Gr\"obner Bases of Bihomogeneous Ideals generated by Polynomials of Bidegree (1,1): Algorithms and Complexity

Solving multihomogeneous systems, as a wide range of structured algebraic systems occurring frequently in practical problems, is of first importance. Experimentally, solving these systems with Gr\"obner bases algorithms seems to be easier than solving homogeneous systems of the same degree. Nevertheless, the reasons of this behaviour are not clear. In this paper, we focus on bilinear systems (i.e. bihomogeneous systems where all equations have bidegree (1,1)). Our goal is to provide a theoretical explanation of the aforementionned experimental behaviour and to propose new techniques to speed up the Gr\"obner basis computations by using the multihomogeneous structure of those systems. The contributions are theoretical and practical. First, we adapt the classical F5 criterion to avoid reductions to zero which occur when the input is a set of bilinear polynomials. We also prove an explicit form of the Hilbert series of bihomogeneous ideals generated by generic bilinear polynomials and give a new upper bound on the degree of regularity of generic affine bilinear systems. This leads to new complexity bounds for solving bilinear systems. We propose also a variant of the F5 Algorithm dedicated to multihomogeneous systems which exploits a structural property of the Macaulay matrix which occurs on such inputs. Experimental results show that this variant requires less time and memory than the classical homogeneous F5 Algorithm.Comment: 31 page

A geometric method for model reduction of biochemical networks with polynomial rate functions

Model reduction of biochemical networks relies on the knowledge of slow and fast variables. We provide a geometric method, based on the Newton polytope, to identify slow variables of a biochemical network with polynomial rate functions. The gist of the method is the notion of tropical equilibration that provides approximate descriptions of slow invariant manifolds. Compared to extant numerical algorithms such as the intrinsic low dimensional manifold method, our approach is symbolic and utilizes orders of magnitude instead of precise values of the model parameters. Application of this method to a large collection of biochemical network models supports the idea that the number of dynamical variables in minimal models of cell physiology can be small, in spite of the large number of molecular regulatory actors

A modern day panopticon: using power and control theory to manage volunteer tourists in Bolivia

Volunteer tourism literature is yet to examine the impact of power and control practices on volunteer tourist compliancy. This paper contributes to closing this research gap by proposing and testing a new theoretical model of power and control practices. Drawing upon the previously un-synthesized theoretical contributions of Foucault (1979) and French & Raven (1959), the model presents power and control practices identified in the extant organizational literature. Using an auto-ethnographic approach, data was collected within a Bolivian volunteer-host community. Examination of results suggested mutually beneficial volunteer-host working relationships occur under ‘softer’ management practices. Our findings also offer insight into the salience of using reward-based management strategies as a control mechanism, as well as identifying two new control practices that emerged empirically. The research suggests several implications for the management of host communities towards creating more harmonious, efficient, and effective working relationships between volunteer tourists and hosts

An Investigation Into the Effects of Various Transport Policies on the Levels of Motorised Traffic in Great Britain in 2006

This Working Paper presents the results of tests of various transport policies which could potentially have a major impact on private car travel and hence gain environmental benefits at a national level. The forecasting methodology was to take OPCS population forecasts for year 2006 in 28 age/sex/area type categories, predict the car available percentage of person in each category in 2006, and then predict trip mileage growth (by three mode types for the 28 categories each subdivided into car available and car non-availahle. For the latter two predications, NTS data for 1985/6 and 1991/3 were compared and projected forward with various adjustments. The effect of individual transport policies on trip rates for individual cells was determined from results derived from other studies, coupled with a consideration of economic theory. Of the tests considered, only the tripling of fuel prices for private mode transport was ahle to hold private mode mileage in 2006 at ahout its 1992 level