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[en] Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized probabilistic theories (GPTs). The current study explores two types of entropic uncertainty relations, preparation and measurement uncertainty relations, in a class of GPTs which can be considered generalizations of quantum theory. Not only a method for obtaining entropic preparation uncertainty relations but also an entropic measurement uncertainty relation similar to the quantum one by Buscemi et al (2014 Phys. Rev. Lett. 112 050401) are proved in those theories. These results manifest that the entropic structure in the uncertainty relations is not restricted to quantum theory and therefore is universal one. Concrete calculations of our relations in GPTs called the regular polygon theories are also demonstrated. (paper)

[en] We consider the scheme to recover nonlocal advantage of quantum coherence (NAQC) for two-qutrit system which suffer from the amplitude damping noises by using weak measurement reversal. The scope of the decay rate of the noise to achieve NAQC can be obviously extended after the application of weak measurement reversal, i.e. NAQC can be recovered in the region that there is no NAQC. The physical reason for the recovery may be attributed to the probabilistic nature of the scheme as well as the shrinking of the range for the state parameter to achieve NAQC. (paper)

[en] Highlights: • System with mission abort and rescue possibilities are considered. • Multiple attempts can be performed if the system survives previous attempts. • Parts of mission task completed in the earlier attempts are saved. • A tradeoff between the mission success and the system loss probabilities is studied. • An algorithm for obtaining the optimal mission aborting rules is suggested. Mission aborts can be executed in many real-world systems when the specified malfunction/deterioration conditions are met and, therefore, a risk of a system's loss in the case of mission continuation becomes too high. After mission aborting, a rescue or recovery procedure is usually initiated. Previous results reported in the literature dealt with the setting when only one attempt to complete a mission is allowed. However, missions with a possibility of multiple attempts can occur in different real-world settings when accomplishing a mission is really important and the cost-related and the time-wise restrictions for this are not very severe. In this paper, we consider the case when a part of the mission task that was accomplished in the earlier attempts can be saved (additively) and not discarded. The probabilistic model for this case is developed and the tradeoff between the overall mission success probability and the system loss probability is studied. The problem of achieving the maximal mission success probability for the given level of system survivability is solved. A detailed example illustrating application of the suggested model is presented. It is shown that, unlike the single attempt case, aborting the mission when multiple attempts are allowed, can be beneficial even when the mission completion is the only concern and no constraint is imposed on the system survival probability.

[en] It is well known that prepivoting reduces level error of confidence sets. We adapt this method to the context of the tail index estimation, introducing a procedure that we call tail prepivoting. We apply this procedure to the Hill estimator and establish its consistency. (paper)

[en] Definition of the clinical target volume (CTV) is one of the weakest links in the radiation therapy chain. In particular, inability to account for uncertainties is a severe limitation in the traditional CTV delineation approach. Here, we introduce and test a new concept for tumor target definition, the clinical target distribution (CTD). The CTD is a continuous distribution of the probability of voxels to be tumorous. We describe an approach to incorporate the CTD in treatment plan optimization algorithms, and implement it in a commercial treatment planning system. We test the approach in two synthetic and two clinical cases, a sarcoma and a glioblastoma case. The CTD is straightforward to implement in treatment planning and comes with several advantages. It allows one to find the most suitable tradeoff between target coverage and sparing of surrounding healthy organs at the treatment planning stage, without having to modify or redraw a CTV. Owing to the variable probabilities afforded by the CTD, a more flexible and more clinically meaningful sparing of critical structure becomes possible. Finally, the CTD is expected to reduce the inter-user variability of defining the traditional CTV. (paper)

[en] We define a variant of team semantics called multiteam semantics based on multisets and study the properties of various logics in this framework. In particular, we define natural probabilistic versions of inclusion and independence atoms and certain approximation operators motivated by approximate dependence atoms of Väänänen.

[en] We give accurate estimates for the bond percolation critical probabilities on seven Archimedean lattices, for which the critical probabilities are unknown, using an algorithm of Newman and Ziff

[en] Short communication

[en] We provide a novel method to estimate in a closed-form solution the option prices of various exotic options, using techniques based on Laplace–Beltrami operator for estimating diffusion boundary times. We estimate exit times and their expectations, the hitting probabilities, boundary local times until the first hitting and other probabilistic quantities and moment generating functions related to local hitting times. Our findings maybe of paramount importance for traders, investors, speculators and more broadly speaking for financial institutions.