Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints

The Tikhonov regularization of linear ill-posed problems with an $\ell^1$ penalty is considered. We recall results for linear convergence rates and results on exact recovery of the support. Moreover, we derive conditions for exact support recovery which are especially applicable in the case of ill-posed problems, where other conditions, e.g. based on the so-called coherence or the restricted isometry property are usually not applicable. The obtained results also show that the regularized solutions do not only converge in the $\ell^1$-norm but also in the vector space $\ell^0$ (when considered as the strict inductive limit of the spaces $\R^n$ as $n$ tends to infinity). Additionally, the relations between different conditions for exact support recovery and linear convergence rates are investigated. With an imaging example from digital holography the applicability of the obtained results is illustrated, i.e. that one may check a priori if the experimental setup guarantees exact recovery with Tikhonov regularization with sparsity constraints

Characteristics of clinical measurements between biomechanical responders and non-responders to a shoe designed for knee osteoarthritis

The purpose of this study was to investigate the characteristics of biomechanical and clinical measurements in relation to the knee adduction moment when wearing a standard shoe and a shoe design for individuals with knee osteoarthritis (Flex-OA). Kinematic and kinetic data were collected from thirty-two healthy individuals (64 knees) using a ten camera motion analysis system and four force plates. Subjects performed 5 walking trials under the two conditions and the magnitude of individuals' biomechanical responses where explored in relation to the clinical assessment of the Foot Posture Index, hip rotation range, strength of hip rotators, and active ankle-foot motion, all of which have been described as possible compensation mechanisms in knee osteoarthritis. Significant reductions in the first peak of the knee adduction moment (KAM) during stance phase (9.3%) were recorded (p<0.0001). However, despite this difference, 22 of 64 knees showed either no change or an increased KAM, indicating a non-response or negative-response to the Flex-OA shoe. Significant differences were observed between the responder and non-responder subgroups in the hip rotation range ratio (p=0.044) and the hip rotators strength ratio (p=0.028). Significant differences were seen in clinical assessments of hip rotation range and hip rotator strength between responders and non-responders using a cut-off of 0.02Nm/kg change in the KAM. [Abstract copyright: Copyright © 2017 Elsevier B.V. All rights reserved.

Benchmark datasets for 3D MALDI- and DESI-imaging mass spectrometry

BACKGROUND: Three-dimensional (3D) imaging mass spectrometry (MS) is an analytical chemistry technique for the 3D molecular analysis of a tissue specimen, entire organ, or microbial colonies on an agar plate. 3D-imaging MS has unique advantages over existing 3D imaging techniques, offers novel perspectives for understanding the spatial organization of biological processes, and has growing potential to be introduced into routine use in both biology and medicine. Owing to the sheer quantity of data generated, the visualization, analysis, and interpretation of 3D imaging MS data remain a significant challenge. Bioinformatics research in this field is hampered by the lack of publicly available benchmark datasets needed to evaluate and compare algorithms. FINDINGS: High-quality 3D imaging MS datasets from different biological systems at several labs were acquired, supplied with overview images and scripts demonstrating how to read them, and deposited into MetaboLights, an open repository for metabolomics data. 3D imaging MS data were collected from five samples using two types of 3D imaging MS. 3D matrix-assisted laser desorption/ionization imaging (MALDI) MS data were collected from murine pancreas, murine kidney, human oral squamous cell carcinoma, and interacting microbial colonies cultured in Petri dishes. 3D desorption electrospray ionization (DESI) imaging MS data were collected from a human colorectal adenocarcinoma. CONCLUSIONS: With the aim to stimulate computational research in the field of computational 3D imaging MS, selected high-quality 3D imaging MS datasets are provided that could be used by algorithm developers as benchmark datasets

Clinical decision-making: midwifery students' recognition of, and response to, post partum haemorrhage in the simulation environment

<p>Abstract</p> <p>Background</p> <p>This paper reports the findings of a study of how midwifery students responded to a simulated post partum haemorrhage (PPH). Internationally, 25% of maternal deaths are attributed to severe haemorrhage. Although this figure is far higher in developing countries, the risk to maternal wellbeing and child health problem means that all midwives need to remain vigilant and respond appropriately to early signs of maternal deterioration.</p> <p>Methods</p> <p>Simulation using a patient actress enabled the research team to investigate the way in which 35 midwifery students made decisions in a dynamic high fidelity PPH scenario. The actress wore a birthing suit that simulated blood loss and a flaccid uterus on palpation. The scenario provided low levels of uncertainty and high levels of relevant information. The student's response to the scenario was videoed. Immediately after, they were invited to review the video, reflect on their performance and give a commentary as to what affected their decisions. The data were analysed using Dimensional Analysis.</p> <p>Results</p> <p>The students' clinical management of the situation varied considerably. Students struggled to prioritise their actions where more than one response was required to a clinical cue and did not necessarily use mnemonics as heuristic devices to guide their actions. Driven by a response to single cues they also showed a reluctance to formulate a diagnosis based on inductive and deductive reasoning cycles. This meant they did not necessarily introduce new hypothetical ideas against which they might refute or confirm a diagnosis and thereby eliminate fixation error.</p> <p>Conclusions</p> <p>The students response demonstrated that a number of clinical skills require updating on a regular basis including: fundal massage technique, the use of emergency standing order drugs, communication and delegation of tasks to others in an emergency and working independently until help arrives. Heuristic devices helped the students to evaluate their interventions to illuminate what else could be done whilst they awaited the emergency team. They did not necessarily serve to prompt the students' or help them plan care prospectively. The limitations of the study are critically explored along with the pedagogic implications for initial training and continuing professional development.</p

