Linearization Instability of Chiral Gravity

Carrying out an analysis of the constraints and their linearizations on a spacelike hypersurface, we show that topologically massive gravity has a linearization instability at the chiral gravity limit about $AdS_3$. We also calculate the symplectic structure for all the known perturbative modes (including the log-mode) for the linearized field equations and find it to be degenerate (non-invertible) hence these modes do not approximate exact solutions and so do not belong to the linearized phase space of the theory. Naive perturbation theory fails: the linearized field equations are necessary but not sufficient in finding viable linearized solutions. This has important consequences for both classical and possible quantum versions of the theory.Comment: 6 pages, version to appear in PR

Holographically Viable Extensions of Topologically Massive and Minimal Massive Gravity?

Recently, an extension of the topologically massive gravity (TMG) in $2+1$ dimensions, dubbed as minimal massive gravity (MMG), was found which is free of the bulk-boundary unitarity clash that inflicts the former theory and all the other known three dimensional theories. Field equations of MMG differ from those of TMG at quadratic terms in the curvature that do not come from the variation of an action depending on the metric alone. Here we show that MMG is a unique theory and there does not exist a deformation of TMG or MMG at the cubic and quartic order (and beyond) in the curvature that is consistent at the level of the field equations. The only extension of TMG with the desired bulk and boundary properties having a single massive degree of freedom is MMG.Comment: 10 pages, references added, almost matches the published versio

Penalty and reward contracts between a manufacturer and its logistics service provider

Contracts are used to coordinate disparate but interdependent members of the supply chain. Conflicting objectives of these members and lack of coordination among the members lead to inefficiencies in matching supply with demand. This study reviews different types of contracts and proposes a methodology to be used by companies for analyzing coordinating contracts with their business partners. Efficiency of the contract is determined by comparing the performance of independent companies under the contract to the supply chain performance under the central decision maker assumption. We propose a penalty and reward contract between a manufacturer and its logistics service provider that distributes the manufacturer’s products on its retail network. The proposed contract analysis methodology is empirically tested with transportation data of a consumer durable goods company (CDG) and its logistics service provider (LSP). The results of this case study suggest a penalty and reward contract between the CDG and its LSP that improves not only the individual firm’s objective functions but also the supply chain costs. Compared to the existing situation, the coordination efficiency of the penalty and reward contract is 96.1 %, proving that optimizing contract parameters improves coordination and leads to higher efficiencies

Using simulation gaming to validate a mathematical modeling platform for resource allocation in disasters

The extraordinary conditions of a disaster require the mobilisation of all available resources, inducing the rush of humanitarian partners into the affected area This phenomenon called the proliferation of actors, causes serious problems during the disaster response phase including the oversupply, duplicated efforts, lack of planning In an attempt to reduce the partner proliferation problem a framework called PREDIS (PREdictive model for DISaster response partner selection) is put forward to configure the humanitarian network within early hours after disaster strike when the information is scarce To verify this model a simulation game is designed using two sets of real decision makers (experts and non-experts) in the disaster Haiyan scenario The result shows that using the PREDIS framework 100% of the experts could make the same decisions less than six hours comparing to 72 hours Also between 71% and 86% of the times experts and non-experts decide similarly using the PREDIS framewor

On Exact Solutions and the Consistency of 3D Minimal Massive Gravity

We show that all algebraic Type-O, Type-N and Type-D and some Kundt-Type solutions of Topologically Massive Gravity are inherited by its holographically well-defined deformation, that is the recently found Minimal Massive Gravity. This construction provides a large class of constant scalar curvature solutions to the theory. We also study the consistency of the field equations both in the source-free and matter-coupled cases. Since the field equations of MMG do not come from a Lagrangian that depends on the metric and its derivatives only, it lacks the Bianchi identity valid for all non-singular metrics. But it turns out that for the solutions of the equations, Bianchi identity is satisfied. This is a necessary condition for the consistency of the classical field equations but not a sufficient one, since the the rank-two tensor equations are susceptible to double-divergence. We show that for the source-free case the double-divergence of the field equations vanish for the solutions. In the matter-coupled case, we show that the double-divergence of the left-hand side and the right-hand side are equal to each other for the solutions of the theory. This construction completes the proof of the the consistency of the field equations.Comment: 8 page

Linearization Instability for Generic Gravity in AdS

In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as {\it linearization instability}, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure of the linear perturbation theory by showing that a certain quadratic (integral) constraint on the linearized solutions is not satisfied. For non-compact Cauchy surfaces, the situation is different and for example, Minkowski space having a non-compact Cauchy surface, is linearization stable. Here we study, the linearization instability in generic metric theories of gravity where Einstein's theory is modified with additional curvature terms. We show that, unlike the case of general relativity, for modified theories even in the non-compact Cauchy surface cases, there are some theories which show linearization instability about their anti-de Sitter backgrounds. Recent $D$ dimensional critical and three dimensional chiral gravity theories are two such examples. This observation sheds light on the paradoxical behavior of vanishing conserved charges (mass, angular momenta) for non-vacuum solutions, such as black holes, in these theories.Comment: 31 pages, 1 figure, some grammatical typos are correcte

An axiomatic approach to the measurement of envy

We characterize a class of envy-as-inequity measures. There are three key axioms. Decomposability requires that overall envy is the sum of the envy within and between subgroups. The other two axioms deal with the two-individual setting and specify how the envy measure should react to simple changes in the individuals’ commodity bundles. The characterized class measures how much one individual envies another individual by the relative utility difference (using the envious’ utility function) between the bundle of the envied and the bundle of the envious, where the utility function that must be used to represent the ordinal preferences is the ‘ray’ utility function. The class measures overall envy by the sum of these (transformed) relative utility differences. We discuss our results in the light of previous contributions to envy measurement and multidimensional inequality measurement

"Time and Poverty from a Developing Country Perspective"

This study is concerned with the measurement of poverty in the context of developing countries. We argue that poverty rankings must take into account time use dimensions of paid and unpaid work jointly. Reviewing the current state of the literature on this topic, our methodology introduces a critical but missing analytical distinction between time poverty and time deprivation. On this basis, we proceed to provide empirical evidence by using South African time use survey data compiled in 2000. Our findings show that existing methods that work well for advanced countries require modification when adopted in the case of a developing country. The results identify a group of adults who previously were inadvertently missing, as they were considered "time wealthy."Time Poverty Measurement; Time Use; Poverty; Policy