Kairos, Chronos and Chaos

2003 ◽  
Vol 36 (2) ◽  
pp. 202-217 ◽  
Author(s):  
Jeff Roberts
Keyword(s):  
Group Analysis ◽  
Space Time ◽  
Ancient Greek ◽  
Time And Space ◽  
The Matrix ◽  
Nature Of Time ◽  
Self Organizing

This paper explores the ancient Greek quasi-mystical concepts of Chronos and then Kairos, particularly in relation to group analysis and individual analytic psychotherapy. It concludes with some thoughts on the nature of time and space and introduces Chaos, a third Greek concept, with a consideration of the chaotic patterns of movement in space-time which are, it seems, self-organizing and have led to the emergence from the matrix of space-time of matter, life and ultimately mind.

Day-ahead Load Probabilistic Forecasting Based on Space-time Correction

2020 ◽  
Vol 13 ◽  
Author(s):  
Fei Jin ◽  
Xiaoliang Liu ◽  
Fangfang Xing ◽  
Guoqiang Wen ◽  
Shuangkun Wang ◽  
...  
Keyword(s):  
Short Term Memory ◽  
Northern China ◽  
Space Time ◽  
Load Prediction ◽  
Probabilistic Forecasting ◽  
Residual Distribution ◽  
Time And Space ◽  
Probability Prediction ◽  
Time Correction ◽  
Interval Coverage

Background : The day-ahead load forecasting is an essential guideline for power generating, and it is of considerable significance in power dispatch. Objective: Most of the existing load probability prediction methods use historical data to predict a single area, and rarely use the correlation of load time and space to improve the accuracy of load prediction. Methods: This paper presents a method for day-ahead load probability prediction based on space-time correction. Firstly, the kernel density estimation (KDE) is employed to model the prediction error of the long short-term memory (LSTM) model, and the residual distribution is obtained. Then the correlation value is used to modify the time and space dimensions of the test set's partial period prediction values. Results: The experiment selected three years of load data in 10 areas of a city in northern China. The MAPE of the two modified models on their respective test sets can be reduced by an average of 10.2% and 6.1% compared to previous results. The interval coverage of the probability prediction can be increased by an average of 4.2% and 1.8% than before. Conclusion: The test results show that the proposed correction schemes are feasible.

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

1. On Scale in Space, Time, and Space–Time

2016 ◽  
pp. 1-10
Author(s):  
Keith C. Clarke ◽  
Ian J. Irmischer
Keyword(s):  
Space Time ◽  
Time And Space

scholarly journals Matrix Neuro-Fuzzy Self-Organizing Clustering Network

2011 ◽  
Vol 45 (1) ◽  
pp. 54-58 ◽  
Author(s):  
Yevgeniy Bodyanskiy ◽  
Valentyna Volkova ◽  
Mark Skuratov
Keyword(s):  
Fuzzy Inference ◽  
Data Sets ◽  
Fuzzy Membership Functions ◽  
Neuro Fuzzy ◽  
The Matrix ◽  
On Line ◽  
Winner Take All ◽  
Overlapping Classes ◽  
Self Learning ◽  
Self Organizing

Matrix Neuro-Fuzzy Self-Organizing Clustering NetworkIn this article the problem of clustering massive data sets, which are represented in the matrix form, is considered. The article represents the 2-D self-organizing Kohonen map and its self-learning algorithms based on the winner-take-all (WTA) and winner-take-more (WTM) rules with Gaussian and Epanechnikov functions as the fuzzy membership functions, and without the winner. The fuzzy inference for processing data with overlapping classes in a neural network is introduced. It allows one to estimate membership levels for every sample to every class. This network is the generalization of a vector neuro- and neuro-fuzzy Kohonen network and allows for data processing as they are fed in the on-line mode.

scholarly journals Visualising higher-dimensional space-time and space-scale objects as projections to ℝ3

2017 ◽  
Vol 3 ◽  
pp. e123 ◽  
Author(s):  
Ken Arroyo Ohori ◽  
Hugo Ledoux ◽  
Jantien Stoter
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Three Dimensions ◽  
Time And Space ◽  
3D Objects ◽  
Levels Of Detail ◽  
Higher Dimensional Space Time ◽  
Space Scale ◽  
Higher Dimensional ◽  
Dimensional Space Time

Objects of more than three dimensions can be used to model geographic phenomena that occur in space, time and scale. For instance, a single 4D object can be used to represent the changes in a 3D object’s shape across time or all its optimal representations at various levels of detail. In this paper, we look at how such higher-dimensional space-time and space-scale objects can be visualised as projections from ℝ4to ℝ3. We present three projections that we believe are particularly intuitive for this purpose: (i) a simple ‘long axis’ projection that puts 3D objects side by side; (ii) the well-known orthographic and perspective projections; and (iii) a projection to a 3-sphere (S3) followed by a stereographic projection to ℝ3, which results in an inwards-outwards fourth axis. Our focus is in using these projections from ℝ4to ℝ3, but they are formulated from ℝnto ℝn−1so as to be easily extensible and to incorporate other non-spatial characteristics. We present a prototype interactive visualiser that applies these projections from 4D to 3D in real-time using the programmable pipeline and compute shaders of the Metal graphics API.

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