloor 3(n-1)/2 \rfloor$. Orientations of $S_n$, called unidirectional star graphs and distributed routing protocols over them were studied by Day and Tripathi [Information Processing Letters (1993)] and Fujita [The First International Symposium on Computing and Networking (CANDAR 2013)]. Fujita showed that the (directed) diameter of this unidirectional star graph $\overrightarrow{S_n}$ is at most $\lceil{5n/2}\rceil + 2$. In this paper, we propose a new distributed routing algorithm for the same $\overrightarrow{S_n}$ analysed by Fujita, which routes a packet from any node $s$ to any node $t$ at an undirected distance $d$ from $s$ using at most $\min\{4d+4, 2n+4\}$ hops. This shows that the (directed) diameter of $\overrightarrow{S_n}$ is at most $2n+4$. We also show that the diameter of $\overrightarrow{S_n}$ is at least $2n$ when $n \geq 7$, thereby showing that our upper bound is tight up to an additive factor., Full version of the paper to be presented in CALDAM 2020
- Published
- 2022
27. An Enhanced Input-Delay Approach to Sampled-Data Stabilization for Nonlinear Stochastic Singular Systems Based on T-S Fuzzy Models
- Author
-
Chunling Chang, Wei Xing Zheng, Shuangyun Xing, and Feiqi Deng
- Subjects
Basis (linear algebra) ,Applied Mathematics ,Fuzzy logic ,Weighting ,Nonlinear system ,Matrix (mathematics) ,Computational Theory and Mathematics ,Artificial Intelligence ,Control and Systems Engineering ,Piecewise ,Applied mathematics ,Convex combination ,Vector-valued function ,Mathematics - Abstract
The sampled-data stabilization problem of nonlinear stochastic singular systems on the basis of the Takagi-Sugeno (T-S) fuzzy models under variable samplings is discussed in this paper. A new piecewise Lyapunov-Krasovskii (L-K) functional is constructed, which can capture the actual sampling mode's available features more fully, and an enhanced input delay method is presented. By using the proper augmented scheme based on the auxiliary vector function, the new mean square admissibility criteria are derived by making good use of the convex combination techniques and the free weighting matrix approach. It is shown that the obtained results in this paper contain less conservatism when compared with the existing ones. The superiority and correctness of our results are verified by an application example of a truck-trailer model.
- Published
- 2022
28. Smoothness of Generalized Solutions of the Neumann Problem for a Strongly Elliptic Differential-Difference Equation on the Boundary of Adjacent Subdomains
- Author
-
D. A. Neverova
- Subjects
Statistics and Probability ,Smoothness (probability theory) ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Neumann boundary condition ,Boundary (topology) ,Differential difference equations ,General Medicine ,Mathematics - Abstract
This paper is devoted to the study of the qualitative properties of solutions to boundary-value problems for strongly elliptic differential-difference equations. Some results for these equations such as existence and smoothness of generalized solutions in certain subdomains of Q were obtained earlier. Nevertheless, the smoothness of generalized solutions of such problems can be violated near the boundary of these subdomains even for infinitely differentiable right-hand side. The subdomains are defined as connected components of the set that is obtained from the domain Q by throwing out all possible shifts of the boundary Q by vectors of a certain group generated by shifts occurring in the difference operators. For the one dimensional Neumann problem for differential-difference equations there were obtained conditions on the coefficients of difference operators, under which for any continuous right-hand side there is a classical solution of the problem that coincides with the generalized solution. 2 Also there was obtained the smoothness (in Sobolev spaces W k ) of generalized solutions of the second and the third boundary-value problems for strongly elliptic differential-difference equations in subdomains excluding -neighborhoods of certain points. However, the smoothness (in Ho lder spaces) of generalized solutions of the second boundary-value problem for strongly elliptic differential-difference equations on the boundary of adjacent subdomains was not considered. In this paper, we study this question in Ho lder spaces. We establish necessary and sufficient conditions for the coefficients of difference operators that guarantee smoothness of the generalized solution on the boundary of adjacent subdomains for any right-hand side from the Ho lder space.
