Modelling Multilateral Negotiation in Linear Logic

We show how to embed a framework for multilateral negotiation, in which a group of agents implement a sequence of deals concerning the exchange of a number of resources, into linear logic. In this model, multisets of goods, allocations of resources, preferences of agents, and deals are all modelled as formulas of linear logic. Whether or not a proposed deal is rational, given the preferences of the agents concerned, reduces to a question of provability, as does the question of whether there exists a sequence of deals leading to an allocation with certain desirable properties, such as maximising social welfare. Thus, linear logic provides a formal basis for modelling convergence properties in distributed resource allocation

Modelling Combinatorial Auctions in Linear Logic

We show that linear logic can serve as an expressive framework in which to model a rich variety of combinatorial auction mechanisms. Due to its resource-sensitive nature, linear logic can easily represent bids in combinatorial auctions in which goods may be sold in multiple units, and we show how it naturally generalises several bidding languages familiar from the literature. Moreover, the winner determination problem, i.e., the problem of computing an allocation of goods to bidders producing a certain amount of revenue for the auctioneer, can be modelled as the problem of finding a proof for a particular linear logic sequent

Nonlinear Modeling and Verification of a Heaving Point Absorber for Wave Energy Conversion

Although the heaving Point Absorber (PA) concept is well known in wave energy conversion research, few studies focus on appropriate modelling of non-linear fluid viscous and mechanical friction dynamics. Even though these concepts are known to have non-linear effects on the hydrodynamic system, most research studies consider linearity as a starting point and in so doing have a weak approach to modelling the true dynamic behaviour, particularly close to resonance. The sole use of linear modelling leads to limited ability to develop control strategies capable of true power capture optimisation and suitable device operation. Based on a 1/50 scale cylindrical heaving PA, this research focuses on a strategy for hydrodynamic model development and experimental verification. In this study, nonlinear dynamics are considered, including the lumped effect of the fluid viscous and mechanical friction forces. The excellent correspondence between the derived non-linear model and wave tank tested PA behaviours provides a strong background for wave energy tuning and control system design

New modelling technique for aperiodic-sampling linear systems

A general input-output modelling technique for aperiodic-sampling linear systems has been developed. The procedure describes the dynamics of the system and includes the sequence of sampling periods among the variables to be handled. Some restrictive conditions on the sampling sequence are imposed in order to guarantee the validity of the model. The particularization to the periodic case represents an alternative to the classic methods of discretization of continuous systems without using the Z-transform. This kind of representation can be used largely for identification and control purposes.Comment: 19 pages, 0 figure

A review of progressive collapse research and regulations

History has demonstrated that buildings designed to conventional design codes can lack the robustness necessary to withstand localised damage, partial or even complete collapse. This variable performance has led governmental organisations to seek ways of ensuring all buildings of significant size possess a minimum level of robustness. The research community has responded by advancing understanding of how structures behave when subjected to localised damage. Regulations and design recommendations have been developed to help ensure more consistent resilience in all framed buildings of significant size, and rigorous design approaches have been specified for buildings deemed potentially vulnerable to extreme loading events. This paper summarises some of the more important progressive collapse events, to identify key attributes that lead to vulnerability to collapse. Current procedures and guidelines for ensuring a minimum level of performance are reviewed and modelling methods for structures subjected to localised damage are described. These include increasingly sophisticated progressive collapse analysis procedures, including linear static and non-linear static analysis, as well as non-linear static pushover and linear dynamic methods. Finally, fully non-linear dynamic methods are considered. Building connections potentially represent the most vulnerable structural elements in steel-framed buildings; their failure can lead to progressive collapses. Steel connections also present difficulties with respect to frame modelling and this paper highlights benefits and drawbacks of some modelling procedures with respect to their treatment of connections

Confinement by biased velocity jumps: aggregation of Escherichia coli

We investigate a linear kinetic equation derived from a velocity jump process modelling bacterial chemotaxis in the presence of an external chemical signal centered at the origin. We prove the existence of a positive equilibrium distribution with an exponential decay at infinity. We deduce a hypocoercivity result, namely: the solution of the Cauchy problem converges exponentially fast towards the stationary state. The strategy follows [J. Dolbeault, C. Mouhot, and C. Schmeiser, Hypocoercivity for linear kinetic equations conserving mass, Trans. AMS 2014]. The novelty here is that the equilibrium does not belong to the null spaces of the collision operator and of the transport operator. From a modelling viewpoint it is related to the observation that exponential confinement is generated by a spatially inhomogeneous bias in the velocity jump process.Comment: 15 page

Economic modelling using constraint logic programming

This paper investigates the use of constraint logic programming (CLP) in economic modelling through the design and implementation of two economic models. The first model, the Desai- Henry model contains only linear equations while the second model, constructed by the author, contains non-linear elements. In order to implement the second model, a non-linear constraint solver was constructed. This was necessary because, although CLP is a very powerful programming paradigm, currently available implementations lack any on-linear constraint solving mechanisms

P/2010 A2 LINEAR II: dynamical dust modelling

P/2010 A2 is an object on an asteroidal orbit that was observed to have an extended tail or debris trail in January 2010. In this work, we fit the outburst of P/2010 A2 with a conical burst model, and verify previous suspicions that this was a one--time collisional event rather than an sustained cometary outburst, implying that P/2010 A2 is not a new Main Belt Comet driven by ice sublimation. We find that the best--fit cone opening angle is about 40 to 50 degrees, in agreement with numerical and laboratory simulations of cratering events. Mapping debris orbits to sky positions suggests that the distinctive arc features in the debris correspond to the same debris cone inferred from the extended dust. From the velocity of the debris, and from the presence of a velocity maximum at around 15 cm/s, we infer that the surface of A2 probably has a very low strength (<1 kPa), comparable to lunar regolith.Comment: 14 pages, 25 figures; accepted by Astronomy and Astrophysic