We present solution methodologies for vehicle routing problems (VRPs) with stochastic demand, with a specific focus on the vehicle routing problem with stochastic demand (VRPSD) and the vehicle routing problem with stochastic demand and duration limits (VRPSDL). The VRPSD and the VRPSDL are fundamental problems underlying many operational challenges in the fields of logistics and supply chain management. We model the VRPSD and the VRPSDL as large-scale Markov decision processes. We develop cyclic-order neighborhoods, a general methodology for solving a broad class of VRPs, and use this technique to obtain static, fixed route policies for the VRPSD. We develop pre-decision, post-decision, and hybrid rollout policies for approximate dynamic programming (ADP). These policies lay a methodological foundation for solving large-scale sequential decision problems and provide a framework for developing dynamic routing policies. Our dynamic rollout policies for the VRPSDL significantly improve upon a method frequently implemented in practice. We also identify circumstances in which our rollout policies appear to offer little or no benefit compared to this benchmark. These observations can guide managerial decision making regarding when the use of our procedures is justifiable. We also demonstrate that our methodology lends itself to real-time implementation, thereby providing a mechanism to make high-quality, dynamic routing decisions for large-scale operations. Finally, we consider a more traditional ADP approach to the VRPSDL by developing a parameterized linear function to approximate the value functions corresponding to our problem formulation. We estimate parameters via a simulation-based algorithm and show that initializing parameter values via our rollout policies leads to significant improvements. However, we conclude that additional research is required to develop a parametric ADP methodology comparable or superior to our rollout policies.

Children who struggle to learn math are often identified by their poor performance on common math learning activities, such as number line estimations. While such behavioral assessments are useful in the classroom, naturalistic neuroimaging of children engaged in real-world math learning activities has the potential to identify concurrent behavioral and neurological correlates to poor math performance. Such correlates may help pinpoint effective teaching strategies for atypical learners, and may highlight instructional methods that elicit typical neurological response patterns to such activities. For example, multisensory stimulation that contains information about number enhances infants' and preschool children's behavioral performance on many numerical tasks and has been shown to elicit neural activation in areas related to number processing and decision-making. Thus, when applied to math teaching tools, multisensory stimulation may provide a platform through which both behavioral and neural math-related processes may be enhanced. Common approaches to neuroimaging of math processing lack ecological validity and are often not analogous to real-world learning activities. However, because of its liberal tolerance of movement, near-infrared spectroscopy (NIRS) provides an ideal platform for such studies. Here, NIRS is used to provide the first concurrent examination of neurological and behavioral data from number line estimation performance within children and adults. Moreover, in an effort to observe the behavioral and neurological benefits to number line estimations that may arise from multisensory stimulation, differential feedback (i.e., visual, auditory, or audiovisual) about estimation performance is provided throughout a portion of the task. Results suggest behavioral and neural performance is enhanced by feedback. Moreover, significant effects of age suggest young children show greater neurological response to feedback, and increase in task difficulty resulted in decreased behavioral performance and increased neurological activation associated with mathematical processing. Thus, typical math learners effectively recruit areas of the brain known to process number when math activities become increasingly difficult. Data inform understanding typical behavioral and neural responses to real-world math learning tasks, and may prove useful in triangulating signatures of atypical math learning. Moreover, results demonstrate the utility of NIRS as a platform to provide simultaneous neurological and behavioral data during naturalistic math learning activities.

This present thesis is focused on the description of relation between brain activity while solving approximate arithmetic tasks and results in Stanford Binet's intelligence test in preschool children. The influence of N1, N2 and P2p components and late posterior components on non-symbolic numerical processing has been validated. Furthermore, it is the influence of maturation with each measured component and also the difference in their amplitude and their commencement after the stimulus presentation that must be pointed out. Our research data show that it is the very amplitude and its commencement that can be used as a potential intelligence indicator in preschool children. Both these components are related to cognitive processing time which has repeatedly proved to correlate with G intelligence factor. It is especially N2 component, which is connected with inhibitiory control of executive functions, that seems to have the potential for this diagnosis. Generally, it is P2p component that is given major attention. Nevertheless, in our research, this component has shown inconsistent results with respect to the amplitude which can be attributed to a low variance of our children's intelligence.

