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Abstract We use an agnostic information-theoretic approach to investigate the statistical properties of natural images. We introduce the Multiscale Relevance (MSR) measure to assess the robustness of images to compression at all scales. Starting in a controlled environment, we characterize the MSR of synthetic random textures as function of image roughness $$\text{ H }$$ H and other relevant parameters. We then extend the analysis to natural images and find striking similarities with critical ( $$\text {H}\approx 0$$ H ≈ 0 ) random textures. We show that the MSR is more robust and informative of image content than classical methods such as power spectrum analysis. Finally, we confront the MSR to classical measures for the calibration of common procedures such as color mapping and denoising. Overall, the MSR approach appears to be a good candidate for advanced image analysis and image processing, while providing a good level of physical interpretability.

Clustering and community detection provide a concise way of extracting meaningful information from large datasets. An ever growing plethora of data clustering and community detection algorithms have been proposed. In this paper, we address the question of ranking the performance of clustering algorithms for a given dataset. We show that, for hard clustering and community detection, Linsker's Infomax principle can be used to rank clustering algorithms. In brief, the algorithm that yields the highest value of the entropy of the partition, for a given number of clusters, is the best one. We show indeed, on a wide range of datasets of various sizes and topological structures, that the ranking provided by the entropy of the partition over a variety of partitioning algorithms is strongly correlated with the overlap with a ground truth partition The codes related to the project are available in https://github.com/Sandipan99/Ranking_cluster_algorithms.

BACKGROUND: The spontaneous activity of neuronal networks has been studied in in vitro models such as brain slices and dissociated cultures. However, a comparison between their dynamical properties in these two types of biological samples is still missing and it would clarify the role of architecture in shaping networks’ operation. METHODS: We used calcium imaging to identify clusters of neurons co-activated in hippocampal and cortical slices, as well as in dissociated neuronal cultures, from GAD67-GFP mice. We used statistical tests, power law fitting and neural modelling to characterize the spontaneous events observed. RESULTS: In slices, we observed intermittency between silent periods, the appearance of Confined Optical Transients (COTs) and of Diffused Optical Transients (DOTs). DOTs in the cortex were preferentially triggered by the activity of neurons located in layer III-IV, poorly coincident with GABAergic neurons. DOTs had a duration of 10.2±0.3 and 8.2±0.4 seconds in cortical and hippocampal slices, respectively, and were blocked by tetrodotoxin, indicating their neuronal origin. The amplitude and duration of DOTs were controlled by NMDA and GABA-A receptors. In dissociated cultures, we observed an increased synchrony in GABAergic neurons and the presence of global synchronous events similar to DOTs, but with a duration shorter than that seen in the native tissues. CONCLUSION: We conclude that DOTs are shaped by the network architecture and by the balance between inhibition and excitation, and that they can be reproduced by network models with a minimal number of parameters.

Abstract Random number generation plays an essential role in technology with important applications in areas ranging from cryptography to Monte Carlo methods, and other probabilistic algorithms. All such applications require high-quality sources of random numbers, yet effective methods for assessing whether a source produce truly random sequences are still missing. Current methods either do not rely on a formal description of randomness (NIST test suite) on the one hand, or are inapplicable in principle (the characterization derived from the Algorithmic Theory of Information), on the other, for they require testing all the possible computer programs that could produce the sequence to be analysed. Here we present a rigorous method that overcomes these problems based on Bayesian model selection. We derive analytic expressions for a model’s likelihood which is then used to compute its posterior distribution. Our method proves to be more rigorous than NIST’s suite and Borel-Normality criterion and its implementation is straightforward. We applied our method to an experimental device based on the process of spontaneous parametric downconversion to confirm it behaves as a genuine quantum random number generator. As our approach relies on Bayesian inference our scheme transcends individual sequence analysis, leading to a characterization of the source itself.

Summary: Loss of functional cardiomyocytes is a major determinant of heart failure after myocardial infarction. Previous high throughput screening studies have identified a few microRNAs (miRNAs) that can induce cardiomyocyte proliferation and stimulate cardiac regeneration in mice. Here, we show that all of the most effective of these miRNAs activate nuclear localization of the master transcriptional cofactor Yes-associated protein (YAP) and induce expression of YAP-responsive genes. In particular, miR-199a-3p directly targets two mRNAs coding for proteins impinging on the Hippo pathway, the upstream YAP inhibitory kinase TAOK1, and the E3 ubiquitin ligase β-TrCP, which leads to YAP degradation. Several of the pro-proliferative miRNAs (including miR-199a-3p) also inhibit filamentous actin depolymerization by targeting Cofilin2, a process that by itself activates YAP nuclear translocation. Thus, activation of YAP and modulation of the actin cytoskeleton are major components of the pro-proliferative action of miR-199a-3p and other miRNAs that induce cardiomyocyte proliferation. : Torrini et al. report that several microRNAs that induce cardiomyocyte proliferation act by stimulating activation of the transcriptional cofactor YAP, a master regulator of cell proliferation. Several microRNAs also act on the cardiomyocyte cytoskeleton by promoting actin polymerization. These microRNAs can be considered as potential treatments for cardiac regeneration. Keywords: cardiomyocyte, cell cycle, Cofilin2, cytoskeleton, Hippo, microRNA, regeneration, YAP

The ability of a society to make the right decisions on relevant matters relies on its capability to properly aggregate the noisy information spread across the individuals of which it is made. In this paper, we study the information aggregation performance of a stylized model of a society, whose most influential individuals—the leaders—are highly connected among themselves and uninformed. Agents update their state of knowledge in a Bayesian manner by listening to their neighbors. We find analytical and numerical evidence of a transition, as a function of the noise level in the information initially available to agents, from a regime where information is correctly aggregated, to one where the population reaches consensus on the wrong outcome with finite probability. Furthermore, information aggregation depends in a non-trivial manner on the relative size of the clique of leaders, with the limit of a vanishingly small clique being singular.

