Stochastic Process Research Articles

Soil animal communities demonstrate simplification without homogenization along an urban gradient.

Urbanization profoundly impacts biodiversity and ecosystem function, exerting an immense ecological filter on the flora and fauna that inhabit it, oftentimes leading to simplistic and homogenous ecological communities. However, the response of soil animal communities to urbanization remains underexplored, and it is unknown whether their response to urbanization is like that of aboveground organisms. This study investigated the influence of urbanization on soil animal communities in 40 public parks along an urbanization gradient. We evaluated soil animal abundance, diversity, and community composition and related these measures to urban and soil characteristics at each park. The most urbanized parks exhibited reduced animal abundance, richness, and Shannon diversity. These changes were influenced by many variables underscoring the multifaceted influence of urbanization on ecological communities. Notably, contrary to our expectation, urbanization did not lead to community homogenization; instead, it acted stochastically, creating unique soil animal assemblages. This suggests that urban soil animal communities are concomitantly shaped by deterministic and stochastic ecological processes in urban areas. Our study highlights the intricate interplay between urbanization and soil animal ecology, challenging the notion of urban homogenization in belowground ecosystems and providing insight for managing and preserving belowground communities in urban areas.

Personalized Model-Driven Interventions for Decisions From Experience.

Cognitive models that represent individuals provide many benefits for understanding the full range of human behavior. One way in which individual differences emerge is through differences in knowledge. In dynamic situations, where decisions are made from experience, models built upon a theory of experiential choice (instance-based learning theory; IBLT) can provide accurate predictions of individual human learning and adaptivity to changing environments. Here, we demonstrate how an instance-based learning (IBL) cognitive model, implemented in a cognitive architecture (Adaptive Control of Thought-Rational), can be used to model an individual's decisions in a cybersecurity defense task, accounting for both population average and individual variances. The same IBL model structure with identical architectural parameters generates the full range of human behavior through stochastic memory retrieval processes operating over and contributing to unique experiences. Recurrence quantification analyses allow us to look beyond average behavior between and within individuals to sequential patterns of trial-to-trial behavior. We show how model-tracing and knowledge-tracing techniques can be used to align the model to an individual in real time to drive adaptive and personalized signaling algorithms for a cybersecurity defense system. We also present a method for introspecting into the cognitive model to gain further insight into the cognitive salience of features factored into individual decisions. The combination of techniques provides a blueprint for personalized modeling of individuals. We discuss the results and implications of this adaptive and personalized method for cybersecurity defense and more generally for intelligent artifacts tailored to individual differences in domains such as human-machine teaming.

Plastic Constitutive Training Method for Steel Based on a Recurrent Neural Network

The deep learning steel plastic constitutive model training method was studied based on the recurrent neural network (RNN) model to improve the allocative efficiency of the deep learning steel plastic constitutive model and promote its application in practical engineering. Two linear hardening constitutive datasets of steel were constructed using the Gaussian stochastic process. The RNN, long short-term memory (LSTM), and gated recurrent unit (GRU) were used as models for training. The effects of the data pre-processing method, neural network structure, and training method on the model training were analyzed. The prediction ability of the model for different scale series and the corresponding data demand were evaluated. The results show that LSTM and the GRU are more suitable for stress–strain prediction. The marginal effect of the stacked neural network depth and number gradually decreases, and the hysteresis curve can be accurately predicted by a two-layer RNN. The optimal structure of the two models is A50-100 and B150-150. The prediction accuracy of the models increased with the decrease in batch size and the increase in training batch, and the training time also increased significantly. The decay learning rate method could balance the prediction accuracy and training time, and the optimal initial learning rate, batch size, and training batch were 0.001, 60, and 100, respectively. The deep learning plastic constitutive model based on the optimal parameters can accurately predict the hysteresis curve of steel, and the prediction abilities of the GRU are 6.13, 6.7, and 3.3 times those of LSTM in short, medium, and long sequences, respectively.

