Continuous Time Research Articles

Diffusion in Porous Rock Is Anomalous.

Molecular diffusion of chemical species in subsurface environments─rock formations, soil sediments, marine, river, and lake sediments─plays a critical role in a variety of dynamic processes, many of which affect water chemistry. We investigate and demonstrate the occurrence of anomalous (non-Fickian) diffusion behavior, distinct from classically assumed Fickian diffusion. We measured molecular diffusion through a series of five chalk and dolomite rock samples over a period of about two months. We demonstrate that in all cases, diffusion behavior is significantly different than Fickian. We then analyze the results using a continuous time random walk framework that can describe anomalous diffusion in heterogeneous porous materials such as rock. This methodology shows extreme long-time tailing of tracer advance as compared to conventional Fickian diffusion processes. The finding that distinct anomalous diffusion occurs ubiquitously implies that diffusion-driven processes in subsurface zones should be analyzed using tools that account for non-Fickian diffusion.

Novel non-linear models for clinical trial analysis with longitudinal data: A tutorial using SAS for both frequentist and Bayesian methods.

Longitudinal data from clinical trials are commonly analyzed using mixed models for repeated measures (MMRM) when the time variable is categorical or linear mixed-effects models (ie, random effects model) when the time variable is continuous. In these models, statistical inference is typically based on the absolute difference in the adjusted mean change (for categorical time) or the rate of change (for continuous time). Previously, we proposed a novel approach: modeling the percentage reduction in disease progression associated with the treatment relative to the placebo decline using proportional models. This concept of proportionality provides an innovative and flexible method for simultaneously modeling different cohorts, multivariate endpoints, and jointly modeling continuous and survival endpoints. Through simulated data, we demonstrate the implementation of these models using SAS procedures in both frequentist and Bayesian approaches. Additionally, we introduce a novel method for implementing MMRM models (ie, analysis of response profile) using the nlmixed procedure.

P-adic Brownian motion is a scaling limit

A p-adic Brownian motion is a continuous time stochastic process in a p-adic state space that has a Vladimirov operator as its infinitesimal generator. The current work shows that any such process is the scaling limit of a discrete time random walk on a discrete group. Earlier work required the exponent of the Vladimirov operator to be in (1,∞) , and the convergence was the weak convergence of probability measures on the Skorohod space of paths on a compact time interval. The current approach simplifies the earlier approach, allows for any positive exponent, eliminates the restriction to compact time intervals, and establishes some moment estimates for the discrete time processes that are of independent interest.

An embedding model for temporal knowledge graphs with long and irregular intervals

As the basis of various downstream applications such as automated question answering and knowledge reasoning, Temporal Knowledge Graph (TKG) embedding learning has attracted many interests. Recent works have explored several methods to learn dynamic embedding for TKGs and led to success in many applications, however, they are difficult to be optimized. In order to accurately catch semantic information propagation of entity-to-entity and entity-to-relation, as well as track dynamics of entities and relations in continuous time, we proposed a novel TKG embedding model ODETKGE. Instead of using recurrent neural network to model dynamics of semantic representations in continuous time, we leverage neural ordinary differential equations to model the dynamic evolution, which enable us to capture long-range dependencies between embeddings at different timestamps, track the dynamics of TKGs with irregular intervals and remain computationally efficient. Furthermore, to effectively model semantics of knowledge graph structure, we combine entity-relation collaboratively updated graph convolutional networks and neural ordinary differential equations. Additionally, to acquire important semantics such as creation and disappearance of relations, we utilize a graph transition layer. Comparing with RNN based models, the proposed ODETKGE can use fewer parameters to achieve deeper layers, and make the transformation of representations between two timestamps smoother. Extensive experiments have been executed on real-world datasets and the results verify that ODETKGE is superior than the state-of-the-art models in link forecasting, long-interval link forecasting, irregular-interval link forecasting, ablation study and training time.

