Membership Distribution Research Articles

Deep graph clustering by integrating community structure with neighborhood information

Deep graph clustering approaches employ deep graph neural networks to encode node embeddings and subsequently partition nodes based on these representations. Recent one-step methods have demonstrated progress; however, they often encounter issues during the representation learning phase. A primary challenge is that the encoding networks fail to capture the high-order structural information of the graph for effective clustering. We believe that combining the two distributions comprehensively characterizes the real node distribution in terms of neighborhood proximity and community aggregation to achieve better clustering. Additionally, the prevalent representation learning paradigms based on adjacency matrix reconstruction are computationally intensive and increase optimization challenges. This paper presents a novel deep graph clustering model, termed Deep Integration of Community structure and Neighborhood information (DICN). The model incorporates a graph self-attention mechanism to aggregate neighborhood-level node information, and utilizes a probabilistic generative model for edge community detection to captain community-level node information. These two-level embeddings are employed to compute explicit node membership distributions for the clustering loss. This ensures that the clustering objective effectively integrates both low-order and high-order node characteristics. The comprehensive learning process of DICN optimizes not only the node embeddings but also the clustering results by integrating the two-level losses from representation learning and the clustering loss with a weak guidance loss for clustering. Experiments on some benchmark datasets illustrate that DICN model has superior performance over existing state-of-the-art methods.

Drug–target interaction prediction based on improved heterogeneous graph representation learning and feature projection classification

Drug–target interaction (DTI) identification is a complex process that is time-consuming, costly and frequently inefficient, with a low success rate, especially with wet-experimental methods. The prediction of DTI by calculational methods is an effective way to solve this problem. However, most existing methods regard drug–target pairs with unknown interaction relationship as negative samples, that the false negative samples will affect the AUC and AUPR evaluation, leading to performance misjudgment. Therefore, in this paper, a new DTI prediction method, DTI-HAN, is proposed to overcome the shortcoming and further improve the predictive performance. In the drug and target feature representation learning stage, this method constructs a drug–target heterogeneous network based on similarity and interaction relationship, and establishes meta-path, node-level and semantic-level bi-attention mechanism. To avoid introducing false negative examples, an improved loss function based only on known edges is proposed. In the DTI prediction stage, feature projection and fuzzy theory are introduced, and membership distribution function is estimated only depended on positive samples. Compared with the DTI prediction methods, DTI-GAT, DTI-GCN and DTI-GraphSAGE, as well as BLM, DTHybrid, SCMLKNN and FPSC-DTI, the experimental results on Enzyme, GPCR, Ion Channel and Nuclear Receptor 4 datasets showed that the DTI-HAN method can greatly improve the AUC and AUPR values on at least 3 datasets to each method. Furthermore, the novel top 100-pair of DTIs prediction were verified by KEGG, DrugBank, ChEMBL and SuperTarget databases, and obtained 21, 48, 61 and 28 validation records, respectively. The top-5 remaining unverified DTIs were performed molecular docking with AutoDock Vina, and the results showed that these drugs and targets have good binding properties. The code and data are available at https://github.com/Yu123456/DTI-HAN.

Poverty Alleviation through Self-Help Groups in Bihar: A case study of Gaya District

This study explores the role of Self-Help Groups (SHGs) in poverty alleviation within Gaya District, Bihar, utilizing data sourced from the Deendayal Antyodaya Yojana-National Rural Livelihoods Mission (DAY-NRLM), Ministry of Rural Development, Government of India. Employing a mixed-methods approach, quantitative analysis of SHG membership trends is complemented by qualitative insights gathered through interviews and focus group discussions with SHG members and stakeholders. Quantitative analysis involves examining data on new and total SHG members across 24 blocks within Gaya District over the past five years. Comparative analysis identifies variations in membership rates among blocks, while geospatial analysis, facilitated by Geographic Information System (GIS) software, visualizes SHG membership distribution. Qualitative insights provide contextual understanding of socio-economic factors influencing SHG participation. Integrated analysis synthesizes findings, elucidating SHG dynamics and their impact on poverty alleviation efforts. Results reveal a notable increase in SHG membership, with approximately 7.88% of the total population joining SHGs in the last five years. Challenges such as inclusivity and access to resources are identified. This study contributes valuable insights to the discourse on SHG effectiveness in poverty alleviation, informing policy formulation and program implementation for sustainable development and poverty reduction in Bihar.

