How to find real-world applications for compressive sensing

The potential of compressive sensing (CS) has spurred great interest in the research community and is a fast growing area of research. However, research translating CS theory into practical hardware and demonstrating clear and significant benefits with this hardware over current, conventional imaging techniques has been limited. This article helps researchers to find those niche applications where the CS approach provides substantial gain over conventional approaches by articulating lessons learned in finding one such application; sea skimming missile detection. As a proof of concept, it is demonstrated that a simplified CS missile detection architecture and algorithm provides comparable results to the conventional imaging approach but using a smaller FPA. The primary message is that all of the excitement surrounding CS is necessary and appropriate for encouraging our creativity but we all must also take off our "rose colored glasses" and critically judge our ideas, methods and results relative to conventional imaging approaches.Comment: 10 page

Renormalization group analysis of turbulence

The objective is to understand and extend a recent theory of turbulence based on dynamic renormalization group (RNG) techniques. The application of RNG methods to hydrodynamic turbulence was explored most extensively by Yakhot and Orszag (1986). An eddy viscosity was calculated which was consistent with the Kolmogorov inertial range by systematic elimination of the small scales in the flow. Further, assumed smallness of the nonlinear terms in the redefined equations for the large scales results in predictions for important flow constants such as the Kolmogorov constant. It is emphasized that no adjustable parameters are needed. The parameterization of the small scales in a self-consistent manner has important implications for sub-grid modeling

Local and Nonlocal Dispersive Turbulence

We consider the evolution of a family of 2D dispersive turbulence models. The members of this family involve the nonlinear advection of a dynamically active scalar field, the locality of the streamfunction-scalar relation is denoted by $\alpha$, with smaller $\alpha$ implying increased locality. The dispersive nature arises via a linear term whose strength is characterized by a parameter $\epsilon$. Setting $0 < \epsilon \le 1$, we investigate the interplay of advection and dispersion for differing degrees of locality. Specifically, we study the forward (inverse) transfer of enstrophy (energy) under large-scale (small-scale) random forcing. Straightforward arguments suggest that for small $\alpha$ the scalar field should consist of progressively larger eddies, while for large $\alpha$ the scalar field is expected to have a filamentary structure resulting from a stretch and fold mechanism. Confirming this, we proceed to forced/dissipative dispersive numerical experiments under weakly non-local to local conditions. For $\epsilon \sim 1$, there is quantitative agreement between non-dispersive estimates and observed slopes in the inverse energy transfer regime. On the other hand, forward enstrophy transfer regime always yields slopes that are significantly steeper than the corresponding non-dispersive estimate. Additional simulations show the scaling in the inverse regime to be sensitive to the strength of the dispersive term : specifically, as $\epsilon$ decreases, the inertial-range shortens and we also observe that the slope of the power-law decreases. On the other hand, for the same range of $\epsilon$ values, the forward regime scaling is fairly universal.Comment: 19 pages, 8 figures. Significantly revised with additional result

Reading and proclaiming the birth narratives from Luke and Matthew : a study in empirical theology amongst curates and their training incumbents employing the SIFT method

Drawing on Jungian psychological type theory, the SIFT method of biblical hermeneutics and liturgical preaching suggests that the reading and proclaiming of scripture reflects the psychological type preferences of the reader and preacher. This thesis is examined amongst two samples of curates and training incumbents (N = 23, 27), serving in one Diocese of the Church of England, who completed the Myers-Briggs Type Indicator. Firstly, the narrative of the shepherds from Luke was discussed by groups organised according to scores on the perceiving process. In accordance with the theory, sensing types focused on details in the passage, but could reach no consensus on the larger picture, and intuitive types quickly identified an imaginative, integrative theme, but showed little interest in the details. Secondly, the narrative of the massacre of the infants from Matthew was discussed by groups organised according to scores on the judging process. In accordance with theory, the thinking types identified and analysed the big themes raised by the passage (political power, theodicy, obedience), whilst the feeling types placed much more emphasis on the impact that the passage may have on members of the congregation mourning the death of their child or grandchild

An Opportunistic Approach to Adding Value to a Photograph Collection

The Semantic Web can, among other things, be used for photograph annotation. Many implementations of this idea exist, but all are limited by the fact that a human must manually create the annotations for the photographs, often using a program with which he or she is not familiar. This poster discusses an opportunistic method of photograph annotation that uses logical inference in conjunction with existing data from various sources in order to obtain information about the images being annotated

On the Two-point Correlation of Potential Vorticity in Rotating and Stratified Turbulence

A framework is developed to describe the two-point statistics of potential vorticity in rotating and stratified turbulence as described by the Boussinesq equations. The Karman-Howarth equation for the dynamics of the two-point correlation function of potential vorticity reveals the possibility of inertial-range dynamics in certain regimes in the Rossby, Froude, Prandtl and Reynolds number parameters. For the case of large Rossby and Froude numbers, and for the case of quasi-geostrophic dynamics, a linear scaling law with 2/3 prefactor is derived for the third-order mixed correlation between potential vorticity and velocity, a result that is analogous to the Kolmogorov 4/5-law for the third-order velocity structure function in turbulence theory.Comment: 10 pages, to appear in Journal of Fluid Mechanics (2006