On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay

This paper studies the robustness of a dynamic average consensus algorithm to communication delay over strongly connected and weight-balanced (SCWB) digraphs. Under delay-free communication, the algorithm of interest achieves a practical asymptotic tracking of the dynamic average of the time-varying agents' reference signals. For this algorithm, in both its continuous-time and discrete-time implementations, we characterize the admissible communication delay range and study the effect of the delay on the rate of convergence and the tracking error bound. Our study also includes establishing a relationship between the admissible delay bound and the maximum degree of the SCWB digraphs. We also show that for delays in the admissible bound, for static signals the algorithms achieve perfect tracking. Moreover, when the interaction topology is a connected undirected graph, we show that the discrete-time implementation is guaranteed to tolerate at least one step delay. Simulations demonstrate our results

Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.Siirretty Doriast

Uncertainty Management of Intelligent Feature Selection in Wireless Sensor Networks

Wireless sensor networks (WSN) are envisioned to revolutionize the paradigm of monitoring complex real-world systems at a very high resolution. However, the deployment of a large number of unattended sensor nodes in hostile environments, frequent changes of environment dynamics, and severe resource constraints pose uncertainties and limit the potential use of WSN in complex real-world applications. Although uncertainty management in Artificial Intelligence (AI) is well developed and well investigated, its implications in wireless sensor environments are inadequately addressed. This dissertation addresses uncertainty management issues of spatio-temporal patterns generated from sensor data. It provides a framework for characterizing spatio-temporal pattern in WSN. Using rough set theory and temporal reasoning a novel formalism has been developed to characterize and quantify the uncertainties in predicting spatio-temporal patterns from sensor data. This research also uncovers the trade-off among the uncertainty measures, which can be used to develop a multi-objective optimization model for real-time decision making in sensor data aggregation and samplin

Development of a prognostic model for Macrophage Activation Syndrome in Systemic Juvenile Idiopathic Arthritis

Introduction: Macrophage activation syndrome (MAS) is a potentially life-threatening complication of systemic juvenile idiopathic arthritis (SJIA) characterized by heterogeneous organ involvement and severity. Early identification of patients at high risk of complicated clinical course may improve outcome by helping initiate prompt, appropriate immunosuppressive and supportive treatments. Yet, despite recent progress in clarifying the underlying immunological mechanisms, factors driving organ damage and severe outcome are not entirely understood, nor has the prognostic value of routinely gathered clinical and laboratory factors been fully explored. Objectives: To develop a prognostic model for SJIA-MAS based on routinely available parameters at disease onset, accounting for patient heterogeneity, possible latent factors, non-linear relationships and confounders. Methods: We examined a retrospective multinational cohort of 362 patients diagnosed with SJIA-MAS. The relationships between demographic, laboratory features at MAS onset (such as hemoglobin, whole blood cells, platelets, ERS, CRP, AST, ALT, bilirubin, fibrinogen, d-dimer, ferritin and creatinine), therapeutic interventions and outcomes were analyzed. Outcomes of interest included a \u201csevere course\u201d (defined as ICU admission or death), occurring of organs failure and CSN dysfunction. To identify potential phenotypes related to clinical features and outcome, we explored laboratory parameter patterns at MAS onset through Latent class modeling, which detects multiple unobserved clusters in heterogeneous populations. A structural causal approach was then used for investigating causal pathways leading to severe outcomes. Directed acyclic graphs (DAGs) were employed to depict possible causal relationships between the candidate biomarkers, potential confounding variables, and the outcomes, and inform the choice of adjustment sets in multivariate regression models. We assessed the possible relationships between variables and outcomes by penalized likelihood logistic regression and identified optimal cut off points for prognostic factors using Multiple Adaptive Regression Splines (MARS) and Classification and Regression Trees (CART). To account for possible treatment confounders, the effect of cyclosporine and etoposide use on outcomes was estimated using augmented inverse probability weighting (IPW) with double robust methods. Finally, results from previous analyses were incorporated in a probabilistic framework through a Bayesian network (BN) model, which provides risk estimates for specific clinical scenarios and quantifies the amount of information contributed from the identified prognostic variables. Results: The latent class model revealed six clusters based on biomarkers at MAS onset, characterized by the following features: mild alterations of white blood cells, platelets, fibrinogen, d-dimer and ferritin values, considered the baseline type (cluster 1, n =115); hyperferritinemia with low organs involvement (cluster 2, n = 101); elevation of inflammatory markers (cluster 3, n =51); hepatobiliary involvement (cluster 4, n = 41); severe pancytopenia, liver and kidney failure with higher elevation of LDH, d-dimer, ferritin (cluster 5, n = 30); biliary and renal dysfunction (cluster 6, n = 24). Cluster 2 and 3 presented lower age and SJIA duration at MAS onset compared to other subgroups. Cluster membership was predictive of severe course (p<0.001), CSN involvement (p<0.001), Hemorrhagic complications (p <0.001) and Heart failure (p<0.001), with patients in cluster 5 showing the highest risk of severe course and heart failure, and increased occurrence of CNS and Hemorrhagic manifestations in both cluster 5 and 6. In multivariate regression models, parameters at onset associated with risk of severe course were creatinine (OR 1,6 [95% CI 1.13\u20132.3]; p = 0.008) and albumin levels (OR 0,65 [95% CI 0.44\u20130.98]; p = 0.044) Higher risk of CNS involvement was found for patients younger at MAS onset (OR 0,62 [95% CI 0.42\u20130.92]; p = 0.018). Na (OR 0.0,89 [95% CI 0.82\u20130.96]; p = 0.006) and creatinine values (OR 1.69 [95% CI 1.14\u20132.5]; p = 0.009) were identified as independent predictors of mortality. There was no evidence for an effect of etoposide (OR 1.03 [95% CI 0.91\u20131.12]) and cyclosporine (OR 1.04 [95% CI 0.92\u20131.19]) on severe course. BNs defined distinct groups with different probability of severe outcomes, achieving a c-index of 0.76 for mortality, 0.81 for severe course and 0.81 for CNS involvement. Adding the obtained latent clusters to the BN model increased the prediction accuracy for severe course up to a c-index of 0.83. Based on information theory metrics (mutual information) from the BN model, decision algorithms for each outcome and a web-based decision support tool for external users were implemented. Conclusions: We developed a probabilistic prognostic model of SJIA-MAS based on routinely available data. This stratification tool may facilitate informed decision-making about the clinical management of these patients. The probabilistic and information-theoretic approach offers a framework for further validation, expansion and integration of the model with emerging molecular biomarkers

Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment