A Constructivist View of Newton’s Mechanics

In the present essay we attempt to reconstruct Newtonian mechanics under the guidance of logical principles and of a constructive approach related to the genetic epistemology of Piaget and García (Psychogenesis and the history of science, Columbia University Press, New York, 1989). Instead of addressing Newton’s equations as a set of axioms, ultimately given by the revelation of a prodigious mind, we search for the fundamental knowledge, beliefs and provisional assumptions that can produce classical mechanics. We start by developing our main tool: the no arbitrariness principle, that we present in a form that is apt for a mathematical theory as classical mechanics. Subsequently, we introduce the presence of the observer, analysing then the relation objective–subjective and seeking objectivity going across subjectivity. We take special care of establishing the precedence among all contributions to mechanics, something that can be better appreciated by considering the consequences of removing them: (a) the consequence of renouncing logic and the laws of understanding is not being able to understand the world, (b) renouncing the early elaborations of primary concepts such as time and space leads to a dissociation between everyday life and physics, the latter becoming entirely pragmatic and justified a-posteriori (because it is convenient), (c) changing our temporary beliefs has no real cost other than effort. Finally, we exemplify the present approach by reconsidering the constancy of the velocity of light. It is shown that it is a result of Newtonian mechanics, rather than being in contradiction with it. We also indicate the hidden assumption that leads to the (apparent) contradiction.Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Natiello, Mario Alberto. Lund University; Sueci

Linear Processes in Stochastic Population Dynamics: Theory and Application to Insect Development

We consider stochastic population processes (Markov jump processes) that develop as a consequence of the occurrence of random events at random time intervals. The population is divided into subpopulations or compartments. The events occur at rates that depend linearly on the number of individuals in the different described compartments. The dynamics is presented in terms of Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time approximations to the problem. While the lowest order approximation matches the Poisson and multinomial heuristics previously proposed, higher-order approximations are completely new. Further, we analyse a model for insect development as a sequence of developmental stages regulated by rates that are linear in the implied subpopulations. Transition to the next stage competes with death at all times. The process ends at a predetermined stage, for example, pupation or adult emergence. In its simpler version all the stages are distributed with the same characteristic time.Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Natiello, Mario A.. Lund University; Sueci

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.Fil: Barmak, Daniel Hernan. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina; Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires; Argentina;Fil: Dorso, Claudio Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires; Argentina; Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina;Fil: Otero, Marcelo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires; Argentina; Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina;Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires; Argentina; Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina

Why Is Aedes aegypti Moving South in South America?

Colonies of Aedes aegypti have been reported at increasingly southern locations. Is this feature a manifestation of climate change or the result of the mosquito’s adaptation? Answering the question requires the testing and comparison of results produced under different, competing, hypotheses. We address the problem using “AedesBA”, a detailed model of the mosquito Aedes aegypti that has been under development for about 20 years. The aim of the model is to promote understanding. We incorporate the recently discovered biological behavior of this mosquito: diapause. Namely, this is the laying of resistance eggs when the day light shortens, entering into the unfavorable season for reproduction in temperate climates, as described from laboratory experiments. When the model is challenged to answer the questions posed, it suggests that climate change, as experienced during the time of the field records, does not explain the observations. Furthermore, the standard climate change argument does not support a detailed analysis. In contrast, we find that while diapause is not expected to be a trait that is selected by natural conditions in a subtropical climate (simulations for Resistencia, AR), within temperate climates such as in Buenos Aires city (AR), there is pressure favoring the selection of the trait. As we move southward (the cities of Dolores, Azul, Tandil, and Mar del Plata), the pressure increases, while the probability of Aedes aegypti to become established in them decreases, being in accordance with the field observations. The model shows in addition that the field-observable effects of diapause depend on weather variables, especially precipitation, and the dynamics of the nutritional resources in the breeding sites.Fil: Alonso, Lucas Ernesto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones en Energía no Convencional. Universidad Nacional de Salta. Facultad de Ciencias Exactas. Departamento de Física. Instituto de Investigaciones en Energía no Convencional; ArgentinaFil: Romeo Aznar, Victoria Teresa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Ecología, Genética y Evolución de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Ecología, Genética y Evolución de Buenos Aires; ArgentinaFil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin

A mathematically assisted reconstruction of the initial focus of the yellow fever outbreak in Buenos Aires (1871)

