Vertex-pursuit in random directed acyclic graphs

We examine a dynamic model for the disruption of information flow in hierarchical social networks by considering the vertex-pursuit game Seepage played in directed acyclic graphs (DAGs). In Seepage, agents attempt to block the movement of an intruder who moves downward from the source node to a sink. The minimum number of such agents required to block the intruder is called the green number. We propose a generalized stochastic model for DAGs with given expected total degree sequence. Seepage and the green number is analyzed in stochastic DAGs in both the cases of a regular and power law degree sequence. For each such sequence, we give asymptotic bounds (and in certain instances, precise values) for the green number

Characterizations and algorithms for generalized Cops and Robbers games

We propose a definition of generalized Cops and Robbers games where there are two players, the Pursuer and the Evader, who each move via prescribed rules. If the Pursuer can ensure that the game enters into a fixed set of final positions, then the Pursuer wins; otherwise, the Evader wins. A relational characterization of the games where the Pursuer wins is provided. A precise formula is given for the length of the game, along with an algorithm for computing if the Pursuer has a winning strategy whose complexity is a function of the parameters of the game. For games where the position of one player does not affect the available moves of he other, a vertex elimination ordering characterization, analogous to a cop-win ordering, is given for when the Pursuer has a winning strategy

Parameterized Complexity of the Anchored k-Core Problem for Directed Graphs

We consider the Directed Anchored k-Core problem, where the task is for a given directed graph G and integers b, k and p, to find an induced subgraph H with at least p vertices (the core) such that all but at most b vertices (the anchors) of H have in-degree at least k. For undirected graphs, this problem was introduced by Bhawalkar, Kleinberg, Lewi, Roughgarden, and Sharma [ICALP 2012]. We undertake a systematic analysis of the computational complexity of Directed Anchored k-Core and show that: - The decision version of the problem is NP-complete for every k>=1 even if the input graph is restricted to be a planar directed acyclic graph of maximum degree at most k+2. - The problem is fixed parameter tractable (FPT) parameterized by the size of the core p for k=1, and W[1]-hard for k>=2. - When the maximum degree of the graph is at most Delta, the problem is FPT parameterized by p+Delta if k>=Delta/2

Aspects of random graphs

The present report aims at giving a survey of my work since the end of my PhD thesis "Spectral Methods for Reconstruction Problems". Since then I focussed on the analysis of properties of different models of random graphs as well as their connection to real-world networks. This report's goal is to capture these problems in a common framework. The very last chapter of this thesis about results in bootstrap percolation is different in the sense that the given graph is deterministic and only the decision of being active for each vertex is probabilistic; since the proof techniques resemble very much results on random graphs, we decided to include them as well. We start with an overview of the five random graph models, and with the description of bootstrap percolation corresponding to the last chapter. Some properties of these models are then analyzed in the different parts of this thesis

