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## What do aggregate saving rates (not) show?

The aggregate saving indicator does not directly reflect changes in individuals’ microeconomic behavior. From the official statistics’ point of view, households choose between spending, which generates additional income and consumption in the economy, and setting money aside, which does not. Formally, households may not (if the authors disregard housing investment) choose to save, because the aggregate saving statistical indicator is a residual concept defined as the ensuing difference between aggregate disposable income and consumption. It measures the change in net worth, which, in a closed economy, may only be generated by the production of capital goods and an increase in inventories. Using an agent-based model, the authors show that shocks unrelated to structural changes in households’ behavior may generate positively correlated fluctuations in the aggregate saving rate, productivity growth and lending. Meanwhile, a genuine increase in the average individual propensity to save is not necessarily associated with a higher aggregate saving rate.

The idea of a “third sector” beyond the arenas of the state and the market is probably one of the most perplexing concepts in modern political and social discourse, encompassing as it does a tremendous diversity of institutions and behaviors that only relatively recently have been perceived in public or scholarly discourse as a distinct sector, and even then with grave misgivings. Initial work on this concept focused on what is still widely regarded as its institutional core, the vast array of private, nonprofit institutions (NPIs), and the volunteer as well as paid workers they mobilize and engage. These institutions share a crucial characteristic that makes it feasible to differentiate from for-profit enterprises: the fact that they are prohibited from distributing any surplus they generate to their investors, directors, or stakeholders and therefore presumptively serve some broader public interest. Many European scholars have considered this conceptualization too narrow; however, arguing that cooperatives, mutual societies, and, in recent years, “social enterprises” as well as social norms should also be included. However, this broader concept has remained under-conceptualized in reliable operational terms. This article corrects this short-coming and presents a consensus operational re-conceptualization of the third sector fashioned by a group of scholars working under the umbrella of the European Union’s Third Sector Impact Project. This re-conceptualization goes well beyond the widely recognized definition of NPIs included in the UN *Handbook on Nonprofit Institutions in the System of National Accounts* by embracing as well some, but not all, of these additional institutions and forms of direct individual activity, and does so in a way that meets demanding criteria of comparability, operationalizability, and potential for integration into official statistical systems.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.