Insider trading at a random deadline with correlation between dynamic asset and stochastic liquidity

We propose a generalized continuous-time insider trading model, building upon the frameworks of Caldentey and Stacchetti (2010) and Collin-Dufresne and Fos (2016), with a correlation between the value of a risky asset following an Ornstein-Uhlenbeck-type process and the noise trading volume with volatility characterized by a general stochastic process. And a closed form of the market equilibrium is established, consisting of the insider's trading strategy and the market makers' pricing rule. It shows that at the equilibrium: (i) all of the insider's private information is released at the end of the transaction; (ii) market depth and market liquidity evolve as semi-martingales, respectively; and (iii) the equilibrium price is driven by a bridge process that solves an Ornstein-Uhlenbeck-type SDE. Numerical simulations show that as the correlation coefficient increases, the equilibrium price becomes more informative, leading to a decrease in both the trading intensity and the expected payoff for the insider.

Application and Empirical Analysis of Random Volatility Model in Financial Markets

The Stochastic Volatility Model (SVM), as a key innovation in modern financial engineering, has profoundly changed our understanding of the volatility characteristics of financial markets. This model not only considers the volatility of asset prices as a time-varying random variable, but also simulates this uncertainty by introducing stochastic processes such as Brownian motion or more complex stochastic differential equations, thereby achieving a precise characterization of the dynamic characteristics of volatility. Compared to traditional fixed or historical average volatility assumptions, SVM can capture sudden changes in market sentiment, the impact of news events, and the influence of macroeconomic factors on volatility, providing investors with a more realistic perspective on the market. This article not only deeply analyzes the theoretical basis and construction methods of SVM, but also verifies its effectiveness and applicability in different financial market environments through empirical analysis and actual market data, providing valuable references and insights for financial practitioners, scholars, and policy makers.

Bearing remaining life prediction method based on ARAD -ELN and multi-stage wiener process

Abstract Stochastic process-based models are extensively utilized in health assessments and Remaining Useful Life (RUL) predictions of bearings. Nevertheless, bearings in actual operation undergo multiple degradation stages, each characterized by its unique trend of degradation. The application of a singular stochastic process for RUL prediction falls short of achieving optimal performance. Consequently, this paper introduces a multi-stage Wiener process-based approach for the prediction of bearings' RUL. Initially, to tackle the challenge of imbalanced sample sizes across different degradation stages of bearings, an ensemble learning-based neural network (ELN) enhanced by ARIMA Residual Anomaly Detection (ARAD) for the identification of bearing degradation stages is proposed. Subsequently, taking into account the temporal, unit-to-unit, and nonlinear variabilities of the degradation process at each stage, a Wiener process-based multi-stage degradation model for bearings is developed. A method for parameter estimation and updating, utilizing Kalman filtering and Maximum Likelihood Estimation (K-M) is introduced. Finally, the proposed model undergoes validation using both simulated data and the XJTU-SY bearing dataset. Experimental results of three RUL predictions show that the proposed method leads the benchmark model with RMSE values of 3.61, 2.92 and 7.24 respectively, affirming that the proposed model can precisely classify equipment degradation stages and predict RUL with high accuracy and stability.

A Lévy-Itô decomposition on a class of topological monoids

We investigate a Lévy-Itô formula on a class of topological monoids with a suitable family of characters. This formula generalizes the classical ones for subordinators. Stochastic processes such as classical subordinators, extremal processes, measured-valued processes and the random interlacements model fall into this category.

Interpreting the power spectral density of a fluctuating colloidal current.

The transport of molecules through biological and synthetic nanopores is governed by multiple stochastic processes that lead to noisy, fluctuating currents. Disentangling the characteristics of different noise-generating mechanisms is central to better understanding molecular transport at a fundamental level but is extremely challenging in molecular systems due to their complexity and relative experimental inaccessibility. Here, we construct a colloidal model microfluidic system for the experimental measurement of particle currents, where the governing physical properties are directly controllable and particle dynamics directly observable, unlike in the molecular case. Currents of hard spheres fluctuate due to the random arrival times of particles into the channel and the distribution of particle speeds within the channel, which results in characteristic scalings in the power spectral density. We rationalize these scalings by quantitatively comparing to a model for shot noise with a finite transit time, extended to include the distribution of particle speeds. Particle velocity distributions sensitively reflect the confining geometry, and we interpret and model these in terms of the underlying fluid flow profiles. Finally, we explore the extent to which details of these distributions govern the form of the resulting power spectral density, thereby establishing concrete links between the power spectral density and underlying mechanisms for this experimental system. This paves the way for establishing a more systematic understanding of the links between characteristics of transport fluctuations and underlying molecular mechanisms in driven systems such as nanopores.

