Scale-invariance underlying the logistic equation and its social applications

On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie a large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logistic equation in an either stochastic or deterministic way.Instituto de Física La PlataConsejo Nacional de Investigaciones Científicas y Técnica

The workings of the maximum entropy principle in collective human behaviour

We present an exhaustive study of the rank-distribution of city-population and population-dynamics of the 50 Spanish provinces (more than 8000 municipalities) in a time-window of 15 years (1996-2010). We exhibit compelling evidence regarding how well the MaxEnt principle describes the equilibrium distributions. We show that the microscopic dynamics that governs population growth is the deciding factor that originates the observed macroscopic distributions. The connection between microscopic dynamics and macroscopic distributions is unravelled via MaxEnt.Instituto de Física La Plat

The workings of the maximum entropy principle in collective human behaviour

We present an exhaustive study of the rank-distribution of city-population and population-dynamics of the 50 Spanish provinces (more than 8000 municipalities) in a time-window of 15 years (1996-2010). We exhibit compelling evidence regarding how well the MaxEnt principle describes the equilibrium distributions. We show that the microscopic dynamics that governs population growth is the deciding factor that originates the observed macroscopic distributions. The connection between microscopic dynamics and macroscopic distributions is unravelled via MaxEnt.Instituto de Física La Plat

MaxEnt and dynamical information

The MaxEnt solutions are shown to display a variety of behaviors (beyond the traditional and customary exponential one) if adequate dynamical information is inserted into the concomitant entropic-variational principle. In particular, we show both theoretically and numerically that power laws and power laws with exponential cut-offs emerge as equilibrium densities in proportional and other dynamics.Instituto de Física La PlataConsejo Nacional de Investigaciones Científicas y Técnica

Space-time correlations in urban sprawl

Understanding demographic and migrational patterns constitutes a great challenge. Millions of individual decisions, motivated by economic, political, demographic, rational and/or emotional reasons underlie the high complexity of demographic dynamics. Significant advances in quantitatively understanding such complexity have been registered in recent years, as those involving the growth of cities but many fundamental issues still defy comprehension. We present here compelling empirical evidence of a high level of regularity regarding time and spatial correlations in urban sprawl, unravelling patterns about the inertia in the growth of cities and their interaction with each other. By using one of the world's most exhaustive extant demographic data basis - that of the Spanish Government's Institute INE, with records covering 111 years and (in 2011) 45 million people, distributed among more than 8000 population nuclei - we show that the inertia of city growth has a characteristic time of 15 years, and its interaction with the growth of other cities has a characteristic distance of 80 km. Distance is shown to be the main factor that entangles two cities (60% of total correlations). The power of our current social theories is thereby enhanced.Facultad de Ciencias Exacta

The workings of the maximum entropy principle in collective human behaviour

We present an exhaustive study of the rank-distribution of city-population and population-dynamics of the 50 Spanish provinces (more than 8000 municipalities) in a time-window of 15 years (1996-2010). We exhibit compelling evidence regarding how well the MaxEnt principle describes the equilibrium distributions. We show that the microscopic dynamics that governs population growth is the deciding factor that originates the observed macroscopic distributions. The connection between microscopic dynamics and macroscopic distributions is unravelled via MaxEnt.Instituto de Física La Plat

Thermodynamics of firms' growth

The distribution of firms' growth and firms' sizes is a topic under intense scrutiny. In this paper, we show that a thermodynamic model based on the maximum entropy principle, with dynamical prior information, can be constructed that adequately describes the dynamics and distribution of firms' growth. Our theoretical framework is tested against a comprehensive database of Spanish firms, which covers, to a very large extent, Spain's economic activity, with a total of 1 155 142 firms evolving along a full decade. We show that the empirical exponent of Pareto's law, a rule often observed in the rank distribution of large-size firms, is explained by the capacity of economic system for creating/destroying firms, and that can be used to measure the health of a capitalist-based economy. Indeed, our model predicts that when the exponent is larger than 1, creation of firms is favoured; when it is smaller than 1, destruction of firms is favoured instead; and when it equals 1 (matching Zipf's law), the system is in a full macroeconomic equilibrium, entailing 'free' creation and/or destruction of firms. For medium and smaller firmsizes, the dynamical regime changes, the whole distribution can no longer be fitted to a single simple analytical form and numerical prediction is required. Our model constitutes the basis for a full predictive framework regarding the economic evolution of an ensemble of firms. Such a structure can be potentially used to develop simulations and test hypothetical scenarios, such as economic crisis or the response to specific policy measures.Instituto de Física La Plat

