Deterministic Model Research Articles

Nonlinear comparative analysis of Greenland and Antarctica ice cores data.

We analyze the temperature time series of the EPICA Dome C ice cores in Antarctica and of the Greenland project, Summit, with durations of 800 000 and 248 000 years, respectively, with a recent mathematical tool defined through the Fourier phases of the series, known as the J-index. This data driven index can differentiate between purely random dynamics and dynamics with a deterministic component. It is sensitive to nonlinear components and robust to the presence of noise. Our J-index data analysis shows that both Greenland and Antarctica climatic fluctuations possess deterministic traits and suggests the presence of an underlying nonlinear dynamics. Furthermore, in both regions, it reveals the simultaneous occurrence of an important global event known as the "Pelukian transgression." For Antarctica, it also detects the marine isotopic stage 11. Additionally, our calculation of the time series Hurst exponents and our detrended fluctuation analysis show the presence of long-range persistent correlations for Antarctica and anti-persistent correlations for Greenland. For the latter case, our fractal dimension determinations are indicative of a more complex climatic dynamics in Greenland with respect to Antarctica. Our results are encouraging for further development of climate variability deterministic models for these regions.

Flight Dynamic Uncertainty Quantification Modeling Using Physics-Informed Neural Networks

When attempting to develop aerodynamic models for extreme flight conditions, including high angle of attack, high rotational rates, and tumbling motion, many classical methods have challenges in accurately modeling the highly nonlinear aerodynamic effects present. Physics-informed neural networks (PINNs) have previously been shown to be a potential technique to model these nonlinear aerodynamic effects when framed as a system identification problem. PINNs are well suited to this problem as they benefit from the universal approximation abilities of neural networks while directly incorporating known physical constraints into the training process. One of the main challenges in machine learning algorithms, including PINNs, is quantifying the confidence in a deterministic model prediction. This work expands on the previous development of PINNs as an aerodynamic and system identification tool by incorporating uncertainty quantification through three ensemble methods to provide calibrated confidence intervals on both aerodynamic coefficients and propagated trajectories. This work demonstrates and evaluates these methods on a simulated F16 case study where up to 100 PINN models are trained on varying training datasets. These models provide aerodynamic coefficients directly and are used to propagate trajectories within a six-degree-of-freedom simulation environment.

Random expansive measures

The notion of expansivity and its generalizations (measure expansive, measure positively expansive, continuum-wise expansive, countably-expansive) are well known for deterministic systems and can be a useful property for studying significant type of behavior, such as chaotic one. This study aims to extend these notions into a random context and prove a relationship between relative positive entropy and random expansive measures and apply it to show that if a random dynamical system has positive relative topological entropy then the w-stable classes have zero measure for the conditional measures. We also prove that there exists a probability measure that is both invariant and expansive. Moreover, we obtain a relation between the notions of random expansive measures and random countably-expansive systems.

Inverse Modeling of Heterogeneous Structures in Electron Probe Microanalysis.

Electron probe microanalysis (EPMA) is a powerful tool for chemical characterization of materials on a microscopic scale. However, EPMA has the drawback that its information volume has a spatial extent of some 100 nm to a few µm. With the introduction of new electron sources, i.e., Schottky Thermal Field and Cold Field Emitter, where the electron beam is focused down to a few nm, measurements can be nowadays performed on the sub-micrometer scale. The goal of the work is to reveal the chemical composition of structures smaller than the excitation volume. New strategies are presented where the acquisition is performed at different positions on the sample and as a scan across a fine structure by using one or more single beam energies. Besides the well-known Monte-Carlo simulation, a deterministic model is also used. The deterministic model is based on moment equations of the Boltzmann equation. Inverse modeling is presented for several case studies. Due to the highly complex nonlinearity of the inverse model, an ill-posed and well-posed problem is shown as well. Finally, the method is extended to reconstruct 2D structures, i.e., rectangular shaped particles, with heterogeneous composition on lateral and depth scale.

