INTERTWINED BASINS OF ATTRACTION

2012 ◽  
Vol 22 (06) ◽  
pp. 1250130
Author(s):  
CHANGMING DING

This paper deals with intertwined basins of attraction for dynamical systems in a metric space. After giving a general definition of intertwining property, which is preserved by a topological equivalence between dynamical systems, we present a sufficient condition to guarantee the existence of intertwined basins for dynamical systems in ℝn.

2009 ◽  
Vol 19 (07) ◽  
pp. 2377-2381 ◽  
Author(s):  
CHANGMING DING

In this paper, we investigate the intertwined basins of attraction. Using a general definition, we discuss the local intertwining properties and present an easy condition to guarantee the existence of intertwined basins for planar dynamical systems.


2013 ◽  
Vol 23 (12) ◽  
pp. 1350197 ◽  
Author(s):  
ZERAOULIA ELHADJ ◽  
J. C. SPROTT

In this letter, we will show the existence of invariant sets called universal basins of attraction for typical nonlinear high-dimensional dynamical systems such as randomly sampled high-dimensional vector fields (ODEs) or maps. The method of analysis is based on the definition of an equivalence class between systems with the same number of neurons, the same number of time lags, and the same upper bound for one family of bifurcation parameters.


2016 ◽  
Vol 14 (1) ◽  
pp. 1122-1124 ◽  
Author(s):  
Ricardo Almeida ◽  
Małgorzata Guzowska ◽  
Tatiana Odzijewicz

AbstractIn this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.


2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 1633.2-1634
Author(s):  
F. Cosan ◽  
O. M. Gedar

Background:Reactive arthritis (ReA) is defined by 1999 ACR criteria as arthritis preceding a bacterial genitourinary (GUS) or gastrointestinal (GIS) infection in 3 days-6 weeks and evidence of triggering infection. Recently, ReA is classified as SpA and patients who do not fulfill SpA criteria are classified as undifferentiated spondyloarthritis (USpA) according to ASAS/EULAR SpA classification criteria.Objectives:In several case reports which are associated with other infective agents are reported and the definition is extended for some clinicians so that SpA which is occurred after any infection is called as ReA. On the other hand, some researchers still accept the classical definition of ReA. The problem with the heterogeneity of opinions and unstandardized definition of ReA hinders studies about pathogenesis and standardization of treatments. In this study, we aimed to determine the spectrum of the use of the definition of reactive arthritis in publications in PubMed between 2009-2019.Methods:The ReA keyword is searched in PubMed for the years between 2009-2019. 248 different publications have been identified and included in this research. 89 articles, 47 reviews, 108 case reports, 2 guidelines, and 2 editorials reviewed for the definition of ReA.Results:Only 42.7% (106 patients) of these publications meet the classical definition which suggests ReA after only GIS and GUS infections. In 4 (1.6%) of the publications ReA was defined after GIS, GUS and oropharyngeal infections; in 3 (1,2%) of the publications after any bacterial infection; in 9 (3.6%) of the publications after any infection. In 8 (3.2%) of the publications, ReA and USPA was used correspondingly. In 39 (15,7%) of the publications the term agent related, ReA was used without making a general definition for ReA. 79 publications (31,9%) have not defined ReA.According to causative agent and ReA relationship, in 64 (24,6%) general infective agents, in 75 (30,2%) classical agents, in 22 (8,9%) other bacterial agents, in 23 (9,3%) streptococcus, in 10(4%) intravesical BCG, in 6 (2.4%) HIV, in 6 (2.4%) tuberculosis, in 12 (4,8%) clostrudium difficle, in 2 (0.8%) parasites were reported. In 31 (12,5%) of the publications the causative agent for the ReA was unknown, the diagnosis was made clinically.Conclusion:In this study, it is aimed to draw attention terminology intricacy and the need for the standardization of the definition of ReA and USpA. It is clear that to standardize the definition of Rea and USpA is necessary. Between 2009-2019 there are reported cases diagnosed as ReA associated with bacterial infections (especially with Clostridium difficile, streptococcus and tuberculosis infections), and viral infections (by a majority with HIV), and parasitic infections. It is not clear if we need to define them classically or define them as USPA. Another important consideration is the necessity of extended laboratory investigations to find out the real causative agent even if the patient is clinically diagnosed with ReA. The requirement of the differentiation between ReA and USpA must be revealed for therapeutic researches.References:[1]A proposal for the classification of patients for clinical and experimental studies on reactive arthritis. Pacheco-Tena C, Burgos-Vargas R, Vázquez-Mellado J, Cazarín J, Pérez-Díaz JA. J Rheumatol. 1999 Jun;26(6):1338-46.[2]The Assessment of SpondyloArthritis International Society classification criteria for peripheral spondyloarthritis and for spondyloarthritis in general. Rudwaleit M, van der Heijde D, Landewé R, Akkoc N, Brandt J, Chou CT, Dougados M, Huang F, Gu J, Kirazli Y, et al. Ann Rheum Dis. 2011;70:25–31.Disclosure of Interests:None declared


