Over the years, technology has rapidly evolved, with social networks and media emerging as prominent examples. Social media facilitates the creation and exchange of content, while social networks connect individuals and organizations based on shared interests or values. Among these platforms, Twitter (now X) has gained significant attention and has been a valuable tool for monitoring reputation and brands, including political discourse. With the widespread use of social networks, the demand for advanced textual data analysis techniques, particularly sentiment analysis, has grown. Sentiment analysis, or polarity classification, aims to gauge the positivity or negativity of textual content, providing information on public opinion dynamics. In the context of the Peruvian presidential elections of 2021, characterized by political uncertainty exacerbated by the COVID-19 pandemic, social media platforms, especially Twitter/X, emerged as vital arenas for political discourse and participation. The election featured various candidates representing a wide spectrum of ideologies, reflecting the complexities of Peruvian society. Against this backdrop, this research uses Twitter/X data to analyze public sentiment toward presidential candidates and election-related topics. Through state-of-the-art sentiment analysis algorithms, this study categorizes tweets into positive, negative, or neutral sentiments, revealing key trends and themes driving public opinion on Twitter/X during the election period. By examining sentiment dynamics in response to major events and comparing Twitter/X sentiment trends with official voting data, the research aims to assess the predictive power of social media sentiment analysis in forecasting electoral outcomes. Therefore, this research contributes to understanding the role of social media in shaping political discourse and public opinion during elections. By conducting sentiment analysis on Twitter data, valuable insights are offered to policymakers, political analysts, and researchers who want to leverage social media to understand and forecast electoral trends.

This paper extends the Deal-Vidal-Wolfe and Lanchester models of duopoly dynamics, which involve two populations, by explicitly introducing a third population of undecided users. An analysis of these extended models establishes conditions for the existence of equilibria, as well as their stability properties under different classes of advertising policies. This analysis also leads to the surprising result that the extended Vidale–Wolfe and Lanchester models, despite having different dynamics, under the general class of decentralized affine feedback advertising policies have equilibria in identical locations, with the same stability properties.

This paper proposes definitions of implementation and adoption delays, arising from firm and client behaviors, in the context of market share dynamics. Information delay refers to the existence of lags in the information used for the advertising policy, while adoption delay refers to the existence of a lag in the effect of the advertising policy. These are natural lags in the flow of information and have not been considered in several models proposed in the literature. In this paper, these delays are introduced into recently proposed extensions of the Vidale-Wolfe-Deal and Lanchester models of market share dynamics subjected to affine advertising control policies. Conditions for stability of the equilibrium market share are derived. In addition, it is shown that Hopf bifurcations leading to oscillatory behavior exist for certain parameter values, and corresponding conditions for these are given. The main results are: the equilibrium market shares of the extended Vidale-Wolfe-Deal and Lanchester models are both robust to implementation delays, but, in the case of adoption delays, for both models, numerical results show that there is a critical value such that if the sum of the adoption delays exceeds this value, there is an onset of oscillations of market shares, through a Hopf bifurcation.

In this study, we conduct an exploratory and econometric assessment of the multidimensional impact of recent immigration, predominantly Venezuelan, on Peru (2000–2022). Utilizing 4565 time-series indicators, we apply a two-stage methodology: Pearson correlations to identify baseline exploratory associations, followed by Ordinary Least Squares (OLS) with temporal controls and First Differences models to isolate genuine structural effects from time-trend artifacts and spurious correlations. Econometric validation refines oversimplified public narratives. Socially, immigration robustly correlates with increased food insecurity, localized detainments, and a reduced youth demographic, while aggregate crime complaints are identified as a time-trend artifact. Economically, migration structurally stimulates income for the poorest 40% and broadens financial inclusion, despite negatively impacting aggregate macroeconomic consumption. Educationally, the influx of skilled migrants robustly drives scientific publications and increases average formal education years, though it introduces challenges like delayed primary school attendance and a negative shift in educational gender parity. Finally, perceived impacts on central government expenditures and consumption tax revenues are econometrically isolated as either time-trend artifacts or spurious correlations rather than direct migratory consequences. This approach separates true structural responses from historical inertia, providing a balanced, quantitative perspective on migration in Peru.