Search Results (71)

This article defines an inverted Topp–Leone distribution. Several mathematical properties and maximum likelihood estimation of parameters of this distribution are considered. The shape of the distribution for different sets of parameters is discussed. Several mathematical properties such as the cumulative distribution function, mode, moment-generating function, survival function, hazard rate function, stress-strength reliability R, moments, Rényi entropy, Shannon entropy, Fisher information matrix, and partial ordering associated with this distribution, have been derived. Distributions of the sum and quotient of two independent inverted Topp–Leone variables have also been obtained. Full article

Milk microbiota is a complex microbial ecosystem with implications for product quality, safety, and animal health. However, limited data exist on goat milk microbiota, particularly in local breeds. This study provides the first detailed characterization of the milk microbiota of Girgentana goats, a resilient Sicilian breed valued for high-quality dairy products. Illumina NovaSeq sequencing was used to analyze the 16S rRNA V3–V4 regions of 44 individual and 3 bulk milk samples. Briefly, 16S rRNA-gene sequencing produced a total of 8,135,944 high-quality reads, identifying 1134 operational taxonomic units (OTUs) across all individual samples. On average, each sample showed 864 OTUs with counts > 0. Alpha diversity metrics, based on richness estimators (Chao1: 948.1; ACE: 936.3) and diversity indices (Shannon: 4.06; Simpson: 0.95; Fisher: 118.5), indicated a heterogeneous community with both common and low-abundance taxa. Firmicutes (51%) and Proteobacteria (27%) were the predominant phyla, with Lactobacillaceae (54%) and Bifidobacteriaceae (22%) dominating at the family level. Notably, farm bulk milk profiles closely mirrored individual samples. These results establish a milk microbiota baseline for the Girgentana breed and offer valuable insights into microbial ecology in traditional dairy systems, supporting future comparisons across breeds and farming practices. Full article

We present a comprehensive information-theoretic evaluation of three widely used rigid water models (TIP3P, SPC, and SPC/$\epsilon$) through systematic analysis of water clusters ranging from single molecules to 11-molecule aggregates. Five fundamental descriptors—Shannon entropy, Fisher information, disequilibrium, LMC complexity, and Fisher–Shannon complexity—were calculated in both position and momentum spaces to quantify electronic delocalizability, localization, uniformity, and structural sophistication. Clusters containing 1, 3, 5, 7, 9, and 11 molecules (denoted 1 M, 3 M, 5 M, 7 M, 9 M, and 11 M) were selected to balance computational tractability with representative scaling behavior. Molecular dynamics simulations validated the force fields against experimental bulk properties (density, dielectric constant, self-diffusion coefficient), while statistical analysis using Shapiro–Wilk normality tests and Student’s t-tests ensured robust discrimination between models. Our results reveal distinct scaling behaviors that correlate with experimental accuracy: SPC/$\epsilon$ demonstrates superior electronic structure representation with optimal entropy–information balance and enhanced complexity measures, while TIP3P shows excessive localization and reduced complexity that worsen with increasing cluster size. The transferability from clusters to bulk properties is established through systematic convergence of information-theoretic measures toward bulk-like behavior. The methodology establishes information-theoretic analysis as a useful tool for comprehensive force field evaluation. Full article

We consider the lossless compression bound of any individual data sequence. Conceptually, its Kolmogorov complexity is such a bound yet uncomputable. According to Shannon’s source coding theorem, the average compression bound is $nH$, where n is the number of words and H is the entropy of an oracle probability distribution characterizing the data source. The quantity $nH\left({\widehat{\theta }}_n\right)$ obtained by plugging in the maximum likelihood estimate is an underestimate of the bound. Shtarkov showed that the normalized maximum likelihood (NML) distribution is optimal in a minimax sense for any parametric family. Fitting a data sequence—without any a priori distributional assumption—by a relevant exponential family, we apply the local asymptotic normality to show that the NML code length is $nH\left({\widehat{\theta }}_n\right)+{\displaystyle \frac{d}{2}}log{\displaystyle \frac{n}{2\pi }}+log{\int }_{\Theta }{\left|I\left(\theta \right)\right|}^{1/2}d\theta +o\left(1\right)$, where d is dictionary size, $\left|I\right(\theta \left)\right|$ is the determinant of the Fisher information matrix, and $\Theta$ is the parameter space. We demonstrate that sequentially predicting the optimal code length for the next word via a Bayesian mechanism leads to the mixture code whose length is given by $nH\left({\widehat{\theta }}_n\right)+{\displaystyle \frac{d}{2}}log{\displaystyle \frac{n}{2\pi }}+log{\displaystyle \frac{|I\left({\widehat{\theta }}_n\right){|}^{1/2}}{w\left({\widehat{\theta }}_n\right)}}+o\left(1\right)$, where $w\left(\theta \right)$ is a prior. The asymptotics apply to not only discrete symbols but also continuous data if the code length for the former is replaced by the description length for the latter. The analytical result is exemplified by calculating compression bounds of protein-encoding DNA sequences under different parsing models. Typically, compression is maximized when parsing aligns with amino acid codons, while pseudo-random sequences remain incompressible, as predicted by Kolmogorov complexity. Notably, the empirical bound becomes more accurate as the dictionary size increases. Full article

