A spin wave majority fork-like structure with feature size of 40 nm, is presented and investigated, through micromagnetic simulations. The structure consists of three merging out-of-plane magnetization spin wave buses and four magneto-electric cells serving as three inputs and an output. The information of the logic signals is encoded in the phase of the transmitted spin waves and subsequently ...

We show that Nechiporuk’s method [14] for proving lower bound for Boolean formulas can be extended to the quantum case. This leads to an Ω(n2/ log n) lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas [15] states that the majority function does not have a linear–size quantum formula.

This paper studies coalition formation, payoff division and expected payoffs in a ”divide the dollar by majority rule” game with random proposers. A power index is called self-confirming if it can be obtained as an equilibrium of the game using the index itself as probability vector. Unlike the Shapley value and other commonly used power indices, the nucleolus has this property. The proof uses ...

We develop a general concept of majority rule for finitely many choice alternatives that is consistent with arbitrary binary preference relations, real-valued utility functions, probability distributions over binary preference relations, and random utility representations. The underlying framework is applicable to virtually any type of choice, rating, or ranking data, not just the linear orders...

In this paper we examine the problem of computing majority functionMAJn on n bits by depthtwo formula, where each gate is a majority function on at most k inputs. We present such formula that gives the first nontrivial upper bound for this problem, with k = 2 3n + 4. This answers an open question in [7]. We also look at this problem in adaptive setting — when we are allowed to query for value o...

Although it may seem easy to compare states in terms of the number of their citizens and the size and shape of their countries, the connection between the democratic state and the numerical and spatial considerations is more subtle and complex, for theoretical views of society and the state tend to diverge into opposing positions that explore themutually exclusive extremes ofatomism and holism....

A new hardware structure for implementation of soft morphological filters is presented in this paper. This is based on the modification of the majority gate technique. A pipelined systolic array architecture suitable to perform real-time soft morphological filtering is presented as an illustrative example. The processing times of the proposed hardware structure do not depend on the data window ...

In digital topology, the use of a pair of connectivities is required to avoid topological paradoxes. In mathematical morphology, selfdual operators and methods also rely on such a pair of connectivities. There are several major issues: self-duality is impure, the image graph structure depends on the image values, it impacts the way small objects and texture are processed, and so on. A sub-class...

X iv :1 61 2. 07 70 8v 1 [ cs .E T ] 1 5 D ec 2 01 6 Experimental prototype of a spin-wave majority gate T. Fischer, 2, a) M. Kewenig, D. A. Bozhko, 2 A. A. Serga, I. I. Syvorotka, F. Ciubotaru, 5 C. Adelmann, B. Hillebrands, and A. V. Chumak Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany Graduate School Materials Sci...

An antimedian of a profile π = (x1, x2, . . . , xk) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the profile. The antimedian function is defined on the set of all profiles on G and has as output the set of antimedians of a profile. It is a typical location function for finding a location for an obnoxious facility. The ‘converse’ of the antimedian f...