Accurate detection of moving targets via random sensor arrays and Kerdock codes

The detection and parameter estimation of moving targets is one of the most important tasks in radar. Arrays of randomly distributed antennas have been popular for this purpose for about half a century. Yet, surprisingly little rigorous mathematical theory exists for random arrays that addresses fundamental question such as how many targets can be recovered, at what resolution, at which noise level, and with which algorithm. In a different line of research in radar, mathematicians and engineers have invested significant effort into the design of radar transmission waveforms which satisfy various desirable properties. In this paper we bring these two seemingly unrelated areas together. Using tools from compressive sensing we derive a theoretical framework for the recovery of targets in the azimuth-range-Doppler domain via random antennas arrays. In one manifestation of our theory we use Kerdock codes as transmission waveforms and exploit some of their peculiar properties in our analysis. Our paper provides two main contributions: (i) We derive the first rigorous mathematical theory for the detection of moving targets using random sensor arrays. (ii) The transmitted waveforms satisfy a variety of properties that are very desirable and important from a practical viewpoint. Thus our approach does not just lead to useful theoretical insights, but is also of practical importance. Various extensions of our results are derived and numerical simulations confirming our theory are presented

3-Factor-criticality in double domination edge critical graphs

A vertex subset $S$ of a graph $G$ is a double dominating set of $G$ if $|N[v]\cap S|\geq 2$ for each vertex $v$ of $G$, where $N[v]$ is the set of the vertex $v$ and vertices adjacent to $v$. The double domination number of $G$, denoted by $\gamma_{\times 2}(G)$, is the cardinality of a smallest double dominating set of $G$. A graph $G$ is said to be double domination edge critical if $\gamma_{\times 2}(G+e)<\gamma_{\times 2}(G)$ for any edge $e \notin E$. A double domination edge critical graph $G$ with $\gamma_{\times 2}(G)=k$ is called $k$-$\gamma_{\times 2}(G)$-critical. A graph $G$ is $r$-factor-critical if $G-S$ has a perfect matching for each set $S$ of $r$ vertices in $G$. In this paper we show that $G$ is 3-factor-critical if $G$ is a 3-connected claw-free $4$-$\gamma_{\times 2}(G)$-critical graph of odd order with minimum degree at least 4 except a family of graphs.Comment: 14 page

Studies on Escherichia Coli Cell Division: Overexpression, Purification, and Quantitative Determination offtsA Protein.

FtsA is an essential cell division protein which is synthesized in minute amounts in Escherichia coli. To study the effects of overexpressing ftsA on the phenotype of E. coli cells, DNA fragments encoding the ftsA gene were subcloned downstream of a lac or a tac promoter in two plasmids. High-level expression of the ftsA gene from these promoters inhibited normal cell septation and caused the cells to become long, nonseptate filaments. Continued overexpression of ftsA resulted in the filaments developing spherical bulges up to 4 um in diameter. It is suggested that these bulges may emanate from septation sites because they were evenly spaced in relation to one another and to the cell poles. Observations of thin sections by electron microscopy demonstrated that these bulges contained small electron dense regions and large electron-lucent plate-like inclusions. A finding that the bulging filamentous cells contain more hexosamine per mass than control cells suggests that abnormal peptidoglycan synthesis might be occurring. FtsA protein was isolated from ftsA-overexpressing cells for the purpose of raising monoclonal antibodies. Mice were immunized with an FtsA fraction and their spleen cells were fused to Sp2/0-AG14 mouse myeloma cells. Hybrid cells were screened and two clones were positively identified as FtsA monoclonal antibody producers by enzyme-linked immunosorbant assays (ELISA) and Western blotting. The isolation of FtsA monoclonal antibodies provided a way to determine the average number of FtsA molecules per cell, that was between 50 and 200. In contrast, the concentration of FtsA normalized to total cell protein was constant over a wide range of growth rates. This finding supports the hypothesis of FtsA protein, being a stoichiometric component in septation