Directed Acyclic Graph Research Articles

Comparing CNN-based Architectures for Dysgraphia Handwriting Classification Performance

Deep learning algorithms are increasingly being used to diagnose dysgraphia by concentrating on the issue of uneven handwriting characteristics, which is common among children in the early stage of basic learning of reading and writing skills. Convolutional Neural Network (CNN) is a deep learning model popular for classification tasks, including the dysgraphia detection process in assisting traditional diagnosis procedures. The CNN-based model is usually constructed by combining layers in the extraction network to capture the features of offline handwriting images before the classification network. However, concerns have been expressed regarding the limited study comparing the performance of the Directed Acyclic Graph (DAG) and Sequential Networks in handwriting-related studies in identifying dysgraphia. The proposed method was employed in this study to compare the two network structures utilized for feature extraction in classifying dysgraphia handwriting To eliminate this gap. Therefore, a new layer structure design in the Sequential and DAG networks was proposed to compare the performance of two feature extraction layers. The findings demonstrated that the DAG network outperforms the Sequential network with 1.75% higher accuracy in classification testing based on confusion matrix analysis. The study provides valuable insights into the efficiency of various network structures in recognizing inconsistencies identified in dysgraphia handwriting, underlining the need for additional research and improvement in this field. Subsequently, these findings highlight the necessity of deep learning approaches to advance dysgraphia identification and establish the framework for future research.

The Influence of Adolescent health-related Behaviors on Degenerative Low Back Pain Hospitalizations and Surgeries in Adulthood: A Longitudinal Study.

Retrospective longitudinal study. This study aims to investigate the influence of adolescent health-related behaviors (physical activity, high BMI, drunkenness, smoking), self-reported chronic disease, and low socioeconomic status (SES) on the development of low back pain requiring hospitalization or surgery. The baseline data were surveys gathered biennially in 1981-1997 (the Adolescent Health and Lifestyle Survey) and individually linked with outcome data, degenerative low back pain hospitalizations, and spine surgeries retrieved from the Care Register for Health Care. A total of 47 724 participants were included. Explanatory variables included physical activity, high BMI, smoking, monthly drunkenness, chronic diseases, and family SES. A logistic regression model was used to analyze the influence of adolescent health-related behaviors (physical activity, high BMI, drunkenness, smoking), self-reported chronic disease, and low socioeconomic status (SES) on degenerative low back pain hospitalization, lumbar disc herniation (LDH) hospitalization and/or spine surgery. Covariates were selected using directed acyclic graphs (DAGs). A total of 5538 participants had degenerative low back pain hospitalizations, 2104 had LDH hospitalizations, and 913 had spinal surgery over an average of 27-years follow-up. High BMI (aOR 1.25, CI 1.12-1.38), smoking (aOR 1.53, CI 1.43-1.62), monthly drunkenness (aOR 1.17, CI 1.10-1.26), and chronic diseases (aOR 1.47, CI 1.35-1.61) in adolescence increased the odds of hospitalizations during follow-up. In addition, high BMI (aOR 1.37, CI 1.09-1.72), smoking (aOR 1.40, CI 1.21-1.61), and monthly drunkenness (aOR 1.19, CI 1.01-1.39) increased the odds of spine surgeries. We found that smoking, high BMI, monthly drunkenness, chronic diseases, and low family SES in adolescence increased the likelihood of degenerative low back pain hospitalizations in adulthood. In addition, high BMI, smoking, and monthly drunkenness in adolescence increased the odds of spinal surgeries.

