The Ellis semigroup of certain constant-length substitutions

2019 ◽  
pp. 1-26
Author(s):  
PETRA STAYNOVA
Keyword(s):  
Dynamical Systems ◽  
Constant Length ◽  
Almost Automorphic ◽  
Recurrent Sequences ◽  
Alternative Approach ◽  
Binary Case ◽  
The One ◽  
Ellis Semigroup ◽  
Cluster Points

In this article, we calculate the Ellis semigroup of a certain class of constant-length substitutions. This generalizes a result of Haddad and Johnson [IP cluster points, idempotents, and recurrent sequences. Topology Proc.22 (1997) 213–226] from the binary case to substitutions over arbitrarily large finite alphabets. Moreover, we provide a class of counterexamples to one of the propositions in their paper, which is central to the proof of their main theorem. We give an alternative approach to their result, which centers on the properties of the Ellis semigroup. To do this, we also show a new way to construct an almost automorphic–isometric tower to the maximal equicontinuous factor of these systems, which gives a more particular approach than the one given by Dekking [The spectrum of dynamical systems arising from substitutions of constant length. Z. Wahrscheinlichkeitstheor. Verw. Geb.41(3) (1977/78) 221–239].

scholarly journals Quotienting the delay monad by weak bisimilarity

2017 ◽  
Vol 29 (1) ◽  
pp. 67-92 ◽  
Author(s):  
JAMES CHAPMAN ◽  
TARMO UUSTALU ◽  
NICCOLÒ VELTRI
Keyword(s):  
Computer Science ◽  
Equivalence Relation ◽  
Type Theory ◽  
Partial Functions ◽  
Homotopy Type Theory ◽  
Inductive Type ◽  
Alternative Approach ◽  
The One ◽  
Axiom Of Countable Choice

The delay datatype was introduced by Capretta (Logical Methods in Computer Science, 1(2), article 1, 2005) as a means to deal with partial functions (as in computability theory) in Martin-Löf type theory. The delay datatype is a monad. It is often desirable to consider two delayed computations equal, if they terminate with equal values, whenever one of them terminates. The equivalence relation underlying this identification is called weak bisimilarity. In type theory, one commonly replaces quotients with setoids. In this approach, the delay datatype quotiented by weak bisimilarity is still a monad–a constructive alternative to the maybe monad. In this paper, we consider the alternative approach of Hofmann (Extensional Constructs in Intensional Type Theory, Springer, London, 1997) of extending type theory with inductive-like quotient types. In this setting, it is difficult to define the intended monad multiplication for the quotiented datatype. We give a solution where we postulate some principles, crucially proposition extensionality and the (semi-classical) axiom of countable choice. With the aid of these principles, we also prove that the quotiented delay datatype delivers free ω-complete pointed partial orders (ωcppos).Altenkirch et al. (Lecture Notes in Computer Science, vol. 10203, Springer, Heidelberg, 534–549, 2017) demonstrated that, in homotopy type theory, a certain higher inductive–inductive type is the free ωcppo on a type X essentially by definition; this allowed them to obtain a monad of free ωcppos without recourse to a choice principle. We notice that, by a similar construction, a simpler ordinary higher inductive type gives the free countably complete join semilattice on the unit type 1. This type suffices for constructing a monad, which is isomorphic to the one of Altenkirch et al. We have fully formalized our results in the Agda dependently typed programming language.

scholarly journals Stability analysis and controller synthesis for hybrid dynamical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4937-4960 ◽  
Author(s):  
W. P. M. H. Heemels ◽  
B. De Schutter ◽  
J. Lunze ◽  
M. Lazar
Keyword(s):  
Dynamical Systems ◽  
Mathematical Models ◽  
Hybrid Systems ◽  
Discrete Event ◽  
Research Area ◽  
Hybrid Dynamical Systems ◽  
Technological Systems ◽  
Analysis And Synthesis ◽  
Control Community ◽  
The One

Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.

scholarly journals Gdy Europa choruje, Rosja nie jest lekarstwem

2020 ◽  
Vol 72 (4) ◽  
pp. 41-57
Author(s):  
Marek Menkiszak
Keyword(s):  
The Other ◽  
The European Union ◽  
European Policy ◽  
Fake News ◽  
Alternative Approach ◽  
The Face ◽  
The One ◽  
New Situation ◽  
The Voice ◽  
Ambiguous Position

