Given the non-graph-changing Hamiltonian $\widehat{H[N]}$ in Loop Quantum Gravity (LQG), $\langle\widehat{H[N]}\rangle$, coherent state expectation value of $\widehat{H[N]}$, admits an semiclassical expansion $\ell^2_{\rm p}$. In this paper, as presenting detailed derivations our previous work arXiv:2012.14242, we explicitly compute $\langle\widehat{H[N]}\rangle$ to linear order p}$ on cubic gr...

Often we build parameter estimators for which it is difficult compute the expectation and covariance analytically. Instead, we can estimate the expected value and the covariance through Monte Carlo Integration. This procedure estimates the expectation and covariance by applying the estimator to synthetic data polluted by random noise.

This manuscript presents an alternative implementation of the truthful-in-expectation (TIE) mechanism of Dughmi, Roughgarden and Yan [2] for combinatorial auctions. Recall that in a combinatorial auction, m goods get allocated to n bidders. Each bidder i has a private valuation vi that describes its value vi(S) for each subset S of goods. The social welfare of an allocation is the sum of the bi...