Comparing Mean Field and Euclidean Matching Problems

Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional systems. Our focus here is on minimum matching problems, because they are computationally tractable while both frustrated and disordered. We first study a mean field model taking the link lengths between points to be independent random variables. For this model we find perfect agreement with the results of a replica calculation. Then we study the case where the points to be matched are placed at random in a d-dimensional Euclidean space. Using the mean field model as an approximation to the Euclidean case, we show numerically that the mean field predictions are very accurate even at low dimension, and that the error due to the approximation is O(1/d^2). Furthermore, it is possible to improve upon this approximation by including the effects of Euclidean correlations among k link lengths. Using k=3 (3-link correlations such as the triangle inequality), the resulting errors in the energy density are already less than 0.5% at d>=2. However, we argue that the Euclidean model's 1/d series expansion is beyond all orders in k of the expansion in k-link correlations.Comment: 11 pages, 1 figur

Spatial Compressive Sensing for MIMO Radar

We study compressive sensing in the spatial domain to achieve target localization, specifically direction of arrival (DOA), using multiple-input multiple-output (MIMO) radar. A sparse localization framework is proposed for a MIMO array in which transmit and receive elements are placed at random. This allows for a dramatic reduction in the number of elements needed, while still attaining performance comparable to that of a filled (Nyquist) array. By leveraging properties of structured random matrices, we develop a bound on the coherence of the resulting measurement matrix, and obtain conditions under which the measurement matrix satisfies the so-called isotropy property. The coherence and isotropy concepts are used to establish uniform and non-uniform recovery guarantees within the proposed spatial compressive sensing framework. In particular, we show that non-uniform recovery is guaranteed if the product of the number of transmit and receive elements, MN (which is also the number of degrees of freedom), scales with K(log(G))^2, where K is the number of targets and G is proportional to the array aperture and determines the angle resolution. In contrast with a filled virtual MIMO array where the product MN scales linearly with G, the logarithmic dependence on G in the proposed framework supports the high-resolution provided by the virtual array aperture while using a small number of MIMO radar elements. In the numerical results we show that, in the proposed framework, compressive sensing recovery algorithms are capable of better performance than classical methods, such as beamforming and MUSIC.Comment: To appear in IEEE Transactions on Signal Processin

AN ASSESSMENT OF DEFICIENCY PAYMENTS TO MILK PRODUCERS IN JAPAN

This article represents an econometric assessment of the role that deficiency payments have played in developing the Japanese fluid and manufacturing milk markets and the potential effects of reducing deficiency payments on these milk markets. Principal findings are: (a) an historical simulation of the model without deficiency payments and import quotas indicates that these measures have reduced the variation in milk prices that would have otherwise occurred under this model, and price supports through these measures have resulted in greater milk production than would have accrued without price supports; and (b) a reduction in deficiency payments beginning in 1998 results in a decrease in milk prices and manufacturing milk supply and an increase in fluid milk supply and dairy imports, but fluid milk prices soon stop declining. The policy implications of such a decline in deficiency payments are discussed.Agricultural and Food Policy, Livestock Production/Industries,

Distribution of the genus Alexandrium (Halim) and paralytic shellfish toxins along the coastline of New South Wales, Australia

Blooms of Alexandrium species, in particular the species Alexandrium catenella, accounted for more than 50% of algal related, shellfish aquaculture harvest zone closures in New South Wales (NSW) Australia since 2005. While there are indications that species of Alexandrium are more abundant than they were formerly, there is little data available on the spatial and temporal distribution and abundance of the genus in NSW. A six and a half year dataset comprising a total of 8649 fortnightly samples from 31 estuaries spread over 2000. km of NSW coastline was analysed. The greatest abundances of Alexandrium spp. were observed during the austral Spring and Summer, in estuaries in the mid and southern latitudes of the state. In identifying these high risk zones, we propose variables such as season, temperature, rainfall and estuarine flushing to be targeted in intensive site specific studies, to support the development of predictive tools for resource managers. © 2013 Elsevier Ltd