A study of the time complexity of an Elitist Genetic Algorithm used for associating optical observations of MEO and GEO Space Debris

Currently several thousands of objects are being tracked in the MEO and GEO regions through optical means. The problem faced in this framework is that of Multiple Target Tracking (MTT). In this context both the correct associations among the observations, and the orbits of the objects have to be determined. The complexity of the MTT problem is defined by its dimension S. Where S stands for the number of ’fences’ used in the problem, each fence consists of a set of observations that all originate from dierent targets. For a dimension of S ˃ the MTT problem becomes NP-hard. As of now no algorithm exists that can solve an NP-hard problem in an optimal manner within a reasonable (polynomial) computation time. However, there are algorithms that can approximate the solution with a realistic computational e ort. To this end an Elitist Genetic Algorithm is implemented to approximately solve the S ˃ MTT problem in an e cient manner. Its complexity is studied and it is found that an approximate solution can be obtained in a polynomial time. With the advent of improved sensors and a heightened interest in the problem of space debris, it is expected that the number of tracked objects will grow by an order of magnitude in the near future. This research aims to provide a method that can treat the correlation and orbit determination problems simultaneously, and is able to e ciently process large data sets with minimal manual intervention.

Optical recording of calcium currents during impulse conduction in cardiac tissue

We explore the feasibility of obtaining a spatially resolved picture of Ca2+Ca2+ inward currents (ICaICa) in multicellular cardiac tissue by differentiating optically recorded Ca2+Ca2+ transients that accompany propagating action potentials. Patterned growth strands of neonatal rat ventricular cardiomyocytes were stained with the Ca2+Ca2+ indicators Fluo-4 or Fluo-4FF. Preparations were stimulated at 1 Hz, and Ca2+Ca2+ transients were recorded with high spatiotemporal resolution (50  μm50  μm, 2 kHz analog bandwidth) with a photodiode array. Signals were differentiated after appropriate digital filtering. Differentiation of Ca2+Ca2+ transients resulted in optically recorded calcium currents (ORCCs) that carried the temporal and pharmacological signatures of L-type Ca2+Ca2+ inward currents: the time to peak amounted to ∼2.1  ms∼2.1  ms (Fluo-4FF) and ∼2.4  ms∼2.4  ms (Fluo-4), full-width at half-maximum was ∼8  ms∼8  ms, and ORCCs were completely suppressed by 50  μmol/L50  μmol/LCdCl2CdCl2. Also, and as reported before from patch-clamp studies, caffeine reversibly depressed the amplitude of ORCCs. The results demonstrate that the differentiation of Ca2+Ca2+ transients can be used to obtain a spatially resolved picture of the initial phase of ICaICa in cardiac tissue and to assess relative changes of activation/fast inactivation of ICaICa following pharmacological interventions.