Reciprocity is central to explanations of cooperation among unrelated individuals in societies of humans and other animals. Most mathematical analyses of the evolution of reciprocity are based on the repeated Prisoner's Dilemma (RPD) and typically assume that new strategies are rarely introduced by mutation or analogous cultural processes, that behavioral errors are absent or infrequent, and that agents are bound to interact with the same partner. Here we analyze a version of the RPD in which new strategies are frequently tested, behavioral errors occur at a non-negligible rate, and actors may have the option to leave their current partner. In this environment, the usual indeterminacy disappears, and the mix of strategies and cooperation levels are quite stable. With the option to leave, cooperation persists at a substantially higher level than without the option to leave. Classical strategies such as Tit-for-Tat, Win-Stay-Lose-Shift, and Grim become rare and are largely displaced by strategies that sanction cheaters by leaving rather than by retaliatory defection. Beyond a threshold, increasing the number of times partners interact decreases the level of cooperation without the option to leave, but increases it when leaving is possible.
Earth-Air Heat Exchangers (EAHEs) are increasingly considered a promising solution for space heating and cooling using renewable energy, owing to the widespread availability and stable thermal conditions of the ground. This interest is reflected in the literature, which includes a large number of studies on these systems. However, studies involving long-term monitoring of real systems installed in operational buildings remain limited, particularly for tertiary-sector buildings. Moreover, to the authors' knowledge, no reported case studies exist of round-duct EAHE installed beneath building foundations. The present study monitors, over one year, a straight, parallel, open-loop EAHE serving a university lecture building in the continental climate of Valladolid, Spain. The system achieved specific heating gains of 37 kWh/m2 year, resulting in 22% reductions in the annual heating ventilation demand of the Air Handling Unit (AHU). Owing to the reduced summer operation of the building, cooling ventilation demand is limited, with the EAHE covering 13.7 kWh/m2 & sdot;year and yielding 90% savings. In winter, the thermal effectiveness of the EAHE approached 0.4 and 0.6 under low and high operating airflow rates, respectively. In summer, effectiveness was marginally higher. The cooling and heating Coefficients of Performance (COP), calculated based on the actual electricity consumption of the fan, reached 3.3 and 3.5, respectively. These results are within the range of values reported in the literature for other EAHEs installed in tertiary buildings and may be considered marginally superior, allowing for the high peak airflow rates of up to 40,000 m3/h handled by the system.
Exponential Runge-Kutta methods are a well-established tool for the numerical integration of parabolic evolution equations. However, these schemes are typically developed under the assumption of homogeneous boundary conditions. In this paper, we extend classical convergence results to the case of non-homogeneous boundary conditions. Since non-homogeneous boundary conditions typically cause order reduction, we introduce a correction strategy based on smooth extensions of the boundary data. This results in a reformulation as a homogeneous problem with modified source term, to which standard exponential integrators can be applied. For linear problems, we prove that the corrected schemes recover the expected convergence order, and hat higher orders can be attained with suitable quadrature rules, reaching order 2s for s-stage Gauss collocation methods. For semilinear problems, our approach preserves the convergence orders guaranteed by exponential Runge-Kutta methods satisfying the corresponding stiff order conditions. Numerical experiments validate the theoretical findings.
Non-invasive brain-computer interfaces (BCIs) aim to restore communication by decoding intended messages directly from neural activity, even without audible speech. However, evidence remains limited that noninvasive signals can support subject-held-out decoding of predefined semantic intentions from covert inner speech. We investigate whether a semantic-aware multimodal framework can generalize from overt spoken commands to covert inner speech using scalp electroencephalography (EEG), auxiliary electromyography (EMG), and overt-speech audio supervision. Ten healthy participants produced four everyday commands (water, toilet, light, pain) in overt and covert phases. Overt trials included synchronized EEG, EMG, and audio, whereas covert trials were evaluated without audio using EEG with auxiliary EMG. The proposed model learns a shared latent representation from overt multimodal supervision and covert training trials from non-held-out subjects, combining supervised contrastive learning, ArcFace classification, semantic prototype alignment, and overt-covert regularization. Evaluation follows a subject-held-out covert protocol with target-subject overt calibration: covert trials from the held-out participant are never used for training, model selection, or calibration. Across subjects, the model achieves a mean overt-validation accuracy of 0.54 and a mean covert-test accuracy of 0.42 on the four-class task, above the 0.25 chance level. Latent-space and semantic-retrieval analyses indicate that the learned representations retain class-related structure and alignment with text-based semantic prototypes. Ablations reveal that multimodal overt information supports within-subject decoding and representational analysis, whereas EEG-only overt supervision is more robust under held-out-subject covert transfer. These results identify subject variability, modality transfer, and calibration as key challenges for future semantic BCIs.
Non-deceptive counterfeiting involves producing and selling counterfeit products without misleading consumers about their authenticity. This practice intensifies price competition for genuine brands while contributing either to brand dilution or network externalities. Using a two-period game modeling approach, we analyze how genuine products should adjust their advertising and pricing strategies in response to non-deceptive counterfeiting. Our findings reveal that in the presence of brand dilution, manufacturers should reduce advertising investments and prices to remain competitive. However, when counterfeiting generates network externalities, the optimal response depends on market conditions and managerial effectiveness. In some cases, a survival strategy (reducing advertising and/or prices) may be necessary to maintain profitability. In other cases, a differentiation strategy (raising advertising and prices) can lead to profit gains. Regardless of the approach adopted, manufacturers must improve the targeting, content, and effectiveness of advertising to further differentiate their offerings and reduce positive spillover effects to counterfeit products.
