Techniques from the theory of matrix problems have proven to be helpful for studying problems within representation theory. In particular, matrix problems are well suited to use in problems related to classifying indecomposable representations of quivers and of posets. However, throughout the literature, there are many different types of matrix problems and little clarification of the relationships between them. In this thesis, we choose six types of matrix problems, place them all within a common framework and find correspondences between them. Moreover, we show that their use in the classification of finite-dimensional representations of quivers and posets are, in general, well-founded. Additionally, we investigate a direct relationship between the problem of classifying quiver representations and the problem of classifying poset representations.

In the last decade, global instability has led to higher demands placed on military members and their families, especially in the area of deployment. Longer and more frequent deployments have had significant psychological consequences on soldiers who have been deployed. Deployment has also been shown to negatively impact child adjustment; however, the research in this area is limited, particularly within a Canadian military context. The purpose for the two current studies was to examine specific areas of child adjustment affected by military status, particularly deployment, and to explore potential pathways through which this impact occurs. Study 1 included an examination of the effect of military status on maternal depressive symptoms, parental stress, and marital satisfaction, as well as on the quality of the child's attachment to the parent at home. Further analyses were conducted to determine if maternal well-being mediated the effect of military status on attachment, and if there was a moderating role of social support on these associations. In Study 2, the unique role of military status in predicting reported behaviour problems over and above what was accounted for by child attachment and parental stress was explored. Findings from these studies revealed an association between deployment and higher levels of insecure attachment; and although deployment modestly predicted maternal depressive symptoms, there was no mediating effect found for maternal well-being. Furthermore, while insecure attachment and higher levels of parental stress were associated with elevated behaviour problems, deployment uniquely predicted conduct problems, internalizing problems, and total behaviour problems. Findings from the current studies add a valuable contribution to the limited available literature on how deployment affects young children in military families. Moreover these findings provide a basis in which to direct further research, and to also guide the development and implementation of interventions to support at-risk children in military families.

Although researchers have often focused on the victims of aggression, the detrimental effects of engaging in aggression and/or displaying symptoms of externalizing disorders have been clearly identified in children and adolescents. Longstanding consequences of externalizing problems include internalizing difficulties such as depression. There is an increasing interest in identifying the direction of effect and understand whether externalizing problems precede internalizing problems, vice-versa, or whether they share a bi-directional relation. However, the study of the temporal sequence between aggression, externalizing disorders, and internalizing disorders in children and adolescents has yielded inconsistent findings. The sequential relation between externalizing and internalizing difficulties in children and adolescents was examined in this dissertation consisting of three studies. In Study 1, the moderating role of worry in the relation between aggression and depression was examined. The sample consisted of girls nominated as either relationally or physically aggressive by their peers. Results indicated that worry exacerbated the risk of reporting elevated depressive symptoms concurrently and one year later for physically aggressive girls. In Study 2, three competing hypotheses on the longitudinal relation between aggression and depression were compared. Findings from this study supported the hypothesis that symptoms of depression are preceded by aggressive behaviour. Additionally, it was found that engaging in physical aggression predicted depressive symptoms for girls but not for boys. The results of the first two studies suggest that for girls, engaging in non-normative forms of aggression is associated with greater mental health problems. In Study 3, the temporal relation between symptoms of externalizing disorders, namely oppositional defiant disorder and conduct disorder, and symptoms of depression was examined. Results provided support that the progressive relation between symptoms of externalizing and internalizing disorders was bi-directional. In summary, although it seems that engaging in externalizing behaviour, such as aggression, predicts symptoms of depression, findings from the third study suggest that the sequential relation between symptoms of externalizing problems, which may or may not include aggressive behaviour, and symptoms of depression seem to share a reciprocal relation.

The transient flow in pipe networks is represented by a pair of quasi-linear hyperbolic partial differential equations. The method of characteristics is used to transform these equations to a set of ordinary differential equations, which are then solved, by a first order finite difference technique using suitable boundary conditions. The main purposes of these investigations are: 1) To derive suitable boundary conditions or boundary condition equations for valves, sprinklers, surge tanks and air chambers, and 2) To investigate the effect of these boundary conditions on the transient flow in pipe systems. Several numerical examples are solved on the digital computer using the method of characteristics. The results are compared with those obtained by the graphical method. Although in this thesis the developed boundary conditions are used to study the transient response of the irrigation pipe systems, the boundary conditions, without any modification, can be used to determine the transient conditions in water supply pipe networks or in pipes carrying other liquids. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

The thesis deals with the main achievements and problems of the Chinese economy. First part analyses the development of China's GDP and its economic growth, monetary policy and international trade. The second part focuses on the main problems which are lack of natural resources, environmental issues and population issues (aging population and social inequalities).

The current study aimed to evaluate multiple longitudinal determinants of externalizing behavior problems in twins/triplets aged 7 to 12 years. Specifically, a prospective longitudinal design was utilized to assess relationships between age 5 sleep problems, age 5 temperament traits, and later externalizing problems. Additionally, heritability of sleep problems was assessed by utilizing the twin method, and genetic contributions of two specific genes – DRD4 and 5-HTTLPR – were evaluated. A total of 93 twins/triplets (40 boys and 53 girls) and their parents participated in the current study, and data were collected through self-report, parent-report, and molecular and behavioral genetic methods. Results suggest that sleep disturbances are significantly heritable, and that neither early sleep problems, temperament traits, nor specific genes significantly predicted follow-up externalizing problems. Post-hoc analyses assessing gene X environment interactions showed that externalizing problems were significantly predicted by the interaction between stressful life events and DRD4 risk, which is consistent with differential susceptibility models. This study has implications for future research as well as clinical practice, including for early screening, prevention, and intervention efforts aimed at decreasing childhood externalizing and sleep problems.

