The use of distributed or parallel processing gained interest in the recent years to fight the state space explosion problem. Many industrial systems are described with large models, and the state space being even larger, it does not fit completely into the memory of a single computer. To avoid the high space requirement, several reduction techniques have been proposed: modular verification, pa...

The modular envelope of a cyclic operad is the smallest modular operad containing it. A modular operad is constructed from moduli spaces of Riemann surfaces with boundary; this modular operad is shown to be the modular envelope of the A∞ cyclic operad. This gives a new proof of the result of Harer-Mumford-Thurston-Penner-Kontsevich that a cell complex built from ribbon graphs is homotopy equiva...

The use of distributed or parallel processing gained interest in the recent years to fight the state space explosion problem. Many industrial systems are described with large models, and the state space being even larger, it does not fit completely into the memory of a single computer. To avoid the high space requirement, several reduction techniques have been proposed: modular verification, pa...

In this paper, we define the modular space Z σ (s, p) by using the Zweier operator and a modular. Then, we consider it equipped with the Luxemburg norm and also examine the uniform Opial property and property β. Finally, we show that this space has the fixed point property.

In Multi-Agent Reinforcement Learning, each agent observe a state of other agents as a part of environment. Therefore, the state space is exponential in the number of agents and learning speed significantly decrease. Modular Q-learning [6] needs very small state space. However, the incomplete observation involves a decline in the performance. In this paper, we improve Modular Q-learning’s perfo...

We generalize the Quantum Geometric Tensor by replacing a Hamiltonian with modular Hamiltonian. The symmetric part of provides Fubini-Study metric, and its anti-symmetric sector gives Berry curvature. Our generalization dubbed Modular metric curvature Kinematic Space. also use result identity Virasoro block to relate connected correlator two Wilson lines two-point function This relation realize...

Our main goal in this paper is to construct the first explicit fundamental domain of the Picard modular group acting on the complex hyperbolic space CH . The complex hyperbolic space is a Hermitian symmetric space, its bounded realization is the unit ball in C equipped with the Bergman metric. The Picard modular group is a discontinuous holomorphic automorphism subgroup of SU(2, 1) with Gaussia...