True Riches

Luke 16:19-31

Sequential inverse problems Bayesian principles and the\ud logistic map example

Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection

The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations

We consider the motion of a thin filament of viscous fluid in a Hele-Shaw cell. The appropriate thin film analysis and use of Lagrangian variables leads to the Cauchy-Riemann system in a surprisingly direct way. We illustrate the inherent ill-posedness of these equations in various contexts

Risk Mitigation through Diversified Farm Production Strategies: The Case in Northern Mozambique

Mozambique, like many other parts of the low-income world, faces perennial challenges with food security. With a rapidly growing population and arable land on the decline, sustainable agriculture is vital to managing the already depleted natural resources of Sub-Saharan Africa more effectively while increasing food security. Food security issues for subsistence farmers in most low-income countries are a product of endogenous (crop yields) and exogenous (currency fluctuations as many agricultural inputs are imported) factors. In Mozambique the value of the local currency, meticals, has decreased by approximately 50% since January 2015 compared to the U.S. dollar. While this makes exporting products out of Mozambique more attractive in a relative sense, it negatively effects those industries which rely on imported inputs such as animal feed and inorganic fertilizer. In response to this exogenous currency crisis, research was conducted in Nampula, Mozambique during the summer of 2016 on a method for implementing crop diversification to reduce the risk that accompanies the devaluation of the metical. This research was undertaken on a poultry operation which is heavily dependent on imported maize and soya. Similar to the market structure of the poultry industry in the United States, all birds are grown by individual out growers who typically also have small plots of land to farm. Objectives for the project included 1) perform on-site crop production evaluations, 2) determine profitability for various row crops, and 3) simulate alternative production practices to increase crop profitability. Of the crops grown (tomatoes, maize, and cabbage), maize required the least labor, lowest initial investment, and the highest probability of breaking even. This research concluded that if poultry producers in Mozambique who rely on imported feed grew maize simultaneously it would reduce the dependency on imported maize and reduce income variability associated with exogenous currency fluctuations. Implementing a program such as this could increase revenue streams as well as reduce variability, thereby enhancing regional food securit

Risk Mitigation through Diversified Farm Production Strategies: The Case in Northern Mozambique

Mozambique, like many other parts of the low-income world, faces perennial challenges with food security. With a rapidly growing population and arable land on the decline, sustainable agriculture is vital to managing the already depleted natural resources of Sub-Saharan Africa more effectively while increasing food security. Food security issues for subsistence farmers in most low-income countries are a product of endogenous (crop yields) and exogenous (currency fluctuations as many agricultural inputs are imported) factors. In Mozambique the value of the local currency, meticals, has decreased by approximately 50% since January 2015 compared to the U.S. dollar. While this makes exporting products out of Mozambique more attractive in a relative sense, it negatively effects those industries which rely on imported inputs such as animal feed and inorganic fertilizer. In response to this exogenous currency crisis, research was conducted in Nampula, Mozambique during the summer of 2016 on a method for implementing crop diversification to reduce the risk that accompanies the devaluation of the metical. This research was undertaken on a poultry operation which is heavily dependent on imported maize and soya. Similar to the market structure of the poultry industry in the United States, all birds are grown by individual out growers who typically also have small plots of land to farm. Objectives for the project included 1) perform on-site crop production evaluations, 2) determine profitability for various row crops, and 3) simulate alternative production practices to increase crop profitability. Of the crops grown (tomatoes, maize, and cabbage), maize required the least labor, lowest initial investment, and the highest probability of breaking even. This research concluded that if poultry producers in Mozambique who rely on imported feed grew maize simultaneously it would reduce the dependency on imported maize and reduce income variability associated with exogenous currency fluctuations. Implementing a program such as this could increase revenue streams as well as reduce variability, thereby enhancing regional food securit

The cause of universality in growth fluctuations

Phenomena as diverse as breeding bird populations, the size of U.S. firms, money invested in mutual funds, the GDP of individual countries and the scientific output of universities all show unusual but remarkably similar growth fluctuations. The fluctuations display characteristic features, including double exponential scaling in the body of the distribution and power law scaling of the standard deviation as a function of size. To explain this we propose a remarkably simple additive replication model: At each step each individual is replaced by a new number of individuals drawn from the same replication distribution. If the replication distribution is sufficiently heavy tailed then the growth fluctuations are Levy distributed. We analyze the data from bird populations, firms, and mutual funds and show that our predictions match the data well, in several respects: Our theory results in a much better collapse of the individual distributions onto a single curve and also correctly predicts the scaling of the standard deviation with size. To illustrate how this can emerge from a collective microscopic dynamics we propose a model based on stochastic influence dynamics over a scale-free contact network and show that it produces results similar to those observed. We also extend the model to deal with correlations between individual elements. Our main conclusion is that the universality of growth fluctuations is driven by the additivity of growth processes and the action of the generalized central limit theorem.Comment: 18 pages, 4 figures, Supporting information provided with the source files