New cutting-planes for the time-and/or precedence-constrained ATSP and directed VRP

In this paper, we introduce five classes of new valid cutting planes for the precedence-constrained (PC) and/or time-window-constrained (TW) Asymmetric Travelling Salesman Problems (ATSPs) and directed Vehicle Routing Problems (VRPs). We show that all five classes of new inequalities are facet-defining for the directed VRP-TW, under reasonable conditions and the assumption that vehicles are identical. Similar proofs can be developed for the VRP-PC. As ATSP-TW and PC-ATSP can be formulated as directed identical-vehicle VRP-TW and PC-VRP, respectively, this provides a link to study the polyhedral combinatorics for the ATSP-TW and PC-ATSP. The first four classes of these new cutting planes are cycle-breaking inequalities that are lifted from the well-known D-k and D+k inequalities (see Gr&ouml;tschel and Padberg in Polyhedral theory. The traveling salesman problem: a guided tour of combinatorial optimization, Wiley, New York, 1985). The last class of new cutting planes, the TW 2 inequalities, are infeasible-path elimination inequalities. Separation of these constraints will also be discussed. We also present prelimanry numerical results to demonstrate the strengh of these new cutting planes.<br /

RNA viruses and autoimmunity: A short overview

RNA viruses are a large group of widespread and extremely prevalent pathogens capable of eliciting a broad spectrum of innate and adaptive immune responses. Additionally, persistent infection by some RNA viruses can induce or enhance accelerated immune activation. The hypothesis that molecular mimicry is implicated in autoimmunity was first proposed in 1987. Since then, a growing evidence from medical literature of a possible role for viral infection in autoimmunity has risen. In particular, enteroviruses have been investigated as possible causes of type 1 diabetes. Some hypotheses have put forward the possible implication of hepatitis A virus in autoimmune phenomena. The two most prevalent RNA viruses causing chronic infection, hepatitis C virus and human immunodeficiency virus type 1 (HIV-1), are both associated with autoimmune disorders. HCV can trigger and sustain a clonal B-cell expansion which causes a wide spectrum of autoimmune/lymphoproliferative disorders, through a multistep process. Similarly, HIV is responsible for derangement of the immune regulation and is associated with some autoimmune disorders, such as autoimmune thrombocytopenia. Nevertheless, a formal scientific demonstration of an etiological relationship between any RNA virus and a major autoimmune disease has not yet been obtained