Stochastic Calculations Research Articles

Simulation of topological data using a stochastic model applied to protein engineering

Topological data analysis (TDA) is a powerful tool used to extract meaningful properties from the topological structure of data, enabling the discovery of complex relationships and patterns within datasets. It provides a unique perspective by focusing on the shape and structure of data rather than traditional statistical methods. In our research, we aim to explore the impact of stochastic processes on TDA. Specifically, we investigate how introducing stochastic calculations can enhance the analysis of topological features, offering a more nuanced understanding of the data. Stochastic processes account for randomness and variability, which are inherent in many real-world datasets. By integrating these processes into TDA, we can uncover more precise relationships between data points and obtain deeper insights into the underlying topological structures. Our work highlights the advantages of this approach, particularly in improving the robustness and accuracy of TDA in the presence of noise and variability. The results of this research have the potential to broaden the applicability of TDA in fields such as biology, neuroscience, and machine learning, where complex data structures are common, and stochastic behavior often plays a critical role in shaping the data’s characteristics.

GW with hybrid functionals for large molecular systems

A low-cost approach for stochastically sampling static exchange during time-dependent Hartree–Fock-type propagation is presented. This enables the use of an excellent hybrid density functional theory (DFT) starting point for stochastic GW quasiparticle energy calculations. Generalized Kohn–Sham molecular orbitals and energies, rather than those of a local-DFT calculation, are used for building the Green function and effective Coulomb interaction. The use of an optimally tuned hybrid diminishes the starting point dependency in one-shot stochastic GW, effectively avoiding the need for self-consistent GW iterations.

Pulse instabilities can shape virus-immune coevolution

Adaptive immune systems engage in an arms race with evolving viruses, trying to generate new responses to viral strains that continually move away from the set of genetically varying strains that have already elicited a functional immune response. It has been argued that this dynamical process can lead to a propagating pulse of an ever-changing viral population and concomitant immune response. Here, we introduce a new stochastic model of viral-host coevolution, taking into account finite-sized host populations and varying processes of immune “forgetting”. Using both stochastic and deterministic calculations, we show that there is indeed a possible pulse solution, but for a large host population size and for finite memory capacity, the pulse becomes unstable to the generation of new infections in its wake. This instability leads to an extended endemic infection pattern, demonstrating that the population-level behavior of virus infections can exhibit a wider range of behavior than had been previously realized. Published by the American Physical Society 2024

Deterministic and stochastic computational models for the analysis of Nuclear Power Plant (NPP) start-up operations

The aim of this paper is to present an overview of both the deterministic and stochastic aspects of nuclear power plant (NPP) start-up and start-up accident scenarios. The neutron kinetics and corresponding nuclear reactor control mechanisms associated with deterministic NPP start-up are explained. The stochastic behaviour of neutron kinetics is explained and the procedures required to safely start-up an NPP due to these stochastic phenomena are outlined. Specific attention is given to the stochastic behaviour of neutrons in a low neutron source regime and the corresponding mathematical methods required for modelling such phenomena during NPP start-up accidents. The Pál-Bell equations are compared against the forward generating function equations utilising the gamma approximation in their ability to model NPP start-up accidents. The Pál-Bell equations are shown to be necessary to accurately calculate the maturity time for systems with either a very low neutron source strength or a very rapid reactivity insertion profile. Both the Hurwitz calculation route and MacMillan calculation route for low neutron source systems are explained. Full deterministic and stochastic calculations are performed for multiple nuclear reactor systems to illustrate the necessary analyses required for low neutron source NPP start-up accident scenarios.

Experimental Validation of Radiance-Based Methods for Simulating Solar Penumbras and Pinhole Projections

ABSTRACT The sun’s vast size creates two distinct shadow phenomena on Earth: solar penumbras and pinhole projections. These sunlight effects are particularly important in daylight perception research and exacting daylighting design. As such, a method to generate accurate and efficient lighting simulations of these sunlight effects is needed to facilitate research and design applications. The present study is the first to investigate the accuracy of three Radiance-based methods for generating solar penumbras and pinhole projections against real-world measurements using various semi-controlled scenarios. In addition, we examine the applicability of these methods in terms of simulation time and file size. These methods involve the use of Radiance’s direct jittering algorithm, utilizing solely Radiance’s stochastic calculation, and subdividing a Radiance sun into many small suns. The simulation results of solar penumbras and pinhole projections per method are compared to real-world measurement data and assessed on their applicability. The results show that employing a subdivided sun offers an accurate and efficient method for simulating scenes with solar penumbras and pinhole projections using Radiance.

