Homomorphic Preimages of Geometric Cycles

A graph G is a homomorphic preimage of another graph H, or equivalently G is H-colorable, if there exists a graph homomorphism from G to H. A classic problem is to characterize the family of homomorphic preimages of a given graph H. A geometric graph is a simple graph G together with a straight line drawing of G in the plane with the vertices in general position. A geometric homomorphism (resp. isomorphism) is a graph homomorphism (resp. isomorphism) that preserves edge crossings (resp. and non-crossings). The homomorphism posetof a graph G is the set of isomorphism classes of geometric realizations of G partially ordered by the existence of injective geometric homomorphisms. A geometric graph G is H-colorable if there is a geometric homomorphism from G to some element of the homomorphism poset of H. We provide necessary and sufficient conditions for a geometric graph to be C_n-colorable for n less than 6.Comment: 11 pages, 9 figure

Trade Liberalisation and Poverty in Nepal A Computable General Equilibrium Micro Simulation Analysis

Concern is growing regarding the poverty impacts of trade liberalization. The strong general equilibrium effects of trade liberalization can only be properly analysed in a CGE model. However, the aggregate nature of CGE models is not suited to detailed poverty analysis. We bridge this gap by constructing a CGE model that explicitly models all households from a nationally representative household survey. We find complex income and consumption effects that would be missed in standard CGE models. Urban poverty falls and rural poverty increases as initial tariffs were highest for agriculture. Impacts increase with income level, resulting in rising income inequality.computable general equilibrium modelling, international trade, poverty, Nepal

Feedback information and the reward positivity

The reward positivity is a component of the event-related brain potential (ERP) sensitive to neural mechanisms of reward processing. Multiple studies have demonstrated that reward positivity amplitude indices a reward prediction error signal that is fundamental to theories of reinforcement learning. However, whether this ERP component is also sensitive to richer forms of performance information important for supervised learning is less clear. To investigate this question, we recorded the electroencephalogram from participants engaged in a time estimation task in which the type of error information conveyed by feedback stimuli was systematically varied across conditions. Consistent with our predictions, we found that reward positivity amplitude decreased in relation to increasing information content of the feedback, and that reward positivity amplitude was unrelated to trial-to-trial behavioral adjustments in task performance. By contrast, a series of exploratory analyses revealed frontal-central and posterior ERP components immediately following the reward positivity that related to these processes. Taken in the context of the wider literature, these results suggest that the reward positivity is produced by a neural mechanism that motivates task performance, whereas the later ERP components apply the feedback information according to principles of supervised learning

The Homomorphism Poset of K_{2,n}

A geometric graph is a simple graph G together with a straight line drawing of G in the plane with the vertices in general position. Two geometric realizations of a simple graph are geo-isomorphic if there is a vertex bijection between them that preserves vertex adjacencies and non-adjacencies, as well as edge crossings and non-crossings. A natural extension of graph homomorphisms, geo-homomorphisms, can be used to define a partial order on the set of geo-isomorphism classes of realizations of a given simple graph. In this paper, the homomorphism poset of the complete bipartite graph K_{2,n} is determined by establishing a correspondence between realizations of K_{2,n} and permutations of S_n, in which crossing edges correspond to inversions. Through this correspondence, geo-isomorphism defines an equivalence relation on S_n, which we call geo-equivalence. The number of geo-isomorphism classes is provided for all n <= 9. The modular decomposition tree of permutation graphs is used to prove some results on the size of geo-equivalence classes. A complete list of geo-equivalence classes and a Hasse diagrams of the poset structure are given for n <= 5.Comment: 31 pages, 16 figures; added connections to permutation graphs; added a new section 4; new co-autho

An experimental program for the investigation of panel instabilities caused by shock waves

Experimental methods and apparatus for studying panel instabilities caused by shock wave

A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations

A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The method is benchmarked against an analytic solution of a dispersive electron acoustic square pulse as well as the two-fluid electromagnetic shock and existing numerical solutions to the GEM challenge magnetic reconnection problem. The algorithm can be generalized to arbitrary geometries and three dimensions. An approach to maintaining small gauge errors based on error propagation is suggested.Comment: 40 pages, 18 figures