Unveiling robustness and heterogeneity through percolation triggered by random-link breakdown

Exploring the Rhizospheric Microbial Communities under Long-Term Precipitation Regime in Norway Spruce Seed Orchard

The rhizosphere is the hotspot for microbial enzyme activities and contributes to carbon cycling. Precipitation is an important component of global climate change that can profoundly alter belowground microbial communities. However, the impact of precipitation on conifer rhizospheric microbial populations has not been investigated in detail. In the present study, using high-throughput amplicon sequencing, we investigated the impact of precipitation on the rhizospheric soil microbial communities in two Norway Spruce clonal seed orchards, Lipová Lhota (L-site) and Prenet (P-site). P-site has received nearly double the precipitation than L-site for the last three decades. P-site documented higher soil water content with a significantly higher abundance of Aluminium (Al), Iron (Fe), Phosphorous (P), and Sulphur (S) than L-site. Rhizospheric soil metabolite profiling revealed an increased abundance of acids, carbohydrates, fatty acids, and alcohols in P-site. There was variance in the relative abundance of distinct microbiomes between the sites. A higher abundance of Proteobacteria, Acidobacteriota, Ascomycota, and Mortiellomycota was observed in P-site receiving high precipitation, while Bacteroidota, Actinobacteria, Chloroflexi, Firmicutes, Gemmatimonadota, and Basidiomycota were prevalent in L-site. The higher clustering coefficient of the microbial network in P-site suggested that the microbial community structure is highly interconnected and tends to cluster closely. The current study unveils the impact of precipitation variations on the spruce rhizospheric microbial association and opens new avenues for understanding the impact of global change on conifer rizospheric microbial associations.

Some Relations of Two Type 2 Polynomials and Discrete Harmonic Numbers and Polynomials

Harmonic numbers appear, for example, in many expressions involving Riemann zeta functions. Here, among other things, we introduce and study discrete versions of those numbers, namely the discrete harmonic numbers. The aim of this paper is twofold. The first is to find several relations between the Type 2 higher-order degenerate Euler polynomials and the Type 2 high-order Changhee polynomials in connection with the degenerate Stirling numbers of both kinds and Jindalrae–Stirling numbers of both kinds. The second is to define the discrete harmonic numbers and some related polynomials and numbers, and to derive their explicit expressions and an identity.

Generalized k-core percolation on correlated and uncorrelated multiplex networks

It has been recognized that multiplexes and interlayer degree correlations can play a crucial role in the resilience of many real-world complex systems. Here we introduce a multiplex pruning process that removes nodes of degree less than k_{i} and their nearest neighbors in layer i for i=1,...,m, and establish a generic framework of generalized k-core (Gk-core) percolation over interlayer uncorrelated and correlated multiplex networks of m layers, where k=(k_{1},...,k_{m}) and m is the total number of layers. Gk-core exhibits a discontinuous phase transition for all k owing to cascading failures. We have unraveled the existence of a tipping point of the number of layers, above which the Gk-core collapses abruptly. This dismantling effect of multiplexity on Gk-core percolation shows a diminishing marginal utility in homogeneous networks when the number of layers increases. Moreover, we have found the assortative mixing for interlayer degrees strengthens the Gk-core but still gives rise to discontinuous phase transitions as compared to the uncorrelated counterparts. Interlayer disassortativity on the other hand weakens the Gk-core structure. The impact of correlation effect on Gk-core tends to be more salient systematically over k for heterogenous networks than homogeneous ones.

Comparison of Splitting Methods for Deterministic/Stochastic Gross–Pitaevskii Equation

In this paper, we discuss the different splitting approaches to numerically solvethe Gross–Pitaevskii equation (GPE). The models are motivated from spinor Bose–Einsteincondensate (BEC). This system is formed of coupled mean-field equations, which are based oncoupled Gross–Pitaevskii equations. We consider conservative finite-difference schemes and spectralmethods for the spatial discretisation. Furthermore, we apply implicit or explicit time-integrators andcombine these schemes with different splitting approaches. The numerical solutions are comparedbased on the conservation of the L2-norm with the analytical solutions. The advantages of the novelsplitting methods for large time-domains are based on the asymptotic conservation of the solution ofthe soliton’s applications. Furthermore, we have the benefit of larger local time-steps and thereforeobtain faster numerical schemes.