- Published
- 2022
29. Maximum likelihood estimation and inference for high dimensional generalized factor models with application to factor-augmented regressions
- Author
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Fa Wang
- Subjects
Mixed model ,Economics and Econometrics ,Applied Mathematics ,Logit ,Asymptotic distribution ,Probability density function ,Poisson distribution ,Conditional expectation ,symbols.namesake ,Statistics ,symbols ,Limit (mathematics) ,Mathematics ,Factor analysis - Abstract
This paper reestablishes the main results in Bai (2003) and Bai and Ng (2006) for generalized factor models, with slightly stronger conditions on the relative magnitude of N (number of subjects) and T (number of time periods). Convergence rates of the estimated factor space and loading space and asymptotic normality of the estimated factors and loadings are established under mild conditions that allow for linear, Logit, Probit, Tobit, Poisson and some other single-index nonlinear models. The probability density/mass function is allowed to vary across subjects and time, thus mixed models are also allowed for. For factor-augmented regressions, this paper establishes the limit distributions of the parameter estimates, the conditional mean, and the forecast when factors estimated from nonlinear/mixed data are used as proxies for the true factors.
- Published
- 2022
30. Asymptotic properties of correlation-based principal component analysis
- Author
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Jungjun Choi and Xiye Yang
- Subjects
Economics and Econometrics ,Delta method ,Covariance matrix ,Applied Mathematics ,Principal component analysis ,Estimator ,Applied mathematics ,Variance (accounting) ,Covariance ,Eigenvalues and eigenvectors ,Statistical hypothesis testing ,Mathematics - Abstract
It is a common practice to conduct principal component analysis (PCA) using standardized data, which is equivalent to applying PCA to the correlation matrix rather than the covariance matrix. Yet little research has been done about such differences in the context of high frequency data. This paper bridges this gap. We derive the analytical forms of the asymptotic biases and variances for the estimators of the integrated eigenvalues and eigenvectors. Furthermore, we propose a novel jackknife-type estimator of the asymptotic variance of the integrated volatility functional estimator. This new variance estimator shows much better finite sample performances compared to other existing ones. This paper also proposes several statistical tests for some commonly tested hypotheses in the literature. Simulation results show that one will get misleading results if one uses the analytical results of the covariance case when applying PCA on the correlation matrix.
- Published
- 2022
31. On the analysis of Caputo fractional order dynamics of Middle East Lungs Coronavirus (MERS-CoV) model
- Author
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Salih Djilali, Naveed Anjum, Zareen A. Khan, Anwarud Din, Anwar Zeb, and Qura Tul Ain
- Subjects
Current (mathematics) ,UH stability ,General Engineering ,MERS-CoV model ,GABMM ,Numerical simulation ,Engineering (General). Civil engineering (General) ,medicine.disease_cause ,Existence and uniqueness ,Stability (probability) ,Article ,Operator (computer programming) ,medicine ,Applied mathematics ,Order (group theory) ,Uniqueness ,TA1-2040 ,Contraction principle ,Disease transmission ,Coronavirus ,Mathematics - Abstract
The current paper deals with the transmission of MERS-CoV model between the humans populace and the camels, which are suspected to be the primary source for the infection. The effect of time MERS-CoV disease transmission is explored using a non-linear fractional order in the sense of Caputo operator in this paper. The considered model is analyzed for the qualitative theory, uniqueness of the solution are discussed by using the Banach contraction principle. Stability analysis is investigated by the aid of Ulam-Hyres (UH) and its generalized version. Finally, we show the numerical results with the help of generalized Adams-Bashforth-Moulton Method (GABMM) are used for the proposed model, for supporting our analytical work.
- Published
- 2022
32. A variety of physical structures to the generalized equal-width equation derived from Wazwaz-Benjamin-Bona-Mahony model
- Author
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Marwan Alquran and Imad Jaradat
- Subjects
Nonlinear system ,Environmental Engineering ,Benjamin bona mahony ,Scheme (mathematics) ,Dispersion (optics) ,Applied mathematics ,Ocean Engineering ,Physical shape ,Variety (universal algebra) ,Oceanography ,Mathematics - Abstract
In this paper we are interested in investigating the physical shape-changed propagations to the generalized Equal-Width equation through studying the explicit solutions of Wazwaz-Benjamin-Bona-Mahony model. Both models are of considerable importance in many disciplines of research, including ocean engineering and science, and describe the propagation of equally-width waves. We highlight the effect of the coefficients of both nonlinearity and dispersion terms on changing the physical shape of both models by implementing the new exponential-expansion scheme. 2D and 3D graphical plots are provided to validate the findings of the paper.
