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The performance and accuracy of a number of propagative algorithms are compared for the simulation of tapered high contrast step index slab waveguides. The considered methods include paraxial as well as nonparaxial formulations of optical field propagation. In particular attention is paid to the validity of the paraxial approximation. To test the internal consistency of the various methods the property of reciprocity is verified and it is shown that for the paraxial algorithms the reciprocity can only be fulfilled if the paraxial approximation of the power flux expression using the Poynting vector is considered. Finally, modeling results are compared with measured fiber coupling losses for an experimentally realized taper structure.

Drug discovery now faces a new challenge, where the availability of experimental data is no longer the limiting step, and instead, making sense of the data has gained a new level of importance, propelled by the extensive incorporation of cheminformatics and bioinformatics methodologies into the drug discovery and development pipeline. These enable, for example, the inference of structure-activity relationships that can be useful in the discovery of new drug candidates. One of the therapeutic applications that could benefit from this type of data mining is proteasome inhibition, given that multiple compounds have been designed and tested for the last 20 years, and this collection of data is yet to be subjected to such type of assessment. This study presents a retrospective overview of two decades of proteasome inhibitors development (680 compounds), in order to gather what could be learned from them and apply this knowledge to any future drug discovery on this subject. Our analysis focused on how different chemical descriptors coupled with statistical tools can be used to extract interesting patterns of activity. Multiple instances of the structure-activity relationship were observed in this dataset, either for isolated molecular descriptors (e.g., molecular refractivity and topological polar surface area) as well as scaffold similarity or chemical space overlap. Building a decision tree allowed the identification of two meaningful decision rules that describe the chemical parameters associated with high activity. Additionally, a characterization of the prevalence of key functional groups gives insight into global patterns followed in drug discovery projects, and highlights some systematically underexplored parts of the chemical space. The various chemical patterns identified provided useful insight that can be applied in future drug discovery projects, and give an overview of what has been done so far.

Recently, at the 119th European Study Group with Industry, the Energy Solutions Operator EDP proposed a challenge concerning electricity prices simulation, not only for risk measures purposes but also for scenario analysis in terms of pricing and strategy. The main purpose was short-term Electricity Price Forecasting (EPF). This analysis is contextualized in the study of time series behavior, in particular multivariate time series, which is considered one of the current challenges in data mining. In this work a short-term EPF analysis making use of vector autoregressive models (VAR) with exogenous variables is proposed. The results show that the multivariate approach using VAR, with the season of the year and the type of day as exogenous variables, yield a model that explains the intra-day and intra-hour dynamics of the hourly prices.

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This study intends to present a representation of a pensions fund through a stochastic network with two infinite servers nodes. With this representation it is allowed to deduce an equilibrium condition of the system with basis on the identity of the random rates expected values, for which the contributions arrive to the fund and the pensions are paid by the fund. In our study a stochastic network is constructed where traffic is represented. This network allows to study the equilibrium in the system and it is admissible to get a balance to a pensions fund. A specific case is studied. When the arrivals from outside at nodes A and B are according to a Poisson process, with rates ! and ! , respectively, the system may be seen as a two nodes network where the first node is a / /∞ queue and second a ! / /∞ queue. For this case in the long term the conditions of equilibrium are as follows: ! ! ! = ! ! + ! !. In this formula it is established a relationship among the two nodes. Several examples are given in the study.

Abstract. The reserves problem is studied through models based on Random Walks. Random walks are a classical particular case in the analysis of stochastic processes. They do not appear only to study reserves evolution models. They are also used to build more complex systems and as analysis instruments, in a theoretical feature, of other kind of systems. In this work by studying the reserves, the main objective is to see and guarantee that pensions funds get sustainable. Being the use of these models considering this goal a classical approach in the study of pensions funds, this work concluded about the problematic of reserves. A concrete example is presented.

The Brownian Motion is commonly used as an approximation for some Random Walks and also for the Classic Risk Process. As the Random Walks and the Classic Risk Process are used frequently as stochastic models to represent reserves, it is natural to consider the Brownian Motion with the same purpose. In this study a model, based on the Brownian Motion, is presented to represent reserves. The Brownian Motion is used in this study to estimate the ruin probability of a fund. This kind of models is considered often in the study of pensions funds.