<p>In order that epistemic formulas might be coupled with approximate databases, it is necessary to have a well-defined semantics for the knowledge operator and a method of reducing epistemic formulas to approximate formulas. In this thesis, two possible definitions of a semantics for the knowledge operator are proposed for use together with an approximate relational database: </p><p>* One based upon logical entailment (being the dominating notion of knowledge in literature); sound and complete rules for reduction to approximate formulas are explored and found not to be applicable to all formulas. </p><p>* One based upon algorithmic computability (in order to be practically feasible); the correspondence to the above operator on the one hand, and to the deductive capability of the agent on the other hand, is explored.</p><p>Also, an inductively defined semantics for a"know whether"-operator, is proposed and tested. Finally, an algorithm implementing the above is proposed, carried out using Java, and tested.</p>

Local feature detection and its applications in different problems are quite popular in vision research. In order to analyze a scene, its invariant features, which are distinguishable in many views of this scene, are used in pose estimation, object detection and augmented reality. However, required performance metrics might change according to the application type / in general, the main metrics are accepted as accuracy and computational complexity. The contributions in this thesis provide improving these metrics and can be divided into three parts, as local feature detection, local feature description and description matching in different views of the same scene. In this thesis an efficient feature detection algorithm with sufficient repeatability performance is proposed. This detection method is convenient for real-time applications. For local description, a novel local binary pattern outperforming state-of-the-art binary pattern is proposed. As a final task, a fuzzy decision tree method is presented for approximate nearest neighbor search. In all parts of the system, computational efficiency is considered and the algorithms are designed according to limited processing time. Finally, an overall system capable of matching different views of the same scene has been proposed and executed in a mobile platform. The results are quite promising such that the presented system can be used in real-time applications, such as augmented reality, object retrieval, object tracking and pose estimation.

<p>This thesis focuses on the development of ABC methods for statistical modeling in complex dynamic systems. Motivated by real applications in biology, I propose computational strategies for Bayesian inference in contexts where standard Monte Carlo methods cannot be directly applied due to the high complexity of the dynamic model and/or data limitations.</p><p> Chapter 2 focuses on stochastic bionetwork models applied to data generated from the marginal distribution of a few network nodes at snapshots in time. I present a Bayesian computational strategy, coupled with an approach to summarizing and numerically characterizing biological phenotypes that are represented in terms of the resulting sample distributions of cellular markers. ABC and mixture modeling are used to define the approach to linking mechanistic mathematical models of network dynamics to snapshot data, using a toggle switch example integrating simulated and real data as context. </p><p> Chapter 3 focuses on the application of the methodology presented in Chapter 2 to the Myc/Rb/E2F network. This network involves a relatively high number of parameters and stochastic equations in the model specification and, thus, is substantially more complex than the toggle switch example. The analysis of the Myc/Rb/E2F network is performed with simulated and real data. I demonstrate that the proposed method can indicate which parameters can be learned about using the marginal data. </p><p> In Chapter 4, I present an ABC SMC method that uses data-based adaptive weights. This easily implemented and computationally trivial extension of ABC SMC can substantially improve acceptance rates. This is demonstrated through a series of examples with simulated and real data, including the toggle switch example. Theoretical justification is also provided to explain why this method is expected to improve the effectiveness of ABC SMC.</p><p> In Chapter 5, I present an integrated Bayesian computational strategy for fitting complex dynamic models to sparse time-series data. This is applied to experimental data from an immunization response study with Indian Rhesus macaques. The computational strategy consists of two stages: first, MCMC is implemented based on simplified sampling steps, and then, the resulting approximate output is used to generate a proposal distribution for the parameters that results in an efficient ABC procedure. The incorporation of ABC as a correction tool improves the model fit, as is demonstrated through predictive posterior analysis on the data sets of the study.</p><p> Chapter 6 presents additional discussion and comments on potential future research directions.</p> / Dissertation

In this thesis, we will study issues related to prediction problems and put an emphasis on those arising when recurrent events are involved. First we define the basic concepts of frequentist and Bayesian statistical prediction in the first chapter. In the second chapter, we study frequentist prediction intervals and their associated predictive distributions. We will then present an approach based on asymptotically uniform pivotals that is shown to dominate the plug-in approach under certain conditions. The following three chapters consider the prediction of recurrent events. The third chapter presents different prediction models when these events can be modeled using homogeneous Poisson processes. Amongst these models, those using random effects are shown to possess interesting features. In the fourth chapter, the time homogeneity assumption is relaxed and we present prediction models for non-homogeneous Poisson processes. The behavior of these models is then studied for prediction problems with a finite horizon. In the fifth chapter, we apply the concepts discussed previously to a warranty dataset coming from the automobile industry. The number of processes in this dataset being very large, we focus on methods providing computationally rapid prediction intervals. Finally, we discuss the possibilities of future research in the last chapter.