Research on the optimal model for the evaluation of new power system investment projects based on the cloud model–DS evidence theory–TOPSIS method

AbstractConsidering that the traditional investment project evaluation system can no longer fully adapt to the characteristics of the new power system under the investment environment of the new power system, this study constructed a new power system investment project evaluation and optimization method based on the combination of the cloud model, evidence theory and the TOPSIS method. First, 16 evaluation indexes were considered based on four dimensions, namely green and low‐carbon, safe and reliable, flexible and intelligent, and economical and efficient, and the optimal evaluation index system of new power system investment projects was designed. Second, the normal cloud model was used to obtain the evaluation membership distribution of each index and turn it into evidence. Considering the conflicts between indicators and the combinational contradictions of traditional evidence theories, an improved DS evidence theory based on a game weight coefficient discount to reduce conflicting evidence was used to fuse the membership information of multiple indicators. On the basis of the evaluation results of each scheme, this study used the TOPSIS method to sort the advantages and disadvantages of each scheme. Finally, the project of planning and putting this model into operation in the 14th Five‐Year project database of a power grid enterprise was selected as an example to carry out empirical analysis, and the effectiveness and superiority of the proposed model were verified.

PPISB: A Novel Network-Based Algorithm of Predicting Protein-Protein Interactions With Mixed Membership Stochastic Blockmodel.

Protein-protein interactions (PPIs) play an essential role for most of biological processes in cells. Many computational algorithms have thus been proposed to predict PPIs. However, most of them heavily rest on the biological information of proteins while ignoring the latent structural features of proteins presented in a PPI network. In this paper, we propose an efficient network-based prediction algorithm, namely PPISB, based on a mixed membership stochastic blockmodel. By simulating the generative process of a PPI network, PPISB is able to capture the latent community structures. The inference procedure adopted by PPISB further optimizes the membership distributions of proteins over different complexes. After that, a distance measure is designed to compute the similarity between two proteins in terms of their likelihoods of being in the same complex, thus verifying whether they interact with each other or not. To evaluate the performance of PPISB, a series of extensive experiments have been conducted with five PPI networks collected from different species and the results demonstrate that PPISB has a promising performance when applied to predict PPIs in terms of several evaluation metrics. Hence, we reason that PPISB is preferred over state-of-the-art network-based prediction algorithms especially for predicting potential PPIs.

Hawkes Processes With Stochastic Exogenous Effects for Continuous-Time Interaction Modelling.

Continuous-time interaction data is usually generated under time-evolving environment. Hawkes processes (HP) are commonly used mechanisms for the analysis of such data. However, typical model implementations (such as e.g., stochastic block models) assume that the exogenous (background) interaction rate is constant, and so they are limited in their ability to adequately describe any complex time-evolution in the background rate of a process. In this paper, we introduce a stochastic exogenous rate Hawkes process (SE-HP) which is able to learn time variations in the exogenous rate. The model affiliates each node with a piecewise-constant membership distribution with an unknown number of changepoint locations, and allows these distributions to be related to the membership distributions of interacting nodes. The time-varying background rate function is derived through combinations of these membership functions. We introduce a stochastic gradient MCMC algorithm for efficient, scalable inference. The performance of the SE-HP is explored on real world, continuous-time interaction datasets, where we demonstrate that the SE-HP strongly outperforms comparable state-of-the-art methods.

Attribute community detection based on latent representation learning and graph regularized non-negative matrix factorization

In recent years, complex networks have become increasingly difficult to detect effectively with the rapid development of networks. On the one hand, the scale of the network has increased sharply, and on the other hand, the nodes in the network contain rich content. The existing algorithms do not take the different richness of attribute information of nodes in the attribute network into account. And the topology information of the node is inconsistent with the attribute information. Thus, this paper proposes an attribute community detection algorithm based on latent representation learning and graph-regularized non-negative matrix factorization (LRL-GNMF). First, the topological information and attribute information in the attribute network is decomposed based on non-negative matrix factorization respectively. Thereby, the member distribution matrix and the attribute distribution matrix are obtained. Secondly, an affinity matrix is constructed for the attribute matrix, and the latent representation of the attribute information is obtained using the latent representation learning method. In addition, a transition matrix is constructed according to the Markov transition probability. The node membership distribution matrix and the attribute distribution matrix are linked. Finally, since the attribute information of nodes in the network is different, a topology-dominated model and an attribute-dominated model are respectively constructed to solve this problem. At the same time, a graph regularization term is introduced to guide the model to obtain more accurate community detection. This paper conducts experimental analysis on 8 real networks. The experimental results show that the proposed algorithm in this paper outperforms the other 11 compared algorithms in the evaluation indicators of community detection accuracy and standard mutual information.

