Graphical Models Research Articles

Bayesian Structure Learning for Climate Model Evaluation

AbstractA Bayesian structure learning approach is employed to compare and contrast interactions between the major climate teleconnections over the recent past as revealed in reanalyses and climate model simulations from leading Meteorological Centers. In a previous study, the authors demonstrated a general framework using homogeneous Dynamic Bayesian Network models constructed from reanalyzed time series of empirical climate indices to compare probabilistic graphical models. Reversible jump Markov Chain Monte Carlo is used to provide uncertainty quantification for selecting the respective network structures. The incorporation of confidence measures in structural features provided by the Bayesian approach is key to yielding informative measures of the differences between products if network‐based approaches are to be used for model evaluation, particularly as point estimates alone may understate the relevant uncertainties. Here we compare models fitted from the NCEP/NCAR and JRA‐55 reanalyses and Coupled Model Intercomparison Project version 5 (CMIP5) historical simulations in terms of associations for which there is high posterior confidence. Examination of differences in the posterior probabilities assigned to edges of the directed acyclic graph provides a quantitative summary of departures in the CMIP5 models from reanalyses. In general terms the climate model simulations are in better agreement with reanalyses where tropical processes dominate, and autocorrelation time scales are long. Seasonal effects are shown to be important when examining tropical‐extratropical interactions with the greatest discrepancies and largest uncertainties present for the Southern Hemisphere teleconnections.

The Florida Scoring System for stratifying children with suspected Sjögren's disease: a cross-sectional machine learning study.

Childhood Sjögren's disease is a rare, underdiagnosed, and poorly-understood condition. By integrating machine learning models on a paediatric cohort in the USA, we aimed to develop a novel system (the Florida Scoring System) for stratifying symptomatic paediatric patients with suspected Sjögren's disease. This cross-sectional study was done in symptomatic patients who visited the Department of Pediatric Rheumatology at the University of Florida, FL, USA. Eligible patients were younger than 18 years or had symptom onset before 18 years of age. Patients with confirmed diagnosis of another autoimmune condition or infection with a clear aetiological microorganism were excluded. Eligible patients underwent comprehensive examinations to rule out or diagnose childhood Sjögren's disease. We used latent class analysis with clinical and laboratory variables to detect heterogeneous patient classes. Machine learning models, including random forest, gradient-boosted decision tree, partial least square discriminatory analysis, least absolute shrinkage and selection operator-penalised ordinal regression, artificial neural network, and super learner were used to predict patient classes and rank the importance of variables. Causal graph learning selected key features to build the final Florida Scoring System. The predictors for all models were the clinical and laboratory variables and the outcome was the definition of patient classes. Between Jan 16, 2018, and April 28, 2022, we screened 448 patients for inclusion. After excluding 205 patients due to symptom onset later than 18 years of age, we recruited 243 patients into our cohort. 26 patients were excluded because of confirmed diagnosis of a disorder other than Sjögren's disease, and 217 patients were included in the final analysis. Median age at diagnosis was 15 years (IQR 11-17). 155 (72%) of 216 patients were female and 61 (28%) were male, 167 (79%) of 212 were White, and 20 (9%) of 213 were Hispanic, Latino, or Spanish. The latent class analysis identified three distinct patient classes: class I (dryness dominant with positive tests, n=27), class II (high symptoms with negative tests, n=98), and class III (low symptoms with negative tests, n=92). Machine learning models accurately predicted patient class and ranked variable importance consistently. The causal graphical model discovered key features for constructing the Florida Scoring System. The Florida Scoring System is a paediatrician-friendly tool that can be used to assist classification and long-term monitoring of suspected childhood Sjögren's disease. The resulting stratification has important implications for clinical management, trial design, and pathobiological research. We found a highly symptomatic patient group with negative serology and diagnostic profiles, which warrants clinical attention. We further revealed that salivary gland ultrasonography can be a non-invasive alternative to minor salivary gland biopsy in children. The Florida Scoring System requires validation in larger prospective paediatric cohorts. National Institute of Dental and Craniofacial Research, National Institute of Arthritis, Musculoskeletal and Skin Diseases, National Heart, Lung, and Blood Institute, and Sjögren's Foundation.

A Spatiotemporal Probabilistic Graphical Model Based on Adaptive Expectation-Maximization Attention for Individual Trajectory Reconstruction Considering Incomplete Observations.

