Accelerating Consensus by Spectral Clustering and Polynomial Filters

It is known that polynomial filtering can accelerate the convergence towards average consensus on an undirected network. In this paper the gain of a second-order filtering is investigated. A set of graphs is determined for which consensus can be attained in finite time, and a preconditioner is proposed to adapt the undirected weights of any given graph to achieve fastest convergence with the polynomial filter. The corresponding cost function differs from the traditional spectral gap, as it favors grouping the eigenvalues in two clusters. A possible loss of robustness of the polynomial filter is also highlighted

The Evolution of Cost Control Systems: a Cultural Phenomenon

This paper only aims at stimulating research and debate, starting from two ideas:• historically, cost control systems have undergone major changes by integrating an increasing level of instability;• the same pattern of evolution can be found in other areas.Evolutions seem to have gone through four stages:1. A static period. Individuals think in terms of a stable environment in which there is only one truth. Problems are solved through an analytical approach.2. A period of static balance. Although there is some movement, unchanging laws prevail. The environment is a deterministic one in which the future is modelled on the past. The only systems that can be conceived are closed , dependent ones.3. A period of dynamic balance. Some change is introduced in the laws regulating trends. The environment may thus be transformed and tentatively brought under control. Systems tend to become open ended and adaptable.4. A period when the probabilistic order of confusion prevails. Although the movement has become widespread, it cannot be foreseen in detail. However, major events are somehow predictable according to statistical laws. Overall transformations remain undetermined. Systems improve and become more effective by constant updating and upgrading.Those four stages have been observed in five different fields:• cost control systems in organisations• the history of economic theory• natural sciences• information technology• philosophy.This evolution of course did not affect the five fields in the same manner or at the same pace. It is however important to note that the stages are identical whatever the field i.e. that changes in thinking patterns shifted from one stage to another.management control

Simulation of quantum walks and fast mixing with classical processes

We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains (LMCs), that is, classical Markov chains with added memory. We show that LMCs can simulate the mixing behavior of any quantum walk, under a commonly satisfied invariance condition. This allows us to answer an open question on how the graph topology ultimately bounds a quantum walk's mixing performance, and that of any stochastic local evolution. The results highlight that speedups in mixing and transport phenomena are not necessarily diagnostic of quantum effects, although superdiffusive spreading is more prominent with quantum walks. The general simulating LMC construction may lead to large memory, yet we show that for the main graphs under study (i.e., lattices) this memory can be brought down to the same size employed in the quantum walks proposed in the literature

Choice under Uncertainty with the Best and Worst in Mind: Neo-additive Capacities.

The concept of a non-extreme-outcome-additive capacity (neo-additive capacity ) is introduced. Neo-additive capacities model optimistic and pessimistic attitudes towards uncer-tainty as observed in many experimental studies. Moreover, neo-additive capacities can be applied easily in economic problems, as we demonstrate by examples. This paper provides an axiomatisation of Choquet expected utility with neo-capacities in a framework of purely subjective uncertainty.