Mg. Rebolledo-Vega, Rodrigo

This paper presents a mathematical programming model to simultaneously create districts and allocate seats in Chile’s Chamber of Deputies, improving representativeness. In addition, it explicitly incorporates constraints that ensure the contiguity of the communes that form the districts while respecting natural and administrative boundaries. Implementing specific strategies and methods has resulted in significant enhancements in particular metrics used to assess the degree of representativeness. These improvements have effectively addressed certain shortcomings and resulted in more accurate and reliable representation measurements in the given context. This study proposes a novel mathematical programming model that simultaneously tackles district creation and seat allocation for Chile’s Chamber of Deputies. This integrated approach aims to achieve a more representative body. The results demonstrate a substantial decrease in malapportionment, from 11.07 in the 2015 reform to 6.55 under the proposed model. Furthermore, the sum of deviations has diminished, and the number of overrepresented districts has decreased from 17 to 13 out of 28 districts. Consequently, the malapportionment has been significantly reduced and falls within the permissible range of deviations, as outlined by the European Commission for Democracy through Law.

To model dynamic systems in various situations results in an ordinary differential equation of the form dy/dt=g(y,t,θ), where g denotes a function and θ stands for a parameter or vector of unknown parameters that require estimation from observations. In order to consider environmental fluctuations and numerous uncontrollable factors, such as those found in forestry, a stochastic noise process ϵt may be added to the aforementioned equation. Thus, a stochastic differential equation is obtained: dYt/dt=f(Yt,t,θ)+ϵt. This paper introduces a method and procedure for parameter estimation in a stochastic differential equation utilising the Richards model, facilitating growth prediction in a forest’s tree population. The fundamental concept of the approach involves assuming that a deterministic differential equation controls the development of a forest stand, and that randomness comes into play at the moment of observation. The technique is utilised in conjunction with the logistic model to examine the progression of an agricultural epidemic induced by a virus. As an alternative estimation method, we present the Random Time Transformation (RTT) method. Thus, this paper’s primary contribution is the application of the RTT method to estimate the Richards model, which has not been conducted previously. The literature often uses the logistic or Gompertz models due to difficulties in estimating the parameter form of the Richards model. Lastly, we assess the effectiveness of the RTT Method applied to the Chapman–Richards model using both simulated and real-life data.