A Double Auction for Charging Scheduling among Vehicles Using DAG-Blockchains

Electric Vehicles (EVs) are becoming more and more popular in our daily life, which replaces traditional fuel vehicles to reduce carbon emissions and protect the environment. EVs need to be charged, but the number of charging piles in a Charging Station (CS) is limited and charging is usually more time-consuming than fueling. According to this scenario, we propose a secure and efficient charging scheduling system based on a Directed Acyclic Graph (DAG)-blockchain and double auction mechanism. In a smart area, it attempts to assign EVs to the available CSs in the light of their submitted charging requests and status information. First, we design a lightweight charging scheduling framework that integrates DAG-blockchain and modern cryptography technology to ensure security and scalability during performing scheduling and completing tradings. In this process, a constrained multi-item double auction problem is formulated because of the limited charging resources in a CS, which motivates EVs and CSs in this area to participate in the market based on their preferences and statuses. Due to this constraint, our problem is more complicated and harder to achieve truthfulness as well as system efficiency compared to the existing double auction model. To adapt to it, we propose two algorithms, namely Truthful Mechanism for Charging (TMC) and Efficient Mechanism for Charging (EMC), to determine an assignment between EVs and CSs and pricing strategies. Then, both theoretical analysis and numerical simulations show the correctness and effectiveness of our proposed algorithms.

The XAI system for answer set programming xASP2

Abstract Explainable artificial intelligence (XAI) aims at addressing complex problems by coupling solutions with reasons that justify the provided answer. In the context of Answer Set Programming (ASP) the user may be interested in linking the presence or absence of an atom in an answer set to the logic rules involved in the inference of the atom. Such explanations can be given in terms of directed acyclic graphs (DAGs). This article reports on the advancements in the development of the XAI system xASP by revising the main foundational notions and by introducing new ASP encodings to compute minimal assumption sets, explanation sequences, and explanation DAGs. DAGs are shown to the user in an interactive form via the xASP navigator application, also introduced in this work.

Preventable sources of bias in subgroup analyses and secondary outcomes of randomized trials

BackgroundRandomized controlled trials are the gold standard for determining treatment efficacy in medicine. To deter harmful practices such as p-hacking and hypothesizing after the results are known, any analysis of subgroups and secondary outcomes must be documented and pre-specified. However, they can still introduce bias (and routinely do) if they are not treated with the same consideration as the primary analysis. MethodsWe describe several sources of bias that affect subgroup and secondary outcome analyses using published randomized trials and causal directed acyclic graphs (DAGs). ResultsWe use the RECOVERY and START trials to elucidate sources of bias in analyses of subgroups and secondary outcomes. Chance imbalance can occur if the distribution of prognostic variables is not sought for any given subgroup analysis as for the main analysis. This differential distribution of prognostic variables can also occur in analyses of secondary outcomes. Selection bias can occur if the subgroup variable is causally related to staying in the trial. Given loss to follow up is not normally addressed in subgroups, attrition bias can pass unnoticed in these cases. In every case, the solution is to take the same considerations for these analyses as we do for primary analyses. ConclusionsApproval of treatments and clinical decisions can occur based on results from subgroup or secondary outcome analyses. Thus, it is important to give them the same treatment as primary analyses to avoid preventable biases.

Association between perception of harm and valence of shoulder movement images with disability levels related to chronic shoulder pain.

Recent studies highlight an interplay between pain perception and emotional responses. This necessitates a thorough investigation into how beliefs and motivational influences respond to visual stimuli of movements. Such an analysis is crucial for understanding the extent to which these factors contribute to disability levels associated with shoulder pain. We aimed to investigate the relationship between the perception of harm and the valence in images depicting shoulder movements and determine how these perceptions are linked to disability levels associated with shoulder pain. This cross-sectional study recruited 42 individuals with chronic shoulder pain. Participants were presented with 58 shoulder movements images. Each participant evaluated these images for emotional valence and arousal using the self-assessment manikin. For every image, they provided their level of avoidance, fear, and perception of harm in a numerical scale. We measured disability levels and pain catastrophizing using the Shoulder Pain and Disability Index and the Pain Catastrophizing Scale. A direct acyclic graph was used. Multiple linear regression analysis was conducted with shoulder disability as the dependent variable and perception of harm and valence as independent variables, adjusted for the confounders catastrophizing and arousal. This analysis resulted in a significant model (F4,37 = 11.44; adjusted R2 = 0.547; P < 0.01). The perception of harm to shoulder movement (β = 0.11; P < 0.001; 95% confidence interval = 5.6-11.8) was significantly associated with the level of shoulder disability, whereas valence did not show a significant association (β = 0.26; P = 0.15; 95% confidence interval = 1.7-10.8). The perception of harm associated with shoulder movements images during daily activities was associated with disability. Individuals who believe that shoulder movements are harmful have greater disability.

