We consider a range of “theories” that violate the uncertainty relation for anti-commuting observables derived in [JMP, 49, 062105 (2008)]. We first show that Tsirelson’s bound for the CHSH inequality can be derived from this uncertainty relation, and that relaxing this relation allows for non-local correlations that are stronger than what can be obtained in quantum mechanics. We continue to co...

We present a two-parameter family (Gm,k)m,k∈N≥2 , of finite, non-abelian random groups and propose that, for each fixed k, as m → ∞ the commuting graph of Gm,k is almost surely connected and of diameter k. We present heuristic arguments in favour of this conjecture, following the lines of classical arguments for the Erdős– Rényi random graph. As well as being of independent interest, our groups...

Most people have certain acceptance of daily travel distance, which determines where they choose to live, to work, and to go for leisure. Such information is an important input for facility location-allocation, urban planning and transport management. Therefore, daily commuting distance has been adopted as an indicator to measure the distance acceptance, the rationality of land use structure, a...

ABSTRACT. The subject of this paper are polynomials in multiple non-commuting variables. For polynomials of this type orthogonal with respect to a state, we prove a Favardtype recursion relation. On the other hand, free Sheffer polynomials are a polynomial family in non-commuting variables with a resolvent-type generating function. Among such families, we describe the ones that are orthogonal. ...

Suppose n is a fixed positive integer. We introduce the relative n-th non-commuting graph ΓH,G, associated to the nonabelian subgroup H of group G. The vertex set is G \ C H,G in which C H,G = {x ∈ G : [x, y] = 1 and [x, y] = 1 for all y ∈ H}. Moreover, {x, y} is an edge if x or y belong to H and xy 6= yx or xy 6= yx. In fact, the relative n-th commutativity degree, Pn(H,G) the probability that...

We investigate under which conditions a mixed state on a finite-dimensional multipartite quantum system may be the unique, globally stable fixed point of frustration-free semigroup dynamics subject to specified quasi-locality constraints. Our central result is a linear-algebraic necessary and sufficient condition for a generic (full-rank) target state to be frustration-free quasi-locally stabil...

Established analyses of labour market commuting are based on random choice models and gravity type models. In these models generalised transport costs are formulated as exponential or log-linear distance dependent functions. This paper presents empirical observations, which imply that time distances influence the commuting behaviour in a non-linear way, such that the time sensitivity is much lo...

Abstract. We prove a weak-type (1,1) inequality involving conditioned square functions of martingales in non-commutative L-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the best constants in the non-commutative Burkholder/Rosenthal inequalities from Ann. Probab. 31 (2003), 948-995. We also discuss BMO-norms of sums of non commuting order...

A master equation (n dimensional non–Abelian current conservation law with mutually commuting current components) is introduced for multi-dimensional non-linear field theories. It is shown that the master equation provides a systematic way to understand 2-d integrable non-linear equations as well as 4-d self-dual equations and, more importantly, their generalizations to higher dimensions.