2,260 research outputs found
Analysis of Daily Streamflow Complexity by Kolmogorov Measures and Lyapunov Exponent
Analysis of daily streamflow variability in space and time is important for
water resources planning, development, and management. The natural variability
of streamflow is being complicated by anthropogenic influences and climate
change, which may introduce additional complexity into the phenomenological
records. To address this question for daily discharge data recorded during the
period 1989-2016 at twelve gauging stations on Brazos River in Texas (USA), we
use a set of novel quantitative tools: Kolmogorov complexity (KC) with its
derivative associated measures to assess complexity, and Lyapunov time (LT) to
assess predictability. We find that all daily discharge series exhibit long
memory with an increasing downflow tendency, while the randomness of the series
at individual sites cannot be definitively concluded. All Kolmogorov complexity
measures have relatively small values with the exception of the USGS (United
States Geological Survey) 08088610 station at Graford, Texas, which exhibits
the highest values of these complexity measures. This finding may be attributed
to the elevated effect of human activities at Graford, and proportionally
lesser effect at other stations. In addition, complexity tends to decrease
downflow, meaning that larger catchments are generally less influenced by
anthropogenic activity. The correction on randomness of Lyapunov time
(quantifying predictability) is found to be inversely proportional to the
Kolmogorov complexity, which strengthens our conclusion regarding the effect of
anthropogenic activities, considering that KC and LT are distinct measures,
based on rather different techniques
Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation?
The difficulty of explaining non-local correlations in a fixed causal
structure sheds new light on the old debate on whether space and time are to be
seen as fundamental. Refraining from assuming space-time as given a priori has
a number of consequences. First, the usual definitions of randomness depend on
a causal structure and turn meaningless. So motivated, we propose an intrinsic,
physically motivated measure for the randomness of a string of bits: its length
minus its normalized work value, a quantity we closely relate to its Kolmogorov
complexity (the length of the shortest program making a universal Turing
machine output this string). We test this alternative concept of randomness for
the example of non-local correlations, and we end up with a reasoning that
leads to similar conclusions as in, but is conceptually more direct than, the
probabilistic view since only the outcomes of measurements that can actually
all be carried out together are put into relation to each other. In the same
context-free spirit, we connect the logical reversibility of an evolution to
the second law of thermodynamics and the arrow of time. Refining this, we end
up with a speculation on the emergence of a space-time structure on bit strings
in terms of data-compressibility relations. Finally, we show that logical
consistency, by which we replace the abandoned causality, it strictly weaker a
constraint than the latter in the multi-party case.Comment: 17 pages, 16 figures, small correction
From Knowledge, Knowability and the Search for Objective Randomness to a New Vision of Complexity
Herein we consider various concepts of entropy as measures of the complexity
of phenomena and in so doing encounter a fundamental problem in physics that
affects how we understand the nature of reality. In essence the difficulty has
to do with our understanding of randomness, irreversibility and
unpredictability using physical theory, and these in turn undermine our
certainty regarding what we can and what we cannot know about complex phenomena
in general. The sources of complexity examined herein appear to be channels for
the amplification of naturally occurring randomness in the physical world. Our
analysis suggests that when the conditions for the renormalization group apply,
this spontaneous randomness, which is not a reflection of our limited
knowledge, but a genuine property of nature, does not realize the conventional
thermodynamic state, and a new condition, intermediate between the dynamic and
the thermodynamic state, emerges. We argue that with this vision of complexity,
life, which with ordinary statistical mechanics seems to be foreign to physics,
becomes a natural consequence of dynamical processes.Comment: Phylosophica
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