In a 350 degree oven, roast beets until cooked through, about 45 minutes. When cool enough to handle, rub skins off and dice into 1/2-inch squares. Place beets, jicima, onion, chilies, and mussels in a bowl with the olive oil, cilantro, juices, salt, and pepper. Refrigerate a few hours to blend flavors. Divide ceviche evenly on tostadas and garnish with a dollop of mashed avocado on each. Serve immediately.