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 on 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., $\pi$ ) 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.

The human leukocyte antigen (HLA) haplotype DRB1*15:01 is the major risk factor for multiple sclerosis (MS). Here, we find that DRB1*15:01 is hypomethylated and predominantly expressed in monocytes among carriers of DRB1*15:01. A differentially methylated region (DMR) encompassing HLA-DRB1 exon 2 is particularly affected and displays methylation-sensitive regulatory properties in vitro. Causal inference and Mendelian randomization provide evidence that HLA variants mediate risk for MS via changes in the HLA-DRB1 DMR that modify HLA-DRB1 expression. Meta-analysis of 14,259 cases and 171,347 controls confirms that these variants confer risk from DRB1*15:01 and also identifies a protective variant (rs9267649, p < 3.32 × 10⁻⁸, odds ratio = 0.86) after conditioning for all MS-associated variants in the region. rs9267649 is associated with increased DNA methylation at the HLA-DRB1 DMR and reduced expression of HLA-DRB1, suggesting a modulation of the DRB1*15:01 effect. Our integrative approach provides insights into the molecular mechanisms of MS susceptibility and suggests putative therapeutic strategies targeting a methylation-mediated regulation of the major risk gene.

We propose an innovative, integrated, cost-effective health system to combat major non-communicable diseases (NCDs), including cardiovascular, chronic respiratory, metabolic, rheumatologic and neurologic disorders and cancers, which together are the predominant health problem of the 21st century. This proposed holistic strategy involves comprehensive patient-centered integrated care and multi-scale, multi-modal and multi-level systems approaches to tackle NCDs as a common group of diseases. Rather than studying each disease individually, it will take into account their intertwined gene-environment, socio-economic interactions and co-morbidities that lead to individual-specific complex phenotypes. It will implement a road map for predictive, preventive, personalized and participatory (P4) medicine based on a robust and extensive knowledge management infrastructure that contains individual patient information. It will be supported by strategic partnerships involving all stakeholders, including general practitioners associated with patient-centered care. This systems medicine strategy, which will take a holistic approach to disease, is designed to allow the results to be used globally, taking into account the needs and specificities of local economies and health systems.

We introduce and develop a method that demonstrates that the algorithmic information content of a system can be used as a steering handle in the dynamical phase space, thus affording an avenue for controlling and reprogramming systems. The method consists of applying a series of controlled interventions to a networked system while estimating how the algorithmic information content is affected. We demonstrate the method by reconstructing the phase space and their generative rules of some discrete dynamical systems (cellular automata) serving as controlled case studies. Next, the model-based interventional or causal calculus is evaluated and validated using (1) a huge large set of small graphs, (2) a number of larger networks with different topologies, and finally (3) biological networks derived from a widely studied and validated genetic network (E. coli) as well as on a significant number of differentiating (Th17) and differentiated human cells from a curated biological network data.

In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure's range of applications and demonstrating the weaknesses of computable measures of complexity.