Statistical design and analysis of controlled human malaria infection trials

BackgroundMalaria is a potentially life-threatening disease caused by Plasmodium protozoa transmitted by infected Anopheles mosquitoes. Controlled human malaria infection (CHMI) trials are used to assess the efficacy of interventions for malaria elimination. The operating characteristics of statistical methods for assessing the ability of interventions to protect individuals from malaria is uncertain in small CHMI studies. This paper presents simulation studies comparing the performance of a variety of statistical methods for assessing efficacy of intervention in CHMI trials.MethodsTwo types of CHMI designs were investigated: the commonly used single high-dose design (SHD) and the repeated low-dose design (RLD), motivated by simian immunodeficiency virus (SIV) challenge studies. In the context of SHD, the primary efficacy endpoint is typically time to infection. Using a continuous time survival model, five statistical tests for assessing the extent to which an intervention confers partial or full protection under single dose CHMI designs were evaluated. For RLD, the primary efficacy endpoint is typically the binary infection status after a specific number of challenges. A discrete time survival model was used to study the characteristics of RLD versus SHD challenge studies.ResultsIn a SHD study with the continuous time survival model, log-rank test and t-test are the most powerful and provide more interpretable results than Wilcoxon rank-sum tests and Lachenbruch tests, while the likelihood ratio test is uniformly most powerful but requires knowledge of the underlying probability model. In the discrete time survival model setting, SHDs are more powerful for assessing the efficacy of an intervention to prevent infection than RLDs. However, additional information can be inferred from RLD challenge designs, particularly using a likelihood ratio test.ConclusionsDifferent statistical methods can be used to analyze controlled human malaria infection (CHMI) experiments, and the choice of method depends on the specific characteristics of the experiment, such as the sample size allocation between the control and intervention groups, and the nature of the intervention. The simulation results provide guidance for the trade off in statistical power when choosing between different statistical methods and study designs.

The spectrum of asymptotic Cayley trees

Abstract We characterize the spectrum of the transition matrix for simple random walk on graphs consisting of a finite graph with a finite number of infinite Cayley trees attached. We show that there is a continuous spectrum identical to that for a Cayley tree and, in general, a non-empty pure point spectrum. We apply our results to studying continuous time quantum walk on these graphs. If the pure point spectrum is nonempty the walk is in general confined with a nonzero probability.

Abstract PO5-24-09: Optimizing the Therapeutic Treatment of Breast Cancer Through a Dual Data-driven Theoretical Model

Abstract Despite rapid advancements in treatments and technology, breast cancer remains the second leading cause of cancer related morbidity in women in the US. As a heterogeneous disease, the unique genetic and phenotypic profile of each tumor complicates the prediction of treatment responses and optimized treatment strategies. One primary manifestation of phenotypic plasticity and concomitant intra-tumoral heterogeneity is the Epithelial-Mesenchymal Transition (EMT). The acquisition of migratory and invasive properties through EMT facilitates tumor metastasis and results in worse patient outcomes. As a result, the EMT and its reverse process (MET) often influence treatment response. However, the different mechanisms through which these therapeutic drugs affect the EMT-related phenotypic switching rates as well as each phenotype’s replication rates are unclear, and further investigation is required for better understanding their precise effect for directing optimal treatment strategies and improved patient outcomes. Here, we compile an atlas of publicly available metastatic and non-metastatic RNA sequencing data of breast cancer cell lines treated with therapeutic and chemotherapeutic drugs and propose a dual data-driven theoretical framework for understanding the effects of each drug on breast cancer treatment response. We infer the cell fractions, EMT phenotypic transition rates and phenotypic replication rates of each case through an extension of our previously developed hybrid data-driven and theoretical model, COMET. We infer single-cell RNA sequencing-derived EMT-related trajectories and apply a continuous time Markov chain model to infer inter-state transition rates. By analyzing the atlas of RNA sequencing data and integration with our framework, we gain novel insights into the context-specific mechanisms by which therapeutic drugs affect the phenotypic transition rates. This comprehensive understanding will contribute to optimizing breast cancer therapy and ultimately improving patient outcomes. Citation Format: A. Najafi. Optimizing the Therapeutic Treatment of Breast Cancer Through a Dual Data-driven Theoretical Model [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO5-24-09.

