Stochastic Rules Research Articles

Calibration of stochastic, agent-based neuron growth models with approximate Bayesian computation.

Understanding how genetically encoded rules drive and guide complex neuronal growth processes is essential to comprehending the brain's architecture, and agent-based models (ABMs) offer a powerful simulation approach to further develop this understanding. However, accurately calibrating these models remains a challenge. Here, we present a novel application of Approximate Bayesian Computation (ABC) to address this issue. ABMs are based on parametrized stochastic rules that describe the time evolution of small components-the so-called agents-discretizing the system, leading to stochastic simulations that require appropriate treatment. Mathematically, the calibration defines a stochastic inverse problem. We propose to address it in a Bayesian setting using ABC. We facilitate the repeated comparison between data and simulations by quantifying the morphological information of single neurons with so-called morphometrics and resort to statistical distances to measure discrepancies between populations thereof. We conduct experiments on synthetic as well as experimental data. We find that ABC utilizing Sequential Monte Carlo sampling and the Wasserstein distance finds accurate posterior parameter distributions for representative ABMs. We further demonstrate that these ABMs capture specific features of pyramidal cells of the hippocampus (CA1). Overall, this work establishes a robust framework for calibrating agent-based neuronal growth models and opens the door for future investigations using Bayesian techniques for model building, verification, and adequacy assessment.

Local volume concentration, packing domains, and scaling properties of chromatin.

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions. The SR-EV rules of return generate conformationally defined domains observed by single-cell imaging techniques. From nucleosome to chromosome scales, the model captures the overall chromatin organization as a corrugated system, with dense and dilute regions alternating in a manner that resembles the mixing of two disordered bi-continuous phases. This particular organizational topology is a consequence of the multiplicity of interactions and processes occurring in the nuclei, and mimicked by the proposed return rules. Single configuration properties and ensemble averages show a robust agreement between theoretical and experimental results including chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. Model and experimental results suggest that there is an inherent chromatin organization regardless of the cell character and resistant to an external forcing such as RAD21 degradation.

Measures of stochastic non-dominance in portfolio optimization

Stochastic dominance rules are well-characterized and widely used. This work aims to describe and better understand the situations when they do not hold by developing measures of stochastic non-dominance. They quantify the error caused by assuming that one random variable dominates another one when it does not. To calculate them, we search for a hypothetical random variable that satisfies the stochastic dominance relationship and is as close to the original one as possible. The Wasserstein distance between the optimal hypothetical random variable and the original one is considered as the measure of stochastic non-dominance. Depending on the conditions imposed on the probability distribution of the hypothetical random variable, we distinguish between general and specific measures of stochastic non-dominance. We derive their exact values for random variables with uniform, normal, and exponential distributions. We present relations to almost first-order stochastic dominance and to tractable almost stochastic dominance. Using monthly returns of twelve assets captured by the German stock index DAX, we solve portfolio optimization problems with the first-order and second-order stochastic dominance constraints. The measures of stochastic non-dominance allow us to compare the optimal portfolios with respect to different orders of stochastic dominance from a new angle. We also defined the closest dominating and closest approximately dominating portfolios. They brought a better understanding of the relationship between the two types of optimal portfolios. Using moving window analysis, the relationship of the in-sample measure of stochastic non-dominance to out-of-sample performance was studied, too.

Information Search Within a Web Page: Modeling the Full Sequence of Eye Movement Decisions, Subjective Value Updating, and First Clicks