The interplay between host-specificity and habitat-filtering influences sea cucumber microbiota across an environmental gradient of pollution

Environmental gradients can influence morpho-physiological and life-history differences in natural populations. It is unclear, however, to what extent such gradients can also modulate phenotypic differences in other organismal characteristics such as the structure and function of host-associated microbial communities. In this work, we addressed this question by assessing intra-specific variation in the diversity, structure and function of environmental-associated (sediment and water) and animal-associated (skin and gut) microbiota along an environmental gradient of pollution in one of the most urbanized coastal areas in the world. Using the tropical sea cucumber Holothuria leucospilota, we tested the interplay between deterministic (e.g., environmental/host filtering) and stochastic (e.g., random microbial dispersal) processes underpinning host-microbiome interactions and microbial assemblages. Overall, our results indicate that microbial communities are complex and vary in structure and function between the environment and the animal hosts. However, these differences are modulated by the level of pollution across the gradient with marked clines in alpha and beta diversity. Yet, such clines and overall differences showed opposite directions when comparing environmental- and animal-associated microbial communities. In the sea cucumbers, intrinsic characteristics (e.g., body compartments, biochemistry composition, immune systems), may underpin the observed intra-individual differences in the associated microbiomes, and their divergence from the environmental source. Such regulation favours specific microbial functional pathways that may play an important role in the survival and physiology of the animal host, particularly in high polluted areas. These findings suggest that the interplay between both, environmental and host filtering underpins microbial community assembly in H. leucospilota along the pollution gradient in Hong Kong.

Random balancing-like sequences

AbstractA balancing-like sequence is a binary recurrence sequence which generalizes the balancing sequence and the sequence of nonnegative integers. This sequence, under certain assumptions, may be used to describe the growth of fortune of a person engaged in some business or profession. Since, in any business or profession, the growth is influenced by many uncertainties, it is more natural to induce some sort of randomness in the balancing-like sequences. If, in a balancing-like sequence, the growth rate is assumed to be a random variable, the resulting sequence will be a stochastic process and the sequence of expectations, in many cases, cannot be described as a binary recurrence sequence. In some cases, the growth rate of expectations increases without limit while, in some cases, it remains finite.

A Stroll Along Australian Ecosystems: Using Bioclimatic Transects to Examine Environmental Drivers of Community Assembly in Birds

ABSTRACTAimVariation in community composition along environmental gradients provides crucial information for identifying zones where species turnover is rapid and to ascertain whether compositional changes occur gradually or rather abruptly. We examined changes in bird community composition along three bioclimatic transects in Australia to test whether drivers of species turnover are consistent, rather than spatially contingent, across biologically contrasting ecosystems. We also detected potential transition zones associated with environmental thresholds and determined whether certain abiotic conditions promote a higher rate of community compositional turnover.LocationMainland Australia.TaxonTerrestrial birds.MethodsWe applied multivariate community analysis, generalised dissimilarity modelling (GDM) and threshold indicator taxa analysis (TITAN).ResultsWe observed that environmental variables are better predictors of community composition than spatial distance, which indicates that species sorting, rather than dispersal, plays a key role in structuring Australian avian communities. Annual precipitation constitutes a key driver of species turnover regardless of the analysed transect. The most humid landscapes and those with a higher tree canopy show lower spatial heterogeneity in community composition compared to those with less benign environmental conditions (e.g., dryer environments). TITAN detected significant transition points and supported the results obtained using GDM, which suggests that bird composition change along the gradients is not monotonic.Main ConclusionsOur results suggest that avian beta diversity increases with increasing environmental harshness, presumably through changes in the relative importance of stochastic versus deterministic processes. The obtained findings show that open forests and woodlands are extremely important ecosystems on this continent and deserve special attention in terms of conservation due to their vulnerability to global change. Lastly, this study exemplifies the value of combining community‐ and taxon‐based analyses to identify and interpret community thresholds, which can serve to pinpoint targets for preserving biodiversity.

