Science, Dualities and the Phenomenological Map.

We present an epistemological schema of natural sciences inspired by Peirce's pragmaticist view, stressing the role of the phenomenological map, that connects reality and our ideas about it. The schema has a recognisable mathematical/logical structure which allows to explore some of its consequences. We show that seemingly independent principles as the requirement of reproducibility of experiments and the Principle of Sufficient Reason are both implied by the schema, as well as Popper's concept of falsifiability. We show that the schema has some power in demarcating science by first comparing with an alternative schema advanced during the first part of the 20th century which has its roots in Hertz and has been developed by Einstein and Popper. Further, the identified differences allow us to focus in the construction of Special Relativity, showing that it uses an intuited concept of velocity that does not satisfy the requirements of reality in Peirce. While the main mathematical observation connected with this issue has been known for more than a century, it has not been investigated from an epistemological point of view. A probable reason could be that the socially dominating epistemology in physics does not encourage such line of work. We briefly discuss the relation of the abduction process presented in this work with discussions regarding "abduction" in the literature and its relation with "analogy".

Stochastic population model of Zea mays L.

We propose a minimalist stochastic population model of maize, focused on the description of the maize vegetative stages (seedlings with different number of leaves) involved in the propagation of vector-borne diseases. This model was parameterized from laboratory and field experiments and from observational field studies for multiple hybrids and different weather and soil conditions, taking into account only temperature as input variable. We propose three different submodels to estimate the distribution of the Final Leaf Number NFLN in the plants and to estimate the tassel initiation probability. The first submodel (submodel A), with a fixed NFLN, is adaptable to any particular hybrid, the second and third submodels allow to simulate plants with an empirical NFLN distribution according to bibliographic averages (submodel B) or according to a Poisson Process (submodel C). The three submodels are able to describe the temporal development of populations and events. A good agreement is observed between the development times predicted by the model and the values obtained from laboratory experiments at constant temperature, field experiments carried out in Brazil and Australia and observational studies performed in Argentina. This model may be improved and coupled to leaf growth models and leaf area estimation models to be able to estimate not only the temporal development of populations and events but also the temporal development of the leaf area by plant, which is believed to be related to the carrying capacity of maize specialists insects, vectors of maize diseases.

Modelling interventions during a dengue outbreak.

We present a stochastic dynamical model for the transmission of dengue that considers the co-evolution of the spatial dynamics of the vectors (Aedes aegypti) and hosts (human population), allowing the simulation of control strategies adapted to the actual evolution of an epidemic outbreak. We observed that imposing restrictions on the movement of infected humans is not a highly effective strategy. In contrast, isolating infected individuals with high levels of compliance by the human population is efficient even when implemented with delays during an ongoing outbreak. We also studied insecticide-spraying strategies assuming different (hypothetical) efficiencies. We observed that highly efficient fumigation strategies seem to be effective during an outbreak. Nevertheless, taking into account the controversial results on the use of spraying as a single control strategy, we suggest that carrying out combined strategies of fumigation and isolation during an epidemic outbreak should account for a suitable strategy for the attenuation of epidemic outbreaks.

Dengue epidemics and human mobility.

In this work we explore the effects of human mobility on the dispersion of a vector borne disease. We combine an already presented stochastic model for dengue with a simple representation of the daily motion of humans on a schematic city of 20 × 20 blocks with 100 inhabitants in each block. The pattern of motion of the individuals is described in terms of complex networks in which links connect different blocks and the link length distribution is in accordance with recent findings on human mobility. It is shown that human mobility can turn out to be the main driving force of the disease dispersal.

Stochastic eco-epidemiological model of dengue disease transmission by Aedes aegypti mosquito.

We present a stochastic dynamical model for the transmission of dengue that takes into account seasonal and spatial dynamics of the vector Aedes aegypti. It describes disease dynamics triggered by the arrival of infected people in a city. We show that the probability of an epidemic outbreak depends on seasonal variation in temperature and on the availability of breeding sites. We also show that the arrival date of an infected human in a susceptible population dramatically affects the distribution of the final size of epidemics and that early outbreaks have a low probability. However, early outbreaks are likely to produce large epidemics because they have a longer time to evolve before the winter extinction of vectors. Our model could be used to estimate the risk and final size of epidemic outbreaks in regions with seasonal climatic variations.

Interface dynamics for copper electrodeposition: the role of organic additives in the growth mode.

An atomistic model for Cu electrodeposition under nonequilibrium conditions is presented. Cu electrodeposition takes place with a height-dependent deposition rate that accounts for fluctuations in the local Cu2+ ions concentration at the interface, followed by surface diffusion. This model leads to an unstable interface with the development of protrusions and grooves. Subsequently the model is extended to account for the presence of organic additives, which compete with Cu2+ for adsorption at protrusions, leading to a stable interface with scaling exponents consistent with those of the Edwards-Wilkinson equation. The model reproduces the interface evolution experimentally observed for Cu electrodeposition in the absence and in the presence of organic additives.

Population dynamics: Poisson approximation and its relation to the Langevin process.

We discuss how to simulate a stochastic evolution process in terms of difference equations with Poisson distributions of independent events when the problem is naturally described by discrete variables. For large populations the Poisson approximation becomes a discrete integration of the Langevin approximation [T. G. Kurtz, J. Appl. Prob. 7, 49 (1970); 8, 344 (1971)]. We analyze when the latter gives a reasonable representation of the original evolution for finite size systems. A simple example of an epidemic process is used to organize the discussion and to perform statistical tests that underline the goodness of the proposed method.

Sustained oscillations in stochastic systems.

Many non-linear deterministic models for interacting populations present damped oscillations towards the corresponding equilibrium values. However, simulations produced with related stochastic models usually present sustained oscillations which preserve the natural frequency of the damped oscillations of the deterministic model but showing non-vanishing amplitudes. The relation between the amplitude of the stochastic oscillations and the values of the equilibrium populations is not intuitive in general but scales with the square root of the populations when the ratio between different populations is kept fixed. In this work, we explain such phenomena for the case of a general epidemic model. We estimate the stochastic fluctuations of the populations around the equilibrium point in the epidemiological model showing their (approximated) relation with the mean values.