Modeling of ice-matrix composite fracture

This article discusses the results of a study that used the structural approach to conduct multiscale modeling of composite materials. These materials are composed of an ice matrix that has been enhanced with high-strength basalt fibers. The research involved numerical modeling to analyze the fracture process of composite materials made by freezing fresh water with added basalt fibers. The analysis included experimental data from samples of pure ice and composites with different amounts of filler. The effective modulus of elasticity of the composites was determined by considering the quantity of basalt fiber reinforcement. The discrepancy between the strength obtained by finite element complex ANSYS numerical calculation and the experimental data was revealed by a series of macroscopic test calculations of the composite material sample, according to which the effective modulus of elasticity of the composite was recalculated and corrections were introduced into the Voight and Reuss models, taking into account the non-uniform distribution of the fibers and the non-ideal adhesion between the fibers and water ice. A stochastic model of crack growth at the micro level was also used with the data on the diameter and length of basalt fibers and their random distribution in the layers of the composite material. Using the newly acquired effective elastic moduli and the SmartCrackGrowth algorithm, a satisfactory agreement of the crack growth rate with the obtained by stochastic calculation was achieved. The refined method of effective elastic moduli and multilevel model of stress-strain state calculation of composite materials are recommended for assessing the strength of ice cover and designing winter roads with high load-bearing capacity and long operational duration in the Arctic and Subarctic environments.

PV/PV-Battery hosting capacity estimation method based on hidden Markov model for effective stochastic computation

Monte Carlo is commonly applied to model uncertainties in the penetration of photovoltaic (PV) systems as random processes. However, Monte Carlo simulations require a large number of stochastic calculations to obtain the desired accuracy. This paper develops a hosting capacity estimation model using hidden Markov to provide an effective stochastic calculation of PV/PV-battery penetration. To improve the representative in modeling actual penetration scenarios, the proposed model considers the probabilities among candidates on the basis of the customer types, the customer with PV-only or the customer with PV-battery, and the size of the PV/PV-battery. To be used in the simulations, a technique is proposed to calculate the min–max load demand and PV generation curves. To assess the computational load of the proposed model, this work provides an accuracy evaluation with respect to the number of stochastic simulations. The findings indicate that the proposed solution can achieve a cost-effective calculation of the hosting capacity. In practice, this work can provide the distribution planner with useful direction to help make informed decisions about the distribution network reinforcement strategy to deal with high PV/PV-battery penetration.

Dimensional Dependence of Binding Kinetics.

In the context of protein-protein binding, the dissociation constant is used to describe the affinity between two proteins. For protein-protein interactions, most experimentally-measured dissociation constants are measured in solution and reported in units of volume concentration. However, many protein interactions take place on membranes. These interactions have dissociation constants with units of areal concentration, rather than volume concentration. Here, we present a novel, stochastic approach to understanding the dimensional dependence of binding kinetics. Using stochastic exit time calculations, in discrete and continuous space, we derive general reaction rates for protein-protein binding in one, two, and three dimensions and demonstrate that dimensionality greatly affects binding kinetics. Further, we present a formula to transform three-dimensional experimentally-measured dissociation constants to two-dimensional dissociation constants. This conversion can be used to mathematically model binding events that occur on membranes.

Multiple stochastic and inverse stochastic resonances with transition phenomena in complex corporate financial systems.

This study examines the role of periodic information, the mechanism of influence, stochastic resonance, and its controllable analysis in complex corporate financial systems. A stochastic predator-prey complex corporate financial system model driven by periodic information is proposed. Additionally, we introduce signal power amplification to quantify the stochastic resonance phenomenon and develop a method for analyzing stochastic resonance in financial predator-prey dynamics within complex corporate financial systems. We optimize a simplified integral calculation method to enhance the proposed model's performance, which demonstrates superiority over benchmark models based on empirical evidence. Based on stochastic simulations and numerical calculations, we can observe multiple stochastic and multiple inverse stochastic resonances. Furthermore, variations in initial financial information, periodic information frequency, and corporate growth capacity induced stochastic resonance and inverse stochastic resonance. These variations also led to state transitions between the two resonance behaviors, indicating transition phenomena. These findings suggest the potential for regulating and controlling stochastic and inverse stochastic resonance in complex corporate finance, enabling controllable stochastic resonance behaviors.

