Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

From Negative to Positive Integration. European State Aid Control through Soft and Hard Law

European state aid control, a part of competition policy, typically follows the logic of negative integration. It constrains the potential for Member States to distort competition by reducing their ability to subsidize industry. In addition, this paper argues, ambiguous Treaty rules and heterogeneous Member States' preferences have enabled the European Commission to act as a supranational entrepreneur, not only enforcing the prohibition of distortive state aid, but also developing its own vision of “good” state aid policy. In order to prevent or to settle political conflict about individual decisions, the Commission has sought to establish more general criteria for the state aid which it still deems admissible. These criteria have been codified into a complex system of soft law and, more recently, hard state aid law. The Commission has thus created positive integration “from above” and increasingly influences the objectives of national state aid policies

Chronic Neurology in COVID-19 Era: Clinical Considerations and Recommendations From the REPROGRAM Consortium

With the rapid pace and scale of the emerging coronavirus 2019 (COVID-19) pandemic, a growing body of evidence has shown a strong association of COVID-19 with pre- and post- neurological complications. This has necessitated the need to incorporate targeted neurological care for this subgroup of patients which warrants further reorganization of services, healthcare workforce, and ongoing management of chronic neurological cases. The social distancing and the shutdown imposed by several nations in the midst of COVID-19 have severely impacted the ongoing care, access and support of patients with chronic neurological conditions such as Multiple Sclerosis, Epilepsy, Neuromuscular Disorders, Migraine, Dementia, and Parkinson disease. There is a pressing need for governing bodies including national and international professional associations, health ministries and health institutions to harmonize policies, guidelines, and recommendations relating to the management of chronic neurological conditions. These harmonized guidelines should ensure patient continuity across the spectrum of hospital and community care including the well-being, safety, and mental health of the patients, their care partners and the health professionals involved. This article provides an in-depth analysis of the impact of COVID-19 on chronic neurological conditions and specific recommendations to minimize the potential harm to those at high risk

Determinants, differentiation, and development of short-term marginal costs in dairy production: an empirical analysis for selected regions of the EU

This work provides evidence on the determinants, cost differentiation, and development of short-term marginal costs of dairy farms in important production regions of the European Union. The empirical study is based on the estimation of multi-input multi-output Symmetric Generalized McFadden cost functions using an unbalanced panel data set of the European Farm Accountancy Data Network. The results show considerable regional differences in the impact of the outputs, input prices, and fixed factors on marginal costs. Strong evidence can be found that marginal costs decrease over time and is further underlined by the development of derived regional aggregated short-term supply curves. Marginal cost elasticities and correlation coefficients validate the hypotheses that a high degree of farm specialization, large milk output, and low milk prices are associated with lower marginal costs. Furthermore, the marginal cost spread in the data sample is analyzed. We show that milk output, milk yield, herd size, labor input, and fodder production can be attributed to significant marginal cost differentiation of farms, whereas for crop and animal output, grassland, stock of other animals, and depreciation only minor differentiation can be found. Copyright 2007 International Association of Agricultural Economists.