Deene the MOD m-degree of a boolean function F to be the smallest degree of any polynomial P, over the ring of integers modulo m, such that for all 0-1 assignments ~ x, F(~ x) = 0 ii P(~ x) = 0. By exploring the periodic property of the binomial coeecients modulo m, two new lower bounds on the MOD m-degree of the MOD l and :MOD m functions are proved, where m is any composite integer and l has ...

British troops surrendering at Yorktown, Virginia in October of 1781 reportedly marched to the 17th century English song “The World Turned Upside Down.”2 Government embodied in the United States and built on the tradition of English Common Law changed the world over subsequent generations. The deceptively simple Enlightenment notion of the “consent of the governed” required majority rule, but t...

Following the seminal work of M. Culler and P. Shalen [Culler & Shalen, 1983], and that of A. Casson [Akbulut & McCarthy, 1990], the theory of representation and character varieties of 3-manifolds has come to be recognized as a powerful tool, and has duly assumed an important place in low-dimensional topology. Among the many papers that have appeared in this context, we mention [Culler et al., ...

A median (antimedian) of a profile of vertices on a graph G is a vertex that minimizes (maximizes) the remoteness value, that is, the sum of the distances to the elements in the profile. The median (or antimedian) function has as output the set of medians (antimedians) of a profile. It is one of the basic models for the location of a desirable (or obnoxious) facility in a network. The median fu...

As noted by Anscombe (1976), the disposition of a set of proposals by majority rule does not preclude the existence of a majority of voters, each of whom disagrees with the outcomes in a majority of cases. It is intuitively clear, however, that when proposals are adopted or rejected, on average, by a sufficiently strong consensus, such a state of affairs cannot materialize. Indeed, we show for ...

We develop a novel coevolutionary algorithm based upon the concept of Pareto optimality. The Pareto criterion is core to conventional multi-objective optimization (MOO) algorithms. We can think of agents in a coevolutionary system as performing MOO, as well: An agent interacts with many other agents, each of which can be regarded as an objective for optimization. We adapt the Pareto concept to ...

Although much evidence indicates that RT increases as a function of computational load in many cognitive tasks, quantification of changes in neural activity related to increasing demand of cognitive control has rarely been attempted. In this fMRI study, we used a majority function task to quantify the effect of computational load on brain activation, reflecting the mental processes instantiated...

The IETF has had a long tradition of doing its technical work through a consensus process, taking into account the different views among IETF participants and coming to (at least rough) consensus on technical matters. In particular, the IETF is supposed not to be run by a "majority rule" philosophy. This is why we engage in rituals like "humming" instead of voting. However, more and more of our...

Some binary linear codes of length 50 and 100 are constructed using the adjacency matrices of the Hooman-Singleton graph and the Higman-Sims graph. Some of the codes are optimal or nearly optimal for the given length and dimension. The dual codes admit majority logic decoding.

We introduce a general setting for information elicitation in multi-agent systems, where agents may be approached both sequentially and simultaneously in order to compute a function that depends on their private secrets. We consider oblivious mechanisms for sequential-simultaneous information elicitation. In such mechanisms the ordering of agents to be approached is fixed in advance. Surprising...