Negative binomial approach: A useful application for the study of Echinococcus granulosus

Cystic Echinococcosis is a parasitic disease caused by the larvae of Echinococcus granulosus. The transmission of E. granulosus is affected by environmental changes and anthropogenic factors, which are in turn influenced by changes in the spatial and population dynamics of animals. The deterministic model can be extended stochastically to address the low prevalence rate, which is often observed in small mammal host populations, and to account for complex processes that reflect the highly widespread disease reservoirs and non-random mixing, such as the heterogeneous contact patterns of susceptible hosts with infectious materials. In this study, a mathematical model based on a set of differential equations that define the continuous transition between different classes was used is not regulated by host. The findings indicate that each protoscolex has an equal chance of developing into a worm and creating a dispersed population. Empirical modeling can be used to represent the frequency distribution of the number of parasites in each host using the negative binomial distribution.

High-dimensional multi-objective optimization of coupled cross-laminated timber walls building using deep learning

This paper introduces a deep learning-based multi-objective optimization framework, applying for advancing the design of the Cross-Laminated Timber Coupled Wall system. While traditional optimization methods often struggle with the curse of dimensionality in high-dimensional problems, the approach proposed in this study employs an autoencoder to effectively reduce the dimensionality of the design space. Subsequently, a neural network establishes a mapping between input variables and latent spaces, with another neural network forming the crucial link between these latent variables and the output responses. The proposed framework is integrated into the design process of a 20-story Cross-Laminated Timber Coupled Wall system, where uncertainties inherent in connection elements are systematically addressed to optimize the structural parameters. The non-dominated sorting genetic algorithm-II is utilized to estimate optimal design variables by minimizing three conflicting objective functions, thereby generating a Pareto front. This optimized design is then bench-marked against three deterministic models with varying coupling beam shear strengths. A two-dimensional numerical model developed in OpenSees facilitates nonlinear time history analysis using 50 bi-directional ground motion records, representative of the seismicity of Vancouver, Canada. The results of this study not only highlight the efficacy of the deep learning-based framework in enhancing the structural integrity and resilience of high-rise timber structures in seismic regions but also significantly contribute to the evolution of computational approaches in structural engineering.

A Deterministic Inventory Model with Two Warehouses and a Finite Rate of Replacement for Deteriorating Products

Abstract: When demand is uniform, shortages are permitted, and the replenishment rate is finite, a deterministic inventory model for degrading items with two warehouses is created. It is anticipated that there may be differences in the rates of item deterioration between the two warehouses. An analysis of the model is conducted for the continuous release pattern situation. The variance in the ideal inventory level and optimum cost for changing shortage costs is illustrated with a numerical example and discussion of several unique instances

A Predator–Prey System with a Modified Leslie–Gower and Prey Stage Structure Scheme in Deterministic and Stochastic Environments

The evolution of the population ecosystem is closely related to resources and the environment. Assuming that the environmental capacity of a predator population is positively correlated with the number of prey, and that the prey population has a sheltered effect, we investigated a predator–prey model with a juvenile–adult two-stage structure. The dynamical behaviour of the model was examined from two distinct environmental perspectives, deterministic and stochastic, respectively. For the deterministic model, the conditions for the existence of equilibrium points were obtained by comprehensive use of analytical and geometric methods, and the local and global asymptotic stability of each equilibrium point was discussed. For the stochastic system, the effect of noise intensity on the long-term dynamic behavior of the population was investigated. By constructing appropriate Lyapunov functions, the criteria that determined the extinction of the system and the ergodic stationary distribution were given. Finally, through concrete examples and numerical simulations, the understanding of the dynamic properties of the model was deepened. The results show that an improvement in the predator living environment would lead to the decrease in the prey population, while more prey shelters could lead to the decline or even extinction of predator populations.

