Functional differential equations with delay have long been studied due to their practical applications. For the delay term is not a constant number, many researches study the case when this deviating argument depends on the state variable. So we deal with the differential and functional equations involving with the compositions of the unknown function, i.e. the iterative functional differential equations (IFDEs) and iterative functional equations (IFEs) without derivative. The main purpose of this dissertation is to investigate the solutions of such equations, including their analytic solutions, numerical solutions and qualitative behaviors. First, we survey some well known differential equations of this type which possess analytic solutions. Then the classical method of undetermined coefficients is used to compute these power series solutions for the first order IFDEs in Chapter 1, the second order IFDEs in Chapter 2 and FDEs in Chapter 3. Taylor series method is also used to get these analytic solutions in Chapter 4. Systematical method is found to locate the fixed point in generalized sense, so we can use these methods to calculate the coefficients of their analytic solutions. Furthermore, we also establish the existence and uniqueness theorem for analytic solution in Chapter 5. Second, we survey the known existence and uniqueness theorems of solutions for these IFDEs and FDEs in Chapter 6. Then we apply Schauder fixed point theorem to establish new existence theorems of local solutions for general IFDEs. Under certain conditions, these local solutions can be extended to global solutions. Chapter 7 deals with the simplest IFDEs the Eder's equation. We extend the qualitative properties of this case and find its solution is not unique. In Chapter 8, we use Euler method to get the numerical solution of IFDEs. Under some conditions, we have the error analysis on these equations. In Chapter 9, we employ the method of undetermined coefficients, Taylor series, Picard's iteration and Si's methods to get their analytic solutions. Their comparisons, the advantage and disadvantage of these methods are also discussed.

Diss. (sammanfattning) Stockholm : Handelshögskolan, 2006.

In this dissertation a class of stochastic differential equations is considered in the limit as mass tends to zero, called the Smoluchowski-Kramers limit. The Smoluchowski-Kramers approximation is useful in simplifying the dynamics of a system. For example, the problems of calculating of rates of chemical reactions, describing dynamics of complex systems with noise, and measuring ultra small forces, are simplified using the Smoluchowski-Kramers approximation. In this study, we prove strong convergence in the small mass limit for a multi-dimensional system with arbitrary state-dependent friction and noise coefficients. The main result is proved using a theory of convergence of stochastic integrals developed by Kurtz and Protter. The framework of the main theorem is sufficiently arbitrary to include systems of stochastic differential equations driven by both white and Ornstein-Uhlenbeck colored noises.

The value of a state is a measure of its worth, so that, for example, waypoints have high value and regions inside of obstacles have very small value. We propose two methods of incorporating world information as state-dependent modifications to the interacting multiple models (IMM) algorithm, and then we use a game's player-controlled trajectories as ground truths to compare the normal IMM algorithm to versions with our proposed modifications. The two methods involve modifying the model probabilities in the update step and modifying the transition probability matrix in the mixing step based on the assigned values of different target states. The state-dependent value assignment modifications are shown experimentally to perform better than the normal IMM algorithm in both estimating the target's current state and predicting the target's next state.

State dependent Riccati equation (SDRE) plays an important role in nonlinear controller design. For autonomous nonlinear systems that can be expressed in linear form with state-dependent coefficients (SDC), SDRE-based controllers guarantee local asymptotic stability of the closed-loop system, under pointwise stabilizability and detectability conditions. Moreover, the optimal control for a quadratic cost function, when it exists, corresponds to an SDRE-based control design for a specific SDC parameterization of the associated nonlinear system. Unfortunately, the implementation of the SDRE-based controllers is computationally expensive. Various techniques have been developed for solving the SDRE, which are either computationally expensive or lack acceptable precision. In this dissertation, a modified state-dependent differential Riccati equation (MSDDRE) is proposed for approximating the solution of the SDRE, which is easy to implement with moderate computation power and its solution can be made arbitrarily close to that of the SDRE. Therefore, it can be used for real-time implementation of near-optimal controllers for nonlinear systems in state-dependent linear form. The proposed technique is then extended to SDRE-based filter design and its application to SDRE-based output feedback control technique. The proposed technique is also extended to state-dependent H-inf; robust control design for a constant noise attenuation bound, when the solution exists. To reduce the design conservativeness, the technique is further extended to state-dependent H-inf; robust control design with adaptive noise attenuation bound, using gain-scheduling technique and linear matrix inequality (LMI) optimization, to approximate H-inf; optimal control with state-dependent noise-attenuation bound. Local asymptotic stability of the closed-loop system is proven for all proposed techniques. Simulation results further confirm the validity of the development and demonstrate the efficiency of the proposed techniques.

