Hodge-Deligne and Poincaré polynomials of ${\bar{\mathcal{M}}}_{1,n}$

By studying wall crossings of Hassett moduli spaces of weighted pointed curves, we prove a recursive formula that reduces the computation of the cohomology of ${\bar{\mathcal{M}}}_{g,n}$ to that of the moduli space ${\bar{\mathcal{M}}}_{g,(0^{+}{)}^n}$ of stable pointed curves of minimal weights. For $g=1$, we further prove an explicit formula for the Hodge-Deligne and Poincaré polynomials of ${\bar{\mathcal{M}}}_{1,(0^{+}{)}^n}$. Combining these, we prove formulas that enable us to compute the cohomology of ${\bar{\mathcal{M}}}_{1,n}$ efficiently.