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

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

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

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

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

Causal Judgment in the Wild:Evidence from the 2020 U.S. Presidential Election

When explaining why an event occurred, people intuitively highlight some causes while ignoring others. How do people decide which causes to select? Models of causal judgment have been evaluated in simple and controlled laboratory experiments, but they have yet to be tested in a complex real-world setting. Here, we provide such a test, in the context of the 2020 U.S. presidential election. Across tens of thousands of simulations of possible election outcomes, we computed, for each state, an adjusted measure of the correlation between a Biden victory in that state and a Biden election victory. These effect size measures accurately predicted the extent to which U.S. participants (N = 207, preregistered) viewed victory in a given state as having caused Biden to win the presidency. Our findings support the theory that people intuitively select as causes of an outcome the factors with the largest standardized causal effect on that outcome across possible counterfactual worlds.</p

A novel DAG-dependent mechanism links PKCa and Cyclin B1 regulating cell cycle progression

Through the years, different studies showed the involvement of Protein Kinase C (PKC) in cell cycle control, in particular during G1/S transition. Little is known about their role at G2/M checkpoint. In this study, using K562 human erythroleukemia cell line, we found a novel and specific mechanism through which the conventional isoform PKC� positively affects Cyclin B1 modulating G2/M progression of cell cycle. Since the kinase activity of this PKC isoform was not necessary in this process, we demonstrated that PKC�, physically interacting with Cyclin B1, avoided its degradation and stimulated its nuclear import at mitosis. Moreover, the process resulted to be strictly connected with the increase in nuclear diacylglycerol levels (DAG) at G2/M checkpoint, due to the activity of nuclear Phospholipase C β1 (PLCβ1), the only PLC isoform mainly localized in the nucleus of K562 cells. Taken together, our findings indicated a novel DAG dependent mechanism able to regulate the G2/M progression of the cell cycle

Erosion of synchronization: Coupling heterogeneity and network structure

We study the dynamics of network-coupled phase oscillators in the presence of coupling frustration. It was recently demonstrated that in heterogeneous network topologies, the presence of coupling frustration causes perfect phase synchronization to become unattainable even in the limit of infinite coupling strength. Here, we consider the important case of heterogeneous coupling functions and extend previous results by deriving analytical predictions for the total erosion of synchronization. Our analytical results are given in terms of basic quantities related to the network structure and coupling frustration. In addition to fully heterogeneous coupling, where each individual interaction is allowed to be distinct, we also consider partially heterogeneous coupling and homogeneous coupling in which the coupling functions are either unique to each oscillator or identical for all network interactions, respectively. We demonstrate the validity of our theory with numerical simulations of multiple network models, and highlight the interesting effects that various coupling choices and network models have on the total erosion of synchronization. Finally, we consider some special network structures with well-known spectral properties, which allows us to derive further analytical results