Technion – Israel Institute of Technology

About: Technion – Israel Institute of Technology is a education organization based out in Haifa, Israel. It is known for research contribution in the topics: Population & Upper and lower bounds. The organization has 31714 authors who have published 79377 publications receiving 2603976 citations. The organization is also known as: Technion Israel Institute of Technology & Ṭekhniyon, Makhon ṭekhnologi le-Yiśraʼel.

Robust Recovery of Signals From a Structured Union of Subspaces

Abstract: Traditional sampling theories consider the problem of reconstructing an unknown signal x from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that x lies in a known subspace. Recently, there has been growing interest in nonlinear but structured signal models, in which x lies in a union of subspaces. In this paper, we develop a general framework for robust and efficient recovery of such signals from a given set of samples. More specifically, we treat the case in which x lies in a sum of k subspaces, chosen from a larger set of m possibilities. The samples are modeled as inner products with an arbitrary set of sampling functions. To derive an efficient and robust recovery algorithm, we show that our problem can be formulated as that of recovering a block-sparse vector whose nonzero elements appear in fixed blocks. We then propose a mixed lscr2/lscr1 program for block sparse recovery. Our main result is an equivalence condition under which the proposed convex algorithm is guaranteed to recover the original signal. This result relies on the notion of block restricted isometry property (RIP), which is a generalization of the standard RIP used extensively in the context of compressed sensing. Based on RIP, we also prove stability of our approach in the presence of noise and modeling errors. A special case of our framework is that of recovering multiple measurement vectors (MMV) that share a joint sparsity pattern. Adapting our results to this context leads to new MMV recovery methods as well as equivalence conditions under which the entire set can be determined efficiently.

Mutual Information and Minimum Mean-square Error in Gaussian Channels

Abstract: This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE estimation. This fundamental information-theoretic result has an unexpected consequence in continuous-time nonlinear estimation: For any input signal with finite power, the causal filtering MMSE achieved at SNR is equal to the average value of the noncausal smoothing MMSE achieved with a channel whose signal-to-noise ratio is chosen uniformly distributed between 0 and SNR.

Optical Spatial Solitons and Their Interactions: Universality and Diversity.

Abstract: Spatial solitons, beams that do not spread owing to diffraction when they propagate, have been demonstrated to exist by virtue of a variety of nonlinear self-trapping mechanisms. Despite the diversity of these mechanisms, many of the features of soliton interactions and collisions are universal. Spatial solitons exhibit a richness of phenomena not found with temporal solitons in fibers, including effects such as fusion, fission, annihilation, and stable orbiting in three dimensions. Here the current state of knowledge on spatial soliton interactions is reviewed.

Complementary Feeding: A Commentary by the ESPGHAN Committee on Nutrition

Abstract: This position paper on complementary feeding summarizes evidence for health effects of complementary foods. It focuses on healthy infants in Europe. After reviewing current knowledge and practices, we have formulated these conclusions: Exclusive or full breast-feeding for about 6 months is a desirable goal. Complementary feeding (ie, solid foods and liquids other than breast milk or infant formula and follow-on formula) should not be introduced before 17 weeks and not later than 26 weeks. There is no convincing scientific evidence that avoidance or delayed introduction of potentially allergenic foods, such as fish and eggs, reduces allergies, either in infants considered at increased risk for the development of allergy or in those not considered to be at increased risk. During the complementary feeding period, >90% of the iron requirements of a breast-fed infant must be met by complementary foods, which should provide sufficient bioavailable iron. Cow's milk is a poor source of iron and should not be used as the main drink before 12 months, although small volumes may be added to complementary foods. It is prudent to avoid both early ( or=7 months) introduction of gluten, and to introduce gluten gradually while the infant is still breast-fed, inasmuch as this may reduce the risk of celiac disease, type 1 diabetes mellitus, and wheat allergy. Infants and young children receiving a vegetarian diet should receive a sufficient amount ( approximately 500 mL) of breast milk or formula and dairy products. Infants and young children should not be fed a vegan diet.