The purpose of these notes is to discuss the relation between the additivity questions regarding the quantities (Holevo) capacity of a quantum channel T and entanglement of formation of a bipartite state ρ. In particular, using the Stinespring dilation theorem, we give a formula for the channel capacity involving entanglement of formation. This can be used to show that additivity of the latter ...

It is commonly assumed that people make intertemporal choices by "discounting" the value of delayed outcomes, assigning discounted values independently to all options, and comparing the discounted values. We identify a class of anomalies to this assumption of alternative-based discounting, which collectively shows that options are not treated independently but rather comparatively: The time dif...

We prove a lemma which allows one to extend results about the additivity of the minimal output entropy from highly symmetric channels to a much larger class. A similar result holds for the maximal output p-norm. Examples are given showing its use in a variety of situations. In particular, we prove the additivity and the multiplicativity for the shifted depolarising channel. A natural and import...

We investigate a series of logics that allow to reason about agents’ actions, abilities, and their knowledge about actions and abilities. These logics include Pauly’s Coalition Logic CL, Alternating-time Temporal Logic ATL, the logic of ‘seeing-to-it-that’ (STIT), and epistemic extensions thereof. While complete axiomatizations of CL and ATL exist, only the fragment of the STIT language without...

Previously, the EEG technique has been used to investigate the spatiotemporal properties of audiovisual (AV) processing by taking advantage of the violation of the "additive model", which is considered to be a very conservative approach. In the present work, we used a less conservative and novel approach than the criterion of superadditivity for estimating AV interactions. Hence, we estimated A...

Abstract A central property of a classical geometry is that the geodesic distance between two events additive. When considering quantum fluctuations in metric or statistical superposition different spacetimes, additivity generically lost at level expectation values. In presence metrics, distances can be made diffeomorphism invariant by frame family free-falling observers pressureless fluid, pro...

The article deals with the actual problem of professional training prospective primary school teachers to work intellectually gifted pupils. It has been shown that giftedness is determined by both innate gifts and social conditions and, course, needs support help on a part trained teacher. level readiness pupils in modern investigated. For this purpose, scientific study was conducted 2021-2022 ...

The superadditivity and monotonicity properties of some functionals associated with convex functions and the Hermite-Hadamard inequality in the general setting of linear spaces are investigated. Applications for norms and convex functions of a real variable are given. Some inequalities for arithmetic, geometric, harmonic, logarithmic and identric means are improved. 1. Introduction For any conv...

A Generalized Additive Game (GAG) (Cesari et al. in Int J Theory 46(4):919–939, 2017) is a Transferable Utility (TU) game (N, v), where each player N provided with an individual value, and the worth v(S) of coalition $$S \subseteq N$$ obtained as sum values players another subset $$\mathcal {M}(S)\subseteq . Based on conditions map {M}$$ (which associates to S set beneficial {M}(S)$$ not necess...

This note is part of implementation of a program in foundations of mathematics to find exact versions of all unprovability theorems known so far, a program initiated by A. Weiermann. In this note we find the exact version of unprovability of the graph minor theorem restricted to planar graphs and some lower and upper bounds in the general case of all graphs. 1 Unlabelled growth constants Let us...