Search Results (65)

In this position paper, we argue that the conventional understanding of ‘information’ (as generally conceived in science, in a digital fashion) is overly simplistic and not consistently applicable to living systems, which are open systems that cannot be reduced to any kind of ‘portion’ (building block) ascribed to the category of quantity. Instead, it is a matter of relationships and qualities in an indivisible analogical (and ontological) relationship between any presumed ‘software’ and ‘hardware’ (information/matter, psyche/soma). Furthermore, in biological systems, contrary to Shannon’s definition, which is well-suited to telecommunications and informatics, any kind of ‘information’ is the opposite of internal entropy, as it depends directly on order: it is associated with distinction and differentiation, rather than flattening and homogenisation. Moreover, the high degree of structural compartmentalisation of living matter prevents its energetics from being thermodynamically described by using a macroscopic, bulk state function. This requires the Second Principle of Thermodynamics to be redefined in order to make it applicable to living systems. For these reasons, any static, bit-related concept of ‘information’ is inadequate, as it fails to consider the system’s evolution, it being, in essence, the organized coupling to its own environment. From the perspective of quantum field theory (QFT), where many vacuum levels, symmetry breaking, dissipation, coherence and phase transitions can be described, a consistent picture emerges that portrays any living system as a relational process that exists as a flux of context-dependent meanings. This epistemological shift is also associated with a transition away from the ‘particle view’ (first quantisation) characteristic of quantum mechanics (QM) towards the ‘field view’ possible only in QFT (second quantisation). This crucial transition must take place in life sciences, particularly regarding the methodological approaches. Foremost because biological systems cannot be conceived as ‘objects’, but rather as non-confinable processes and relationships. Full article

The use of gait analysis to differentiate among paediatric populations with neurological and developmental conditions such as idiopathic toe walking (ITW), cerebral palsy (CP), and hereditary spastic paraplegia (HSP) remains challenging due to the insufficient precision of current diagnostic approaches, leading in some cases to misdiagnosis. Existing methods often isolate the analysis of gait variables, overlooking the whole complexity of biomechanical patterns and variations in motor control strategies. While previous studies have explored the use of statistical physics principles for the analysis of impaired gait patterns, gaps remain in integrating both kinematic and kinetic information or benchmarking these approaches against Deep Learning models. This study evaluates the robustness of statistical physics metrics in differentiating between normal and abnormal gait patterns and quantifies how the data source affects model performance. The analysis was conducted using gait data sets from two research institutions in Madrid and Dublin, with a total of 81 children with ITW, 300 with CP, 20 with HSP, and 127 typically developing children as controls. From each kinematic and kinetic time series, Shannon’s entropy, permutation entropy, weighted permutation entropy, and time irreversibility metrics were derived and used with Random Forest models. The classification accuracy of these features was compared to a ResNet Deep Learning model. Further analyses explored the effects of inter-laboratory comparisons and the spatiotemporal resolution of time series on classification performance and evaluated the impact of age and walking speed with linear mixed models. The results revealed that statistical physics metrics were able to differentiate among impaired gait patterns, achieving classification scores comparable to ResNet. The effects of walking speed and age on gait predictability and temporal organisation were observed as disease-specific patterns. However, performance differences across laboratories limit the generalisation of the trained models. These findings highlight the value of statistical physics metrics in the classification of children with different toe walking conditions and point towards the need of multimetric integration to improve diagnostic accuracy and gain a more comprehensive understanding of gait disorders. Full article

