On attractors, spectra and bifurcations of random dynamical systems

In this thesis a number of related topics in random dynamical systems theory are studied: local attractors and attractor-repeller pairs, the exponential dichotomy spectrum and bifurcation theory. We review two existing theories in the literature on local attractors for random dynamical systems on compact metric spaces and associated attractor-repeller pairs and Morse decompositions, namely, local weak attractors and local pullback attractors. We extend the theory of past and future attractor-repeller pairs for nonautonomous systems to the setting of random dynamical systems, and define local strong attractors, which both pullback and forward attract a random neighbourhood. Some examples are given to illustrate the nature of these different attractor concepts. For linear systems considered on the projective space, it is shown that a local strong attractor that attracts a uniform neighbourhood is an object with sufficient properties to prove an analogue of Selgrade's Theorem on the existence of a unique finest Morse decomposition. We develop the dichotomy spectrum for random dynamical systems and investigate its relationship to the Lyapunov spectrum. We demonstrate the utility of the dichotomy spectrum for random bifurcation theory in the following example. Crauel and Flandoli [Journal of Dynamics and Differential Equations, 10(2):259–274, 1998] studied the stochastic differential equation formed from the deterministic pitchfork normal form with additive noise. It was shown that for all parameter values this system possesses a unique invariant measure given by a globally attracting random fixed point with negative Lyapunov exponent, and hence the deterministic bifurcation scenario is destroyed by additive noise. Here, however, we show that one may still observe qualitative changes in the dynamics at the underlying deterministic bifurcation point, in terms of: a loss of hyperbolicity of the dichotomy spectrum; a loss of uniform attractivity; a qualitative change in the distribution of finite-time Lyapunov exponents; and that whilst for small parameter values the systems are topologically equivalent, there is a loss of uniform topological equivalence.Open Acces

Physical activity is prospectively associated with adolescent nonalcoholic fatty liver disease

Objectives: The aim of the present study was to assess whether objectively measured physical activity at mean ages 12 and 14 years are prospectively associated with ultrasound scan liver fat and stiffness (alanine aminotransferase, aspartate aminotransferase [AST], and [gamma]-glutamyl transferase [GGT]) assessed at mean age 17.8 years. Methods: Participants were from the Avon Longitudinal Study of Parents and Children. Total physical activity (counts per minute) and minutes of moderate to vigorous physical activity (MVPA) were measured using ActiGraph accelerometers at mean ages 12 and 14 years. Results: Greater total physical activity and MVPA at ages 12 and 14 years were associated with lower odds of liver fat and lower GGT levels at mean age 17.8 years, such as per 15-minute increase in daily MVPA at age 12 years, the confounder adjusted odds ratio of liver fat was 0.47 (95% confidence interval [CI] 0.27–0.84). Associations attenuated after additional adjustment for fat mass as a potential confounder (eg, per 15-minute increase in daily MVPA at age 12 years, the odds ratio of liver fat attenuated to 0.65 [95% CI 0.35–1.21]) or a potential mediator (eg, per 15-minute increase in daily MVPA at age 12 years the odds ratio of liver fat attenuated to 0.59 [95% CI 0.32–1.09]). Results did not further attenuate after additional adjustment for insulin resistance. There was some evidence that greater total physical activity and MVPA at age 12 years were associated with the higher AST levels. Conclusions: Adolescents who were more active in childhood have lower odds of fatty liver and lower GGT levels. These findings are likely to be, at least in part, explained by adiposity

Weight trajectories through infancy and childhood and risk of non-alcoholic fatty liver disease in adolescence: the ALSPAC study

Background and Aims: Adiposity is a key risk factor for NAFLD. Few studies have examined prospective associations of infant and childhood adiposity with subsequent NAFLD risk. We examined associations of weight-for-height trajectories from birth to age 10 with liver outcomes in adolescence, and assessed the extent to which associations are mediated through fat mass at the time of outcome assessment.<p></p> Methods: Individual trajectories of weight and height were estimated for participants in the Avon Longitudinal Study of Parents and Children using random-effects linear-spline models. Associations of birthweight (adjusted for birth length) and weight change (adjusted for length/height change) from 0–3 months, 3 months–1 y, 1–3 y, 3–7 y, and 7–10 y with ultrasound scan (USS) determined liver fat and stiffness, and serum alanine aminotransferase (ALT), aspartate aminotransferase (AST), and gamma-glutamyl transferase (GGT) at mean age 17.8 y were assessed with linear and logistic regressions. Mediation by concurrent fat mass was assessed with adjustment for fat mass at mean age 17.8 y.<p></p> Results: Birth weight was positively associated with liver stiffness and negatively with ALT and AST. Weight change from birth to 1 y was not associated with outcomes. Weight change from 1–3 y, 3–7 y, and 7–10 y was consistently positively associated with USS and blood-based liver outcomes. Adjusting for fat mass at mean age 17.8 y attenuated associations toward the null, suggesting associations are largely mediated by concurrent body fatness.<p></p> Conclusions: Greater rates of weight-for-height change between 1 y and 10 y are consistently associated with adverse liver outcomes in adolescence. These associations are largely mediated through concurrent fatness