Distinct bacterial and eukaryotic communities reflect the specificity of different coral reefs in the South China Sea

The microbial composition of surrounding waters is crucial for the health of coral reefs and holds significant value for understanding the complexity and environmental adaptability of coral reef ecosystems. This study reveals the spatial heterogeneity and diversity characteristics of bacterial and eukaryotic communities in different coral reef regions of the South China Sea. Chao and Shannon indices showed significant differences (p < 0.05) in diversity of bacterial and eukaryotic communities across different coral reefs. PCoA (principal coordinate analysis) indicates significant differences in community composition among regions, highlighting the crucial role of coral reef environmental heterogeneity on microbial community. NST (normalized stochasticity ratio) analysis indicates that community assembly in coral reef areas is more influenced by ecological stochastic processes. Major bacterial groups include Proteobacteria, Cyanobacteria, and Bacteroidota, while dominant eukaryotic groups include Dinophyceae, Apicomplexa, Bacillariophyta, Florideophyceae, Mamiellophyceae, Syndiniales, Prasino-Clade-VII, and Ascomycota, each showing significant abundance differences across coral reef regions (p < 0.05). High abundance of Rhodobacterales and Flavobacteriales are detected in all coral reef waters. Correlation analysis indicates that temperature, pH, and salinity are important factors affecting the bacterial and eukaryotic communities. This study reveals the spatial heterogeneity of microbial communities in coral reef regions of South China Sea and underscores the significant impact of marine environmental heterogeneity on community structure.

Space and spatially structured environmental variables account for variation in blackfly and mayfly communities in sub-tropical South African rivers

Using aquatic invertebrate assemblages for bioassessment of streams and rivers is a fast and cost-effective approach to studying the impact of environmental stressors in aquatic ecosystems. The use of aquatic invertebrates is premised on their predictable responses to environmental stressors. Assemblage structure is not, however, only influenced by environment, but also neutral processes and temporal variation. This study quantified the relative roles of the environment (niche processes), space (neutral processes) and temporal factors in structuring mayfly and blackfly assemblages at family and species levels. Asymmetric eigenvector maps in conjunction with canonical redundancy analysis and variation partitioning were used to explore the relative roles of these three factors in structuring macroinvertebrate assemblages. At a species level, flow and water temperature were more important in explaining assemblage structure than at the family level. At the family level, space was more important than temporal and environmental factors. Unexplained variation at species and family level was more than 50%. This suggests (i) caution in using family-level rapid assessments to infer the role of the environment in structuring aquatic macroinvertebrate assemblages, as neutral processes are also dominant; and (ii) that the importance of stochastic processes, such as dispersal, should not be underestimated in rapid assessments.

Instabilities and Pattern Formation in Epidemic Spread Induced by Nonlinear Saturation Effects and Ornstein–Uhlenbeck Noise

Abstract We analytically study the emergence of instabilities and the consequent steady-state pattern formation in a stochastic partial differential equation (PDE) based, compartmental model of spatiotemporal epidemic spread. The model is characterized by: (1) strongly nonlinear forces representing the infection transmission mechanism and (2) random environmental forces represented by the Ornstein–Uhlenbeck (O–U) stochastic process which better approximates real-world uncertainties. Employing second-order perturbation analysis and computing the local Lyapunov exponent, we find the emergence of diffusion-induced instabilities and analyze the effects of O–U noise on these instabilities. We obtain a range of values of the diffusion coefficient and correlation time in parameter space that support the onset of instabilities. Notably, the stability and pattern formation results depend critically on the correlation time of the O–U stochastic process; specifically, we obtain lower values of steady-state infection density for higher correlation times. Also, for lower correlation times the results approach those obtained in the white noise case. The analytical results are valid for lower-order correlation times. In summary, the results provide insights into the onset of noise-induced, and Turing-type instabilities in a stochastic PDE epidemic model in the presence of strongly nonlinear deterministic infection forces and stochastic environmental forces represented by Ornstein–Uhlenbeck noise.