Background/Objectives: Selective serotonin reuptake inhibitors (SSRIs), widely prescribed for anxiety disorders, may negatively impact the gut microbiota, contributing to dysbiosis. Considering the gut–brain axis’s importance in mental health, probiotics could represent an effective adjunctive strategy. This study evaluated the effects of Lactobacillus helveticus R0052 and Bifidobacterium longum R0175 on microbiota composition, metabolic activity, and immune markers in fecal samples from patients with anxiety on SSRIs, using the SHIME^® (Simulator of the Human Intestinal Microbial Ecosystem) model. Methods: The fecal microbiotas of four patients using sertraline or escitalopram were inoculated in SHIME^® reactors simulating the ascending colon. After stabilization, a 14-day probiotic intervention was performed. Microbial composition was assessed by 16S rRNA sequencing. Short-chain fatty acids (SCFAs), ammonia, and GABA were measured, along with the prebiotic index (PI). Intestinal barrier integrity was evaluated via transepithelial electrical resistance (TEER), and cytokine levels (IL-6, IL-8, IL-10, TNF-α) were analyzed using a Caco-2/THP-1 co-culture system. The statistical design employed in this study for the analysis of prebiotic index, metabolites, intestinal barrier integrity and cytokines levels was a repeated measures ANOVA, complemented by post hoc Tukey’s tests to assess differences across treatment groups. For the 16S rRNA sequencing data, alpha diversity was assessed using multiple metrics, including the Shannon, Simpson, and Fisher indices to evaluate species diversity, and the Chao1 and ACE indices to estimate species richness. Beta diversity, which measures microbiota similarity across groups, was analyzed using weighted and unweighted UniFrac distances. To assess significant differences in beta diversity between groups, a permutational multivariate analysis of variance (PERMANOVA) was performed using the Adonis test. Results: Probiotic supplementation increased Bifidobacterium and Lactobacillus, and decreased Klebsiella and Bacteroides. Beta diversity was significantly altered, while alpha diversity remained unchanged. SCFA levels increased after 7 days. Ammonia levels dropped, and PI values rose. TEER values indicated enhanced barrier integrity. IL-8 and TNF-α decreased, while IL-6 increased. GABA levels remained unchanged. Conclusions: The probiotic combination of Lactobacillus helveticus R0052 and Bifidobacterium longum R0175 modulated gut microbiota composition, metabolic activity, and inflammatory responses in samples from individuals with anxiety on SSRIs, supporting its potential as an adjunctive strategy to mitigate antidepressant-associated dysbiosis. However, limitations—including the small pooled-donor sample, the absence of a healthy control group, and a lack of significant GABA modulation—should be considered when interpreting the findings. Although the SHIME^® model is considered a gold standard for microbiota studies, further clinical trials are necessary to confirm these promising results. Full article

This study investigates the capability of Sentinel-1 (S1) SAR time series to identify vegetation sites affected by pest infestations. For this purpose, the statistical method of the Fisher–Shannon analysis was employed to discern infected from unifected forest trees. The analysis was performed on a case study (Castel Porziano) located in the urban and peri-urban areas of Rome (Italy), which have been significantly impacted by Toumeyella parvicornis (TP) in recent years. For comparison, the area of Follonica (Italy), which has not yet been affected by this insect, was also analyzed. Two polarizations (VV and VH) and two orbit types (Ascending and Descending) were analyzed. The results, supported by Receiver Operating Characteristic (ROC) analysis, demonstrated that VH polarization in the Descending orbit provided the best performance in identifying TP-infected sites. Full article