Physics-informed neural networks in groundwater flow modeling: Advantages and future directions

In recent years, there has been enormous development in soft computing, especially artificial intelligence (AI), which has developed robust methods for solving complex engineering problems. Researchers in the field of water resources engineering have applied these AI methods to solve a variety of hydrological problems. Despite their widespread use in the surface and atmospheric hydrology fields, groundwater hydrologists have not widely used AI methods in their routine field-scale modeling efforts. This is because AI models have been primarily considered black box models that lack physical meaning. Furthermore, using AI models to generate the space-time distribution of transient groundwater level variations is challenging and requires further flux balance and mass transport analyses. More recently, a new type of physics-informed neural network (PINN) model has been developed to address several limitations by integrating governing physics (groundwater flow equations) into the AI tools. This study presents the systematic advantages of the PINN algorithm for solving groundwater problems using a set of classic test problems. As discussed in detail in the article, these advantages and potentials are associated with the meshless nature of PINN, its continuous time and space dimensions, its independence from time-stepping and incremental marching in space, and its efficiency in running time. However, despite PINN's promising attributes, it is important to acknowledge its nascent stage of development and the inherent limitations of all neural network models, such as training challenges and hyperparameter selection. Thus, collaborative efforts between groundwater modelers and computer scientists are imperative to explore and exploit the full potential of PINN in tackling increasingly complex groundwater problems and nurturing PINN into a dependable modeling tool in industry and academia.

Extended State Observer-Based Continuous Finite Time Control for a Fixed-Wing Vertical Take-Off and Landing Unmanned Aerial Vehicle

Dual system Vertical Take-Off and Landing (VTOL) fixed-wing Unmanned Aerial Vehicles (UAVs) combine the advantages of both the rotorcraft and fixed-wing UAV, characterizing horizontal and vertical flight capabilities. However, they face challenges such as aerodynamic coupling between propulsion systems, model uncertainty, and external disturbances, significantly deteriorating the tracking accuracy and robustness. This paper proposes an Extended State Observer based Continuous Finite-Time Control (ESO-CFTC) scheme to solve the attitude and trajectory tracking problem of such a VTOL fixed-wing UAV. Initially, the Nonsingular Fast Terminal Sliding Mode (NFTSM) controller guarantees the tracking errors reach a prescribed manifold in finite time with a continuous reaching law, then converge to the origin in finite time while avoiding singularities. To suppress the inherent chattering problem of the sliding mode control, an ESO technique is incorporated into the ESO-CFTC scheme, which is completely decoupled with the basic NFTSM controller. The supremum of the estimation residual set is derivated theoretically. The scheme forces the tracking errors to converge into the neighborhood of the origin in finite time without requiring prior knowledge of lumped disturbance supremum values. Finally, the numerical simulation results in a Matlab/Simulink environment demonstrate that the presented method outperforms existing benchmark in terms of disturbance estimation, tracking accuracy, convergence rate, and robustness.

Time-dependent dispersion coefficients for the evolution of displacement fronts in heterogeneous porous media

We present an approach for the quantification of displacement fronts in heterogeneous porous media based on the concept of time-dependent apparent dispersion coefficients. The concept of constant asymptotic macrodispersion generally overestimates the area swept by a displacement front and leads to unrealistic upstream dispersion. We show that the large-scale front spreading can be captured by a one-dimensional advection–dispersion equation that is parameterized by a suitably chosen, temporally evolving dispersion coefficient. For purely advective front spreading, we derive an analytical expression based on a predictive continuous time random walk approach, which applies to highly heterogeneous porous media. This analysis elucidates the variability of solute travel times as the key longitudinal spreading mechanisms. It shows that the evolution of dispersion can be captured the sum of exponentials that decay on two dominant time scales. In a particle-based picture, these scales mark the (short) time at which transported particles start exploring the flow variability, and the (large) time at which the slowest particles start decorrelating their transport velocity. Based on these insights, we propose a heuristic formula that accounts for the impact of local scale dispersion as an additional decorrelation mechanisms. The heuristic expression for the longitudinal dispersion coefficient captures solute spreading for a broad range of Péclet numbers and heterogeneity variances. The proposed approach is tested against direct numerical simulations. It provides a robust and fast method for quantifying the evolution of displacement fronts in heterogeneous porous media, with possible applications, for example, in the modelling of groundwater contamination, underground gas storage, and geothermal energy production.