How collider bias affects the relationship between skin color and heart attack using directed acyclic graphs, propensity scores, and stepwise approaches

BackgroundStatistical methods are essential in epidemiology research, but they can generate erroneous estimates when selecting variables based only on statistical criteria. The use of directed acyclic graphs (DAG) helps to understand the causal relationships between variables and to avoid biases.ObjectiveCompare the estimate of the effect of skin color on heart attack obtained from three data analysis techniques: a stepwise approach based on statistical criteria, a propensity score technique, and a graphical approach based on causal criteria.MethodsPopulation-based cross-sectional study using data from the second National Health and Nutrition Examination Survey (NHANES). The exposure variable was skin color (black or non-black) and the outcome was heart attack (yes or no). Multivariable logistic regressions were carried out using the stepwise, propensity score techniques and the DAG-based approach to identify the association between the variables. In the stepwise technique, all variables potentially related to the outcome were included in the model and a forward or backward algorithm was used. The propensity score was applied, estimating the probability of exposure based on the covariates and helping to create balanced groups for comparison. Different possible causal models were developed between the variables in the DAG-based approach, identifying confounding, mediation, and collision factors. The models were created considering self-rated health as a confounding or collider variable, and the modeling results were verified.ResultsA total of 10,351 adults were evaluated, the majority female (52.1%), aged 20 to 39 years (48.5%), and with non-black skin color (90.4%). The prevalence of heart attacks was 3.0%, and 17% rated their health as fair or poor. Using different modeling techniques, no association was found between skin color and heart attack (p > 0.05), except when self-rated health, a collider variable, was included in the stepwise models. In this case, there was an inverse and biased association between the two variables, indicating a collision bias (stepwise-backward-OR 0.48; 95%CI 0.33–0.70; stepwise-forward-OR 0.64; 95%CI 0.44–0.94).ConclusionSkin color was not associated with heart attack when controlling for appropriate confounding factors. However, when adjusting for self-rated health in stepwise techniques, a colliding variable, there was an inverse and distorted association between the two variables, indicating a collider bias. The DAG-based approach and propensity score can avoid this bias by correctly identifying confounding factors and colliders.

A novel bayesian network-based ensemble classifier chains for multi-label classification

In this paper, we address the challenges of random label ordering and limited interpretability associated with Ensemble Classifier Chains (ECC) by introducing a novel ECC method, ECC-MOO&BN, which integrates Bayesian Networks (BN) and Multi-Objective Optimization (MOO). This approach is designed to concurrently overcome these ECC limitations. The ECC-MOO&BN method focuses on extracting diverse and interpretable label orderings for the ECC classifier. We initiated this process by employing mutual information to investigate label relationships and establish the initial structures of the BN. Subsequently, an enhanced NSGA-II algorithm was applied to develop a series of Directed Acyclic Graphs (DAGs) that effectively balance the likelihood and complexity of the BN structure. The rationale behind using the MOO method lies in its ability to optimize both complexity and likelihood simultaneously, which not only diversifies DAG generation but also helps avoid overfitting during the production of label orderings. The DAGs, once sorted topologically, yielded a series of label orderings, which were then seamlessly integrated into the ECC framework for addressing multi-label classification (MLC) problems. Experimental results show that when benchmarked against eleven leading-edge MLC algorithms, our proposed method achieves the highest average ranking across seven evaluation criteria on nine out of thirteen MLC datasets. The results of the Friedman test and Nemenyi test also indicate that the performance of the proposed method has a significant advantage compared to other algorithms.

