Maximally-fast coarsening algorithms

We present maximally-fast numerical algorithms for conserved coarsening systems that are stable and accurate with a growing natural time-step $\Delta t=A t_s^{2/3}$. For non-conserved systems, only effectively finite timesteps are accessible for similar unconditionally stable algorithms. We compare the scaling structure obtained from our maximally-fast conserved systems directly against the standard fixed-timestep Euler algorithm, and find that the error scales as $\sqrt{A}$ -- so arbitrary accuracy can be achieved.Comment: 5 pages, 3 postscript figures, Late

Controlling the accuracy of unconditionally stable algorithms in Cahn-Hilliard Equation

Given an unconditionally stable algorithm for solving the Cahn-Hilliard equation, we present a general calculation for an analytic time step \d \tau in terms of an algorithmic time step \dt. By studying the accumulative multi-step error in Fourier space and controlling the error with arbitrary accuracy, we determine an improved driving scheme \dt=At^{2/3} and confirm the numerical results observed in a previous study \cite{Cheng1}.Comment: 4 pages, late

Intentional commitment as a spontaneous presentation of self

Commitment is a defining feature of human rationality. This study explores a social origin of spontaneous intentional commitment, assuming commitment in individual decision-making arises from an internalized self-presentation, transferring the audience of commitment from a real partner to an inner eye perspective. To test this "social inner eye" hypothesis, we exposed participants to different social contexts while maintaining the individual nature of the task. Across three experiments, we found that (a) individuals consistently showed stronger commitment when acting in front of others, (b) different social contexts had different impacts on the process of commitment formation, with the mere outside observer accelerating commitment, while a parallel player delays it, (c) participants spontaneously coordinated their intentions to avoid conflicts when playing with another parallel player, despite no coordination was required. Taken together, we demonstrated how social context influences the strength, content, and timing of individual commitment. These findings align with the perspective that individual commitment has a social origin. They also contribute to an understanding of why commitment is universally valued across cultures and is seen as a virtue rather than a weakness in human decision-making

The development of commitment: Attention for intention

The ability to take action according to a partially defined plan allows humans to resolve a distant future, even when steps are missing between the present and that future. Adhering to this partial plan requires an intentional commitment that curbs distracting desires conflicting with the planned course of action, enabling humans to act coherently over long horizons. This research (N = 50, 23 boys, ages 5-6, Chinese) explored the cognitive development of commitment to partial plans in a sequential decision-making task, and its correlation to participant capacity for attentional control. Our results suggest that only 6-year-olds committed to partial plans, and moreover, that in both age groups, intentional commitment was positively correlated with the use of proactive control. These findings indicate that intentional commitment does not develop simultaneously with the understanding of intention at infancy, but rather matures gradually in parallel with the development of attentional control

Intentional commitment through an internalized theory of mind: Acting in the eyes of an imagined observer

The ancient Greek hero Ulysses chose to bind himself to resist the temptation of Sirens, highlighting the fact that humans may voluntarily sacrifice their freedom of choice to achieve committed goals. In this work, we propose a computational model for such commitment under the framework of Bayesian Theory of Mind. The model is based on the idea that even when alone, humans act to better demonstrate their intentions to an imagined third-party observer (ITO) censoring their actions. Our model successfully captures the Ulysses-constraint of freedom, as the freedom confuses the ITO’s inference of their intention. We further show that, trajectories generated both by human actors and actors modeled with ITO censorship are easy to interpret both in the eyes of an actual human ob- server and an ITO. The results demonstrate that under conflict- ing desires, humans achieve commitment by spontaneously censoring their actions with an internalized theory of mind

Intention beyond Desire: Humans Spontaneously Commit to Future Actions

It is an ancient insight that human actions are driven by desires. Yet it misses one mental representation, intention, with which agents regulate conflicting desires by committing to an admissible plan. Here we demonstrate four behavioral signatures of intention only observed in humans: disruption resistance as sticking with a plan despite setbacks; exclusiveness as avoiding paths with temptations of re-planning; deliberation as the gradual emergence of a commitment plan; temporal leap as forming future plans before finishing the current one. Humans were compared against an optimal model formulated as Markov Decision Process (MDP), who acts only to maximize expected future rewards. Conflicting desires are defined as a reward function returning positive rewards for multiple states. It showed none of the behavioral signatures of intention. These results reveal that humans regulate conflicting desires with intentions, which directly drive actions