Resource-rational Task Decomposition to Minimize Planning Costs

People often plan hierarchically. That is, rather than planning over a monolithic representation of a task, they decompose the task into simpler subtasks and then plan to accomplish those. Although much work explores how people decompose tasks, there is less analysis of why people decompose tasks in the way they do. Here, we address this question by formalizing task decomposition as a resource-rational representation problem. Specifically, we propose that people decompose tasks in a manner that facilitates efficient use of limited cognitive resources given the structure of the environment and their own planning algorithms. Using this model, we replicate several existing findings. Our account provides a normative explanation for how people identify subtasks as well as a framework for studying how people reason, plan, and act using resource-rational representations.Comment: The first two authors contributed equally. To appear in Proceedings of the 42nd Annual Conference of the Cognitive Science Society (CogSci 2020

Toward Bio-Inspired Tactile Sensing Capsule Endoscopy for Detection of Submucosal Tumors

© 2016 IEEE. Here, we present a method for lump characterization using a bio-inspired remote tactile sensing capsule endoscopy system. While current capsule endoscopy utilizes cameras to diagnose lesions on the surface of the gastrointestinal tract lumen, this proposal uses remote palpation to stimulate a bio-inspired tactile sensing surface that deforms under the impression of both hard and soft raised objects. Current capsule endoscopy utilizes cameras to visually diagnose lesions on the surface of the gastrointestinal tract. Our approach introduces remote palpation by deploying a bio-inspired tactile sensor that deforms when pressed against soft or hard lumps. This can enhance visual inspection of lesions and provide more information about the structure of the lesions. Using classifier systems, we have shown that lumps of different sizes, shapes, and hardnesses can be distinguished in a synthetic test environment. This is a promising early start toward achieving a remote palpation system used inside the GI tract that will utilize the clinician's sense of touch

A novel bio-inspired tactile tumour detection concept for capsule endoscopy

Examination of the gastrointestinal(GI) tract has traditionally been performed using endoscopy tools that allow a surgeon to see the inside of the lining of the digestive tract. Endoscopes are rigid or flexible tubes that use fibre-optics or cameras to visualise tissues in natural orifices. This can be an uncomfortable and very invasive procedure for the patient. © 2014 Springer International Publishing

Humans decompose tasks by trading off utility and computational cost

Human behavior emerges from planning over elaborate decompositions of tasks into goals, subgoals, and low-level actions. How are these decompositions created and used? Here, we propose and evaluate a normative framework for task decomposition based on the simple idea that people decompose tasks to reduce the overall cost of planning while maintaining task performance. Analyzing 11,117 distinct graph-structured planning tasks, we find that our framework justifies several existing heuristics for task decomposition and makes predictions that can be distinguished from two alternative normative accounts. We report a behavioral study of task decomposition ($N=806$) that uses 30 randomly sampled graphs, a larger and more diverse set than that of any previous behavioral study on this topic. We find that human responses are more consistent with our framework for task decomposition than alternative normative accounts and are most consistent with a heuristic -- betweenness centrality -- that is justified by our approach. Taken together, our results provide new theoretical insight into the computational principles underlying the intelligent structuring of goal-directed behavior

Association of maternal diabetes/glycosuria and pre-pregnancy body mass index with offspring indicators of non-alcoholic fatty liver disease

