Guaranteed clustering and biclustering via semidefinite programming

Identifying clusters of similar objects in data plays a significant role in a wide range of applications. As a model problem for clustering, we consider the densest k-disjoint-clique problem, whose goal is to identify the collection of k disjoint cliques of a given weighted complete graph maximizing the sum of the densities of the complete subgraphs induced by these cliques. In this paper, we establish conditions ensuring exact recovery of the densest k cliques of a given graph from the optimal solution of a particular semidefinite program. In particular, the semidefinite relaxation is exact for input graphs corresponding to data consisting of k large, distinct clusters and a smaller number of outliers. This approach also yields a semidefinite relaxation for the biclustering problem with similar recovery guarantees. Given a set of objects and a set of features exhibited by these objects, biclustering seeks to simultaneously group the objects and features according to their expression levels. This problem may be posed as partitioning the nodes of a weighted bipartite complete graph such that the sum of the densities of the resulting bipartite complete subgraphs is maximized. As in our analysis of the densest k-disjoint-clique problem, we show that the correct partition of the objects and features can be recovered from the optimal solution of a semidefinite program in the case that the given data consists of several disjoint sets of objects exhibiting similar features. Empirical evidence from numerical experiments supporting these theoretical guarantees is also provided

Breakdown of Fermi-liquid theory in a cuprate superconductor

The behaviour of electrons in solids is remarkably well described by Landau's Fermi-liquid theory, which says that even though electrons in a metal interact they can still be treated as well-defined fermions, called ``quasiparticles''. At low temperature, the ability of quasiparticles to transport heat is strictly given by their ability to transport charge, via a universal relation known as the Wiedemann-Franz law, which no material in nature has been known to violate. High-temperature superconductors have long been thought to fall outside the realm of Fermi-liquid theory, as suggested by several anomalous properties, but this has yet to be shown conclusively. Here we report on the first experimental test of the Wiedemann-Franz law in a cuprate superconductor, (Pr,Ce)$_2$CuO$_4$. Our study reveals a clear departure from the universal law and provides compelling evidence for the breakdown of Fermi-liquid theory in high-temperature superconductors.Comment: 7 pages, 3 figure

Tumor innate immunity primed by specific interferon-stimulated endogenous retroviruses.

Mesenchymal tumor subpopulations secrete pro-tumorigenic cytokines and promote treatment resistance1-4. This phenomenon has been implicated in chemorefractory small cell lung cancer and resistance to targeted therapies5-8, but remains incompletely defined. Here, we identify a subclass of endogenous retroviruses (ERVs) that engages innate immune signaling in these cells. Stimulated 3 prime antisense retroviral coding sequences (SPARCS) are oriented inversely in 3' untranslated regions of specific genes enriched for regulation by STAT1 and EZH2. Derepression of these loci results in double-stranded RNA generation following IFN-γ exposure due to bi-directional transcription from the STAT1-activated gene promoter and the 5' long terminal repeat of the antisense ERV. Engagement of MAVS and STING activates downstream TBK1, IRF3, and STAT1 signaling, sustaining a positive feedback loop. SPARCS induction in human tumors is tightly associated with major histocompatibility complex class 1 expression, mesenchymal markers, and downregulation of chromatin modifying enzymes, including EZH2. Analysis of cell lines with high inducible SPARCS expression reveals strong association with an AXL/MET-positive mesenchymal cell state. While SPARCS-high tumors are immune infiltrated, they also exhibit multiple features of an immune-suppressed microenviroment. Together, these data unveil a subclass of ERVs whose derepression triggers pathologic innate immune signaling in cancer, with important implications for cancer immunotherapy

Quantum Communication

Quantum communication, and indeed quantum information in general, has changed the way we think about quantum physics. In 1984 and 1991, the first protocol for quantum cryptography and the first application of quantum non-locality, respectively, attracted a diverse field of researchers in theoretical and experimental physics, mathematics and computer science. Since then we have seen a fundamental shift in how we understand information when it is encoded in quantum systems. We review the current state of research and future directions in this new field of science with special emphasis on quantum key distribution and quantum networks.Comment: Submitted version, 8 pg (2 cols) 5 fig