Inverse problems arise in many fields such as radar imaging, medical imaging and geophysics. It draws much attention in both mathematical communities and industrial members. Mathematically speaking, many inverse problems can be formulated by one or several physical equations and mathematical models. For example, the signal used in radar imaging is governed by Maxwell's equation, and most of geophysical studies can be formulated using elastic equation. Therefore, rigorous mathematical theories can be applied to study the inverse problems coming from this complex world. Random inverse problem is a fascinating area studying how to extract useful statistical information from unknown object coming from real world. In this thesis, we focus on the study of inverse problem related to random Schrödinger operators. We are particularly interested in the case where both the source and the potential of the Schrödinger system are random. In our first topic, we are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schrödinger equation with unknown random source and unknown potential. The well-posedness of the direct scattering problem is first established. Three uniqueness results are then obtained for the corresponding inverse problems in determining the variance of the source, the potential and the expectation of the source, respectively, by the associated far-field measurements. First, a single realization of the passive scattering measurement can uniquely recover the variance of the source without the a priori knowledge of the other unknowns. Second, if active scattering measurement can be further obtained, a single realization can uniquely recover the potential function without knowing the source. Finally, both the potential and the first two statistic moments of the random source can be uniquely recovered with full measurement data. Our second topic also focuses on the case where only the source is random. But in the second topic, the random model is different from our first topic. The second random model has received intensive study in recent years due to the reason that this random model has more flexibility fitting with different regularities. The recovering framework is similar to our first topic, but we shall develop different asymptotic estimates of the higher order terms, which is more difficult than the first one. Lastly, based on the previous two results, we study the case where both the source and the potential are random and unknown. The ergodicity is used to establish the single realization recovery. The asymptotic estimates of higher order terms are based on pseudodifferential operators and microlocal analysis. Three major novelties of our works in this thesis are that, first, we studied the case where both the source and the potential are unknown; second, both passive and active scattering measurements are used for the recovery in different scenarios; finally, only a single realization of the random sample is required to establish the recovery of useful information.

The set of transverse homoclinic intersections for a saddle-focus equilibrium in the planar equilateral restricted four body problem admits certain simple homoclinic orbits which form the skeleton of the complete homoclinic intersection, or homoclinic web. In this thesis, the planar restricted four body problem is viewed as an invariant subsystem of the spatial problem, and the influence of this planar homoclinic skeleton on the spatial dynamics is studied from a numerical point of view. Starting from the vertical Lyapunov families emanating from saddle focus equilibria, we compute the stable/unstable manifolds of these spatial periodic orbits and look for intersections between these manifolds near the fundamental planar homoclinics. In this way, we are able to continue all of the basic planar homoclinic motions into the spatial problem as homoclinics for appropriate vertical Lyapunov orbits which, by the Smale Tangle theorem, suggest the existence of chaotic motions in the spatial problem. While the saddle-focus equilibrium solutions in the planar problems occur only at a discrete set of energy levels, the cycle-to-cycle homoclinics in the spatial problem are robust with respect to small changes in energy. The method uses high order Fourier-Taylor and Chebyshev series approximations in conjunction with the parameterization method, a general functional analytic framework for invariant manifolds. Tools that admit a natural notion of a-posteriori error analysis. Finally, we develop and implement a validation algorithm which we later use to obtain Theorems confirming the existence of homoclinic dynamics. This approach, known as the Radii polynomial, is a contraction mapping argument which can be applied to both the parameterized manifold and the Chebyshev arcs. When the Theorem applies, it guarantees the existence of a true solution near the approximation and it provides an upper bound on the C0 norm of the truncation error. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2021. / FAU Electronic Theses and Dissertations Collection

<div><div><div><p>Several socially and economically important real-world systems comprise large numbers of interacting constituent entities. Examples include the World Wide Web and Online Social Networks (OSNs). Developing the capability to forecast the macroscopic behavior of such systems based on the microscopic interactions of the constituent parts is of considerable economic importance.</p><p>Previous researchers have investigated phenomenological forecasting models in such contexts as the spread of diseases in the real world and the diffusion of innovations in the OSNs. The previous forecasting models work well in predicting future states of a system that are at equilibrium or near equilibrium. However, forecasting non-equilibrium states – such as the transient emergence of hotspots in web traffic – remains a challenging problem. In this thesis we investigate a hypothesis, rooted in Ludwig Boltzmann's celebrated H-theorem, that the evolutionary dynamics of a large system – such as the World Wide Web – is driven by the system's innate tendency to evolve towards a state of maximum entropy.</p><p>Whereas closed systems may be expected to evolve towards a state of maximum entropy, most real-world systems are not closed. However, the stipulation that if a system is closed then it should asymptotically approach a state of maximum entropy provides a strong constraint on the inverse problem of formulating the microscopic interaction rules that give rise to the observed macroscopic behavior. We make the constraint stronger by insisting that, if closed, a system should evolve monotonically towards a state of maximum entropy and formulate microscopic interaction rules consistent with the stronger constraint.</p><p>We test the microscopic interaction rules that we formulate by applying them to two real world phenomena: the flow of web traffic in the gaming forums on Reddit and the spread of Covid-19 virus. We show that our hypothesis leads to a statistically significant improvement over the existing models in predicting the traffic flow in gaming forums on Reddit. Our interaction rules are also able to qualitatively reproduce the heterogeneity in the number of COVID-19 cases across the cities around the globe. The above experiments provide supporting evidence for our hypothesis, suggesting that our approach is worthy of further investigation.</p><p>In addition to the above stochastic model, we also study a deterministic model of attention flow over a network and establish sufficient conditions that, when met, signal imminent parabolic accretion of attention at a node<br></p></div></div></div>

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