Unified predictive modeling of supercontinuum spectra: Using multi-material data with Closed-Form Continuous Time Neural Networks

This paper explores the application of the Closed-Form Continuous-Time Neural Networks (CfC) model in predicting supercontinuum spectra in a unified dataset of various core materials in a planar waveguide. Through numerical simulations and dataset generation, the study constructs a robust model capable of accurately predicting spectral behavior under different conditions and material variation. Initially, the unified dataset comprises spectral data for three materials: Silicon Nitride (Si3N4), Lithium Niobate (LiNbO3), and Silicon Carbide (SiC). The CfC model demonstrates remarkable accuracy in capturing spectral nuances and exhibits a minimal Mean Squared Error (MSE) loss value of 7.2537×10−4. Subsequently, the dataset is expanded to include Tantalum Pentoxide (Ta2O5), introducing a fourth material for evaluation. The inclusion of Ta2O5 data further validates the model’s scalability and generalization capabilities with Mean Squared Error (MSE) loss value of 6.7894×10−4. The advantage of the CfC model in precisely predicting supercontinuum spectra while retaining computational efficiency is demonstrated by comparisons with conventional methods. The CfC model is a viable tool for enhancing predictive modeling in photonics research because of its scalability and generalization characteristics. This will pave the way for future developments in deep learning techniques for optical device optimization.

Switching positive system event triggering T-S fuzzy control

This paper presents a saturation control problem with a positive switching T-S fuzzy system based on event-triggering mechanism under continuous time. Firstly, a 1-norm event triggering mechanism is designed. Then, the multilinear co-positive Lyapunov function is applied to the closed-loop positive switching system with a T-S fuzzy control strategy under continuous time. Next, we consider constructing a cone invariant set to transform the actuator saturation problem into an interval form. The designed controller with a linear programming method guarantees both the positivity and stability of the closed-loop system. Finally, an example of a communication data network proves the effectiveness of the design. The main contents are (i) The event-triggering strategy under continuous time is used in the T-S switching positive system. (ii) A controller with input saturation is introduced into controllable subsystems. (iii) When determining the attractor domain of the system state, a cone domain is considered as a potential restriction.

Modeling spillover dynamics: understanding emerging pathogens of public health concern

The emergence of infectious diseases with pandemic potential is a major public health threat worldwide. The World Health Organization reports that about 60% of emerging infectious diseases are zoonoses, originating from spillover events. Although the mechanisms behind spillover events remain unclear, mathematical modeling offers a way to understand the intricate interactions among pathogens, wildlife, humans, and their shared environment. Aiming at gaining insights into the dynamics of spillover events and the outcome of an eventual disease outbreak in a population, we propose a continuous time stochastic modeling framework. This framework links the dynamics of animal reservoirs and human hosts to simulate cross-species disease transmission. We conduct a thorough analysis of the model followed by numerical experiments that explore various spillover scenarios. The results suggest that although most epidemic outbreaks caused by novel zoonotic pathogens do not persist in the human population, the rising number of spillover events can avoid long-lasting extinction and lead to unexpected large outbreaks. Hence, global efforts to reduce the impacts of emerging diseases should not only address post-emergence outbreak control but also need to prevent pandemics before they are established.

