The Analog Ensemble (AnEn) method is used to reconstruct incomplete time series, particularly in meteorological contexts. However, the large volume of data and the need for repeated searches for nearest neighbours makes the method computationally intensive. This study explores the k-d tree data structure as an efficient alternative to accelerate the analog search process within the AnEn framework. By organising high-dimensional data hierarchically, the k-d tree significantly reduces search time. CPU-based implementations in the C language of the classical AnEn and k-d tree-based AnEn method were developed and evaluated. The results show that even in single-threaded execution, the k-d tree approach delivers substantial efficiency gains without compromising reconstruction accuracy or introducing significant memory overhead.

The Analog Ensemble (AnEn) method is widely used to reconstruct incomplete time series, especially in meteorological contexts. However, the large volume of data and the need for exhaustive comparisons make the method computationally intensive. With its most important hotspot - the analogs search - being easily parallelizable, two multithreaded Pthreads-based implementations are presented in this paper, based on two distinct serial versions recently developed in C: one that closely follows the original AnEn algorithm and another in which a k-d tree is used as an index of the predictors training period to accelerate the analogs search. The parallel versions preserve the relative speedup ratio of the serial ones (~1.4x) and are highly efficient, showing super-linear scalability with a moderate number of threads and speedups of ~56x (parallelized classical AnEn) and ~52x (parallelized k-d tree assisted AnEN) with 64 threads.

The Analog Ensemble (AnEn) method allows to reconstruct incomplete time series, based on correlated series with full records. It has been extensively applied to meteorological data, which may involve many variables and stations, and span many years, slowing down the reconstruction. To accelerate this process, Principal Component Analysis (PCA) may be employed, to combine several input series into a few principal components (PCs), over which AnEn is then applied for a faster data reconstruction. The integration of PCA with K-means clustering further amplifies efficiency. In this paper, multicore-based implementations of non-PCA and PCA-based methods, in MATLAB, R, and Python, were scrutinized to ascertain numerical consistency and evaluate relative performance. The experiments show that when using PCA, accuracy is kept, or even improved, despite lowering the number of input time series. Performance-wise, the experiments revealed a distinct edge for the Python code, for which the benefits of parallel processing were most evident. Preliminary results are also shown for a Python variant that exploits GPUs for the analog search, with very promising speedups.

The Analog Ensemble (AnEn) method can be used to reconstruct incomplete time series using correlated series. Since the AnEn method may use data including several variables through long periods of time, its storage and computational cost may be substantial, slowing down reconstructions. This paper presents a full GPU implementation of the AnEn method, based on PyCUDA, that leads to a significant a cceleration of its execution. The implementation resorts to several techniques that seek to minimize the consumption of GPU global memory in the various steps of the AnEn algorithm, thus making room for larger input datasets. This is further reinforced by the use of batch processing as a way to automatically adapt the datasets size to the GPU memory available. The GPU implementation was tested on a meteorological dataset spanning 10 years, exhibiting a 30-fold speedup in the reconstruction time against a comparable CPUbased multicore version executed with up to 48 cores. The impact on the reconstruction error of changes on several important parameters of the implementation was also assessed.

This work focuses on optimizing the displacement of a passive particle interacting with vortices located on the surface of a sphere. The goal is to minimize the energy expended during the displacement within a fixed time. The modeling of particle dynamics, whether in Cartesian or spherical coordinates, gives rise to alternative formulations of the identical problem. Thanks to these two versions of the same problem, we can assert that the algorithm, employed to transform the optimal control problem into an optimization problem, is effective, as evidenced by the obtained controls. The numerical resolution of these formulations through a direct approach consistently produces optimal solutions, regardless of the selected coordinate system.

The Partial Least Squares Regression is an efficient method for the filling of gaps in meteorological time series. It enables to reduce the dimension of the predictor dataset to a reduced number of latent variables, without loss of significant information. Defining the number of latent variables to be used is an essential aspect of the success of the method. This study is about the comparison between eight different criteria, used in the choice of latent variables. The results indicate that the criteria based on cross-validation are the most efficient, being, however, more computationally demanding.

The Analog Ensemble (AnEn) method has been used to reconstruct missing data in time series with base on other correlated time series with full data. As the AnEn method benefits from the use of large volumes of data, there is a great interest in improving its efficiency. In this paper, the Principal Component Analysis (PCA) technique is combined with the classical AnEn method and a K-means cluster-based variant, within the context of reconstructing missing meteorological data at a particular station using information from neighboring stations. This combination allows to reduce the dimension of the number of predictor time series, while ensuring better accuracy and higher computational performance than the AnEn methods: it reduces prediction errors by up to 30% and achieves a computational speedup of up to 2x.

