We formulate and interpret several multi-modal registration methods in the context of a unified statistical and information theoretic framework. A unified interpretation clarifies the implicit assumptions of each method yielding a better understanding of their relative strengths and weaknesses. Additionally, we discuss a generative statistical model from which we derive a novel analysis tool, the "auto-information function", as a means of assessing and exploiting the common spatial dependencies inherent in multi-modal imagery. We analytically derive useful properties of the "auto-information" as well as verify them empirically on multi-modal imagery. Among the useful aspects of the "auto-information function" is that it can be computed from imaging modalities independently and it allows one to decompose the search space of registration problems.

We formulate and interpret several multi-modal registration methods inthe context of a unified statistical and information theoretic framework. A unified interpretation clarifies the implicit assumptionsof each method yielding a better understanding of their relativestrengths and weaknesses. Additionally, we discuss a generativestatistical model from which we derive a novel analysis tool, the"auto-information function", as a means of assessing and exploiting thecommon spatial dependencies inherent in multi-modal imagery. Weanalytically derive useful properties of the "auto-information" aswell as verify them empirically on multi-modal imagery. Among theuseful aspects of the "auto-information function" is that it canbe computed from imaging modalities independently and it allows one todecompose the search space of registration problems.

Philosophiae Doctor - PhD / Adaptive networks are complex networks with nontrivial topological features and connection patterns between their elements which are neither purely regular nor purely random. Their applications are in sociology, biology, physics, genetics, epidemiology, chemistry, ecology, materials science, the traditional Internet and the emerging Internet of-Things. For example, their applications in sociology include social networks such as Facebook which have recently raised the interest of the research community. These networks may hide patterns which, when revealed, can be of great interest in many practical applications. While the current adaptive network models remain mostly theoretical and conceptual, however, there is currently no unified modelling framework for implementing the development, comparison, communication and validation of agent-based adaptive network models through using proper empirical data and computation models from different research fields. In this thesis, a unified framework has been developed that combines agent- based adaptive network models and adaptive control structures. In this framework, the control parameters of adaptive network models are included as a part of the state- topology coevolution and are automatically adjusted according to the observations obtained from the system being studied. This allows the automatic generation of enhanced adaptive networks by systematically adjusting both the network topology and the control parameters at the same time to accurately reflect the real-world complex system. We develop three different applications within the general framework for agent- based adaptive network modelling and simulation of real-world complex systems in different research fields. First, a unified framework which combines adaptive net- work models and adaptive control structures is proposed for modelling and simulation of fractured-rock aquifer systems. Moreover, we use this unified modelling framework to develop an automatic modelling tool, Fracture3D, for automatically building enhanced fracture adaptive network models of fractured-rock aquifer systems, in which the fracture statistics and the structural properties can both follow the observed statistics from natural fracture networks. We show that the coupling between the fracture adaptive network models and the adaptive control structures with iterative parameter identification can drive the network topology towards a desired state by dynamically updating the geometrical states of fractures with a proper adaptive control structure. Second, we develop a unified framework which combines adaptive network models and multiple model adaptive control structures for modelling and simulation of social network systems. By using such a unified modelling framework, an automatic modelling tool, SMRI, is developed for automatically building the enhanced social adaptive network models through using mobile-phone-centric multimodal data with suitable computational models of behavioural state update and social interaction update. We show that the coupling between the social adaptive network models and the multiple model adaptive control structures can drive the community structure of a social adaptive network models towards a desired state through using the suitable computational models of behavioural state update and social interaction update predetermined by the multiple model adaptive control structure. Third, we develop a unified framework which combines adaptive network models and support vector machine based adaptive control structures for modelling and simulation of multicast congestion in mobile ad hoc network systems. Moreover, a multicast congestion detection scheme, WMCD, has been developed for the unified modelling framework, in which the incipient congestions of group members can be predicted by using support vector machine-based prediction models and current traffic states. We show that the network’s throughput capacity is efficiently improved through using the unified modelling framework, which dynamically adjusting the group structures according to the updated congestion states of group members generated by the WMCD scheme in order to relieve the high load.