Nationwide Clinical Practice Patterns of Anesthesiology Critical Care Physicians: A Survey to Members of the Society of Critical Care Anesthesiologists.

Despite the growing contributions of critical care anesthesiologists to clinical practice, research, and administrative leadership of intensive care units (ICUs), relatively little is known about the subspecialty-specific clinical practice environment. An understanding of contemporary clinical practice is essential to recognize the opportunities and challenges facing critical care anesthesia, optimize staffing patterns, assess sustainability and satisfaction, and strategically plan for future activity, scope, and training. This study surveyed intensivists who are members of the Society of Critical Care Anesthesiologists (SOCCA) to evaluate practice patterns of critical care anesthesiologists, including compensation, types of ICUs covered, models of overnight ICU coverage, and relationships between these factors. We hypothesized that variability in compensation and practice patterns would be observed between individuals. Board-certified critical care anesthesiologists practicing in the United States were identified using the SOCCA membership distribution list and invited to take a voluntary online survey between May and June 2021. Multiple-choice questions with both single- and multiple-select options were used for answers with categorical data, and adaptive questioning was used to clarify stem-based responses. Respondents were asked to describe practice patterns at their respective institutions and provide information about their demographics, salaries, effort in ICUs, as well as other activities. A total of 490 participants were invited to take this survey, and 157 (response rate 32%) surveys were completed and analyzed. The majority of respondents were White (73%), male (69%), and younger than 50 years of age (82%). The cardiothoracic/cardiovascular ICU was the most common practice setting, with 69.5% of respondents reporting time working in this unit. Significant variability was observed in ICU practice patterns. Respondents reported spending an equal proportion of their time in clinical practice in the operating rooms and ICUs (median, 40%; interquartile range [IQR], 20%-50%), whereas a smaller proportion-primarily those who completed their training before 2009-reported administrative or research activities. Female respondents reported salaries that were $36,739 less than male respondents; however, this difference was not statistically different, and after adjusting for age and practice type, these differences were less pronounced (-$27,479.79; 95% confidence interval [CI], -$57,232.61 to $2273.03; P = .07). These survey data provide a current snapshot of anesthesiology critical care clinical practice patterns in the United States. Our findings may inform decision-making around the initiation and expansion of critical care services and optimal staffing patterns, as well as provide a basis for further work that focuses on intensivist satisfaction and burnout.

Three-way decision theory based on interval type-2 fuzzy linguistic term sets

This study examines decision theory based on interval type-2 fuzzy sets with linguistic information for the three-way decision approach by addressing the challenge of uncertainty for information analysis and fusion in subjective decision-making processes. First, the interval type-2 fuzzy linguistic term sets (IT2 FLTSs) are defined to represent and normalize the uncertain preference information in linguistic decision-making. Subsequently, perception computing based on computing with words paradigm is introduced to implement information fusion among different decision-makers in the linguistic information-based fuzzy logic reasoning process. Then, a three-way decision (3WD) theory based on IT2 FLTSs with fuzzy neighborhood covering is proposed, and the corresponded tri-partitioning strategies that satisfy Jaccard similarity of membership distributions are given. Finally, 3WD theory is applied to multi-criteria group decision-making with linguistic terms, and the algorithm steps are illustrated by a promising application under the background of coronavirus disease 2019 to reveal the feasibility and practicability of the proposed approach.

Influential groups for seeding and sustaining nonlinear contagion in heterogeneous hypergraphs

Contagion phenomena are often the results of multibody interactions—such as superspreading events or social reinforcement—describable as hypergraphs. We develop an approximate master equation framework to study contagions on hypergraphs with a heterogeneous structure in terms of group size (hyperedge cardinality) and of node membership (hyperdegree). By mapping multibody interactions to nonlinear infection rates, we demonstrate the influence of large groups in two ways. First, we characterize the phase transition, which can be continuous or discontinuous with a bistable regime. Our analytical expressions for the critical and tricritical points highlight the influence of the first three moments of the membership distribution. We also show that heterogeneous group sizes and nonlinear contagion promote a mesoscopic localization regime where contagion is sustained by the largest groups, thereby inhibiting bistability. Second, we formulate an optimal seeding problem for hypergraph contagion and compare two strategies: allocating seeds according to node or group properties. We find that, when the contagion is sufficiently nonlinear, groups are more effective seeds than individual hubs.