In the face of a new serious crisis in Europe caused by the coronavirus pandemic, Russia has taken an ambiguous position. On the one hand, it was spreading fake news and, on the other hand, it was providing Italy with symbolic support. Russia’s immediate goal was to persuade the European Union (EU) to reduce or lift sanctions. The new situation provides a new argument to those participants of the European debate who are in favour of normalisation and even reset of relations with Russia. Among them, the voice of France is particularly clear since its President Emanuel Macron has taken up the initiative to build the ‘architecture of trust and security’ with Russia. These proposals, which are now quite vague, are based on questionable  assumptions and deepen divisions in Europe and the crisis in transatlantic relations. By rising Moscow’s hopes for some form of (geo)political bargain, they in fact encourage Russia to continue its aggressive policy towards its European neighbours. An alternative approach based on several principles is needed in the debate on EU policy towards Russia: developing all five Mogherini’s points; maintaining sanctions against Russia until the reasons for their introduction cease to exist; symmetry of commitments and benefits related to limited cooperation with Russia; inviolability of key interests, security and sovereignty of EU and NATO member and partner states; and balancing the dialogue with the Russian authorities by supporting Russian civil society. Europe can survive without Russia but Russia cannot survive without Europe, which is why European policy needs consistency and strategic patience.

Mathematical Entities without Objects. On Realism in Mathematics and a Possible Mathematization of (Non)Platonism: Does Platonism Dissolve in Mathematics?

2020 ◽  
pp. 1-21
Author(s):  
Thierry Paul
Keyword(s):  
Dynamical Systems ◽  
Real World ◽  
Ground Level ◽  
Ground Floor ◽  
Mathematical Platonism ◽  
Levels Of Reality ◽  
Upper Level ◽  
The One

By looking at three significant examples in analysis, geometry and dynamical systems, I propose the possibility of having two levels of realism in mathematics: the upper one, the one of entities; and a subordinated ground one, the one of objects. The upper level (entities) is more the one of ‘operations’, of mathematics in action, of the dynamics of mathematics, whereas the ground floor (objects) is more dedicated to culturally well-defined objects inherited from our perception of the physical or real world. I will show that the upper level is wider than the ground level, therefore foregrounding the possibility of having in mathematics entities without underlying objects. In the three examples treated in this article, this splitting of levels of reality is created directly by the willingness to preserve different symmetries, which take the form of identities or equivalences. Finally, it is proposed that mathematical Platonism is – in fine – a true branch of mathematics in order for mathematicians to avoid the temptation of falling into the Platonist alternative ‘everything is real’/‘nothing is real’.

scholarly journals A Dynamical Systems Approach to Nonlinear Stellar Pulsations

1993 ◽  
Vol 134 ◽  
pp. 9-31
Author(s):  
J. R. Buchler
Keyword(s):  
Dynamical Systems ◽  
Ad Hoc ◽  
Systems Approach ◽  
Chaotic Behavior ◽  
Theoretical Explanation ◽  
Modal Interactions ◽  
Reduction Techniques ◽  
Numerical Hydrodynamics ◽  
Stellar Pulsations ◽  
The One

AbstractOver the last decade we have seen the application of novel techniques to the old problem of nonlinear stellar pulsations. Together with numerical hydrodynamics this approach provides a more fundamental understanding of the systematics of the pulsational behavior. For weakly nonadiabatic pulsations, whether regular or multi-periodic, dimensional reduction techniques lead to amplitude equations and to a description in terms of modal interactions and resonances. In particular they shed new light on the bump progression in the classical Cepheids. In more dissipative stars numerical hydrodynamical modelling has uncovered the existence of irregular variability, both in radiative and in convective models. An application of modern dynamical systems techniques has shown that this behavior occurs according to well understood routes from regular to chaotic behavior. The mechanism is very robust and represents the first non ad hoc theoretical explanation of irregular stellar variability. Finally, we discuss how a comparison with observations of irregular variability shows the need for more suitable observations, on the one hand, and of better techniques of signal processing, on the other.

scholarly journals Family Farming and The Emergence of an Alternative Sociotechnical Imaginary in Argentina

2020 ◽  
Vol 25 (1) ◽  
pp. 86-105
Author(s):  
Frédéric Goulet
Keyword(s):  
Agricultural Sector ◽  
Political Action ◽  
Science And Technology ◽  
Family Farming ◽  
Alternative Approach ◽  
Counter Model ◽  
Science And Politics ◽  
Security Challenge ◽  
Underlying Mechanisms ◽  
The One

