Information Flow in Chaotic Symbolic Dynamics for Finite and Infinitesimal Resolution

1997 ◽  
Vol 07 (01) ◽  
pp. 97-105 ◽  
Author(s):  
Gustavo Deco ◽  
Christian Schittenkopf ◽  
Bernd Schürmann
Keyword(s):  
Mutual Information ◽  
Information Flow ◽  
Symbolic Dynamics ◽  
Initial Conditions ◽  
Deterministic Chaos ◽  
Conditional Entropy ◽  
Information Loss ◽  
Statistical Correlations ◽  
The Future ◽  
One Step

We introduce an information-theory-based concept for the characterization of the information flow in chaotic systems in the framework of symbolic dynamics for finite and infinitesimal measurement resolutions. The information flow characterizes the loss of information about the initial conditions, i.e. the decay of statistical correlations (i.e. nonlinear and non-Gaussian) between the entire past and a point p steps into the future as a function of p. In the case where the partition generating the symbolic dynamics is finite, the information loss is measured by the mutual information that measures the statistical correlations between the entire past and a point p steps into the future. When the partition used is a generator and only one step ahead is observed (p = 1), our definition includes the Kolmogorov–Sinai entropy concept. The profiles in p of the mutual information describe the short- and long-range forecasting possibilities for the given partition resolution. For chaos it is more relevant to study the information loss for the case of infinitesimal partitions which characterizes the intrinsic behavior of the dynamics on an extremely fine scale. Due to the divergence of the mutual information for infinitesimal partitions, the "intrinsic" information flow is characterized by the conditional entropy which generalizes the Kolmogorov–Sinai entropy for the case of observing the uncertainty more than one step into the future. The intrinsic information flow offers an instrument for characterizing deterministic chaos by the transmission of information from the past to the future.

MULTIFRACTAL DESCRIPTION OF THE STATISTICAL EQUILIBRIUM OF CHAOTIC DYNAMICAL SYSTEMS

1989 ◽  
Vol 03 (06) ◽  
pp. 821-852 ◽  
Author(s):  
JOSEPH L. McCAULEY
Keyword(s):  
Information Flow ◽  
Symbolic Dynamics ◽  
Chaotic Maps ◽  
Thermodynamic Formalism ◽  
Deterministic Chaos ◽  
Statistical Equilibrium ◽  
Coarse Grained ◽  
Matrix Formulation ◽  
Liapunov Exponents ◽  
Time Average

In this review, we apply the method of backward iteration to chaotic maps of the interval to illustrate how both the f(α) spectrum and its underlying statistical mechanics follow directly from the dynamics in statistical equilibrium. The sizes of intervals in the coarse-grained phase space are expressed directly in terms of finite-time average Liapunov exponents, representing the reverse of the information flow that is the underlying cause of deterministic chaos. The transfer matrix formulation follows directly from the method of backward iteration when addresses generated from symbolic dynamics are assigned to tree-branches. The inverse temperature is interpreted in terms of classes of initial data of the dynamical system. Finally, the usefulness of the thermodynamic formalism is illustrated by showing how the pore distribution of sandstone can be modeled by a certain two-scale Cantor set on an octal tree.

Август и Агриппа: развитие системы соправления с 29 по 18 г. до н. э.

2017 ◽  
pp. 126-169
Author(s):  
S.E. Tariverdieva
Keyword(s):  
Political Life ◽  
The Political ◽  
State Administration ◽  
Inheritance System ◽  
The Future ◽  
One Step ◽  
Formal Equality ◽  
Different Parts

The article deals with the development of the coregency system of Augustus and Agrippa from 29 to 18 BC: from formal and actual disparity of the coregents to their formal equality with the dominance of the princeps auctoritas. Particular attention is paid to the earlier stages of this development and to the crisis of 23 BC. The coregency system created by Augustus is often regarded by modern historians as means of ensuring uninterrupted succession of power. Agrippa as his coregent often is thought to have assumed the role of the regent who temporally replaces the princeps, just as it was in formal monarchies, or that of the tutor of the future rulers. However, the Roman system of state administration did not allow such type of regency. The princeps coregent, who was his equal in formal credentials but his inferior in terms of auctoritas, in case of the princeps death had to become the next princeps as his immediate successor. It is unlikely that later he was expected to voluntarily give up his power in favour of younger heir and to vanish from the political life altogether. The inheritance system under Augustus was like a ladder with the princeps at the top, the coregent who was also the immediate successor one step below, heirs of the next degree further down. In case of death of one of them, successors shifted one step up. The coregency had one more function: geographically it allowed Augustus and Agrippa to rule jointly the empire while staying in different parts of it.В статье исследуется развитие системы соправления Августа и Агриппы с 29 по 12 гг. до н. э.: от формального и фактического неравенства соправителей до их формального равенства при преобладании auctoritas принцепса, причём особое внимание уделяется раннему этапу этого развития и кризису 23 г. до н. э. Институт соправления, созданный Августом, часто рассматривается, как средство обеспечения бесперебойного перехода власти, причем Агриппе, как соправителю, НЕРЕДКО отводится роль регента, временно замещающего принцепса или воспитателя будущих правителей. Однако римская система государственного управления не предполагала регентства. Соправитель принцепса, равный ему по формальным полномочиям, но уступавший по auctoritas, в случае его смерти должен был СТАТЬ следующим принцепсом, ближайшим его наследником. Вряд ли предполагалось, что в будущем он должен добровольно уступить власть более молодому наследнику и исчезнуть из политической жизни. Система наследования при Августе представляла собой нечто вроде лестницы, на вершине которой стоял принцепс, на следующей ступени соправитель, он же избранный преемник, ниже наследники следующей очереди в случае смерти когото из них происходило продвижение наследников по ступеням вверх. Кроме того, соправление имело и иное значение позволяло Августу и Агриппе совместно управлять империей, находясь в разных ее частях.

