Abstract

Abstract
This work addresses the joint challenges of layout design and power output smoothing in Airborne Wind Energy farms. The problem is deciding the power units' location and their synchronization, as well as balancing the power output in Airborne Wind Energy Farms, while maximizing the average power output. Airborne Wind Energy systems, particularly the ground-generation type, are susceptible to significant power output fluctuations, which must be mitigated to ensure a stable power flow injected into the electrical grid. We propose and evaluate various synchronization strategies, along with an innovative retraction method introduced in this work, which eliminates the need for synchronized operational cycles among kites. This approach increases flexibility in production cycle selection, leading to a significantly smoother power output signal.

Abstract
The notion of Union is strength is essential for preserving public goods and mitigating public bads such as air quality. International environmental agreements serve this role by forming stable coalitions, in which agents join or leave based on free-riding incentives. Building on the Baliga-Maskin model, we show that such coalitions can emerge from a simple Markov chain mechanism where agents enter or exit through utility-based bargaining. However, stable coalition formation is challenging, as members may receive substantially lower utility than free-riders. This asymmetry gives rise to Barrett's paradox of cooperation: even with large coalitions and strong preferences among free-riders, overall utility may remain far below that of the grand coalition. Encouragingly, the paradox of cooperation can be resolved when free-riders have sufficiently low preferences.

Abstract
A central issue in price competition with positive network effects is the potential for small price changes to trigger abrupt chain reactions, leading to market tipping, winner-take-all scenarios, and zero-profit equilibria. We show that in a duopoly where consumers are not anonymous but partitioned into at least two groups, a simple group-based network structure can, by itself, generate downward-sloping demand and support profitable shared-market equilibria. These are subgame-perfect pure price equilibria in which both firms earn strictly positive profit. Triggering a bandwagon effect and tipping the market remains possible, but requires aggressive price deviations, or price shocks, that produce demand jumps. However, this is not always profitable, and the fear of bankruptcy can be sufficient to stabilize firms in equilibrium. The result relies on having one group with centripetal influence (stronger impact on peers) and another with centrifugal influence (stronger impact on outsiders). It requires no additional sources of heterogeneity or product differentiation. This mechanism shows that positive network effects - when group structured - can endogenously generate stability in price competition. The analysis reconciles the coexistence of local stability and the potential for tipping, offering a unified explanation of how markets with strong network effects can sustain both competition and profitability. We draw a parallel to Turing's reaction-diffusion patterns and reinterpret Becker's intuition that social influence can produce stable outcomes, even when demand may exhibit upward-sloping segments.

Abstract
When directional data fall in the positive orthant of the unit hypersphere, a folded directional distribution is preferred over a simple directional distribution for modeling the data. Since directional data, especially axial data, can be modeled using a Watson distribution, this paper considers a folded Watson distribution for such cases. We first address the parameter estimation of this distribution using maximum likelihood, which requires a numerical algorithm to solve the likelihood equations. We use the Expectation-Maximization (EM) algorithm to obtain these estimates and to analyze the properties of the concentration estimator through simulation. Next, we propose the Bayes rule for a folded Watson distribution and evaluate its performance through simulation in various scenarios, comparing it with the Bayes rule for the Watson distribution. Finally, we present examples using both simulated and real data available in the literature.

Abstract
This study aims to understand the EU countries progress towards the Europe 2030 sustainable development goals (SDGs) in the areas of good health and well-being, gender equality and reduction of inequalities. Data for some indicators related to these areas were collected from the Eurostat database for the period 2010-2023. In order to analyze this three-way data, we first carried out a preliminary analysis through some graphical representations of the data, and then, we used a method of multivariate data analysis, Double Principal Component Analysis, which allows to identify which countries and/or indicators are close to or quite far from the targets. © 2026 Author(s).