The minimal overlap cost sharing rule

In this paper we introduce a new cost sharing rule-the minimal overlap cost sharing rule-which is associated with the minimal overlap rule for claims problems defined by O'Neill (1982). An axiomatic characterization is given by employing a unique axiom: demand separability. Variations of this axiom enable the serial cost sharing rule (Moulin and Shenker, 1992) and the rules of a family (Albizuri, 2010) that generalize the serial cost sharing rule to be characterized. Finally, a family that includes the minimal overlap cost sharing rule is defined and obtained by means of an axiomatic characterization.

Effective herding of flatfish by cables with minimal seafloor contact

Otter trawls are very effective at capturing flatfish, but they can affect the seaf loor ecosystems where they are used. Alaska f latf ish trawlers have very long cables (called sweeps) between doors and net to herd fish into the path of the trawl. These sweeps, which ride on and can disturb the seaf loor, account for most of the area affected by these trawls and hence a large proportion of the potential for damage to seaf loor organisms. We examined modifications to otter trawls, such that disk clusters were installed at 9-m intervals to raise trawl sweeps small distances above the seafloor, greatly reducing the area of direct seafloor contact. A critical consideration was whether flatfish would still be herded effectively by these sweeps. We compared conventional and modified sweeps using a twin trawl system and analyzed the volume and composition of the resulting catches. We tested sweeps raised 5, 7.5, and 10 cm and observed no significant losses of flatfish catch until sweeps were raised 10 cm, and those losses were relatively small (5–10%). No size composition changes were detected in the flatfish catches. Alaska pollock (Theragra chalcogramma) were captured at higher rates with two versions of the modified sweeps. Sonar observations of the sweeps in operation and the seaf loor after passage confirmed that the area of direct seafloor contact was greatly reduced by the modified sweep

Diet of the minimal armhook squid (Berryteuthis anonychus) (Cephalopoda: Gonatidae) in the northeast Pacific during spring

The stomach contents of the minimal armhook squid (Berryteuthis anonychus) were examined for 338 specimens captured in the northeast Pacific during May 1999. The specimens were collected at seven stations between 145−165°W and 39−49°N and ranged in mantle length from 10.3 to 102.2 mm. Their diet comprised seven major prey groups (copepods, chaetognaths, amphipods, euphausiids, ostracods, unidentified fish, and unidentified gelatinous prey) and was dominated by copepods and chaetognaths. Copepod prey comprised four genera, and 86% by number of the copepods were from the genus Neocalanus. Neocalanus cristatus was the most abundant prey taxa, composing 50% by mass and 35% by number of the total diet. Parasagitta elegans (Chaetognatha) occurred in more stomachs (47%) than any other prey taxon. Amphipods occurred in 19% of the stomachs but composed only 5% by number and 3% by mass of the total prey consumed. The four remaining prey groups (euphausiids, ostracods, unidentified fish, and unidentified gelatinous prey) together composed <2% by mass and <1% by number of the diet. There was no major change in the diet through the size range of squid examined and no evidence of cannibalism or predation on other cephalopod species.

Decentralised minimal-time consensus

This study considers the discrete-time dynamics of a network of agents that exchange information according to the nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically. We present a fully decentralised algorithm that allows any agent to compute the consensus value of the whole network in finite time using only the minimal number of successive values of its own history. We show that this minimal number of steps is related to a Jordan block decomposition of the network dynamics and present an algorithm to obtain the minimal number of steps in question by checking a rank condition on a Hankel matrix of the local observations. Furthermore, we prove that the minimal number of steps is related to other algebraic and graph theoretical notions that can be directly computed from the Laplacian matrix of the graph and from the underlying graph topology. © 2011 IEEE.

Decentralised minimal-time dynamic consensus

This paper considers a group of agents that aim to reach an agreement on individually received time-varying signals by local communication. In contrast to static network averaging problem, the consensus considered in this paper is reached in a dynamic sense. A discrete-time dynamic average consensus protocol can be designed to allow all the agents tracking the average of their reference inputs asymptotically. We propose a minimal-time dynamic consensus algorithm, which only utilises a minimal number of local observations of a randomly picked node in a network to compute the final consensus signal. Our results illustrate that with memory and computational ability, the running time of distributed averaging algorithms can be indeed improved dramatically as suggested by Olshevsky and Tsitsiklis. © 2012 AACC American Automatic Control Council).

Off-wall boundary conditions for turbulent flows obtained from buffer-layer minimal flow units

There is strong evidence that the transport processes in the buffer region of wall-bounded turbulence are common across various flow configurations, even in the embryonic turbulence in transition (Park et al., Phys. Fl. 24). We use this premise to develop off-wall boundary conditions for turbulent simulations. Boundary conditions are constructed from DNS databases using periodic minimal flow units and reduced order modeling. The DNS data was taken from a channel at Reτ=400 and a zero-pressure gradient transitional boundary layer (Sayadi et al., submitted to J. Fluid Mech.). Both types of boundary conditions were first tested on a DNS of the core of the channel flow with the aim of extending their application to LES and to spatially evolving flows.

Calculations of the minimal perimeter for N deformable cells of equal area confined in a circle

Cox, S.J. (2006) Calculations of the minimal perimeter for N deformable cells of equal area confined in a circle. Philosophical Magazine Letters. 86:569-578.