The cyclicality of cash flow and investment in U.S. manufacturing

Cash flow ; Manufactures

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

Simultaneous sparse approximation via greedy pursuit

A simple sparse approximation problem requests an approximation of a given input signal as a linear combination of T elementary signals drawn from a large, linearly dependent collection. An important generalization is simultaneous sparse approximation. Now one must approximate several input signals at once using different linear combinations of the same T elementary signals. This formulation appears, for example, when analyzing multiple observations of a sparse signal that have been contaminated with noise. A new approach to this problem is presented here: a greedy pursuit algorithm called simultaneous orthogonal matching pursuit. The paper proves that the algorithm calculates simultaneous approximations whose error is within a constant factor of the optimal simultaneous approximation error. This result requires that the collection of elementary signals be weakly correlated, a property that is also known as incoherence. Numerical experiments demonstrate that the algorithm often succeeds, even when the inputs do not meet the hypotheses of the proof

Globalization and National Sovereignty: Controlling the International Food Supply in the Age of Biotechnology

This article examines the biotechnology industry in the area of genetically modified organisms (GMOs) in foods through the lens of globalization and national sovereignty. Does the World Trade Organization (WTO) have the authority to compel the European Union (EU) to lift GMO bans, or should another supranational organization be formed to regulate the world’s food supply as a scientific and policy-making entity? What implications does the WTO’s decision on the food trade dispute have on state sovereignty, nation-state control and regulation of its food supply, and future multilateral environmental and trade agreements? This article discusses GMO’s historic, scientific, and environmental impacts, how globalization and biotechnology have changed the world food supply, and how these developments affect free trade. In addition, this article explores the regulatory reach of organizations such as the WTO, World Health Organization (WHO), and the Food and Agriculture Organization of the United Nations (FAO) on global food security. Finally, this article analyzes the future of the biotechnology industry and GMOs, considering the impact of the WTO’s decisions on developing nations, food labeling, nation- state control and, ultimately, its own credibility

Pos- en telekommunikasie in Suid-Afrika en elders in Afrika

Dit is vir ons ’n voorreg om ’n bydrae — beskeie soos dit mag wees — te kan Iewer tot 'n oorsig van ons land se posen telekommunikasiedienste. Aan prof. Coetzee is ons dank verskuldig vir 'n baie interessante en insiggewende inleidende oorsig. Ons het met groot belangstelling daarop gelet en is veral getref deur sy s telling dat kommunikasiemediums soos die lugvaart en die radio deur sommige van die nuwe Afrikastate aangegryp word as „bewyse” van hulle pas verkree onafhanklikheid en selfbeskikkingsreg. Met ander woorde, as statussimbole op nasionale vlak

Approximate Sparse Recovery: Optimizing Time and Measurements

An approximate sparse recovery system consists of parameters $k,N$, an $m$-by-$N$ measurement matrix, $\Phi$, and a decoding algorithm, $\mathcal{D}$. Given a vector, $x$, the system approximates $x$ by $\widehat x =\mathcal{D}(\Phi x)$, which must satisfy $\| \widehat x - x\|_2\le C \|x - x_k\|_2$, where $x_k$ denotes the optimal $k$-term approximation to $x$. For each vector $x$, the system must succeed with probability at least 3/4. Among the goals in designing such systems are minimizing the number $m$ of measurements and the runtime of the decoding algorithm, $\mathcal{D}$. In this paper, we give a system with $m=O(k \log(N/k))$ measurements--matching a lower bound, up to a constant factor--and decoding time $O(k\log^c N)$, matching a lower bound up to $\log(N)$ factors. We also consider the encode time (i.e., the time to multiply $\Phi$ by $x$), the time to update measurements (i.e., the time to multiply $\Phi$ by a 1-sparse $x$), and the robustness and stability of the algorithm (adding noise before and after the measurements). Our encode and update times are optimal up to $\log(N)$ factors