We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model b...
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In this work, a type III thermo-porous elastic system is considered. First, we use the semigroup theory to demonstrate that the system is well-posed. Second, we show that the system is exponentially stable under a nat...
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Numerous studies have shown that label noise can lead to poor generalization performance, negatively affecting classification accuracy. Therefore, understanding the effectiveness of classifiers trained using deep neur...
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In this paper, a new class of structured polynomials, which we dub the separable plus lower degree (SPLD in short) polynomials, is introduced. The formal definition of an SPLD polynomial, which extends the concept of ...
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We use experiments and theory to elucidate the size effect in capillary breakup rheometry, where pre-stretching in the visco-capillary stage causes the apparent relaxation time to be consistently smaller than the actu...
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Understanding how cooperation emerges in public goods games is crucial for addressing societal challenges. While optional participation can establish cooperation without identifying cooperators, it relies on specific ...
Understanding how cooperation emerges in public goods games is crucial for addressing societal challenges. While optional participation can establish cooperation without identifying cooperators, it relies on specific assumptions—that individuals abstain and receive a non-negative payoff, or that nonparticipants cause damage to public goods—which limits our understanding of its broader role. We generalize this mechanism by considering nonparticipants' payoffs and their potential direct influence on public goods, allowing us to examine how various strategic motives for nonparticipation affect cooperation. Using replicator dynamics, we find that cooperation thrives only when nonparticipants are motivated by individualistic or prosocial values, with individualistic motivations yielding optimal cooperation. These findings are robust to mutation, which slightly enlarges the region where cooperation can be maintained through cyclic dominance among strategies. Our results suggest that while optional participation can benefit cooperation, its effectiveness is limited and highlights the limitations of bottom-up schemes in supporting public goods.
The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to a convex optimization problem, which ...
The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to a convex optimization problem, which generally needs to be solved by iterative methods such as proximal gradient algorithm. However, these algorithms essentially belong to some iterative methods of fixed point problems of averaged mappings, and their convergence speed is generally slow. Furthermore, there is seldom research on the termination rule of these iterative algorithms solving the subproblem of DCA. To overcome these defects, we firstly show that the subproblem of the linearized proximal method (LPM) in each iteration is equal to the fixed point problem of a contraction. Secondly, by using Picard iteration to approximately solve the subproblem of LPM in each iteration, we propose a contractive difference-of-convex algorithm (cDCA) where an adaptive termination rule is presented. Both global subsequential convergence and global convergence of the whole sequence of cDCA are established. Finally, preliminary results from numerical experiments are promising.
Two-phase heterogeneous materials arising in a variety of natural and synthetic situations exhibit a wide-variety of microstructures and thus display a broad-spectrum effective physical properties. Given that such pro...
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With the rise of artificial intelligence, many people nowadays use artificial intelligence to help solve some problems in life, and the medical field is also with the rise of artificial intelligence, many people are s...
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We investigate the structural and observable impacts of dark matter (DM) on neutron stars (NSs) using a combined equation of state that integrates the relativistic mean-field (RMF) model for baryonic matter with a var...
We investigate the structural and observable impacts of dark matter (DM) on neutron stars (NSs) using a combined equation of state that integrates the relativistic mean-field (RMF) model for baryonic matter with a variable density profile for DM, incorporating DM-baryon interactions mediated by the Higgs field. Employing three RMF parameter sets (NL3, BigApple, and IOPB-I) for baryonic matter, we analyze mass-radius relations, maximum mass, and tidal deformability, focusing on DM density scaling (α) and steepness (β) parameters. Our findings reveal that increased DM concentration significantly enhances NS compactness, shifting mass-radius profiles and reducing tidal deformability. The DM influence strongly depends on the steepness of the DM density profile, where high β values lead to strongly confined DM within the NS core, resulting in more compact and less deformable configurations. Observational constraints from PSR J0740+6620 and GW170817 impose consistent structural limits on DM fractions across different equations of state models, narrowing the allowable parameter space for DM and linking specific combinations of αMχ (Mχ being the mass of dark matter particle) and β values to viable NS structures. This study highlights the interplay among DM concentration, nuclear stiffness, and observational data in shaping NS structure, offering insights into future constraints on DM in high-density astrophysical environments.
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