The intersection of some classical equivalence classes of matrices

Let A be an n x n complex matrix. Let Sim(A) denote the similarity equivalence class of A, Conj(A) denote the conjunctivity equivalence class of A, UEquiv(A) denote the unitary-equivalence equivalence class of A, and UA denote the unitary similarity equivalence class of A. Each of these equivalence classes has been studied for some time and is generally well-understood. In particular, canonical forms have been given for each equivalence class. Since the intersection of any two equivalence classes of A is again an equivalence class of A, we consider two such intersections: CS(A) ≡ Sim(A) ∩ Conj(A) and UES(A) ≡ Sim( A) ∩ UEquiv(A). Though it is natural to first think that each of these is simply UA , for each A, we show by examples that this is not the case. We then try to classify which matrices A have CS( A) = UA . For matrices having CSA≠U A , we try to count the number of disjoint unitary similarity classes contained in CS(A). Though the problem is not completely solved for CS(A), we reduce the problem to non-singular, non-co-Hermitian matrices A. A similar analysis is performed for UES(A), and a (less simple) reduction of the problem is also achieved

Lessons from the first generation of marine ecological forecast products

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LSST Science Book, Version 2.0

A survey that can cover the sky in optical bands over wide fields to faint magnitudes with a fast cadence will enable many of the exciting science opportunities of the next decade. The Large Synoptic Survey Telescope (LSST) will have an effective aperture of 6.7 meters and an imaging camera with field of view of 9.6 deg^2, and will be devoted to a ten-year imaging survey over 20,000 deg^2 south of +15 deg. Each pointing will be imaged 2000 times with fifteen second exposures in six broad bands from 0.35 to 1.1 microns, to a total point-source depth of r~27.5. The LSST Science Book describes the basic parameters of the LSST hardware, software, and observing plans. The book discusses educational and outreach opportunities, then goes on to describe a broad range of science that LSST will revolutionize: mapping the inner and outer Solar System, stellar populations in the Milky Way and nearby galaxies, the structure of the Milky Way disk and halo and other objects in the Local Volume, transient and variable objects both at low and high redshift, and the properties of normal and active galaxies at low and high redshift. It then turns to far-field cosmological topics, exploring properties of supernovae to z~1, strong and weak lensing, the large-scale distribution of galaxies and baryon oscillations, and how these different probes may be combined to constrain cosmological models and the physics of dark energy.Comment: 596 pages. Also available at full resolution at http://www.lsst.org/lsst/sciboo

Towards a multi-arm multi-stage platform trial of disease modifying approaches in Parkinson’s disease

An increase in the efficiency of clinical trial conduct has been successfully demonstrated in the oncology field, by the use of multi-arm, multi-stage trials allowing the evaluation of multiple therapeutic candidates simultaneously, and seamless recruitment to phase 3 for those candidates passing an interim signal of efficacy. Replicating this complex innovative trial design in diseases such as Parkinson’s disease is appealing, but in addition to the challenges associated with any trial assessing a single potentially disease modifying intervention in Parkinson’s disease, a multiarm platform trial must also specifically consider the heterogeneous nature of the disease, alongside the desire to potentially test multiple treatments with different mechanisms of action. In a multi-arm trial, there is a need to appropriately stratify treatment arms to ensure each are comparable with a shared placebo/standard of care arm; however, in Parkinson’s disease there may be a preference to enrich an arm with a subgroup of patients that may be most likely to respond to a specific treatment approach. The solution to this conundrum lies in having clearly defined criteria for inclusion in each treatment arm as well as an analysis plan that takes account of predefined subgroups of interest, alongside evaluating the impact of each treatment on the broader population of Parkinson’s disease patients. Beyond this, there must be robust processes of treatment selection, and consensus derived measures to confirm target engagement and interim assessments of efficacy, as well as consideration of the infrastructure needed to support recruitment, and the long-term funding and sustainability of the platform. This has to incorporate the diverse priorities of clinicians, triallists, regulatory authorities and above all the views of people with Parkinson’s disease.</p

Towards a multi-arm multi-stage platform trial of disease modifying approaches in Parkinson’s disease

An increase in the efficiency of clinical trial conduct has been successfully demonstrated in the oncology field, by the use of multi-arm, multi-stage trials allowing the evaluation of multiple therapeutic candidates simultaneously, and seamless recruitment to phase 3 for those candidates passing an interim signal of efficacy. Replicating this complex innovative trial design in diseases such as Parkinson’s disease is appealing, but in addition to the challenges associated with any trial assessing a single potentially disease modifying intervention in Parkinson’s disease, a multiarm platform trial must also specifically consider the heterogeneous nature of the disease, alongside the desire to potentially test multiple treatments with different mechanisms of action. In a multi-arm trial, there is a need to appropriately stratify treatment arms to ensure each are comparable with a shared placebo/standard of care arm; however, in Parkinson’s disease there may be a preference to enrich an arm with a subgroup of patients that may be most likely to respond to a specific treatment approach. The solution to this conundrum lies in having clearly defined criteria for inclusion in each treatment arm as well as an analysis plan that takes account of predefined subgroups of interest, alongside evaluating the impact of each treatment on the broader population of Parkinson’s disease patients. Beyond this, there must be robust processes of treatment selection, and consensus derived measures to confirm target engagement and interim assessments of efficacy, as well as consideration of the infrastructure needed to support recruitment, and the long-term funding and sustainability of the platform. This has to incorporate the diverse priorities of clinicians, triallists, regulatory authorities and above all the views of people with Parkinson’s disease.</p

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts

Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas

Although theMYConcogene has been implicated incancer, a systematic assessment of alterations ofMYC, related transcription factors, and co-regulatoryproteins, forming the proximal MYC network (PMN),across human cancers is lacking. Using computa-tional approaches, we define genomic and proteo-mic features associated with MYC and the PMNacross the 33 cancers of The Cancer Genome Atlas.Pan-cancer, 28% of all samples had at least one ofthe MYC paralogs amplified. In contrast, the MYCantagonists MGA and MNT were the most frequentlymutated or deleted members, proposing a roleas tumor suppressors.MYCalterations were mutu-ally exclusive withPIK3CA,PTEN,APC,orBRAFalterations, suggesting that MYC is a distinct onco-genic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such asimmune response and growth factor signaling; chro-matin, translation, and DNA replication/repair wereconserved pan-cancer. This analysis reveals insightsinto MYC biology and is a reference for biomarkersand therapeutics for cancers with alterations ofMYC or the PMN

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin