In this paper, we introduce and study the notion of rough I₂-lacunary statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough I₂-lacunary statistical limit set of a double sequence and discuss about some properties of this set.

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

Current progress in the prediction of mechanical behavior of solids requires understanding of spatiotemporal complexity of plastic flow caused by self-organization of crystal defects. It may be particularly important in hexagonal materials because of their strong anisotropy and combination of different mechanisms of plasticity, such as dislocation glide and twinning. These materials often display complex behavior even on the macroscopic scale of deformation curves, e.g., a peculiar three-stage elastoplastic transition, the origin of which is a matter of debates. The present work is devoted to a multiscale study of plastic flow in α-Ti, based on simultaneous recording of deformation curves, 1D local strain field, and acoustic emission (AE). It is found that the average AE activity also reveals three-stage behavior, but in a qualitatively different way depending on the crystallographic orientation of the sample axis. On the finer scale, the statistical analysis of AE events and local strain rates testifies to an avalanche-like character of dislocation processes, reflected in power-law probability distribution functions. The results are discussed from the viewpoint of collective dislocation dynamics and are confronted to predictions of a recent micromechanical model of Ti strain hardening.

Oscillometric blood pressure (BP) devices currently estimate a single point but do not identify fluctuations in BP or distinguish them from variations in response to physiological properties. In this paper, to analyze BP normality based on oscillometric measurements, we use statistical approaches including kurtosis, skewness, Kolmogorov-Smirnov, and correlation tests. Then, to mitigate uncertainties, we use a deep neural network (DNN) to determine the confidence limits (CLs) of BP measurements based on their normality. The proposed DNN regression model decreases the standard deviation of error (SDE) of the mean error (ME) and the mean absolute error (MAE) and reduces the uncertainty of the CLs and SDEs of the proposed technique. We validate the normality of the distribution of the BP estimation distribution which fits the Gaussian distribution very well. We use a rank test in the DNN regression model to demonstrate the independence of the artificial SBP and DBP estimations. First, we perform statistical tests to verify the normality of the BP measurements for individual subjects. The proposed methodology provides accurate BP estimations and reduces the uncertainties associated with the CLs and SDEs based on the DNN regression estimator.

Electrification coverage in Sarawak is the lowest at 78.74%, compared to Peninsular Malaysia at 99.62% and Sabah at 82.51%. Kapit, Sarawak with its 88.4% populations located in rural areas and mostly situated along the main riverbanks has great potential to generate electrical energy by hydrokinetic system. Yearly water velocity data is the most significant parameter to perform hydrokinetic analysis study. Nevertheless, the data retrieved from local river databases are inadequate for river energy analysis, thus hindering its progression. Instead, flow rates and rainfall data had been utilised to estimate the water velocity data. This signifies no estimation of water velocity in an unregulated river by using water level data had been made. Therefore, a novel technique of estimating the daily average water velocity data in unregulated rivers is proposed. The modelling of regression equation for water velocity estimation was performed and two regression model equations were generated to estimate both water level and water velocity on-site and proven to be valid as the coefficient of determination values had been R² = 87.4% and R²=87.9%, respectively. The combination of both regression model equations can be used to estimate long-term time series water velocity data for type-C unregulated river in remote areas.

We report the application of a recently proposed approach for modeling biological systems using a maximum entropy production rate principle in lieu of having in vivo rate constants. The method is applied in four steps: (1) a new ODE-based optimization approach based on Marcelin’s 1910 mass action equation is used to obtain the maximum entropy distribution, (2) the predicted metabolite concentrations are compared to those generally expected from experiment using a loss function from which post-translational regulation of enzymes is inferred, (3) the system is re-optimized with the inferred regulation from which rate constants are determined from the metabolite concentrations and reaction fluxes, and finally (4) a full ODE-based, mass action simulation with rate parameters and allosteric regulation is obtained. From the last step, the power characteristics and resistance of each reaction can be determined. The method is applied to the central metabolism of Neurospora crassa and the flow of material through the three competing pathways of upper glycolysis, the non-oxidative pentose phosphate pathway, and the oxidative pentose phosphate pathway are evaluated as a function of the NADP/NADPH ratio. It is predicted that regulation of phosphofructokinase (PFK) and flow through the pentose phosphate pathway are essential for preventing an extreme level of fructose 1, 6-bisphophate accumulation. Such an extreme level of fructose 1,6-bisphophate would otherwise result in a glassy cytoplasm with limited diffusion, dramatically decreasing the entropy and energy production rate and, consequently, biological competitiveness.

