We deal with the problem of storing a set of K elements that are taken from a large universe of size N , such that membership in the set can be determined with high probability by looking at just one bit of the representation. Buhrman et al. show an explicit construction with about K2 logN storing bits. We show an explicit construction with about K1+o(1) storing bits, that gets closer to the op...

Abstract A 43-year-old woman presented with a 3-year history of gradually enlarging lesion on the right upper chest. Her comorbidities included ankylosing spondylitis and recurrent anterior uveitis, she was taking no regular medications. She had systemic symptoms. initially seen by breast team, who organized an ultrasound that showed chronic inflammation, biopsy granulomatous inflammatory tissu...

We assess how firms' incentives to operate and invest in energy storage depend on the market structure. For this purpose, we characterize equilibrium outcomes allowing for power and/or production, as well vertical integration between production. Market reduces overall efficiency through two channels: It induces an inefficient use of facilities, it distorts investment incentives. The worst outco...