abstract: Foraging has complex effects on whole-organism homeostasis, and there is considerable evidence that foraging behavior is influenced by both environmental factors (e.g., food availability, predation risk) and the physiological condition of an organism. The optimization of foraging behavior to balance costs and benefits is termed state-dependent foraging (SDF) while behavior that seeks to protect assets of fitness is termed the asset protection principle (APP). A majority of studies examining SDF have focused on the role that energy balance has on the foraging of organisms with high metabolism and high energy demands ("high-energy systems" such as endotherms). In contrast, limited work has examined whether species with low energy use ("low-energy systems" such as vertebrate ectotherms) use an SDF strategy. Additionally, there is a paucity of evidence demonstrating how physiological and environmental factors other than energy balance influence foraging behavior (e.g. hydration state and free-standing water availability). Given these gaps in our understanding of SDF behavior and the APP, I examined the state-dependency and consequences of foraging in a low-energy system occupying a resource-limited environment - the Gila monster (Heloderma suspectum, Cope 1869). In contrast to what has been observed in a wide variety of taxa, I found that Gila monsters do not use a SDF strategy to manage their energy reserves and that Gila monsters do not defend their energetic assets. However, hydration state and free-standing water availability do affect foraging behavior of Gila monsters. Additionally, as Gila monsters become increasingly dehydrated, they reduce activity to defend hydration state. The SDF behavior of Gila monsters appears to be largely driven by the fact that Gila monsters must separately satisfy energy and water demands with food and free-standing water, respectively, in conjunction with the timescale within which Gila monsters balance their energy and water budgets (supra-annually versus annually, respectively). Given these findings, the impact of anticipated changes in temperature and rainfall patterns in the Sonoran Desert are most likely going to pose their greatest risks to Gila monsters through the direct and indirect effects on water balance. / Dissertation/Thesis / Ph.D. Biology 2014

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20924号 / 理博第4376号 / 新制||理||1628(附属図書館) / 京都大学大学院理学研究科地球惑星科学専攻 / (主査)教授 田上 高広, 教授 山路 敦, 教授 平原 和朗 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Stroke is the main cause of adult motor disability. Nevertheless, recent meta-analyses show that the theoretical models conceived to explain the post-stroke brain reorganization are inaccurate and therefore misleading in laying the theoretical foundation for rehabilitation protocols. Mixed results are reported especially in works investigating the excitability properties of the stroke injured brain. Shedding light on the reasons that brought to such mixed results is the central topic of this doctoral thesis. In particular, this confounding evidence is here discussed and tackled in the light of recent works employing brain-state dependent stimulation protocols. These works have been of paramount importance, as they showed that the effects of non-invasive stimulation (TMS and/or rTMS) on the hand knob of the motor cortex depend on the instantaneous sensorimotor state. This local state is largely determined by the phase of the mu-alpha oscillations, with the negative peak representing a high excitability condition. Brain-state dependent results show that controlling for the local state at the moment of stimulation is crucial in order to reduce variability in studies investigating cortical excitability: an approach that has never been employed in stroke literature, so far. In this doctoral thesis, new evidence is provided on affected and unaffected hemispheres’ excitability properties depending on the local state at the moment of stimulation. This previously uncontrolled state-dependent variability is here proposed as one of the factors at the basis of the mixed results in stroke literature. Furthermore, the current models aimed at explaining post-stroke brain reorganization do not take into account factors that recent works suggest might contribute to stroke recovery. In fact, it is here suggested that: interhemispheric inhibition should not be interpreted as competition, structural reserve should be assessed also at the level of the corpus callosum, diaschisis processes should be taken into account and structural and functional connectivity patterns should be included in patients’ assessment. Finally, the excitability properties of the stroke brain have been often inferred comparing stroke patients’ with young healthy controls’. In this regard, it is here proposed that only healthy peers should be included in the control groups, as brain structural changes due to healthy aging have an impact on corticospinal excitability. The aforementioned functional and structural issues are addressed in the following chapters by means of different techniques (i.e. TMS-EEG, MRI, MEG). In particular, in Chapter 1, a new framework of post-stroke brain reorganization is proposed, in which previously over-looked factors are suggested to be essential in the understanding of the potential plastic changes following stroke. Specifically, a new account where interhemispheric inhibition is interpreted in terms of integration and not competition, is supported. Moreover, the proposed framework includes recent pieces of evidence suggesting that structural reserve should be evaluated in the individual patient not only at the level of the cortex, but also in the different sections of the callosum. Finally, it is proposed that structural damage is not static, but rather dynamic as it continues also after the stroke episode through dischiasis processes. In Chapter 2, new knowledge is provided on the different excitability properties of the two hemispheres of stroke patients. In this chapter, TMS-EEG data of stimulation on both the affected and unaffected motor cortex in severe chronic strokes are analysed with a brain-state dependent approach. For the first time, it is shown that the excitability properties of the affected and unaffected hemispheres differ as the local state at the moment of stimulation influences the two hemispheres’ response differently. In particular, the strong and simplified TMS-evoked response in the affected hemisphere, previously reported in severe patients, is shown to depend on a disruption of the differentiation between the high and low excitability states of the motor cortex, determined by the instantaneous phase of alpha oscillations. This low differentiation between excitability states in the affected hemisphere should be systematically investigated, as it could be a potential feature of patients who experience poor recovery. Furthermore, in Chapter 3, connectivity at the individual alpha peak is investigated in a big cohort of healthy participants, in a resting state MEG dataset. This work was implemented because alpha connectivity networks have been shown to predict stroke recovery. For this reason, there is a necessity to reliably assess connectivity at alpha before and after rehabilitation, as this could be informative on the efficacy of rehabilitation. Specifically, it is shown that using complementary phase-coherence metrics is more effective to estimate connectivity patterns at source level. This compound approach is proposed as a tool to better control the modulatory effects of rehabilitation stimulation protocols, in order to identify which are the changes in activity patterns that are potentially responsible for recovery. Finally, in Chapter 4 brain structural changes associated with healthy aging are investigated in a big cohort of participants aged between 18 and 90 years old, both in terms of cortical thinning and cortical myelin concentration loss. In particular, given recent evidence on the relationship between cortical myelin content and corticospinal excitability, it is shown that age-dependent myelin loss occurs mostly at the level of the premotor, motor and sensory cortices. These structural changes need to be taken into account when stroke patients are compared with controls. In fact, since stroke patients are often in their elderly, these age-related structural changes need to be controlled by including only age-matched healthy participants in control groups, as this is not often a fulfilled criterion in stroke studies. To conclude, this doctoral thesis proposes that the current models’ inaccuracy depends on 1) patients’ individual structural and functional factors that have not been taken into account in previous models of brain reorganization post-stroke (Chapter 1), 2) brain-state dependent variability in stimulation effects that have not been controlled for in stroke literature (Chapter 2), 3) a lack of a systematic method to assess the effects of stimulation rehabilitation protocols (Chapter 3) and 4) structural brain changes due to healthy aging, that affect also the stroke brain, and that are not taken into account when patients are compared with young controls in corticospinal excitability studies (Chapter 4). To the author’s knowledge, this is the first work aimed at explaining mixed results in stroke literature from different perspectives and using different neuroimaging techniques for functional and structural anomalies, exploiting recent brain-state dependent approaches for the analysis of stroke patients’ data.