The contribution of seasonal variations and Zostera marina presence to the bacterial community assembly of seagrass bed sediments

BackgroundMicroorganisms play pivotal roles in seagrass ecosystems by facilitating material and elemental cycling as well as energy flux. However, our understanding of how seasonal factors and seagrass presence influence the assembly of bacterial communities in seagrass bed sediments is limited. Employing high-throughput sequencing techniques, this study investigates and characterizes bacterial communities in the rhizosphere of eelgrass (Zostera marina) and the bulk sediments across different seasons. The research elucidates information on the significance of seasonal variations and seagrass presence in impacting the microbial communities associated with Zostera marina.ResultsThe results indicate that seasonal variations have a more significant impact on the bacterial community in seagrass bed sediments than the presence of seagrass. We observed that the assembly of bacterial communities in bulk sediments primarily occurs through stochastic processes. However, the presence of seagrass leading to a transition from stochastic to deterministic processes in bacterial community assembly. This shift further impacts the complexity and stability of the bacterial co-occurrence network. Through LEfSe analysis, different candidate biomarkers were identified in the bacterial communities of rhizosphere sediments in different seasons, indicating that seagrass may possess adaptive capabilities to the environment during different stages of growth and development.ConclusionsSeasonal variations play a significant role in shaping these communities, while seagrass presence influences the assembly processes and stability of the bacterial community. These insights will provide valuable information for the ecological conservation of seagrass beds.

TT Arietis: New approach to the analysis of quasi-periodic oscillations

TT Arietis (TT Ari) is a nova-like cataclysmic variable of the VY Scl subtype with light-curve variations on multiple timescales. In addition to the superhump modulation, quasi-periodic oscillations (QPOs) have been found. Our aim is to determine the occurrence, strength, and variability of QPOs in TT Ari based on more complete data than in previous works. The data were obtained during the high state of TT Ari in October 2012 by the MOST space telescope, covering a total of 361.2 hours of continuous observation. We searched for frequencies over subsets of time using a Fourier-like power spectrum and then added the frequencies together, forming groups. Our method has revealed QPOs that occur in `frequency groups', which are events with a continuous oscillation of similar, constant or slowly variable frequency. We report a total of 160 frequency groups in the period range between 14 and 53 minutes (27 and 98 days$^ $), with two peaks in the power spectrum at 18.5 and 33.8 minutes (42.5 and 77.5 days$^ $). The duration of these frequency groups varies between 0.72 and 7.5 hours (average 2.8 hours) revealing between 3 and 18 complete cycles in the light curve. Most of them show significant frequency variations over the course of their duration. Sometimes two frequency groups occur simultaneously. An analysis with randomised data confirms that stochastic processes can only explain a fraction of the QPOs found. The occurrence of QPOs appears not to be related to the superhump phase.

Decoupled fungal and bacterial functional responses to biochar amendment drive rhizosphere priming effect on soil organic carbon mineralization

The application of biochar to soil is widely recognized as a promising strategy for enhancing the accumulation and stability of soil organic carbon (SOC), which is crucial in mitigating climate change. However, the influence of interactions between plants and biochar on soil microbial communities and their involvement in SOC mineralization and stability remains unclear. This understanding is essential for optimizing carbon (C) sequestration in systems involving plants, soil, and biochar. In this study, employing a 13C natural abundance approach, we investigated the effect of biochar on the maize rhizosphere priming effect (RPE) in paddy soil. We also examined alterations in microbial communities and functional genes related to C degradation and fixation. Over the 99 days of maize growth, biochar application increased RPE and total SOC while decreasing dissolved organic C. It also elevated soil pH, resulting in shifts in fungal and bacterial community structure, favoring oligotrophic species. Fungal and bacterial assemblies were dominated by deterministic and stochastic processes, respectively. While the abundance of fungal guilds varied irregularly, bacterial guilds were uniformly enriched under biochar-plant interactions. Functional traits such as ecoenzymatic activities, bacterial guilds, and functional genes predominantly affected RPE under biochar application. Bacterial functional genes associated with C degradation and fixation were concurrently enhanced with biochar application. Our results indicate that interactions between plants and biochar can enhance native SOC mineralization and accumulation in a short timeframe by modulating functional traits of soil microorganisms, particularly the bacterial community involved in C degradation and fixation.Graphical

