Robust constrained model predictive control based on parameter-dependent Lyapunov functions

The problem of robust constrained model predictive control (MPC) of systems with polytopic uncertainties is considered in this paper. New sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed in terms of linear matrix inequalities (LMIs), which will reduce the conservativeness resulting from using a single Lyapunov function. At each sampling instant, the corresponding parameter-dependent Lyapunov function is an upper bound for a worst-case objective function, which can be minimized using the LMI convex optimization approach. Based on the solution of optimization at each sampling instant, the corresponding state feedback controller is designed, which can guarantee that the resulting closed-loop system is robustly asymptotically stable. In addition, the feedback controller will meet the specifications for systems with input or output constraints, for all admissible time-varying parameter uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques

On stability of discretizations of the Helmholtz equation (extended version)

We review the stability properties of several discretizations of the Helmholtz equation at large wavenumbers. For a model problem in a polygon, a complete $k$-explicit stability (including $k$-explicit stability of the continuous problem) and convergence theory for high order finite element methods is developed. In particular, quasi-optimality is shown for a fixed number of degrees of freedom per wavelength if the mesh size $h$ and the approximation order $p$ are selected such that $kh/p$ is sufficiently small and $p = O(\log k)$, and, additionally, appropriate mesh refinement is used near the vertices. We also review the stability properties of two classes of numerical schemes that use piecewise solutions of the homogeneous Helmholtz equation, namely, Least Squares methods and Discontinuous Galerkin (DG) methods. The latter includes the Ultra Weak Variational Formulation

CD1a expression by Barrett's metaplasia of gastric type may help to predict its evolution towards cancer

As emerging in the recent literature, CD1a has been regarded as a molecule whose expression may reflect tumour evolution. The aim of the present work was to investigate the expression of CD1a in a series of Barrett's metaplasia (BM), gastric type (GTBM), with and without follow-up, in order to analyse whether its expression may help to diagnose this disease and to address the outcome. Indeed, GTBM may be confused sometimes with islets of ectopic gastric mucosa and its evolution towards dysplasia (Dy) or carcinoma (Ca) could not be foreseen. We showed a significant higher expression of CD1a in GTBM than in both Dy and Ca; nevertheless, the number of positive GTBM was significantly lower in the group of cases that at follow-up underwent Dy or Ca. Our data address that CD1a may be a novel biomarker for BM and that its expression may help to predict the prognosis of this pathology

Prophylactic Mastectomy in BRCA1/2 Mutation Carriers and Women at Risk of Hereditary Breast Cancer: Long-Term Experiences at the Rotterdam Family Cancer Clinic

Background BRCA1/2 mutation carriers and women from a hereditary breast(/ovarian) cancer family have a highly increased risk of developing breast cancer (BC). Prophylactic mastectomy (PM) results in the greatest BC risk reduction. Long-term data on the efficacy and sequels of PM are scarce. Methods From 358 high-risk women (including 236 BRCA1/2 carriers) undergoing PM between 1994 and 2004, relevant data on the occurrence of BC in relation to PM, complications in relation to breast reconstruction (BR), mutation status, age at PM and preoperative imaging examination results were extracted from the medical records, and analyzed separately for women without (unaffected, n = 177) and with a BC history (affected, n = 181). Results No primary BCs occurred after PM (median follow-up 4.5 years). In one previously unaffected woman, metastatic BC was detected almost 4 years after PM (primary BC not found). Median age at PM was younger in unaffected women (P < .001), affected women more frequently were 50% risk carriers (P < .001). Unexpected (pre)malignant changes at PM were found in 3% of the patients (in 5 affected, and 5 unaffected women, respectively). In 49.6% of the women opting for BR one or more complications were registered, totaling 215 complications, leading to 153 surgical interventions (71%). Complications were mainly related to cosmetic outcome (36%) and capsular formation (24%). Conclusions The risk of developing a primary BC after PM remains low after longer follow-up. Preoperative imaging and careful histological examination is warranted because of potential unexpected (pre)malignant findings. The high complication rate after breast reconstruction mainly concerns cosmetic issues

Prognostic Factors in 77 Curative Chest Wall Resections for Isolated Breast Cancer Recurrence

Background: Full-thickness chest wall resection (CWR) is the preferred treatment for breast cancer (BC) patients with extensive isolated locoregional recurrence. It remains a challenge to select patients that will benefit most from this treatment. The aim of this study was to define prognostic factors in patients who undergo CWR with curative intent. Methods: BC patients who underwent a CWR with curative intent for recurrence of disease between 1986 and 2006 were included in this retrospective study. Twenty-two factors were studied in a univariate analyses, and multivariate stepwise Cox regression analyses was performed. Results: Seventy-seven patients were included in this study. The 5-year overall survival was 25%. There was one postoperative death. Univariate analyses showed that three prognostic factors were significantly correlated with OS and disease-free survival: (1) interval between primary treatment and CWR (P = .02 and .004, respectively), (2) chemotherapy for recurrence (P = .05 and .05, respectively), and (3) resection specimen smaller than 150 cm2(P = .03 and .009, respectively). An interval lasting >10 years between primary treatment and CWR remained statistically significantly correlated with better overall survival and disease-free survival after multivariate analyses. Conclusions: CWR is a safe treatment in patients who have isolated extensive BC recurrence. The best survival outcome was seen in patients after a disease-free interval of >10 years. Existing data show that adjuvant radiotherapy and adjuvant hormone therapy for estrogen-positive tumors improves overall survival. Neoadjuvant chemotherapy may be considered in individual patients

The degree of segmental aneuploidy measured by total copy number abnormalities predicts survival and recurrence in superficial gastroesophageal adenocarcinoma

Background: Prognostic biomarkers are needed for superficial gastroesophageal adenocarcinoma (EAC) to predict clinical outcomes and select therapy. Although recurrent mutations have been characterized in EAC, little is known about their clinical and prognostic significance. Aneuploidy is predictive of clinical outcome in many malignancies but has not been evaluated in superficial EAC. Methods: We quantified copy number changes in 41 superficial EAC using Affymetrix SNP 6.0 arrays. We identified recurrent chromosomal gains and losses and calculated the total copy number abnormality (CNA) count for each tumor as a measure of aneuploidy. We correlated CNA count with overall survival and time to first recurrence in univariate and multivariate analyses. Results: Recurrent segmental gains and losses involved multiple genes, including: HER2, EGFR, MET, CDK6, KRAS (recurrent gains); and FHIT, WWOX, CDKN2A/B, SMAD4, RUNX1 (recurrent losses). There was a 40-fold variation in CNA count across all cases. Tumors with the lowest and highest quartile CNA count had significantly better overall survival (p = 0.032) and time to first recurrence (p = 0.010) compared to those with intermediate CNA counts. These associations persisted when controlling for other prognostic variables. Significance: SNP arrays facilitate the assessment of recurrent chromosomal gain and loss and allow high resolution, quantitative assessment of segmental aneuploidy (total CNA count). The non-monotonic association of segmental aneuploidy with survival has been described in other tumors. The degree of aneuploidy is a promising prognostic biomarker in a potentially curable form of EAC. © 2014 Davison et al