Low levels of potentially toxic elements in workers are associated with self-reported health outcomes

Occupational exposure to toxic elements can adversely affect health. The current study evaluated blood concentrations of potentially toxic elements (PTE) including As, Cd, Cr, Cu, Hg, Mn, Ni, Pb, Sb, Sn, and Zn in formal and informal workers. Additionally, the study investigated the associations between blood PTE concentrations and reported health outcomes in the study population. The exposed group included women engaged in informal jewelry welding within their homes in Limeira, São Paulo state, Brazil (n = 36) and men who worked at a steel company in Volta Redonda, Rio de Janeiro state, Brazil (n = 22). The control group comprised residents of the same neighborhoods as the workers but without occupational exposure to chemicals (n = 28 in Limeira; n = 27 in Volta Redonda). Triple Quadrupole Inductively Coupled Plasma Mass Spectrometry (TQ ICP-MS) was used to determine PTE concentrations in blood samples. Glycemia, insulin, and lipid profile tests were performed. All participants completed questionnaires on household risk and reported morbidity. The blood concentrations of Cd, As, and Pb, as well as glycemia, were higher in informal workers than in control subjects. No significant differences were observed between formal workers and control subjects. A robust Poisson regression model, adjusted for variables suggested by a Directed Acyclic Graph, disclosed associations of blood lead and arsenic concentrations with the prevalence of neurological manifestations in Limeira. Blood lead levels > 2.6 μg dL−1 were associated with 2.3 times the prevalence of self-reported neurological manifestations (95 % CI: 1.17–4.58; p = 0.02) than lower blood lead concentrations. Furthermore, a positive association between blood cadmium concentrations and glycemia was observed. Informal occupational exposure to these elements may indicate an increased risk of developing diseases. Monitoring exposure and implementing interventions to reduce PTE exposure in the work environment represent significant steps toward prevention.

LATA: learning automata-based task assignment on heterogeneous cloud computing platform

A cloud computing environment is a distributed system where idle resources are accessible across a wide area network, such as the Internet. Due to the diverse specifications of these resources, computational clouds exhibit high heterogeneity. Task scheduling, the process of dispatching cloud applications onto processing nodes, becomes a critical challenge in such environments. Ensuring high utilization in this heterogeneous environment entails identifying suitable machines or virtual machines capable of efficiently executing jobs, constituting a multi-objective optimization problem. This paper proposes a dynamic Learning Automata-based Task Assignment algorithm, named LATA, to address this challenge. In the algorithm, each application is represented as a Directed Acyclic Graph, with tasks as nodes and data dependencies as edges. Initially, tasks are grouped based on their data dependencies to consolidate independent tasks into one group. Subsequently, a variable-structure learning automaton is assigned to each group of tasks to identify appropriate task-machine combinations. The primary objectives of LATA include minimizing makespan and energy consumption by facilitating efficient task placement to achieve load balance and maximize resource utilization. Additionally, an enhancement is proposed, involving the use of a different grouping policy prior to task assignment to further improve performance. Computer simulation results demonstrate the superior performance of the proposed algorithms in highly heterogeneous environments compared to state-of-the-art algorithms. Notably, total execution time and energy consumption decrease by up to 50% and 37%, respectively.

Computing the Heaviest Conflict-free Sub-DAG in DAG-based DLTs

In this paper, we consider DAG-based Distributed Ledger Technologies (DLTs), i.e. , DLTs where each block can reference several previous blocks hence forming a Directed Acyclic Graph of Blocks (BDAG). Each block has a weight (usually a constant normalized to one) and our goal is to compute the heaviest sub-BDAG that does not contain conflicting blocks. First, we prove that computing such a sub-BDAG is NP-complete. Then, we show that the difficulty comes from concurrent conflicts and we present an optimal algorithm that is polynomial if the number of concurrent conflicts is bounded. We also give an efficient incremental version of our algorithm. Finally, we evaluate the performance of our algorithm on random BDAGs against an existing algorithm called GHOSTDAG and show that, in addition to being optimal, our algorithm is also more efficient in practice.

