On the Existence of Quality Measures in Random Utility Models

Random Utitly Models (RUMs) are a particularly convenient way of modelling product differentiation. In this paper we demonstrate that they can be used to examine the possibilities of creating quality measures from data on prices and sales volumes. We formulate conditions sufficient for the existence of quality measures in two broad families of RUMs: additive random utility models and pure vertical differentiation models

On the Raşa Inequality for Higher Order Convex Functions

We study the following (q−1)th convex ordering relation for qth convolution power of the difference of probability distributions μ and ν (ν−μ)∗q≥(q−1)cx0,q≥2, and we obtain the theorem providing a useful sufficient condition for its verification. We apply this theorem for various families of probability distributions and we obtain several inequalities related to the classical interpolation operators. In particular, taking binomial distributions, we obtain a new, very short proof of the inequality given recently by Abel and Leviatan (2020)

On the Existence of Quality Measures in Random Utility Models

Random Utitly Models (RUMs) are a particularly convenient way of modelling product differentiation. In this paper we demonstrate that they can be used to examine the possibilities of creating quality measures from data on prices and sales volumes. We formulate conditions sufficient for the existence of quality measures in two broad families of RUMs: additive random utility models and pure vertical differentiation models

How many orthonormal bases are needed to distinguish all pure quantum states?

We collect some recent results that together provide an almost complete answer to the question stated in the title. For the dimension d=2 the answer is three. For the dimensions d=3 and d>4 the answer is four. For the dimension d=4 the answer is either three or four. Curiously, the exact number in d=4 seems to be an open problem

DNA damage by lipid peroxidation products: implications in cancer, inflammation and autoimmunity

Oxidative stress and lipid peroxidation (LPO) induced by inflammation, excess metal storage and excess caloric intake cause generalized DNA damage, producing genotoxic and mutagenic effects. The consequent deregulation of cell homeostasis is implicated in the pathogenesis of a number of malignancies and degenerative diseases. Reactive aldehydes produced by LPO, such as malondialdehyde, acrolein, crotonaldehyde and 4-hydroxy-2-nonenal, react with DNA bases, generating promutagenic exocyclic DNA adducts, which likely contribute to the mutagenic and carcinogenic effects associated with oxidative stress-induced LPO. However, reactive aldehydes, when added to tumor cells, can exert an anticancerous effect. They act, analogously to other chemotherapeutic drugs, by forming DNA adducts and, in this way, they drive the tumor cells toward apoptosis. The aldehyde-DNA adducts, which can be observed during inflammation, play an important role by inducing epigenetic changes which, in turn, can modulate the inflammatory process. The pathogenic role of the adducts formed by the products of LPO with biological macromolecules in the breaking of immunological tolerance to self antigens and in the development of autoimmunity has been supported by a wealth of evidence. The instrumental role of the adducts of reactive LPO products with self protein antigens in the sensitization of autoreactive cells to the respective unmodified proteins and in the intermolecular spreading of the autoimmune responses to aldehyde-modified and native DNA is well documented. In contrast, further investigation is required in order to establish whether the formation of adducts of LPO products with DNA might incite substantial immune responsivity and might be instrumental for the spreading of the immunological responses from aldehyde-modified DNA to native DNA and similarly modified, unmodified and/or structurally analogous self protein antigens, thus leading to autoimmunity