Patch Model Research Articles

Effects of asymptomatic infections and population movements on the geographical spread of Nipah virus.

Abstract We develop a deterministic patch model for the transmission of Nipah virus in bat, pig, and
 human populations. The mathematical analysis of the model reveals that the disease-free
 equilibrium is globally asymptotically stable when the basic reproduction number R0 is less
 than 1, and unstable when R0 > 1. In the case where R0 > 1, there exists at least one
 positive equilibrium. Under the assumption of symmetric connectivity matrices, the basic
 reproduction number is increasing in terms of the dispersal rate of exposed humans, if the
 dispersal rates of symptomatic and asymptomatic humans are zero. On the other hand, if
 the direct transmission rates of symptomatic and asymptomatic infections are equal and the
 dispersal rates of exposed and symptomatic humans are zero, the basic reproduction number is
 increasing in terms of asymptomatic humans. For small dispersal rates, the endemic equilibrium
 approaches an endemic equilibrium with relatively lower endemic level.

Saturated incidence tends to ease disease persistence: Analysis of an SIS epidemic patch model

Saturated incidence tends to ease disease persistence: Analysis of an SIS epidemic patch model

Propagation dynamics for an epidemic patch model with variable incubation period

Abstract We study an epidemic patch model that describes the disease spread in population with variable latency due to the differences in immunologic tolerance between individuals. We focus on whether the disease can spread in space that leads to the emergence of epidemic wave, that is the travelling wave solution with constant speed. We first establish some properties of the linearized wave profile equations, which are helpful in obtaining the priori estimates of travelling waves and wave speeds. Then, applying the truncation method and limiting arguments, we can obtain threshold propagation dynamics of the epidemic model. Our result gives a complete characterization of the existence, nonexistence and minimal wave speed of travelling waves. To the best of our knowledge, this is the first time to characterize the propagation dynamics of epidemic patch model with variable latency, which contributes to the understanding of the transmission phenomenon of disease.

Optimal Suturing Techniques in Patch-Bridging Reconstruction for Massive Rotator Cuff Tears: A Finite Element Analysis

PurposeTo use a finite element method to construct a patch-bridge repair model for MRCTs and investigate the effects of different suture methods and knot numbers on postoperative biomechanics. MethodsA finite element model based on intact glenohumeral joint data was used for a biomechanical study. A full-thickness defect and retraction model of the supraspinatus tendon simulated MRCTs. Patch, suture, and anchor models were constructed, and the Marlow method was used to assign the material properties. Three suturing models were established: 1-knot simple, 1-knot mattress, and 2-knot mattress. The ultimate failure load, failure mode, stress distribution of each structure, and other biomechanical results of the different models were calculated and compared. ResultsThe ultimate failure load of the 1-knot mattress suture (71.3 N) was 5.6% greater than that of the 1-knot simple suture (67.5 N), while that (81.5 N) of the 2-knot mattress was 14.3% greater than that of the 1-knot mattress. The stress distribution on the patch and supraspinatus tendon was concentrated on suture perforation. Failure of the bridging reconstruction mainly occurred at the suture perforation of the patch, and the damage forms included cutting-through and isthmus pull-out. ConclusionA finite element model for the patch-bridging reconstruction of MRCTs was established, and patch-bridging restored the mechanical integrity of the rotator cuff. The 2-knot mattress suture was optimal for patch-bridging reconstruction of MRCTs.

Hopf bifurcations for a delayed discrete single population patch model in advective environments

Abstract In this paper, we consider a delayed discrete single population patch model in advective environments. The individuals are subject to both random and directed movements, and there is a net loss of individuals at the downstream end due to the flow into a lake. Choosing time delay as a bifurcation parameter, we show the existence of Hopf bifurcations for the model. In homogeneous non-advective environments, it is well known that the first Hopf bifurcation value is independent of the dispersal rate. In contrast, for homogeneous advective environments, the first Hopf bifurcation value depends on the dispersal rate. Moreover, we show that the first Hopf bifurcation value in advective environments is larger than that in non-advective environments if the dispersal rate is large or small, which suggests that directed movements of the individuals inhibit the occurrence of Hopf bifurcations.