A Novel Network-Based Algorithm for Predicting Protein-Protein Interactions Using Gene Ontology

Proteins are one of most significant components in living organism, and their main role in cells is to undertake various physiological functions by interacting with each other. Thus, the prediction of protein-protein interactions (PPIs) is crucial for understanding the molecular basis of biological processes, such as chronic infections. Given the fact that laboratory-based experiments are normally time-consuming and labor-intensive, computational prediction algorithms have become popular at present. However, few of them could simultaneously consider both the structural information of PPI networks and the biological information of proteins for an improved accuracy. To do so, we assume that the prior information of functional modules is known in advance and then simulate the generative process of a PPI network associated with the biological information of proteins, i.e., Gene Ontology, by using an established Bayesian model. In order to indicate to what extent two proteins are likely to interact with each other, we propose a novel scoring function by combining the membership distributions of proteins with network paths. Experimental results show that our algorithm has a promising performance in terms of several independent metrics when compared with state-of-the-art prediction algorithms, and also reveal that the consideration of modularity in PPI networks provides us an alternative, yet much more flexible, way to accurately predict PPIs.

A generalized cost-sensitive model for decision-theoretic three-way approximation of fuzzy sets

Decision-theoretic three-way approximation of a fuzzy set F exploits a three-element set { 0 , 0.5 , 1 } in order to approximate F . By relying on an optimum pair of thresholds ( α , β ) , it changes elements’ membership grade μ F ( x ) to 0 , 0.5 and 1 if μ F ( x ) < α , α ⩽ μ F ( x ) ⩽ β and μ F ( x ) > β respectively. A general three-element system, { n , m , p } , 0 ⩽ n < m < p ≤ 1 , has been proposed in the literature. However, the main issue is to determine appropriate n ≠ 0 , m ≠ 0.5 and p ≠ 1 . A recent advancement has determined m ( 0 < m < 1 ) . However, n = 0 and p = 1 are still imposed by the model. This restriction on the values of n and p lacks general adaptation for different types of membership distribution. In this paper, a novel way of determining appropriate values of n , m , and p is given without the aforesaid restriction. We consider an alternative { n , m , p } formula for computing the optimum pair ( α , β ) in cost-sensitive three-way approximation context. We use synthetic fuzzy sets and some datasets from UCI Machine Learning repository to demonstrate the suitability of the { n , m , p } system in minimizing approximation error and producing well-guided approximation regions.

Attack sample generation algorithm based on data association group by GAN in industrial control dataset

The importance of industrial control networks security is growing, but the intrusion detection research of industrial control networks is seriously restricted by the existing attack samples of the business dataset, especially the quantity and quality. In order to solve the problem of the scarcity of attack industrial control datasets, this paper proposes an attack sample generation algorithm. Firstly, based on the weight and degree of membership distribution, calculate the value of membership distance between dimensions, and the data association is strong when the membership distance of dimensions is small. Then, divide dimensions which have small distance into a group, so as to realize the association grouping of the original data. The data association of dimensions in an association group is strong when the association group appears frequently. According to the frequency of the association group, all the association groups are divided into strong association group and weak association group. Attack all the dimensions of one strong association group in the original data by false data injection attack, realized attack sample generation algorithm in the original data. Finally, expand the attack sample into a large amount of attack sample industrial control dataset by the Generative Adversarial Network. In this paper, the attack samples are generated by the BATADAL dataset and the business dataset of an oil depot, and the data is expanded by 100 times through the algorithm. Compared with the attack samples provided by the BATADAL dataset, the coincidence degree and fitting degree of generated data is improved by 38.20%–42.94% and 98.22%–98.36%, respectively. The classification results of XGBoost and SVM are 100% and 98.01%, which is close to the classification result of attack samples provided by BATADAL dataset.

Local sensitivity analysis of failure possibility and its universal solution by fuzzy simulation

Failure possibility (FP) is widely used to measure safety degree of structure in the presence of fuzzy uncertainty, but how to quantify the effect of fuzzy distribution parameter on FP is seldom investigated. For searching the important parameter to FP and guiding the FP-based design optimization, the local sensitivity of FP (LS-FP) is firstly defined by the partial derivative of FP with respect to the fuzzy distribution parameter in this paper. Then, the analytical solution is derived for the LS-FP in special cases; a universal algorithm is proposed to solve LS-FP by use of the fuzzy simulation. The proposed universal algorithm includes three creative steps. The first is explicitly expressing FP as the joint membership function of the fuzzy inputs at the fuzzy most possible failure point (F-MPP) by use of the fuzzy simulation, on which LS-FP can be equivalently transformed as the partial derivative of F-MPP with respect to the fuzzy distribution parameter. The second is using the characteristic of F-MPP to derive the analytical solution of the partial derivative of F-MPP. The third is establishing an efficient method to estimate F-MPP for completing LS-FP, where new learning function and stopping criterion are proposed to improve the computational efficiency. The proposed algorithm has no limitation on the nonlinearity of performance function and can be applied in any fuzzy membership distribution form of the fuzzy input. Several examples are used to validate the wide applicability, the accuracy, and the efficiency of the proposed algorithm to solve LS-FP.

