12,794 research outputs found
Signatures of Infinity: Nonergodicity and Resource Scaling in Prediction, Complexity, and Learning
We introduce a simple analysis of the structural complexity of
infinite-memory processes built from random samples of stationary, ergodic
finite-memory component processes. Such processes are familiar from the well
known multi-arm Bandit problem. We contrast our analysis with
computation-theoretic and statistical inference approaches to understanding
their complexity. The result is an alternative view of the relationship between
predictability, complexity, and learning that highlights the distinct ways in
which informational and correlational divergences arise in complex ergodic and
nonergodic processes. We draw out consequences for the resource divergences
that delineate the structural hierarchy of ergodic processes and for processes
that are themselves hierarchical.Comment: 8 pages, 1 figure; http://csc.ucdavis.edu/~cmg/compmech/pubs/soi.pd
Self-Referential Noise and the Synthesis of Three-Dimensional Space
Generalising results from Godel and Chaitin in mathematics suggests that
self-referential systems contain intrinsic randomness. We argue that this is
relevant to modelling the universe and show how three-dimensional space may
arise from a non-geometric order-disorder model driven by self-referential
noise.Comment: Figure labels correcte
Discovering transcriptional modules by Bayesian data integration
Motivation: We present a method for directly inferring transcriptional modules (TMs) by integrating gene expression and transcription factor binding (ChIP-chip) data. Our model extends a hierarchical Dirichlet process mixture model to allow data fusion on a gene-by-gene basis. This encodes the intuition that co-expression and co-regulation are not necessarily equivalent and hence we do not expect all genes to group similarly in both datasets. In particular, it allows us to identify the subset of genes that share the same structure of transcriptional modules in both datasets.
Results: We find that by working on a gene-by-gene basis, our model is able to extract clusters with greater functional coherence than existing methods. By combining gene expression and transcription factor binding (ChIP-chip) data in this way, we are better able to determine the groups of genes that are most likely to represent underlying TMs
Punctuated vortex coalescence and discrete scale invariance in two-dimensional turbulence
We present experimental evidence and theoretical arguments showing that the
time-evolution of freely decaying 2-d turbulence is governed by a {\it
discrete} time scale invariance rather than a continuous time scale invariance.
Physically, this reflects that the time-evolution of the merging of vortices is
not smooth but punctuated, leading to a prefered scale factor and as a
consequence to log-periodic oscillations. From a thorough analysis of freely
decaying 2-d turbulence experiments, we show that the number of vortices, their
radius and separation display log-periodic oscillations as a function of time
with an average log-frequency of ~ 4-5 corresponding to a prefered scaling
ratio of ~ 1.2-1.3Comment: 22 pages and 38 figures. Submitted to Physica
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