749 research outputs found
D-modules on Spaces of Rational Maps and on other Generic Data
Let X be an algebraic curve. We study the problem of parametrizing geometric
data over X, which is only generically defined. E.g., parametrizing generically
defined (aka rational) maps from X to a fixed target scheme Y. There are three
methods for constructing functors of points for such moduli problems (all
originally due to Drinfeld), and we show that the resulting functors are
equivalent in the fppf Grothendieck topology. As an application, we obtain
three presentations for the category of D-modules "on" B (K) \G (A) /G (O), and
we combine results about this category coming from the different presentations.Comment: 55 page
Synchronization of Network Coupled Chaotic and Oscillatory Dynamical Systems
We consider various problems relating to synchronization in networks of coupled oscillators. In Chapter 2 we extend a recent exact solution technique developed for all-to-all connected Kuramoto oscillators to certain types of networks by considering large ensembles of system realizations. For certain network types, this description allows for a reduction to a low dimensional system of equations. In Chapter 3 we compute the Lyapunov spectrum of the Kuramoto model and contrast our results both with the results of other papers which studied similar systems and with those we would expect to arise from a low dimensional description of the macroscopic system state, demonstrating that the microscopic dynamics arise from single oscillators interacting with the mean field. Finally, Chapter 4 considers an adaptive coupling scheme for chaotic oscillators and explores under which conditions the scheme is stable, as well as the quality of the stability
Multiscale Dynamics in Communities of Phase Oscillators
We investigate the dynamics of systems of many coupled phase oscillators with
het- erogeneous frequencies. We suppose that the oscillators occur in M groups.
Each oscillator is connected to other oscillators in its group with
"attractive" coupling, such that the coupling promotes synchronization within
the group. The coupling between oscillators in different groups is "repulsive";
i.e., their oscillation phases repel. To address this problem, we reduce the
governing equations to a lower-dimensional form via the ansatz of Ott and
Antonsen . We first consider the symmetric case where all group parameters are
the same, and the attractive and repulsive coupling are also the same for each
of the M groups. We find a manifold L of neutrally stable equilibria, and we
show that all other equilibria are unstable. For M \geq 3, L has dimension M -
2, and for M = 2 it has dimension 1. To address the general asymmetric case, we
then introduce small deviations from symmetry in the group and coupling param-
eters. Doing a slow/fast timescale analysis, we obtain slow time evolution
equations for the motion of the M groups on the manifold L. We use these
equations to study the dynamics of the groups and compare the results with
numerical simulations.Comment: 29 pages, 6 figure
The stability of adaptive synchronization of chaotic systems
In past works, various schemes for adaptive synchronization of chaotic
systems have been proposed. The stability of such schemes is central to their
utilization. As an example addressing this issue, we consider a recently
proposed adaptive scheme for maintaining the synchronized state of identical
coupled chaotic systems in the presence of a priori unknown slow temporal drift
in the couplings. For this illustrative example, we develop an extension of the
master stability function technique to study synchronization stability with
adaptive coupling. Using this formulation, we examine local stability of
synchronization for typical chaotic orbits and for unstable periodic orbits
within the synchronized chaotic attractor (bubbling). Numerical experiments
illustrating the results are presented. We observe that the stable range of
synchronism can be sensitively dependent on the adaption parameters, and we
discuss the strong implication of bubbling for practically achievable adaptive
synchronization.Comment: 21 pages, 6 figure
Core intuitions about persons co-exist and interfere with acquired Christian beliefs about God
In three experiments, using a novel sentence verification paradigm, we tested the hypothesis that acquired Christian beliefs about God which are inconsistent with core intuitions about persons co-exist with, rather than replace, those intuitions in the minds of religious believers. Participants were asked to evaluate a series of statements for which core intuitions and acquired religious beliefs were consistent (i.e. true according to both [e.g. āGod has beliefs that are trueā] or false according to both [e.g. āall beliefs God has are falseā]) or inconsistent (i.e. true on intuition but false theologically [e.g. āGod has beliefs that are falseā] or false on intuition but true theologically [e.g. āall beliefs God has are trueā]). Participants (1) were less accurate and took longer to respond to the inconsistent statements, suggesting that core intuitions both co-exist alongside and interfere with acquired religious beliefs (Experiments 1 and 2), (2) were disproportionately more likely to make errors on the inconsistent statements when responding under time pressure than when responding with no time pressure, suggesting that the resolution of conflicts between inconsistent co-existing beliefs requires cognitive resources (Experiment 2). Experiment 3 ruled-out a plausible alternative interpretation of these results
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How the mind builds evolutionarily new concepts
The human mind is equipped with a variety of evolved mechanisms, each specialized for representing concepts from an adaptively important domain, such as persons and their mental states, animals and their biology, plants, and physical objects and their mechanical properties. But how does the mind build concepts that were not targets of natural selection, that is, concepts that go beyond or even conflict with the inferences engineered into these evolved mechanisms? Are evolutionarily new concepts built out of nothing (as domain-general learning theories predict), or are they built by initially co-opting evolved concepts? And if evolutionary new concepts initially co-opt evolved ones, do they later revise the evolved concepts, or do they co-exist alongside them? I evaluate these questions using the Christian God concept as a case study.I demonstrate using a novel sentence verification paradigm that, first, the God concept is built by co-opting the evolved person concept, and, second, that in the minds of Christian religious adherents, acquired theological representations of God which conflict with person representations (e.g. infallibility) co-exist alongside and do not revise them. In the experiments reported here, Christian religious adherents were asked to evaluate statements for which core knowledge intuitions about persons and acquired Christian theology about God were consistent (i.e., true according to both [e.g., āGod has beliefs that are trueā] or false according to both [e.g., āAll beliefs God has are falseā]) or inconsistent (i.e., true on intuition but false theologically [e.g., āGod has beliefs that are falseā] or false on intuition but true theologically [e.g., āAll beliefs God has are trueā]). Exp. 1 demonstrated that participants were less accurate and slower responding to inconsistent versus consistent statements, suggesting that the core knowledge intuitions both co-existed alongside and interfered with the acquired theological representations. Exp. 2 tested the effects of cognitive load on response interference. Exp. 3 ruled out a plausible alternative interpretation of these findings, by demonstrating that response interference is found for God but not for an ordinary entity (a priest). Exp. 4 demonstrated that response interference is invariant with age and with theological experience. Indeed, response interference was found even in Christian religious adherents with a lifetime of theological experience. Finally, Exp. 5-6 expanded on the findings of the previous experiments, which primarily focused on Godās psychology, to Godās physicality. I discuss the implications of these findings to domain-general versus domain-specific theories of learning
Population preference values for health states in relapsed or refractory B-precursor acute lymphoblastic leukemia in the United Kingdom
Health state descriptions. (DOCX 41 kb
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