Pancreatic cancer: Surgery is a feasible therapeutic option for elderly patients

<p>Abstract</p> <p>Background</p> <p>Compromised physiological reserve, comorbidities, and the natural history of pancreatic cancer may deny pancreatic resection from elderly patients. We evaluated outcomes of elderly patients amenable to pancreatic surgery.</p> <p>Methods</p> <p>The medical records of all patients who underwent pancreatic resection at our institution (1995-2007) were retrospectively reviewed. Patient, tumor, and outcomes characteristics in elderly patients aged ≥ 70 years were compared to a younger cohort (<70y).</p> <p>Results</p> <p>Of 460 patients who had surgery for pancreatic neoplasm, 166 (36%) aged ≥ 70y. Compared to patients < 70y (n = 294), elderly patients had more associated comorbidities; 72% vs. 43% (p = 0.01) and a higher rate of malignant pathologies; 73% vs. 59% (p = 0.002). Operative time and blood products consumption were comparable; however, elderly patients had more post-operative complications (41% vs. 29%; p = 0.01), longer hospital stay (26.2 vs. 19.7 days; p < 0.0001), and a higher incidence of peri-operative mortality (5.4% vs. 1.4%; p = 0.01). Multivariable analysis identified age ≥ 70y as an independent predictor of shorter disease-specific survival (DSS) among patients who had surgery for pancreatic adenocarcinoma (n = 224). Median DSS for patients aged ≥ 70y vs. < 70y were 15 months (SE: 1.6) vs. 20 months (SE: 3.4), respectively (p = 0.05). One, two, and 5-Y DSS rates for the cohort of elderly patients were 58%, 36% and 23%, respectively.</p> <p>Conclusions</p> <p>Properly selected elderly patients can undergo pancreatic resection with acceptable post-operative morbidity and mortality rates. Long term survival is achievable even in the presence of adenocarcinoma and therefore surgery should be seriously considered in these patients.</p

Greedy Solution of Ill-Posed Problems: Error Bounds and Exact Inversion

The orthogonal matching pursuit (OMP) is an algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the solution of ill-posed inverse problems in general and in particular for two deconvolution examples from mass spectrometry and digital holography respectively. In sparse approximation problems one often has to deal with the problem of redundancy of a dictionary, i.e. the atoms are not linearly independent. However, one expects them to be approximatively orthogonal and this is quantified by the so-called incoherence. This idea cannot be transfered to ill-posed inverse problems since here the atoms are typically far from orthogonal: The ill-posedness of the operator causes that the correlation of two distinct atoms probably gets huge, i.e. that two atoms can look much alike. Therefore one needs conditions which take the structure of the problem into account and work without the concept of coherence. In this paper we develop results for exact recovery of the support of noisy signals. In the two examples in mass spectrometry and digital holography we show that our results lead to practically relevant estimates such that one may check a priori if the experimental setup guarantees exact deconvolution with OMP. Especially in the example from digital holography our analysis may be regarded as a first step to calculate the resolution power of droplet holography

Zebrafish usp39 Mutation Leads to rb1 mRNA Splicing Defect and Pituitary Lineage Expansion

Loss of retinoblastoma (Rb) tumor suppressor function is associated with human malignancies. Molecular and genetic mechanisms responsible for tumorigenic Rb downregulation are not fully defined. Through a forward genetic screen and positional cloning, we identified and characterized a zebrafish ubiquitin specific peptidase 39 (usp39) mutation, the yeast and human homolog of which encodes a component of RNA splicing machinery. Zebrafish usp39 mutants exhibit microcephaly and adenohypophyseal cell lineage expansion without apparent changes in major hypothalamic hormonal and regulatory signals. Gene expression profiling of usp39 mutants revealed decreased rb1 and increased e2f4, rbl2 (p130), and cdkn1a (p21) expression. Rb1 mRNA overexpression, or antisense morpholino knockdown of e2f4, partially reversed embryonic pituitary expansion in usp39 mutants. Analysis of pre-mRNA splicing status of critical cell cycle regulators showed misspliced Rb1 pre-mRNA resulting in a premature stop codon. These studies unravel a novel mechanism for rb1 regulation by a neuronal mRNA splicing factor, usp39. Zebrafish usp39 regulates embryonic pituitary homeostasis by targeting rb1 and e2f4 expression, respectively, contributing to increased adenohypophyseal sensitivity to these altered cell cycle regulators. These results provide a mechanism for dysregulated rb1 and e2f4 pathways that may result in pituitary tumorigenesis