A Note on Type 2 Degenerate q-Euler Polynomials

Recently, type 2 degenerate Euler polynomials and type 2 q-Euler polynomials were studied, respectively, as degenerate versions of the type 2 Euler polynomials as well as a q-analog of the type 2 Euler polynomials. In this paper, we consider the type 2 degenerate q-Euler polynomials, which are derived from the fermionic p-adic q-integrals on Z p , and investigate some properties and identities related to these polynomials and numbers. In detail, we give for these polynomials several expressions, generating function, relations with type 2 q-Euler polynomials and the expression corresponding to the representation of alternating integer power sums in terms of Euler polynomials. One novelty about this paper is that the type 2 degenerate q-Euler polynomials arise naturally by means of the fermionic p-adic q-integrals so that it is possible to easily find some identities of symmetry for those polynomials and numbers, as were done previously.

The Influence of a Network’s Spatial Symmetry, Topological Dimension, and Density on Its Percolation Threshold

Analyses of the processes of information transfer within network structures shows that the conductivity and percolation threshold of the network depend not only on its density (average number of links per node), but also on its spatial symmetry groups and topological dimension. The results presented in this paper regarding conductivity simulation in network structures show that, for regular and random 2D and 3D networks, an increase in the number of links (density) per node reduces their percolation threshold value. At the same network density, the percolation threshold value is less for 3D than for 2D networks, whatever their structure and symmetry may be. Regardless of the type of networks and their symmetry, transition from 2D to 3D structures engenders a change of percolation threshold by a value exp{−(d − 1)} that is invariant for transition between structures, for any kind of network (d being topological dimension). It is observed that in 2D or 3D networks, which can be mutually transformed by deformation without breaking and forming new links, symmetry of similarity is observed, and the networks have the same percolation threshold. The presence of symmetry axes and corresponding number of symmetry planes in which they lie affects the percolation threshold value. For transition between orders of symmetry axes, in the presence of the corresponding planes of symmetry, an invariant exists which contributes to the percolation threshold value. Inversion centers also influence the value of the percolation threshold. Moreover, the greater the number of pairs of elements of the structure which have inversion, the more they contribute to the fraction of the percolation threshold in the presence of such a center of symmetry. However, if the center of symmetry lies in the plane of mirror symmetry separating the layers of the 3D structure, the mutual presence of this group of symmetry elements do not affect the percolation threshold value. The scientific novelty of the obtained results is that for different network structures, it was shown that the percolation threshold for the blocking of nodes problem could be represented as an additive set of invariant values, that is, as an algebraic sum, the value of the members of which is stored in the transition from one structure to another. The invariant values are network density, topological dimension, and some of the elements of symmetry (axes of symmetry and the corresponding number of symmetry planes in which they lie, centers of inversion).

A Multi-Objective Optimization Model for the Design of Biomass Co-Firing Networks Integrating Feedstock Quality Considerations

The growth in energy demand, coupled with declining fossil fuel resources and the onset of climate change, has resulted in increased interest in renewable energy, particularly from biomass. Co-firing, which is the joint use of coal and biomass to generate electricity, is seen to be a practical immediate solution for reducing coal use and the associated emissions. However, biomass is difficult to manage because of its seasonal availability and variable quality. This study proposes a biomass co-firing supply chain optimization model that simultaneously minimizes costs and environmental emissions through goal programming. The economic costs considered include retrofitting investment costs, together with fuel, transport, and processing costs, while environmental emissions may come from transport, treatment, and combustion activities. This model incorporates the consideration of feedstock quality and its impact on storage, transportation, and pre-treatment requirements, as well as conversion yield and equipment efficiency. These considerations are shown to be important drivers of network decisions, emphasizing the importance of managing biomass and coal blend ratios to ensure that acceptable fuel properties are obtained.

A Note on States and Traces from Biorthogonal Sets

In this paper, following Bagarello, Trapani, and myself, we generalize the Gibbs states and their related KMS-like conditions. We have assumed that H 0 , H are closed and, at least, densely defined, without giving information on the domain of these operators. The problem we address in this paper is therefore to find a dense domain D that allows us to generalize the states of Gibbs and take them in their natural environment i.e., defined in L † ( D ) .

