Continuous logic extends the multi-valued Lukasiewicz logic by adding a halving operator on propositions. This extension is designed to give a more satisfactory model theory for continuous structures. The semantics of these logics can be given using specialisations of algebraic structures known as hoops and coops. As part of an investigation into the metatheory of propositional continuous logic...

In this paper we show how theorems of Borsuk-Ulam and Tucker can be used to construct a consensus-halving: a division of an object into two portions so that each of n people believes the portions are equal. Moreover, the division takes at most n cuts, which is best possible. This extends prior work using methods from combinatorial topology to solve fair division problems. Several applications o...

Ghana is a middle-income West African country which experienced impressive economic growth from 2005 to 2012. This growth has slowed significantly since 2013 in light of macro-economic challenges, such as high budget deficit and inflation, but is still expected to remain positive, due to the country’s stable democratic institutions and rich natural resources.1 Per capita GDP reached US$ 1 858 i...

With 2015 only eight years away, it is becoming clear that many countries in the developing world will not be able to meet the first Millennium Development Goal (MDG1) of halving absolute poverty. In fact, many countries in Sub-Saharan Africa and several in Asia and Latin America are seriously off track for meeting that goal. In a large number of cases, this is related to poor growth performanc...

A set of input vectors S is conclusive for a certain functionality if, for every comparator network, correct functionality for all input vectors is implied by correct functionality for all vectors in S. We consider four functionalities of comparator networks: sorting, merging, sorting of bitonic vectors, and halving. For each of these functionalities, we present two conclusive sets of minimal c...

Diquarks are found to have the right degrees of freedom to describe the tetraquark poles in hiddencharm to open-charm meson-meson amplitudes. Compact tetraquarks result as intermediate states in non-planar diagrams of the 1/N expansion and the corresponding resonances are narrower than what estimated before. The proximity of tetraquarks to meson-thresholds has an apparent role in this analysis ...

A recently derived basic theorem on the decomposition of SO(2N) vertices is used to obtain a complete analytic determination of all SO(10) invariant cubic superpotential couplings involving 16± semispinors of SO(10) chirality ± and tensor representations. In addition to the superpotential couplings computed previously using the basic theorem involving the 10, 120 and 126 tensor representations ...

Efficient halving of divisor classes offers the possibility to improve scalar multiplication on hyperelliptic curves and is also a step towards giving hyperelliptic curve cryptosystems all the features that elliptic curve systems have. We present a halving algorithm for divisor classes of genus 2 curves over finite fields of characteristic 2. We derive explicit halving formulae from a doubling ...