Online retail settings often present shoppers with large, complex choice sets where they need to quickly and dynamically weigh the benefits and costs of search within each web page. We build a model of information search within a web page using eye-tracking data collected during two incentive-compatible online shopping experiments, in which participants browsed the websites of two different clothing retailers (Experiments 1 and 2), as well as previously reported data from a laboratory experiment involving choices among snack food assortments (Experiment 3). Our model incorporates features that build upon recent advances in descriptive and normative models of information sampling and search in psychology and economics. First, our model captures how people decide where to look by treating eye fixations on clickable options as a series of “split-second” decisions that depend on estimates of option attractiveness and navigation effort. Second, our model assumes that the value of each option is learned via Bayesian updating. Third, the choice to end search on the web page depends on a dynamic decision threshold. Our model outperforms benchmarks that assume random search, instant learning, fixed thresholds, nonheterogeneous thresholds, and stochastic accumulator stopping rules. Explicitly modeling the sequence of eye fixation decisions results in accurate counterfactual simulations of the effects of hypothetical product orderings on search duration and quality as verified using experimental manipulation, and it can be applied flexibly to a wide range of web-page layouts. Systematic differences across experiments highlight the importance of accounting for product familiarity, choice-set size, and the role of category outside options. This paper was accepted by Ilia Tsetlin, behavioral economics and decision analysis. Funding: This work was supported by the Jay H. Baker Retailing Center and the Wharton Behavioral Lab at the University of Pennsylvania. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.02983 .

Design Algorithmic Trading Strategies with Expert Advisor Using Linear Weighted Moving Average (LWMA) and Stochastic Oscillator Technical Indicators

Earlier this decade, the financial sector saw a paradigm change, with automated trading (AT) systems gaining popularity as essential tools for traders and investors. This research explores deeply the design and implementation of Expert Advisors (EAs) for automated financial built using a combination of the Linear Weighted Moving Average (LWMA) and Stochastic oscillator technical indicators. The EAs are built using the programming language MetaQuotes Language 4 (MLQ4) at Metatrader 4 (MT4) platform, enabling automated trade execution. It implements a machine learning genetic algorithm, trained on historical data to optimize the parameters of the LWMA and Stochastic trading rules. The core strategy relies on the LWMA to identify the overall market trend direction while the Stochastic oscillator provides additional signals for timing entry and exit points based on momentum. The EAs were coded to generate automated buy and sell signals for algorithmic trading (AT) based on a set of defined rules using thresholds for each indicators. Extensive historical backtesting using Gold (XAU/USD) currency pair across multiple timeframes from 5-minute (M5) up to 4-hour (H4) charts was conducted using 5 years of price data from 2019 to 2023 for evaluation. The goal of this study is to assess if the EAs could potentially produce consistent profits over time while minimizing drawdowns in different market conditions. The results demonstrate that the system was able to generate annual returns ranging from 3.04% up to 232.19% depending on the aggression of the timeframe settings. Meanwhile, maximum drawdowns were controlled to reasonable levels between 0.5% to 8.27% which is below 10% of potential loss throughout the backtests. An hourly timeframe configuration provided a balanced blend between strong profitability and drawdown control based on the backtest analysis. All the timeframes used for the test show positive results and the M5 timeframe is the best chosen timeframe to trade using this EAs implementation.

Estimating Probability Weighting Functions through Option Pricing Bounds

Abstract This paper proposes a novel approach to estimating the probability weighting function (PWF) of investors in the option market. We match observed option prices to the option pricing bounds under stochastic dominance rules. Using 1-month S&P 500 index option data, we find that investors could subjectively employ an inverse S-shaped probability weighting function, which increases the weights on extreme returns and asymmetrically assigns greater weights to extremely low returns than to extremely high returns. Our findings suggest that the inverse S-shaped nature of the PWFs is robust across various estimation specifications, such as adopting an alternative methodology to construct the return distribution, and employing option data with different times to maturity. (JEL G12)

Spatial transcriptome-guided multi-scale framework connects P. aeruginosa metabolic states to oxidative stress biofilm microenvironment.