- Published
- 2022
33. A Novel Extension of Best-Worst Method With Intuitionistic Fuzzy Reference Comparisons
- Author
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Shu-Ping Wan and Jiu-Ying Dong
- Subjects
Mathematical optimization ,Linear programming ,Applied Mathematics ,Decision problem ,Multiple-criteria decision analysis ,Fuzzy logic ,Computational Theory and Mathematics ,Artificial Intelligence ,Control and Systems Engineering ,Consistency (statistics) ,Weight ,Preference relation ,Preference (economics) ,Mathematics - Abstract
Best-worst method (BWM) has attracted increasing attention. It has been generalized to different fuzzy environments and applied to various real-life decision problems. This paper develops a new intuitionistic fuzzy (IF) best-worst method (IFBWM) for multi-criteria decision-making (MCDM). When a decision maker (DM) makes comparisons, there may be some hesitancies. Thus, the reference comparisons are represented as intuitionistic fuzzy values (IFVs), the Best-to-Others vector and the Others-to-Worst vector are IF vectors. According to the multiplicative consistency of intuitionistic fuzzy preference relation, this paper gives the consistency equations and views them as IF equations. The derivation of optimal IF weights of criteria is formulated as an IF decision-making problem. Thereby, a mathematical programming model is constructed to assure that the derived optimal IF weights of criteria is a normalized IF weight vector. Depending on the risk preference of DM, four linear programming models are presented to obtain the optimal IF weights based on the constructed mathematical programming model for the optimistic DM, the pessimistic DM and the neutral DM, respectively. Furthermore, this paper investigates the process of improving the consistency. Several examples are demonstrated to show the application and effectiveness of the proposed IF BWM.
- Published
- 2022
34. Virtual element approximation of two-dimensional parabolic variational inequalities
- Author
-
Sundararajan Natarajan, Dibyendu Adak, and Gianmarco Manzini
- Subjects
Polynomial ,Degrees of freedom (statistics) ,010103 numerical & computational mathematics ,01 natural sciences ,Upper and lower bounds ,Projection (linear algebra) ,010101 applied mathematics ,Computational Mathematics ,Quadratic equation ,Computational Theory and Mathematics ,Rate of convergence ,Modeling and Simulation ,Variational inequality ,Applied mathematics ,0101 mathematics ,Voronoi diagram ,Mathematics - Abstract
We design a virtual element method for the numerical treatment of the two-dimensional parabolic variational inequality problem on unstructured polygonal meshes. Due to the expected low regularity of the exact solution, the virtual element method is based on the lowest-order virtual element space that contains the subspace of the linear polynomials defined on each element. The connection between the nonnegativity of the virtual element functions and the nonnegativity of the degrees of freedom, i.e., the values at the mesh vertices, is established by applying the Maximum and Minimum Principle Theorem. The mass matrix is computed through an approximate L 2 polynomial projection, whose properties are carefully investigated in the paper. We prove the well-posedness of the resulting scheme in two different ways that reveal the contractive nature of the VEM and its connection with the minimization of quadratic functionals. The convergence analysis requires the existence of a nonnegative quasi-interpolation operator, whose construction is also discussed in the paper. The variational crime introduced by the virtual element setting produces five error terms that we control by estimating a suitable upper bound. Numerical experiments confirm the theoretical convergence rate for the refinement in space and time on three different mesh families including distorted squares, nonconvex elements, and Voronoi tesselations.
