List decoding of noisy Reed-Muller-like codes

First- and second-order Reed-Muller (RM(1) and RM(2), respectively) codes are two fundamental error-correcting codes which arise in communication as well as in probabilistically-checkable proofs and learning. In this paper, we take the first steps toward extending the quick randomized decoding tools of RM(1) into the realm of quadratic binary and, equivalently, Z_4 codes. Our main algorithmic result is an extension of the RM(1) techniques from Goldreich-Levin and Kushilevitz-Mansour algorithms to the Hankel code, a code between RM(1) and RM(2). That is, given signal s of length N, we find a list that is a superset of all Hankel codewords phi with dot product to s at least (1/sqrt(k)) times the norm of s, in time polynomial in k and log(N). We also give a new and simple formulation of a known Kerdock code as a subcode of the Hankel code. As a corollary, we can list-decode Kerdock, too. Also, we get a quick algorithm for finding a sparse Kerdock approximation. That is, for k small compared with 1/sqrt{N} and for epsilon > 0, we find, in time polynomial in (k log(N)/epsilon), a k-Kerdock-term approximation s~ to s with Euclidean error at most the factor (1+epsilon+O(k^2/sqrt{N})) times that of the best such approximation

Algorithmic linear dimension reduction in the l_1 norm for sparse vectors

This paper develops a new method for recovering m-sparse signals that is simultaneously uniform and quick. We present a reconstruction algorithm whose run time, O(m log^2(m) log^2(d)), is sublinear in the length d of the signal. The reconstruction error is within a logarithmic factor (in m) of the optimal m-term approximation error in l_1. In particular, the algorithm recovers m-sparse signals perfectly and noisy signals are recovered with polylogarithmic distortion. Our algorithm makes O(m log^2 (d)) measurements, which is within a logarithmic factor of optimal. We also present a small-space implementation of the algorithm. These sketching techniques and the corresponding reconstruction algorithms provide an algorithmic dimension reduction in the l_1 norm. In particular, vectors of support m in dimension d can be linearly embedded into O(m log^2 d) dimensions with polylogarithmic distortion. We can reconstruct a vector from its low-dimensional sketch in time O(m log^2(m) log^2(d)). Furthermore, this reconstruction is stable and robust under small perturbations

Fluorescein angiography compared to three-dimensional measurements by the retinal thickness analyzer in classic choroidal neovascularization

Purpose: To compare and correlate imaging of classic subfoveal choroidal neovascularization (CNV) with noninvasive 3-dimensional imaging by the retinal thickness analyzer (RTA) to conventional fluorescein angiography (FA). Methods: A total of 29 eyes of 29 consecutive patients with predominantly classic CNV eligible for photodynamic therapy underwent FA and RTA imaging. The FA dimensions of the CNV were measured independently by two graders. With the RTA, masked to FA the size of the CNV itself as imaged in 3-dimensional reconstruction, the size of significantly thickened retina overlying the CNV and the maximum retinal thickness were measured. Results: The mean diameter of the CNV determined from 3-dimensional RTA reconstructions showed an excellent correlation with measurements from FA (r = 0.91, p < 0.001). The area of retinal thickening was by a mean of 0.7 mm in diameter larger and correlated moderately well with the size of the CNV on FA (r = 0.65, p < 0.001). In contrast, there was no correlation between the absolute retinal thickness and the CNV size on FA. Conclusions: Noninvasive quantitative mapping of predominantly classic CNV by RTA is feasible and also allows 3-dimensional measurement of the lesion itself. The results correlate well with FA assessment but visualize different properties of the disease. Copyright (c) 2007 S. Karger AG, Basel

nanoTRON: a Picasso module for MLP-based classification of super-resolution data

Motivation: Classification of images is an essential task in higher-level analysis of biological data. By bypassing the diffraction limit of light, super-resolution microscopy opened up a new way to look at molecular details using light microscopy, producing large amounts of data with exquisite spatial detail. Statistical exploration of data usually needs initial classification, which is up to now often performed manually. Results: We introduce nanoTRON, an interactive open-source tool, which allows super-resolution data classification based on image recognition. It extends the software package Picasso with the first deep learning tool with a graphic user interface