Spatiotemporal information on individual trajectories in urban rail transit is important for operational strategy adjustment, personalized recommendation, and emergency command decision-making. However, due to the lack of journey observations, it is difficult to accurately infer unknown information from trajectories based only on AFC and AVL data. To address the problem, this paper proposes a spatiotemporal probabilistic graphical model based on adaptive expectation maximization attention (STPGM-AEMA) to achieve the reconstruction of individual trajectories. The approach consists of three steps: first, the potential train alternative set and the egress time alternative set of individuals are obtained through data mining and combinatorial enumeration. Then, global and local potential variables are introduced to construct a spatiotemporal probabilistic graphical model, provide the inference process for unknown events, and state information about individual trajectories. Further, considering the effect of missing data, an attention mechanism-enhanced expectation-maximization algorithm is proposed to achieve maximum likelihood estimation of individual trajectories. Finally, typical datasets of origin-destination pairs and actual individual trajectory tracking data are used to validate the effectiveness of the proposed method. The results show that the STPGM-AEMA method is more than 95% accurate in recovering missing information in the observed data, which is at least 15% more accurate than the traditional methods (i.e., PTAM-MLE and MPTAM-EM).

Evaluation of Teaching Effectiveness Based on Bayesian Network Algorithm in Teaching and Learning Process in Higher Education Institutions

The Bayesian network algorithm plays a pivotal role in enhancing the teaching and learning process in higher education institutions by facilitating personalized and adaptive learning experiences. This algorithm leverages probabilistic graphical models to represent relationships among various educational variables, such as student performance, learning resources, and teaching methods. Additionally, Bayesian networks aid instructors in optimizing course design and instructional strategies by identifying areas for improvement and evaluating the effectiveness of different teaching approaches. This paper explores the application of Hidden Markov Chain Bayesian Networks (HMCBN) in analyzing teaching effectiveness within higher education institutions. Teaching effectiveness is a multifaceted concept influenced by various factors, including teaching strategies, student characteristics, and learning outcomes. Traditional statistical methods often struggle to capture the dynamic and interdependent nature of these factors. Through the construction of HMCBN models, this study investigates the probabilistic relationships between teaching strategies, student characteristics, learning outcomes, and teaching effectiveness. For teaching strategies, the probabilities [0.3, 0.5, 0.2] indicate the likelihood of each strategy being employed, suggesting that Strategy 2 is the most frequently utilized, followed by Strategy 1 and Strategy 3. Similarly, the probabilities [0.4, 0.3, 0.3] for student characteristics suggest a relatively balanced distribution among the three characteristic categories. In terms of learning outcomes, the conditional probabilities reflect the influence of both teaching strategies and student characteristics on the outcomes achieved. For each combination of teaching strategy and student characteristic, the probabilities [0.1, 0.3, 0.6], [0.4, 0.5, 0.1], [0.3, 0.4, 0.3], [0.2, 0.5, 0.3], [0.3, 0.4, 0.3], [0.4, 0.3, 0.3], [0.1, 0.7, 0.2], [0.4, 0.5, 0.1], and [0.5, 0.4, 0.1] represent the probabilities of achieving different learning outcomes given specific combinations of teaching strategies and student characteristics.

A Blended Teaching Model of College English Based on Deep Learning

Blending traditional face-to-face instruction with online learning components, this model aims to enhance student engagement and improve learning outcomes. This paper introduces a novel blended teaching model for college English courses, integrating Conditional Random Field (CRF) techniques with deep learning frameworks. Blended learning, combining traditional face-to-face instruction with online learning components, has gained traction in higher education for its potential to enhance student engagement and learning outcomes. CRF blended teaching integrates the principles of conditional random fields, a powerful probabilistic graphical model, with traditional teaching methodologies to enhance learning outcomes. Unlike conventional teaching approaches that often rely on linear or static instructional methods, CRF blended teaching embraces a more dynamic and adaptive framework. By leveraging CRF, which models the dependencies between different instructional variables, educators can design personalized learning experiences tailored to individual student needs and learning styles. This approach enables the seamless integration of diverse instructional modalities, including face-to-face instruction, online resources, and interactive learning activities. The proposed model CRF algorithms to effectively capture the sequential dependencies inherent in language learning tasks, such as sentence parsing and part-of-speech tagging. By integrating deep learning architectures, including recurrent neural networks (RNNs) and transformers, model with large-scale linguistic corpora to improve accuracy and generalization. The model achieves a 15% increase in students' English proficiency scores and a 25% improvement in comprehension compared to traditional teaching methods, underscoring its effectiveness in enhancing learning outcomes.