- Published
- 2022
35. The geometry of diagonal groups
- Author
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Peter J. Cameron, Cheryl E. Praeger, Csaba Schneider, R. A. Bailey, University of St Andrews. Pure Mathematics, University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra, and University of St Andrews. Statistics
- Subjects
Mathematics(all) ,South china ,Primitive permutation group ,General Mathematics ,Diagonal group ,T-NDAS ,Library science ,Group Theory (math.GR) ,O'Nan-Scott Theorem ,01 natural sciences ,Hospitality ,FOS: Mathematics ,NCAD ,Mathematics - Combinatorics ,QA Mathematics ,0101 mathematics ,Diagonal semilattice ,QA ,Cartesian lattice ,Mathematics ,business.industry ,20B05 ,Applied Mathematics ,010102 general mathematics ,Latin square ,Semilattice ,Latin cube ,010101 applied mathematics ,Hamming graph ,Research council ,Diagonal graph ,Combinatorics (math.CO) ,business ,Mathematics - Group Theory ,Partition - Abstract
Part of the work was done while the authors were visiting the South China University of Science and Technology (SUSTech), Shenzhen, in 2018, and we are grateful (in particular to Professor Cai Heng Li) for the hospitality that we received.The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Groups, representations and applications: new perspectives (supported by EPSRC grant no.EP/R014604/1), where further work on this paper was undertaken. In particular we acknowledge a Simons Fellowship (Cameron) and a Kirk Distinguished Visiting Fellowship (Praeger) during this programme. Schneider thanks the Centre for the Mathematics of Symmetry and Computation of The University of Western Australia and Australian Research Council Discovery Grant DP160102323 for hosting his visit in 2017 and acknowledges the support of the CNPq projects Produtividade em Pesquisa (project no.: 308212/2019-3) and Universal (project no.:421624/2018-3). Diagonal groups are one of the classes of finite primitive permutation groups occurring in the conclusion of the O'Nan-Scott theorem. Several of the other classes have been described as the automorphism groups of geometric or combinatorial structures such as affine spaces or Cartesian decompositions, but such structures for diagonal groups have not been studied in general. The main purpose of this paper is to describe and characterise such structures, which we call diagonal semilattices. Unlike the diagonal groups in the O'Nan-Scott theorem, which are defined over finite characteristically simple groups, our construction works over arbitrary groups, finite or infinite. A diagonal semilattice depends on a dimension m and a group T. For m=2, it is a Latin square, the Cayley table of T, though in fact any Latin square satisfies our combinatorial axioms. However, for m≥3, the group T emerges naturally and uniquely from the axioms. (The situation somewhat resembles projective geometry, where projective planes exist in great profusion but higher-dimensional structures are coordinatised by an algebraic object, a division ring.) A diagonal semilattice is contained in the partition lattice on a set Ω, and we provide an introduction to the calculus of partitions. Many of the concepts and constructions come from experimental design in statistics. We also determine when a diagonal group can be primitive, or quasiprimitive (these conditions turn out to be equivalent for diagonal groups). Associated with the diagonal semilattice is a graph, the diagonal graph, which has the same automorphism group as the diagonal semilattice except in four small cases with m
- Published
- 2022
36. Analytical approach for designing accelerated degradation tests under an exponential dispersion model
- Author
-
I-Chen Lee, Sheng-Tsaing Tseng, and Hung-Ping Tung
- Subjects
Statistics and Probability ,Optimal design ,Mathematical optimization ,Conjecture ,Applied Mathematics ,Path (graph theory) ,Direct proof ,Statistics, Probability and Uncertainty ,Equivalence (measure theory) ,Reliability (statistics) ,Task (project management) ,Exponential dispersion model ,Mathematics - Abstract
To provide timely lifetime information of manufactured products to potential customers, designing an efficient accelerated degradation test (ADT) is an important task for reliability analysts. In the literature, several papers have addressed a general k -level ADT design problem (including the determinations of the number of stress levels ( k ), testing stresses, allocation of test units and termination times) when the underlying degradation path follows an exponential dispersion model. The results are practical and interesting. However, most of those studies only addressed the case of k ≤ 4 . Generally, if a direct proof (such as using the Karush–Kuhn–Tucker conditions) for the case of k > 4 is intractable, we can consider an indirect proof via the general equivalence theorem. In this paper, we first propose a conjecture optimal design for a k -level ADT design problem and then apply the general equivalence theorem to show that this conjecture design turns out to be the global V-optimal design. In addition, an example is used to illustrate the proposed procedure. The main contribution of this work is that this analytical approach can provide reliability analysts with better insight for designing an efficient ADT plan.
- Published
- 2022
37. Variation and efficiency of high-frequency betas
- Author
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Viktor Todorov, George Tauchen, Jia Li, and Congshan Zhang
- Subjects
Economics and Econometrics ,Applied Mathematics ,05 social sciences ,Type test ,01 natural sciences ,010104 statistics & probability ,Fixed time ,0502 economics and business ,Adaptive estimator ,Jump ,Econometrics ,0101 mathematics ,Volatility (finance) ,050205 econometrics ,Mathematics - Abstract
This paper studies the efficient estimation of betas from high-frequency return data on a fixed time interval. Under an assumption of equal diffusive and jump betas, we derive the semiparametric efficiency bound for estimating the common beta and develop an adaptive estimator that attains the efficiency bound. We further propose a Hausman type test for deciding whether the common beta assumption is true from the high-frequency data. In our empirical analysis we provide examples of stocks and time periods for which a common market beta assumption appears true and ones for which this is not the case. We further quantify empirically the gains from the efficient common beta estimation developed in the paper.