Stability analysis of a nonlinear malaria transmission epidemic model using an effective numerical scheme

Malaria is a fever condition that results from Plasmodium parasites, which are transferred to humans by the attacks of infected female Anopheles mosquitos. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. More so, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The reproduction number R o\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left(o\\right)$$\\end{document} was determined to be an asymptotically stable condition for disease free and endemic equilibria. In this paper, we used various schemes such as Runge–Kutta order 4 (RK-4) and non-standard finite difference (NSFD). All of the schemes produce different results, but the most appropriate scheme is NSFD. This is true for all step sizes. Various criteria are used in the NSFD scheme to assess the local and global stability of disease-free and endemic equilibrium points. The Routh–Hurwitz condition is used to validate the local stability and Lyapunov stability theorem is used to prove the global asymptotic stability. Global asymptotic stability is proven for the disease-free equilibrium when R0≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}_{0}\\le 1$$\\end{document}. The endemic equilibrium is investigated for stability when R0≥1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}_{0}\\ge 1$$\\end{document}. All of the aforementioned schemes and their effects are also numerically demonstrated. The comparative analysis demonstrates that NSFD is superior in every way for the analysis of deterministic epidemic models. The theoretical effects and numerical simulations provided in this text may be used to predict the spread of infectious diseases.

Geological Modeling of Shale Oil in Member 7 of the Yanchang Formation, Heshui South Area, Ordos Basin

In recent years, the Chang 7 member of the Mesozoic Triassic Yanchang Formation in the Ordos Basin has emerged as a significant repository of abundant and distinctive unconventional oil resources. The Heshui area boasts substantial shale oil reserves, with reported third-level reserves surpassing 600 million tons. However, the region in the southern part of Heshui is marked by pronounced variability in reservoir quality, intricate oil–water dynamics, low formation energy, and suboptimal fluid properties, leading to divergent development outcomes for horizontal wells. There is an imperative need to devise and refine new geological models to underpin the efficient exploitation of shale oil in the southern Heshui area. This study focuses on the shale oil reservoir of the Chang 7 member in the southern Heshui area of the Ordos Basin, conducting detailed stratigraphic correlation and establishing a refined isochronous stratigraphic framework. Utilizing PetrelTM modeling software (version 2018), we integrate deterministic and stochastic modeling approaches, adhering to the principles of isochronous and phased modeling. By assessing the thickness of sand and mudstone layers and the overall stratigraphic sequence, we derive a geological probability surface. Subsequently, this surface is harnessed to constrain the lithofacies, yielding a constrained lithofacies model. Employing sequential indicator simulation and sequential Gaussian stochastic simulation, we develop a reservoir attribute model that is anchored in the lithofacies model and its controls, culminating in a robust and dependable static model. Employing the geological probability surface constraint method, we meticulously construct the reservoir matrix model, amalgamating individual well data with the inherent certainty and randomness of reservoir plane thickness. This approach further enhances the model’s accuracy and mitigates the uncertainty and randomness associated with inter-well interpolation to a significant degree.

A Mathematical Model for the Co-infection Dynamics of Pneumocystis Pneumonia and HIV/AIDS with Treatment

The control of opportunistic infections among HIV infected individuals should be one of the major public health concerns in reducing mortality rate of individuals living with HIV/AIDS. In this study a deterministic co-infection mathematical model is developed to provide a quantification of treatment at each contagious stage against Pneumocystis Pneumonia (PCP) among HIV infected individuals on ART. The goal is to minimize the co-infection burden by putting the curable PCP under control. The disease-free equilibria for the HIV/AIDS sub-model, PCP sub-model and the co-infection model are shown to be locally asymptotically stable when their associated disease threshold parameter is less than a unity. By use of suitable Lyapunov functions, the endemic equilibria corresponding to HIV/AIDS and PCP sub-models are globally asymptotically stable whenever the HIV/AIDS related basic reproduction number <I>R</I><sub>0<I>H</I></sub> and the PCP related reproduction number <I>R</I><sub>0<I>P</I></sub> are respectively greater than a unity. The sensitivity analysis results implicate that the effective contact rates are the main mechanisms fueling the proliferation of the two diseases and on the other hand treatment efforts play an important role in reducing the incidence. The model numerical results reveal that PCP carriers have a considerable contribution in the transmission dynamics of PCP. Furthermore, treatment of PCP at all contagious phases significantly reduces the burden with HIV/AIDS and PCP co-infection.

