Internal Mammary Sentinel Lymph Node Biopsy

The conception of internal mammary sentinel lymph node biopsy (IM‐SLNB) has been added to the 2009 American Joint Committee on Cancer breast cancer staging manual. However, there has still been slight variation in the surgical treatment model owing to the low visualization rate of internal mammary sentinel lymph nodes (IM‐SLN) with the traditional radiotracer injection technique. According to the hypothesis of IM‐SLN, a modified injection technique (periareolar intraparenchymal, high volume, and ultrasound guidance) was established, which could significantly improve the IM‐SLN visualization rate, and make the IM‐SLNB procedure possible in routine practice. IM‐SLNB could provide minimally invasive staging, prognosis, and decision‐making individually, especially for the patients with clinically positive axilla lymph nodes. Moreover, radiotherapy targeting on internal mammary lymph nodes (IMLN) should be tailored and balanced between the potential benefit and toxicity, and radiotherapy guided by IM‐SLNB could achieve this goal. In the era of emphasizing the effective adjuvant therapy, within the changing therapy approach—more systemic treatment, less loco‐regional treatment—oncologist should reconsider the application of regional IMLN therapy

Distorted optimal transport

Classic optimal transport theory is built on minimizing the expected cost between two given distributions. We propose the framework of distorted optimal transport by minimizing a distorted expected cost. This new formulation is motivated by concrete problems in decision theory, robust optimization, and risk management, and it has many distinct features compared to the classic theory. We choose simple cost functions and study different distortion functions and their implications on the optimal transport plan. We show that on the real line, the comonotonic coupling is optimal for the distorted optimal transport problem when the distortion function is convex and the cost function is submodular and monotone. Some forms of duality and uniqueness results are provided. For inverse-S-shaped distortion functions and linear cost, we obtain the unique form of optimal coupling for all marginal distributions, which turns out to have an interesting ``first comonotonic, then counter-monotonic" dependence structure; for S-shaped distortion functions a similar structure is obtained. Our results highlight several challenges and features in distorted optimal transport, offering a new mathematical bridge between the fields of probability, decision theory, and risk management

Exposure of the Hidden Anti-Ferromagnetism in Paramagnetic CdSe:Mn Nanocrystals

We present theoretical and experimental investigations of the magnetism of paramagnetic semiconductor CdSe:Mn nanocrystals and propose an efficient approach to the exposure and analysis of the underlying anti-ferromagnetic interactions between magnetic ions therein. A key advance made here is the build-up of an analysis method with the exploitation of group theory technique that allows us to distinguish the anti-ferromagnetic interactions between aggregative Mn2+ ions from the overall pronounced paramagnetism of magnetic ion doped semiconductor nanocrystals. By using the method, we clearly reveal and identify the signatures of anti-ferromagnetism from the measured temperature dependent magnetisms, and furthermore determine the average number of Mn2+ ions and the fraction of aggregative ones in the measured CdSe:Mn nanocrystals.Comment: 26 pages, 5 figure