On the magnitude of spheres, surfaces and other homogeneous spaces

In this paper we define the magnitude of metric spaces using measures rather than finite subsets as had been done previously and show that this agrees with earlier work with Leinster in arXiv:0908.1582. An explicit formula for the magnitude of an n-sphere with its intrinsic metric is given. For an arbitrary homogeneous Riemannian manifold the leading terms of the asymptotic expansion of the magnitude are calculated and expressed in terms of the volume and total scalar curvature of the manifold. In the particular case of a homogeneous surface the form of the asymptotics can be given exactly up to vanishing terms and this involves just the area and Euler characteristic in the way conjectured for subsets of Euclidean space in previous work.Comment: 21 pages. Main change from v1: details added to proof of Theorem

Characterization of Yoga-Associated Teaching Format, Barriers, And Injuries During COVID-19

poste

Assessment of Connections Between Knowledge- Based Economy Characteristics and Selected Macroeconomic Categories in the European Union's Countries by Means of Panel Models

The aim of the article is to analyze the impact of knowledge-based economy variables on the selected macroeconomic categories - the share of total investments in GDP and the employment rate- in European Union's countries in the years 2000-2007, conducted with application of panel models.Celem artykułu jest analiza wpływu zmiennych opisujących gospodarkę opartą na wiedzy na podstawowe kategorie makroekonomiczne - udział całkowitych inwestycji w PKB i stopę zatrudnienia - w krajach Unii Europejskiej (z podziałem na kraje UE-15 i nowe kraje członkowskie UE) w latach 2000-2007, przeprowadzona w oparciu o modele panelowe

Sustainability, innovation, and efficiency:A key relationship

Sustainability has become the emerging goal for countries, companies, and people. Sustainability usually refers to the need to develop models necessary for both human beings and our planet to survive. However, sustainability is not a short-term problem; it is above all a long-term issue, posing intergenerational equity problems. Moreover, sustainability needs efficiency. The efficient use of energy, natural, material, and informational resources is vital for sustainability and sustainable development, which should be the major goal of every country, as established in Rio in 1992, and reaffirmed at Rio+ 20 in 2012. But any strategy aiming at sustainability and efficient use of resources must focus on innovation and technological progress. Consequently, innovation is fundamental to making sustainability possible and improving efficiency. Yet, innovation for sustainability must be environmentally friendly (e.g., green technologies). The principle behind such a strategy is better instead of more. This paper aims at highlighting the key relationship among sustainability, innovation, and efficiency. First, it examines the concept of sustainability, looking at the neoclassical literature on sustainability and its relationship with innovation. Then, it analyzes different theoretical approaches and discusses the policy issues for sustainability where innovation, natural capital, human capital, population, and institutions are fundamental factors

Substitutes or complements? Relationship between natural resources and physical capital–a few stylised facts

This paper considers the complementarity and substitutability of natural resources and physical capital. Unlike existing empirical research, concentrated on the estimation of the elasticity of substitution between energy and capital, the author focuses on macro data and the growth theory approach. The author considers the standard economic long-run growth models with substitutability or complementarity among natural resource use and physical capital in the production process. He derives from these models empirically verifiable theoretical relationships between their rates of growth. The author also uses cross-country long-run data to obtain an empirical correlation between these growth rates and finds evidence in favour of gross complementarity between the examined factors of production on the macro level in the long ru

Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie

Social networks and labour productivity in Europe: An empirical investigation

This paper uses firm-level data recorded in the AMADEUS database to investigate the distribution of labour productivity in different European countries. We find that the upper tail of the empirical productivity distributions follows a decaying power-law, whose exponent $\alpha$ is obtained by a semi-parametric estimation technique recently developed by Clementi et al. (2006). The emergence of "fat tails" in productivity distribution has already been detected in Di Matteo et al. (2005) and explained by means of a model of social network. Here we show that this model is tested on a broader sample of countries having different patterns of social network structure. These different social attitudes, measured using a social capital indicator, reflect in the power-law exponent estimates, verifying in this way the existence of linkages among firms' productivity performance and social network.Comment: LaTeX2e; 18 pages with 3 figures; Journal of Economic Interaction and Coordination, in pres

WARNING: Physics Envy May Be Hazardous To Your Wealth!

The quantitative aspirations of economists and financial analysts have for many years been based on the belief that it should be possible to build models of economic systems - and financial markets in particular - that are as predictive as those in physics. While this perspective has led to a number of important breakthroughs in economics, "physics envy" has also created a false sense of mathematical precision in some cases. We speculate on the origins of physics envy, and then describe an alternate perspective of economic behavior based on a new taxonomy of uncertainty. We illustrate the relevance of this taxonomy with two concrete examples: the classical harmonic oscillator with some new twists that make physics look more like economics, and a quantitative equity market-neutral strategy. We conclude by offering a new interpretation of tail events, proposing an "uncertainty checklist" with which our taxonomy can be implemented, and considering the role that quants played in the current financial crisis.Comment: v3 adds 2 reference

Priority for the Worse Off and the Social Cost of Carbon

The social cost of carbon (SCC) is a monetary measure of the harms from carbon emission. Specifically, it is the reduction in current consumption that produces a loss in social welfare equivalent to that caused by the emission of a ton of CO2. The standard approach is to calculate the SCC using a discounted-utilitarian social welfare function (SWF)—one that simply adds up the well-being numbers (utilities) of individuals, as discounted by a weighting factor that decreases with time. The discounted-utilitarian SWF has been criticized both for ignoring the distribution of well-being, and for including an arbitrary preference for earlier generations. Here, we use a prioritarian SWF, with no time-discount factor, to calculate the SCC in the integrated assessment model RICE. Prioritarianism is a well-developed concept in ethics and theoretical welfare economics, but has been, thus far, little used in climate scholarship. The core idea is to give greater weight to well-being changes affecting worse off individuals. We find substantial differences between the discounted-utilitarian and non-discounted prioritarian SCC