In this article, we analyse the mechanisms by which family farming established itself in Argentina over the 2004–2016 period as a legitimate solution to the food security challenge. We show that this process has played a role in the emergence of an alternative sociotechnical imaginary built as a counter-model to the one associated with industrial agriculture. We highlight the importance of the processes of demarcation and detachment at the heart of this shift, in the political, techno-scientific and agricultural spheres. The actors involved in the promotion of family farming associate this alternative approach to the development of the agricultural sector with the implementation of an alternative practice and organisation of science and technology. These shifts correspond to a narrative and mode of political action that put the emphasis on the production of a national future liberated from the mistakes and injustices of the past, in which science and technology play a central role. By highlighting the tensions at the heart of this dynamic, between the establishment of new boundaries and the challenging of existing ones, the article contributes to the analysis of the formation of alternative sociotechnical imaginaries, and in particular the underlying mechanisms of co-production between science and politics.

scholarly journals Micronutrients in support to the one carbon cycle for the modulation of blood fasting homocysteine in PCOS women

2019 ◽  
Vol 43 (6) ◽  
pp. 779-786 ◽  
Author(s):  
N. Schiuma ◽  
A. Costantino ◽  
T. Bartolotti ◽  
M. Dattilo ◽  
V. Bini ◽  
...  
Keyword(s):  
Carbon Cycle ◽  
Normal Limit ◽  
Control Group ◽  
Pharmacological Treatments ◽  
Open Label ◽  
Parallel Group ◽  
Alternative Approach ◽  
The Mean ◽  
The One

Abstract Purpose Fasting blood homocysteine is increased in PCOS women and is involved in several of its co-morbidities including cardiovascular disease and infertility. Corrective interventions based on the administration of supra-physiologic doses of folic acid work to a low extent. We aimed to test an alternative approach. Methods This was a prospective, randomized, parallel group, open label, controlled versus no treatment clinical study. PCOS women aged > 18, free from systemic diseases and from pharmacological treatments were randomized with a 2:1 ratio for treatment with activated micronutrients in support to the carbon cycle (Impryl, Parthenogen, Switzerland—n = 22) or no treatment (n = 10) and followed-up for 3 months. Fasting blood homocysteine, AMH, testosterone, SHBGs, and the resulting FTI were tested before and at the end of the follow-up. Results The mean baseline fasting blood homocysteine was above the normal limit of 12 μMol/L and inversely correlated with SHBG. AMH was also increased, whereas testosterone, SHBG, and FTI were within the normal limit. The treatment achieved a significant reduction of homocysteine, that did not change in the control group, independently of the starting value. The treatment also caused an increase of AMH and a decrease of SHBGs only in the subgroup with a normal homocysteine at baseline. Conclusions In PCOS ladies, blood homocysteine is increased and inversely correlated with the SHBGs. Physiologic amounts of activated micronutrients in support to the carbon cycle achieve a reduction virtually in all exposed patients. Whether this is of clinical benefit remains to be established.

scholarly journals DIFFERENTIAL GEOMETRY AND MECHANICS: APPLICATIONS TO CHAOTIC DYNAMICAL SYSTEMS

2006 ◽  
Vol 16 (04) ◽  
pp. 887-910 ◽  
Author(s):  
JEAN-MARC GINOUX ◽  
BRUNO ROSSETTO
Keyword(s):  
Differential Geometry ◽  
Dynamical Systems ◽  
Slow Manifold ◽  
Van Der Pol ◽  
New Approach ◽  
Metric Properties ◽  
Chaotic Dynamical Systems ◽  
Mechanics Concepts ◽  
The One ◽  
Curvature And Torsion

The aim of this article is to highlight the interest to apply Differential Geometry and Mechanics concepts to chaotic dynamical systems study. Thus, the local metric properties of curvature and torsion will directly provide the analytical expression of the slow manifold equation of slow-fast autonomous dynamical systems starting from kinematics variables (velocity, acceleration and over-acceleration or jerk). The attractivity of the slow manifold will be characterized thanks to a criterion proposed by Henri Poincaré. Moreover, the specific use of acceleration will make it possible on the one hand to define slow and fast domains of the phase space and on the other hand, to provide an analytical equation of the slow manifold towards which all the trajectories converge. The attractive slow manifold constitutes a part of these dynamical systems attractor. So, in order to propose a description of the geometrical structure of attractor, a new manifold called singular manifold will be introduced. Various applications of this new approach to the models of Van der Pol, cubic-Chua, Lorenz, and Volterra–Gause are proposed.

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