We consider a setting in which a single divisible good (“cake”) needs to be divided between n players, each with a possibly different valuation function over pieces of the cake. For this setting, we address the problem of finding divisions that maximize the utilitarian social welfare, focusing on divisions where each player needs to get one contiguous piece of the cake. We provide a constant fa...

Stem cells and neuroblasts derived from mouse embryos undergo repeated asymmetric cell divisions, generating neural lineage trees similar to those of invertebrates. In Drosophila, unequal distribution of Numb protein during mitosis produces asymmetric cell divisions and consequently diverse neural cell fates. We investigated whether a mouse homologue m-numb had a similar role during mouse corti...

The problem studied in this paper arises from a simple practical problem: how to divide a cake among the children attending a birthday p a r t y i n s u c h a way that each c hild gets the same amount o f c a k e and (perhaps more important to them) the same amount of icing. Let S be a convex set contained in the (xx y)-plane. In mathematical terms, a c a k e C with base S is a solid containing...

Immediately following fertilisation in Drosophila and many other arthropods, the embryo undergoes a series of rapid syncytial nuclear divisions. These divisions are driven by maternally supplied components and occur in the absence of zygotic transcription. Unlike typical cell divisions, these divisions alternate between S and M phases, resulting in cell cycles that last only from 10 to 25 min. ...

Divisions of labor are ubiquitous in nature and can be found at nearly every level of biological organization, from the individuals of a shared society to the cells of a single multicellular organism. Many different types of microbes have also evolved a division of labor among its colony members. Here we review several examples of microbial divisions of labor, including cases from both multicel...

Let us consider a financially constrained leveraged financial firm having some divisions which have invested into some risky assets. Using coherent measures of risk the sum of the capital requirements of the divisions is larger than the capital requirement of the firm itself, there is some diversification benefit that should be allocated somehow for proper performance evaluation of the division...

Operation Management is an important and complex task for a divisional structured organization, especially when the divisions are distributed geographically. In most cases, such organizations didn’t not urge all of it’s divisions to use an integrated information system at the very beginning. But with the development and the expanding of the organization, they sometimes found themselves in the t...

Neocortical precursor cells undergo symmetric and asymmetric divisions while producing large numbers of diverse cortical cell types. In Drosophila, cleavage plane orientation dictates the inheritance of fate-determinants and the symmetry of newborn daughter cells during neuroblast cell divisions. One model for predicting daughter cell fate in the mammalian neocortex is also based on cleavage pl...

Division of a resource among multiple agents is a frequent problem in multiagent systems and fair, efficient, and decentralized allocation procedures are highly valued. A division of a resource or good is envy-free when every agent believes that its share is not less than anyone else’s share by its own estimate. As envy-free procedures are not efficient (in the sense of Pareto optimality) we ha...