Polynomial Time Algorithms in Invariant Theory for Torus Actions

An action of a group on a vector space partitions the latter into a set of orbits. We consider three natural and useful algorithmic "isomorphism" or "classification" problems, namely, orbit equality, orbit closure intersection, and orbit closure containment. These capture and relate to a variety of problems within mathematics, physics and computer science, optimization and statistics. These orbit problems extend the more basic null cone problem, whose algorithmic complexity has seen significant progress in recent years. In this paper, we initiate a study of these problems by focusing on the actions of commutative groups (namely, tori). We explain how this setting is motivated from questions in algebraic complexity, and is still rich enough to capture interesting combinatorial algorithmic problems. While the structural theory of commutative actions is well understood, no general efficient algorithms were known for the aforementioned problems. Our main results are polynomial time algorithms for all three problems. We also show how to efficiently find separating invariants for orbits, and how to compute systems of generating rational invariants for these actions (in contrast, for polynomial invariants the latter is known to be hard). Our techniques are based on a combination of fundamental results in invariant theory, linear programming, and algorithmic lattice theory

A prospective, multi‐center study of the chocolate balloon in femoropopliteal peripheral artery disease: The Chocolate BAR registry

The Chocolate BAR study is a prospective multicenter post‐market registry designed to evaluate the safety and performance of the Chocolate percutaneous transluminal angioplasty balloon catheter in a broad population with symptomatic peripheral arterial disease. The primary endpoint is acute procedural success (defined as ≤30% residual stenosis without flow‐limiting dissection); secondary long‐term outcomes include freedom from target lesion revascularization (TLR), major unplanned amputation, survival, and patency. A total of 262 patients (290 femoropopliteal lesions) were enrolled at 30 US centers between 2012 and 2014. The primary endpoint of procedure success was achieved in 85.1% of cases, and freedom from stenting occurred in 93.1%. Bail out stenting by independent adjudication occurred in 1.6% of cases and there were no flow limiting dissections. There was mean improvement of 2.1 Rutherford classes (±1.5) at 12‐months, with 78.5% freedom from TLR, 97.2% freedom from major amputation, and 93.3% freedom from all‐cause mortality. Core Lab adjudicated patency was 64.1% at 12 months. Use of the Chocolate balloon in an “all‐comers” population achieved excellent procedural outcomes with low dissection rates and bailout stent use.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143650/1/ccd27565_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/143650/2/ccd27565.pd

Cause of Death and Predictors of All-Cause Mortality in Anticoagulated Patients With Nonvalvular Atrial Fibrillation : Data From ROCKET AF

M. Kaste on työryhmän ROCKET AF Steering Comm jäsen.Background-Atrial fibrillation is associated with higher mortality. Identification of causes of death and contemporary risk factors for all-cause mortality may guide interventions. Methods and Results-In the Rivaroxaban Once Daily Oral Direct Factor Xa Inhibition Compared with Vitamin K Antagonism for Prevention of Stroke and Embolism Trial in Atrial Fibrillation (ROCKET AF) study, patients with nonvalvular atrial fibrillation were randomized to rivaroxaban or dose-adjusted warfarin. Cox proportional hazards regression with backward elimination identified factors at randomization that were independently associated with all-cause mortality in the 14 171 participants in the intention-to-treat population. The median age was 73 years, and the mean CHADS(2) score was 3.5. Over 1.9 years of median follow-up, 1214 (8.6%) patients died. Kaplan-Meier mortality rates were 4.2% at 1 year and 8.9% at 2 years. The majority of classified deaths (1081) were cardiovascular (72%), whereas only 6% were nonhemorrhagic stroke or systemic embolism. No significant difference in all-cause mortality was observed between the rivaroxaban and warfarin arms (P=0.15). Heart failure (hazard ratio 1.51, 95% CI 1.33-1.70, P= 75 years (hazard ratio 1.69, 95% CI 1.51-1.90, P Conclusions-In a large population of patients anticoagulated for nonvalvular atrial fibrillation, approximate to 7 in 10 deaths were cardiovascular, whereasPeer reviewe

HER2-enriched subtype and novel molecular subgroups drive aromatase inhibitor resistance and an increased risk of relapse in early ER+/HER2+ breast cancer

BACKGROUND: Oestrogen receptor positive/ human epidermal growth factor receptor positive (ER+/HER2+) breast cancers (BCs) are less responsive to endocrine therapy than ER+/HER2- tumours. Mechanisms underpinning the differential behaviour of ER+HER2+ tumours are poorly characterised. Our aim was to identify biomarkers of response to 2 weeks’ presurgical AI treatment in ER+/HER2+ BCs. METHODS: All available ER+/HER2+ BC baseline tumours (n=342) in the POETIC trial were gene expression profiled using BC360™ (NanoString) covering intrinsic subtypes and 46 key biological signatures. Early response to AI was assessed by changes in Ki67 expression and residual Ki67 at 2 weeks (Ki672wk). Time-To-Recurrence (TTR) was estimated using Kaplan-Meier methods and Cox models adjusted for standard clinicopathological variables. New molecular subgroups (MS) were identified using consensus clustering. FINDINGS: HER2-enriched (HER2-E) subtype BCs (44.7% of the total) showed poorer Ki67 response and higher Ki672wk (p<0.0001) than non-HER2-E BCs. High expression of ERBB2 expression, homologous recombination deficiency (HRD) and TP53 mutational score were associated with poor response and immune-related signatures with High Ki672wk. Five new MS that were associated with differential response to AI were identified. HER2-E had significantly poorer TTR compared to Luminal BCs (HR 2.55, 95% CI 1.14–5.69; p=0.0222). The new MS were independent predictors of TTR, adding significant value beyond intrinsic subtypes. INTERPRETATION: Our results show HER2-E as a standardised biomarker associated with poor response to AI and worse outcome in ER+/HER2+. HRD, TP53 mutational score and immune-tumour tolerance are predictive biomarkers for poor response to AI. Lastly, novel MS identify additional non-HER2-E tumours not responding to AI with an increased risk of relapse