From multiscale modeling to metamodeling of geomechanics problems

In numerical simulations of geomechanics problems, a grand challenge consists of overcoming the difficulties in making accurate and robust predictions by revealing the true mechanisms in particle interactions, fluid flow inside pore spaces, and hydromechanical coupling effect between the solid and fluid constituents, from microscale to mesoscale, and to macroscale. While simulation tools incorporating subscale physics can provide detailed insights and accurate material properties to macroscale simulations via computational homogenizations, these numerical simulations are often too computational demanding to be directly used across multiple scales. Recent breakthroughs of Artificial Intelligence (AI) via machine learning have great potential to overcome these barriers, as evidenced by their great success in many applications such as image recognition, natural language processing, and strategy exploration in games. The AI can achieve super-human performance level in a large number of applications, and accomplish tasks that were thought to be not feasible due to the limitations of human and previous computer algorithms. Yet, machine learning approaches can also suffer from overfitting, lack of interpretability, and lack of reliability. Thus the application of machine learning into generation of accurate and reliable surrogate constitutive models for geomaterials with multiscale and multiphysics is not trivial. For this purpose, we propose to establish an integrated modeling process for automatic designing, training, validating, and falsifying of constitutive models, or "metamodeling". This dissertation focuses on our efforts in laying down step-by-step the necessary theoretical and technical foundations for the multiscale metamodeling framework. The first step is to develop multiscale hydromechanical homogenization frameworks for both bulk granular materials and granular interfaces, with their behaviors homogenized from subscale microstructural simulations. For efficient simulations of field-scale geomechanics problems across more than two scales, we develop a hybrid data-driven method designed to capture the multiscale hydro-mechanical coupling effect of porous media with pores of various different sizes. By using sub-scale simulations to generate database to train material models, an offline homogenization procedure is used to replace the up-scaling procedure to generate path-dependent cohesive laws for localized physical discontinuities at both grain and specimen scales. To enable AI in taking over the trial-and-error tasks in the constitutive modeling process, we introduce a novel “metamodeling” framework that employs both graph theory and deep reinforcement learning (DRL) to generate accurate, physics compatible and interpretable surrogate machine learning models. The process of writing constitutive models is simplified as a sequence of forming graph edges with the goal of maximizing the model score (a function of accuracy, robustness and forward prediction quality). By using neural networks to estimate policies and state values, the computer agent is able to efficiently self-improve the constitutive models generated through self-playing. To overcome the obstacle of limited information in geomechanics, we improve the efficiency in utilization of experimental data by a multi-agent cooperative metamodeling framework to provide guidance on database generation and constitutive modeling at the same time. The modeler agent in the framework focuses on evaluating all modeling options (from domain experts’ knowledge or machine learning) in a directed multigraph of elasto-plasticity theory, and finding the optimal path that links the source of the directed graph (e.g., strain history) to the target (e.g., stress). Meanwhile, the data agent focuses on collecting data from real or virtual experiments, interacts with the modeler agent sequentially and generates the database for model calibration to optimize the prediction accuracy. Finally, we design a non-cooperative meta-modeling framework that focuses on automatically developing strategies that simultaneously generate experimental data to calibrate model parameters and explore weakness of a known constitutive model until the strengths and weaknesses of the constitutive law on the application range can be identified through competition. These tasks are enabled by a zero-sum reward system of the metamodeling game and robust adversarial reinforcement learning techniques

Probabilistic Failure Analysis of Complex Systems with Case Studies in Nuclear and Hydropower Industries

Detailed Monte-Carlo simulation of a complex system is the benchmark method used in probabilistic analysis of engineering systems under multiple uncertain sources of failure modes; such simulations typically involve a large amount of CPU time. This makes the probabilistic failure analysis of complex systems, having a large number of components and highly nonlinear interrelationships, computationally intractable and challenging. The objective of this thesis is to synthesize existing methods to analyze multifactorial failure of complex systems which includes predicting the probability of the systems failure and finding its main causes under different situations/scenarios. Bayesian Networks (BNs) have potentials in probabilistically representing complex systems, which is beneficial to predicting the systems failure probability and diagnosing its causes using limited data, logic inference, expert knowledge or simulation of system operations. Compared to other graphical representation techniques such as Event Tree Analysis (ETA) and Fault Tree Analysis (FTA), BNs can deal with complex networks that have multiple initiating events and different types of variables in one graphical representation with the ability to predict the effects, or diagnose the causes leading to a certain effect. This thesis proposes a multifactor failure analysis of complex systems using a number of BN-based approaches. In order to overcome limitations of traditional BNs in dealing with computationally intensive systems simulation and the systems having cyclic interrelationships (or feedbacks) among components, Simulation Supported Bayesian Networks (SSBNs) and Markov Chain Simulation Supported Bayesian Networks (MCSSBNs) are respectively proposed. In the latter, Markov Chains and BNs are integrated to acquire analysis for systems with cyclic behavior when needed. Both SSBNs and MCSSBNs have the distinction of decomposing a complex system to many sub-systems, which makes the system easier to understand and faster to be simulated. The efficiency of these techniques is demonstrated first through their application to a pilot system of two dam reservoirs, where the results of SSBNs and MCSSBNs are compared with those of the entire system operations simulation. Subsequently, two real-world problems including failure analysis of hydropower dams and nuclear waste systems are studied. For such complex networks, a bag of tools that depend on logically inferred data and expert knowledge and judgement are proposed for efficiently predicting failure probabilities in cases where limited operational and historical data are available. Results demonstrate that using the proposed SSBN method for estimating the failure probability of a two dam reservoir system of different connections/topologies results in probability estimates in the range of 3%, which are close to those coming from detailed simulation for the same system. Increasing the number of states per BN variables in the states’ discretization stage makes the SSBN results converge to the simulation results. When Markov chains are integrated with SSBN (i.e. MCSSBN), the results depend on the MCSSBN approach that is used according to the scenarios of interest that need to be included in the BN representation. Evidence of system failure can be used to diagnose the main contributors to the failure (i.e. inflow, reservoir level, or defected gates). This posterior diagnostic capability of the BN is distinctive for the real world case studies presented in this thesis. In Mountain Chute Dam that is operated by Ontario Power Generation, the main contributors to system failure, according to the logically inferred data and expert knowledge, are inadequate discharge capacity of the sluiceway, electromechanical equipment failure, head gates failure, non-safe ice loading, high inflow, high rain/precipitation, sluice gate failure, and high water pressure. While for the Nuclear Waste Management system, the main contributors to system failure according to the known and assumed data are due to high pressures and bentonite failures. In summary, modelling, validating, and developing appropriate modifications of the BN method for applications in complex systems failure analysis is the major contribution of this thesis

