Gaussian Behavior of Quadratic Irrationals

We study the probabilistic behaviour of the continued fraction expansion of a quadratic irrational number, when weighted by some "additive" cost. We prove asymptotic Gaussian limit laws, with an optimal speed of convergence. We deal with the underlying dynamical system associated with the Gauss map, and its weighted periodic trajectories. We work with analytic combinatorics methods, and mainly with bivariate Dirichlet generating functions; we use various tools, from number theory (the Landau Theorem), from probability (the Quasi-Powers Theorem), or from dynamical systems: our main object of study is the (weighted) transfer operator, that we relate with the generating functions of interest. The present paper exhibits a strong parallelism with the methods which have been previously introduced by Baladi and Vall\'ee in the study of rational trajectories. However, the present study is more involved and uses a deeper functional analysis framework.Comment: 39 pages In this second version, we have added an annex that provides a detailed study of the trace of the weighted transfer operator. We have also corrected an error that appeared in the computation of the norm of the operator when acting in the Banach space of analytic functions defined in the paper. Also, we give a simpler proof for Theorem

Connection between the Burgers equation with an elastic forcing term and a stochastic process

We present a complete analytical resolution of the one dimensional Burgers equation with the elastic forcing term $-\kappa^{2} x+f(t)$, $\kappa\in\mathbb{R}$. Two methods existing for the case $\kappa=0$ are adapted and generalized using variable and function transformations, valid for all values of space an time. The emergence of a Fokker-Planck equation in the method allows to connect a fluid model, depicted by the Burgers equation, with an Ornstein-Uhlenbeck process

Beyond financial repression and regulatory capture: the recomposition of European financial ecosystems after the crisis. LEQS Paper No. 147/2019 September 2019

The financial crisis has radically changed the political economy of the European financial system. The evolution of relations between European states and their respective financial systems has given rise to two competing narratives. On the one hand, government agencies are often described as being at the mercy of the financial sector, regularly hijacking political, regulatory and supervisory processes. This trend is often referred to as "regulatory capture" and would explain the "soft touch" regulation and bank bailout. On the other hand, governments are portrayed as subverting markets and abusing the financial system for their benefit, mainly to obtain better financing conditions and allocate credit to the economy on preferential terms, a trend called "financial repression" that is considered corrosive to the proper functioning of free markets and a source of capital misallocation. This paper takes a critical look at this debate and argues that the relationship between governments and financial systems in Europe cannot be reduced to the polar notions of "capture" and "repression", but that the channels of pressure and influence between governments and their financial systems have often been bi-directional and mutually reinforcing

Convergence in the Finite Cournot Oligopoly with Social and Individual Learning

Convergence to the Nash equilibrium in a Cournot oligopoly is a question that recurrently arises as a subject of controversy in economics. The development of evolutionary game theory has provided an equilibrium concept more directly connected with adjustment dynamics, and the evolutionary stability of the equilibria of the Cournot game has been extensively studied in the literature. Several articles show that the Walrasian equilibrium is the stable ESS of the Cournot game. But no general result has been established for the difficult case of simultaneous heterogenous mutations.Authors propose specific selection dynamics to analyze this case. Vriend (2000) proposes using a genetic algorithm for studying learning dynamics in this game and obtains convergence to Cournot equilibrium with individual learning. The resulting convergence has been questioned by Arifovic and Maschek (2006). The aim of this article is to clarify this controversy: it analyzes the mechanisms that are behind these contradictory results and underlines the specific role of the spite effect. We show why social learning gives rise to the Walrasian equilibrium and why, in a general setup, individual learning can effectively yield convergence to the Cournot equilibrium. We also illustrate these general results by systematic computational experiments.Cournot oligopoly; Learning; Evolution; Selection; Evolutionary stability; Nash equilibrium; Genetic algorithms