This work presents a mathematical toy model for a process of garbage collection encompassing the coordination of a vast array of autonomous devices, where each device needs only a few trajectory adjustments. This simplified conceptual model serves as a valuable tool for both educational and initial research purposes. In this model, each autonomous device is represented by a passive particle, while the environmental currents are depicted by the dynamic behavior of point vortices on a spherical surface. In order to maintain device autonomy, a system of piecewise constant controls is utilized, which involves a limited set of predetermined switching points to adjust the trajectory. Each control incurs an energy expense, and the model aims to minimize this cost by solving a nonlinear optimization problem. The preliminary findings suggest the presence of multiple potential trajectories for autonomous devices, each associated with different energy costs.

A small number of individuals infected within a community can lead to the rapid spread of the disease throughout that community, leading to an epidemic outbreak. This is even more true for highly contagious diseases such as COVID-19, known to be caused by the new coronavirus SARS-CoV-2. Mathematical models of epidemics allow estimating several impacts on the population and, therefore, are of great use for the definition of public health policies. Some of these measures include the isolation of the infected (also known as quarantine), and the vaccination of the susceptible. In a possible scenario in which a vaccine is available, but with limited access, it is necessary to quantify the levels of vaccination to be applied, taking into account the continued application of preventive measures. This work concerns the simulation of the spread of the COVID-19 disease in a community by applying the Monte Carlo method to a Susceptible-Exposed-Infective-Recovered (SEIR) stochastic epidemic model. To handle the computational effort involved, a simple parallelization approach was adopted and deployed in a small HPC cluster. The developed computational method allows to realistically simulate the spread of COVID-19 in a medium-sized community and to study the effect of preventive measures such as quarantine and vaccination. The results show that an effective combination of vaccination with quarantine can prevent the appearance of major epidemic outbreaks, even if the critical vaccination coverage is not reached.

The focus of this study is the reconstruction of missing meteorological data at a station based on data from neighboring stations. To that end, the Principal Components Analysis (PCA) method was applied to the Analogue Ensemble (AnEn) method to reduce the data dimensionality. The proposed technique is greatly influenced by the choice of stations according to proximity and correlation to the predicted one. PCA associated with AnEn decreased the errors in the prediction of some meteorological variables by 30

Vortex points on a sphere can be considered as simplified models of atmospheric circulation. The use of these models allows the simulation of displacements of passive particles advected by vortex flow. In this study, a strategy is proposed to determine the optimal trajectory between two given points on the sphere, taking into account that the displacement occurs due to a vortex flow. It is an alternative numerical strategy to the methods proposed by the theory of optimal control. The original problem is discretized into a constrained optimization problem. The solution of this problem by two alternative numerical optimization methods shows that the strategy is feasible and leads to optimal or quasi-optimal solutions.

Despite the end of the COVID-19 pandemic was decreed by the WHO, this disease has not disappeared and continues to claim victims. Thus, it remains important to follow up, monitor, and project its evolution in the short term. To that end, mathematical models are a precious tool. Based on its results, it is possible to take preventive measures that minimize the spread of this contagious disease. This study focuses on the stochastic SEIR epidemic model adapted to a post-pandemic scenario. The main factors that influence the spread and containment of the disease are considered, namely, the rates of transmission, vaccination, and quarantine. The results obtained point to a probability of nearly 12

The reconstruction or prediction of meteorological records through the Analog Ensemble (AnEn) method is very efficient when the number of predictor time series is small. Thus, in order to take advantage of the richness and diversity of information contained in a large number of predictors, it is necessary to reduce their dimensions. This study presents methods to accomplish such reduction, allowing the use of a high number of predictor variables. In particular, the techniques of Principal Component Analysis (PCA) and Partial Least Squares (PLS) are used to reduce the dimension of the predictor dataset without loss of essential information. The combination of the AnEn and PLS techniques results in a very efficient hybrid method (PLSAnEn) for reconstructing or forecasting unstable meteorological variables, such as wind speed. This hybrid method is computationally demanding but its performance can be improved via parallelization or the introduction of variants in which all possible analogs are previously clustered. The multivariate linear regression methods used on the new variables resulting from the PCA or PLS techniques also proved to be efficient, especially for the prediction of meteorological variables without local oscillations, such as the pressure.