- Published
- 2022
38. Stability Analysis of Semi-Markov Jump Stochastic Nonlinear Systems
- Author
-
Peng Shi, Xiaotai Wu, Yang Tang, Feng Qian, and Shuai Mao
- Subjects
Lyapunov function ,Exponential distribution ,Markov chain ,Stochastic process ,Stability (probability) ,Computer Science Applications ,Nonlinear system ,symbols.namesake ,Exponential stability ,Control and Systems Engineering ,Jump ,symbols ,Applied mathematics ,Electrical and Electronic Engineering ,Mathematics - Abstract
This paper is concerned with the problem of exponential stability for semi-Markov jump stochastic nonlinear systems. It is well known that the semi-Markov chain is an extension of the Markov chain, whose sojourn time distribution depends on the current and next state, and is no longer limited to the exponential distribution. However, in existing works, the independence and the distribution function limitation are imposed on the sojourn time of semi-Markov jump systems. In this paper, by developing a new stochastic analysis method, the problem of exponential stability is investigated for semi- Markov jump stochastic nonlinear systems without additional constraints for the sojourn time. In addition, mode-dependent linear comparable relationships are assumed among Lyapunov like functions, which can effectively reduce the conservatism caused by mode-independent case. Two examples are presented to demonstrate the effectiveness of the proposed results.
- Published
- 2022
39. Semistrictly and neatly quasiconvex programming using lower global subdifferentials
- Author
-
A. Kabgani and F. Lara
- Subjects
Control and Optimization ,Economics ,Applied Mathematics ,Business, Management and Accounting (miscellaneous) ,Management Science and Operations Research ,Mathematics ,Computer Science Applications - Abstract
The main goal of this paper is to investigate the properties and connections of neatly and semistrictly quasiconvex functions, especially when they appear in constrained and unconstrained optimization problems. The lower global subdifferential, recently introduced in the literature, plays an essential role in this study. We present several optimality conditions for constrained and unconstrained nonsmooth neatly/semistrictly quasiconvex optimization problems in terms of lower global subdifferentials. To this end, for a constrained optimization problem, we present some characterizations for the normal and tangent cones and the cone of feasible directions of the feasible set. Some relationships between the Greenberg-Pierskalla, tangentially and lower global subdifferentials of neatly and semistrictly quasiconvex functions are also given. The mentioned relationships show that the outcomes of this paper generalize some results existing in the literature.
- Published
- 2023
40. Estimating change-point latent factor models for high-dimensional time series
- Author
-
Ting Zhang and Xialu Liu
- Subjects
Statistics and Probability ,Noise ,Stationary process ,Rate of convergence ,Series (mathematics) ,Applied Mathematics ,Structural break ,Consistent estimator ,Applied mathematics ,Estimator ,Statistics, Probability and Uncertainty ,Mathematics ,Factor analysis - Abstract
We consider estimating a factor model for high-dimensional time series that contains structural breaks in the factor loading space at unknown time points. We first study the case when there is one change point in factor loadings, and propose a consistent estimator for the structural break location, whose convergence rate is shown to depend on an interplay between the dimension of the observed time series and the strength of the underlying factor structure. Our results reveal that the asymptotic behavior of the proposed estimator can be asymmetric in the sense that a larger estimation error can occur toward the regime with weaker factor strength. Based on the proposed estimator for the structural break location, we also consider the problem of estimating the factor loading spaces before and after the structural break. We show that the proposed estimators for change-point location and loading spaces are consistent when the numbers of factors are correctly estimated or overestimated. The algorithm for multiple change-point detection is also developed in the paper. Compared with existing results on change-point factor analyses of high-dimensional time series, a distinguished feature of the current paper is that the noise process is not necessarily assumed to be idiosyncratic and as a result we allow the noise process with potentially strong cross-sectional dependence. Another advantage for the proposed method is that it is specifically designed for the changes in the factor loading space and the stationarity assumption is not imposed on either the factor or noise process, while most existing methods for change-point detection of high-dimensional time series with/without a factor structure require the data to be stationary or ’close’ to a stationary process between two change points, which is rather restrictive. Numerical experiments including a Monte Carlo simulation and a real data application are presented to illustrate the proposed estimators perform well.
