A DEA-based incentives system for centrally managed multi-unit organisations

In multi-unit organisations such as a bank and its branches or a national body delivering publicly funded health or education services through local operating units, the need arises to incentivize the units to operate efficiently. In such instances, it is generally accepted that units found to be inefficient can be encouraged to make efficiency savings. However, units which are found to be efficient need to be incentivized in a different manner. It has been suggested that efficient units could be incentivized by some reward compatible with the level to which their attainment exceeds that of the best of the rest, normally referred to as “super-efficiency”. A recent approach to this issue (Varmaz et. al. 2013) has used Data Envelopment Analysis (DEA) models to measure the super-efficiency of the whole system of operating units with and without the involvement of each unit in turn in order to provide incentives. We identify shortcomings in this approach and use it as a starting point to develop a new DEA-based system for incentivizing operating units to operate efficiently for the benefit of the aggregate system of units. Data from a small German retail bank is used to illustrate our method.

Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser

We report for the first time, rogue waves generation in a mode-locked fiber laser that worked in multiple-soliton state in which hundreds of solitons occupied the whole laser cavity. Using real-time spatio-temporal intensity dynamics measurements, it is unveiled that nonlinear soliton collision accounts for the formation of rogue waves in this laser state. The nature of interactions between solitons are also discussed. Our observation may suggest similar formation mechanisms of rogue waves in other systems.

Temporal solitonic crystals and non-Hermitian informational lattices

Clusters of temporal optical solitons—stable self-localized light pulses preserving their form during propagation—exhibit properties characteristic of that encountered in crystals. Here, we introduce the concept of temporal solitonic information crystals formed by the lattices of optical pulses with variable phases. The proposed general idea offers new approaches to optical coherent transmission technology and can be generalized to dispersion-managed and dissipative solitons as well as scaled to a variety of physical platforms from fiber optics to silicon chips. We discuss the key properties of such dynamic temporal crystals that mathematically correspond to non-Hermitian lattices and examine the types of collective mode instabilities determining the lifetime of the soliton train. This transfer of techniques and concepts from solid state physics to information theory promises a new outlook on information storage and transmission.