With the generation of spatially resolved transcriptomics of microbial biofilms, computational tools can be used to integrate this data to elucidate the multi-scale mechanisms controlling heterogeneous biofilm metabolism. This work presents a Multi-scale model of Metabolism In Cellular Systems (MiMICS) which is a computational framework that couples a genome-scale metabolic network reconstruction (GENRE) with Hybrid Automata Library (HAL), an existing agent-based model and reaction-diffusion model platform. A key feature of MiMICS is the ability to incorporate multiple -omics-guided metabolic models, which can represent unique metabolic states that yield different metabolic parameter values passed to the extracellular models. We used MiMICS to simulate Pseudomonas aeruginosa regulation of denitrification and oxidative stress metabolism in hypoxic and nitric oxide (NO) biofilm microenvironments. Integration of P. aeruginosa PA14 biofilm spatial transcriptomic data into a P. aeruginosa PA14 GENRE generated four PA14 metabolic model states that were input into MiMICS. Characteristic of aerobic, denitrification, and oxidative stress metabolism, the four metabolic model states predicted different oxygen, nitrate, and NO exchange fluxes that were passed as inputs to update the agent's local metabolite concentrations in the extracellular reaction-diffusion model. Individual bacterial agents chose a PA14 metabolic model state based on a combination of stochastic rules, and agents sensing local oxygen and NO. Transcriptome-guided MiMICS predictions suggested microscale denitrification and oxidative stress metabolic heterogeneity emerged due to local variability in the NO biofilm microenvironment. MiMICS accurately predicted the biofilm's spatial relationships between denitrification, oxidative stress, and central carbon metabolism. As simulated cells responded to extracellular NO, MiMICS revealed dynamics of cell populations heterogeneously upregulating reactions in the denitrification pathway, which may function to maintain NO levels within non-toxic ranges. We demonstrated that MiMICS is a valuable computational tool to incorporate multiple -omics-guided metabolic models to mechanistically map heterogeneous microbial metabolic states to the biofilm microenvironment.

Taxonomic and functional β-diversity patterns reveal stochastic assembly rules in microbial communities of seagrass beds.

Microorganisms are important members of seagrass bed ecosystems and play a crucial role in maintaining the health of seagrasses and the ecological functions of the ecosystem. In this study, we systematically quantified the assembly processes of microbial communities in fragmented seagrass beds and examined their correlation with environmental factors. Concurrently, we explored the relative contributions of species replacement and richness differences to the taxonomic and functional β-diversity of microbial communities, investigated the potential interrelation between these components, and assessed the explanatory power of environmental factors. The results suggest that stochastic processes dominate community assembly. Taxonomic β-diversity differences are governed by species replacement, while for functional β-diversity, the contribution of richness differences slightly outweighs that of replacement processes. A weak but significant correlation (p < 0.05) exists between the two components of β-diversity in taxonomy and functionality, with almost no observed significant correlation with environmental factors. This implies significant differences in taxonomy, but functional convergence and redundancy within microbial communities. Environmental factors are insufficient to explain the β-diversity differences. In conclusion, the assembly of microbial communities in fragmented seagrass beds is governed by stochastic processes. The patterns of taxonomic and functional β-diversity provide new insights and evidence for a better understanding of these stochastic assembly rules. This has important implications for the conservation and management of fragmented seagrass beds.

The physical mechanism of stochastic calculus in random walks

Stochastic differential equations (SDEs) play an important role in fields ranging from physics and biology to economics. The interpretation of stochastic calculus in the presence of multiplicative noise continues to be an open question. Commonly, the choice of stochastic calculus rules is largely based on empirical knowledge and lacks quantitative substantiation. In this study, we introduce a functional method that quantitatively links stochastic calculus rules to the underlying physical mechanisms in random walks. For a given diffusion coefficient, we construct three models to exemplify the physical features of conventional stochastic calculus. Our work provides a new perspective for quantitatively addressing state-dependent noise and aims to contribute to the understanding of the physical factors underlying uncertainty in SDEs.

