Summary Hematopoiesis is arguably one of the best understood stem cell systems; however, significant challenges remain to reach a consensus understanding of the lineage potential, heterogeneity, and relationships of hematopoietic stem and progenitor cell populations. To gain new insights, we performed quantitative analyses of mature cell production from hematopoietic stem cells (HSCs) and multiple hematopoietic progenitor populations. Assessment of the absolute numbers of mature cell types produced by each progenitor cell revealed a striking erythroid dominance of all myeloid-competent progenitors assessed, accompanied by strong platelet reconstitution. All populations with myeloid potential also produced robust numbers of red blood cells and platelets in vivo . Clonal analysis by single-cell transplantation and by spleen colony assays revealed that a significant fraction of HSCs and multipotent progenitors have multilineage potential at the single-cell level. These new insights prompt an erythroid-focused model of hematopoietic differentiation.

In this paper, we address the spectrum portfolio optimization (SPO) question in the context of secondary spectrum markets, where bandwidth (spectrum access rights) can be bought in the form of primary and secondary contracts. While a primary contract on a channel provides guaranteed access to the channel bandwidth (possibly at a higher per-unit price), the bandwidth available to use from a secondary contract (possibly at a discounted price) is typically uncertain/stochastic. The key problem for the buyer (service provider) in this market is to determine the amount of primary and secondary contract units needed to satisfy its uncertain user demand.We formulate single and multi-region spectrum portfolio optimization problems as one of minimizing the cost of the spectrum portfolio subject to constraints on bandwidth shortage. Two different forms of bandwidth shortage constraints are considered, namely, the demand satisfaction rate constraint, and the demand satisfaction probability constraint. While the SPO problem under demand satisfaction rate constraint is shown to be convex for all density functions, the SPO problem under demand satisfaction probability constraint is not convex in general. We derive some sufficient conditions for convexity in this case. We also discuss application of the Bernstein approximation technique to approximate a non-convex demand satisfaction probability constraint by a convex constraint. The SPO problems can therefore be solved efficiently using standard convex optimization techniques. We then consider a discrete version of the SPO problem, in which the primary and secondary contracts can bought/sold in discrete units. We study the submodularity property of the discrete SPO problem and discuss a branch-and-bound algorithm algorithm to solve it efficiently. Finally, we perform a thorough simulation-based study of the single-region and the multiple-region problems for different choices of the problem parameters, and provide key insights regarding the portfolio composition. We provide several insights about the scaling behavior of the unit prices of the secondary contracts, as the stochastic characterization of the bandwidth available from secondary contracts change.

In this paper, we address the spectrum portfolio optimization (SPO) question in the context of secondary spectrum markets, where bandwidth (spectrum access rights) can be bought in the form of primary and secondary contracts. While a primary contract on a channel provides guaranteed access to the channel bandwidth (possibly at a higher per-unit price), the bandwidth available to use from a secondary contract (possibly at a discounted price) is typically uncertain/stochastic. The key problem for the buyer (service provider) in this market is to determine the amount of primary and secondary contract units needed to satisfy its uncertain user demand. We formulate single and multi-region spectrum portfolio optimization problems as one of minimizing the cost of the spectrum portfolio subject to constraints on bandwidth shortage. Two different forms of bandwidth shortage constraints are considered, namely, the demand satisfaction rate constraint, and the demand satisfaction probability constraint. While the SPO problem under demand satisfaction rate constraint is shown to be convex for all density functions, the SPO problem under demand satisfaction probability constraint is not convex in general. We derive some sufficient conditions for convexity in this case. We also discuss application of the Bernstein approximation technique to approximate a non-convex demand satisfaction probability constraint by a convex constraint. The SPO problems can therefore be solved efficiently using standard convex optimization techniques. We then consider a discrete version of the SPO problem, in which the primary and secondary contracts can bought/sold in discrete units. We study the NP-hardness submodularity property of the discrete SPO problem and discuss a branch-and-bound algorithm to obtain the optimal solution for this problem. Finally, we perform a thorough simulation-based study of the single-region and the multiple-region problems for different choices of the problem parameters, and provide key insights regarding the portfolio composition, the efficiency of the Bernstein convex approximation technique, and the closeness of the optimal discrete spectrum portfolio solutions to their continuous approximations. We provide several insights about the scaling behavior of the unit prices of the secondary contracts, as the stochastic characterization of the bandwidth available from secondary contracts change.

Abstract-We address the question of optimal trading of bandwidth (service) contracts in wireless spectrum markets, for the primary spectrum providers. We propose a structured spectrum market and consider two basic types of spectrum contracts that can help attain desired flexibilities and tradeoffs in terms of service quality, spectrum usage efficiency and pricing: long-term guaranteed-bandwidth contracts, and shortterm opportunistic-access contracts. A primary provider (seller) creates and maintains a portfolio composed of an appropriate mix of these two types of contracts. The optimal contract trading question in this context amounts to how the spectrum contract portfolio of a seller in the spectrum market should be dynamically adjusted, so as to maximize return subject to meeting the bandwidth demands of its own subscribers. We formulate the optimal contract trading question as a stochastic dynamic programming problem, and obtain structural properties of the optimal dynamic trading strategy that takes into account the current market prices of the contracts and the subscriber demand process in the decision-making.

We consider the contract-switching paradigm for studying the inter-domain traffic engineering problem. In the contract-switching paradigm, each ISP in the Internet is abstracted as a set of edge-to-edge contract links. We formulate the optimal routing problem for the contract-switching paradigm by considering three objectives, namely: 1) maximizing throughput, 2) minimizing delay, and 3) minimizing bandwidth usage. We solve the optimization problems on realistic network topologies and show that the routing solutions developed using the contractswitching paradigm provides significant improvement in performance compare to the BGP routing framework with respect to the three objectives. Moreover, our simulation study also reveals that the contract-switching paradigm performs close to the best performance that can be achieved in the Internet in the absence of any abstractions.