Elementary vectors and conformal sums in polyhedral geometry and their relevance for metabolic pathway analysis

A fundamental result in metabolic pathway analysis states that every flux mode can be decomposed into a sum of elementary modes. However, only a decomposition without cancelations is biochemically meaningful, since a reversible reaction cannot have different directions in the contributing elementary modes. This essential requirement has been largely overlooked by the metabolic pathway community. Indeed, every flux mode can be decomposed into elementary modes without cancelations. The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear subspace is a conformal sum (a sum without cancelations) of elementary vectors (support-minimal vectors). In this work, we extend the theorem, first to "subspace cones" and then to general polyhedral cones and polyhedra. Thereby, we refine Minkowski's and Carath\'eodory's theorems, two fundamental results in polyhedral geometry. We note that, in general, elementary vectors need not be support-minimal, in fact, they are conformally non-decomposable and form a unique minimal set of conformal generators. Our treatment is mathematically rigorous, but suitable for systems biologists, since we give self-contained proofs for our results and use concepts motivated by metabolic pathway analysis. In particular, we study cones defined by linear subspaces and nonnegativity conditions - like the flux cone - and use them to analyze general polyhedral cones and polyhedra. Finally, we review applications of elementary vectors and conformal sums in metabolic pathway analysis

Hierarchical Crossover and Probability Landscapes of Genetic Operators

The time evolution of a simple model for crossover is discussed. A variant of this model with an improved exploration behavior in phase space is derived as a subset of standard one- and multi-point crossover operations. This model is solved analytically in the flat fitness case. Numerical simulations compare the way of phase space exploration of different genetic operators. In the case of a non-flat fitness landscape, numerical solutions of the evolution equations point out ways to estimate premature convergence.Comment: 11 pages, uuencoded postcript fil

Income tax deduction of commuting expenses and tax funding in an urban CGE study: the case of German cities

Germany like many other European countries subsidize commuting by granting the right to deduct commuting expenses from the income tax base. This regulation has often been changed and has regularly been under debate during the last decades. The pros (e.g. causing efficiency gains with respect to the spatial allocation of labor) and cons (e.g. causing urban sprawl) are well documented. Nonetheless, there is need for further research. For reasons of tractability the few models applied in the tax deduction related literature are based on restrictive assumptions particularly concerning the design of the income taxation scheme and the structure of households (neglecting household heterogeneity) and, most importantly, they do not integrate labor supply and location decision problems simultaneously. Here, for the first time, those and more features are taken into account in a full spatial general equilibrium simulation approach calibrated to an average German city. This model is applied to calculate the impacts of tax deductions on an urban economy thereby considering different funding schemes. Our results suggest that the tax deduction level currently chosen is below the optimal level in the case of income tax funding. If a change in the tax base occurs, e.g. toward consumption tax or energy tax funding, the optimal size of the subsidy should be even higher. Furthermore, the different policy packages cause a very differentiated pattern regarding welfare distribution, environmental (CO2 emissions) and congestion effects. We also find surprisingly small effects on urban sprawl characterized by suburbanization of residences and jobs, increasing commuting distances and spatial city growth. --urban general equilibrium model,commuting subsidies,income tax deduction

How does the household structure shape the urban economy?

Households in real cities are heterogeneous regarding their size and composition. This implies that the household structure -i.e. the (average) household size, the composition, the relative share of different household types, and the number of households - differs across cities. This aspect is usually neglected in urban models used to study economic and policy issues that arise in today's cities. Furthermore, the household structure might change over time. For instance, over the last decades average household size has decreased in many countries. Several implications of this change have been discussed, but usually not in regard to an urban economy with its interdependencies. We develop an applied urban general equilibrium model which explicitly takes the household structure into account and thus allows studying the impacts of changes in the household structure on an urban economy and its spatial pattern. The paper shows that changes in the household structure affect an urban economy in various ways and may contribute to explain economic and spatial effects on cities. Compared to a 'Base City' which reflects the actual household structure in the United States, urban labor force participation, housing demand, rents, wages as well as urban commuting and shopping patterns are considerably affected by, e.g., changes in the average household size in a city. For instance, wage inequality between differently skilled workers rises and extreme cross commuting drops to almost zero when the city turns into a pure 'Singles City'. --General equilibrium,Household structure,Household size,Location,Commuting