Joint structure learning and causal effect estimation for categorical graphical models.

The scope of this paper is a multivariate setting involving categorical variables. Following an external manipulation of one variable, the goal is to evaluate the causal effect on an outcome of interest. A typical scenario involves a system of variables representing lifestyle, physical and mental features, symptoms, and risk factors, with the outcome being the presence or absence of a disease. These variables are interconnected in complex ways, allowing the effect of an intervention to propagate through multiple paths. A distinctive feature of our approach is the estimation of causal effects while accounting for uncertainty in both the dependence structure, which we represent through a directed acyclic graph (DAG), and the DAG-model parameters. Specifically, we propose a Markov chain Monte Carlo algorithm that targets the joint posterior over DAGs and parameters, based on an efficient reversible-jump proposal scheme. We validate our method through extensive simulation studies and demonstrate that it outperforms current state-of-the-art procedures in terms of estimation accuracy. Finally, we apply our methodology to analyze a dataset on depression and anxiety in undergraduate students.

Poster 350: Do Early Radiographic Changes at 2 Years Predict Increased Pain at 6 Years After ACL Reconstruction?

Objectives: Even young patients without prior injury to the knee develop radiographic changes during the first two years after anterior cruciate ligament reconstruction (ACLR), but it’s unknown whether these early changes are predictive of increased pain over the next several years. The purpose of this study is to determine whether radiographic changes at 2 years are predictive of increased pain at 6 years while controlling for factors known to be predictive of worse pain after ACLR. We hypothesized that worse radiographic changes would not be predictive of increased pain. Methods: Patients were part of a nested cohort who underwent ACLR for an athletic injury, had no prior injury to their knee, and were 35 years of age or younger at 2-year follow-up. These patients underwent standardized posteroanterior semi-flexed knee radiographs using the metatarsophalangeal (MTP) positioning technique at 2 years and completed questionnaires at baseline (at time of enrollment, just prior to their ACL surgery), 2 years, and 6 years. These questionnaires included demographic questions, the SF-36, the Knee Injury and Osteoarthritis Outcome Score (KOOS), and the Marx Activity Level Scale. Surgeons completed an intraoperative data form that included physical examination and arthroscopy findings and treatments administered to the knee. Radiographs were graded by 2 graders using the semiquantitative atlas-based Osteoarthritis Research Society International (OARSI) scoring system, where scores of 0-3 are assigned in the medial and lateral compartments for features including osteophytes, joint space narrowing, sclerosis, and bony attrition. A directed acyclic graph (DAG) was used to plan the statistical models to assess the direct effect of radiographic change on pain at 6 years. A model was built using proportional odds logistic regression, and missing data were imputed using multivariate imputation via chained equation (MICE) for 20 cycles. The model controlled for baseline pain, age, sex, body mass index, years of education, baseline Marx, baseline SF-36, medial and lateral meniscus treatment, presence of cartilage lesion(s), allograft use, and incidence of subsequent surgery before 2 years. Results: A total of 421 subjects were included in the analysis cohort. The median age was 18 years at the time of enrollment (interquartile range [IQR]16-21 years), and 216 (51.3%) were female. 297 subjects (70.5%) had a normal medial meniscus, 85 (20.2%) had a repair, and 39 (9.3%) had a partial meniscectomy. A total of 257 subjects (61.0%) had a normal lateral meniscus, 30 (7.1%) had a repair, and 134 (31.8%) had a partial meniscectomy. 107 subjects (25.4%) had at least 1 Outerbridge grade 2 or worse cartilage lesion. Fifty-three subjects (12.6%) had subsequent surgery prior to their 2-year follow-up. The median total radiographic score on the 2-year radiographs was 4 (IQR 2.0-5.5) and ranged from 0 to 12.5. Median KOOS pain (where 100 = no pain) was 75 (IQR 63.9 to 86.1) at baseline, 96.9 (IQR 91.7 to 100) at 2 years, and 97.2 (IQR 88.9 to 100) at 6 years. Marx activity level (where 16 points = highest activity level) at baseline was 16 (IQR 12 to 16). After controlling for the other variables in the model, subjects with a total radiographic score of 5.5 had 6% increased odds of having increased KOOS pain at 6 years compared to patients with a total radiographic score 2, but this effect was not statistically significant (odds ratio = 1.06, 95% CI, 0.79-1.42, p = .698). Greater baseline pain (odds ratio 1.41, 95% CI 1.06-1.86, p = .018) and subsequent surgery prior to 2 years (odds ratio 0.52, 95% CI, 0.3-0.93, p = .026) were both statistically significant predictors of worse pain at 6-year follow-up. Conclusions: Even young, active patients begin to develop radiographic changes by 2 years after ACLR; however, these changes are not associated with increased pain up to 6 years postoperatively. This information is important for counseling patients who may be concerned about radiographic changes that are seen on x-rays obtained during the first few years after ACLR. In addition, this study suggests that treatment decisions around the time of surgery that can minimize baseline pain and decrease the incidence of subsequent surgery may improve patient pain levels at 6 years postoperatively.

