1,148 research outputs found
Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability
Previously referred to as `miraculous' in the scientific literature because
of its powerful properties and its wide application as optimal solution to the
problem of induction/inference, (approximations to) Algorithmic Probability
(AP) and the associated Universal Distribution are (or should be) of the
greatest importance in science. Here we investigate the emergence, the rates of
emergence and convergence, and the Coding-theorem like behaviour of AP in
Turing-subuniversal models of computation. We investigate empirical
distributions of computing models in the Chomsky hierarchy. We introduce
measures of algorithmic probability and algorithmic complexity based upon
resource-bounded computation, in contrast to previously thoroughly investigated
distributions produced from the output distribution of Turing machines. This
approach allows for numerical approximations to algorithmic
(Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a
computational hierarchy. We demonstrate that all these estimations are
correlated in rank and that they converge both in rank and values as a function
of computational power, despite fundamental differences between computational
models. In the context of natural processes that operate below the Turing
universal level because of finite resources and physical degradation, the
investigation of natural biases stemming from algorithmic rules may shed light
on the distribution of outcomes. We show that up to 60\% of the
simplicity/complexity bias in distributions produced even by the weakest of the
computational models can be accounted for by Algorithmic Probability in its
approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity
calculator: http://complexitycalculator.com
Training-free Measures Based on Algorithmic Probability Identify High Nucleosome Occupancy in DNA Sequences
We introduce and study a set of training-free methods of
information-theoretic and algorithmic complexity nature applied to DNA
sequences to identify their potential capabilities to determine nucleosomal
binding sites. We test our measures on well-studied genomic sequences of
different sizes drawn from different sources. The measures reveal the known in
vivo versus in vitro predictive discrepancies and uncover their potential to
pinpoint (high) nucleosome occupancy. We explore different possible signals
within and beyond the nucleosome length and find that complexity indices are
informative of nucleosome occupancy. We compare against the gold standard
(Kaplan model) and find similar and complementary results with the main
difference that our sequence complexity approach. For example, for high
occupancy, complexity-based scores outperform the Kaplan model for predicting
binding representing a significant advancement in predicting the highest
nucleosome occupancy following a training-free approach.Comment: 8 pages main text (4 figures), 12 total with Supplementary (1 figure
Emergence and algorithmic information dynamics of systems and observers
Previous work has shown that perturbation analysis in software space can
produce candidate computable generative models and uncover possible causal
properties from the finite description of an object or system quantifying the
algorithmic contribution of each of its elements relative to the whole. One of
the challenges for defining emergence is that one observer's prior knowledge
may cause a phenomenon to present itself to such observer as emergent while for
another as reducible. When attempting to quantify emergence, we demonstrate
that the methods of Algorithmic Information Dynamics can deal with the richness
of such observer-object dependencies both in theory and practice. By
formalising the act of observing as mutual algorithmic perturbation, the
emergence of algorithmic information is rendered invariant, minimal, and robust
in the face of information cost and distortion, while still observer-dependent.
We demonstrate that the unbounded increase of emergent algorithmic information
implies asymptotically observer-independent emergence, which eventually
overcomes any formal theory that an observer might devise to finitely
characterise a phenomenon. We discuss observer-dependent emergence and
asymptotically observer-independent emergence solving some previous suggestions
indicating a hard distinction between strong and weak emergence
The Thermodynamics of Network Coding, and an Algorithmic Refinement of the Principle of Maximum Entropy
The principle of maximum entropy (Maxent) is often used to obtain prior
probability distributions as a method to obtain a Gibbs measure under some
restriction giving the probability that a system will be in a certain state
compared to the rest of the elements in the distribution. Because classical
entropy-based Maxent collapses cases confounding all distinct degrees of
randomness and pseudo-randomness, here we take into consideration the
generative mechanism of the systems considered in the ensemble to separate
objects that may comply with the principle under some restriction and whose
entropy is maximal but may be generated recursively from those that are
actually algorithmically random offering a refinement to classical Maxent. We
take advantage of a causal algorithmic calculus to derive a thermodynamic-like
result based on how difficult it is to reprogram a computer code. Using the
distinction between computable and algorithmic randomness we quantify the cost
in information loss associated with reprogramming. To illustrate this we apply
the algorithmic refinement to Maxent on graphs and introduce a Maximal
Algorithmic Randomness Preferential Attachment (MARPA) Algorithm, a
generalisation over previous approaches. We discuss practical implications of
evaluation of network randomness. Our analysis provides insight in that the
reprogrammability asymmetry appears to originate from a non-monotonic
relationship to algorithmic probability. Our analysis motivates further
analysis of the origin and consequences of the aforementioned asymmetries,
reprogrammability, and computation.Comment: 30 page
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