Computability of ordinary differential equations

In this paper we provide a brief review of several results about the computability of initial-value problems (IVPs) defined with ordinary differential equations (ODEs). We will consider a variety of settings and analyze how the computability of the IVP will be affected. Computational complexity results will also be presented, as well as computable versions of some classical theorems about the asymptotic behavior of ODEs.info:eu-repo/semantics/publishedVersio

On the Complexity of Quadratization for Polynomial Differential Equations

Chemical reaction networks (CRNs) are a standard formalism used in chemistry and biology to reason about the dynamics of molecular interaction networks. In their interpretation by ordinary differential equations, CRNs provide a Turing-complete model of analog computattion, in the sense that any computable function over the reals can be computed by a finite number of molecular species with a continuous CRN which approximates the result of that function in one of its components in arbitrary precision. The proof of that result is based on a previous result of Bournez et al. on the Turing-completeness of polyno-mial ordinary differential equations with polynomial initial conditions (PIVP). It uses an encoding of real variables by two non-negative variables for concentrations, and a transformation to an equivalent quadratic PIVP (i.e. with degrees at most 2) for restricting ourselves to at most bimolecular reactions. In this paper, we study the theoretical and practical complexities of the quadratic transformation. We show that both problems of minimizing either the number of variables (i.e., molecular species) or the number of monomials (i.e. elementary reactions) in a quadratic transformation of a PIVP are NP-hard. We present an encoding of those problems in MAX-SAT and show the practical complexity of this algorithm on a benchmark of quadratization problems inspired from CRN design problems

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

The N-P-K soil nutrient balance of portuguese cropland in the 1950s: the transition from organic to chemical fertilization

Agricultural nutrient balances have been receiving increasing attention in both historical and nutrient management research. The main objectives of this study were to further develop balance methodologies and to carry out a comprehensive assessment of the functioning and nutrient cycling of 1950s agroecosystems in Portugal. Additionally, the main implications for the history of agriculture in Portugal were discussed from the standpoint of soil fertility. We used a mass balance approach that comprises virtually all nitrogen (N), phosphorus (P) and potassium (K) inputs and outputs from cropland topsoil for average conditions in the period 1951–56. We found a consistent deficit in N, both for nationwide (−2.1 kg.ha−1.yr−1) and arable crops (−1.6 kg.ha−1.yr−1) estimates, that was rectified in the turn to the 1960 decade. P and K were, in contrast, accumulating in the soil (4.2–4.6 kg.ha−1.yr−1 and 1.0–3.0 kg.ha−1.yr−1, respectively). We observed that the 1950s is the very moment of inflection from an agriculture fertilized predominantly through reused N in biomass (livestock excretions plus marine, plant and human waste sources) to one where chemical fertilizers prevailed. It is suggested that N deficiency played an important role in this transitioninfo:eu-repo/semantics/publishedVersio

Proteases of haematophagous arthropod vectors are involved in blood-feeding, yolk formation and immunity : a review

Ticks, triatomines, mosquitoes and sand flies comprise a large number of haematophagous arthropods considered vectors of human infectious diseases. While consuming blood to obtain the nutrients necessary to carry on life functions, these insects can transmit pathogenic microorganisms to the vertebrate host. Among the molecules related to the blood-feeding habit, proteases play an essential role. In this review, we provide a panorama of proteases from arthropod vectors involved in haematophagy, in digestion, in egg development and in immunity. As these molecules act in central biological processes, proteases from haematophagous vectors of infectious diseases may influence vector competence to transmit pathogens to their prey, and thus could be valuable targets for vectorial control

Deforestation and Carbon Stock Loss in Brazil’s Amazonian Settlements

We estimate deforestation and the carbon stock in 2740 (82 %) of the 3325 settlements in Brazil’s Legal Amazonia region. Estimates are made both using available satellite data and a carbon map for the “pre-modern” period (prior to 1970). We used data from Brazil’s Project for Monitoring Deforestation in Amazonia updated through 2013 and from the Brazilian Biomes Deforestation Monitoring Project (PMDBBS) updated through 2010. To obtain the pre-modern and recent carbon stocks we performed an intersection between a carbon map and a map derived from settlement boundaries and deforestation data. Although the settlements analyzed occupied only 8 % of Legal Amazonia, our results indicate that these settlements contributed 17 % (160,410 km2) of total clearing (forest + non-forest) in Legal Amazonia (967,003 km2). This represents a clear-cutting of 41 % of the original vegetation in the settlements. Out of this total, 72 % (115,634 km2) was in the “Federal Settlement Project” (PA) category. Deforestation in settlements represents 20 % (2.6 Pg C) of the total carbon loss in Legal Amazonia (13.1 Pg C). The carbon stock in remaining vegetation represents 3.8 Pg C, or 6 % of the total remaining carbon stock in Legal Amazonia (58.6 Pg C) in the periods analyzed. The carbon reductions in settlements are caused both by the settlers and by external actors. Our findings suggest that agrarian reform policies contributed directly to carbon loss. Thus, the implementation of new settlements should consider potential carbon stock losses, especially if settlements are created in areas with high carbon stocks. © 2016, The Author(s)