Higher Toda brackets and the Adams spectral sequence in triangulated categories

The Adams spectral sequence is available in any triangulated category equipped with a projective or injective class. Higher Toda brackets can also be defined in a triangulated category, as observed by B. Shipley based on J. Cohen's approach for spectra. We provide a family of definitions of higher Toda brackets, show that they are equivalent to Shipley's, and show that they are self-dual. Our main result is that the Adams differential $d_r$ in any Adams spectral sequence can be expressed as an $(r+1)$-fold Toda bracket and as an $r^{\text{th}}$ order cohomology operation. We also show how the result simplifies under a sparseness assumption, discuss several examples, and give an elementary proof of a result of Heller, which implies that the three-fold Toda brackets in principle determine the higher Toda brackets.Comment: v2: Added Section 7, about an application to computing maps between modules over certain ring spectra. Minor improvements elsewhere. v3: Minor updates throughout; closely matches published versio

Sensitivity to initial conditions in self-organized critical systems

We discuss sensitivity to initial conditions in a model for avalanches in granular media displaying self-organized criticality. We show that damage, due to a small perturbation in initial conditions, does not spread. The damage persists in a statistically time-invariant and scale-free form. We argue that the origin of this behavior is the Abelian nature of the model, which generalizes our results to all Abelian models, including the BTW model and the Manna model. An ensemble average of the damage leads to seemingly time dependent damage spreading. Scaling arguments show that this numerical result is due to the time lag before avalanches reach the initial perturbation.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

A CGE model with ICT and R&D-driven endogenous growth: A detailed model description

We present a multi-country, multi-sector dynamic general equilibrium model with ICT and R&D-driven endogenous growth. The model presented has been developed to study the economic effects of public support to ICT R&D in the European Union. It accommodates alternative policy instruments that could be used in an attempt to stimulate private ICT R&D expenditures, including general production grants, tax credit or subsidies targeted at specific inputs. The model is calibrated to data from four country blocs Germany, France, the Rest of the EU and the Rest of the World.JRC.J.3-Information Societ

A CGE model with ICT and R&D-driven endogenous growth: A general description

This report describes the first release of the macroeconomic model developed under the project Prospective Insights on R&D in ICT (PREDICT 2), a research project co-financed by the Directorate General for Communications Networks, Content and Technology and the JRC-IPTS. One of the objectives of PREDICT 2 is the development of a macroeconomic model which allows the economic analysis of public support to ICT R&D in the European Union. This report provides a motivation for the chosen modelling approach, describes the model structure and the calibration of the model to a reference growth path.JRC.J.3-Information Societ

Alien Registration- Christensen, Martin (Baldwin, Cumberland County)

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