Fuzzy Separation And Shrinkage Clustering

Clustering has many applications in data mining and machine learning. Fuzzy clustering methods have been widely used in clustering. However, fuzzy clustering methods still have a fatal problem: the cluster radius sensitivity problem. The cluster radius sensitivity problem means that clusters with smaller radius will predominate in clustering and obtain more data points. Aiming at this problem, we propose a fuzzy separation and shrinkage clustering algorithm (FSC). FSC uses cluster membership degrees and cluster sizes to construct a new membership distribution, and then moves the data points according to this new membership distribution. The accuracies of our algorithm on wine, iris, balance scale and seeds are as follows: 98.82%, 97.27%, 63.07% and 91.34%. Our contributions are: (1) We propose a fuzzy separation and shrinkage clustering algorithm, which can solve the cluster radius sensitivity problem. (2) The performance of our algorithm on the UCI datasets goes beyond the benchmark algorithms.

International Survey Reveals Opportunities to Improve Tuberculous Meningitis Management and the Need for Standardized Guidelines.

BackgroundTuberculous meningitis (TBM) is a medical emergency, yet there are no standardized treatment guidelines for the medical or neurosurgical management of these patients and little data on neurocritical care. We conducted an international survey to understand current medical and neurosurgical TBM management and resource availability to provide baseline data needed for future multicenter trials addressing unanswered clinical research questions and the establishment of standardized guidelines.MethodsAn online survey of 77 questions covering medical and neurosurgical TBM management aimed at clinicians/nurses treating TBM was distributed as an anonymous link through email invitation, international organizations’ membership distribution, and direct links on organizational webpages or social media. The survey remained open for 5 months. Data were summarized with frequencies and percentages.ResultsThe survey had 222 responses from 43 countries representing 6 continents. Most respondents were from tertiary care facilities, with broad access to medical and neurosurgical resources. There was significant heterogeneity in general supportive care, and TBM-specific management demonstrated considerable divergence from current standard-of-care practices. The lack of standardized guidelines was identified as a major challenge in TBM management. General and neurocritical care were largely absent. Resources for bedside supportive care and noninvasive monitoring were broadly accessible.ConclusionsThese findings suggest that current TBM management could be improved by the establishment of internationally accepted treatment guidelines based on available evidence, and that numerous centers have resources available to participate in future multicenter trials, even for basic interventions, that may further improve patient outcomes globally.

A new hybrid model of information entropy and unascertained measurement with different membership functions for evaluating destressability in burst-prone underground mines

The occurrence of unpredictable hazards are frequent with the increased depth of mining, especially the hazards caused by stress concentration. In order to mitigate the negative effectiveness results from mining-induce stress, various approaches have been employed in underground mines. Destress blasting, as an efficient method, has gained a lot of popularity in recent years. However, it is crucial to estimate the destressability of specific area before conducting destress blasting. In this study a combination model on the basis of both unascertained measurement (UM) and entropy coefficients was applied to observe the performance of destressability evaluation. Eight representative parameters, i.e., stiffness of the rock mass, brittleness of the rock mass, degree of fracturing, proximity to failure, destress blast orientation, width of the target zone, unit explosive energy, and confinement of the charges were chosen as initial input parameters, and their membership distributions were described by four types of membership methodologies, i.e., line, parabolic curve, exponential curve, and sine curve. Meanwhile, the weights of each index could be computed based on the single measurement matrix. Then, destressability of the samples was easily identified with Euclidean distance and comprehensive measurement vectors which were computed by single measurement vectors and weight coefficients. Finally, it was found that the assessment results are in accordance with those calculated by destressability index. It can be concluded that the proposed hybrid model is able to eliminate the disturbance of subjective factors and ensure the reliability of these outcomes. At the same time, it can provide a novel idea/process for the destressability evaluation.

