MOTIVATION: Genome-wide chromosomal contact maps are widely used to uncover the 3D organization of genomes. They rely on collecting millions of contacting pairs of genomic loci. Contacts at short range are usually well measured in experiments, while there is a lot of missing information about long-range contacts. RESULTS: We propose to use the sparse information contained in raw contact maps to infer high-confidence contact counts between all pairs of loci. Our algorithmic procedure, Boost-HiC, enables the detection of Hi-C patterns such as chromosomal compartments at a resolution that would be otherwise only attainable by sequencing a hundred times deeper the experimental Hi-C library. Boost-HiC can also be used to compare contact maps at an improved resolution. AVAILABILITY AND IMPLEMENTATION: Boost-HiC is available at https://github.com/LeopoldC/Boost-HiC. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Statistical entropy was introduced by Shannon as a basic concept in information theory measuring the average missing information in a random source. Extended into an entropy rate, it gives bounds in coding and compression theorems. In this paper, I describe how statistical entropy and entropy rate relate to other notions of entropy that are relevant to probability theory (entropy of a discrete probability distribution measuring its unevenness), computer sciences (algorithmic complexity), the ergodic theory of dynamical systems (Kolmogorov–Sinai or metric entropy) and statistical physics (Boltzmann entropy). Their mathematical foundations and correlates (the entropy concentration, Sanov, Shannon–McMillan–Breiman, Lempel–Ziv and Pesin theorems) clarify their interpretation and offer a rigorous basis for maximum entropy principles. Although often ignored, these mathematical perspectives give a central position to entropy and relative entropy in statistical laws describing generic collective behaviours, and provide insights into the notions of randomness, typicality and disorder. The relevance of entropy beyond the realm of physics, in particular for living systems and ecosystems, is yet to be demonstrated.

MOTIVATION: Multidimensional scaling (MDS) is a well-known multivariate statistical analysis method used for dimensionality reduction and visualization of similarities and dissimilarities in multidimensional data. The advantage of MDS with respect to singular value decomposition (SVD) based methods such as principal component analysis is its superior fidelity in representing the distance between different instances specially for high-dimensional geometric objects. Here, we investigate the importance of the choice of initial conditions for MDS, and show that SVD is the best choice to initiate MDS. Furthermore, we demonstrate that the use of the first principal components of SVD to initiate the MDS algorithm is more efficient than an iteration through all the principal components. Adding stochasticity to the molecular dynamics simulations typically used for MDS of large datasets, contrary to previous suggestions, likewise does not increase accuracy. Finally, we introduce a k nearest neighbor method to analyze the local structure of the geometric objects and use it to control the quality of the dimensionality reduction. RESULTS: We demonstrate here the, to our knowledge, most efficient and accurate initialization strategy for MDS algorithms, reducing considerably computational load. SVD-based initialization renders MDS methodology much more useful in the analysis of high-dimensional data such as functional genomics datasets.

Nicotinic acetylcholine receptors (nAChRs) are widely expressed throughout the central nervous system and modulate neuronal function in most mammalian brain structures. The contribution of defined nAChR subunits to a specific behavior is thus difficult to assess. Mice deleted for beta2-containing nAChRs (beta2-/-) have been shown to be hyperactive in an open-field paradigm, without determining the origin of this hyperactivity. We here develop a quantitative description of mouse behavior in the open field based upon first order Markov and variable length Markov chain analysis focusing on the time-organized sequence that behaviors are composed of. This description reveals that this hyperactivity is the consequence of the absence of specific inactive states or "stops". These stops are associated with a scanning of the environment in wild-type mice (WT), and they affect the way that animals organize their sequence of behaviors when compared with stops without scanning. They characterize a specific "decision moment" that is reduced in beta2-/- mutant mice, suggesting an important role of beta2-nAChRs in the strategy used by animals to explore an environment and collect information in order to organize their behavior. This integrated analysis of the displacement of an animal in a simple environment offers new insights, specifically into the contribution of nAChRs to higher brain functions and more generally into the principles that organize sequences of behaviors in animals.

The relationship between continuous-time dynamics and the corresponding discrete schemes, and its generally limited validity, is an important and widely acknowledged field within numerical analysis. In this paper, we propose another, more physical, viewpoint on this topic in order to understand the possible failure of discretisation procedures and the way to fix it. Three basic examples, the logistic equation, the Lotka–Volterra predator–prey model and Newton's law for planetary motion, are worked out. They illustrate the deep difference between continuous-time evolutions and discrete-time mappings, hence shedding some light on the more general duality between continuous descriptions of natural phenomena and discrete numerical computations.

This paper presents a sample of the deep and multiple interplay between discrete and continuous behaviours and the corresponding modellings in physics. The aim of this overview is to show that discrete and continuous features coexist in any natural phenomenon, depending on the scales of observation. Accordingly, different models, either discrete or continuous in time, space, phase space or conjugate space can be considered. Some caveats about their limits of validity and their interrelationships (discretisation and continuous limits) are pointed out. Difficulties and gaps arising from the singular nature of continuous limits and from the information loss accompanying discretisation are discussed.