Numerical analysis of Gaussian potential patches model depending on the substrate doping in inhomogeneous Schottky barrier diodes over a wide temperature range

The current-voltage (I-V-T) characteristics of an inhomogeneous n-type GaAs Schottky barrier diode have been investigated by numerical analysis using the modified thermionic emission (TE) current equation by Tung in the 40–320 K range at 40 K intervals. This total current (TC) equation consists of TE current and the patch current components. The patch current dominates through the low Schottky barrier height patches at low temperatures. From the I-V-T characteristics given for three different standard deviations (σ) at each substrate doping value Nd, we have determined the temperatures at which the patch current begins to dominate. The starting temperature of the patch current has decreased as the σ and Nd values decrease. It has been seen that the temperature at which the patch current component begins to dominate is about 120, 80, and 60 K for σ4, σ3, and σ2 at Nd=1.0×1014cm−3 or Nd=1.0×1015cm−3, respectively; 160, 120, and 80 K at Nd=5.0×1015cm−3; and 200, 160, and 80 K at Nd=1.0×1016cm−3, respectively. Moreover, for the substrate with high doping, it has been observed that the I-V curve of the patch current component or the TC shifts toward higher voltages than the expected position at low temperatures. Thus, from the I-V-T characteristics, it has appeared that Tung’s pinch-off model tends to be more applicable to lightly doped semiconductors. Moreover, the TC equation should be used at high temperatures because the I-V curves at high temperatures belong to the TE component, and the patch current expression without the TE component should be especially used for fit to the experimental curves at low temperatures.

Whole slide image-based weakly supervised deep learning for predicting major pathological response in non-small cell lung cancer following neoadjuvant chemoimmunotherapy: a multicenter, retrospective, cohort study.

Develop a predictive model utilizing weakly supervised deep learning techniques to accurately forecast major pathological response (MPR) in patients with resectable non-small cell lung cancer (NSCLC) undergoing neoadjuvant chemoimmunotherapy (NICT), by leveraging whole slide images (WSIs). This retrospective study examined pre-treatment WSIs from 186 patients with non-small cell lung cancer (NSCLC), using a weakly supervised learning framework. We employed advanced deep learning architectures, including DenseNet121, ResNet50, and Inception V3, to analyze WSIs on both micro (patch) and macro (slide) levels. The training process incorporated innovative data augmentation and normalization techniques to bolster the robustness of the models. We evaluated the performance of these models against traditional clinical predictors and integrated them with a novel pathomics signature, which was developed using multi-instance learning algorithms that facilitate feature aggregation from patch-level probability distributions. Univariate and multivariable analyses confirmed histology as a statistically significant prognostic factor for MPR (P-value< 0.05). In patch model evaluations, DenseNet121 led in the validation set with an area under the curve (AUC) of 0.656, surpassing ResNet50 (AUC = 0.626) and Inception V3 (AUC = 0.654), and showed strong generalization in external testing (AUC = 0.611). Further evaluation through visual inspection of patch-level data integration into WSIs revealed XGBoost's superior class differentiation and generalization, achieving the highest AUCs of 0.998 in training and robust scores of 0.818 in validation and 0.805 in testing. Integrating pathomics features with clinical data into a nomogram yielded AUC of 0.819 in validation and 0.820 in testing, enhancing discriminative accuracy. Gradient-weighted Class Activation Mapping (Grad-CAM) and feature aggregation methods notably boosted the model's interpretability and feature modeling. The application of weakly supervised deep learning to WSIs offers a powerful tool for predicting MPR in NSCLC patients treated with NICT.

KPP transition fronts in a one-dimensional two-patch habitat.

