Utility Functions Invariant with Respect to Some Classes of Shifts

A utility function U is said to be invariant with respect to a family of transformations Γ provided, for every member γ of Γ , U and U • γ represent the same preference relation over lotteries. An invariance with respect to a wide class of transformations can be reduced to an invariance with respect to the shift transformations. We give a complete answer to the following question: given a nonempty set T of shifts determine all utility functions invariant with respect to the shift transformations by every element of T . As a consequence of our results we obtain the forms of utility functions invariant with respect to the families of commuting transformations

Homomorphisms from functional equations: the Goldie equation

The theory of regular variation, in its Karamata and Bojani´c-Karamata/de Haan forms, is long established and makes essential use of the Cauchy functional equation. Both forms are subsumed within the recent theory of Beurling regular variation, developed elsewhere. Various generalizations of the Cauchy equation, including the Gołab–Schinzel functional equation (GS) and Goldie's equation (GBE) below, are prominent there. Here we unify their treatment by algebraicization: extensive use of group structures introduced by Popa and Javor in the 1960s turn all the various (known) solutions into homomorphisms, in fact identifying them 'en passant', and show that (GS) is present everywhere, even if in a thick disguise

Effects of Blood Products on Inflammatory Response in Endothelial Cells In Vitro

BACKGROUND: Transfusing blood products may induce inflammatory reactions within the vascular compartment potentially leading to a systemic inflammatory response. Experiments were designed to assess the inflammatory potential of different blood products in an endothelial cell-based in vitro model and to compare baseline levels of potentially activating substances in transfusion products. METHODS: The inflammatory response from pre-activated (endotoxin-stimulated) and non-activated endothelial cells as well as neutrophil endothelial transmigration in response to packed red blood cells (PRBC), platelet concentrates (PC) and fresh frozen plasma (FFP) was determined. Baseline inflammatory mediator and lipid concentrations in blood products were evaluated. RESULTS: Following incubation with all blood products, an increased inflammatory mediator release from endothelial cells was observed. Platelet concentrates, and to a lesser extent also FFP, caused the most pronounced response, which was accentuated in already pre-stimulated endothelial cells. Inflammatory response of endothelial cells as well as blood product-induced migration of neutrophils through the endothelium was in good agreement with the lipid content of the according blood product. CONCLUSION: Within the group of different blood transfusion products both PC and FFP have a high inflammatory potential with regard to activation of endothelial cells. Inflammation upon blood product exposure is strongly accentuated when endothelial cells are pre-injured. High lipid contents in the respective blood products goes along with an accentuated inflammatory reaction from endothelial cells

Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

Vasculogenic mimicry in small cell lung cancer.

Small cell lung cancer (SCLC) is characterized by prevalent circulating tumour cells (CTCs), early metastasis and poor prognosis. We show that SCLC patients (37/38) have rare CTC subpopulations co-expressing vascular endothelial-cadherin (VE-cadherin) and cytokeratins consistent with vasculogenic mimicry (VM), a process whereby tumour cells form 'endothelial-like' vessels. Single-cell genomic analysis reveals characteristic SCLC genomic changes in both VE-cadherin-positive and -negative CTCs. Higher levels of VM are associated with worse overall survival in 41 limited-stage patients' biopsies (P<0.025). VM vessels are also observed in 9/10 CTC patient-derived explants (CDX), where molecular analysis of fractionated VE-cadherin-positive cells uncovered copy-number alterations and mutated TP53, confirming human tumour origin. VE-cadherin is required for VM in NCI-H446 SCLC xenografts, where VM decreases tumour latency and, despite increased cisplatin intra-tumour delivery, decreases cisplatin efficacy. The functional significance of VM in SCLC suggests VM regulation may provide new targets for therapeutic intervention

Positive Homogeneity of the Principle of Equivalent Utility

We prove that if the principle of equivalent utility under the cumulative prospect theory is positively homogeneous on a relatively small family of risks for every non-negative initial wealth level, then a value function is linear for gains and losses, but, in general, it needs not be linear