The computational resources required by atomistic simulations of biomolecular systems still limit their applicability to relatively short time and length scales, at odds with those typically characterising biological processes. By integrating out most of the microscopic degrees of freedom in favor of a description in terms of few sites interacting through effective potentials, coarse-grained (CG) models constitute a powerful instrument for broadening the class of accessible phenomena, at the same time providing accurate results [1]. Also an exact CG procedure, however, inherently comes at a price: a loss of information, quantified by an increase in entropy, arising when a system is observed through "CG glasses" [2]. Interestingly, this loss only depends on the mapping, i.e., the sites one employs to represent the system at the CG level, which are often a priori selected only based on physical intuition [3].

Several questions follow: how wide and diverse is the space of possible CG mappings of a biomolecule? Within this space, are there representations that minimise the information loss, and do these "privileged" mappings give hints on the underlying biological processes? In this work, we address these topics by first characterising the space of CG representations of a system through the definition of a distance between mappings. Subsequently, we develop a workflow enabling to estimate the increase in entropy of a protein arising from CG'ing. Finally, we show that minimising this quantity over the space of possible CG representations suggests a connection between the biological relevance of a chemical fragment composing the biomolecule and the amount of information it contains [4].

[1] R. Menichetti, A. Pelissetto and F. Randisi, J. Chem. Phys. 146, 244908 (2017).
[2] J. F. Rudzinski and W. G. Noid, J. Chem. Phys. 135, 214101 (2011).
[3] P. Diggins IV et al., J. Chem. Theory Comput. 15, 648 (2019).
[4] M. Giulini, et al., J. Chem. Theory Comput. 16, 6795 (2020).

The computational study of soft matter systems lies at the nexus among several disciplines, including material science, biophysics, statistical mechanics, and information theory. Each of them contributes objects of investigation as well as tools and perspectives unique from each field, all of these being necessary to attain a multifaceted picture of complex systems.
The construction of in silico models of biomolecules, in particular, requires one to combine the background biological knowledge of a system with the quantitative description of the latter in those terms characteristic of mechanics and statistical physics. This is particularly true in the field of coarse-grained modelling, in which the effort to attain an ever larger accuracy of a model is replaced by the attempt to simplify it as much as possible, while at the same time retaining those essential features which make the model predictive.
This talk will provide an overview of the problem of designing effective, coarse-grained models of large biomolecules. Particular attention will be posed on the issue of representability and mapping, the preservation of information content, and the extraction of biological knowledge from resolution modulation.

Action (@) is a state property with physical dimensions of angular momentum (mrv=mr²ω). But it is scalar, rather than a vector, with a finite phase angle for change (mr²ωδθ). We have shown (Entropy 21,454) that molecular entropy (s) is a logarithmic function of mean values of action (s = kln[e^u(@_t/ħ)³(@_r/ħ)^2,3(@_v/ħ)], where k is Boltzmann’s constant, ħ Planck's quantum of action, u the kinetic molecular freedom; mean action values for translation (@_t), rotation (@_r) and vibration (@_v) are easily calculated from molecular properties. This is a novel development from statistical mechanics, mindful of Nobel laureate Richard Feynman’s favored principle of least action. The heat flow powering each engine cycle is reversibly partitioned between external mechanical work with compensating internal changes in the action and chemical potential of the working fluid. Equal entropy changes at the high temperature source and the low temperature sink match equal action and entropy changes in the working fluid. Asymmetric variations in quantum states with volume occur isothermally but constant action (mr²ω) is maintained during the adiabatic or isentropic phases. The maximum work possible per reversible cycle (-ΔG) is the net variation in the configurational Gibbs function of the working fluid between the source and sink temperatures. The engine’s inertia compensates so that external kinetic work performed adiabatically in the expansion phase is restored to the working fluid during the adiabatic compression, allowing its enthalpy to return to the same value, as claimed by Carnot. Restoring Carnot’s non-sensible heat or calorique as action as a basis for entropy will be discussed in the context of designing more efficient heat engines, including that powering the Earth’s climate cycles where we introduce the concept of vortical entropy for cyclones and anticyclones.