An urban general equilibrium model with multiple household structures and travel mode choice

Households in real cities are heterogeneous regarding their size and composition. An aspect usually neglected in urban models used to study economic and policy issues that arise in today's cities. We develop an urban general equilibrium model that takes a more complex household structure explicitly into account. The model is based on the single consumer type model of Anas and Xu (1999) or Anas and Rhee (2006) and treats the interactions of urban product, labor and land markets as well as linkages between city firms and different consumer types living in different household structures. Households differ not only in endowments, preferences and their valuation in regard to different travel modes, but also in size and the composition regarding their members. The implementation of a more complex household structure then allows studying a broad range of further urban economic issues, which treat different household structures differently. --Urban Economics,General Equilibrium,Household structure,Location choice

Income tax deduction of commuting expenses and tax funding in an urban CGE study: the case of German cities

Germany like many other European countries subsidize commuting by granting the right to deduct commuting expenses from the income tax base. This regulation has often been changed and has regularly been under debate during the last decades. The pros (e.g. causing efficiency gains with respect to the spatial allocation of labor) and cons (e.g. causing urban sprawl) are well documented. Nonetheless, there is need for further research. For reasons of tractability the few models applied in the tax deduction related literature are based on restrictive assumptions particularly concerning the design of the income taxation scheme and the structure of households (neglecting household heterogeneity) and, most importantly, they do not integrate labor supply and location decision problems simultaneously. Here, for the first time, those and more features are taken into account in a full spatial general equilibrium simulation approach calibrated to an average German city. This model is applied to calculate the impacts of tax deductions on an urban economy thereby considering different funding schemes. Our results suggest that the tax deduction level currently chosen is below the optimal level in the case of income tax funding. If a change in the tax base occurs, e.g. toward consumption tax or energy tax funding, the optimal size of the subsidy should be even higher. Furthermore, the different policy packages cause a very differentiated pattern regarding welfare distribution, environmental (COâ‚‚ emissions) and congestion effects. We also find surprisingly small effects on urban sprawl characterized by suburbanization of residences and jobs and increasing commuting distances.

An urban general equilibrium model with multiple household structures and travel mode choice

Households in real cities are heterogeneous regarding their size and composition. An aspect usually neglected in urban models used to study economic and policy issues that arise in today's cities. We develop an urban general equilibrium model that takes a more complex household structure explicitly into account. The model is based on the single consumer type model of Anas and Xu (1999) or Anas and Rhee (2006) and treats the interactions of urban product, labor and land markets as well as linkages between city firms and different consumer types living in different household structures. Households differ not only in endowments, preferences and their valuation in regard to different travel modes, but also in size and the composition regarding their members. The implementation of a more complex household structure then allows studying a broad range of further urban economic issues, which treat different household structures differentlyurban economics; general equilibrium; household structure; location choice

Windows Vista: Securing Itself against Competition?

About the end of 2006, Microsoft began delivering its new Windows Vista PC operating system to large commercial customers, followed by final users and small businesses. Even before the product reached the market, the dominant provider of PC operating systems worldwide was accused over and over of abusing its market power in order to hinder competitors. After the integration of Internet Explorer (Windows 95) and the Windows Media Player (Windows XP), competitors today are objecting most strongly to the new security components associated with the Windows Vista Security Center, and the EU Commission has joined in these objections. Opponents have criticized the bundling of previously independent components (transfer of market power through bundling), and security software providers like Symantec and McAfee have argued that limiting access to the core of the operating system will hinder their product development activities. In line with the tradition in EU competition policy, Microsoft's dominance of the PC operating system market justifies supervision of that provider in the interests of preventing abuse. However, the final assessment must take into account unique circumstances arising from the specific market and competitive conditions in the standard software markets. In particular, competition policy should intervene in the PC operating system market only if a demonstrable improvement in the public welfare can be attained as a result. In essence, this means that policymakers should intervene to ensure fair innovation competition, including the introduction of reasonable transparency requirements with respect to operating system interfaces in order to allow regulators to manage potential conflicts between the operating system manufacturer and providers of competing software components (e.g. web browsers, media players or security software). There is need for reform in this area in order to create a reliable and functional system of rules for all market participants. However, unbundling decrees which require strict separation of certain system components are an unsuitable instrument for this purpose.competition policy, Microsoft, operating system markets, platform competition