Author(s):  
M. Ferrara ◽  
M. Trombetti

AbstractLet G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice $$\mathcal {L}(H)$$ L ( H ) embeds in $$\mathcal {L}(G)$$ L ( G ) . It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity.


Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 32
Author(s):  
Pragati Gautam ◽  
Luis Manuel Sánchez Ruiz ◽  
Swapnil Verma

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result.


2020 ◽  
pp. 1-23
Author(s):  
TUYEN TRUNG TRUONG

Abstract A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By the Hahn–Banach theorem, a positive strong submeasure is the supremum of a non-empty collection of measures whose masses are uniformly bounded from above. There are many natural examples of continuous maps of the form $f:U\rightarrow X$ , where X is a compact metric space and $U\subset X$ is an open-dense subset, where f cannot extend to a reasonable function on X. We can mention cases such as transcendental maps of $\mathbb {C}$ , meromorphic maps on compact complex varieties, or continuous self-maps $f:U\rightarrow U$ of a dense open subset $U\subset X$ where X is a compact metric space. For the aforementioned mentioned the use of measures is not sufficient to establish the basic properties of ergodic theory, such as the existence of invariant measures or a reasonable definition of measure-theoretic entropy and topological entropy. In this paper we show that strong submeasures can be used to completely resolve the issue and establish these basic properties. In another paper we apply strong submeasures to the intersection of positive closed $(1,1)$ currents on compact Kähler manifolds.


2021 ◽  
Author(s):  
Andrea Marin ◽  
Carla Piazza ◽  
Sabina Rossi

AbstractIn this paper, we deal with the lumpability approach to cope with the state space explosion problem inherent to the computation of the stationary performance indices of large stochastic models. The lumpability method is based on a state aggregation technique and applies to Markov chains exhibiting some structural regularity. Moreover, it allows one to efficiently compute the exact values of the stationary performance indices when the model is actually lumpable. The notion of quasi-lumpability is based on the idea that a Markov chain can be altered by relatively small perturbations of the transition rates in such a way that the new resulting Markov chain is lumpable. In this case, only upper and lower bounds on the performance indices can be derived. Here, we introduce a novel notion of quasi-lumpability, named proportional lumpability, which extends the original definition of lumpability but, differently from the general definition of quasi-lumpability, it allows one to derive exact stationary performance indices for the original process. We then introduce the notion of proportional bisimilarity for the terms of the performance process algebra PEPA. Proportional bisimilarity induces a proportional lumpability on the underlying continuous-time Markov chains. Finally, we prove some compositionality results and show the applicability of our theory through examples.


2002 ◽  
Vol 27 (1) ◽  
pp. 42-55 ◽  
Author(s):  
Brian R. Macintosh ◽  
Dilson E. Rassier

Fatigue and potentiation are two forms of force modulation. A general definition of fatigue is "a circumstance where less than the anticipated contractile response is obtained." Fatigue is associated with depressed Ca2+ release and possibly decreased Ca2+ sensitivity. Potentiation results from increased Ca2+ sensitivity due to regulatory light chain phosphorylation. Muscle fatigue and potentiation can coexist, making it difficult to quantify these processes. With repetitive 10 Hz stimulation, the developed tension first increases, then decreases. Is fatigue present when developed tension first begins to decrease or when it falls below the developed tension of the first response? Intermittent incompletely fused tetanic contractions for which peak developed tension first decreases, then increases, is another unusual example of fatigue. A third example is when twitch contractions following a tetanic contraction decrease to a level below the pretetanic twitch amplitude, indicating that fatigue may have been coexistent with posttetanic potentiation. These observations illustrate the complexity of detecting fatigue, based on the simple, but commonly accepted definition presented above. Care must be taken in interpreting "before vs. after" contractile responses. Even when the contraction amplitude is greater than the initial response, there is no guarantee that mechanisms associated with fatigue are not present. Key words: calcium sensitivity, staircase, posttetanic potentiation, myosin light chains, skeletal muscle


2004 ◽  
Vol 2004 (05) ◽  
pp. 043-043 ◽  
Author(s):  
T Harmark ◽  
N.A Obers

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