I study a lattice with periodic boundary conditions using a non-local master equation that evolves over time. I investigate different system regimes using classical theories like Fisher information, Shannon entropy, complexity, and the Cramér–Rao bound. To simulate spatial continuity, I employ a large number of sites in the ring and compare the results with continuous spatial systems like the Telegrapher’s equations. The Fisher information revealed a power-law decay of $t^{-\nu }$, with $\nu =2$ for short times and $\nu =1$ for long times, across all jump models. Similar power-law trends were also observed for complexity and the Fisher information related to Shannon entropy over time. Furthermore, I analyze toy models with only two ring sites to understand the behavior of the Fisher information and Shannon entropy. As expected, a ring with a small number of sites quickly converges to a uniform distribution for long times. I also examine the Shannon entropy for short and long times. Full article

When evaluating sensory stimuli, people tend to prefer those with not too little or not too much complexity. A recent theoretical proposal for this phenomenon is that preference has a direct link to the Observed Fisher Information that a stimulus carries about the environment. To make this theory complete, one must specify the model that the brain has about complexities in the world. Here, we develop this model by first obtaining the distributions of three indices of complexity measured as normalized Shannon Entropy in real-world images from seven environments. We then search for a parametric model that accounts for these distributions. Finally, we measure the Observed Fisher Information that each image has about the parameters of this model. The results show that with few exceptions, the distributions of image complexities are unimodal, have negative skewness, and are leptokurtotic. Moreover, the sign and magnitude of the skewness varies systematically with the location of the mode. After investigating tens of models for these distributions, we show that the Logit-Losev function, a generalization of the hyperbolic-secant distribution, fits them well. The Observed Fisher Information for this model shows the inverted-U-shape behavior of complexity preference. Finally, we discuss ways to test our Fisher-Information theory. Full article

In this study, we examined how the nonlinearity $\alpha$ of the Langevin equation influences the behavior of extremes in a generated time series. The extremes, defined according to run theory, result in two types of series, run lengths and surplus magnitudes, whose complex structure was investigated using the visibility graph (VG) method. For both types of series, the information measures of the Shannon entropy measure and Fisher Information Measure were utilized for illustrating the influence of the nonlinearity $\alpha$ on the distribution of the degree, which is the main topological parameter describing the graph constructed by the VG method. The main finding of our study was that the Shannon entropy of the degree of the run lengths and the surplus magnitudes of the extremes is mostly influenced by the nonlinearity, which decreases with with an increase in $\alpha$. This result suggests that the run lengths and surplus magnitudes of extremes are characterized by a sort of order that increases with increases in nonlinearity. Full article

The diversity and floristic composition of a primeval forest was studied, located in the district of Yambrasbamba–Bongará–Amazonas, delimiting a 1 ha area, and at an altitude of 1890 m.a.s.l. All individuals with diameter at breast height (DBH) ≥ 10 cm were inventoried. The plant diversity in the area was measured and a description of its composition and floristic structure was made. The following were recorded: a total of 640 trees distributed in 39 families, 60 genera and 152 species. The value of the Simpson’s index (D) was 0.974 and that of the Shannon–Wiener index was 4.264, indicating that the species had a high abundance of individuals. In turn, Fisher’s alpha value (α) was 23.744, indicating a regular diversity in montane forests in relation to different altitudinal gradients. The families with the highest number of individuals were Melastomataceae, Rubiaceae, Euphorbiaceae, Phyllanthaceae, and Lauraceae. The most abundant species were Alchornea acutifolia Müll.Arg. with 47 individuals (7.34%), Chimarrhis glabriflora Ducke with 39 individuals (6.09%), Hieronyma alchorneoides Allemão with 39 individuals (6.09%), and Cyathea lasiosora (Kuhn) Domin with 33 individuals (5.16%). A comparative analysis was carried out of plots of montane and premontane forests, and the studied plot presented had the third-highest register of families and genera, behind the plots studied in the provinces of Oxapampa and Chanchamayo. Full article