This paper is concerned with the existence of transition fronts for a one-dimensional two patch model with KPP reaction terms. Density and flux conditions are imposed at the interface between the two patches. We first construct a pair of suitable super- and sub solutions by making full use of information of the leading edges of two KPP fronts and gluing them through the interface conditions. Then, an entire solution obtained thanks to a limiting argument is shown to be a transition front moving from one patch to the other one. This propagating solution admits asymptotic past and future speeds, and it connects two different fronts, each associated with one of the two patches. The paper thus provides the first example of a transition front for a KPP-type two-patch model with interface conditions.

An Efficient Scattering Center Extraction Method Based on Stationary Phase Method With Quadratic Patch Models

An Efficient Scattering Center Extraction Method Based on Stationary Phase Method With Quadratic Patch Models

Influence of Tire-Enveloping Model Complexity on High-Frequency Simulations

ABSTRACT Race tires are subject to high speeds and high vertical loads during cornering. They are also subject to extreme stress when they are driven over high-frequency and low-amplitude curbs, often leading to tire failures. Research and development by D. C. Davis and P. W. A. Zegelaar has shown that when the tire moves over high-frequency, low-amplitude, and short-wavelength obstacles, it exhibits obstacle-enveloping properties. Tire response over such obstacles includes vertical force variation, longitudinal force variation, and rotational speed variation. Additionally, such road inputs excite tire belt dynamics that include high-frequency modes. Therefore, a single-contact-point model is no longer sufficient to predict tire response over such obstacles. To better capture the tire obstacle-enveloping behavior, advanced contact patch models such as the tandem-cam model by P. W. A. Zegelaar, the radial–interradial spring model by J. M. Badalmenti and G. R. Davis Jr., and the flexible ring model by S. Gong have been developed. To capture high-frequency tire belt dynamics, the rigid-ring model has been developed by P. W. A. Zegelaar. Previous work combines the rigid-ring model with the tandem-cam model to capture obstacle-enveloping behavior and tire belt dynamics up to 60–100 Hz. This paper presents a comparative study of different tire–road contact models to simulate high-frequency curbs typically found at racetracks. The curb profile of the Singes corner at the Paul Ricard racetrack is chosen for simulations as it is known to be extremely demanding on the tires, often causing failures. An advanced four-wheel model is used to simulate a race car at high speeds. Metrics to quantify the tire response over these high-frequency curbs are created and an investigation is conducted to quantify the influence of tire model complexity on the metrics.

Modelling daisy quorum drive: A short-term bridge across engineered fitness valleys.

Engineered gene-drive techniques for population modification and/or suppression have the potential for tackling complex challenges, including reducing the spread of diseases and invasive species. Gene-drive systems with low threshold frequencies for invasion, such as homing-based gene drive, require initially few transgenic individuals to spread and are therefore easy to introduce. The self-propelled behavior of such drives presents a double-edged sword, however, as the low threshold can allow transgenic elements to expand beyond a target population. By contrast, systems where a high threshold frequency must be reached before alleles can spread-above a fitness valley-are less susceptible to spillover but require introduction at a high frequency. We model a proposed drive system, called "daisy quorum drive," that transitions over time from a low-threshold daisy-chain system (involving homing-based gene drive such as CRISPR-Cas9) to a high-threshold fitness-valley system (requiring a high frequency-a "quorum"-to spread). The daisy-chain construct temporarily lowers the high thresholds required for spread of the fitness-valley construct, facilitating use in a wide variety of species that are challenging to breed and release in large numbers. Because elements in the daisy chain only drive subsequent elements in the chain and not themselves and also carry deleterious alleles ("drive load"), the daisy chain is expected to exhaust itself, removing all CRISPR elements and leaving only the high-threshold fitness-valley construct, whose spread is more spatially restricted. Developing and analyzing both discrete patch and continuous space models, we explore how various attributes of daisy quorum drive affect the chance of modifying local population characteristics and the risk that transgenic elements expand beyond a target area. We also briefly explore daisy quorum drive when population suppression is the goal. We find that daisy quorum drive can provide a promising bridge between gene-drive and fitness-valley constructs, allowing spread from a low frequency in the short term and better containment in the long term, without requiring repeated introductions or persistence of CRISPR elements.

