Johan Philip

ALGORITHMS FOR THE VECTOR MAXIMIZATION PROBLEM

AbstractWe consider a convex setB inRn described as the intersection of halfspacesaiTx ≦bi(i ∈ I) and a set of linear objective functionsfj =cjTx (j ∈ J). The index setsI andJ are allowed to be infinite in one of the algorithms. We give the definition of theefficient points ofB (also called functionally efficient or Pareto optimal points) and present the mathematical theory which is needed in the algorithms. In the last section of the paper, we present algorithms that solve the following problems:I.To decide if a given point inB is efficient.II.To find an efficient point inB.III.To decide if a given efficient point is the only one that exists, and if not, find other ones.IV.The solutions of the above problems do not depend on the absolute magnitudes of thecj. They only describe the relative importance of the different activitiesxi. Therefore we also consider

Estimation three-dimensional motion of rigid objects from noisy observations

\begin{gathered} \max G^T x \hfill \\ x efficient \hfill \\ \end{gathered}

Theoretical investigation of the signal-to-noise ratio for different fluorescence lifetime imaging techniques

for some vectorG.

Vector maximization at a degenerate vertex

We deduce the signal-to-noise ratio for fluorescence lifetime imaging when using frequency-domain methods. We assume mono-exponential decay and quantum-noise-limited performance. The results are compared with Monte Carlo simulations with good agreement. We also compare our results with previous investigations of time-domain methods for fluorescence lifetime imaging. For a given number of detected photons, we find that frequency-domain and time-domain methods are equally good. The correct choice of detection technique and its parameters is important for obtaining good results.

Optical transfer function in three dimensions for a large numerical aperture

An estimate is made of the motion of a rigid body from two noisy 2-D perspective projections using the least-squares method and the algebra of R.Y. Tsai and T.S. Huang (1984). The accuracy of the estimated motion parameters is influenced by the position of the features of the object used in the calculation. Four test variables are derived that indicate how the accuracy is affected, and they are used for discarding inaccurate estimates. Monte Carlo tests demonstrate the obtained accuracy. >

Use of UV excitation in confocal laser scanning fluorescence microscopy

Confocal microscopes are often used to study specimens labelled with fluorophores. A commonly used method for simultaneous recording of the distribution of multiple fluorophores is to divide the fluorescent light emitted by the specimen into different wavelength regions using dichroic and bandpass filters. These different wavelength regions are then distributed to multiple detectors. However, the broad and overlapping spectra of commonly used fluorophores often result in considerable crosstalk between channels. A new technique, intensity‐modulated multiple‐beam scanning (IMS) microfluorometry, can be used to reduce this cross‐talk substantially.

An Algorithm for Combined Quadratic and Multiobjective Programming

Using Monte-Carlo methods, we have investigated the signal- to-noise ratio obtainable for different fluorescence lifetime imaging methods. Quantum noise limited performance and mono-exponential decays were assumed. We have also investigated the importance of parameter choice and implementation for the different methods. In addition, our simulations were in many cases compared with analytical theoretical investigations. The results from the simulations proved to be in good agreement with the theoretical results. It was found that all the investigated lifetime imaging methods have the potential to produce a high signal-to-noise ratio, but careful attention must be paid to implementation method and parameter choice in order to get optimal results.

Plane sections of simplices

Method II.2 of our paper [2] on vector maximization published earlier in this journal may fail at a degenerate vertex. The modification of the method needed to overcome this defect is described.