This paper establishes methods that quantify the structure of statistical interactions within a given data set using the characterization of information theory in cohomology by finite methods, and provides their expression in terms of statistical physic and machine learning. Following [1–3], we show directly that k multivariate mutual-informations (I_k) are k-coboundaries. The k-cocycles are given by I_k = 0, which generalize statistical independence to arbitrary dimension k. The topological approach allows to investigate Shannon’s information in the multivariate case without the assumptions of independent identically distributed variables. We develop the computationally tractable subcase of simplicial information cohomology represented by entropy H_k and information I_k landscapes. The I₁ component defines a self-internal energy functional U_k, and (−1)^k I_k,k≥2 components define the contribution to a free energy functional G_k of the k-body interactions. The set of information paths in simplicial structures is in bijection with the symmetric group and random processes, provides a topological expression of the 2nd law and points toward a discrete Noether theorem (1st law). The local minima of free-energy, related to conditional information negativity and the non-Shannonian cone of Yeung [4], characterize a minimum free energy complex. This complex formalizes the minimum free-energy principle in topology, provides a definition of a complex system, and characterizes a multiplicity of local minima that quantifies the diversity observed in biology. Finite data size effects and estimation bias severely constrain the effective computation of the information topology on data, and we provide simple statistical tests for the undersampling bias and for the k-dependences following [5]. We give an example of application of these methods to genetic expression and cell-type classification. The maximal positive I_k identifies the variables that co-vary the most in the population, whereas the minimal negative I_k identifies clusters and the variables that differentiate-segregate the most. The methods unravel biologically relevant I₁₀ with a sample size of 41. It establishes generic methods to quantify the epigenetic information storage and a unified epigenetic unsupervised learning formalism.

In the frame of a broader project, we were interested at comparing the amino acid profile in a specific variety of onion, Rossa da inverno sel. Rojo Duro, produced in two different Italian sites: Cannara (Umbria region) and Imola (Emilia Romagna region). In both places, onions were cultivated and harvested in the same way, and irrigated by water sprinkler method. A further group of Cannara onions, growth by microirrigation, was also evaluated. After the extraction of free amino acid mixture from onion samples, an ion-pairing RP-HPLC method allowed the separation and the evaporative light scattering detection of almost all underivatized proteinogenic amino acids. However, only the peaks corresponding to Leu, Phe, Trp, were present in all the investigated samples and unaffected from matrix interfering peaks. The application of the beeswarm/box plots with the ANOVA/TukeyHSD statistical approach revealed a content of Leu and Phe markedly influenced by the geographical origin of the onions, while not by the irrigation procedure. The developed HPLC method was validated in terms of specificity, linearity, LOD and LOQ, accuracy and precision, before the quantitative assay of Leu, Phe and Trp in the onion samples. Although further studies are necessary, these preliminary findings can represent a good starting point for considering the quantity of specific amino acids in the Rossa da inverno sel. Rojo Duro variety as a fingerprint of its geographical origin. In principle, the developed approach might be applied to other onion varieties, thus contributing to their characterization and traceability, also contributing to limit commercial frauds.

Personalized medicine is an aspect of the P4 medicine (predictive, preventive, personalized and participatory) based precisely on the customization of all medical characters of each subject. In personalized medicine, the development of medical treatments and drugs is tailored to the individual characteristics and needs of each subject, according to the study of diseases at different scales from genotype to phenotype scale. To make concrete the goal of personalized medicine, it is necessary to employ high-throughput methodologies such as Next Generation Sequencing (NGS), Genome-Wide Association Studies (GWAS), Mass Spectrometry or Microarrays, that are able to investigate a single disease from a broader perspective. For example, by using genotyping microarrays (e.g. collections of Single Nucleotide Polymorphism - SNP) it is possible to uncover the reasons (i.e. mutation in genes) because a treatment works properly in some patients (for example absence of mutated genes), but it does not work (presence of mutated genes) in others. A side effect of high-throughput methodologies is the massive amount of data produced for each single experiment, that poses several challenges (e.g. high execution time and required memory) to bioinformatic software. Thus a main requirement of modern bioinformatic software is the use of good software engineering methods and efficient programming techniques, able to face those challenges, that include the use of parallel programming and efficient and compact data structures. Thus, to exploit all the potential of this massive amount of data in the short possible time (before that data becomes obsolete), the necessity to develop parallel software tools for efficient data collection and analysis arise. Moreover, due to the heterogeneity of the data produced by the different kinds of experimental platforms, it is necessary to automatize in a comprehensive software pipeline, the various steps that compose a bioinformatic analysis, such as: the preprocessing of raw data to remove noise or corrupted data; the annotation of data with external knowledge (e.g. Gene Ontology), and the integration of molecular data with clinical data. It should be noted that such steps are necessary to make statistical or data mining analysis more effective. This paper presents the design and the experimentation of a comprehensive software pipeline, named microPipe, for the preprocessing, annotation and analysis of microarray-based SNP genotyping data. A case study in pharmacogenomics is presented. The main advantages of using microPipe are: the reduction of errors that may happen when trying to make data compatible among different tools; the possibility to analyze in parallel huge datasets; the easy annotation and integration of data.