A risk-induced dispersal strategy of the infected population for a disease-free state in the SIS epidemic model

This article proposes a dispersal strategy for infected individuals in a spatial susceptible-infected-susceptible (SIS) epidemic model. The presence of spatial heterogeneity and the movement of individuals play crucial roles in determining the persistence and eradication of infectious diseases. To capture these dynamics, we introduce a moving strategy called risk-induced dispersal (RID) for infected individuals in a continuous-time patch model of the SIS epidemic. First, we establish a continuous-time n-patch model and verify that the RID strategy is an effective approach for attaining a disease-free state. This is substantiated through simulations conducted on 7-patch models and analytical results derived from 2-patch models. Second, we extend our analysis by adapting the patch model into a diffusive epidemic model. This extension allows us to explore further the impact of the RID movement strategy on disease transmission and control. We validate our results through simulations, which provide the effects of the RID dispersal strategy.

Threshold dynamics and bifurcation analysis of an SIS patch model with delayed media impact

AbstractIn this paper, an susceptible–infected–susceptible (SIS) epidemic patch model with media delay is proposed at first. Then the basic reproduction number is defined, and the threshold dynamics are studied. It is shown that the disease‐free equilibrium is globally asymptotically stable if and the disease is uniformly persistent if . When the dispersal rates of susceptible and infected populations are identical and less than a critical value, it is proved that the limiting model has a unique positive equilibrium. Furthermore, the stability of the positive equilibrium and the existence of local and global Hopf bifurcations are obtained. Finally, some numerical simulations are performed.

Deceptive Patch Solutions for Protecting Industrial Control Systems Based on Discovered Vulnerabilities

An increase has been observed in concerns about cyber security threats in smart energy management on a global scale. Industrial Control Systems, or simply ICSs, are frequently present in industries and essential infrastructures, e.g., water treatment facilities, nuclear and thermal plants, heavy industries, power production, and distribution systems. ICS devices are high-risk targets for attacks and exploitation with significant security difficulties for ICS vendors and asset owners. Like many consumer electronics, industrial systems are susceptible to a bevy of vulnerabilities that hackers can exploit to launch cyber attacks. Extensive use of ICSs in Critical Infrastructures (CI) increases the vulnerability of CI to cyber attacks and makes their protection a critical subject. This study first contributes to a novel line of research considering how deception can be used by defenders in strategic terms with the objective of introducing uncertainty into an adversary’s perception of a system patch management process in order to protect ICSs. Thus, we mention the advantages of patch models to improve the vulnerabilities of ICSs. We explore deceptive patch management models for the purpose of providing better insight into developing future cyber security techniques for ICS attacks. We propose deceptive patch management solutions as case studies for common ICS attacks.

Destabilization of synchronous periodic solutions for patch models: A criterion by period functions

In this paper, we study the destabilization of synchronous periodic solutions for patch models. By applying perturbation theory for matrices, we derive asymptotic expressions of the Floquet spectra and provide a destabilization criterion for synchronous periodic solutions arising from closed orbits or degenerate Hopf bifurcations in terms of period functions. Finally, we apply the main results to the well-known two-patch Holling-Tanner model.

Analysis of a patch epidemic model incorporating population migration and entry–exit screening

This paper presents an SIQR patch model that combines population migration and entry–exit screening. The threshold for disease extinction is determined using the next-generation matrix method. By constructing the Lyapunov function, the global asymptotic stability of the disease-free equilibrium is demonstrated when R0 &amp;lt; 1. The local asymptotic stability of the endemic equilibrium is shown using the Hurwitz criterion, and it is found that the disease is uniformly persistent when R0 &amp;gt; 1. The influence of screening and migration on disease dynamics is discussed via numerical simulations. Our findings highlight the significance of the detection rate as a vital index in disease transmission and emphasize the effectiveness of screening strategies in preventing outbreaks. Therefore, during an outbreak, it is recommended to establish checkpoints in regions with high mobility to identify and isolate potentially infected individuals, thereby reducing the widespread dissemination of the pandemic.