Algebraic Entropy of a Class of Five-Point Differential-Difference Equations

We compute the algebraic entropy of a class of integrable Volterra-like five-point differential-difference equations recently classified using the generalised symmetry method. We show that, when applicable, the results of the algebraic entropy agrees with the result of the generalised symmetry method, as all the equations in this class have vanishing entropy.

Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials

In this paper, we consider sums of finite products of Chebyshev polynomials of the first, third, and fourth kinds, which are different from the previously-studied ones. We represent each of them as linear combinations of Chebyshev polynomials of all kinds whose coefficients involve some terminating hypergeometric functions 2 F 1 . The results may be viewed as a generalization of the linearization problem, which is concerned with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials. These representations are obtained by explicit computations.

Network Approach to Understanding Emotion Dynamics in Relation to Childhood Trauma and Genetic Liability to Psychopathology: Replication of a Prospective Experience Sampling Analysis

Background: The network analysis of intensive time series data collected using the Experience Sampling Method (ESM) may provide vital information in gaining insight into the link between emotion regulation and vulnerability to psychopathology. The aim of this study was to apply the network approach to investigate whether genetic liability (GL) to psychopathology and childhood trauma (CT) are associated with the network structure of the emotions "cheerful," "insecure," "relaxed," "anxious," "irritated," and "down"-collected using the ESM method. Methods: Using data from a population-based sample of twin pairs and siblings (704 individuals), we examined whether momentary emotion network structures differed across strata of CT and GL. GL was determined empirically using the level of psychopathology in monozygotic and dizygotic co-twins. Network models were generated using multilevel time-lagged regression analysis and were compared across three strata (low, medium, and high) of CT and GL, respectively. Permutations were utilized to calculate p values and compare regressions coefficients, density, and centrality indices. Regression coefficients were presented as connections, while variables represented the nodes in the network. Results: In comparison to the low GL stratum, the high GL stratum had significantly denser overall (p = 0.018) and negative affect network density (p < 0.001). The medium GL stratum also showed a directionally similar (in-between high and low GL strata) but statistically inconclusive association with network density. In contrast to GL, the results of the CT analysis were less conclusive, with increased positive affect density (p = 0.021) and overall density (p = 0.042) in the high CT stratum compared to the medium CT stratum but not to the low CT stratum. The individual node comparisons across strata of GL and CT yielded only very few significant results, after adjusting for multiple testing. Conclusions: The present findings demonstrate that the network approach may have some value in understanding the relation between established risk factors for mental disorders (particularly GL) and the dynamic interplay between emotions. The present finding partially replicates an earlier analysis, suggesting it may be instructive to model negative emotional dynamics as a function of genetic influence.

Abnormal Behavior in Cascading Dynamics with Node Weight

Considering a preferential selection mechanism of load destination, we introduce a new method to quantify initial load distribution and subsequently construct a simple cascading model. By attacking the node with the highest load, we investigate the cascading dynamics in some synthetic networks. Surprisingly, we observe that for several networks of different structural patterns, a counterintuitive phenomenon emerges if the highest load attack is applied to the system, i.e., investing more resources to protect every node in a network inversely makes the whole network more vulnerable. We explain this ability paradox by analyzing the micro-structural components of the underlying network and therefore reveals how specific structural patterns may influence the cascading dynamics. We discover that the robustness of the network oscillates as the capacity of each node increases. The conclusion of the paper may shed lights on future investigations to avoid the demonstrated ability paradox and subsequent cascading failures in real-world networks.

Impact of self-healing capability on network robustness

A wide spectrum of real-life systems ranging from neurons to botnets display spontaneous recovery ability. Using the generating function formalism applied to static uncorrelated random networks with arbitrary degree distributions, the microscopic mechanism underlying the depreciation-recovery process is characterized and the effect of varying self-healing capability on network robustness is revealed. It is found that the self-healing capability of nodes has a profound impact on the phase transition in the emergence of percolating clusters, and that salient difference exists in upholding network integrity under random failures and intentional attacks. The results provide a theoretical framework for quantitatively understanding the self-healing phenomenon in varied complex systems.