Brightest Cluster Galaxies at the Present Epoch

We have observed 433 z<=0.08 brightest cluster galaxies (BCGs) in a full-sky survey of Abell clusters. The BCG Hubble diagram is consistent to within 2% of a Omega_m=0.3, Lambda=0.7 Hubble relation. The L_m-alpha relation for BCGs, which uses alpha, the log-slope of the BCG photometric curve of growth, to predict metric luminosity, L_m, has 0.27 mag residuals. We measure central stellar velocity dispersions, sigma, of the BCGs, finding the Faber-Jackson relation to flatten as the metric aperture grows to include an increasing fraction of the total BCG luminosity. A 3-parameter "metric plane" relation using alpha and sigma together gives the best prediction of L_m, with 0.21 mag residuals. The projected spatial offset, r_x, of BCGs from the X-ray-defined cluster center is a gamma=-2.33 power-law over 1<r_x<10^3 kpc. The median offset is ~10 kpc, but ~15% of the BCGs have r_x>100 kpc. The absolute cluster-dispersion normalized BCG peculiar velocity |Delta V_1|/sigma_c follows an exponential distribution with scale length 0.39+/-0.03. Both L_m and alpha increase with sigma_c. The alpha parameter is further moderated by both the spatial and velocity offset from the cluster center, with larger alpha correlated with the proximity of the BCG to the cluster mean velocity or potential center. At the same time, position in the cluster has little effect on L_m. The luminosity difference between the BCG and second-ranked galaxy, M2, increases as the peculiar velocity of the BCG within the cluster decreases. Further, when M2 is a close luminosity "rival" of the BCG, the galaxy that is closest to either the velocity or X-ray center of the cluster is most likely to have the larger alpha. We conclude that the inner portions of the BCGs are formed outside the cluster, but interactions in the heart of the galaxy cluster grow and extend the envelopes of the BCGs.Comment: Accepted for publication in the Astrophysical Journa

Myomectomy as a pregnancy-preserving option in the carefully selected patient

Objectives: To present the indications for myomectomy during pregnancy and to discuss complications possibly related and unrelated to the procedure. Method and Results: A 33-year-old patient at 18 weeks of gestation underwent removal of a 1,570-gram symptomatic fundic myoma. Histologically the patient had a leiomyomatous neoplasm of uncertain malignant potential. The pregnancy was continued under sequential observation with magnetic resonance imaging and ultrasound. At 36 weeks of gestation a healthy girl with an upper extremity limb defect was born via cesarean section. Follow-up of the mother and the child was uneventful. Conclusions: Certain known risk factors in pregnant women with myomas can predispose to complications during pregnancy. Women with such risk factors or women who have failed medical therapy should be offered the option of undergoing myomectomy as a pregnancy-preserving procedure. Copyright (C) 2002 S. Karger AG, Basel

The moral muteness of managers: an Anglo-American phenomenon? German and British managers and their moral reasoning about environmental sustainability in business

Several studies in the Anglo-American context have indicated that managers present themselves as morally neutral employees who act only in the best interest of the company by employing objective skills. The reluctance of managers to use moral arguments in business is further accentuated in the now common argument presented as a neutral fact that the company must always prioritise shareholder value. These and other commercial aims are seen as an objective reality in business, whilst questions about sustainability, environmental problems or fair trade are seen as emotional or moral ones; a phenomenon described as ‘moral muteness’. This research explores whether this ‘moral muteness’ is an Anglo-American phenomenon and/or whether managers in other countries - in this case Germany - might express themselves in a different way. The focus is on moral arguments around environmental sustainability and the implications of this study for cross-cultural management. This article is based on a qualitative, comparative cross-cultural study of British and German managers in the Food Retail and Energy Sectors. In line with the studies mentioned above, British managers placed a strong emphasis on their moral neutrality. In contrast, German managers tended to use moral arguments when discussing corporate greening, often giving such arguments more weight than financial arguments. Overall, the study suggests that the ‘moral muteness’ of managers is a British phenomenon and quite distinct from the German approach. The article ends in a short exploration of how this understanding can help managers better manage people, organisations and change across cultures