In this thesis, we will study issues related to prediction problems and put an emphasis on those arising when recurrent events are involved. First we define the basic concepts of frequentist and Bayesian statistical prediction in the first chapter. In the second chapter, we study frequentist prediction intervals and their associated predictive distributions. We will then present an approach based on asymptotically uniform pivotals that is shown to dominate the plug-in approach under certain conditions. The following three chapters consider the prediction of recurrent events. The third chapter presents different prediction models when these events can be modeled using homogeneous Poisson processes. Amongst these models, those using random effects are shown to possess interesting features. In the fourth chapter, the time homogeneity assumption is relaxed and we present prediction models for non-homogeneous Poisson processes. The behavior of these models is then studied for prediction problems with a finite horizon. In the fifth chapter, we apply the concepts discussed previously to a warranty dataset coming from the automobile industry. The number of processes in this dataset being very large, we focus on methods providing computationally rapid prediction intervals. Finally, we discuss the possibilities of future research in the last chapter.

Applications of the existing steady-state plant-wide optimization and the single-scale fast-rate dynamic optimization strategies to an integrated plant with material recycle have been impeded by several factors. While the steady-state optimization formulation is very simple, the very long transient dynamics of an integrated plant have limited the optimizers execution rate to be extremely low, yielding a suboptimal performance. In contrast, performing dynamic plant-wide optimization at the same rate as local controllers requires exorbitant on-line computational load and may increase the sensitivity to high-frequency dynamics that are irrelevant to the plant-level interactions, which are slow-scale in nature. This thesis proposes a novel multi-scale dynamic optimization and control strategy suitable for an integrated plant. The dynamic plant-wide optimizer in this framework executes at a slow rate to track the slow-scale plant-wide interactions and economics, while leaving the local controllers to handle fast changes related to the local units. Moreover, this slow execution rate demands less computational and modeling requirement than the fast-rate optimizer. An important issue of this method is obtaining a suitable dynamic model when first-principles are unavailable. The difficulties in the system identification process are designing proper input signal to excite this ill-conditioned system and handling the lack of slow-scale dynamic data when the plant experiment cannot be conducted for a long time compared to the settling time. This work presents a grey-box modeling method to incorporate steady-state information to improve the model prediction accuracy. A case study of an integrated plant example is presented to address limitations of the nonlinear model predictive control (NMPC) in terms of the on-line computation and its inability to handle stochastic uncertainties. Then, the approximate dynamic programming (ADP) framework is investigated. This method computes an optimal operating policy under uncertainties off-line. Then, the on-line multi-stage optimization can be transformed into a single-stage problem, thus reducing the real-time computational effort drastically. However, the existing ADP framework is not suitable for an integrated plant with high dimensional state and action space. In this study, we combine several techniques with ADP to apply nonlinear optimal control to the integrated plant example and show its efficacy over NMPC.

With the increase in the complexity of computer systems, existing security measures are not enough to prevent attacks. Intrusion detection systems have become an integral part of computer security to detect attempted intrusions. Intrusion detection systems need to be fast in order to detect intrusions in real time. Furthermore, intrusion detection systems need to be robust against the attacks which are disguised to evade them. We improve the runtime complexity and space requirements of a host-based anomaly detection system that uses q-gram matching. q-gram matching is often used for approximate substring matching problems in a wide range of application areas, including intrusion detection. During the text pre-processing phase, we store all the q-grams present in the text in a tree. We use a tree redundancy pruning algorithm to reduce the size of the tree without losing any information. We also use suffix links for fast linear-time q-gram search during query matching. We compare our work with the Rabin-Karp based hash-table technique, commonly used for multiple q-gram matching. To analyze the robustness of network anomaly detection systems, we develop a new class of polymorphic attacks called polymorphic blending attacks, that can effectively evade payload-based network anomaly IDSs by carefully matching the statistics of the mutated attack instances to the normal profile. Using PAYL anomaly detection system for our case study, we show that these attacks are practically feasible. We develop a formal framework which is used to analyze polymorphic blending attacks for several network anomaly detection systems. We show that generating an optimal polymorphic blending attack is NP-hard for these anomaly detection systems. However, we can generate polymorphic blending attacks using the proposed approximation algorithms. The framework can also be used to improve the robustness of an intrusion detector. We suggest some possible countermeasures one can take to improve the robustness of an intrusion detection system against polymorphic blending attacks.