In this article, a simplified mathematical model is presented to depict the process of collecting ocean debris. The responsible autonomous vehicles for transporting the trash are represented as passive particles, while the ocean current is simulated by the movement of point vortices on a sphere. To ensure the autonomy of the vehicles, a system of piecewise constant controls is employed, using a limited number of predetermined switching points that determine their trajectories. Each control incurs an energy cost that is aimed to be minimized. This minimization is achieved by solving a nonlinear optimization problem on the spherical surface. The initial findings indicate the existence of multiple possible trajectories for autonomous vehicles.

With the current recession of the global COVID-19 pandemic, the corresponding epidemic models need to be adapted to reflect this new reality and continue assisting public health authorities in the definition of policies and decision making. With that aim, this paper presents a SEIR epidemic model for the representation of the COVID-19 pos-pandemic scenario. The model considers the effect of countermeasures such as vaccination and quarantine, and the consequences of the progressive loss of immunity. A deterministic formulation and a first stochastic version of the model are presented, and their implementation in MATLAB is evaluated and compared. To cope with the computational demands of the application of the Monte Carlo method, the implementation of the stochastic version follows a parallel approach that proved to be highly scalable and efficient in a multi-core computational system. The preliminary evaluation results, with fixed parameters, point to a cyclic evolution of the pandemic and a tendency for stabilization in the future.

This work investigates the fire effect on the bending resistance of the composite slab reinforced with steel deck, comparing the behavior of Normal Weight Concrete (NWC) and Light Weight Concrete (LWC) during a standard fire ISO834. This analysis is required for structures in fire and is mainly affected by two factors: the thermal and mechanical properties of the materials. The results of the simplified method are compared with the numerical results obtained by a two-dimensional and a three-dimensional thermal analysis, with regards to the temperature effect from each component in to the bending resistance of the composite slab. This analysis consists of a non-linear transient thermal analysis using the finite element method, using two different software: ANSYS and MATLAB. Based on the average temperature of each component, new coefficients and a new proposal for annex D of Eurocode 1994-1.2 are presented. The reduction of the load bearing capacity is also determined.

A three-dimensional computational model based on finite elements was developed to evaluate the thermal behaviour of composite slabs with steel deck exposed to a standard fire. The resulting numerical temperatures are then used to obtain a new analytical method, which is an alternative to the simplified method provided by the standard, to accurately determine the temperatures at the reinforcing bars (rebar). The fitting of the analytical model to the numerical data was done by solving a linear least squares problem using the singular value decomposition. The resulting formula fits very well the numerical data, allowing to make predictions of the temperature in the rebar with an approximation error equal to zero and an estimating error at least 77% lower than that obtained with the proposal included in the standard.

The Analogue Ensemble (AnEn) method enables the reconstruction of meteorological observations or deterministic predictions for a certain variable and station by using data from the same station or from other nearby stations. However, depending on the dimension and granularity of the historical datasets used for the reconstruction, this method may be computationally very demanding even if parallelization is used. In this work, the classical AnEn method is modified so that analogues are determined using K-means clustering. The proposed combined approach allows the use of several predictors in a dependent or independent way. As a result of the flexibility and adaptability of this new approach, it is necessary to define several parameters and algorithmic options. The effects of the critical parameters and main options were tested on a large dataset from real-world meteorological stations. The results show that adequate monitoring and tuning of the new method allows for a considerable improvement of the computational performance of the reconstruction task while keeping the accuracy of the results. Compared to the classical AnEn method, the proposed variant is at least 15-times faster when processing is serial. Both approaches benefit from parallel processing, with the K-means variant also being always faster than the classic method under that execution regime (albeit its performance advantage diminishes as more CPU threads are used).

The dynamics of passive tracers in flows dominated by perfect or viscous point vortices is a broad area of research that continues to attract the attention of numerous studies. Recently, there has been a particular interest in the application of control theory to these issues. Viscous point vortices are singular solutions of the two-dimensional incompressible Navier-Stokes equations in which the vorticity is concentrated at a finite number of points in the flow domain, each of which carries a certain amount of time-invariant circulation. By definition, a passive tracer is a point vortex with zero circulation. This paper describes some numerical investigations of passive tracers performed by viscous point vortices to find the energy-optimal displacement of a passive particle. The numerical results show the existence of near/quasi-optimal controls.

The objective of this study is to control the motion of a passive particle advected by N point vortices in a sphere. The square of the L-2 norm of control, necessary for the system to evolve from a starting point to an end point in an a priori fixed time, must be minimized. If the motion is generated by a single vortex (N = 1), we show that the system is controllable. The problem is also solved by a direct approach, where the control problem is transformed into a nonlinear optimization problem that is solved numerically. In the case of one (N = 1), two (N = 2), or three (N = 3) point vortices, the numerical results show the existence of near/quasi-optimal control.