The Application of Differentiated Pricing Strategy in M&A Practice of Listed Companies

In recent years, with the continuous active market of listed companies M&A and reorganization, the phenomenon of differentiated transaction pricing M&A is very common. In order to quickly shorten the transaction process, the initial design of the transaction plan needs to pay attention to the demands of the transaction parties, and the application of differentiated pricing strategy meets the diversified needs of the transaction parties. Based on the historical wave of M&A and the development status of Chinese listed companies, this paper analyzes the applicability and defects of M&A pricing of Chinese listed companies from the point of view of the core issue in the M&A process. This paper studies the pricing problem from two aspects. First, starting from the deterministic system, it analyzes the pricing of M&A enterprises under the perfect market system. The second is from the actual situation of China, the use of AMPS model for analysis. The research results show that the practice of differentiated pricing strategy of listed companies can not only deepen the understanding of the role of corporate governance in M&A, but also promote the effective risk control and profit maximization of listed companies. The research significance is to have a further understanding of the M&A pricing of China's joint-stock enterprises.

Cashflow-driven investment beyond expectations

ABSTRACT This paper presents a computationally tractable optimization model for cashflow-driven investment where the aim is to find asset portfolios whose future payouts cover given liability payments as well as possible. While current industry solutions are largely based on expected future cash flows, we use a stochastic optimization model that seeks portfolios that give the best possible match across time as well as scenarios. Cashflow matching across scenarios is controlled by risk aversion while the timing is driven by illiquidity of money markets. When illiquidity increases, the hedging strategy quickly shifts towards portfolios suggested by deterministic models, but significant uncertainty remains. The model can incorporate hundreds of quoted instruments in the construction of optimal hedging strategies. The hedging strategies are able to employ any statistical connections between the liabilities and publicly quoted assets. The model is solved with simple Monte Carlo approximations and off-the-shelf convex optimization software. Besides optimal hedging strategies, we find the least cost of hedging which provides a market-consistent valuation based on the current quotes and the liquidity factors as well as the views and risk preferences of the investor/regulator. The approach is illustrated by pricing and hedging defined benefit pension liabilities which depend on uncertain longevity developments and the consumer price index. The hedging strategies are constructed from 128 publicly quoted instruments including index-linked bonds and equities. We find that the optimized hedging strategies achieve lower risk at a lower cost than the strategies obtained by matching expected cashflows. The hedging-based liability valuations are robust with respect to model parameters and the additional risk reduction achieved by optimization does not add much to the overall hedging cost.

Extension of dual equivalent linearization to analysis of deterministic dynamic systems: Part 2—multi-parameter equivalent linearization

Extension of dual equivalent linearization to analysis of deterministic dynamic systems: Part 2—multi-parameter equivalent linearization

Testing and Treatment Interventions in Community Settings Key to Controlling a Recent Human Immunodeficiency Virus Outbreak Among People Who Inject Drugs in Glasgow: A Modeling Study.

A human immunodeficiency virus (HIV) outbreak was identified among people who inject drugs (PWID) in Glasgow in 2015, with >150 diagnoses by the end of 2019. The outbreak response involved scaling up HIV testing and improving HIV treatment initiation and retention. We parameterized and calibrated a dynamic, deterministic model of HIV transmission among PWID in Glasgow to epidemiological data. We use this model to evaluate HIV testing and treatment interventions. We present results in terms of relative changes in HIV prevalence, incidence, and cases averted. If the improvements in both testing and treatment had not occurred, we predict that HIV prevalence would have reached 17.8% (95% credible interval [CrI], 14.1%-22.6%) by the beginning of 2020, compared to 5.9% (95% CrI, 4.7%-7.4%) with the improvements. If the improvements had been made on detection of the outbreak in 2015, we predict that peak incidence would have been 26.2% (95% CrI, 8.8%-49.3%) lower and 62.7% (95% CrI, 43.6%-76.6%) of the outbreak cases could have been averted. The outbreak could have been avoided if the improvements had already been in place. Our modeling suggests that the HIV testing and treatment interventions successfully brought the HIV outbreak in Glasgow under control by the beginning of 2020.