The second law of thermodynamics states the increase of entropy, ΔS > 0, for real processes from state A to state B at constant energy from chemistry over biological life and engines to cosmic events. The connection of entropy to information, phase-space and heat is helpful, but does not immediately convince observers of the validity and basis of the second law. This gave grounds for finding a rigorous, but more easily acceptable reformulation. Here we show using statistical mechanics that this principle is equivalent to a force law ⟨⟨f⟩⟩> 0 in systems where mass centres and forces can be identified. The sign of this net force - the average mean force along a path from A to B - determines the direction of the process. The force law applies to a wide range of processes from machines to chemical reactions. The explanation of irreversibility by a driving force appears more plausible than the traditional formulation as it emphasizes the cause instead of the effect of motions.

The statistical bundle is the set of couples $(Q,W)$ of a probability density Q and a random variable W such that $\mathbb{E}$_Q [W] = 0. On a finite state space, we assume Q to be a probability density with respect to the uniform probability and give an affine atlas of charts such that the resulting manifold is a model for Information Geometry. Velocity and accelleration of a one-dimensional statistical model are computed in this set up. The Euler-Lagrange equations are derived from the Lagrange action integral. An example of Lagrangian using minus the entropy as potential energy is briefly discussed.

We examine how observations can be used to evaluate an air quality analysis by verifying against passive observations (i.e. cross-validation) that are not used to create the analysis and we compare these verifications to those made against the same set of (active) observations that were used to generate the analysis. The results show that both active and passive observations can be used to evaluate of first moment metrics (e.g. bias) but only passive observations are useful to evaluate second moment metrics such as variance of observed-minus-analysis and correlation between observations and analysis. We derive a set of diagnostics based on passive observation–minus-analysis residuals and we show that the true analysis error variance can be estimated, without relying on any statistical optimality assumption. This diagnostic is used to obtain near optimal analyses that are then used to evaluate the analysis error using several different methods. We compare the estimates according to the method of Hollingsworth Lonnberg, Desroziers, a diagnostic we introduce, and the perceived analysis error computed from the analysis scheme, to conclude that as long as the analysis is optimal, all estimates agrees within a certain error margin. The analysis error variance at passive observation sites is also obtained.

Many species of plants are found in regions to which they are alien. Their global distributions are characterised by a family of exponential functions of the kind that arise in elementary statistical mechanics (an example in ecology is MacArthur's broken stick). We show here that all these functions are quantitatively reproduced by a model containing a single parameter – some global resource partitioned at random on the two axes of species number and site number. A dynamical model generating this equilibrium is a two fold stochastic process and suggests a curious and interesting biological interpretation in terms of niche structures fluctuating with time and productivity; with sites and species highly idiosyncratic. Idiosyncrasy implies that attempts to identify a priori those species likely to become naturalized are unlikely to be successful. Although this paper is primarily concerned with a particular problem in population biology, the two fold stochastic process may be of more general interest.

The utilization for water resource has been of great concern to human life. To assess the natural water system in Kangding County, the integrated methods of hydrochemcial analysis, multivariate statistics and geochemical modelling were conducted on surface water, groundwater and thermal water samples. Surface water and groundwater were dominated by Ca-HCO₃ type, while thermal water belonged to Ca-HCO₃ and Na-Cl type. The analyzing results concluded the driving factors that affect hydrochemical components. Following the results of the combined assessments, hydrochemcial process was controlled by the dissolution of carbonate and silicate minerals with slight influence from anthropogenic activity. The mixing model of groundwater and thermal water was calculated using silica-enthalpy method, yielding cold-water fraction of 0.56-0.79 and estimated reservoir temperature of 130-199 ^oC, respectively. δD and δ¹⁸O isotopes suggested surface water, groundwater and thermal springs were of meteoric origin. Thermal water should have deep circulation through the Xianshuihe fault zone, while groundwater flows through secondary fractures where it recharges with thermal water. Those analytical results were used to construct a hydrological conceptual model, providing a better understanding of the natural water system in Kangding County.

We present a general theory of estimation of analysis error covariances based on cross-validation as well as a geometric interpretation of the method. In particular we use the variance of passive observation–minus-analysis residuals and show that the true analysis error variance can be estimated, without relying on the optimality assumption. This approach is used to obtain near optimal analyses that are then used to evaluate the air quality analysis error using several different methods at active and passive observation sites. We compare the estimates according to the method of Hollingsworth-Lönnberg, Desroziers et al., a new diagnostic we developed, and the perceived analysis error computed from the analysis scheme, to conclude that, as long as the analysis is near optimal, all estimates agree within a certain error margin.

