How best to market a crowdsourced product?

In the old days, companies developed products for their customers. The idea that the customer would have any role in the process beyond expressing a particular colour or flavour preference seemed unthinkable. Henry Ford supposedly said that if he had asked people what they wanted, they would have said, a faster horse. Today, more and more companies have concluded that Ford was too pessimistic and that customers actually have a lot of imagination

From Dynkin diagram symmetries to fixed point structures

Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody algebra induces an automorphism of the algebra and a mapping between its highest weight modules. For a large class of such Dynkin diagram automorphisms, we can describe various aspects of these maps in terms of another Kac-Moody algebra, the `orbit Lie algebra'. In particular, the generating function for the trace of the map on modules, the `twining character', is equal to a character of the orbit Lie algebra. Orbit Lie algebras and twining characters constitute a crucial step towards solving the fixed point resolution problem in conformal field theory.Comment: Latex, 60 pages (extended version 63 pages), 4 uuencoded figures Formula (6.25) corrected. While this correction might be important in applications of our work, the results of the paper are not affected by it. In the present submission the "extended version" is default. In this version the corrected formula is (6.32

From non-semisimple Hopf algebras to correlation functions for logarithmic CFT

We use factorizable finite tensor categories, and specifically the representation categories of factorizable ribbon Hopf algebras H, as a laboratory for exploring bulk correlation functions in local logarithmic conformal field theories. For any ribbon Hopf algebra automorphism omega of H we present a candidate for the space of bulk fields and endow it with a natural structure of a commutative symmetric Frobenius algebra. We derive an expression for the corresponding bulk partition functions as bilinear combinations of irreducible characters; as a crucial ingredient this involves the Cartan matrix of the category. We also show how for any candidate bulk state space of the type we consider, correlation functions of bulk fields for closed oriented world sheets of any genus can be constructed that are invariant under the natural action of the relevant mapping class group.Comment: 41 pages, several figures. version 2: typos corrected, bibliography updated, introduction extended, a few minor clarifications adde

Customer empowerment in new product development

Companies have traditionally taken responsibility for deciding what products and product innovations are offered to customers. However, a growing number of companies are turning this relationship on its head by asking customers not only for help in creating new products, but also in deciding which ones should be produced

Topological defects for the free boson CFT

Two different conformal field theories can be joined together along a defect line. We study such defects for the case where the conformal field theories on either side are single free bosons compactified on a circle. We concentrate on topological defects for which the left- and right-moving Virasoro algebras are separately preserved, but not necessarily any additional symmetries. For the case where both radii are rational multiples of the self-dual radius we classify these topological defects. We also show that the isomorphism between two T-dual free boson conformal field theories can be described by the action of a topological defect, and hence that T-duality can be understood as a special type of order-disorder duality.Comment: 43 pages, 4 figure

Guidelines for choosing between multi-item and single-item scales for construct measurement: A predictive validity perspective

Establishing predictive validity of measures is a major concern in marketing research. This paper investigates the conditions favoring the use of single items versus multi-item scales in ter

The fusion algebra of bimodule categories

We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This provides a purely categorical proof of a conjecture by Ostrik concerning the structure of F. As a by-product we obtain a concrete expression for the structure constants of the Grothendieck ring of the bimodule category in terms of endomorphisms of the tensor unit of the underlying modular tensor category.Comment: 16 page

Test of the semischematic model for a liquid of linear molecules

We apply to a liquid of linear molecules the semischematic mode-coupling model, previously introduced to describe the center of mass (COM) slow dynamics of a network-forming molecular liquid. We compare the theoretical predictions and numerical results from a molecular dynamics simulation, both for the time and the wave-vector dependence of the COM density-density correlation function. We discuss the relationship between the presented analysis and the results from an approximate solution of the equations from molecular mode-coupling theory [R. Schilling and T. Scheidsteger, Phys. Rev. E 56 2932 (1997)].Comment: Revtex, 10 pages, 4 figure

Refractory and relapsed paediatric ACC in the MET studies – a challenging situation necessitating novel diagnostic and therapeutic concepts

Background Paediatric adrenocortical carcinomas (ACC) are highly aggressive malignancies with a dismal prognosis in advanced and metastatic disease. Little is known about outcome of patients with refractory and relapsed (r/r) disease. Procedure National retrospective multicentre study including r/r ACC diagnosed in patients aged <18 years registered in the MET studies between January 1997 and December 2021 Results A total of 16 patients (5 male; median age 12.9 years) with refractory disease were included. Median time to progression was 0.6 years [0.0-1.3]. Site of progression was locoregional (n=1), distant (n=3), and combined (n=12). 3-year overall (OS) and progression-free (PFS) survival were both 0%. Thirty patients with relapse (11 male; median age 7.3 years) were identified. Median time to relapse was 0.7 years [0.1-3.2]. Site of relapse was locoregional (n=8), distant (n=15), and combined (n=7). At last follow-up, 20 patients had died of disease or complications or were alive with disease, 10 patients were in second complete remission (median follow-up: 6.8 years [0-10.5]). 3-year OS and PFS following relapse were 39.1% and 31.9%. Survival was superior in patients with distant relapse (59.6%) compared to locoregional (28.6%) and combined (14.3%) (p=0.028) and in patients with complete surgical resection of all sites of recurrence (70.0%) compared to incomplete (21.4%) and no surgery (0%) (p=0.003). Conclusions For patients nonresponsive to first-line therapy or who experience relapse, prognosis is dismal and options are scarce. Site of relapse and resectability define prognosis. Novel therapeutic concepts are needed to improve the outcome of paediatric patients with r/r ACC