Relative used capital price, the measure of irreversibility, is fixed in almost all the investment literature. This dissertation introduces investment models with state-dependent irreversibility and tests whether these models outperform fixed irreversibility cases, at both the macro and micro levels. Since there is currently no historical data available on the issue of used capital prices, the first chapter uses an indirect inference procedure to estimate the cyclical property of irreversibility at the micro-level. In the second chapter, I propose a dynamic investment model with endogenous irreversibility arising from the lemons problem in the used capital market and examine the cyclical implication of irreversibility. Data evidence shows that capital reallocation, or used capital expenditure, is pro-cyclical. In a general equilibrium framework, the third chapter reveals that the investment model with state-dependent irreversibility explains this phenomenon while the model with fixed irreversibility does not. / text

The topic of badgers in the UK is often a contentious one, dividing opinions and sparking political debate. On one hand, badgers represent an important part of the British ecosystem but on the other a wildlife reservoir of disease implicated in the transmission of bovine tuberculosis (TB) to livestock in the UK. This has prompted strong interest in their population dynamics and epidemiology. Using data from a long-term study of a naturally infected badger population in Woodchester Park, Gloucestershire, this thesis explores a range of capture-mark-recapture (CMR) models to further understand disease and demographic processes. The first section examines long term population dynamics, simultaneously estimating demographic rates alongside their drivers using integrated population models (IPMs). The findings provide new insight into badger demography, highlighting density-dependent mechanisms, vulnerabilities to changing climate and disease prevalence and subsequently how multi-factorial analyses are required to explain fluctuating badger populations. The following sections use multistate models to answer pertinent questions regarding individual disease dynamics, revealing rates of TB infection, progression and disease-induced mortality. A key finding was sex-differences in disease response, with males more susceptible to TB infection. After applying a survival trajectory analysis we suggest sex differences are due to male immune defence deficiencies. A comparative analysis demonstrated similarities between epidemiological processes at Woodchester Park to an unconnected population of badgers from a vaccine study, supporting its continued use as a model population. The final study in this thesis constructs an IPM to estimate disease and population dynamics and in doing so uncovers disease-state recruitment allocation rates, demographic and population estimates of badgers in varying health-states and predicts future dynamics. This model aims to encapsulate the more commonly held notion of populations as dynamic entities with numerous co-occurring processes, opening up avenues for future analyses within both the badger-TB system and possible extensions to other wildlife reservoir populations.