Topos-Theoretic Extension of a Modal Interpretation of Quantum Mechanics

This paper deals with topos-theoretic truth-value valuations of quantum propositions. Concretely, a mathematical framework of a specific type of modal approach is extended to the topos theory, and further, structures of the obtained truth-value valuations are investigated. What is taken up is the modal approach based on a determinate lattice \Dcal(e,R), which is a sublattice of the lattice \Lcal of all quantum propositions and is determined by a quantum state $e$ and a preferred determinate observable $R$. Topos-theoretic extension is made in the functor category \Sets^{\CcalR} of which base category \CcalR is determined by $R$. Each true atom, which determines truth values, true or false, of all propositions in \Dcal(e,R), generates also a multi-valued valuation function of which domain and range are \Lcal and a Heyting algebra given by the subobject classifier in \Sets^{\CcalR}, respectively. All true propositions in \Dcal(e,R) are assigned the top element of the Heyting algebra by the valuation function. False propositions including the null proposition are, however, assigned values larger than the bottom element. This defect can be removed by use of a subobject semi-classifier. Furthermore, in order to treat all possible determinate observables in a unified framework, another valuations are constructed in the functor category \Sets^{\Ccal}. Here, the base category \Ccal includes all \CcalR's as subcategories. Although \Sets^{\Ccal} has a structure apparently different from \Sets^{\CcalR}, a subobject semi-classifier of \Sets^{\Ccal} gives valuations completely equivalent to those in \Sets^{\CcalR}'s.Comment: LaTeX2

International Forum on Policies and Practice for Transfusion of ABO and RhD Non-Identical Platelets: Summary

Immunobiology of allogeneic stem cell transplantation and immunotherapy of hematological disease

International Forum on Policies and Practice for Transfusion of ABO and RhD Non-Identical Platelets: Responses

Immunobiology of allogeneic stem cell transplantation and immunotherapy of hematological disease

Surgical Management of Melanoma in Situ on Chronically Sun-Damaged Skin

Lentigo maligna (LM) commonly presents as a slow-growing pigmented macular lesion in chronically sun-damaged skin and may progress to invasive melanoma. Many regard it as a subtype of melanoma in situ (MIS), and surgical excision remains the preferred treatment, but standard 5-mm surgical margins recommended for typical MIS are often insufficient for LM due to its indistinct borders both clinically and histologically. A search of the literature was conducted to review specialized surgical techniques for the treatment of LM, focusing on methods that employ total peripheral margin assessment prior to definitive closure, using either frozen or permanent histologic sections. Many investigators have reported surgical modalities utilizing permanent sections for margin control, including variations of the "square" procedure and "perimeter" technique. Recurrence rates are low with these methods, but only short-term data have been reported. Similarly, several studies have demonstrated the efficacy of Mohs micrographic surgery (MMS) for treatment of MIS, with recurrence rates generally less than 1% over 3 to 5 years of follow-up. Many investigators have had success with immunohistochemical stains to identify melanocytes on frozen sections, aiding margin assessment in MMS. Compared to standard excision, methods that employ surgical margin control offer superior cure rates for LM and should be utilized when available. Total peripheral margin assessment using staged excisions and permanent sections is a simple and effective alternative to MMS for institutions that lack the resources for intraoperative frozen section analysis