Constituents of Coliform Species Contained in the Permeate of Microfiltration Membranes in Wastewater Treatment

MBRs (Membrane bioreactors) have been increasingly employed for municipal and industrial wastewater treatment in the last decades for their small footprint and excellent effluent quality. However, microorganisms are often detected in the permeates of microfiltration (MF) membranes even with small pore sizes. Coliform bacteria are known for indicating the potential presence of pathogenic bacteria that cause infectious disease such as bacteremia, respiratory tract infections, and urinary tract infections. Thus, the retention of coliform bacteria by membrane processes is important when the membrane process is utilized in water reclamation. In this study, a microbial community of coliform bacteria in the permeates of MF membranes with different pore sizes (0.2, 0.4, and 0.8 µm) was identified. The results showed that the dominant coliform bacteria changed from Enterobacter spp. and Citrobacter spp. in the activated sludge to Enterobacter spp. and Klebsiella spp. in the permeate of MF membranes, while some pieces of membranes showed complete retention. The bacterial regrowth on the surface of the piping system on the permeate side could be a significant factor contributing to the frequent and exclusive detection of Enterobacter spp. and Klebsiella spp. in the case of membranes with small pore size (0.2 and 0.4 µm) after a long continuous filtration time. To indicate the public health-related risk of treated wastewater by MF, Escherichia coli may not be a suitable indicator species because E. coli is relatively retentive in MF compared to other coliforms.

Multi-objective optimization for low hydrogen consumption and long useful life in fuel cell emergency power supply systems

The power system using hydrogen fuel cells (FCs) as the primary energy source holds significant potential for applications in emergency fields such as post-disaster relief and outdoor power supply. The operational environment of the FC emergency power supply system (FCEPSS) is challenging, with long continuous operation time, difficulties in hydrogen supply, high maintenance costs, and, accordingly, requirements for hydrogen consumption and useful life of FCs are heightened. Hence, this paper proposes a multi-objective energy management strategy (EMS) for FCEPSS. First, the structure of FCEPSS is designed based on the demand analysis in emergency scenarios. Then, the hydrogen consumption and life degradation models of FCEPSS are established. Aiming at the multi-objective optimization problem of minimizing hydrogen consumption and life degradation value in the FCEPSS, an improved multi-objective optimization algorithm is proposed. This paper converts complex constraints into the penalty term and incorporates it as one of the objectives, constructing a three-objective optimization model. To enhance the solution of multi-objective optimization problems, an improved strategy based on relaxation-tightening and three-objective sorting is proposed. Combining the fast non-dominated sorting genetic algorithm-II and the above improved strategy, an improved multi-objective optimization algorithm (IMOOA) is constructed. In the simulation, the advantages of the proposed IMOOA algorithm are verified. In the experimental part, compared with the logical threshold strategy, the proposed strategy saves 0.60% of hydrogen consumption and reduces 5.65% of life degradation within 24 h, respectively. Finally, the superiority of the multi-objective EMS utilizing the IMOOA is demonstrated.

Power generation–network–load–energy storage co-planning under uncertainty

With the aggregation of renewable energy in the power system, the uncertainty caused by the renewable energy affects the planning and operation of power systems. Meanwhile, the existing planning models fail to consider renewable energy uncertainty methods, specifically concerning renewable energy confidence and future possible scenarios; thus, a confidence-based scenario cluster method is presented. A novel generator, network, load, and energy storage (GNLS) co-planning model is proposed in the paper. First, a confidence-based scenario cluster is built, which can reflect uncertainties by clustering and analyzing wind, solar, and load. Second, the proposed model focuses on load and energy storage co-planning, and in addition, relevant flexible indices are used to assess the model. Finally, the GNLS co-planning model is built as a bi-level stochastic model on continuous time scales. The model is solved using the Benders decomposition algorithm. The method in this paper is validated using an IEEE RTS 24-bus and a real test system in China to demonstrate the reduction in renewable energy curtailment and optimization of economic factors in power system planning.

