Convolutional compressed sensing using deterministic sequences

This is the author's accepted manuscript (with working title "Semi-universal convolutional compressed sensing using (nearly) perfect sequences"). The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, a new class of orthogonal circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain

It's My Turn ... Please, After You: An Experimental Study of Cooperation and Social Conventions

We introduce a class of two-player cooperation games where each player faces a binary decision, enter or exit. These games have a unique Nash equilibrium of entry. However, entry imposes a large enough negative externality on the other player such that the unique social optimum involves the player with the higher value to entry entering and the other player exiting. When the game is repeated and players' values to entry are private, cooperation admits the form of either taking turns entering or using a cutoff strategy and entering only for high private values of entry. Even with conditions that provide opportunities for unnoticed or non-punishable 'cheating', our empirical analysis including a simple strategy inference technique reveals that the Nash-equilibrium strategy is never the modal choice. In fact, most subjects employ the socially optimal symmetric cutoff strategy. These games capture the nature of cooperation in many economic and social situations such as bidding rings in auctions, competition for market share, labor supply decisions in the face of excess supply, queuing in line and courtship.cooperation, incomplete information, random payoffs, strategy inference, experimental economics.

New Sets of Optimal Odd-length Binary Z-Complementary Pairs

A pair of sequences is called a Z-complementary pair (ZCP) if it has zero aperiodic autocorrelation sums (AACSs) for time-shifts within a certain region, called zero correlation zone (ZCZ). Optimal odd-length binary ZCPs (OB-ZCPs) display closest correlation properties to Golay complementary pairs (GCPs) in that each OB-ZCP achieves maximum ZCZ of width (N+1)/2 (where N is the sequence length) and every out-of-zone AACSs reaches the minimum magnitude value, i.e. 2. Till date, systematic constructions of optimal OB-ZCPs exist only for lengths $2^{\alpha} \pm 1$, where $\alpha$ is a positive integer. In this paper, we construct optimal OB-ZCPs of generic lengths $2^\alpha 10^\beta 26^\gamma +1$ (where $\alpha,~ \beta, ~ \gamma$ are non-negative integers and $\alpha \geq 1$) from inserted versions of binary GCPs. The key leading to the proposed constructions is several newly identified structure properties of binary GCPs obtained from Turyn's method. This key also allows us to construct OB-ZCPs with possible ZCZ widths of $4 \times 10^{\beta-1} +1$, $12 \times 26^{\gamma -1}+1$ and $12 \times 10^\beta 26^{\gamma -1}+1$ through proper insertions of GCPs of lengths $10^\beta,~ 26^\gamma, \text{and } 10^\beta 26^\gamma$, respectively. Our proposed OB-ZCPs have applications in communications and radar (as an alternative to GCPs)

A direct construction of even length ZCPs with large ZCZ ratio

This paper presents a direct construction of aperiodic q-ary (q is a positive even integer) even length Z-complementary pairs (ZCPs) with large zero-correlation zone (ZCZ) width using generalised Boolean functions (GBFs). The applicability of ZCPs increases with the increasing value of ZCZ width, which plays a significant role in reducing interference in a communication system with asynchronous surroundings. For q = 2, the proposed ZCPs reduce to even length binary ZCPs (EB-ZCPs). However, to the best of the authors’ knowledge, the highest ZCZ ratio for even length ZCPs which are directly constructed to date using GBFs is 3/4. In the proposed construction, we provide even length ZCPs with ZCZ ratios 5/6 and 6/7, which are the largest ZCZ ratios achieved to date through direct construction.acceptedVersio

Finding approximate palindromes in strings

We introduce a novel definition of approximate palindromes in strings, and provide an algorithm to find all maximal approximate palindromes in a string with up to $k$ errors. Our definition is based on the usual edit operations of approximate pattern matching, and the algorithm we give, for a string of size $n$ on a fixed alphabet, runs in $O(k^2 n)$ time. We also discuss two implementation-related improvements to the algorithm, and demonstrate their efficacy in practice by means of both experiments and an average-case analysis

Non-stationary problem optimization using the primal-dual genetic algorithm

This article is posted here with permission from IEEE - Copyright @ 2003 IEEEGenetic algorithms (GAs) have been widely used for stationary optimization problems where the fitness landscape does not change during the computation. However, the environments of real world problems may change over time, which puts forward serious challenge to traditional GAs. In this paper, we introduce the application of a new variation of GA called the primal-dual genetic algorithm (PDGA) for problem optimization in nonstationary environments. Inspired by the complementarity and dominance mechanisms in nature, PDGA operates on a pair of chromosomes that are primal-dual to each other in the sense of maximum distance in genotype in a given distance space. This paper investigates an important aspect of PDGA, its adaptability to dynamic environments. A set of dynamic problems are generated from a set of stationary benchmark problems using a dynamic problem generating technique proposed in this paper. Experimental study over these dynamic problems suggests that PDGA can solve complex dynamic problems more efficiently than traditional GA and a peer GA, the dual genetic algorithm. The experimental results show that PDGA has strong viability and robustness in dynamic environments