Xylella Fastidiosa has been recently detected for the first time in southern Italy, representing a very dangerous phytobacterium capable of inducing severe diseases in many plants. In particular, the disease induced in olive trees is called olive quick decline syndrome (OQDS), which provokes the rapid desiccation and, ultimately, death of the infected plants. In this paper, we analyse about two thousands pixels of MODIS satellite evapotranspiration time series, covering infected and uninfected olive groves in southern Italy. Our aim is the identification of Xylella Fastidiosa-linked patterns in the statistical features of evapotranspiration data. The adopted methodology is the well-known Fisher–Shannon analysis that allows one to characterize the time dynamics of complex time series by means of two informational quantities, the Fisher information measure (FIM) and the Shannon entropy power (SEP). On average, the evapotranspiration of Xylella Fastidiosa-infected sites is characterized by a larger SEP and lower FIM compared to uninfected sites. The analysis of the receiver operating characteristic curve suggests that SEP and FIM can be considered binary classifiers with good discrimination performance that, moreover, improves if the yearly cycle, very likely linked with the meteo-climatic variability of the investigated areas, is removed from the data. Furthermore, it indicated that FIM exhibits superior effectiveness compared to SEP in discerning healthy and infected pixels. Full article

Human gut microbiome richness, diversity, and composition are associated with physical activity and impaired glycemic control; however, the associations with sedentary behavior and screen time are not as well-established. This study evaluated associations of sedentary behavior and screen time with the alpha diversity and composition of the human gut microbiome in adults with and without impaired glycemic control. Sedentary behavior and screen time data were collected via survey from 47 adults (38% with impaired glycemic control). Microbiome composition and alpha diversity were determined in fecal microbial DNA. Sedentary behavior was negatively associated with the number of observed operational taxonomic units (OTUs), Chao 1 Index, and Fisher’s Alpha Index. These associations were slightly attenuated but remained significant when controlling for covariates. Screen time was negatively associated with the number of observed OTUs, Shannon Index, and Fisher’s Alpha Index; however, only the association with observed OTUs was independent of all covariates. Our findings suggest sedentary behavior and screen time may be significant influencers of compositional changes in human gut microbiota. This may be a potential mechanism linking sedentary behavior and screen time to an increased risk of type 2 diabetes. Full article

Tropical coastal freshwater forested wetlands in coastal regions are rapidly disappearing as a result of various disturbance agents, mainly wildfires caused by high accumulations of forest fuels. The objective of this study was to characterize the structure and composition of fuel beds in tropical coastal freshwater forested wetlands with three levels of disturbance at El Castaño, La Encrucijada Biosphere Reserve. Seventeen sampling units were used to describe the structure of the forest’s fuel beds (canopy, sub-canopy, and understory). Fallen woody material and litter (surface and fermented) were characterized using the planar intersection technique. Diversity comprised eight species of trees, two shrubs, five lianas, and two herbaceous species. The vertical strata were dominated by trees between 2 and 22 m in height. The horizontal structure had a higher percentage of trees with normal diameter between 2.5 and 7.5 cm (61.4%) of the total. Sites with low disturbance had the highest arboreal density (2686 ind. ha⁻¹). Diversity of species showed that the Fisher, Margalef, Shannon, and Simpson α indices were higher in the low disturbance sites. The Berger–Parker index exhibited greater dominance in the sites with high disturbance. Pachira aquatica Aubl. Showed the highest importance value index and was the largest contributor to fuel beds. Sites with the highest disturbance had the highest dead fuel load (222.18 ± 33.62 Mg ha⁻¹), with woody fuels of classes 1, 10, and 1000 h (rotten) being the most representative. This study contributes to defining areas prone to fire in these ecosystems and designing prevention strategies. 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

Diverse forms of nonlinearity within stochastic equations give rise to varying dynamics in processes, which may influence the behavior of extreme values. This study focuses on two nonlinear models of the discrete Langevin equation: one with a fixed diffusion function (M1) and the other with a fixed marginal distribution (M2), both characterized by a nonlinearity parameter. Extremes are defined according to the run theory with thresholds based on percentiles. The behavior of inter-extreme times and run lengths is examined by employing Fisher’s Information Measure and the Shannon Entropy. Our findings reveal a clear relationship between the entropic and informational measures and the nonlinearity of model M1—these measures decrease as the nonlinearity parameter increases. Similar relationships are evident for the M2 model, albeit to a lesser extent, even though the background data’s marginal distribution remains unaffected by this parameter. As thresholds increase, both the values of Fisher’s Information Measure and the Shannon Entropy also increase. Full article