Revised and New Proper Motions for Confirmed and Candidate Milky Way Dwarf Galaxies

Abstract A new derivation of systemic proper motions of Milky Way satellites is presented and applied to 59 confirmed or candidate dwarf galaxy satellites using Gaia Data Release 2. This constitutes all known Milky Way dwarf galaxies (and likely candidates) as of 2020 May, except for the Magellanic Clouds, the Canis Major and Hydra 1 stellar overdensities, and the tidally disrupting Bootes III and Sagittarius dwarf galaxies. We derive systemic proper motions for the first time for Indus 1, DES J0225+0304, Cetus 2, Pictor 2, and Leo T, but note that the latter three rely on photometry that is of poorer quality than that of the rest of the sample. We cannot resolve a signal for Bootes 4, Cetus 3, Indus 2, Pegasus 3, or Virgo 1. Our method is inspired by the maximum likelihood approach of Pace &amp; Li and examines simultaneously the spatial, color–magnitude, and proper motion distribution of sources. Systemic proper motions are derived without the need to identify confirmed radial velocity members, although the proper motions of these stars, where available, are incorporated into the analysis through a prior on the model. The associated uncertainties on the systemic proper motions are on average a factor of ∼1.4 smaller than existing literature values. Analysis of the implied membership distribution of the satellites suggests that we accurately identify member stars with a contamination rate lower than 1 in 20.

1064 Sleep Patterns Among Urban Haitian Earthquake Survivors Who Experienced the Trauma of Nonpartner Sexual Violence: A Latent Class Analysis Approach

Abstract Introduction Sleep health is crucial to recovery from trauma. Haiti’s Cité Soleil residents (approximately 350,000) live in extreme poverty and regularly experience or witness life-threatening events, including gang and non-partner sexual violence (NPSV). Differences in levels of sleep disturbance among men and women in resource-limited settings who survive disasters as well as NPSV are understudied. In a larger study in which we investigated trauma symptoms among 2010 Haiti earthquake survivors via the Trauma-symptom checklist -40 (N=526; 290 males, 236 females), we also assessed self-reported frequency of sleep disturbance symptoms using the measure’s sleep disturbance subscale, comparing the latter by NPSV victim status and by gender. Methods SAS enabled 3-Class Latent Class Analysis (LCA): Class 1 (“No symptoms”), Class 2 (“Some symptoms”), Class 3 (“All Symptoms)”. Results Distribution of class membership differed by gender (χ2 = 23.9, df = 2, p &amp;lt; .0001). Proportions of respondents assigned to the three classes differed between genders (Females: Class 1, 29.2%; Class 2, 35.5%; Class 3, 35.3%); Males: Class 1, 25.7%; Class 2, 54.4%; Class 3, 19.9%). NPSV status influenced levels of sleep disturbance symptoms, and membership distribution differed across classes by gender (χ2 = 23.9, df = 2, p &amp;lt; .0001). Class 2 membership was greater for men (65.9%), but class 3 membership was greater for women (59.3%). Women who experienced NPSV were statistically more likely members of sleep disturbance symptom classes (Class 2 or Class 3) than Class 1 (χ2= 14.9, df = 2, p = 0.0006). No difference was found in Class membership for men reporting NPSV (χ2= 1.6, df = 2, p = 0.45). Conclusion Investigating the sleep health of Cité Soleil residents adds to the body of literature on sleep health, sleep equity and gendered vulnerability. Findings suggest women in post-disaster settings, especially in LMICs, are at even greater risk for a variety of adverse health outcomes and for suboptimal sleep, even when local men have similar traumatogenic experiences, such as NPSV. Girls and women in post-disaster LMIC settings need trauma-informed sleep health promotion and NPSV-prevention. Support N/A

A numerical method to solve a fuzzy differential equation via differential inclusions

This article provides a numerical method to solve a fuzzy differential equation via differential inclusions. The method obtains response solutions with their membership distribution functions. To do that, the fuzzy differential equation in the form of differential inclusions is transformed into the governing equation of the membership degree and the membership distribution of the fuzzy solution is composed of the membership degrees solved from the governing equation. In the procedure, no comparison or data storage is required, which makes the method have high computational efficiency and low memory cost. Since the governing equation of the membership degree is derived from the master equation of fuzzy dynamics, the method is validated by our theoretically proving the equivalence of the solution of the fuzzy differential equation via differential inclusions and that of the fuzzy master equation. Furthermore, the new method is verified by our comparing the numerical solution with the analytical solution in two examples. Finally, with use of the method, the response solutions are obtained for the Mathieu system and the rotor/stator contact system with fuzzy uncertainties.