How Being Inside or Outside of Buildings Affects the Causal Relationship between Weather and Pain among People Living with Chronic Pain

Abstract Although many people believe their pain fluctuates with weather conditions, both weather and pain may be associated with time spent outside. For example, pleasant weather may mean that people spend more time outside doing physical activity and are exposed to the weather, leading to more (or less) pain, and poor weather or severe pain may keep people inside, sedentary, and not exposed to the weather. We conducted a smartphone study where participants with chronic pain reported daily pain severity, as well as time spent outside. We address the relationship between four weather variables (temperature, dewpoint temperature, pressure, and wind speed) and pain by proposing a three-step approach to untangle their effects: (i) propose a set of plausible directed acyclic graphs (DAGs) that account for potential roles of time spent outside (e.g., collider, effect modifier, mediator); (ii) analyze the compatibility of the observed data with the assumed model; and (iii) identify the most plausible model by combining evidence from the observed data and domain-specific knowledge. We found that the data do not support time spent outside as a collider or mediator of the relationship between weather variables and pain. On the other hand, time spent outside modifies the effect between temperature and pain, as well as wind speed and pain, with the effect being absent on days that participants spent inside and present if they spent some or all of the day outside. Our results show the utility of using directed acyclic graphs for studying causal inference. Significance Statement Three-quarters of people living with chronic pain believe that weather influences their pain. However, people staying inside would not be exposed to the weather outside, and good weather may mean that people are more active outside, leading to more or less pain. To obtain data to calculate how the amount of time spent outside affects the weather–pain relationship, we conducted a 15-month smartphone study collecting daily pain reports and nearby weather for nearly 5000 participants in the United Kingdom. We found that time spent outside modifies the relationship between temperature/wind speed and pain, showing the importance of accounting for other factors when investigating the association between weather and chronic pain, which could guide future research into pain mitigation and management.

PPB-MCTS: A novel distributed-memory parallel partial-backpropagation Monte Carlo tree search algorithm

