Application of semidefinite programming to maximize the spectral gap produced by node removal

The smallest positive eigenvalue of the Laplacian of a network is called the spectral gap and characterizes various dynamics on networks. We propose mathematical programming methods to maximize the spectral gap of a given network by removing a fixed number of nodes. We formulate relaxed versions of the original problem using semidefinite programming and apply them to example networks.Comment: 1 figure. Short paper presented in CompleNet, Berlin, March 13-15 (2013

Coordination in multiagent systems and Laplacian spectra of digraphs

Constructing and studying distributed control systems requires the analysis of the Laplacian spectra and the forest structure of directed graphs. In this paper, we present some basic results of this analysis partially obtained by the present authors. We also discuss the application of these results to decentralized control and touch upon some problems of spectral graph theory.Comment: 15 pages, 2 figures, 40 references. To appear in Automation and Remote Control, Vol.70, No.3, 200

Different species of basil need different ammonium to nitrate ratio in hydroponics' system

Basil is a very important medicinal plant and culinary spice, and is marketed fresh, dried or frozen. In crop nutrition, nitrogen is essential for plant growth and as a macro-element, is part of the proteins’ structure and participates in the metabolic processes involved in the synthesis and energy transfer. It has been shown that a balance between ammonium and nitrate favors plant growth and that the degree of benefit varies among crops. This study was conducted to evaluate the growth of two varieties of basil in function of four nutrient solutions containing different NH4+/NO3- ratios. Results showed that different variety response differently to nutrient solution. Although the highest yield in both varieties (sweet and purple) was obtained when fed by nutrient solution without ammonium but their response on quality indices were different due to nitrate ammonium ratio in nutrient solutions. The highest total phenol content of sweet and purple basil was 92 and 100 mg gallic acid equivalent per gram of dry weight respectively, while the highest antioxidant capacity was obtained in purple variety grown in nutrient solution 2 (NH4+:1/NO3:4) and the lowest value were related to sweet variety with the same nutrient solution. Moderate content of total nitrogen can be suitable for sweet variety while for purple variety nutrient solution with low amount of ammonium can be more suitable