Decorous lower bounds for minimum linear arrangement

Minimum Linear Arrangement is a classical basic combinatorial optimization problem from the 1960s, which turns out to be extremely challenging in practice. In particular, for most of its benchmark instances, even the order of magnitude of the optimal solution value is unknown, as testified by the surveys on the problem that contain tables in which the best known solution value often has one more digit than the best known lower bound value. In this paper, we propose a linear-programming based approach to compute lower bounds on the optimum. This allows us, for the first time, to show that the best known solutions are indeed not far from optimal for most of the benchmark instances

Bit Representation Can Improve SDP Relaxations of Mixed-Integer Quadratic Programs

A standard trick in integer programming is to replace bounded integer variables with binary variables, using a bit representation. In a previous paper, we showed that this process can be used to improve linear programming relaxations of mixed-integer quadratic programs. In this paper, we show that it can also be used to improve {\em semidefinite}\/ programming relaxations

A guide to conic optimisation and its applications

Most OR academics and practitioners are familiar with linear programming (LP) and its applications. Many are however unaware of conic optimisation, which is a powerful generalisation of LP, with a prodigious array of important real-life applications. In this invited paper, we give a gentle introduction to conic optimisation, followed by a survey of applications in OR and related areas. Along the way, we try to help the reader develop insight into the strengths and limitations of conic optimisation as a tool for solving real-life problems

Investigations of excitation energy transfer and intramolecular interactions in a nitrogen corded distrylbenzene dendrimer system.

The photophysics of an amino-styrylbenzene dendrimer (A-DSB) system is probed by time-resolved and steady state luminescence spectroscopy. For two different generations of this dendrimer, steady state absorption, emission, and photoluminescence excitation spectra are reported and show that the efficiency of energy transfer from the dendrons to the core is very close to 100%. Ultrafast time-resolved fluorescence measurements at a range of excitation and detection wavelengths suggest rapid (and hence efficient) energy transfer from the dendron to the core. Ultrafast fluorescence anisotropy decay for different dendrimer generations is described in order to probe the energy migration processes. A femtosecond time-scale fluorescence depolarization was observed with the zero and second generation dendrimers. Energy transfer process from the dendrons to the core can be described by a Förster mechanism (hopping dynamics) while the interbranch interaction in A-DSB core was found to be very strong indicating the crossover to exciton dynamics