This study investigates the mechanisms underlying the diffusion of risk information about genetically modified organisms (GMOs) on the Chinese social media platform Weibo. Drawing upon social contagion theory, we examine how endogenous and exogenous mechanisms shape users’ information-sharing behaviors. An analysis of 388,722 reposts from 2444 original GMO risk-related texts enabled the construction of a comprehensive sharing network, with computational text-mining techniques employed to detect users’ attitudes toward GMOs. To bridge the gap between descriptive and inferential network analysis, we employ a Shannon entropy-based approach to quantify the uncertainty and concentration of attitudinal differences and similarities among sharing and non-sharing dyads, providing an information-theoretic foundation for understanding positional and differential homophily. The entropy-based analysis reveals that information-sharing ties are characterized by lower entropy in attitude differences, indicating greater attitudinal alignment among sharing users, especially among GMO opponents. Building on these findings, the Exponential Random Graph Model (ERGM) further demonstrates that both endogenous network mechanisms (reciprocity, preferential attachment, and triadic closure) and positional homophily influence GMO risk information sharing and dissemination. A key finding is the presence of a differential homophily effect, where GMO opponents exhibit stronger homophilic tendencies than non-opponents. Despite the prevalence of homophily, this paper uncovers substantial cross-attitude interactions, challenging simplistic notions of echo chambers in GMO risk communication. By integrating entropy and ERGM analyses, this study advances a more nuanced, information-theoretic understanding of how digital platforms mediate public perceptions and debates surrounding controversial socio-scientific issues, offering valuable implications for developing effective risk communication strategies in increasingly polarized online spaces. Full article

This paper introduces a functional framework for modeling cyclical and feedback-driven information flow using a generalized family of derangetropy operators. In contrast to scalar entropy measures such as Shannon entropy, these operators act directly on probability densities, providing a topographical representation of information across the support of the distribution. The proposed framework captures periodic and self-referential aspects of information evolution through functional transformations governed by nonlinear differential equations. When applied recursively, these operators induce a spectral diffusion process governed by the heat equation, with convergence toward a Gaussian characteristic function. This convergence result establishes an analytical foundation for describing the long-term dynamics of information under cyclic modulation. The framework thus offers new tools for analyzing the temporal evolution of information in systems characterized by periodic structure, stochastic feedback, and delayed interaction, with potential applications in artificial neural networks, communication theory, and non-equilibrium statistical mechanics. Full article

We introduce derangetropy, which is a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation that captures the dispersion of information across the entire support of a distribution. By incorporating self-referential and periodic properties, it provides insights into information dynamics governed by differential equations and equilibrium states. Through combinatorial justifications and empirical analysis, we demonstrate the utility of derangetropy in depicting distribution behavior and evolution, providing a new tool for analyzing complex and hierarchical systems in information theory. Full article

This paper introduces hybrid models designed to analyze daily and weekly bitcoin return spanning the periods from 18 July 2010 to 28 December 2023 for daily data, and from 18 July 2010 to 24 December 2023 for weekly data. Firstly, the fractal and chaotic structure of the selected variables was explored. Asymmetric Cantor set, Boundary of the Dragon curve, Julia set z² −1, Boundary of the Lévy C curve, von Koch curve, and Brownian function (Wiener process) tests were applied. The R/S and Mandelbrot–Wallis tests confirmed long-term dependence and fractionality. The largest Lyapunov test, the Rosenstein, Collins and DeLuca, and Kantz methods of Lyapunov exponents, and the HCT and Shannon entropy tests tracked by the Kolmogorov–Sinai (KS) complexity test determined the evidence of chaos, entropy, and complexity. The BDS test of independence test approved nonlinearity, and the TeraesvirtaNW and WhiteNW tests, the Tsay test for nonlinearity, the LR test for threshold nonlinearity, and White’s test and Engle test confirmed nonlinearity and heteroskedasticity, in addition to fractionality and chaos. In the second stage, the standard ARFIMA method was applied, and its results were compared to the LieNLS and LieOLS methods. The results showed that, under conditions of chaos, entropy, and complexity, the ARFIMA method did not yield successful results. Both baseline models, LieNLS and LieOLS, are enhanced by integrating them with deep learning methods. The models, LieLSTMOLS and LieLSTMNLS, leverage manifold-based approaches, opting for matrix representations over traditional differential operator representations of Lie algebras were employed. The parameters and coefficients obtained from LieNLS and LieOLS, and the LieLSTMOLS and LieLSTMNLS methods were compared. And the forecasting capabilities of these hybrid models, particularly LieLSTMOLS and LieLSTMNLS, were compared with those of the main models. The in-sample and out-of-sample analyses demonstrated that the LieLSTMOLS and LieLSTMNLS methods outperform the others in terms of MAE and RMSE, thereby offering a more reliable means of assessing the selected data. Our study underscores the importance of employing the LieLSTM method for analyzing the dynamics of bitcoin. Our findings have significant implications for investors, traders, and policymakers. Full article