Query-driven adaptive sampling

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2022.Automated information gathering allows exploration of environments where data is limited and gathering observations introduces risk, such as underwater and planetary exploration. Typically, exploration has been performed in service of a query, with a unique algorithm developed for each mission. Yet this approach does not allow scientists to respond to novel questions as they are raised. In this thesis, we develop a single approach for a broad range of adaptive sampling missions with risk and limited prior knowledge. To achieve this, we present contributions in planning adaptive missions in service of queries, and modeling multi-attribute environments. First, we define a query language suitable for specifying diverse goals in adaptive sampling. The language fully encompasses objectives from previous adaptive sampling approaches, and significantly extends the possible range of objectives. We prove that queries expressible in this language are not biased in a way that avoids information. We then describe a Monte Carlo tree search approach to plan for all queries in our language, using sample based objective estimators embedded within tree search. This approach outperforms methods that maximize information about all variables in hydrocarbon seep search and fire escape scenarios. Next, we show how to plan when the policy must bound risk as a function of reward. By solving approximating problems, we guarantee risk bounds on policies with large numbers of actions and continuous observations, ensuring that risks are only taken when justified by reward. Exploration is limited by the quality of the environment model, so we introduce Gaussian process models with directed acyclic structure to improve model accuracy under limited data. The addition of interpretable structure allows qualitative expert knowledge of the environment to be encoded through structure and parameter constraints. Since expert knowledge may be incomplete, we introduce efficient structure learning over structural models using A* search with bounding conflicts. By placing bounds on likelihood of substructures, we limit the number of structures that are trained, significantly accelerating search. Experiments modeling geographic data show that our model produces more accurate predictions than existing Gaussian process methods, and using bounds allows structure to be learned in 50% of the time.The work in this thesis was supported by the Exxon Mobil Corporation as part of the MIT Energy Initiative under the project ‘Autonomous System for Deep Sea Hydrocarbon Detection and Monitoring’, NASA’s PSTAR program under the project ‘Cooperative Exploration with Under-actuated Autonomous Vehicles in Hazardous Environments’, and the Vulcan Machine Learning Center for Impact under the project ‘Machine Learning Based Persistent Autonomous Underwater Scientific Studies’