Prevalence of and risk factors for suicidal ideation in adolescents during the COVID-19 pandemic: a cross-sectional study.

Pandemic-related life changes may have had a deleterious impact on suicidal behaviours. Early detection of suicidal ideation and identification of subgroups at increased risk could help prevent suicide, one of the leading causes of death among adolescents worldwide. Here, we aimed to investigate the prevalence of and risk factors for suicidal ideation in adolescents using a population-based sample from Switzerland, two years into the pandemic. Between December 2021 and June 2022, adolescents aged 14 to 17 years already enrolled in a population-based cohort study (State of Geneva, Switzerland) were asked about suicidal ideation over the previous year. In addition to a regression model, we conducted a network analysis of exposures which identified direct and indirect risk factors for suicidal ideation (i.e. those connected through intermediate risk factors) using mixed graphical models. Among 492 adolescents, 14.4% (95% CI: 11.5-17.8) declared having experienced suicidal ideation over the previous year. Using network analysis, we found that high psychological distress, low self-esteem, identifying as lesbian, gay or bisexual, suffering from bullying, extensive screen time and a severe COVID-19 pandemic impact were major risk factors for suicidal ideation, with parent-adolescent relationship having the highest centrality strength in the network. Our results show that a significant proportion of adolescents experience suicidal ideation, yet these rates are comparable with pre-pandemic results. Providing psychological support is fundamental, with a focus on improving parent-adolescent relationships.

Bioinformatics-based analysis of potential therapeutic target genes for polycystic ovary syndrome.

The purpose of this study was to screen differentially expressed genes in PCOS using gene chip data and investigate the biological functions of these DEGs in PCOS. Additionally, the study aimed to analyze the potential clinical significance of these genes using clinical data. In this study, we first screened the DEGs related to PCOS by using the gene chip data (GSE5090) from GEO database. Target gene prediction software was used to predict the target genes for these DEGs, and their functional enrichment was analysed. Subsequently, the STRING online tool and Cytoscape software were utilized to identify key genes by constructing protein-protein interaction networks (PPI). In the analysis of the GSE5090 dataset, seventeen differentially expressed genes (DEGs) were identified. Functional enrichment analysis revealed that these DEGs are predominantly associated with biological functions related to polycystic ovary syndrome (PCOS). Moreover, the tissue-specific expression analysis highlighted immune system markers, with a notable difference observed in 18 of these markers, accounting for 20.5% of the total. By constructing PPI networks and key gene regulatory networks, a total of three genes (RPL13, LEP, and ANXA1) were identified as key genes. In addition, the column-line graphical model performed well in predicting the risk of PCOS. Using ROC curves, the model proved to be effective in diagnosis. This study represents the first application of a bioinformatics approach to identify and confirm high expression levels of RPL13, LEP, and ANXA1 in patients with Polycystic Ovary Syndrome (PCOS). These key genes-RPL13, LEP, and ANXA1-may present viable targets for therapeutic interventions in PCOS, underscoring their potential clinical importance.

Dimensions of early life adversity and their associations with functional brain organisation

Abstract Early life adversity is associated with differences in brain function and an elevated risk for poor mental health. Using data from children aged 10 (N = 5,798) from the Adolescent Brain Cognitive Development (ABCD) cohort, we investigated how adversity relates to functional brain organisation using a network neuroscience approach. We derived four data-driven categories of adversity by fitting a mixed graphical model: household/community instability, physical/sexual abuse, parental neglect, and financial difficulties. Analyses revealed that multiple forms of adversity were associated with reduced clustering and increased assortativity across the entire brain and that these local measures of organisation captured greater adversity-related variance than mesoscale measures like modularity. The most pronounced effects were in the somatosensory and subcortical networks. Financial difficulties showed the strongest and most widespread associations with brain organisation, with evidence of a mediating effect of assortativity on the association between financial difficulties and internalising symptoms. Adding race as a covariate attenuated most brain-adversity relationships, suggesting that experiences of adversity are strongly related to race/ethnicity in the ABCD sample. These results demonstrate that different forms of adversity are associated with both shared and unique variations in functional brain organisation, highlighting its potential significance for explaining individual differences in mental health outcomes following early life adversity.