RNA-seq faces persistent challenges due to the ongoing, expanding array of data processing workflows, none of which have yet achieved standardization to date. It is imperative to determine which method most effectively preserves biological facts. Here, we used Shannon entropy as a tool for depicting the biological status of a system. Thus, we assessed the measurement of Shannon entropy by several RNA-seq workflow approaches, such as DESeq2 and edgeR, but also by combining nine normalization methods with log₂ fold change on paired samples of TCGA RNA-seq representing datasets of 515 patients and spanning 12 different cancer types with 5-year overall survival rates ranging from 20% to 98%. Our analysis revealed that TPM, RLE, and TMM normalization, coupled with a threshold of log₂ fold change ≥1, for identifying differentially expressed genes, yielded the best results. We propose that Shannon entropy can serve as an objective metric for refining the optimization of RNA-seq workflows and mRNA sequencing technologies. Full article

In this paper, we present a novel approach for the optimal camera selection in video games. The new approach explores the use of information theoretic metrics f-divergences, to measure the correlation between the objects as viewed in camera frustum and the ideal or target view. The f-divergences considered are the Kullback–Leibler divergence or relative entropy, the total variation and the ${\chi }^2$ divergence. Shannon entropy is also used for comparison purposes. The visibility is measured using the differential form factors from the camera to objects and is computed by casting rays with importance sampling Monte Carlo. Our method allows a very fast dynamic selection of the best viewpoints, which can take into account changes in the scene, in the ideal or target view, and in the objectives of the game. Our prototype is implemented in Unity engine, and our results show an efficient selection of the camera and an improved visual quality. The most discriminating results are obtained with the use of Kullback–Leibler divergence. Full article

A measurement performed on a quantum system is an act of gaining information about its state. However, in the foundations of quantum theory, the concept of information is multiply defined, particularly in the area of quantum reconstruction, and its conceptual foundations remain surprisingly under-explored. In this paper, we investigate the gain of information in quantum measurements from an operational viewpoint in the special case of a two-outcome probabilistic source. We show that the continuous extension of the Shannon entropy naturally admits two distinct measures of information gain, differential information gain and relative information gain, and that these have radically different characteristics. In particular, while differential information gain can increase or decrease as additional data are acquired, relative information gain consistently grows and, moreover, exhibits asymptotic indifference to the data or choice of Bayesian prior. In order to make a principled choice between these measures, we articulate a Principle of Information Increase, which incorporates a proposal due to Summhammer that more data from measurements leads to more knowledge about the system, and also takes into consideration black swan events. This principle favours differential information gain as the more relevant metric and guides the selection of priors for these information measures. Finally, we show that, of the symmetric beta distribution priors, the Jeffreys binomial prior is the prior that ensures maximal robustness of information gain for the particular data sequence obtained in a run of experiments. Full article

This paper analyzes the temporal evolution of streamflow for different rivers in Argentina based on information quantifiers such as statistical complexity and permutation entropy. The main objective is to identify key details of the dynamics of the analyzed time series to differentiate the degrees of randomness and chaos. The permutation entropy is used with the probability distribution of ordinal patterns and the Jensen–Shannon divergence to calculate the disequilibrium and the statistical complexity. Daily streamflow series at different river stations were analyzed to classify the different hydrological systems. The complexity-entropy causality plane (CECP) and the representation of the Shannon entropy and Fisher information measure (FIM) show that the daily discharge series could be approximately represented with Gaussian noise, but the variances highlight the difficulty of modeling a series of natural phenomena. An analysis of stations downstream from the Yacyretá dam shows that the operation affects the randomness of the daily discharge series at hydrometric stations near the dam. When the station is further downstream, however, this effect is attenuated. Furthermore, the size of the basin plays a relevant role in modulating the process. Large catchments have smaller values for entropy, and the signal is less noisy due to integration over larger time scales. In contrast, small and mountainous basins present a rapid response that influences the behavior of daily discharge while presenting a higher entropy and lower complexity. The results obtained in the present study characterize the behavior of the daily discharge series in Argentine rivers and provide key information for hydrological modeling. Full article