- Published
- 2022
41. Life cycle maintenance costs for a non-exponential component
- Author
-
Haim Livni
- Subjects
Set (abstract data type) ,Applied Mathematics ,Modeling and Simulation ,Spare part ,Monte Carlo method ,Applied mathematics ,Dot product ,Function (mathematics) ,Turnaround time ,Weibull distribution ,Mathematics ,Exponential function - Abstract
The paper presents a method for determining maintenance and spare provisioning costs, for systems containing a non exponential component. The input data of the model are R ( t ) - the reliability function with time of the component, T the duration of the life cycle, cost of a repair, cost of a spare part and the turnaround time. The model is applicable for any form of R ( t ) : Weibull, Normal, expressed by an explicit or implicit set of equations and even in the form of discrete frequency table. The calculations can be performed by a simple Excel worksheet and do not require expensive tools (e.g. a flexible Monte Carlo package): The algorithm requires a few iterations of the dot product of two matrices. The entries of the matrices are calculated from the input values and the results of previous iterations, at M equidistant time points along the life cycle. M determines the accuracy of the calculations. The paper indicates sufficient conditions for M , which ensure a desired accuracy. Numerical examples performed on an Excel worksheet are presented. Since the model is applicable for any R ( t ) , it was applied, for verification purposes for R ( t ) = e − λ t , which has well known accurate results. The comparison confirmed the accuracy of the approximations.
- Published
- 2022
42. Hopf bifurcation and global exponential stability of an epidemiological smoking model with time delay
- Author
-
Zizhen Zhang, Aying Wan, Xiaomei Hu, and A. Pratap
- Subjects
Hopf bifurcation ,medicine.medical_specialty ,Correctness ,Public health ,General Engineering ,Stability (learning theory) ,Engineering (General). Civil engineering (General) ,respiratory tract diseases ,Smoking model ,symbols.namesake ,Exponential stability ,Global exponential stability ,Epidemiology ,behavior and behavior mechanisms ,symbols ,medicine ,Applied mathematics ,TA1-2040 ,Time delay ,Mathematics - Abstract
There are many harmful effects of smoking. It not only engulfs the health and life of smokers, but also pollutes the air, endangers the life and health of others, and brings a heavy burden to public health. To this end, a delayed smoking model including potential smokers, occasional smokers, smokers, temporary quitters, permanent quitters and smokers with some illness, is investigated in the present paper. Firstly, local stability and existence of Hopf bifurcation of the model is conducted. Secondly, global exponential stability is explored. Lastly, we numerically simulate the correctness of the obtained theoretical results in the paper.
- Published
- 2022
43. A New Power Flow Model With a Single Nonconvex Quadratic Constraint: The LMI Approach
- Author
-
Mohammad Reza Hesamzadeh, Roozbeh Abolpour, and Maryam Dehghani
- Subjects
Constraint (information theory) ,Power flow ,Quadratic equation ,Nonlinear matrix inequality ,Computer Science::Systems and Control ,Bilinear matrix inequality ,Mathematics::Optimization and Control ,Linear matrix inequality ,Energy Engineering and Power Technology ,Applied mathematics ,Network size ,Electrical and Electronic Engineering ,Mathematics - Abstract
In this paper, we propose a new mathematical model for power flow problem based on the linear and nonlinear matrix inequality theory. We start with rectangular model of power flow (PF) problem and then reformulate it as a Bilinear Matrix Inequality (BMI) model. A Theorem is proved which is able to convert this BMI model to a Linear Matrix Inequality (LMI) model along with One Nonconvex Quadratic Constraint (ONQC). Our proposed LMI-ONQC model for PF problem has only one single nonconvex quadratic constraint irrespective of the network size, while in the rectangular and BMI models the number of nonconvex constraints grows as the network size grows. This interesting property leads to reduced complexity level in our LMI-ONQC model. The non-conservativeness, iterative LMI solvability, well-defined and easy-to-understand geometry, and pathwise connectivity of feasibility region are other important properties of proposed LMI-ONQC model which are discussed in this paper. An illustrative two-bus example is carefully studied to show different properties of our LMI-ONQC model. We have also tested our LMI-ONQC model on 30 different power-system cases. The numerical results show the promising performance of our LMI-ONQC model and its solution algorithm to find a PF solution.