VertiBayes: learning Bayesian network parameters from vertically partitioned data with missing values

Federated learning makes it possible to train a machine learning model on decentralized data. Bayesian networks are widely used probabilistic graphical models. While some research has been published on the federated learning of Bayesian networks, publications on Bayesian networks in a vertically partitioned data setting are limited, with important omissions, such as handling missing data. We propose a novel method called VertiBayes to train Bayesian networks (structure and parameters) on vertically partitioned data, which can handle missing values as well as an arbitrary number of parties. For structure learning we adapted the K2 algorithm with a privacy-preserving scalar product protocol. For parameter learning, we use a two-step approach: first, we learn an intermediate model using maximum likelihood, treating missing values as a special value, then we train a model on synthetic data generated by the intermediate model using the EM algorithm. The privacy guarantees of VertiBayes are equivalent to those provided by the privacy preserving scalar product protocol used. We experimentally show VertiBayes produces models comparable to those learnt using traditional algorithms. Finally, we propose two alternative approaches to estimate the performance of the model using vertically partitioned data and we show in experiments that these give accurate estimates.

The Mediating Role of Anxiety/Depression Between Auditory Verbal Hallucinations and the Level of Insight in Schizophrenia.

Auditory verbal hallucination (AVH) is a prominent symptom of schizophrenia causing profound distress. The influence of AVHs on insight appears to be intricate and contingent on other accompanying symptoms. This study investigated the relationship and possible mediators between AVHs and the degree of insight. One hundred patients with schizophrenia participated in the study. Scales were used to evaluate the hallucinatory experience, the level of insight and other psychopathology. Complex relationships between variables were envisaged as a path model, whose initial structure was constructed via Gaussian Graphical Model. The validity of the final model was verified by Structural Equation Modeling. Separate analyses were performed for self-reported and clinician-rated data to enhance the model's robustness. The greater the severity of the physical aspects of AVHs, the lower the level of insight observed. Conversely, higher emotional distress was associated with increased insight. These relationships were only evident in the self-reported results and were not reflected in the clinician-rated results. The path model suggested that the Positive and Negative Syndrome Scale (PANSS) anxiety/depression factor was an important mediator that linked the found association. Notably, the PANSS negative symptom had the opposite effect on the PANSS anxiety/depression factor and insight, making it difficult to define its overall effect. The findings of this study provided one possible route for the positive influence of AVH experience in gaining insight. The mediating role of anxiety/depression modified by negative symptoms emerged as a valuable concept for clarifying this intricate relationship.

3D Multiresolution Velocity Model Fusion with Probability Graphical Models

ABSTRACT The variability in spatial resolution of seismic velocity models obtained via tomographic methodologies is attributed to many factors, including inversion strategies, ray-path coverage, and data integrity. Integration of such models, with distinct resolutions, is crucial during the refinement of community models, thereby enhancing the precision of ground-motion simulations. Toward this goal, we introduce the probability graphical model (PGM), combining velocity models with heterogeneous resolutions and nonuniform data point distributions. The PGM integrates data relations across varying resolution subdomains, enhancing detail within low-resolution (LR) domains by utilizing information and prior knowledge from high-resolution (HR) subdomains through a maximum posterior problem. Assessment of efficacy, utilizing both 2D and 3D velocity models—consisting of synthetic checkerboard models and a fault-zone model from Ridgecrest, California—demonstrates noteworthy improvements in accuracy, compared to state-of-the-art fusion techniques. Specifically, we find reductions of 30% and 44% in computed travel-time residuals for 2D and 3D models, respectively, as compared to conventional smoothing techniques. Unlike conventional methods, the PGM’s adaptive weight selection facilitates preserving and learning details from complex, nonuniform HR models and applies the enhancements to the LR background domain.

Unveiling Fall Triggers in Older Adults: A Machine Learning Graphical Model Analysis.