Modelling the implementation of narrow versus broader spectrum antibiotics in the empiric treatment of E. coli bacteraemia

The implementation of new antimicrobial resistance stewardship programs is crucial in optimizing antibiotic use. However, prescription choices can be difficult during empiric therapy; clinicians must balance the survival benefits of broader spectrum antibiotics with associated increases in resistance. The aim of this study was to evaluate the overall feasibility of switching to narrow spectrum antibiotics during the empiric treatment of E. coli bacteraemia by quantifying changes in resistance rates, antibiotic usage, and mortality using a deterministic state-transition model. Three unique model scenarios (A, B, and C), each representing a progressively broader spectrum empiric treatment regimen, were used to compare outcomes at 5 years. We show that the empiric use of the narrowest spectrum (first-line) antibiotics can lead to reductions in resistance to second-line antibiotics and the use of third-line antibiotics, but they also lead to increases in resistance to first-line therapy and higher mortality. Crucially, we find that shortening the duration of empiric and overall treatment, as well as reducing the baseline mortality rate, are important for increasing the feasibility of switching to narrow spectrum antibiotics in the empiric treatment of E. coli bacteraemia. We provide a flexible model design to investigate optimal treatment approaches for other bacterial infections.

Quantum Effects in Synaptic Activity: Challenging the Deterministic Model of Neural Processes

Quantum Effects in Synaptic Activity: Challenging the Deterministic Model of Neural Processes

Policy gradient methods for designing dynamic output feedback controllers

This paper proposes model-based and model-free policy gradient methods (PGMs) for designing dynamic output feedback controllers for discrete-time partially observable deterministic systems without noise. To fulfill this objective, we first show that any dynamic output feedback controller design is equivalent to a state-feedback controller design for a newly introduced system whose internal state is a finite-length input–output history (IOH). Next, based on this equivalence, we propose a model-based PGM and show its global linear convergence by proving that the Polyak–Łojasiewicz inequality holds for a reachability-based lossless projection of the IOH dynamics. Moreover, we propose a model-free implementation of the PGM with a sample complexity analysis. Finally, the effectiveness of the model-based and model-free PGMs is investigated through numerical simulations.

Simulation of geological uncertainty based on improved three-dimensional coupled Markov chain model

The natural stratigraphic distribution is uncertain due to the geological tectonic movements and sedimentation. It is a challenge for traditional deterministic models to capture geological uncertainty. The objective of this study is to develop an improved three-dimensional coupled Markov chain (ICMC3D) model based on limited boreholes. The proposed method enhances the traditional three-dimensional coupled Markov chain model by modifying the transition probability equation for predicting unknown elements. The dip data is added to estimate the transition probability matrix with the borehole information. On this basis, a back analysis method is proposed for estimating the horizontal transition probability matrics. The method makes the predicted results more suitable for the possible stratigraphic distribution. The accuracy of the proposed method is verified through some applications. In this paper, an improved three-dimensional coupled Markov chain model and transition probability matrix estimation method are illustrated by the borehole data collected from a tunnel project in Qingdao. The results show that the presented method can reflect the asymmetry, continuity and anisotropy of the three-dimensional stratum. The exceedance probability is proposed to predict the fault zone development range in order to reduce the geological uncertainty.

DiffPoseTalk: Speech-Driven Stylistic 3D Facial Animation and Head Pose Generation via Diffusion Models

The generation of stylistic 3D facial animations driven by speech presents a significant challenge as it requires learning a many-to-many mapping between speech, style, and the corresponding natural facial motion. However, existing methods either employ a deterministic model for speech-to-motion mapping or encode the style using a one-hot encoding scheme. Notably, the one-hot encoding approach fails to capture the complexity of the style and thus limits generalization ability. In this paper, we propose DiffPoseTalk, a generative framework based on the diffusion model combined with a style encoder that extracts style embeddings from short reference videos. During inference, we employ classifier-free guidance to guide the generation process based on the speech and style. In particular, our style includes the generation of head poses, thereby enhancing user perception. Additionally, we address the shortage of scanned 3D talking face data by training our model on reconstructed 3DMM parameters from a high-quality, in-the-wild audio-visual dataset. Extensive experiments and user study demonstrate that our approach outperforms state-of-the-art methods. The code and dataset are at https://diffposetalk.github.io.