The classic fair cake-cutting problem [Steinhaus, 1948] is extended by introducing geometric constraints on the allocated pieces. Specifically, agents may demand to get their share as a square or a rectangle with a bounded length/width ratio. This is a plausible constraint in realistic cake-cutting applications, notably in urban and agricultural economics where the “cake” is land. Geometric con...

This paper proposes a cake-cutting protocol using cryptography when the cake is a heterogeneous good that is represented by an interval on a real line. Although the Dubins-Spanier moving-knife protocol with one knife achieves simple fairness and truthfulness, all players must execute the protocol synchronously. Thus, the protocol cannot be executed on asynchronous networks such as the Internet....

Kurt Mehlhorn’s foundational results in computational geometry provide not only a basis for practical geometry systems such as Leda and CGAL, they also, in the spirit of Euclid, provide a sound basis for geometric truth. This article shows how Mehlhorn’s ideas from computational geometry have influenced work on the logical basis for constructive geometry. In particular there is a sketch of new ...

There is a vast riches of limit theorems for sums of independent random variables: theorems about weak convergence, on large deviations, theorems with asymptotic expansions, etc. We can try to obtain the same kinds of theorems for families of stochastic processes. If X1, X2, ..., Xn, ... is a sequence of independent identically distributed random variables with expectation EXi = 0 and variance ...

This paper describes a new XML compression scheme that offers both high compression ratios and short query response time. Its core is a fully reversible transform featuring substitution of every word in an XML document using a semi-dynamic dictionary, effective encoding of dictionary indices, as well as numbers, dates and times found in the document, and grouping data within the same structural...

An ad-hoc mobile network is a collection of mobile hosts, with wireless communication capability, forming a temporary network without the aid of any established xed infrastructure. In such a (dynamically changing) network it is not at all easy to avoid broadcasting (and ooding). In this paper we propose, theoretically analyse and experimentally validate a new and eecient protocol for pairwise c...

The efficient coding hypothesis holds that neural receptive fields are adapted to the statistics of the environment, but is agnostic to the timescale of this adaptation, which occurs on both evolutionary and developmental timescales. In this work we focus on that component of adaptation which occurs during an organism’s lifetime, and show that a number of unsupervised feature learning algorithm...

the portfolio is a perfect combination of stock or assets, which an investor buys them. the objective of the portfolio is to divide the investment risk among several shares. using non-parametric dea and dea-r methods can be of great significance in estimating portfolio. in the present paper, the efficient portfolio is estimated by using non-radial dea and dea-r models. by proposing non-radial m...

An efficient and environmental-friendly synthetic route to 1,8-dioxodecahydroacridines derivatives have been developed via multi-component one-pot Hantzsch reaction of various aldehydes and ammonium acetate with 2 equivalents dimedone in the presence of Phosphorus pentoxide supported on aluminaas catalyst under solvent-free conditions. The present approach offersseveral advantages such as s...