Approximability of Connected Factors

Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte's reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the d-factor is connected, these problems become NP-hard - finding a minimal connected 2-factor is just the traveling salesman problem (TSP). Given a complete graph with edge weights that satisfy the triangle inequality, we consider the problem of finding a minimal connected $d$-factor. We give a 3-approximation for all $d$ and improve this to an (r+1)-approximation for even d, where r is the approximation ratio of the TSP. This yields a 2.5-approximation for even d. The same algorithm yields an (r+1)-approximation for the directed version of the problem, where r is the approximation ratio of the asymmetric TSP. We also show that none of these minimization problems can be approximated better than the corresponding TSP. Finally, for the decision problem of deciding whether a given graph contains a connected d-factor, we extend known hardness results.Comment: To appear in the proceedings of WAOA 201

Bound States and Power Counting in Effective Field Theories

The problem of bound states in effective field theories is studied. A rescaled version of nonrelativistic effective field theory is formulated which makes the velocity power counting of operators manifest. Results obtained using the rescaled theory are compared with known results from NRQCD. The same ideas are then applied to study Yukawa bound states in 1+1 and 3+1 dimensions, and to analyze when the Yukawa potential can be replaced by a delta-function potential. The implications of these results for the study of nucleon-nucleon scattering in chiral perturbation theory is discussed.Comment: 23 pages, eps figures, uses revte

A 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem

We give a 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem.Comment: 6 figure

Supersymmetric Model of Muon Anomalous Magnetic Moment and Neutrino Masses

We propose the novel lepton-number relationship $L_\tau = L_e + L_\mu$, which is uniquely realized by the interaction $(\hat \nu_e \hat \mu - \hat e \hat \nu_\mu) \hat \tau^c$ in supersymmetry and may account for a possibly large muon anomalous magnetic moment. Neutrino masses (with bimaximal mixing) may be generated from the spontaneous and soft breaking of this lepton symmetry.Comment: 10 pages, including 2 figure

Challenges of open innovation: the paradox of firm investment in open-source software

Open innovation is a powerful framework encompassing the generation, capture, and employment of intellectual property at the firm level. We identify three fundamental challenges for firms in applying the concept of open innovation: finding creative ways to exploit internal innovation, incorporating external innovation into internal development, and motivating outsiders to supply an ongoing stream of external innovations. This latter challenge involves a paradox, why would firms spend money on R&D efforts if the results of these efforts are available to rival firms? To explore these challenges, we examine the activity of firms in opensource software to support their innovation strategies. Firms involved in open-source software often make investments that will be shared with real and potential rivals. We identify four strategies firms employ – pooled R&D/product development, spinouts, selling complements and attracting donated complements – and discuss how they address the three key challenges of open innovation. We conclude with suggestions for how similar strategies may apply in other industries and offer some possible avenues for future research on open innovation

Diffraction Symmetry in Crystalline, Close-Packed C60

We have grown crystals of the carbon structure C60 by sublimation. In contrast to solution-grown crystals, the sublimed crystals have long range order with no evidence of solvent inclusions. Sublimed C60 forms three dimensional, faceted crystals with a close-packed, face-centered cubic unit cell. We have refined a crystal structure using the "soccer ball" model of the C60 molecule. The results indicate that the C60 molecule has the expected spherical shape, however the data are not sufficiently accurate to unambiguously determine atomic positions

Social determinants of content selection in the age of (mis)information

Despite the enthusiastic rhetoric about the so called \emph{collective intelligence}, conspiracy theories -- e.g. global warming induced by chemtrails or the link between vaccines and autism -- find on the Web a natural medium for their dissemination. Users preferentially consume information according to their system of beliefs and the strife within users of opposite narratives may result in heated debates. In this work we provide a genuine example of information consumption from a sample of 1.2 million of Facebook Italian users. We show by means of a thorough quantitative analysis that information supporting different worldviews -- i.e. scientific and conspiracist news -- are consumed in a comparable way by their respective users. Moreover, we measure the effect of the exposure to 4709 evidently false information (satirical version of conspiracy theses) and to 4502 debunking memes (information aiming at contrasting unsubstantiated rumors) of the most polarized users of conspiracy claims. We find that either contrasting or teasing consumers of conspiracy narratives increases their probability to interact again with unsubstantiated rumors.Comment: misinformation, collective narratives, crowd dynamics, information spreadin