A Temperature Control Method of Lysozyme Fermentation Based on LRWOA-LSTM-PID

In order to overcome the difficulty of parameter tuning caused by the large lag and time-varying nonlinearity of the tank for lysozyme fermentation, a temperature control method based on LRWOA-LSTM-PID is proposed in this paper. Firstly, according to the intrinsic mechanism of the fermenter, a temperature mechanism model based on a dynamic equation is designed, which can better reflect the temperature changes in the fermenter. Secondly, a Proportional Integral Derivative (PID) parameter tuning method based on a Long-Short Term Memory Network (LSTM) is proposed, which takes advantage of the ability of LSTM to learn time sequence information and obtains the variation trend between error sequences under continuous time sampling, thereby adjusting network weights more reasonably and accelerating PID parameter tuning. Finally, a Whale Optimization Algorithm (WOA) based on the Lévy flight and random walk strategy (LRWOA) is proposed for the initialization of LSTM parameters; this algorithm has excellent optimization capabilities and overcomes the problem of LSTM falling into local optimal solutions prematurely during parameter randomization. The results show that the method proposed in this paper can achieve rapid tuning of PID parameters, thereby improving the convergence speed of the system and reducing system overshoot.

A controller-stopper-game with hidden controller type

We consider a continuous time stochastic dynamic game between a stopper (the owner of an asset) and a controller (the manager) who is either effective or non-effective. An effective manager can exert high or low effort which corresponds to a high or a low positive drift for the accumulated income of the owner with random noise in terms of Brownian motion. The manager earns a salary until the owner stops the game. A non-effective manager cannot act but receives a salary. We find a threshold (Nash) equilibrium using stochastic filtering methods in a weak formulation.

Ultrasound enhanced diffusion in hydrogels: An experimental and non-equilibrium molecular dynamics study.

Focused ultrasound has experimentally been found to enhance the diffusion of nanoparticles; our aim with this work is to study this effect closer using both experiments and non-equilibrium molecular dynamics. Measurements from single particle tracking of 40nm polystyrene nanoparticles in an agarose hydrogel with and without focused ultrasound are presented and compared with a previous experimental study using 100nm polystyrene nanoparticles. In both cases, we observed an increase in the mean square displacement during focused ultrasound treatment. We developed a coarse-grained non-equilibrium molecular dynamics model with an implicit solvent to investigate the increase in the mean square displacement and its frequency and amplitude dependencies. This model consists of polymer fibers and two sizes of nanoparticles, and the effect of the focused ultrasound was modeled as an external oscillating force field. A comparison between the simulation and experimental results shows similar mean square displacement trends, suggesting that the particle velocity is a significant contributor to the observed ultrasound-enhanced mean square displacement. The resulting diffusion coefficients from the model are compared to the diffusion equation for a two-time continuous time random walk. The model is found to have the same frequency dependency. At lower particle velocity amplitude values, the model has a quadratic relation with the particle velocity amplitude as described by the two-time continuous time random walk derived diffusion equation, but at higher amplitudes, the model deviates, and its diffusion coefficient reaches the non-hindered diffusion coefficient. This observation suggests that at higher ultrasound intensities in hydrogels, the non-hindered diffusion coefficient can be used.

A 16 Gb/s serial link transceiver with active inductor based CTLE and 3-tap DFE in 12-nm FinFET CMOS

This paper presents a 16 Gb/s serial link transceiver implemented in 12-nm FinFET CMOS technology. The equalization scheme incorporates a 3-tap feed-forward equalizer (FFE) in the transmitter, a 5-stage continuous time linear equalizer (CTLE), and a 3-tap decision-feedback equalizer (DFE) in the receiver. The proposed FFE structure offers small step size and flexible configuration. The CTLE's high-frequency boost is augmented by integrating an active inductor. A high-accuracy clock and data recovery (CDR) circuit, featuring a cascaded two-step analog phase interpolator (PI) structure, is developed for data retiming. Occupying a footprint of 0.26 mm × 0.63 mm per lane, the transceiver test chip is packaged in a flip chip ball grid array (FC-BGA) module. Measurement results demonstrate a horizontal eye opening of 38 % at a bit error rate (BER) of 10−12 over a channel with 28 dB loss at 8 GHz. Moreover, the power consumption is 68.85 mW per lane at 16 Gb/s.