This paper explores the concept of residual extropy as an uncertainty measure for order statistics. We specifically derive the residual extropy for the ith-order statistic and establish its relationship with the residual extropy of the ith-order statistic from a random sample generated from a uniform distribution. By employing this approach, we obtain a formula for the residual extropy of order statistics applicable to general continuous distributions. In addition, we offer two lower bounds that can be applied in situations where obtaining closed-form expressions for the residual extropy of order statistics in diverse distributions proves to be challenging. Additionally, we investigate the monotonicity properties of the residual extropy of order statistics. Furthermore, we present other aspects of the residual extropy of order statistics, including its dependence on the position of order statistics and various features of the underlying distribution. Full article

Soil researchers are interested in a gaining better understanding of the soil system state by analyzing its properties and their dynamics in time as well as in relation to land use change. Tilled, abandoned, and forest soils were assessed regarding attribute–response relationships for the bulk density (BD), total porosity (TP), volumetric moisture (θv), and penetration resistance (PR) with the use of the interquartile ratio (IRI) integrated into a resilience formula and Shannon entropy indices. The IRI results differentiated soil properties according to agrotechnics (wheel track vs. between wheels) and the state of the system (tilled vs. abandoned vineyard). Entropy (En) indicated a high level of uncertainty for PR. The linear regression applied to the pairs of BD-TP, TP-θv, and PR-θv showed better results for the IRI weight (IRI_weight) compared to the entropy weight (En_weight) for the soil between the wheels. The soil of the abandoned vineyard showed a faster tendency toward resilience that was more pronounced in the tilled wheel tracks than in the area between the wheels. The IRI can thus be an alternative to entropy in the evaluation of the response of some soil properties according to their use. When integrated into a resilience formula, the IRI can estimate the dynamics of soil properties for abandoned land compared to reference soil. Full article

A fundamental factor in relevant applications is the predictability of the life cycle of a coherent system consisting of more than one component. In this context, we examine how entropy can be applied to evaluate the degree of predictability. In particular, in order to calculate the Tsallis entropy of the past life, we consider a scenario in which all components of the system fail at a given time t and use the system signature to calculate the Tsallis entropy of the past life. We examine a number of analytical results, e.g., expressions, thresholds and orders for the measure at issue in our study. The results may provide insights into the predictability of a coherent system’s life cycle. Full article

In parallel with the concept of Rényi entropy for residual lifetime distributions, the Rényi entropy of inactivity time of lifetime distributions belonging to asymmetric distributions is a useful measure of independent interest. For a system that turns out to be inactive in time t, the past entropy is considered as an uncertainty measure for the past lifetime distribution. In this study, we consider a coherent system that includes n components and has the property that all the components of the system have failed at time t. To assess the predictability of the coherent system’s lifetime, we use the system’s signature to determine the Rényi entropy of its past lifetime. We study several analytical results, including expressions, bounds, and order properties for this measure. Full article

We calculate differential Shannon entropies derived from time-dependent coordinate-space and momentum-space probability densities. This is performed for a prototype system of a coupled electron–nuclear motion. Two situations are considered, where one is a Born–Oppenheimer adiabatic dynamics, and the other is a diabatic motion involving strong non-adiabatic transitions. The information about coordinate- and momentum-space dynamics derived from the total and single-particle entropies is discussed and interpreted with the help of analytical models. From the entropies, we derive mutual information, which is a measure for the electron–nuclear correlation. In the adiabatic case, it is found that such correlations are manifested differently in coordinate- and momentum space. For the diabatic dynamics, we show that it is possible to decompose the entropies into state-specific contributions. Full article