We discuss the historic mortality record corresponding to the initial focus of the yellow fever epidemic outbreak registered in Buenos Aires during the year 1871 as compared to simulations of a stochastic population dynamics model. This model incorporates the biology of the urban vector of yellow fever, the mosquito Aedes aegypti, the stages of the disease in the human being as well as the spatial extension of the epidemic utbreak.After introducing the historical context and the restrictions it puts on  initial conditions and ecological parameters, we discuss the general features of the simulation and the dependence on initial conditions and available sites for breeding the vector. We discuss the sensitivity, to the free parameters, of statistical estimators such as: nal death toll, day of the year when the outbreak reached half the total mortality and the normalized daily mortality, showing some striking regularities. The model is precise and accurate enough to discuss the truthfulness of the  resently accepted historic discussions of the epidemic causes, showing that there are more likely scenarios for the historic facts.Fil: Fernández, María Laura. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina; Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina;Fil: Otero, Marcelo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires; Argentina; Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina;Fil: Schweigmann, Nicolas Joaquin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ecología, Genética y Evolución; Argentina; Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Ecología, Genética y Evolución de Buenos Aires; Argentina;Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires; Argentina; Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina

Dispersal of Aedes aegypti: Field study in temperate areas using a novel method

Background & objectives: Since Aedes aegypti was identified as vector of yellow fever and dengue, its dispersal is relevant for disease control. We studied the dispersal of Ae. aegypti in temperate areas of Argentina during egglaying, using the existing population and egg traps. Methods: Two independent replicas of a unique experimental design involving mosquitoes dispersing from an urbanized area to adjacent non-urbanized locations were carried out and analyzed in statistical terms. Results: We found relationship between stochastic variables related to the egg-laying mosquito activity (ELMA), useful to assess dispersal probabilities, despite the lack of knowledge of the total number of ovipositions in the zone. We propose to evaluate the egg-laying activity as minus the logarithm of the fraction of negative ovitraps at different distances from the buildings. Interpretation & conclusion: Three zones with different oviposition activity were determined, a corridor surrounding the urbanization, a second region between 10 and 25 m and the third region extending from 30 to 45 m from the urbanization. The landscape (plant cover) and the human activity in the area appear to have an influence in the dispersal of Ae. aegypti. The proposed method worked consistently in two different replicas.Fil: Bergero, Paula Elena. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Ruggerio, Carlos Alberto. Universidad Nacional de General Sarmiento. Instituto del Conurbano; ArgentinaFil: Lombardo Berchesi, Ruben Jorge. Universidad Nacional de General Sarmiento. Instituto del Conurbano; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ecología, Genética y Evolución; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Schweigmann, Nicolas Joaquin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ecología, Genética y Evolución; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin

Minimal periodic orbit structure of 2-dimensional homeomorphisms

We present a method for estimating the minimal periodic orbit structure, the topological entropy, and a fat representative of the homeomorphism associated with the existence of a finite collection of periodic orbits of an orientation-preserving homeomorphism of the disk D 2. The method focuses on the concept of fold and recurrent bogus transition and is more direct than existing techniques. In particular, we introduce the notion of complexity to monitor the modification process used to obtain the desired goals. An algorithm implementing the procedure is described and some examples are presented at the end. © 2005 Springer.Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Natiello, M.A.. Lund University; Sueci

The topological reconstruction of forced oscillators

Periodically forced oscillators are among the simplest dynamical systems capable to display chaos. They can be described by the variables position and velocity, together with the phase of the force. Their phase-space corresponds therefore to R2 × S1. The organization of the periodic orbits can be displayed with braids having only positive crossings. Topological characterization of dynamical systems actually began to be explored in physics on this family of problems. In this work we show that, in general, it is not possible to produce a 3-dimensional imbedding of the solutions of a forced oscillator in terms of differential imbeddings based on sampling the position only. However, it may be possible to uncover a description of the phase variable from the sampled time-series, thus producing a faithful representation of the data. We proceed to formulate new tests in order to check whether proposed imbeddings can be accepted as such. We illustrate the manuscript throughout with an example corresponding to a model of Bénard-Marangoni convection. © 2009 Elsevier Ltd. All rights reserved.Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Natiello, Mario A.. Lund University; Sueci

On the removal of infinities from divergent series

The consequences of adopting other definitions of the concepts of sum and convergence of a series are discussed in the light of historical and epistemological contexts. We show that some divergent series appearing in the context of renormalization methods cannot be assigned finite values while preserving a minimum of consistency with standard summation, without at the same time obtaining contradictions, thus destroying the mathematical building (the conditions are known as Hardy’s axioms). We finally discuss the epistemological costs of accepting these practices in the name of instrumentalism.Fil: Natiello, Mario A.. Lund University; SueciaFil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin

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. © 2009 Elsevier Inc. All rights reserved.Fil: Otero, Marcelo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin