What happens if the Xi ’s take values in a (real) Banach space (B, ‖ · ‖)? In such cases, in particular when the square of the norm ‖ · ‖ is not given by an inner product, we are aiming at inequalities of the following type: Let X1, X2, . . . , Xn be independent random vectors with values in (B, ‖ · ‖) with EXi = 0 and E‖Xi‖2 < ∞. With Sn := ∑n i=1 Xi we want to show that E‖Sn‖ ≤ K n ∑ i=1 E‖Xi...

In important papers on cake-cutting – one of the key areas in fair division and resource allocation – the measuretheoretical fundamentals are not fully correctly given. It is not clear (i) which family of sets should be taken for the pieces of cake, (ii) which set-functions should be used for evaluating the pieces, and (iii) which is the relationship between various continuity properties appear...

Abst rac t . We give an overview of the LEDA platform for combinatorial and geometric computing and an account of its development. We discuss our motivation for building LEDA and to what extent we have reached our goals. We also discuss some recent theoretical developments. This paper contains no new technical material. It is intended as a guide to existing publications about the system. We ref...

This paper presents a novel method to compensate the eeects of exi-bility in belt-driven drive trains. Such drives are found in robot manipulators, for example, where drive exibility is undesirable. Unfortunately, the eeects of exibility can be diicult to compensate using the primary actuator, due to bandwidth limitations. By introducing a second actuator, which applies a force to the belt at a...

Statistical approaches to study the properties of neurons in sensory system ascribe the selectivity of neurons in visual and auditory cortices to regularities of signals in natural environment. “Efficient coding” hypothesis is an outstanding theory that explains the work of sensory system in discarding unnecessary data and supplying higher order brain areas with the most informative features in...

Cloutier, Nyman, and Su (Mathematical Social Sciences 59 (2005), 26–37) initiated the study of envy-free cake-cutting problems involving several cakes. The classical result in this area is that when there are q players and one cake, an envy-free cake-division requiring only q − 1 cuts exists under weak and natural assumptions. Among other results, Cloutier, Nyman, and Su showed that when there ...

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