Monte-Carlo Tree Search (MCTS) is an adaptive and heuristic tree-search algorithm designed to uncover sub-optimal actions at each decision-making point. This method progressively constructs a search tree by gathering samples throughout its execution. Predominantly applied within the realm of gaming, MCTS has exhibited exceptional achievements. Additionally, it has displayed promising outcomes when employed to solve NP-hard combinatorial optimization problems. MCTS has been adapted for distributed-memory parallel platforms. The primary challenges associated with distributed-memory parallel MCTS are the substantial communication overhead and the necessity to balance the computational load among various processes. In this work, we introduce a novel distributed-memory parallel MCTS algorithm with partial backpropagations, referred to as Parallel Partial-Backpropagation MCTS (PPB-MCTS). Our design approach aims to significantly reduce the communication overhead while maintaining, or even slightly improving, the performance in the context of combinatorial optimization problems. To address the communication overhead challenge, we propose a strategy involving transmitting an additional backpropagation message. This strategy avoids attaching an information table to the communication messages exchanged by the processes, thus reducing the communication overhead. Furthermore, this approach contributes to enhancing the decision-making accuracy during the selection phase. The load balancing issue is also effectively addressed by implementing a shared transposition table among the parallel processes. Furthermore, we introduce two primary methods for managing duplicate states within distributed-memory parallel MCTS, drawing upon techniques utilized in addressing duplicate states within sequential MCTS. Duplicate states can transform the conventional search tree into a Directed Acyclic Graph (DAG). To evaluate the performance of our proposed parallel algorithm, we conduct an extensive series of experiments on solving instances of the Job-Shop Scheduling Problem (JSSP) and the Weighted Set-Cover Problem (WSCP). These problems are recognized for their complexity and classified as NP-hard combinatorial optimization problems with considerable relevance within industrial applications. The experiments are performed on a cluster of computers with many cores. The empirical results highlight the enhanced scalability of our algorithm compared to that of the existing distributed-memory parallel MCTS algorithms. As the number of processes increases, our algorithm demonstrates increased rollout efficiency while maintaining an improved load balance across processes.

Depicting deterministic variables within directed acyclic graphs (DAGs): An aid for identifying and interpreting causal effects involving derived variables and compositional data.

Deterministic variables are variables that are functionally determined by one or more parent variables. They commonly arise when a variable has been functionally created from one or more parent variables, as with derived variables, and in compositional data, where the 'whole' variable is determined from its 'parts'. This article introduces how deterministic variables may be depicted within directed acyclic graphs (DAGs) to help with identifying and interpreting causal effects involving derived variables and/or compositional data. We propose a two-step approach in which all variables are initially considered, and a choice is made whether to focus on the deterministic variable or its determining parents. Depicting deterministic variables within DAGs brings several benefits. It is easier to identify and avoid misinterpreting tautological associations, i.e., self-fulfilling associations between deterministic variables and their parents, or between sibling variables with shared parents. In compositional data, it is easier to understand the consequences of conditioning on the 'whole' variable, and correctly identify total and relative causal effects. For derived variables, it encourages greater consideration of the target estimand and greater scrutiny of the consistency and exchangeability assumptions. DAGs with deterministic variables are a useful aid for planning and interpreting analyses involving derived variables and/or compositional data.

Constrained flows in networks

The support of a flow x in a network is the subdigraph induced by the arcs uv for which x(uv)>0. We discuss a number of results on flows in networks where we put certain restrictions on structure of the support of the flow. Many of these problems are NP-hard because they generalize linkage problems for digraphs. For example deciding whether a network N=(D,s,t,c) has a maximum flow x such that the maximum out-degree of the support Dx of x is at most 2 is NP-complete as it contains the 2-linkage problem as a very special case.Another problem which is NP-complete for the same reason is that of computing the maximum flow we can send from s to t along p paths (called a maximum p-path-flow) in N. Baier et al. (2005) gave a polynomial time algorithm which finds a p-path-flow x whose value is at least 23 of the value of a optimum p-path-flow when p∈{2,3}, and at least 12 when p≥4. When p=2, they show that this is best possible unless P=NP. We show for each p≥2 that the value of a maximum p-path-flow cannot be approximated by any ratio larger than 911, unless P=NP. We also consider a variant of the problem where the p paths must be disjoint. For this problem, we give an algorithm which gets within a factor 1H(p) of the optimum solution, where H(p) is the p'th harmonic number (H(p)∼ln⁡(p)). We show that in the case where the network is acyclic, we can find such a maximum p-path-flow in polynomial time for every p.We determine the complexity of a number of related problems concerning the structure of flows. For the special case of acyclic digraphs, some of the results we obtain are in some sense best possible.