Simulation of Flood-Induced Human Migration at the Municipal Scale: A Stochastic Agent-Based Model of Relocation Response to Coastal Flooding

Human migration triggered by flooding will create sociodemographic, economic, and cultural challenges in coastal communities, and adaptation to these challenges will primarily occur at the municipal level. However, existing migration models at larger spatial scales do not necessarily capture relevant social responses to flooding at the local and municipal levels. Furthermore, projecting migration dynamics into the future becomes difficult due to uncertainties in human–environment interactions, particularly when historic observations are used for model calibration. This study proposes a stochastic agent-based model (ABM) designed for the long-term projection of municipal-scale migration due to repeated flood events. A baseline model is demonstrated initially, capable of using stochastic bottom-up decision rules to replicate county-level population. This approach is then combined with physical flood-exposure data to simulate how population projections diverge under different flooding assumptions. The methodology is applied to a study area comprising 16 counties in coastal Virginia and Maryland, U.S., and include rural areas which are often overlooked in adaptation research. The results show that incorporating flood impacts results in divergent population growth patterns in both urban and rural locations, demonstrating potential municipal-level migration response to coastal flooding.

Agent-based approach for elucidating the release from collective arrest of cell motion in corneal epithelial cell sheet

Changes in cell fluidity have been observed in various cellular tissues and are strongly linked to biological phenomena such as self-organization. Recent studies suggested variety of mechanisms and factors, which are still being investigated. This study aimed to investigate changes in cell fluidity in multi-layered cell sheets, by exploring the collective arrest of cell motion and its release in cultures of corneal epithelial cells. We constructed mathematical models to simulate the behaviors of individual cells, including cell differentiation and time-dependent changes in cell-cell connections, which are defined by stochastic or kinetic rules. Changes in cell fluidity and cell sheet structures were expressed by simulating autonomous cell behaviors and interactions in tissues using an agent-based model. A single-cell level spatiotemporal analysis of cell state transition between migratable and non-migratable states revealed that the release from collective arrest of cell motion was initially triggered by a decreased ability to form cell-cell connections in the suprabasal layers, and was propagated by chain migration. Notably, the disruption of cell-cell connections and stratification occurred in the region of migratable state cells. Hence, a modeling approach that considers time-dependent changes in cell properties and behavior, and spatiotemporal analysis at the single-cell level can effectively delineate emergent phenomena arising from the complex interplay of cells.

Effective precursors for self-organization of complex systems into a critical state based on dynamic series data

Many different precursors are known, but not all of which are effective, i.e., giving enough time to take preventive measures and with a minimum number of false early warning signals. The study aims to select and study effective early warning measures from a set of measures directly related to critical slowing down as well as to the change in the structure of the reconstructed phase space in the neighborhood of the critical transition point of sand cellular automata. We obtained a dynamical series of the number of unstable nodes in automata with stochastic and deterministic vertex collapse rules, with different topological graph structure and probabilistic distribution law for pumping of automata. For these dynamical series we computed windowed early warning measures. We formulated the notion of an effective measure as the measure that has the smallest number of false signals and the longest early warning time among the set of early warning measures. We found that regardless of the rules, topological structure of graphs, and probabilistic distribution law for pumping of automata, the effective early warning measures are the embedding dimension, correlation dimension, and approximation entropy estimated using the false nearest neighbors algorithm. The variance has the smallest early warning time, and the largest Lyapunov exponent has the greatest number of false early warning signals. Autocorrelation at lag-1 and Welch’s estimate for the scaling exponent of power spectral density cannot be used as early warning measures for critical transitions in the automata. The efficiency definition we introduced can be used to search for and investigate new early warning measures. Embedding dimension, correlation dimension and approximation entropy can be used as effective real-time early warning measures for critical transitions in real-world systems isomorphic to sand cellular automata such as microblogging social network and stock exchange.

A stochastic evaluation of quantum Fisher information matrix with generic Hamiltonians

Quantum Fisher information matrix (QFIM) is a fundamental quantity in quantum physics, which closely links to diverse fields such as quantum metrology, phase transitions, entanglement witness, and quantum speed limit. It is crucial in quantum parameter estimation, central to the ultimate Cramér-Rao bound. Recently, the evaluation of QFIM using quantum circuit algorithms has been proposed for systems with multiplicative parameters Hamiltonian. However, systems with generic Hamiltonians still lack these proposed schemes. This work introduces a quantum-circuit-based approach for evaluating QFIM with generic Hamiltonians. We present a time-dependent stochastic parameter-shift rule for the derivatives of evolved quantum states, whereby the QFIM can be obtained. The scheme can be executed in universal quantum computers under the family of parameterized gates. In magnetic field estimations, we demonstrate the consistency between the results obtained from the stochastic parameter-shift rule and the exact results, while the results obtained from a standard parameter-shift rule slightly deviate from the exact ones. Our work sheds new light on studying QFIM with generic Hamiltonians using quantum circuit algorithms.