On the dynamics of an epidemic patch model with mass‐action transmission mechanism and asymmetric dispersal patterns

AbstractThis paper examines an epidemic patch model with mass‐action transmission mechanism and asymmetric connectivity matrix. Results on the global dynamics of solutions and the spatial structures of endemic equilibrium (EE) solutions are obtained. In particular, we show that when the basic reproduction number is less than one and the dispersal rate of the susceptible population is large, the population would eventually stabilize at the disease‐free equilibrium. However, the disease may persist if is small, even if . In such a scenario, explicit conditions on the model parameters that lead to the existence of multiple EE are identified. These results provide new insights into the dynamics of infectious diseases in multipatch environments. Moreover, results in Li and Peng (Stud Appl Math. 2023;150(3):650‐704), which is for the same model but with symmetric connectivity matrix, are generalized and improved.

Dynamics of Lotka-Volterra Competition Patch Models in Streams with Two Branches.

Streams may have many branches and form complex river networks. We investigate two competition patch models associated with two different river network modules, where one is a distributary stream with two branches at the downstream end, and the other is a tributary stream with two branches at the upstream end. Treating one species as resident species and the other one as mutant species, it is shown that, for each model, there exists a invasion curve such that the mutant species can invade when rare if and only if its dispersal strategy is below this curve, but the shapes of the invasion curves are different. Moreover, we show that the global dynamics of the two models can be similar or different depending on river networks. Especially, if the drift rates of the two species are equal, then the global dynamics are similar for small drift rate and different for large drift rate. Our results also confirm a conjecture in Jiang et al. (Bull Math Biol 82:131, 2020).

Tribocharging of granular materials flowing in grounded inclined tubes.

Granular materials charge as they flow through inclined tubes due to the triboelectric effect. This charging persists even when the tube is grounded and is influenced by the tube's angle. In this study, we demonstrate that the tribocharging of granular materials can be accurately replicated through numerical simulations using the patch model. Charge transfers occur between the grains and the tube from donor patches to acceptor patches, ensuring the tube does not retain charge to simulate grounded conditions. Interactions between the grains and the tube are modeled using the method of image charges. We conducted experiments to validate the numerical results. Our findings reveal that the density difference between donor patches on the grains and the tube determines the charge acquired by the granular materials. Additionally, we observed both in experiments and simulations that granular materials charge less with the tube when it is shorter or less tilted. We interpret the influence of the tube's angle and length using the patch model. This model offers valuable insights into the tribocharging mechanisms of various materials.

POS-BERT: Point cloud one-stage BERT pre-training

Recently, the pre-training paradigm combining Transformer and masked language modeling in BERT has achieved tremendous success not only in NLP, but also in images and point clouds. However, directly extending BERT from NLP to point clouds requires first training a discrete Variational AutoEncoder (dVAE) as the tokenizer, which results in a complex two-stage process, as in Point-BERT. Inspired by BERT and MoCo, we propose POS-BERT, a one-stage BERT pre-training method for point clouds. Specifically, we use the masked patch modeling (MPM) task to perform point cloud pre-training, which aims to recover masked patch information under the supervision of a tokenizer’s output. Unlike Point-BERT, whose tokenizer is extra-trained and frozen, we propose a momentum tokenizer which is dynamically updated during training the Transformer. Furthermore, in order to better learn high-level semantic representation, we integrate contrastive learning into the proposed framework to maximize the class token consistency between augmented point cloud pairs. Experiments show that POS-BERT achieves the state-of-the-art performance on linear SVM classification of ModelNet40 with fixed feature extractors, and it exceeds Point-BERT by 3.5%. In addition, POS-BERT has significantly improved many downstream tasks, including fine-tuned classification, few-shot classification and part segmentation. The code and trained models will be released on https://github.com/fukexue/POS-BERT.git.