This is a preliminary version of a Chapter on Algebraic Algorithms in the up-

Abstract—Traditional radar sensing typically employs matched filtering between the received signal and the shape of the transmitted pulse. Matched filtering is conventionally carried out digitally, after sampling the received analog signals. Here, principles from classic sampling theory are generally employed, requiring that the received signals be sampled at twice their baseband bandwidth. The resulting sampling rates necessary for correlation based radar systems become quite high, as growing demands for target distinction capability and spatial resolution stretch the bandwidth of the transmitted pulse. The large amounts of sampled data also necessitate vast memory capacity. In addition, real-time processing of the data typically results in high power consumption. Recently, new approaches for radar sensing and estimation were introduced, based on the Finite Rate of Innovation and Xampling frameworks. Exploiting the parametric nature of the radar problem, these techniques allow significant reduction in sampling rate, implying potential power savings, while maintaining the systems estimation capabilities at sufficiently high signal-to-noise ratios. Here we present for the first time a design and implementation of a Xampling based hardware prototype that allows sampling of radar signals at rates much lower than Nyquist. We demonstrate by real-time analog experiments that our system is able to maintain reasonable recovery capabilities, while sampling radar signals that require sampling at a rate of about 30MHz at a total rate of 1MHz.

Algebraic algorithms deal with numbers, vectors, matrices, polynomials, for-mal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matri-ces and polynomials is fundamental for modern computations

Digital signatures are an important primitive for building secure systems and are used in most real world security protocols. However, almost all popular signature schemes are either based on the factoring as-sumption (RSA) or the hardness of the discrete logarithm problem (DSA/ECDSA). In the case

legacy queries and updates under schema and integrity constraints evolution. The PRISM/PRISM++ approach consists in providing the users with a set of SQL-based Schema Modification Opera-tors (SMOs), which describe how the tables in the old schema are modified into those in the new schema. In order to sup

Commutative, idempotent groupoids and the

. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1-bit CS framework leads us to scenarios where it may be more appropriate to reduce bit-depth instead of sampling rate. We find

and backchase

Abstract | This review provides an introduction to Sup-

for mean-square stabilization are presented, which reveal signal-to-noise ratio requirements for stabilization which are tight in certain class of settings. Optimal linear policies are constructed, global optimality and sub-optimality of such policies are investigated in a variety of settings. We also