Picosecond solvation dynamics of alkali cations in superfluid 4He nanodroplets

The dynamics following the photoionization of neutral Rb and Cs atoms residing in a dimple at the surface of a superfluid 4He1000 nanodroplet has been investigated within time-dependent density functional theory, complementing a previous study on Ba. The calculations reveal that structured high density helium solvation layers form around both the Rb+ and Cs+ cation on a picosecond time scale, forming so-called snowballs. In contrast to the Rb+ ion, Cs+ is not solvated by the 4He1000 droplet but rather desorbs from it as a Cs+Hen snowball. This outcome is partially related to the large size of Cs+ cation in relation to the helium droplet as is revealed by calculations performed using a planar helium surface. The large droplet deformations induced by the solvation of the Rb+ cation is found to lead to efficient nucleation of quantized vortex loops or rings

Critical Landau velocity in helium nanodroplets

The best-known property of superfluid helium is the vanishing viscosity that objects experience while moving through the liquid with speeds below the so-called critical Landau velocity. This critical velocity is generally considered a macroscopic property as it is related to the collective excitations of the helium atoms in the liquid. In the present work we determine to what extent this concept can still be applied to nanometer-scale, finite size helium systems. To this end, atoms and molecules embedded in helium nanodroplets of various sizes are accelerated out of the droplets by means of optical excitation, and the speed distributions of the ejected particles are determined. The measurements reveal the existence of a critical Landau velocity in these systems, even for nanodroplets consisting of less than a thousand helium atoms. Accompanying theoretical simulations based on a time-dependent density functional description of the helium confirm and further elucidate this experimental finding

Payment Systems Report - June of 2019

For the last decade, Banco de la República has provided oversight of the local financial infrastructure as an additional contribution to support the country’s financial stability. This is a function performed by most central banks the world over, because they recognize infrastructure as being an essential component of financial markets. Infrastructure that functions properly helps to maintain and promote financial stability, being that it plays a fundamental role in the financial system and in the economy. In the Colombian case, the oversight of the country’s financial infrastructures began formally a decade ago, when External Resolution 5/2009 was issued and the authority to oversight that infrastructures was given to Banco de la República by its Board of Directors. Since then, the oversight has been formal and systematic. To commemorate ublication of the tenth edition of the Payment Systems Report, which is one of the products of financial infrastructure oversight, a section describing this function is included herein, explaining its need, responsibilities, scope, and activities. On this occasion, in addition to the traditional section providing figures on the local financial infrastructure and describing its behavior (Section One), we have included several highlights that underscore the more relevant aspects of how infrastructure for clearing and settling financial assets has evolved in the last decade. Special emphasis is afforded to the Colombian Central Counterparty Clearing House (CRCC), marking its ten years of operation. There also is a box describing how the company has increased its supply of products for clearing and settlement, and how, as a result, the open positions of its settlement members have performed likewise. At the same time, its risk management model has evolved structurally in response to regulatory adjustments, compliance with international standards, or decisions taken unilaterally by the CRCC, the idea being to have the necessary resources to mitigate exposure to counterparty and liquidity risk. In this way, the CRCC has become a undamentally important player in the Colombian financial market. Therefore, it is appropriate that the CRCC continue to be monitored by the country’s financial authorities. Another box included in this report offers an analysis of the advantages and disadvantages of lengthening the cash market settlement period in Colombia, which is another topic of interest. Currently, the clearing and settlement time for a cash transaction in most international markets is two business days (t + 2). In Colombia, nearly all peso/dollar and government and private debt transactions on the spot market are cleared and settled on the same trading day (t + 0). This box analyzes the possible implications of Colombia approximating the international standard. Retail-value payment systems (understood as operations carried out within the circuit of private individuals and companies), such as the use of payment instruments (cash, debit and credit cards, checks and electronic funds transfers), also must be monitored to identify their availability and the public’s preferences for these instruments and their acceptance by commercial establishments. With that in mind, three surveys have been conducted in the last decade to gauge how the use of payment instruments is perceived. A comparison of the findings of these three measurements is presented in a section of this report, and an analysis of that comparison indicates the use of payment instruments other than cash for daily payments is still low. Although their ownership and use by the general public is increasing, their acceptance by some commercial establishments remains limited. In keeping with efforts to oversight innovations in payment processes, the report also includes a box that explores the participation of large, global technology companies in the retail-value payment market. The payment services they offer are associated with innovative payment methods, such as “non-contact” or indirect technology, or by means of devices such as mobile phones, the use of debit and credit cards via applications, and channels such as the mobile network, POS terminals, and the Internet. In other words, these innovations are concentrated in the first stage of the payment process, without altering the other stages, such as traditional payment instruments, channels and systems. Finally, with respect to work in the area of applied research, the fourth section of this report describes how the cryptoasset system operates. It has two fundamental elements. The first is comprised of the agents who participate in the system; namely, cryptoasset users, and the agents who provide them with services. The second includes the digital asset and the underlying technology platform; together they support interaction between the agents in the crypto asset system. As explained in the respective box, the cryptoasset system is not isolated entirely from the financial system, which it pretends do without. In other words, users cannot extract themselves from the traditional financial system as long as cryptoassets have yet to be adopted on a mass scale, which so far assumes there is a connection between both systems. Juan José Echavarría Governo