- Published
- 2022
44. Commutative, Engel and Solvable EQ-Algebras
- Author
-
Akbar Paad
- Subjects
Human-Computer Interaction ,Computational Mathematics ,Pure mathematics ,Computational Theory and Mathematics ,Applied Mathematics ,Commutative property ,Physics::Geophysics ,Computer Science Applications ,Mathematics - Abstract
The main goal of this paper is to introduce commutative, Engel and solvable EQ-algebras. To begin with, the notion of commutators of two elements in EQ-algebras is introduced and several properties of them are obtained. In this paper, the notions of commutative, Engel and solvable EQ-algebras are introduced and some of their properties are investigated. Specially, it is proved that any good EQ-algebra is a 2-Engel EQ-algebra. In addition, the relation between fantastic filters and good commutative EQ-algebras is investigated and it is proved that a filter [Formula: see text] of good EQ-algebra [Formula: see text] is fantastic if and only if the quotient EQ-algebra [Formula: see text] is commutative. Finally, it is proved that if an EQ-algebra separated, then it is a commutative EQ-algebra if and only if it is solvable if and only if it is a 1-Engel EQ-algebra.
- Published
- 2022
45. Survival functions versus conditional aggregation-based survival functions on discrete space
- Author
-
Borzová Jana, Halčinová Lenka, and Basarik Stanislav
- Subjects
Mathematical theory ,Information Systems and Management ,Survival function ,Artificial Intelligence ,Control and Systems Engineering ,Discrete space ,Applied mathematics ,State (functional analysis) ,Characterization (mathematics) ,Software ,Computer Science Applications ,Theoretical Computer Science ,Mathematics - Abstract
In this paper we deal with conditional aggregation-based survival functions recently introduced by Boczek et al. (2020). The concept is worth to study because of its possible implementation in real-life situations and mathematical theory as well. The aim of this paper is the comparison of this new notion with the standard survival function. We state sufficient and necessary conditions under which the generalized and the standard survival function equal. The main result is the characterization of the family of conditional aggregation operators (on discrete space) for which these functions coincide.
- Published
- 2022
46. Rough L-fuzzy sets: Their representation and related structures
- Author
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Sándor Radeleczki and Dávid Gégény
- Subjects
Pure mathematics ,Representation theorem ,Mathematics::General Mathematics ,Applied Mathematics ,Fuzzy set ,Theoretical Computer Science ,Connection (mathematics) ,Set (abstract data type) ,Lattice (module) ,Artificial Intelligence ,Rough set ,Representation (mathematics) ,Software ,Mathematics - Abstract
The combination of fuzzy set theory and rough set theory has been discussed in a lot of research papers over the years. In this paper, we examine one such combination, namely the notion of rough L-fuzzy sets. We provide a representation theorem that determines when a pair of L-fuzzy sets is a rough L-fuzzy set, and we establish a connection between the lattice of rough fuzzy sets and the lattice of rough relations. Furthermore, we investigate the properties of the lattice of rough L-fuzzy sets and characterize the case when a three-valued Łukasiewicz-algebra can be defined on it.
- Published
- 2022
47. Exact LMI Conditions for Stability and $\mathcal {L}_2$ Gain Analysis of 2-D Mixed Continuous–Discrete Time Systems via Quadratically Frequency-Dependent Lyapunov Functions
- Author
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Graziano Chesi
- Subjects
Lyapunov function ,Quadratic growth ,Generalization ,Linear matrix inequality ,Stability (probability) ,Upper and lower bounds ,Computer Science Applications ,symbols.namesake ,Discrete time and continuous time ,Control and Systems Engineering ,Structural stability ,symbols ,Applied mathematics ,Electrical and Electronic Engineering ,Mathematics - Abstract
This paper addresses the problems of establishing structural stability and the L2 gain of 2D mixed continuous-discrete-time systems. The first contribution is to show that Lyapunov functions quadratically dependent on the frequency are exact for establishing structural stability. This is particularly important since the existing works that exploit Lyapunov functions provide a much larger upper bound on the dependence on the frequency or other parameters. The second contribution is to propose a novel linear matrix inequality (LMI) necessary and sufficient condition for establishing the existence of such Lyapunov functions. It is shown, analytically and through several examples, for both best and worst cases, that the numerical complexity of this novel condition is much smaller than that of the existing methods. The third contribution is to show that the proposed methodology can be used to establish upper bounds on the L2 gain, in particular, deriving a novel necessary and sufficient LMI condition based on Lyapunov functions quadratically dependent on the frequency. Lastly, the paper presents the generalization of the proposed methodology to non-mixed 2D systems.