In the Minimum Description Length (MDL) principle, learning from the data is equivalent to an optimal coding problem. We show that the codes that achieve optimal compression in MDL are critical in a very precise sense. First, when they are taken as generative models of samples, they generate samples with broad empirical distributions and with a high value of the relevance, defined as the entropy of the empirical frequencies. These results are derived for different statistical models (Dirichlet model, independent and pairwise dependent spin models, and restricted Boltzmann machines). Second, MDL codes sit precisely at a second order phase transition point where the symmetry between the sampled outcomes is spontaneously broken. The order parameter controlling the phase transition is the coding cost of the samples. The phase transition is a manifestation of the optimality of MDL codes, and it arises because codes that achieve a higher compression do not exist. These results suggest a clear interpretation of the widespread occurrence of statistical criticality as a characterization of samples which are maximally informative on the underlying generative process.

Models can be simple for different reasons: because they yield a simple and computationally efficient interpretation of a generic dataset (e.g., in terms of pairwise dependencies)—as in statistical learning—or because they capture the laws of a specific phenomenon—as e.g., in physics—leading to non-trivial falsifiable predictions. In information theory, the simplicity of a model is quantified by the stochastic complexity, which measures the number of bits needed to encode its parameters. In order to understand how simple models look like, we study the stochastic complexity of spin models with interactions of arbitrary order. We show that bijections within the space of possible interactions preserve the stochastic complexity, which allows to partition the space of all models into equivalence classes. We thus found that the simplicity of a model is not determined by the order of the interactions, but rather by their mutual arrangements. Models where statistical dependencies are localized on non-overlapping groups of few variables are simple, affording predictions on independencies that are easy to falsify. On the contrary, fully connected pairwise models, which are often used in statistical learning, appear to be highly complex, because of their extended set of interactions, and they are hard to falsify.

Maximum entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a model from data, that affords predictions on all other (dependent) variables. Conversely, maximum entropy can be invoked to retrieve the relevant variables (sufficient statistics) directly from the data, once a model is identified by Bayesian model selection. We explore this approach in the case of spin models with interactions of arbitrary order, and we discuss how relevant interactions can be inferred. In this perspective, the dimensionality of the inference problem is not set by the number of parameters in the model, but by the frequency distribution of the data. We illustrate the method showing its ability to recover the correct model in a few prototype cases and discuss its application on a real dataset.

Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is "interrupted" by a sharp cut-off in its upper tail, where it is totally dominated by financial firms. This flattening of the distribution contrasts with a large body of empirical literature which finds a Pareto distribution for firm sizes both across countries and over time. Pareto distributions are generally traced back to a mechanism of proportional random growth, based on a regime of constant returns to scale. This makes our findings of an "interrupted" Pareto distribution all the more puzzling, because we provide evidence that financial firms in our sample should operate in such a regime. We claim that the missing mass from the upper tail of the asset size distribution is a consequence of shadow banking activity and that it provides an (upper) estimate of the size of the shadow banking system. This estimate-which we propose as a shadow banking index-compares well with estimates of the Financial Stability Board until 2009, but it shows a sharper rise in shadow banking activity after 2010. Finally, we propose a proportional random growth model that reproduces the observed distribution, thereby providing a quantitative estimate of the intensity of shadow banking activity.

Social learning is defined as the ability of a population to aggregate information, a process which must crucially depend on the mechanisms of social interaction. Consumers choosing which product to buy, or voters deciding which option to take with respect to an important issue, typically confront external signals to the information gathered from their contacts. Economic models typically predict that correct social learning occurs in large populations unless some individuals display unbounded influence. We challenge this conclusion by showing that an intuitive threshold process of individual adjustment does not always lead to such social learning. We find, specifically, that three generic regimes exist separated by sharp discontinuous transitions. And only in one of them, where the threshold is within a suitable intermediate range, the population learns the correct information. In the other two, where the threshold is either too high or too low, the system either freezes or enters into persistent flux, respectively. These regimes are generally observed in different social networks (both complex or regular), but limited interaction is found to promote correct learning by enlarging the parameter region where it occurs.

The geography of codon bias distributions over prokaryotic genomes and its impact upon chromosomal organization are analyzed. To this aim, we introduce a clustering method based on information theory, specifically designed to cluster genes according to their codon usage and apply it to the coding sequences of Escherichia coli and Bacillus subtilis. One of the clusters identified in each of the organisms is found to be related to expression levels, as expected, but other groups feature an over-representation of genes belonging to different functional groups, namely horizontally transferred genes, motility, and intermediary metabolism. Furthermore, we show that genes with a similar bias tend to be close to each other on the chromosome and organized in coherent domains, more extended than operons, demonstrating a role of translation in structuring bacterial chromosomes. It is argued that a sizeable contribution to this effect comes from the dynamical compartimentalization induced by the recycling of tRNAs, leading to gene expression rates dependent on their genomic and expression context.