Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms

This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and coordinate-wise optimality. These conditions are then used to derive three numerical algorithms aimed at finding points satisfying the resulting optimality criteria: the iterative hard thresholding method and the greedy and partial sparse-simplex methods. The first algorithm is essentially a gradient projection method while the remaining two algorithms are of coordinate descent type. The theoretical convergence of these methods and their relations to the derived optimality conditions are studied. The algorithms and results are illustrated by several numerical examples.Comment: submitted to SIAM Optimizatio

GESPAR: Efficient Phase Retrieval of Sparse Signals

We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of the Fourier phase information, this problem is ill-posed. Therefore, prior information on the signal is needed in order to enable its recovery. In this work we consider the case in which the signal is known to be sparse, i.e., it consists of a small number of nonzero elements in an appropriate basis. We propose a fast local search method for recovering a sparse signal from measurements of its Fourier transform (or other linear transform) magnitude which we refer to as GESPAR: GrEedy Sparse PhAse Retrieval. Our algorithm does not require matrix lifting, unlike previous approaches, and therefore is potentially suitable for large scale problems such as images. Simulation results indicate that GESPAR is fast and more accurate than existing techniques in a variety of settings.Comment: Generalized to non-Fourier measurements, added 2D simulations, and a theorem for convergence to stationary poin

Acceptable costs and risk adjustment: policy choices and ethical trade-offs

The main objective of risk adjustment in systems of regulated competition on health insurance markets is the removal of incentives for undesirable risk selection. We introduce a simple conceptual framework to clarify how the definition of "acceptable costs" and the distinction between legitimate and illegitimate risk adjusters imply difficult ethical trade-offs between equity, avoidance of undesirable risk selection and cost-effectiveness. Focusing on the situation in Belgium, Germany, Israel, the Netherlands and Switzerland, we show how differences in the importance attached to solidarity and in the beliefs about market efficiency, have led to different decisions with respect to the definition of the basic benefits package, the choice of risk-adjusters, the possibilities of managed care, the degree of consumer choice and the relative importance of income-related financing sources in the overall system.

Thermal Monitoring of Embankment Dams by Fiber Optics

International audienceInternal erosion is the main cause of failure of earthen hydraulic structures. Moreover, it is often difficult for the operator to detect internal erosion at an early stage. For the last twenty years, leakage detection by thermometry has been developed mainly in Europe. The principle is based on the fact that a leakage through an embankment dam changes its temperature field. In this regard, fiber optics buried in the structures can be used as temperature sensors. Their principal advantage is distributed temperature measurements, at every meter along their length, and over long distances. Indeed, once deployed, optical fiber proves to be an effective mean of probing several kilometers, making it extremely useful for monitoring dikes. Various methods have been developed for analysis of temperature data acquired by these powerful sensors. Thesephysico-statistical and signal processing methods allow to propose a system for "early warning" or for long-term monitoring. Based on the results of several tests at controlled and industrial sites, this presentation will demonstrate the improvement of this surveillance methodology for the safety procedures of embankment dam

The problem of globalization

There is a general consensus that the contemporary world is best under-stood through the prism of globalization. This view is shared by most social scientists, politicians, journalists, businesses, and indeed broad sectors of the general population. Opinions differ as to whether global-ization is a positive or a negative development, but there is general agreement that whatever is going on is either a symptom or a consequence of globalization. There are many good reasons for this view. The number of passengers on scheduled international flights has risen by a factor of six between 1975 and 2000. The number of international tourist arrivals rose by three and a half times during the same period. Much less happily, the number of internationally displaced refugees rose by around 50 percent in the 20 years before 2000. During the quarter of a century after 1975, the duration of international voice telephone calls rose by around 25 times. We could go on multiplying such striking figures i

Surgical closure of spinal cerebrospinal fluid leaks improves symptoms in patients with superficial siderosis.

BACKGROUND AND PURPOSE Spinal cerebrospinal fluid (CSF) leaks may cause a myriad of symptoms, most common being orthostatic headache. In addition, ventral spinal CSF leaks are a possible etiology of superficial siderosis (SS), a rare condition characterized by hemosiderin deposits in the central nervous system (CNS). The classical presentation of SS involves ataxia, bilateral hearing loss, and myelopathy. Unfortunately, treatment options are scarce. This study was undertaken to evaluate whether microsurgical closure of CSF leaks can prevent further clinical deterioration or improve symptoms of SS. METHODS This cohort study was conducted using data from a prospectively maintained database in two large spontaneous intracranial hypotension (SIH) referral centers in Germany and Switzerland of patients who meet the modified International Classification of Headache Disorders, 3rd edition criteria for SIH. Patients with spinal CSF leaks were screened for the presence of idiopathic infratentorial symmetric SS of the CNS. RESULTS Twelve patients were included. The median latency between the onset of orthostatic headaches and symptoms attributed to SS was 9.5 years. After surgical closure of the underlying spinal CSF leak, symptoms attributed to SS improved in seven patients and remained stable in three. Patients who presented within 1 year after the onset of SS symptoms improved, but those who presented in 8-12 years did not improve. We could show a significant association between patients with spinal longitudinal extrathecal collections and SS. CONCLUSIONS Long-standing untreated ventral spinal CSF leaks can lead to SS of the CNS, and microsurgical sealing of spinal CSF leaks might stop progression and improve symptoms in patients with SS in a time-dependent manner

Investigation of attentional bias in obsessive compulsive disorder with and without depression in visual search

Copyright: © 2013 Morein-Zamir et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are creditedWhether Obsessive Compulsive Disorder (OCD) is associated with an increased attentional bias to emotive stimuli remains controversial. Additionally, it is unclear whether comorbid depression modulates abnormal emotional processing in OCD. This study examined attentional bias to OC-relevant scenes using a visual search task. Controls, non-depressed and depressed OCD patients searched for their personally selected positive images amongst their negative distractors, and vice versa. Whilst the OCD groups were slower than healthy individuals in rating the images, there were no group differences in the magnitude of negative bias to concern-related scenes. A second experiment employing a common set of images replicated the results on an additional sample of OCD patients. Although there was a larger bias to negative OC-related images without pre-exposure overall, no group differences in attentional bias were observed. However, OCD patients subsequently rated the images more slowly and more negatively, again suggesting post-attentional processing abnormalities. The results argue against a robust attentional bias in OCD patients, regardless of their depression status and speak to generalized difficulties disengaging from negative valence stimuli. Rather, post-attentional processing abnormalities may account for differences in emotional processing in OCD.Peer reviewedFinal Published versio