A novel stochastic power flow calculation and optimal control method for microgrid based on multivariate stochastic factors fusion – Sensitivity

The stochasticity of power flow of distributed generations (DGs) and load in the microgrid has great influence on power flow distribution and voltage quality of the distribution network. For improving the voltage quality of the distribution network, the questions need to be further studied, which include the description of the stochasticity of the power flow in the microgrid and the impact of the microgrid into the distribution network on the power flow. Therefore, a novel stochastic power flow calculation and optimal control method for the microgrid based on multivariate stochastic factors fusion-sensitivity (MSFF-sensitivity) is proposed in this paper. Firstly, the multivariate stochastic factors fusion (MSFF) function is developed by using the probability density function to extract the stochasticity and correlation of power flow among different stochastic factors in the microgrid, which are effectively unified. Furthermore, the fusion-sensitivity (F-sensitivity) of the power flow in the microgrid integrated into the distribution network is constructed to accurately characterize the influence degree of various stochastic factors in the microgrid on the power flow of the distribution network. Based on this, the output power of the stochastic factor is adjusted to optimally control the power flow of the distribution network. Finally, the algorithm verification suggests that, compared with the conventional power flow methods, the method proposed in this paper is more suitable for the microgrid. The influence of stochastic power flow on the distribution network can be effectively reduced and the voltage quality of the distribution network can be improved by optimizing control of the power flow in the microgrid integrated into the distribution network.

Risk-Informed Performance-Based methods for cyber-attack on nuclear power facilities

A new approach is described that offers a Risk-Informed Performance-Based (RIPB) framework for quantifying the risk associated with a cyber-attack on a nuclear power-generating facility. The first part of the method involves 1) the creation of a simplified 10 CFR 73.54 compliant cyber infrastructure, 2) modeling of design basis threats against the network and passive defense of the network and 3) applying the model metrics as inputs into a Bayesian analysis to calculate the exploit probability of a plant controller. The RAVEN code package was used to perform a stochastic calculation to quantify the aleatory uncertainty associated with exploiting a plant controller and produce basic statistics associated with those outputs, such as the standard deviation and standard error. Other tools, such as ADAPT, were also explored, which could be leveraged for direct DPRA analysis of network topology, such that new failure modes or initiating events could be discovered. The second aspect of the RIPB method considers the impact of the controller on the physical plant. This evaluation was conducted by postulating an accident scenario possibly caused by the dynamics of an exploited process controller, initiating that event in a RELAP5 model controlled by the RAVEN risk analysis package, and demonstrating the types of algorithms that can be used to quantify the consequences of the accident scenario. The new two-part method explored in this work provides the uncertainty associated with a cyber-initiating event and the associated consequences of a postulated accident resulting from that exploit, as well as example tools and algorithms for performing the analysis.

Update of [formula omitted]: Newly added functions and methods in versions 2 and 3