Modeling patterns in temporal data has arisen as an important problem in engineering and science. This has led to the popularity of several dynamic models, in particular the renowned hidden Markov model (HMM) [Rabiner, 1989]. Despite its widespread success in many cases, the standard HMM often fails to model more complex data whose elements are correlated hierarchically or over a long period. Such problems are, however, frequently encountered in practice. Existing efforts to overcome this weakness often address either one of these two aspects separately, mainly due to computational intractability. Motivated by this modeling challenge in many real world problems, in particular, for video surveillance and segmentation, this thesis aims to develop tractable probabilistic models that can jointly model duration and hierarchical information in a unified framework. We believe that jointly exploiting statistical strength from both properties will lead to more accurate and robust models for the needed task. To tackle the modeling aspect, we base our work on an intersection between dynamic graphical models and statistics of lifetime modeling. Realizing that the key bottleneck found in the existing works lies in the choice of the distribution for a state, we have successfully integrated the discrete Coxian distribution [Cox, 1955], a special class of phase-type distributions, into the HMM to form a novel and powerful stochastic model termed as the Coxian Hidden Semi-Markov Model (CxHSMM). We show that this model can still be expressed as a dynamic Bayesian network, and inference and learning can be derived analytically. / Most importantly, it has four superior features over existing semi-Markov modelling: the parameter space is compact, computation is fast (almost the same as the HMM), close-formed estimation can be derived, and the Coxian is flexible enough to approximate a large class of distributions. Next, we exploit hierarchical decomposition in the data by borrowing analogy from the hierarchical hidden Markov model in [Fine et al., 1998, Bui et al., 2004] and introduce a new type of shallow structured graphical model that combines both duration and hierarchical modelling into a unified framework, termed the Coxian Switching Hidden Semi-Markov Models (CxSHSMM). The top layer is a Markov sequence of switching variables, while the bottom layer is a sequence of concatenated CxHSMMs whose parameters are determined by the switching variable at the top. Again, we provide a thorough analysis along with inference and learning machinery. We also show that semi-Markov models with arbitrary depth structure can easily be developed. In all cases we further address two practical issues: missing observations to unstable tracking and the use of partially labelled data to improve training accuracy. Motivated by real-world problems, our application contribution is a framework to recognize complex activities of daily livings (ADLs) and detect anomalies to provide better intelligent caring services for the elderly. / Coarser activities with self duration distributions are represented using the CxHSMM. Complex activities are made of a sequence of coarser activities and represented at the top level in the CxSHSMM. Intensive experiments are conducted to evaluate our solutions against existing methods. In many cases, the superiority of the joint modeling and the Coxian parameterization over traditional methods is confirmed. The robustness of our proposed models is further demonstrated in a series of more challenging experiments, in which the tracking is often lost and activities considerably overlap. Our final contribution is an application of the switching Coxian model to segment education-oriented videos into coherent topical units. Our results again demonstrate such segmentation processes can benefit greatly from the joint modeling of duration and hierarchy.

<div>In the era of big data, the sheer volume and widespread spatial distribution of information has been promoting extensive research on distributed optimization over networks. Each computing unit has access only to a relatively small portion of the entire data and can only communicate with a relatively small number of neighbors. The goal of the system is to reach consensus on the optimal parametric model with respect to the entire data among all computing units. Existing work has provided various decentralized optimization algorithms for the purpose. However, some important questions remain unclear: (I) what is the intrinsic connection among different existing algorithms? (II) what is the min-max lower complexity bound for decentralized algorithms? Can one design an optimal decentralized algorithm in the sense that it achieves the lower complexity bound? and (III) in the presence of asynchrony and imperfect communications, can one design linearly convergent decentralized algorithms?</div><div><br></div><div> This thesis aims at addressing the above questions. (I) Abstracting from ad-hoc, specific solution methods, we propose a unified distributed algorithmic framework and analysis for a general class of optimization problems over networks. Our method encapsulates several existing first-order distributed algorithms. Distinguishing features of our scheme are: (a) When each of the agent’s functions is strongly convex, the algorithm converges at a linear rate, whose dependence on the agents’ functions and network topology is decoupled; (b) When the objective function is convex, but not strongly convex, similar decoupling as in (a) is established for the coefficient of the proved sublinear rate. This also reveals the role of function heterogeneity on the convergence rate; (c) The algorithm can adjust the ratio between the number of communications and computations to achieve a rate (in terms of computations) independent on the network connectivity; and (d) A by-product of our analysis is a tuning recommendation for several existing (non-accelerated) distributed algorithms, yielding provably faster (worst-case) convergence rate for the class of problems under consideration. (II) Referring to lower complexity bounds, the proposed novel family of algorithms, when equipped with acceleration, are proved to be optimal, that is, they achieve convergence rate lower bounds. (III) Finally, to make the proposed algorithms practical, we break the synchronism in the agents’ updates: agents wake up and update without any coordination, using information only from immediate neighbors with unknown, arbitrary but bounded delays. Quite remarkably, even in the presence of asynchrony, the proposed algorithmic framework is proved to converge at a linear rate (resp. sublinear rate) when applied to strongly convex (resp. non strongly convex) optimization problems.</div>

Interactive software systems have both functional and user interface components. User interface design and development requires specialized usability engineering (UE) knowledge, training, and experience in topics such as psychology, cognition, specialized design guidelines, and task analysis. The design and development of a functional core requires specialized software engineering (SE) knowledge, training, and experience in topics such as algorithms, data structures, software architectures, calling structures, and database management. Given that the user interface and the functional core are two closely coupled components of an interactive software system, with each constraining the design of the other, there is a need for the SE and UE life cycles to be connected to support communication among roles between the two development life cycles. Additionally, there is a corresponding need for appropriate computer science curricula to train the SE and UE roles about the connections between the two processes. In this dissertation, we connected the SE and UE life cycles by creating the Ripple project development environment which fosters communication between the SE and UE roles and by creating a graduate-level cross-pollinated SE-UE joint course offering, with student teams spanning the two classes, to educate students about the intricacies of interactive-software development. Using this joint course we simulated different conditions of interactive-software development (i.e. with different types of project constraints and role playing) and assigned different teams to these conditions. As part of semester-long class projects these teams developed prototype systems for a real client using their assigned development condition. Two of the total of eight teams in this study used the Ripple framework. As part of this experimental course offering, various instruments were employed throughout the semester to assess the effectiveness of a framework like Ripple and to investigate candidate factors that impact the quality of product and process of interactive-software systems. The study highlighted the importance of communication among the SE and UE roles and exemplified the need for the two roles to respect each other and to have the willingness to work with one another. Also, there appears to exist an inherent conflict of interest when the same people play both UE and SE roles as they seem to choose user interface features that are easy to implement and not necessarily easy to use by system's target users. Regarding pedagogy, students in this study indicated that this joint SE-UE course was more useful in learning about interactive-software development and that it provided a better learning experience than traditional SE-only or UE-only courses. / Ph. D.