Currently more and more agents are involved in human routine activities and a mixed human-agent society is thus formed by the humans and the agents involved. The relationship between humans and agents in this mixed society is subtle and it is vital to explore the influence that agents bring into the society. In this paper, we try to investigate a few questions: will humans act differently towar...

Let X1,X2, . . . , be independent random variables with EXi = 0 and write Sn = ∑ n i=1 Xi and V 2 n = ∑ n i=1 X i . This paper provides an overview of current developments on the functional central limit theorems (invariance principles), absolute and relative errors in the central limit theorems, moderate and large deviation theorems and saddle-point approximations for the self-normalized sum S...

A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envyfree, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are satisfied, however many cuts are made. It turns out that two of the three properties can be satisfied by ...

Fair Division, unlike most research on fairness in the social sciences and mathematics, is devoted solely to the analysis of constructive procedures for actually dividing things up and resolving disputes, including...

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...