Technological and Social Costs and Benefits of Patent Systems

"If we did not have a patent system, it would be irresponsible, on the basis of our present knowledge of its economic consequences, to recommend instituting one. But since we have had a patent system for a long time, it would be irresponsible, on the basis of our present knowledge, to recommend abolishing it." Machlup (1958) - cited by Hall (2002) The demand for a stronger patenting system has become in the recent period a major source of tension between the U.S. government and the E.U. The US demand is generally motivated by the conventional economic wisdom affirming that a strong patenting system yields convenient incentives for the private investment in Research and Development (R&D) and hence, for technical progress in Society. This rather mechanistic approach of technological dynamics and of the role of the patenting is mainly based on the neoclassical theory of technical progress that strongly focuses on the agents' incentives rather than on the dynamics of the existent technological systems. Other appreciations of the existing patenting systems have nevertheless continued to be quite critical (see Machlup (1958) and Penrose (1951)). These appreciations are generally based on approaches where the nature of the actual technologies plays a central role. Moreover, the first part of the opinion emitted by Machlup in the above excerpt becomes very urgent since the question of establishing a strong patenting system is actually scrutinized for some industries in Europe (like the software industry) and in some countries (like Russia and China). We should hence consider the social costs of the patenting system, as well as its advantages, in order to guide such decisions. More specifically, it is time to seriously consider and check the old and new criticism of this system. The shortcomings of the standard wisdom have more recently been pointed out by Merges & Nelson (1990) and Mazzoleni & Nelson (1998). We propose to reassess the theoretical social value of patenting through a model founded on the approach adopted by these more empirical and conceptual studies. We develop a simulation model based on the Nelson & Winter (1982), part V. This basic model is completed by a patent system that allows the protection of the innovations. We therefore use this model for evaluating the efficiency of this system under different technological conditions emphasized by Merges & Nelson (1990) and as a function of different dimensions of patents (mainly their length and their breadth). An econometric study of the results from Monte Carlo simulations is used to evaluate the determinants of the Social costs and benefits of patents. These social effects are mainly characterized at two levels: at the level of the efficiency of the technical progress in the industry, and at the level of the social surplus. The neoclassical approaches conclude to a positive effect on both dimensions. Evolutionary approaches point at the contingency of these results with respect to the technological particularities of the industries. For example, Merges & Nelson (1990) distinguishes four classes of technologies in which the role of patents can be strongly contrasted: discrete inventions, cumulative technologies, chemical technologies and sciencebased technologies. We propose to include the specificities of these classes in our analysis, through different calibrations of the technology space of our industry dynamics model. The results of the simulations will then allow us to check the effectiveness of the patenting system in different configurations and with different characteristics measuring its strength. References Hall, B. (2002), "Current issues and trends in the economics of patents", Lecture to the ESSID Summer School in Industrial Dynamics Hall, B. & Ham Ziedonis, R. M. (2001), The effects of strengthening patent rights on firms engaged in cumulative innovation: Insights from the semiconductor industry, in G. Libecap, ed., "Entrepreneurial Inputs and Outcomes: New Studies of Entrepreneurship in the United States", Vol. 13 of Advances in the Study of Entrepreneurship, Innovation, and Economic Growth, Elsevier Science, Amsterdam. Jaffe, A. B. (2000), "The u.s. patent system in transition: Policy innovation and the innovation process", Research Policy 29, 531–557. Machlup, F. (1958), "An economic review of the patent system", Study No. 15 of Commission on Judiciary, Sub comm. on Patents, Trademarks, and Copyrights, 85th Congress, 2d Session. Mazzoleni, R. & Nelson, R. R. (1998), "The benefits and costs of strong patent protection: A contribution to the current debate", Research Policy 27, 273–284. Merges, R. & Nelson, R. R. (1990), "On the complex economics of patent scope", Columbia Law Review 90, 839–916. Nelson, R. R. & Winter, S. (1982), An Evolutionary Theory of Economic Change, The Belknap Press of Harvard University, London. Penrose, E. (1951), The Economics of the International Patent System, John Hopkins University Press, BaltimorePatent system, social welfare, public policy, intellectual property rights, industrial dynamics

A Cluster of Compact Radio Sources in W40

We present deep 3.6 cm radio continuum observations of the HII region W40 obtained using the Very Large Array in its A and B configurations. We detect a total of 20 compact radio sources in a region of 4 x 4 arcmin, with 11 of them concentrated in a band with 30 arcsec of extent. We also present JHK photometry of the W40 cluster taken with the QUIRC instrument on the University of Hawaii 2.2 meter telescope. These data reveal that 15 of the 20 VLA sources have infrared counterparts, and 10 show radio variability with periods less than 20 days. Based on these combined radio and IR data, we propose that 8 of the radio sources are candidate ultracompact HII regions, 7 are likely to be young stellar objects, and 2 may be shocked interstellar gas.Comment: Accepted for publication in the Astronomical Journal. 10 pages, 4 figures, plus online table in electronic versio

Beyond financial repression and regulatory capture. The recomposition of European financial ecosystems after the crisis

The financial crisis has radically and rapidly changed the political economy of the European financial system. The evolution of relations between European states and their respective financial systems has given rise to two competing narratives. On the one hand, government agencies are often described as being at the mercy of the financial sector, regularly highjacking political, regulatory and supervisory processes. This trend is often referred to as "regulatory capture" and would explain the "soft touch" regulation and bank bailout. On the other hand, governments are portrayed as subverting markets and abusing the financial system for their benefit, mainly to obtain better financing conditions and allocate credit to the economy on preferential terms, a trend called "financial repression" that is considered corrosive to the proper functioning of free markets and a source of capital misallocation. This paper takes a critical look at this debate in the European context. First, he argues that the relationship between governments and financial systems in Europe cannot be reduced to the polar notions of "capture" and "repression", but that the channels of pressure and influence between governments and their financial systems have often been two-way. Secondly, it puts these issues in a historical perspective and shows that the current reconfiguration of national financial systems in Europe is not simply a return to the "interventionist" policies of the past, although it is influenced by the path-dependency of national institutions and characterised by a broader political and economic role for public bodies (public credit institutions, financial supervision agencies, central bank, European relief fund, etc.)