Background: Little is known about early life determinants of non-alcoholic fatty liver disease (NAFLD). We examined associations of maternal pregnancy diabetes/glycosuria and pre-pregnancy body mass index (BMI) with offspring markers of NAFLD and liver pathology and examined mediation by birthweight and concurrent offspring adiposity. Methods: We used data from a UK prospective pregnancy cohort. Offspring underwent abdominal ultrasonography (USS) at mean age 17.8 years. Outcomes included USS-assessed fatty liver, estimated liver volume and shear velocity, a variant of elastography (a marker of liver fibrosis) (N = 1 215) and blood-based markers of liver pathology [alanine amino transferase, aspartate amino transferase, gamma- glutamyltransferase and haptoglobin] (N = 2 359). Results: 2.1 % (N = 25) of participants had USS-assessed fatty liver [maternal diabetes/glycosuria (N = 7) and no diabetes/glycosuria (N = 18)]. Maternal diabetes/glycosuria was associated with greater odds of offspring USS fatty liver in confounder adjusted models [adjusted odds ratio (aOR) 6.74 (95 % confidence interval (CI) 2.47, 18.40)] and higher shear velocity [adjusted ratio of geometric mean (aRGM):1.10 (95 % CI 1.05, 1.15)]. These associations were not mediated by offspring birthweight or concurrent adiposity. Maternal diabetes/glycosuria was not associated with liver volume or blood-based outcomes. Greater maternal pre-pregnancy BMI was associated with greater odds of offspring USS fatty liver [aOR 2.72 (95 % CI: 1.20, 6.15)], higher liver volume [aRGM 1.03 (95 % CI 1.00, 1.07)] and shear velocity [aRGM1.03 (95 % CI: 1.01, 1.06)] in confounder adjusted models. These associations were largely mediated by offspring adiposity. Maternal pre-pregnancy BMI was not consistently associated with blood-based outcomes. Conclusions: Results suggest that maternal pregnancy diabetes/glycosuria is associated with offspring NAFLD through mechanisms other than offspring’s own adiposity

Exploring the hierarchical structure of human plans via program generation

Human behavior is inherently hierarchical, resulting from the decomposition of a task into subtasks or an abstract action into concrete actions. However, behavior is typically measured as a sequence of actions, which makes it difficult to infer its hierarchical structure. In this paper, we explore how people form hierarchically-structured plans, using an experimental paradigm that makes hierarchical representations observable: participants create programs that produce sequences of actions in a language with explicit hierarchical structure. This task lets us test two well-established principles of human behavior: utility maximization (i.e. using fewer actions) and minimum description length (MDL; i.e. having a shorter program). We find that humans are sensitive to both metrics, but that both accounts fail to predict a qualitative feature of human-created programs, namely that people prefer programs with reuse over and above the predictions of MDL. We formalize this preference for reuse by extending the MDL account into a generative model over programs, modeling hierarchy choice as the induction of a grammar over actions. Our account can explain the preference for reuse and provides the best prediction of human behavior, going beyond simple accounts of compressibility to highlight a principle that guides hierarchical planning

Childhood energy intake is associated with nonalcoholic fatty liver disease in adolescents

Background: Greater adiposity is an important risk factor for nonalcoholic fatty liver disease (NAFLD). Thus, it is likely that dietary intake is involved in the development of the disease. Prospective studies assessing the relation between childhood dietary intake and risk of NAFLD are lacking. Objective: This study was designed to explore associations between energy, carbohydrate, sugar, starch, protein, monounsaturated fat, polyunsaturated fat, saturated fat, and total fat intake by youth at ages 3, 7, and 13 y and subsequent (mean age: 17.8 y) ultrasound scan (USS)–measured liver fat and stiffness and serum alanine aminotransferase, aspartate aminotransferase, and γ-glutamyltransferase. We assessed whether observed associations were mediated through fat mass at the time of outcome assessment. Methods: Participants were from the Avon Longitudinal Study of Parents and Children. Trajectories of energy and macronutrient intake from ages 3–13 y were obtained with linear-spline multilevel models. Linear and logistic regression models examined whether energy intake and absolute and energy-adjusted macronutrient intake at ages 3, 7, and 13 y were associated with liver outcomes. Results: Energy intake at all ages was positively associated with liver outcomes; for example, the odds of having a USS-measured liver fat per 100 kcal increase in energy intake at age 3 y were 1.79 (95% CI: 1.14, 2.79). Associations between absolute macronutrient intake and liver outcomes were inconsistent and attenuated to the null after adjustment for total energy intake. The majority of associations attenuated to the null after adjustment for fat mass at the time liver outcomes were assessed. Conclusion: Higher childhood and early adolescent energy intake is associated with greater NAFLD risk, and the macronutrients from which energy intake is derived are less important. These associations appear to be mediated, at least in part, by fat mass at the time of outcome assessment