“The culture of New Orleans — the thoroughly local music, food and rituals that are connected to African processions, European carnivals, Caribbean rhythms and America’s history of slavery and intermingling — is a draw not just for tourists, but for New Orleanians. Through sheer perseverance, it is being rebuilt.” Over the weekend, the “38th annual Jazzfest was its old celebratory self, with an undercurrent of determination.”