The Knapsack Problem with Setup (KPS) is a generalization of the classical Knapsack problem (KP), where items are divided into families. An individual item can be selected only if a setup is incurred for the family to which it belongs. This paper provides a dynamic programming (DP) algorithm for the KPS that produces optimal solutions in pseudo-polynomial time. In order to reduce the storage re...

The dimensions of the symmetry classes of tensors, associated with a certain cyclic subgroup of $n which is generated by a product of disjoint cycles is explicitly given in terms of the generalized Ramanujan sum. These dimensions can also be expressed as the Euler φ-function and the Möbius function. In the following we show some results appeared in [2]. Definition 2.1 Let n1, . . . , np be posi...

A long series of runoff data is the basis for water conservancy project planning, resource management, and so on. When in short supply, it needs to be extended reconstructed. Taking Zhiyan Reservoir Qiantanglong Lanxi City as research objects, based on Water balance model with double parameters (WBM-DP) Quantile Mapping (QM) methods, monthly income two reservoirs 59 years from 1960 2018 was ana...

DAP kinases are a family of serine/threonine kinases known to regulate intrinsic apoptotic processes. DAP-related apoptotic kinase-2 (DRAK2) is highly expressed in lymphoid organs, with differential expression during thymocyte development. Low levels of transcript were observed in CD4/CD8 double-positive (DP) and double-negative populations, whereas single-positive thymocytes possessed elevated...

A central task in multiagent resource allocation, which provides mechanisms to allocate (bundles of) resources to agents, is to maximize social welfare. We assume resources to be indivisible and nonshareable and agents to express their utilities over bundles of resources, where utilities can be represented in the bundle form, the k-additive form, and as straight-line programs. We study the comp...

OBJECTIVE Fibrotic skin changes in systemic sclerosis (SSc) are preceded by the appearance of an inflammatory infiltrate rich in T cells. Since no direct comparison with T cells in normal skin has been performed previously, this study was undertaken to functionally characterize T cells in the skin of patients with early active SSc and in normal skin. METHODS We characterized coreceptor expres...

Notch1 signaling is required for T cell development. We have previously demonstrated that expression of a dominant active Notch1 (ICN1) transgene in hematopoietic stem cells (HSCs) leads to thymic-independent development of CD4(+)CD8(+) double-positive (DP) T cells in the bone marrow (BM). To understand the function of Notch1 in early stages of T cell development, we assessed the ability of ICN...

An important task in multiagent resource allocation, which provides mechanisms to allocate bundles of (indivisible and nonshareable) resources to agents, is to maximize social welfare. We study the computational complexity of exact social welfare optimization by the Nash product, which can be seen as a sensible compromise between the well-known notions of utilitarian and egalitarian social welf...

Notch signaling is essential for the development of T cell progenitors through the interaction of NOTCH1 receptor on their surface with the ligand, Delta-like 4 (DLL4), which is expressed by the thymic epithelial cells. Notch signaling is quickly shut down once the cells pass β-selection, and CD4/CD8 double positive (DP) cells are unresponsive to Notch. Over the past two decades a number of pap...