Successive monoculture of Eucalyptus spp. alters the structure and network connectivity, rather than the assembly pattern of rhizosphere and bulk soil bacteria

Eucalyptus as a fast-growing timber tree plays a crucial role in maintaining wood supplication and ecosystem balance worldwide. Nonetheless, the management practices of Eucalyptus plantation in southern China have resulted in productivity decline and soil degradation due to high-intensity successive cultivation. Soil bacteria is a sensitive indicator of soil quality, how does the successive planting of Eucalyptus regulate the soil bacterial community structure for instance the abundance of oligotrophic bacteria, network complexity, and soil bacteria assembly remain ambiguity. To explicate the underlying influencing mechanisms of successive cultivation of Eucalyptus plantations on soil bacterial community structure. Four harvests of Eucalyptus plantations that underwent 0, 1, 2, and 3 times of harvesting were conducted to examine variations in the bacterial community between rhizosphere and bulk soils after successive planting of Eucalyptus. An adjacent evergreen broadleaf forest was employed as control. The present study revealed that successive planting of Eucalyptus increased and reduced the relative abundance of Chloroflexi (oligotrophic bacteria) and Proteobacteria (copiotrophic bacteria), respectively. Continuous planting of Eucalyptus did not modify the assembly pattern of soil bacterial communities, which was governed by stochastic processes. Successive planting of Eucalyptus decreased co-occurrence network complexity, and elevated the proportion of rare microorganisms in the keystone bacterial taxa. Soil particle size composition (clay, silt, sand) indirectly influenced the structure of soil bacterial communities by directly affecting pH, carbon, nutrients, and their stoichiometric ratios. Improving soil physical structure, increasing the input of soil carbon, nitrogen, and other nutrient resources, and maintaining a balanced resource allocation may be effective strategies for ensuring enhanced productivity and sustainable utilization of soil in successive Eucalyptus plantations.

Congruence between co-occurrence and trait-based networks is scale-dependent: a case study with flea parasites of small mammalian hosts.

We applied a novel framework based on network theory and a concept of modularity that estimates congruence between trait-based ( = functional) co-occurrence networks, thus allowing the inference of co-occurrence patterns and the determination of the predominant mechanism of community assembly. The aim was to investigate the relationships between species co-occurrence and trait similarity in flea communities at various scales (compound communities: across regions within a biogeographic realm or across sampling sites within a geographic region; component communities: across sampling sites within a geographic region; and infracommunities: within a sampling site). We found that compound communities within biogeographic realms were assembled via environmental or host-associated filtering. In contrast, functional and spatial/host-associated co-occurrence networks, at the scale of regional compound communities, mostly indicated either stochastic processes or the lack of dominance of any deterministic process. Analyses of congruence between functional and either spatial (for component communities) or host-associated (for infracommunities) co-occurrence networks demonstrated that assembly rules in these communities varied among host species. In component communities, stochastic processes prevailed, whereas environmental filtering was indicated in 4 and limiting similarity/competition in 9 of 31 communities. Limiting similarity/competition processes dominated in infracommunities, followed by stochastic mechanisms. We conclude that assembly processes in parasite communities are scale-dependent, with different mechanisms acting at different scales.

A doubly stochastic point process approach for spatio-temporal dynamics of crime data

Crime, in general, is at the base of crucial issues for many societies living in large cities worldwide. Indeed, crime and neighbourhood disorder may negatively impact the health of urban residents. Thus, the crime rate reduction is at the core of many local policies driven by active plans supported by police action and local authorities. Considering crime reports as a spatio-temporal point pattern, we propose spatio-temporal log-Gaussian Cox processes as a modelling framework for crimes in space and time. We model the spatial and temporal variation through generalized parametric additive and linear models, and a Gaussian space-time process approximates the residual variation. The inference is performed via Markov chain Monte Carlo through MALA algorithms. We provide short-term forecasts of future crimes and suggest a surveillance system that operates by reporting predictive probabilities. Our data come from the reported crimes in the locality of Kennedy (Bogota) over several years and several types of crimes. The police department may use our method to help allocate police resources and design crime prevention strategies and policies, such as surveillance, in specific zonal planning units.