- Published
- 2022
48. Exact confidence limits compatible with the result of a sequential trial
- Author
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Chris Lloyd
- Subjects
Statistics and Probability ,Discrete mathematics ,Acceptance sampling ,Applied Mathematics ,Sample (material) ,Sample space ,Test statistic ,Inference ,Limit (mathematics) ,Statistics, Probability and Uncertainty ,Confidence interval ,Mathematics ,Type I and type II errors - Abstract
Sequential (or adaptive) designs are common in acceptance sampling and pharmaceutical trials. This is because they can achieve the same type 1 and type 2 error rate with fewer subjects on average than fixed sample trials. After the trial is completed and the test result decided, we need full inference on the main parameter Δ . In this paper, we are interested in exact one-sided lower and upper limits. Unlike standard trials, for sequential trials there need not be an explicit test statistic, nor even p -value. This motivates the more general approach of defining an ordering on the sample space and using the construction of Buehler (1957). This is guaranteed to produce exact limits, however, there is no guarantee that the limits will agree with the test. For instance, we might reject Δ ≤ Δ 0 at level α but have a lower 1 − α limit being less then Δ 0 . This paper gives a very simple condition to ensure that this unfortunate feature does not occur. When the condition fails, the ordering is easily modified to ensure compatibility.
- Published
- 2022
49. On the geometry of irreversible metric-measure spaces: Convergence, stability and analytic aspects
- Author
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Wei Zhao and Alexandru Kristály
- Subjects
Pure mathematics ,Class (set theory) ,Applied Mathematics ,General Mathematics ,Stability (learning theory) ,Function (mathematics) ,Stability result ,Measure (mathematics) ,Metric (mathematics) ,Convergence (routing) ,Mathematics::Metric Geometry ,Mathematics::Differential Geometry ,Topology (chemistry) ,Mathematics - Abstract
The paper is devoted to the study of Gromov-Hausdorff convergence and stability of irreversible metric-measure spaces, both in the compact and noncompact cases. While the compact setting is mostly similar to the reversible case developed by J. Lott, K.-T. Sturm and C. Villani, the noncompact case provides various surprising phenomena. Since the reversibility of noncompact irreversible spaces might be infinite, it is motivated to introduce a suitable nondecreasing function that bounds the reversibility of larger and larger balls. By this approach, we are able to prove satisfactory convergence/stability results in a suitable – reversibility depending – Gromov-Hausdorff topology. A wide class of irreversible spaces is provided by Finsler manifolds, which serve to construct various model examples by pointing out genuine differences between the reversible and irreversible settings. We conclude the paper by proving various geometric and functional inequalities (as Brunn-Minkowski, Bishop-Gromov, log-Sobolev and Lichnerowicz inequalities) on irreversible structures.
- Published
- 2022
50. Some iterative approaches for Sylvester tensor equations, Part I: A tensor format of truncated Loose Simpler GMRES
- Author
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Farid Saberi-Movahed, Lakhdar Elbouyahyaoui, Mohammed Heyouni, and Azita Tajaddini
- Subjects
Computational Mathematics ,Numerical Analysis ,Applied Mathematics ,Convergence (routing) ,Applied mathematics ,Acceleration (differential geometry) ,Krylov subspace ,Tensor ,Residual ,Orthogonalization ,Generalized minimal residual method ,Connection (mathematics) ,Mathematics - Abstract
In recent years, Krylov subspace methods based on the tensor format have demonstrated their superiority over classical ones for handling various kinds of tensor equations. In this paper, according to the efficient computational cost of the classical Simpler GMRES method (SGMRES), we adopt the tensor format of this method, which is called SGMRES−BTF, for solving the Sylvester tensor equations. This paper is divided into two parts describing the tensor format of two types of acceleration approaches to tackle some serious problems of the restarted methods GMRES−BTF and SGMRES−BTF, such as the “stalling” and “alternating phenomenon”. In the first part of this two-part work, the truncated Loose Simpler GMRES based on the tensor format (LSGMRES−BTF) is introduced, which is an acceleration approach that aims to construct an augmented tensor Krylov subspace by means of approximation error tensors. Moreover, a detailed study is carried out on the connection between the values of sequential and skip angles and the convergence behavior of both SGMRES−BTF and truncated LSGMRES−BTF. In the second part of this paper, an acceleration approach based on the idea of inner-outer iteration in the truncated version of the generalized conjugate residual with inner orthogonalization (GCRO) method is developed. In this method, SGMRES−BTF is applied in the inner iteration, and the generalized conjugate residual based on the tensor format (GCR−BTF) method is used in the outer iteration. Numerical experiments show that SGMRES−BTF achieves an appropriate performance compared with GMRES−BTF. In addition, the numerical results reveal the high potential of the presented accelerating strategies to deal with Sylvester tensor equations.
- Published
- 2022
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