HΦ [aitch-phi] is an open-source software package of numerically exact and stochastic calculations for a wide range of quantum many-body systems. In this paper, we present the newly added functions and the implemented methods in vers. 2 and 3. In ver. 2, we implement spectrum calculations by the shifted Krylov method, and low-energy excited state calculations by the locally optimal block preconditioned conjugate gradient (LOBPCG) method. In ver. 3, we implement the full diagonalization method using ScaLAPACK and GPGPU computing via MAGMA. We also implement a real-time evolution method and the canonical thermal pure quantum (cTPQ) state method for finite-temperature calculations. The Wannier90 format for specifying the Hamiltonians is also implemented. Using the Wannier90 format, it is possible to perform the calculations for the abinitio low-energy effective Hamiltonians of solids obtained by the open-source software RESPACK. We also update Standard mode—simplified input format in HΦ—to use these functions and methods. We explain the basics of the implemented methods and how to use them. Program summaryProgram Title:HΦ [aitch-phi]CPC Library link to program files:https://doi.org/10.17632/vnfthtyctm.2Developer's repository link:https://github.com/issp-center-dev/HPhiLicensing provisions: GPLv3Programming language: C, FortranJournal reference of previous version: Comput. Phys. Commun. 217 (2017) 180–192Does the new version supersede the previous version?: Yes. The latest version has compatibility with the old versions. Although most functions are available in newer versions, some redundant/unnecessary functions were abolished in newer versions.Reasons for the new version: Implementation of new functions and methods, development of utilities, and bug fixes.Summary of revisions: We added new functions to obtain excited spectrum, low-energy excited states, and time-dependent physical quantities. We also implemented the full diagonalization method by using MAGMA on GPGPUs and finite-temperature simulations by using the canonical thermal pure quantum state method. In addition, we developed utilities for connection with RESPACK and a submodule for a generator of input files.Nature of problem: Physical properties in quantum lattice models with finite system sizesSolution method: In HΦ, we implemented several numerical methods such as the Lanczos method, the full diagonalization method, the locally optimal block preconditioned conjugate gradient (LOBPCG) method, the real-time evolution method based on the Taylor expansion, the shifted Krylov method, and the microcanonical/canonical thermal pure quantum state method.

A Robust Data-Driven Process Modeling Applied to Time-Series Stochastic Power Flow

In this paper, we propose a robust data-driven process model whose hyperparameters are robustly estimated using the Schweppe-type generalized maximum likelihood estimator. The proposed model is trained on recorded time-series data of voltage phasors and power injections to perform a time-series stochastic power flow calculation. Power system data are often corrupted with outliers caused by large errors, fault conditions, power outages, and extreme weather, to name a few. The proposed model downweights vertical outliers and bad leverage points in the measurements of the training dataset. The weights used to bound the influence of the outliers are calculated using projection statistics, which are a robust version of Mahalanobis distances of the time series data points. The proposed method is demonstrated on the IEEE 33-Bus power distribution system and a real-world unbalanced 240-bus power distribution system heavily integrated with renewable energy sources. Our simulation results show that the proposed robust model can handle up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$25\%$</tex-math></inline-formula> of outliers in the training data set.

A novel stochastic calculation scheme for dynamic response analysis of FG-GPLRC plate subject to a moving load

A novel stochastic calculation scheme for dynamic response analysis of FG-GPLRC plate subject to a moving load

Assessment of uncertainties in damping reduction factors using ANN for acceleration, velocity and displacement spectra

Structure's damping force during an earthquake is very different from what was anticipated during design. This adds uncertainty to the process of designing structures exposed to seismic loads which may be a major cause of significant variation in the seismic response reliability of these structures. This work is focused on the investigation of the structural damping uncertainties effect on the structure’s response spectra through the assessment of uncertainties in the damping reduction factors (DRF) derived from the acceleration, velocity and displacement spectra. An Artificial Neural Networks (ANN) was also developed for the stochastic DRF calculation. The Monte Carlo method, one of the methods of computational algorithms that rely on repeated random sampling to obtain numerical results, is used for the estimation of the stochastic DRF. The obtained results indicates that the difference between the deterministic and the stochastic DRF are around of 21 % for displacement and velocity and 28.7 % for acceleration spectra. As a consequence, the DRF derived from the acceleration spectra is more sensible to the uncertainties inherent on damping than the DRF obtained from displacement and velocity. Therefore, it is important to take this conclusion into account when using these factors previously. The ANN constitutes a sample and efficiency method to predict the stochastic DRF since the error obtained is always less than 6 %. Practice oriented results are searched for, to be incorporated in future seismic standards.

Dynamic reconfiguration of distribution network considering the uncertainty of distributed generation and loads

This study presents a new methodology to perform the distribution network dynamic reconfiguration (DNDR), taking into consideration the stochastic variations of loads and distributed generation (DG) of power. To solve the heavy computational burden that exists in traditional algorithms of the DNDR, this study first establishes the nodal sensitivity models to calculate the nodal variations caused by nodal power variations. Then, the DNDR is executed utilizing a co-evolutionary algorithm with the goal of loss minimization. The stochastic power flow calculations (PFCs) based on the nodal sensitivity are performed in the DNDR to handle the power fluctuations of the DGs and loads. Finally, the modified IEEE 33-bus test system and a practical distribution system are used for simulations. The simulation results validate the quickness and effectiveness of the proposed DNDR method.