Discovering the effective connectome of the brain with dynamic Bayesian DAG learning

Understanding the complex mechanisms of the brain can be unraveled by extracting the Dynamic Effective Connectome (DEC). Recently, score-based Directed Acyclic Graph (DAG) discovery methods have shown significant improvements in extracting the causal structure and inferring effective connectivity. However, learning DEC through these methods still faces two main challenges: one with the fundamental impotence of high-dimensional dynamic DAG discovery methods and the other with the low quality of fMRI data. In this paper, we introduce Bayesian Dynamic DAG learning with M-matrices Acyclicity characterization (BDyMA) method to address the challenges in discovering DEC. The presented dynamic DAG enables us to discover direct feedback loop edges as well. Leveraging an unconstrained framework in the BDyMA method leads to more accurate results in detecting high-dimensional networks, achieving sparser outcomes, making it particularly suitable for extracting DEC. Additionally, the score function of the BDyMA method allows the incorporation of prior knowledge into the process of dynamic causal discovery which further enhances the accuracy of results. Comprehensive simulations on synthetic data and experiments on Human Connectome Project (HCP) data demonstrate that our method can handle both of the two main challenges, yielding more accurate and reliable DEC compared to state-of-the-art and traditional methods. Additionally, we investigate the trustworthiness of DTI data as prior knowledge for DEC discovery and show the improvements in DEC discovery when the DTI data is incorporated into the process.

Synthesizing Subject-matter Expertise for Variable Selection in Causal Effect Estimation: A Case Study.

Causal graphs are an important tool for covariate selection but there is limited applied research on how best to create them. Here, we used data from the Coronary Drug Project trial to assess a range of approaches to directed acyclic graph (DAG) creation. We focused on the effect of adherence on mortality in the placebo arm, since the true causal effect is believed with a high degree of certainty. We created DAGs for the effect of placebo adherence on mortality using different approaches for identifying variables and links to include or exclude. For each DAG, we identified minimal adjustment sets of covariates for estimating our causal effect of interest and applied these to analyses of the Coronary Drug Project data. When we used only baseline covariate values to estimate the cumulative effect of placebo adherence on mortality, all adjustment sets performed similarly. The specific choice of covariates had minimal effect on these (biased) point estimates, but including nonconfounding prognostic factors resulted in smaller variance estimates. When we additionally adjusted for time-varying covariates of adherence using inverse probability weighting, covariates identified from the DAG created by focusing on prognostic factors performed best. Theoretical advice on covariate selection suggests that including prognostic factors that are not exposure predictors can reduce variance without increasing bias. In contrast, for exposure predictors that are not prognostic factors, inclusion may result in less bias control. Our results empirically confirm this advice. We recommend that hand-creating DAGs begin with the identification of all potential outcome prognostic factors.

Synchronous Dynamical Systems on Directed Acyclic Graphs: Complexity and Algorithms

Discrete dynamical systems serve as useful formal models to study diffusion phenomena in social networks. Several recent articles have studied the algorithmic and complexity aspects of some decision problems on synchronous Boolean networks, which are discrete dynamical systems whose underlying graphs are directed, and may contain directed cycles. Such problems can be regarded as reachability problems in the phase space of the corresponding dynamical system. Previous work has shown that some of these decision problems become efficiently solvable for systems on directed acyclic graphs (DAGs). Motivated by this line of work, we investigate a number of decision problems for dynamical systems whose underlying graphs are DAGs. We show that computational intractability (i.e., PSPACE -completeness) results for reachability problems hold even for dynamical systems on DAGs. We also identify some restricted versions of dynamical systems on DAGs for which reachability problem can be solved efficiently. In addition, we show that a decision problem (namely, Convergence), which is efficiently solvable for dynamical systems on DAGs, becomes PSPACE -complete for Quasi-DAGs (i.e., graphs that become DAGs by the removal of a single edge). In the process of establishing the above results, we also develop several structural properties of the phase spaces of dynamical systems on DAGs.