Forbidden triads and Creative Success in Jazz: The Miles Davis Factor

This article argues for the importance of forbidden triads - open triads with high-weight edges - in predicting success in creative fields. Forbidden triads had been treated as a residual category beyond closed and open triads, yet I argue that these structures provide opportunities to combine socially evolved styles in new ways. Using data on the entire history of recorded jazz from 1896 to 2010, I show that observed collaborations have tolerated the openness of high weight triads more than expected, observed jazz sessions had more forbidden triads than expected, and the density of forbidden triads contributed to the success of recording sessions, measured by the number of record releases of session material. The article also shows that the sessions of Miles Davis had received an especially high boost from forbidden triads

A Characterization of Bispecial Sturmian Words

A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of segments in the Euclidean plane. This result is an extension of the known relation between central words and primitive Christoffel words. Our characterization allows us to give an enumerative formula for bispecial Sturmian words. We also investigate the minimal forbidden words for the set of Sturmian words.Comment: Accepted to MFCS 201

Bounds to the normal for proximity region graphs

In a proximity region graph ${\cal G}$ in $\mathbb{R}^d$, two distinct points $x,y$ of a point process $\mu$ are connected when the 'forbidden region' $S(x,y)$ these points determine has empty intersection with $\mu$. The Gabriel graph, where $S(x,y)$ is the open disc with diameter the line segment connecting $x$ and $y$, is one canonical example. When $\mu$ is a Poisson or binomial process, under broad conditions on the regions $S(x,y)$, bounds on the Kolmogorov and Wasserstein distances to the normal are produced for functionals of ${\cal G}$, including the total number of edges and the total length. Variance lower bounds, not requiring strong stabilization, are also proven to hold for a class of such functionals.Comment: 33 pages; changes in response to referees' comment

Invariants of Welded Virtual Knots Via Crossed Module Invariants of Knotted Surfaces

We define an invariant of welded virtual knots from each finite crossed module by considering crossed module invariants of ribbon knotted surfaces which are naturally associated with them. We elucidate that the invariants obtained are non trivial by calculating explicit examples. We define welded virtual graphs and consider invariants of them defined in a similar way.Comment: New results. A perfected version will appear in Compositio Mathematic

Nuclear structure and double beta decay

Study of the neutrinoless double beta decay, $0\nu\beta\beta$, includes a variety of problems of nuclear structure theory. They are reviewed here. The problems range from the mechanism of the decay, i.e. exchange of the light Majorana neutrino neutrino versus the exchange of some heavy, so far unobserved particle. Next, the proper expressions for the corresponding operator are described that should include the effects of the nucleon size and of the recoil order terms in the hadronic current. The issue of proper treatment of the short range correlations, in particular for the case of the heavy particle exchange, is discussed also. The variety of methods employed these days in the theoretical evaluation of the nuclear matrix elements $M^{0\nu}$ is briefly described and the difficulties causing the spread and hence uncertainty in the values of $M^{0\nu}$ are discussed. Finally, the issue of the axial current quenching, and of the resonance enhancement in the case of double electron capture are described.Comment: Review paper accepted for publication in the special issue of J. Phys. G: Nucl. Phys. devoted to the double beta deca