In building software architectures, the relations between elements in different diagrams are often overlooked. When constructing software architecture, IT architects more or less consciously however introduce elements that represent the same object instance on different diagrams with similar names. These connections are called consistency rules and are usually not saved in any way in the modeling tool. It was mathematically proved that the application of consistency rules increases the information content of software architecture. The feelings about increasing readability and ordering of software architecture by means of consistency rules have their mathematical rationale. In this article it was carried out a proof of decreasing information entropy while applying consistency rules in the construction of software architecture of IT systems. Therefore, it has been shown that marking selected elements in different diagrams with similar names is therefore an implicit way to increase the information content of software architecture while simultaneously improving its orderliness and readability.

Atrial fibrillation is a cardiac arrhythmia characterized by rapid and irregular heartbeats that could be sustained by repetitive and cyclic activations around a core, known as rotors. Intracardiac electrograms studies have related the occurrence of a signal waveform pattern, called complex fragmented atrial electrograms (CFAE), with the surroundings of the rotor core.

Recurrence quantification analysis (RQA) has been proposed as a tool to detect CFAE. In RQA, the phase space trajectories are computed from the signal and the appropriates time delay embedding. In this work, we propose the computation of cross RQA (cRQA) using two distinct electrograms. We hypothesized that there is low recurrence rate when cRQA is estimated from a signal recorded near a rotor core and another in an adjacent point around the core.

We test the sample entropy, RQA and cRQA in five 2D in-silico simulations of atrial fibrillation sustained by different mechanisms: i) a single stable rotor, ii) a figure-of-eight re-entry with two stable rotors, iii) a figure-of-eight re-entry with two meandering rotors, iv) a single stable rotor and multiple propagating waves, v) semi-stable rotors, meandering rotors and multiple propagating waves. Unipolar electrograms are simulated for each fibrillatory episode.

Our results show that, by applying sample entropy, the core of stable rotors, meandering rotors and multiples waves collision are associated with, by applying RQA the core of stable rotors and some areas with multiples waves collision exhibit low recurrence rates, notwithstanding meandering rotors were not detected. Differently, by applying cRQA only the cores of stable rotors are detected through low recurrence rates. These results suggest that cQRA could be a useful tool for stable rotors detection with high specificity. Future studies should include real electrograms recorded from patients with atrial fibrillation.

In this work we study the effect of natural stability mechanisms in stochastic trajectories produced by deviations of the operation regime due to fluctuations on the heat exchanges between the heat device and the thermal reservoirs. Perturbations on the operation regime from external sources produce stochastic trajectories along one cycle and the energetic consequences of the restitution forces are then analyzed. The main energetic functions such as power output, efficiency and entropy production, as well as compromise based functions are analyzed and the role of the stability basin, the so-called nullcline (which determine the restitution strength) and the endoreversible and irreversible limits (linked to a thermodynamic optimization) are put together to establish a connection between stability and a self-optimization feature.

The return maps of the dynamics allow us to understand the biggest contribution of the stability in the energetic evolution of the system. Additionally, fluctuations of the thermodynamic functions allow us to deepen into the susceptibility of each energetic function.

In classification tasks the increase in the number of dimensions of a data makes the learning process harder. In this context feature selection usually allows to induce simpler classifier models while keeping the accuracy. However, some factors, such as the presence of irrelevant and redundant features, make the feature selection process challenging. Symmetrical Uncertainty (SU) is an entropy-based measure widely used to identify subsets of useful features for the classification task. However, SU is a bivariate measure and, so, it ignores possible dependencies among more than two features. In order to overcome this issue, SU has been extended to the multivariate case. This extension, called Multivariate Symmetrical Uncertainty (MSU), is time-consuming and may become impracticable when evaluating larger subsets of features during the search. In this work we propose a MSU based Feature Selection (MSUFS) heuristic to address feature selection on high-dimensional data. In order to design MSUFS, the concept of Approximate Markov Blanket is redefined to take into account the MSU measure. The performance of MSUFS is tested on high-dimensional datasets from different domains and its results where compared with popular and competitive techniques. Results show that MSUFS is capable of identifying possible correlations and interaction among features and, therefore, it achieves competitive results. Finally, the proposed strategy is also applied to a case study regarding melanoma skin cancer.

Acknowledgments: This work is partially supported by the research project PINV15-0257 from CONACyT-Paraguay. Authors are also thankful to the Andalusian Scientific Computer Science Centre (CICA) for allowing us to use their computing infrastructures.