scholarly journals Mindful energy and information flow: A reflective account of S.E.L.F connection during COVID-19

2020 ◽  
pp. 147332502097330
Author(s):  
James J Lucas
Keyword(s):  
Social Work ◽  
Social Workers ◽  
Information Flow ◽  
Work Practice ◽  
Social Work Practice ◽  
The Future ◽  
Sanctuary Model ◽  
Reflective Essay ◽  
Energy Information ◽  
Practice Education

Life during the COVID-19 pandemic is uncertain, intense, and traumatic. At the same time, there is room for hope, inspiration, and meaning for social workers through mindfully connecting with energy-information flow as it influences our Safety, Emotions, Loss, and Future – S.E.L.F. As adapted from the Sanctuary Model®, this S.E.L.F connection is an opportunity to discover within ourselves our unwavering core that is grounded, present, and connected and sustain an ethical and compassionate approach to social work practice, education, and research during this time of pandemic. The aim in this reflective essay is to provide an example of S.E.L.F. connection from the perspective of a Buddhist and social work academic at an Australian university during the COVID-19 pandemic. While beneficial, ongoing S.E.L.F. connections are necessary for social workers if we are to stay mindful of energy-information flow and steer this flow towards the creation of a story of relationship, compassion, and connection into the future.

One step forward, two steps back: women in the post-communist states

2001 ◽  
Vol 34 (2) ◽  
pp. 203-220 ◽  
Author(s):  
Suzanne LaFont
Keyword(s):  
Gender Gap ◽  
Gender Discrimination ◽  
Social Economic ◽  
Political Representation ◽  
Women's Organizations ◽  
Political Dynamics ◽  
The Future ◽  
One Step ◽  
Communist Countries ◽  
Status Of Women

The role and status of women in the post-communist countries has been and continues to be varied and full of contradictions. This article discusses the historical, social, economic, and political dynamics affecting the lives of women during the transition from communism to democracy. It argues that democracy, rather than diminishing gender discrimination, has widened the gender gap through declines in women's political representation and increases in women's unemployment and underemployment. Recently, however, the proliferation of women's organizations and the growth of women's studies programs suggests a more optimistic outlook for the future.

Applying a storyline approach to explore the impact of future Atmospheric River induced floods in western Norway 

2021 ◽  
Author(s):  
Trine Jahr Hegdahl ◽  
Kolbjørn Engeland ◽  
Malte Müller ◽  
Jana Sillman
Keyword(s):  
Extreme Precipitation ◽  
Initial Conditions ◽  
Future Climate ◽  
Meteorological Forcing ◽  
Extreme Precipitation Events ◽  
Western Norway ◽  
Current Climate ◽  
The Future ◽  
Climate Events ◽  
Precipitation Events

<p>Atmospheric rivers (AR) are responsible for the most extreme precipitation events causing devastating landslides and floods in western Norway. In this study an event-based storyline approach is used to compare the flood impact of extreme AR events in a warmer climate to those of the current climate.  The four most extreme precipitation events were selected from 30 years of present and future climate simulations from the high-resolution global climate model, the EC-Earth model. For each of the four events, EC-Earth was rerun creating 10 perturbed realizations. A regional convective permitting weather prediction model, AROME-MetCoOp, was used to further downscale the events, and thereafter the operational Norwegian flood-forecasting model was used to estimate the flood levels for 37 catchments in western Norway. The magnitude and the spatial impact were analyzed, and different hydrological initial conditions, which affect the total flooding, were analyzed.</p><p>The results show that more catchments were affected with larger floods in the future climate events compared to the current climate events. In addition, the combination of multiple realizations of meteorological forcing and different hydrological initial conditions, for example soil saturation and snow storage, were important for the estimation of the maximum flood level. The meteorological forcing had the highest overall effect on flood magnitude; however, varying and depending on event and catchment. Finally, operational flood warning levels were used to visualize the difference between future and current climate flood events. Applying a setup similar to the one used operationally and relating the future events to known current events associated with ARs, enables a common reference and ease communication with end-users and decision makers.</p>

Boundedness and Other Theories for Complex Systems

2013 ◽  
pp. 108-125
Keyword(s):  
Initial Conditions ◽  
Traditional Approach ◽  
Deterministic Chaos ◽  
Mathematical Object ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Universal Properties ◽  
The One ◽  
Global Invariant ◽  
Sensitivity To Initial Conditions

A comparison between the concept of boundedness on the one hand, and the theory of self-organized criticality (SOC) and the deterministic chaos on the other hand, is made. The focus is put on the methodological importance of the general frame through which an enormous class of empirical observations is viewed. The major difference between the concept of boundedness and the theory of self organized criticality is that under boundedness, the response comprises both specific and universal part, and thus a system has well defined “identity,” while SOC assumes response as a global invariant which has only universal properties. Unlike the deterministic chaos, the boundedness is free to explain the sensitivity to initial conditions independently from the mathematical object that generates them. Alongside, it turns out that the traditional approach to the deterministic chaos has its ample understanding under the concept of boundedness.

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