We investigate the properties of a Block Decomposition Method (BDM), which extends the power of a Coding Theorem Method (CTM) that approximates local estimations of algorithmic complexity based upon Solomonoff-Levin's theory of algorithmic probability providing a closer connection to algorithmic complexity than previous attempts based on statistical regularities such as popular lossless compression schemes. The strategy behind BDM is to find small computer programs that produce the components of a larger, decomposed object. The set of short computer programs can then be artfully arranged in sequence so as to produce the original object. We show that the method provides efficient estimations of algorithmic complexity but that it performs like Shannon entropy when it loses accuracy. We estimate errors and study the behaviour of BDM for different boundary conditions, all of which are compared and assessed in detail. The measure may be adapted for use with more multi-dimensional objects than strings, objects such as arrays and tensors. To test the measure we demonstrate the power of CTM on low algorithmic-randomness objects that are assigned maximal entropy (e.g. π) but whose numerical approximations are closer to the theoretical low algorithmic-randomness expectation. We also test the measure on larger objects including dual, isomorphic and cospectral graphs for which we know that algorithmic randomness is low. We also release implementations of the methods in most major programming languages-Wolfram Language (Mathematica), Matlab, R, Perl, Python, Pascal, C++, and Haskell -and an online algorithmic complexity calculator.
RIG-I is a major innate immune sensor for viral infection, triggering an interferon (IFN)-mediated antiviral response upon cytosolic detection of viral RNA. Double-strandedness and 5-terminal triphosphates were identified as motifs required to elicit optimal immunological signaling. However, very little is known about the response dynamics of the RIG-I pathway, which is crucial for the ability of the cell to react to diverse classes of viral RNA while maintaining self-tolerance. In the present study, we addressed the molecular mechanism of RIG-I signal detection and its translation into pathway activation. By employing highly quantitative methods, we could establish the length of the double-stranded RNA (dsRNA) to be the most critical determinant of response strength. Size exclusion chromatography and direct visualization in scanning force microscopy suggested that this was due to cooperative oligomerization of RIG-I along dsRNA. The initiation efficiency of this oligomerization process critically depended on the presence of high affinity motifs, like a 5-triphosphate. It is noteworthy that for dsRNA longer than 200 bp, internal initiation could effectively compensate for a lack of terminal triphosphates. In summary, our data demonstrate a very flexible response behavior of the RIG-I pathway, in which sensing and integration of at least two distinct signals, initiation efficiency and double strand length, allow the host cell to mount an antiviral response that is tightly adjusted to the type of the detected signal, such as viral genomes, replication intermediates, or small by-products.
Complex data usually results from the interaction of objects produced by different generating mechanisms. Here we introduce a universal, unsupervised and parameter-free model-oriented approach, based upon the seminal concept of algorithmic probability, that decomposes an observation into its most likely algorithmic generative sources. Our approach uses a causal calculus to infer model representations. We demonstrate its ability to deconvolve interacting mechanisms regardless of whether the resultant objects are strings, space-time evolution diagrams, images or networks. While this is mostly a conceptual contribution and a novel framework, we provide numerical evidence evaluating the ability of our methods to separate data from observations produced by discrete dynamical systems such as cellular automata and complex networks. We think that these separating techniques can contribute to tackling the challenge of causation, thus complementing other statistically oriented approaches.
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