50,833 research outputs found
List Approximation for Increasing Kolmogorov Complexity
It is impossible to effectively modify a string in order to increase its Kolmogorov complexity. But is it possible to construct a few strings, not longer than the input string, so that most of them have larger complexity? We show that the answer is yes. We present an algorithm that on input a string x of length n returns a list with O(n^2) many strings, all of length n, such that 99% of them are more complex than x, provided the complexity of x is less than n. We obtain similar results for other parameters, including a polynomial-time construction
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
Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow
We investigate the dynamics of the two-dimensional periodic Kolmogorov flow
of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct
numerical simulations. Above a critical Weissenberg number the flow displays a
transition from stationary to randomly fluctuating states, via periodic ones.
The increasing complexity of the flow in both time and space at progressively
higher values of elasticity accompanies the establishment of mixing features.
The peculiar dynamical behavior observed in the simulations is found to be
related to the appearance of filamental propagating patterns, which develop
even in the limit of very small inertial non-linearities, thanks to the
feedback of elastic forces on the flow.Comment: 10 pages, 14 figure
Correlation of Automorphism Group Size and Topological Properties with Program-size Complexity Evaluations of Graphs and Complex Networks
We show that numerical approximations of Kolmogorov complexity (K) applied to
graph adjacency matrices capture some group-theoretic and topological
properties of graphs and empirical networks ranging from metabolic to social
networks. That K and the size of the group of automorphisms of a graph are
correlated opens up interesting connections to problems in computational
geometry, and thus connects several measures and concepts from complexity
science. We show that approximations of K characterise synthetic and natural
networks by their generating mechanisms, assigning lower algorithmic randomness
to complex network models (Watts-Strogatz and Barabasi-Albert networks) and
high Kolmogorov complexity to (random) Erdos-Renyi graphs. We derive these
results via two different Kolmogorov complexity approximation methods applied
to the adjacency matrices of the graphs and networks. The methods used are the
traditional lossless compression approach to Kolmogorov complexity, and a
normalised version of a Block Decomposition Method (BDM) measure, based on
algorithmic probability theory.Comment: 15 2-column pages, 20 figures. Forthcoming in Physica A: Statistical
Mechanics and its Application
Computing by nowhere increasing complexity
A cellular automaton is presented whose governing rule is that the Kolmogorov
complexity of a cell's neighborhood may not increase when the cell's present
value is substituted for its future value. Using an approximation of this
two-dimensional Kolmogorov complexity the underlying automaton is shown to be
capable of simulating logic circuits. It is also shown to capture trianry logic
described by a quandle, a non-associative algebraic structure. A similar
automaton whose rule permits at times the increase of a cell's neighborhood
complexity is shown to produce animated entities which can be used as
information carriers akin to gliders in Conway's game of life
Approximations of Algorithmic and Structural Complexity Validate Cognitive-behavioural Experimental Results
We apply methods for estimating the algorithmic complexity of sequences to
behavioural sequences of three landmark studies of animal behavior each of
increasing sophistication, including foraging communication by ants, flight
patterns of fruit flies, and tactical deception and competition strategies in
rodents. In each case, we demonstrate that approximations of Logical Depth and
Kolmogorv-Chaitin complexity capture and validate previously reported results,
in contrast to other measures such as Shannon Entropy, compression or ad hoc.
Our method is practically useful when dealing with short sequences, such as
those often encountered in cognitive-behavioural research. Our analysis
supports and reveals non-random behavior (LD and K complexity) in flies even in
the absence of external stimuli, and confirms the "stochastic" behaviour of
transgenic rats when faced that they cannot defeat by counter prediction. The
method constitutes a formal approach for testing hypotheses about the
mechanisms underlying animal behaviour.Comment: 28 pages, 7 figures and 2 table
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