Stochastic RNA editing of the Complexin C-terminus within single neurons regulates neurotransmitter release

Neurotransmitter release requires assembly of the SNARE complex fusion machinery, with multiple SNARE-binding proteins regulating when and where synaptic vesicle fusion occurs. The presynaptic protein Complexin (Cpx) controls spontaneous and evoked neurotransmitter release by modulating SNARE complex zippering. Although the central SNARE-binding helix is essential, post-translational modifications to Cpx's C-terminal membrane-binding amphipathic helix regulate its ability to control synaptic vesicle fusion. Here, we demonstrate that RNA editing of the Cpx C-terminus modifies its ability to clamp SNARE-mediated fusion and alters presynaptic output. RNA editing of Cpx across single neurons is stochastic, generating up to eight edit variants that fine tune neurotransmitter release by altering the subcellular localization and clamping properties of the protein. Similar stochastic editing rules for other synaptic genes were observed, indicating editing variability at single adenosines and across multiple mRNAs generates unique synaptic proteomes within the same population of neurons to fine tune presynaptic output.

Nonequilibrium Thermodynamics of the Majority Vote Model.

The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. This model, as well as many other stochastic lattice models, are formulated in terms of stochastic rules with no connection to thermodynamics, precluding the achievement of quantities such as power and heat, as well as their behaviors at phase transition regimes. Here, we circumvent this limitation by introducing the idea of a distinct and well-defined thermal reservoir associated to each local configuration. Thermodynamic properties are derived for a generic majority vote model, irrespective of its neighborhood and lattice topology. The behavior of energy/heat fluxes at phase transitions, whether continuous or discontinuous, in regular and complex topologies, is investigated in detail. Unraveling the contribution of each local configuration explains the nature of the phase diagram and reveals how dissipation arises from the dynamics.

Towards Efficient Federated Learning: Layer-Wise Pruning-Quantization Scheme and Coding Design.

As a promising distributed learning paradigm, federated learning (FL) faces the challenge of communication-computation bottlenecks in practical deployments. In this work, we mainly focus on the pruning, quantization, and coding of FL. By adopting a layer-wise operation, we propose an explicit and universal scheme: FedLP-Q (federated learning with layer-wise pruning-quantization). Pruning strategies for homogeneity/heterogeneity scenarios, the stochastic quantization rule, and the corresponding coding scheme were developed. Both theoretical and experimental evaluations suggest that FedLP-Q improves the system efficiency of communication and computation with controllable performance degradation. The key novelty of FedLP-Q is that it serves as a joint pruning-quantization FL framework with layer-wise processing and can easily be applied in practical FL systems.

Network topology and movement cost, not updating mechanism, determine the evolution of cooperation in mobile structured populations.

Evolutionary models are used to study the self-organisation of collective action, often incorporating population structure due to its ubiquitous presence and long-known impact on emerging phenomena. We investigate the evolution of multiplayer cooperation in mobile structured populations, where individuals move strategically on networks and interact with those they meet in groups of variable size. We find that the evolution of multiplayer cooperation primarily depends on the network topology and movement cost while using different stochastic update rules seldom influences evolutionary outcomes. Cooperation robustly co-evolves with movement on complete networks and structure has a partially detrimental effect on it. These findings contrast an established principle from evolutionary graph theory that cooperation can only emerge under some update rules and if the average degree is lower than the reward-to-cost ratio and the network far from complete. We find that group-dependent movement erases the locality of interactions, suppresses the impact of evolutionary structural viscosity on the fitness of individuals, and leads to assortative behaviour that is much more powerful than viscosity in promoting cooperation. We analyse the differences remaining between update rules through a comparison of evolutionary outcomes and fixation probabilities.