Recent academic literature has confirmed the existence of robust structures characterizing most of many real world systems described by the power law(PL). Intuitively, PL becomes more legible at the level of high frequency series fluctuations in their upper part (thus an asymptotic law), knowing that for certain phenomena the lower part could be generated by this same law. In phenomenological terms, fluctuations in the upper part of natural or social series generally lead to the criticality point at the eve of phase change (e.g. change in physical properties and behavior of matter at a certain temperature human eccentric behavior under the effect of higher emotion, financial crash, etc.).The present proposal goes beyond the traditional statistical methodology mainly based on the Central Limit Theorem(CLT) which presents serious limits when dealing with complex dynamic phenomena. In front of such endogenous methodological problem, a large community of statisticians instead try to find out new techniques fundamentally within the traditional CLT. In line with recent research, this paper recall and extends the fundaments of a recent approach of non-extensive cross-entropy econometrics(NCEE)(Bwanakare(2019). Equivalently, and to honor Rosen (see Rosen 1981, Gabaix 2009) who, for the first time, used the expression of “Economics of Superstars” to exemplify the presence of PL in the case of artistic earnings (stars inclusively), we propose here the expression of Superstars Generalized statistical regresion(SGSR). Thus, this paper proposes a theoretical, power law- based simultaneous regression equation to be estimated trough the q-generalised Kullback-Leibler statistical theory of information.

The understanding of the physico-chemical basis of the intracellular processes requires determination of local concentrations of cell chemical constituents. For that, light microscopy is the irreplaceable method. Using an example of a (auto)fluorescent tissue, we clarify some still ignored aspects of image build-up in the light microscope for maximal extraction of information from the 3D microscopic experiments. We introduce an algorithm based on the Rényi entropy approach, namely on the Point Divergence Gain (see Entropy 20(2), p. 106):

PDG_α^l-m = 1/(1-α) log₂ {[(n_l-1)^α - n_l + (n_m+1)^α - n_m]/C_α +1},

where α is the Rényi coefficient; and n_l and n_m are frequencies of occurrence of phenomena (intensity) l in the 1^st matrix (digital image) and of phenomena (intensity) m in the 2^nd matrix (digital image). The digital images are optical cuts consecutive in a stack obtained along the microscope optical path between which we exchange a pixel of intensity l for a pixel of intensity m. The term C_α is a sum of α-weighted frequencies of occurrences of all phenomena (intensities) in the 1^st matrix (digital image).

We removed an image background using PDG₅₀^l-m = 0 which is an approximation to PDG_∞^l-m = 0 (analogy to min entropy). Then, we sought voxels (3D pixels) called 3D electromagnetic centroids that corresponded to PDG₂^l-m = 0 (i.e., multifractality approximation to subtraction of two images consecutive in a z-stack). This localized the information about the object independently of the size of this voxel (see Ultramicroscopy 179, p. 1-14) and gave us cores of the objects’ images. At PDG₁₀^l-m = 0, we obtained extended 3D images of the observed objects called spread functions.

This approach enables us to localize positions of individual fluorophores and their general spectral properties and, consequently, to make approximative conclusions about intracellular biochemistry.

Experimental measurement or computational inference/prediction of the enzyme regulation needed in a metabolic pathway is hard problem. Consequently, regulation is known only for well-studied reactions of central metabolism in a few organisms. In this study, we use statistical thermodynamics and metabolic control theory as a theoretical framework to determine the enzyme activities that are needed to control metabolite concentrations such that they are consistent with experimentally measured values. A reinforcement learning approach is utilized to learn optimal regulation policies that match physiological levels of metabolites while maximizing the entropy production rate and minimizing the work to maintain a steady state. The learning takes a minimal amount of time, and efficient regulation schemes were learned that agree surprisingly well with known regulation. The learning is facilitated by a new approach in which steady state solutions are obtained by convex optimization based on maximum entropy rather than ODE solvers, making the time to solution seconds rather than days. The optimization is based on the Marcelin-De Donder formulation of mass action kinetics, from which rate constants are inferred. Consequently, a full ODE-based, mass action simulation with rate parameters and post-translational regulation is obtained. We demonstrate the process on three pathways in the central metabolism E. coli (gluconeogenesis, glycolysis-TCA, Pentose Phosphate-TCA) that each require different regulation schemes.