This paper proposes a real-time price (RTP)-based demand-response (DR) algorithm for achieving optimal load control of devices in a facility by forming a virtual electricity-trading process, where the energy management center of the facility is the virtual retailer (leader) offering virtual retail prices, from which devices (followers) are supposed to purchase energy. A one-leader, N-follower Stackelberg game is formulated to capture the interactions between them, and optimization problems are formed for each player to help in selecting the optimal strategy. The existence of a unique Stackelberg equilibrium that provides optimal energy demands for each device was demonstrated. The simulation analysis showed that the Stackelberg game-based DR algorithm is effective for achieving the optimal load control of devices in response to RTP changes with a trivial computation burden.

We examined the expression of two members of theNotch family, Notch-1 and Notch-2, and one Notch ligand, Jagged-1, in hematopoietic cells. Both Notch-1 and Notch-2 were detected in murine marrow precursors (Lin−Sca-1+c-kit+). The Notch ligand, Jagged-1, was not detected in whole marrow or in precursors. However, Jagged-1 was seen in cultured primary murine fetal liver stroma, cultured primary murine bone marrow stroma, and in stromal cell lines. These results indicate a potential role for Notch-Notch ligand interactions in hematopoiesis. To further test this possibility, the effect of Jagged-1 on murine marrow precursor cells was assessed by coculturing sorted precursor cells (Lin−Sca-1+c-kit+) with a 3T3 cell layer that expressed human Jagged-1 or by incubating sorted precursors with beads coated with the purified extracellular domain of human Jagged-1 (Jagged-1ext). We found that Jagged-1, presented both on the cell surface and on beads, promoted a twofold to threefold increase in the formation of primitive precursor cell populations. These results suggest a potential use for Notch ligands in expanding precursor cell populations in vitro.