Analysis of Agglomerative Clustering

The diameter k-clustering problem is the problem of partitioning a finite subset of R^d into k subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes a hierarchy of approximate solutions to this problem for all values of k is the agglomerative clustering algorithm with the complete linkage strategy. For decades this algorithm has been widely used by practitioners. However, it is not well studied theoretically. In this paper we analyze the agglomerative complete linkage clustering algorithm. Assuming that the dimension dis a constant, we show that for any k the solution computed by this algorithm is an O(log k)-approximation to the diameter k-clustering problem. Moreover, our analysis does not only hold for the Euclidean distance but for any metric that is based on a norm

Analysis of Agglomerative Clustering

The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes a hierarchy of approximate solutions to this problem (for all values of $k$) is the agglomerative clustering algorithm with the complete linkage strategy. For decades, this algorithm has been widely used by practitioners. However, it is not well studied theoretically. In this paper, we analyze the agglomerative complete linkage clustering algorithm. Assuming that the dimension $d$ is a constant, we show that for any $k$ the solution computed by this algorithm is an $O(\log k)$-approximation to the diameter $k$-clustering problem. Our analysis does not only hold for the Euclidean distance but for any metric that is based on a norm. Furthermore, we analyze the closely related $k$-center and discrete $k$-center problem. For the corresponding agglomerative algorithms, we deduce an approximation factor of $O(\log k)$ as well.Comment: A preliminary version of this article appeared in Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS '11), March 2011, pp. 308-319. This article also appeared in Algorithmica. The final publication is available at http://link.springer.com/article/10.1007/s00453-012-9717-

De Svppvratione A Visceribvs Arcenda Et Cohibenda

Frankfurt/Oder, Univ., Med. Diss., 1791Consentiente Illvstri Medicorvm Ordine Ad Demerendos Doctoris Medici Honores D. VI. Ivlii MDCCLXXXXI. Pvblice Disseret Iohannes Daniel Kvntze Lesna - PolonusVorlageform des Erscheinungsvermerks: Traiecti Ad Viadrvm, E Typographeo Apitziano

Optically Controlled Construction of Three-Dimensional Protein Arrays

| openaire: EC/H2020/101002258/EU//ProCrystal Funding Information: This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No. 101002258). We acknowledge the funding from the Jane and Aatos Erkko Foundation, the Magnus Ehrnrooth Foundation, Tampere University Graduate School, the National Nature Science Foundation of China (No. 22277018), the Zhejiang Provincial Natural Science Foundation for Distinguished Young Scholar (LR23B030001), and Wenzhou Institute, University of Chinese Academy of Sciences (No. WIUCASQD2020015, No. WIUCASQD2022006, No. WIUCASQD2021048). We acknowledge the provision of facilities and technical support by Aalto University Bioeconomy Facilities and OtaNano‐Nanomicroscopy Center (Aalto‐NMC). The authors thank Jani Seitsonen from the Department of Applied Physics, Aalto University, for the support in cryo‐TEM measurements. This work was carried out under the Academy of Finland's Centers of Excellence Programme, Life Inspired Hybrid Materials (LIBER) Center of Excellence (2022–2029), and the Flagship Programme PREIN (No. 320165). Publisher Copyright: © 2023 The Authors. Angewandte Chemie International Edition published by Wiley-VCH GmbH.Protein crystallization is an important tool for structural biology and nanostructure preparation. Here, we report on kinetic pathway-dependent protein crystals that are controlled by light. Photo-responsive crystallites are obtained by complexing the model proteins with cationic azobenzene dyes. The crystalline state is readily switched to a dispersed phase under ultraviolet light and restored by subsequent visible-light illumination. The switching can be reversibly repeated for multiple cycles without noticeable structure deterioration. Importantly, the photo-treatment not only significantly increases the crystallinity, but creates crystallites at conditions where no ordered lattices are observed upon directly mixing the components. Further control over the azobenzene isomerization kinetics produces protein single crystals of up to ≈50 μm. This approach offers an intriguing method to fabricate metamaterials and study optically controlled crystallization.Peer reviewe

Overcoming MET-mediated resistance in oncogene-driven NSCLC

Summary: This study evaluates the efficacy of combining targeted therapies with MET or SHP2 inhibitors to overcome MET-mediated resistance in different NSCLC subtypes. A prevalence study was conducted for MET amplification and overexpression in samples from patients with NSCLC who relapsed on ALK, ROS1, or RET tyrosine kinase inhibitors. MET-mediated resistance was detected in 37.5% of tissue biopsies, which allow the detection of MET overexpression, compared to 7.4% of liquid biopsies. The development of drug resistance by MET overexpression was confirmed in EGFRex19del-, KRASG12C-, HER2ex20ins-, and TPM3-NTRK1-mutant cell lines. The combination of targeted therapy with MET or SHP2 inhibitors was found to overcome MET-mediated resistance in both in vitro and in vivo assays. This study highlights the importance of considering MET overexpression as a resistance driver to NSCLC targeted therapies to better identify patients who could potentially benefit from combination approaches with MET or SHP2 inhibitors