Evaluación de las causas de falla de un dique usando redes bayesianas

Context: Forensic geotechnical engineering aims to determine the most likely causes leading to geotechnical failures. Standard practice tests a set of credible hypotheses against the collected evidence using backward analysis and complex but deterministic geotechnical models. Geotechnical models involving uncertainty are not usually employed to analyze the causes of failure, even though soil parameters are uncertain, and evidence is often incomplete. Method: This paper introduces a probabilistic model approach based on Bayesian Networks to test hypotheses in light of collected evidence. Bayesian networks simulate patterns of human reasoning under uncertainty through a bidirectional inference process known as “explaining away.” In this study, Bayesian Networks are used to test several credible hypotheses about the causes of levee failures. Probability queries and the K-Most Probable Explanation algorithm (K-MPE) are used to assess the hypotheses. Results: This approach was applied to the analysis of a well-known levee failure in Breitenhagen, Germany, where previous forensic studies found a multiplicity of competing explanations for the causes of failure. The approach allows concluding that the failure was most likely caused by a combination of high phreatic levels, a conductive layer, and weak soils, thus allowing to discard a significant number of competing explanations. Conclusions: The proposed approach is expected to improve the accuracy and transparency of conclusions about the causes of failure in levee structures.Contexto: La ingeniería geotécnica forense tiene como objetivo determinar las causas más probables que conducen a fallas de tipo geotécnico. La práctica habitual pone a prueba un conjunto de hipótesis a la luz de la evidencia, utilizando análisis retrospectivos y modelos geotécnicos complejos pero deterministas. Los modelos geotécnicos que involucran incertidumbre no suelen emplearse para analizar las causas de falla, a pesar de que los parámetros del suelo son inciertos y la evidencia suele ser incompleta. Método: Este artículo presenta un enfoque de modelo probabilístico basado en redes bayesianas para evaluar hipótesis con base en la evidencia recolectada. Las redes bayesianas simulan patrones de razonamiento humano bajo incertidumbre a través de un proceso de inferencia bidireccional conocido como explaining away [explicación]. En este estudio, las redes bayesianas se utilizan para probar hipótesis creíbles sobre las causas de falla de un dique. Para evaluar las hipótesis se utilizan consultas de probabilidad y el algoritmo de explicación más probable (K-MPE). Resultados: El enfoque se empleó en el análisis de un dique en Breitenhagen, Alemania, donde varios estudios forenses anteriores encontraron multiplicidad de explicaciones contrapuestas acerca de las causas de falla. El enfoque permite concluir que la causa más probable de falla fue una combinación de altos niveles freáticos, una capa de suelo de alta permeabilidad y suelos de baja resistencia, lo que permitió descartar un número significativo de explicaciones contrapuestas. Conclusiones: Se espera que el enfoque probabilístico propuesto mejore la precisión y la transparencia de las conclusiones sobre las causas de falla en estructuras tipo dique

Degradation and aquatic toxicity of oil sands naphthenic acids using simulated wetlands

