Flexible combination of multiple diagnostic biomarkers to improve diagnostic accuracy

In medical research, it is common to collect information of multiple continuous biomarkers to improve the accuracy of diagnostic tests. Combining the measurements of these biomarkers into one single score is a popular practice to integrate the collected information, where the accuracy of the resultant diagnostic test is usually improved. To measure the accuracy of a diagnostic test, the Youden index has been widely used in literature. Various parametric and nonparametric methods have been proposed to linearly combine biomarkers so that the corresponding Youden index can be optimized. Yet there seems to be little justification of enforcing such a linear combination. This paper proposes a flexible approach that allows both linear and nonlinear combinations of biomarkers. The proposed approach formulates the problem in a large margin classification framework, where the combination function is embedded in a flexible reproducing kernel Hilbert space. Advantages of the proposed approach are demonstrated in a variety of simulated experiments as well as a real application to a liver disorder study

Lusztig sheaves and tensor products of integrable highest weight modules

By introducing $N$-framed quivers, we define the localization of Lusztig's sheaves for $N$-framed quivers and functors $E^{(n)}_{i}, F^{(n)}_{i}, K^{\pm}_i$ for localizations. This gives a categorical realization of tensor products of integrable highest weight modules of the quantized enveloping algebra. The simple perverse sheaves in the localization provide the canonical basis of tensor products. It is bar-invariant and has positivity. Moreover, we give a categorical interpretation of the Yang-Baxter equation.Comment: 35 pages, arXiv admin note: text overlap with arXiv:2307.1613

Establishing in China’s ‘good-enough’ market - - A benchmarking study on Scandinavian engineering industries’ further establishment in China

Title: Establishing in China’s ‘good-enough’ market - A benchmarking study on Scandinavian engineering industries’ further establishment in China. Problem discussion: The Chinese market is gaining importance for Scandinavian engineering industries and is by many considered a crucial market to be successful in. These companies have a tradition of producing premium products for premium customers. However, in China many are currently experiencing the threat from local competitors producing products of somewhat less quality aimed at the vast Chinese middle market - the good-enough market. Entering this market mean a first time venture into a lower quality segment for the Scandinavian companies. Hence the questions of if the good-enough market should be entered or not and what trends that can be distinguished. Purpose: The purpose with this thesis is to examine how Scandinavian engineering industries producing premium products for premium customers, enter local middle markets in China. Methodology: The research consisted of a benchmarking study where Scandinavian engineering industries in China were studied in order to distinguish an eventual pattern and trends. Distinguished trends were finally analysed according to the Uppsala internationalisation model and the theory of good-enough markets. Conclusions: It is possible to merge segmentation theories with the Uppsala internationalisation model; it acts as a complement in order to better understand the mechanisms in the initial phases. The decision-making process remains incremental during the entire establishment chain where R&D is a natural continuation. The same internalisation model can also be distinguished during further establishment of an existing market, as in the case of the good-enough market. Companies that acknowledge this market tend to also see the threat aspect of it. Hence the trend of acquiring a good-enough company and get rid of a potential threat

Sheaf realization of Bridgeland's Hall algebra of Dynkin type

As one of results in [6], Bridgeland realized the quantum group $\mathrm{U}_v(\mathfrak{g})$ via the localization of Ringel-Hall algebra for two-periodic projective complexes of quiver representations over a finite field. In the present paper, we generalize Lusztig's categorical construction and (dual) canonical basis for the nilpotent part $\mathrm{U}_v(\mathfrak{n}^+)$ to Bridgeland's Hall algebra of Dynkin type, and obtain a perverse sheaf realization of global basis for Bridgeland's localizing algebra. In particular, we prove that the dual of canonical basis elements are part of our basis up to powers of $v$.Comment: In the new version, we add some content including: in section 6, we refine our construction and complete the perverse sheaves realization of Bridgeland's Hall algebra which is essentially isomorphic to the integral form of the whole quantum group; in section 7, we obtain new results about the global basis; in section 8, we compare our basis with Lusztig's (dual) canonical basi