By Terry Bossomaier, Lionel Barnett, Michael Harré, Joseph T. Lizier
This publication considers a comparatively new metric in complicated platforms, move entropy, derived from a sequence of measurements, often a time sequence. After a qualitative advent and a bankruptcy that explains the main principles from data required to appreciate the textual content, the authors then current details idea and move entropy intensive. A key function of the procedure is the authors' paintings to teach the connection among details circulate and complexity. The later chapters display details move in canonical structures, and purposes, for instance in neuroscience and in finance.
The e-book can be of price to complex undergraduate and graduate scholars and researchers within the components of laptop technological know-how, neuroscience, physics, and engineering.
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Additional resources for An Introduction to Transfer Entropy: Information Flow in Complex Systems
Sample text
2. For a, b, ω ∈ Ω , we define an event as a subset of the sample space xi = {ω | a ≤ x(ω) ≤ b} = {a ≤ x ≤ b}, and we define a probability p just as we did before: p({ω ∈ Ω : x(ω) ∈ xi }) ∈ [0, 1]. 25) a where p(x) for continuous x is the probability density function (PDF)2 at x. Analogous to axioms 1 and 2 in Sect. 26) and p(x) ≥ 0 in analogy to axiom 3 in Sect. 2. 2 The attentive reader will notice that we use PDF as an abbreviation for both probability distribution function and probability density function; one can decipher which it refers to by whether the argument is discrete or continuous.
Back in the 19th century, Rudolf Clausius came up with the term in thermodynamics. Nearly a century later, Claude Shannon introduced the idea for communications and his new ideas of information theory, now fundamental to all things computational [304]. He reputedly selected this name following a suggestion from computer pioneer John von Neumann; according to Tribus [327]: The same function appears in statistical mechanics and, on the advice of John von Neumann, Claude Shannon called it ‘entropy’.
An ) and an approximation to p(a1 , . . , an ) given by ∏k p(ak |Ak ), where Ak ∩ ak = 0/ and Ak is a single-element set. Fig. 5 Time-Series Data and Embedding Dimensions A time series is a temporally indexed sequence of data points or events; the index is usually denoted by t and can be either be a continuous parameter: t ∈ IR; or a discrete parameter: t ∈ {0, 1, 2, 3, . }. So in general, if there is a sequence of temporally ordered random events, we denote the random variable xti ∈ {xt1 , xt2 , xt3 , .