Heisenberg Spin Exchange Between Nitroxide Probes Diffusing in a Percolation Network

AbstractHeisenberg spin exchange between nitroxide (Tempone) spin probes has been measured as a function of concentration in the aqueous phase of the hydrated ion exchange membrane Nafion 117. The observed fast-motional electron paramagnetic resonance spectra were analyzed in terms of the stochastic Liouville equation lineshape calculation of Freed and coworkers and the “new paradigm” for interpreting spin exchange effects proposed by Salikhov. Differences between the effective spin exchange measured from the spectrum by these methods are presented and compared, and indicate that dipolar interactions make a significant contribution to spin exchange in this system. In acidic Nafion membranes, the spin probes are deactivated over time, allowing simultaneous measurement of the decay kinetics and spin exchange as a function of paramagnetic probe concentration. Both these processes deviate from the behavior that would be expected from classical chemical kinetics in isotropic media. The results are discussed in terms of currently available models for diffusion and reaction in a percolation network.

АНАЛИЗ ВОЗНИКНОВЕНИЯ И ПРОФИЛАКТИКА ПОЖАРООПАСНЫХ РЕЖИМОВ В ЭЛЕКТРОСЕТИ АВТОМОБИЛЯ

The issues of research of fire-hazardous modes of operation of the electric network of the car are considered. Emergency modes of operation of the electrical elements of the car can lead to a fire with varying degrees of probability, depending on the service life of the machine and external influences. The article proposes a software package based on the use of stochastic calculation methods. This will allow you to get more specific information about the likelihood of a fire-hazardous emergency mode in the vehicle's electrical network, depending on external factors and its service life. It is proposed to use the results obtained for effective management of prevention and prevention of fire-hazardous modes in the vehicle's electrical network. The relevance of such information increases in the case of car parks, where the degree of operation, the brand of the manufacturer, the year of manufacture and the scheme of use of electrical elements of each car differ.

Rockfill material uncertainty inversion analysis of concrete-faced rockfill dams using stacking ensemble strategy and Jaya optimizer

Numerical simulation of concrete-faced rockfill dams (CFRDs) considering the spatial variability of rockfill has become a popular research topic in recent years. In order to determine uncertain rockfill properties efficiently and reliably, this study developed an uncertainty inversion analysis method for rockfill material parameters using the stacking ensemble strategy and Jaya optimizer. The comprehensive implementation process of the proposed model was described with an illustrative CFRD example. First, the surrogate model method using the stacking ensemble algorithm was used to conduct the Monte Carlo stochastic finite element calculations with reduced computational cost and improved accuracy. Afterwards, the Jaya algorithm was used to inversely calculate the combination of the coefficient of variation of rockfill material parameters. This optimizer obtained higher accuracy and more significant uncertainty reduction than traditional optimizers. Overall, the developed model effectively identified the random parameters of rockfill materials. This study provided scientific references for uncertainty analysis of CFRDs. In addition, the proposed method can be applied to other similar engineering structures.

Consider Carbon Emission Flow Analysis of Power System with Regards to Power Loss and Wind Power Uncertainty

A method for analyzing the impact of wind power uncertainty and active power loss on carbon emission flow in power systems is proposed. Based on the stochastic power flow calculation of wind power injection, the correlation function between wind power output and the total carbon injection rate into the system is determined. Meanwhile, the reverse power flow method is used to analyze the contribution of each unit to the active power flow in different parts of the system and calculate the corresponding carbon emissions. Under the assumption that wind power fluctuations are borne by balancing units, this method combines a conventional unit and a system node, branch, load, and active network loss correlation matrix calculation model to solve the average impact factor of wind power injection on other nodes and branches, thereby determining the uncertain characteristics of carbon emission flow in power systems under stochastic and intermittent wind power injection. The correctness and effectiveness of the method are proved by analyzing the IEEE 14-node standard example, providing new theoretical support and ideas for quantitatively evaluating the low-carbon contribution of wind power generation to the system.