Oil sands process-affected waters (OSPW) from the Athabasca oil sands (AOS) located in northern Alberta, Canada, are toxic to aquatic organisms due to the presence of organic and inorganic constituents. Much of this toxicity is related to a group of dissolved organic acids known as naphthenic acids (NAs). Naphthenic acids are a natural component of bitumen and are released into process water during the caustic hot water extraction process used to separate the bitumen from the oil sand ore. This complex mixture of non-cyclic and mono- and poly-cyclic alkanes containing carboxyl groups are characterized by the general formula CnH2n+zO2, where n indicates the carbon number, and Z represents the number of fused rings in the structure. Currently, all process-affected waters are stored within large holding ponds and settling basins on the oil sands mining lease sites with the understanding that eventual reclamation of this water must be undertaken. Successful reclamation of OSPW is expected to require a reduction in total NAs concentrations in the OSPW and the removal of the toxic character of the water. Natural or enhanced bioremediation in lakes and wetlands within the lease closure landscapes will play a critical role in meeting these two requirements. This research investigated the potential for the reduction of total NAs concentrations in OSPW due to biotic (e.g., biodegradation) and abiotic (e.g., sorption) processes, and its relationship to the overall toxicity of OSPW. The specific goals of this research were to determine if natural degradation of NAs in simulated wetland environments could be enhanced by manipulating various physical and chemical factors of the environment, to describe and quantify the selective biodegradation rates of NAs congeners, and to correlate observed changes in total NAs concentration and composition with changes in the aquatic toxicity of OSPW. The complexity of both OSPW and NAs mixtures presented an unusual set of challenges. A preliminary investigation was used to determine the contributions of salinity and NAs to the total aquatic toxicity of OSPW in order to identify a suitable test organism that would respond to NAs concentrations while tolerating the high ionic content of OSPW for the main simulated wetland microcosm study. Seven-day Ceriodaphnia dubia chronic toxicity tests, using both un-manipulated (containing NAs) and manipulated (substantially reduced NAs) samples of OSPW, identified salinity as a potential contributing factor to the overall toxicity of this complex water. Only a 5% reduction in acute toxicity and an 11% reduction in chronic toxicity was observed with a 91% reduction in total NAs concentration (from 67.2 to 5.9 mg/L; removed by solvent extraction). However, when the same samples were tested using the salt tolerant bacteria Vibrio fischeri in the Microtox® bioassay system, the 91% reduction in total NAs concentration, the toxicity was removed (EC50 changed from 57.8 to >100%). These results suggested that salts in OSPW may drive the toxicity of OSPW to some freshwater invertebrates, such as C. dubia, and that the Microtox® bioassay was better suited to track the overall toxic potential of NAs in OSPW. Using flow-through, laboratory microcosms to mimic natural wetlands, it was demonstrated that the reduction in total NAs concentration, based on the Fourier Transform Infrared (FTIR) spectroscopy analysis, was dependent upon hydraulic retention time (HRT), but appeared to be unaffected by nutrient addition (nitrogen and phosphorus). Microcosms with a longer HRT (for two OSPW types; Syncrude and Suncor) showed higher reductions in total NAs concentrations (64¬ to 74% NAs reduction) after the 52-week test period, while nutrient enrichment appeared to have little effect. While the total NAs concentrations decreased in the waters from the microcosms, a 96-hr static acute rainbow trout (Oncorhynchus mykiss) bioassay showed that the initial acute toxicity of Syncrude OSPW (LC50 = 67% v/v) was reduced (LC50 >100% v/v) independent of HRT. However, EC20s from the Microtox® bioassays were relatively unchanged when comparing the input and output microcosm waters maintained at both HRTs over the 52-week study period, indicating that some sub-lethal toxicity persisted under these experimental conditions. The study demonstrated that given sufficiently long HRTs, simulated wetland microcosms containing OSPW significantly reduced total NAs concentrations and acute toxicity, but left behind a persistent component of the NAs mixture associated with residual toxicity. Further investigations aimed to describe and quantify the selective biodegradation of NAs congeners and correlate the observed changes in total NAs concentration and composition (i.e., NAs fingerprint profile) with the aquatic toxicity of OSPW. High performance liquid chromatography/quadrupole time of flight-mass spectrometry (HPLC/QTOF-MS) analysis was used to track the changes in NAs mixture profiles or ‘fingerprints’ in each experimental treatment over time. Based on first-order degradation kinetics, rapid degradation was observed for NAs that had lower carbon numbers (11 to 16) and fewer degrees of cyclization (Z series -2 to -4; half-lives between 19 to 28 weeks). Within the NAs mixture fingerprint, the two most persistent groups of NAs homologues were identified (NAs with carbon numbers 17 to 20 and Z series -6 to -12; half-lives between 37 to 52 weeks). Their persistence may have resulted in the residual chronic toxicological response as measured by the Microtox® bioassay (EC20). An additional study was conducted to characterize potential changes in the total concentration and composition of NAs in OSPW due to sorption to organic wetland sediments. The batch-reactor investigation showed a rapid (<1 day) and significant reduction in total NAs concentrations in OSPW when mixed with the wetland sediment at a ratio of 2:1 v/v (OSPW:sediment). The mean percent reduction of NAs in OSPW was 67% during the 14-day test period, suggesting a significant influence of sorption on the removal of NAs than previously expected. However, no preferential sorption was observed based on the distribution of NAs congeners with respect to carbon number, Z series, and arbitrarily defined clusters. The potential sorption of OSPW NAs as a result of using substrates with high organic carbon content (e.g., 27.6% total organic carbon content) in designed wetlands may enhance the mitigative capabilities of these reclamation landscapes at the AOS. Further investigations into understanding NAs sorption kinetics without substrate agitation are warranted before these results can be extrapolated to the field. Finally, to test the hypothesis that persistent components of an OSPW NAs mixture (e.g., NAs congeners with higher carbon numbers and degrees of cyclization) may be responsible for the observed residual chronic toxicity identified in the previous simulated wetland microcosm study, the fractionation of OSPW NAs was attempted using both off-line anion exchange chromatography and batch-wise co-polymer filtration and elution. Although complete separation was not achieved in this investigation, the results suggested that specific variations of the co-polymer were most effective and showed the most promise for separating the NAs mixtures based on polarity and size. With further refinements to the procedure, future investigations may be able to achieve adequate separation of the NAs mixture into fractions with compositions different enough to conduct toxicity bioassays