Stratonovich framework into Markovian satellite dynamics of Carleman-based filtering using energy function observables approach

In this paper the satellite system in which fluctuating aerodynamic torque and the radial perturbation about the pitch motion of orbit is analyzed. The objectives of the paper are three-fold. The first objective is the ‘Carleman linearization representation into the nonlinear stochastic evolution of the Markov process’. The second is to filter process and measurement noises in the satellite dynamics parameters in the Carleman setting. The third is to find the stability and convergence condition of satellite dynamics. The first is achieved by unifying the generating function, Carleman embedding, Itô stochastic differential rules and the finite closure with Kronecker algebra. Concerning the second objective, we recast the finite-dimensional Stochastic Differential Equations (SDE) of the satellite dynamics into a finite system of bilinear SDE via the Carleman embedding. The third objective is to achieve the Lyapunov function and asymptotic stability condition for the satellite stochastic dynamics involving the ‘Stratonovich differential’. In this paper, we demonstrate the utility of the satellite dynamics filtering in the Carleman-based filtering via ‘its convergence analysis as well as its superiority with available methods’, i.e., the benchmark extended Kalman filter, Gaussian second-order filter and Kushner–Stratonovich higher-order filter. From simulation performed it can be said that the Carleman-based filtering is superior than other benchmark filters in terms of their Absolute Filtering Error (AFE) of conditional means and conditional variances of the satellite dynamics states.

How to promote municipal household waste management by waste classification and recycling? A stochastic tripartite evolutionary game analysis

Municipal household waste management (MHWM) is crucial for urban governance and sustainable development. Currently, Chinese governments at all levels are making great effort to implement MHWM through waste classification and recycling (WCR). However, the major participants in WCR, such as urban residents, property management companies and government departments, may act in their self-interest and hinder the MHWM goals. Therefore, it has become an imperative initiative to promote MHWM by effectively coordinate their conflicts of interest. Considering that external factors with complexity and uncertainty may also affect participants' behaviors, we develop a stochastic tripartite evolutionary game to model behavioral interaction of the three participants. Then we derive theoretical results and simulate different scenarios to examine the effects of key factors on participants’ strategy evolution. The results show that stochastic interference, cost reduction and rules simplification contribute to WCR of MHWM, and reward and performance improvement benefits have different incentive effects. Moreover, credit-based punishment and disclosure of non-compliance are more effective than financial-based penalty. To promote MHWM, policymakers should not only simplify classification rules, lower participation cost and enhance credit-based punishment system, but also encourage anonymous report and apply well-designed financial-based incentive and penalty.

Customer satisfaction evaluation for drugs: A research based on online reviews and PROMETHEE-Ⅱ method.

Online reviews of consumers after purchasing drugs online reflect the factors affecting their satisfaction. How to understand customer satisfaction through online reviews and tapping their needs to improve satisfaction has become an urgent issue facing pharmaceutical e-commerce companies. Based on the online reviews of Alibaba Health Pharmacy, six representative OTC online medicines were selected for this study, including the following categories: tonics, anti-cold drugs, rheumatism and orthopaedic drugs, skin drugs, gastrointestinal drugs, vitamins, and calcium. By training and testing the LDA topic model, five potential topics are extracted as factors affecting customer satisfaction, including drug efficacy, drug cost performance, online customer service, logistics and transportation, and packaging. In this paper, Sentiment Analysis is used to process the review text to quantify the sentiment tendency of the review, and determine the evaluation scale value. Then, the random dominance among various drug factors is determined based on the Stochastic Dominance Rules. Finally, the PROMETHEE-Ⅱ method is used to determine the ranking value of the importance of each factor. The results suggest that the factors in different types of OTC drugs rank differently, which is also rationalized in this paper. This study provides a significant reference for improving customer satisfaction with pharmaceutical e-commerce.