The launch of the RadioAstron space radio telescope provides a unique opportunity to study the extreme high brightness temperature of Active Galactic Nuclei (AGNs) with unprecedented long baselines of up to 28 Earth diameters. A coordinated ground-based flux density monitoring of RadioAstron targets is essential to determine the effect of interstellar scintillation (ISS) on the Space Very Long Baseline Interferometry (SVLBI) visibilities. Moreover, a combination/comparison of scintillation with SVLBI observations is expected to reveal the relative influence of source brightness temperature, compactness, and properties of the interstellar medium on the observed variability at centimeter wavelengths. In 2014 we started a RadioAstron target triggered flux monitoring with the Effelsberg 100-m radio telescope in support of this SVLBI mission. A total of 112 targets were observed during the five-session monitoring performed so far. In this paper we present a statistical study on the short-term flux density variability of the sample, which is focused on the variability characteristics and derived physical properties of the observed sources.

Graphs are largely used in computer science to model relations, or associations, among entities the compose complex systems. More recently, they found a broad field of application in bioinformatics and medical informatics supporting modelling, analysis of many systems. The applications span from representing interactions among molecules within cells, to model the functions of the brains. In order to support research, algorithms from graph theory that are able to extract knowledge from network should be coupled to efficient visualisation techniques. Although the importance of such topic, we retain that many challenges should be faced in the futures, such as automated pathway and network layout to better match biologists’ needs, the developing of a standard able to give more and better choices to represent nodes, edges finally, the developing of automated mechanism able to improve the network navigation methods that help users manage large and complex networks with the goal to improve the usability.

We investigate the stationary and dynamic properties of the celebrated Nosé-Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé-Hoover dynamics aims to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé-Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a size-independent timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that diverges with the system size. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé-Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé-Hoover and canonical equilibrium.

Studies on the structure of economic systems are, most frequently, carried out by the methods of informational statistics. These methods, often accompanied by a wide range of indicators (Shannon entropy, Balassa coefficient, Herfindahl specialty index, Gini coefficient, Theil index etc.) around which a wide literature has been created over time, have a major disadvantage. Such weakness is related to the imposition of the system condition, therefore the need to know all the components of the system (as absolute values or as weights). This restriction is difficult to accomplish in some situations, and in others, this knowledge may be irrelevant, especially when there is an interest in structural changes only in some of the components of the economic system (either we refer to the typology of economic activities - NACE or of territorial units – NUTS). This article presents a procedure for characterizing the structure of a system and for comparing its evolution over time, in the case of incomplete information, thus eliminating the restriction existent in the classical methods. The proposed methodological alternative uses a parametric distribution, with subunit values for the variable. The application refers to Gross Domestic Product values for five of the 28 European Union countries, with annual values of over 1,000 billion Euros (Germany, Spain, France, Italy and United Kingdom) for the years 2003 and 2015. A form of the Wald sequential test is applied to measure changes in the structure of this group of countries, between the years compared. The results of this application validate the proposed method.

Daily maximum surface air temperature (Tamax) is a crucial factor for understanding complex land surface processes under rapid climate change. Remote detection of Tamax has widely relied on the empirical relationship between air temperature and land surface temperature (LST), a product derived from remote sensing. However, little is known about how such a relationship is affected by the high heterogeneity in landscapes and dynamics in seasonality. This study aims to advance our understanding of the roles of land cover and seasonal variation in the estimation of Tamax using the MODIS (Moderate Resolution Imaging Spectroradiometer) LST product. We developed statistical models to link Tamax and LST in the middle and lower reaches of the Yangtze River in China for five major land-cover types (i.e., forest, shrub, water, impervious surface, cropland, and grassland) and two seasons (i.e., growing season and non-growing season). Results show that the performance of modeling the Tamax-LST relationship was highly dependent on land cover and seasonal variation. Estimating Tamax over grasslands and water bodies achieved superior performance; while uncertainties were high over forested lands that contained extensive heterogeneity in species types, plant structure, and topography. We further found that all the land-cover specific models developed for the plant non-growing season outperformed the corresponding models developed for the growing season. Discrepancies in model performance mainly occurred in the vegetated areas (forest, cropland, and shrub), suggesting an important role of plant phenology in defining the statistical relationship between Tamax and LST. For impervious surfaces, the challenge of capturing the high spatial heterogeneity in urban settings using the low-resolution MODIS data made Tamax estimation a difficult task, which was especially true in the growing season.