While existing research has identified diverse fall risk factors in adults aged 60 and older across various areas, comprehensively examining the interrelationships between all factors can enhance our knowledge of complex mechanisms and ultimately prevent falls. This study employs a novel approach-a mixed undirected graphical model (MUGM)-to unravel the interplay between sociodemographics, mental well-being, body composition, self-assessed and performance-based fall risk assessments, and physical activity patterns. Using a parameterized joint probability density, MUGMs specify the higher-order dependence structure and reveals the underlying graphical structure of heterogeneous variables. The MUGM consisting of mixed types of variables (continuous and categorical) has versatile applications that provide innovative and practical insights, as it is equipped to transcend the limitations of traditional correlation analysis and uncover sophisticated interactions within a high-dimensional data set. Our study included 120 elders from central Florida whose 37 fall risk factors were analyzed using an MUGM. Among the identified features, 34 exhibited pairwise relationships, while COVID-19-related factors and housing composition remained conditionally independent from all others. The results from our study serve as a foundational exploration, and future research investigating the longitudinal aspects of these features plays a pivotal role in enhancing our knowledge of the dynamics contributing to fall prevention in this population.

The structure of psychosocial factors in academic success: A gaussian graphical model approach

The structure of psychosocial factors in academic success: A gaussian graphical model approach

Causal chain event graphs for remedial maintenance.

The analysis of system reliability has often benefited from graphical tools such as fault trees and Bayesian networks. In this article, instead of conventional graphical tools, we apply a probabilistic graphical model called the chain event graph (CEG) to represent the failures and processes of deterioration of a system. The CEG is derived from an event tree and can flexibly represent the unfolding of asymmetric processes. For this application, we need to define a new class of formal intervention we call remedial to model the causal effects of remedial maintenance. This fixes the root causes of a failure and returns the status of the system to as good as new. We demonstrate that the semantics of the CEG are rich enough to express this novel type of intervention. Furthermore, through the bespoke causal algebras, the CEG provides a transparent framework with which to guide and express the rationale behind predictive inferences about the effects of various types of remedial intervention. A backdoor theorem is adapted to apply to these interventions to help discover when a system is only partiallyobserved.

Моделирование транспортной инфраструктуры в условиях Крайнего Севера

The article discusses the key problems of transport communication of the Far North regions. There are two difficulties in the construction of highways and railroads in the Far North: ultra-low temperatures and permafrost. The presence of centuries-old frozen rocks, or permafrost, containing ice in its composition, also greatly complicates the work of the transport infrastructure of the Far North. Air communication with these territories of the rest of the country is characterized by insufficient frequency and volume of material flows. Water routes that connect the territory of the Far North, in turn, are limited in terms of time of use, as well as the volume of goods transported. The wide variability of transport and logistics directions determines the possibility of their representation in the form of graphs. The aim of the work was to investigate the prospects of using modeling tools for designing transport infrastructure in the Far North. In the course of the study the hypothesis about the feasibility of using graph-analytical models to address complex integrated tasks was confirmed. In practice, they allow to combine mathematical and graphical models in various software products. Using graph theory, which is one of the key research methods, graph-analytical models have been constructed and analyzed, which allow solving applied problems of an unlimited number of industries.

The Idea of an Integration Interface for Model-based Software Development's Processor-in-the-Loop (PiL) Simulation

Model-based design (MBD) has become a cornerstone in the development of embedded software, particularly in the automotive industry. Processor-in-the- Loop (PiL) simulation bridges the gap between virtual simulation environments and real hardware, enabling early verification and validation of control algorithms running on target processors. The design and implementation of toolchain is required for target specific code generation, compilation, and execution. Developing a toolchain specifically for the target architecture is crucial to preventing errors and ensuring smooth production. The configuration and designing of toolchain are one time effort of all Simulink model which want to be test on board. This research investigates the importance of PiL for embedded systems in the automobile area. It describes the construction of a toolchain that integrates PiL simulation with Simulink, a popular MBD tool. The paper discusses the unique integration of TRACE32, a debugger and code analysis tool, with Simulink for testing programmes on Infineon devices. TPT makes use of graphical test models that are easy to understand and have the capacity to automate complex closed loop tests in real time. It was Daimler Software Technology Research that initially developed TPT. Nowadays, vendors and automakers employ it in their development projects for production vehicles.

Graphical models for identifying pore-forming proteins.

Pore-forming toxins (PFTs) are proteins that form lesions in biological membranes. Better understanding of the structure and function of these proteins will be beneficial in a number of biotechnological applications, including the development of new pest control methods in agriculture. When searching for new pore formers, existing sequence homology-based methods fail to discover truly novel proteins with low sequence identity to known proteins. Search methodologies based on protein structures would help us move beyond this limitation. As the number of known structures for PFTs is very limited, it's quite challenging to identify new proteins having similar structures using computational approaches like deep learning. In this article, we therefore propose a sample-efficient graphical model, where a protein structure graph is first constructed according to consensus secondary structures. A semi-Markov conditional random fields model is then developed to perform protein sequence segmentation. We demonstrate that our method is able to distinguish structurally similar proteins even in the absence of sequence similarity (pairwise sequence identity < 0.4)-a feat not achievable by traditional approaches like HMMs. To extract proteins of interest from a genome-wide protein database for further study, we also develop an efficient framework for UniRef50 with 43 million proteins.

Identifying candidate mechanisms of comorbidity in disordered eating and posttraumatic stress disorder symptoms among U.S. veterans: A network analytic approach.

Comorbidity between posttraumatic stress disorder (PTSD) and disordered eating (DE) symptoms is common, reflecting a possible reciprocal relationship between these disorders. Network analysis may reveal candidate mechanisms underlying their comorbidity and highlight important treatment targets. Two national samples of U.S. veterans endorsing trauma exposure self-reported PTSD and DE symptoms. The discovery sample included veterans from all service eras (n = 434). The validation sample included recently separated post-9/11 veterans (n = 507). We fit graphical lasso models to evaluate the network structure of PTSD factors based on the seven-factor "hybrid" model and DE symptoms within each sample. We used strength scores to identify the most central symptoms within the networks and identified bridge symptoms connecting PTSD and DE features. We tested for network invariance between self-identified men and women within each sample and across the studies. PTSD and DE symptoms clustered as expected within networks for each sample. The strongest nodes in the networks included both PTSD and DE features. The strongest bridge symptoms in both studies included overevaluation of shape and weight, negative affect, and avoidance. Networks were invariant across men and women in each sample and largely invariant across samples. Cross-sectional network models of PTSD and DE symptoms largely replicated across national samples of U.S. veterans and between men and women within samples. Cognitive features of both disorders, along with avoidance, may partially underlie comorbidity and represent potential treatment targets. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Enhancing Breast Cancer Detection with Ensemble Machine Learning Models

Breast cancer remains a significant public health issue worldwide, underlining the need for accurate and efficient diagnostic methods. In this paper, we propose a new technique to enhance breast cancer diagnosis through the integration of multiple machine-learning models. Our strategy employs a combination of the Naive Bayes classifier, Stochastic Gradient Descent (SGD), Bagging, and the ZeroR classifier, alongside Bayes Network learning. The cornerstone of our approach is Bayes Network learning, a probabilistic graphical model designed to map out the intricate interconnections among various diagnostic factors. This is significant in the way that it can help to uncover complex relationships in the data for the sake of leading to more accurate predictions. Added to the above, we use the Naïve Bayes classifier, a classifier showing good validity in classification tasks and based on probabilistic reasoning, for the screening of breast cancer. Further, a refined model's parameter is included using the SGD and leads to enhancement of the generalization and overall performance of the model. In addition, as part of controlling overfitting, one can also use Bagging. It is an ensemble method in the sense that it considers several models. ZeroR classifier is a very basic classifier and is just used to compare its performance with our composite approach. We are comparing complex ensemble results to its simplicity. We will validate the ability of our proposed methodology to compare the performance of our integrated models against ZeroR.

Modeling Neurodegeneration and Regeneration in Parkinson's Disease

The diagnosis and prevention of neurodegenerative diseases is a heavily examined topic in the neuroscience discipline. Whether it be from the anatomical and biological perspectives or the psychological and sociological perspectives, the ultimate goal is to discover strategies to pinpoint the infection as soon as possible. This article begins with reviewing the small-world network structure and then combines the sociological and anatomical perspectives to explain the progression of neuronal death within the brain by using rsfMRI data and the Hegselmann-Krause Model of Opinion Dynamics to illustrate critical interactions between brain regions, and to predict the ultimate behavior of the neural network after initial degeneration Following experimentation–in which critical regions related to Parkinson’s Disease were studied–thresholds were identified in specific regions which exhibited consistent converging behavior of the neural network toward either degenerative or regenerative directions. Furthermore, a simple graphical model is proposed to demonstrate the ranges of values in which current brain health could be of concern. We concluded that neuron death in one brain region can lead to further infection in the resulting system; however, some regions can also directly/indirectly compensate for the system’s decreased function. In future research endeavors, this could provide insight into developing more accurate predictive models for the goal of early detection of a diseased brain and its recovery.