Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

A computable general equilibrium analysis of the relative price sensitivity required to induce rebound effects in response to an improvement in energy efficiency in the UK economy

In recent years there has been extensive debate in the energy economics and policy literature on the likely impacts of improvements in energy efficiency. This debate has focussed on the notion of rebound effects. Rebound effects occur when improvements in energy efficiency actually stimulate the direct and indirect demand for energy in production and/or consumption. This phenomenon occurs through the impact of the increased efficiency on the effective, or implicit, price of energy. If demand is stimulated in this way, the anticipated reduction in energy use, and the consequent environmental benefits, will be partially or possibly even more than wholly (in the case of ‘backfire’ effects) offset. A recent report published by the UK House of Lords identifies rebound effects as a plausible explanation as to why recent improvements in energy efficiency in the UK have not translated to reductions in energy demand at the macroeconomic level, but calls for empirical investigation of the factors that govern the extent of such effects. Undoubtedly the single most important conclusion of recent analysis in the UK, led by the UK Energy Research Centre (UKERC) is that the extent of rebound and backfire effects is always and everywhere an empirical issue. It is simply not possible to determine the degree of rebound and backfire from theoretical considerations alone, notwithstanding the claims of some contributors to the debate. In particular, theoretical analysis cannot rule out backfire. Nor, strictly, can theoretical considerations alone rule out the other limiting case, of zero rebound, that a narrow engineering approach would imply. In this paper we use a computable general equilibrium (CGE) framework to investigate the conditions under which rebound effects may occur in the Scottish regional and UK national economies. Previous work has suggested that rebound effects will occur even where key elasticities of substitution in production are set close to zero. Here, we carry out a systematic sensitivity analysis, where we gradually introduce relative price sensitivity into the system, focusing in particular on elasticities of substitution in production and trade parameters, in order to determine conditions under which rebound effects become a likely outcome. We find that, while there is positive pressure for rebound effects even where (direct and indirect) demand for energy is very price inelastic, this may be partially or wholly offset by negative income and disinvestment effects, which also occur in response to falling energy prices.

A comparison of results from MRIO and interregional computable general equilibrium (CGE) analyses of the impacts of a positive demand shock on the ‘CO2 trade balance’ between Scotland and the rest of the UK

In previous work we have applied the environmental multi-region input-output (MRIO) method proposed by Turner et al (2007) to examine the ‘CO2 trade balance’ between Scotland and the Rest of the UK. In McGregor et al (2008) we construct an interregional economy-environment input-output (IO) and social accounting matrix (SAM) framework that allows us to investigate methods of attributing responsibility for pollution generation in the UK at the regional level. This facilitates analysis of the nature and significance of environmental spillovers and the existence of an environmental ‘trade balance’ between regions. While the existence of significant data problems mean that the quantitative results of this study should be regarded as provisional, we argue that the use of such a framework allows us to begin to consider questions such as the extent to which a devolved authority like the Scottish Parliament can and should be responsible for contributing to national targets for reductions in emissions levels (e.g. the UK commitment to the Kyoto Protocol) when it is limited in the way it can control emissions, particularly with respect to changes in demand elsewhere in the UK. However, while such analysis is useful in terms of accounting for pollution flows in the single time period that the accounts relate to, it is limited when the focus is on modelling the impacts of any marginal change in activity. This is because a conventional demand-driven IO model assumes an entirely passive supply-side in the economy (i.e. all supply is infinitely elastic) and is further restricted by the assumption of universal Leontief (fixed proportions) technology implied by the use of the A and multiplier matrices. In this paper we argue that where analysis of marginal changes in activity is required, a more flexible interregional computable general equilibrium approach that models behavioural relationships in a more realistic and theory-consistent manner, is more appropriate and informative. To illustrate our analysis, we compare the results of introducing a positive demand stimulus in the UK economy using both IO and CGE interregional models of Scotland and the rest of the UK. In the case of the latter, we demonstrate how more theory consistent modelling of both demand and supply side behaviour at the regional and national levels affect model results, including the impact on the interregional CO2 ‘trade balance’.

Who Matters in Coordination Problems?

We consider a common investment project that is vulnerable to a self-ful lling coordination failure and hence is strategically risky. Based on their private information, agents - who have heterogeneous investment incentives - form expectations or 'sentiments' about the project's outcome. We find that the sum of these sentiments is constant across di erent strategy profiles and it is independent of the distribution of incentives. As a result, we can think of sentiment as a scarce resource divided up among the di erent payo types. Applying this nding, we show that agents who bene t little from the project's success have a large impact on the coordination process. The agents with small bene ts invest only if their sentiment towards the project is large per unit investment cost. As the average sentiment is constant, a subsidy decreasing the investment costs of these agents will \free up" a large amount of sentiment, provoking a large impact on the whole economy. Intuitively, these agents, insensitive to the project's outcome and hence to the actions of others, are in uential because they modify their equilibrium behavior only if the others change theirs substantially.

The Rebound Effect with Energy Production: A Partial Equilibrium Analysis

Rebound is the extent to which improvements in energy efficiency fail to translate fully into reductions in energy use because of the implicit fall in the price of energy, when measured in efficiency units. This paper discusses aspects of the rebound effect that are introduced once energy is considered as a domestically produced commodity. A partial equilibrium approach is adopted in order to incorporate both energy use and production in a conceptually tractable way. The paper explores analytically two interesting results revealed in previous numerical simulations. The first is the possibility that energy use could fall by more than the implied improvement in efficiency. This corresponds to negative rebound. The second is the finding that the short-run rebound value can be greater than the corresponding long-run value.

On problems of calculating energy expenditure and substrate utilization from respiratory exchange data.

Indirect calorimetry based on respiratory exchange measurement has been successfully used from the beginning of the century to obtain an estimate of heat production (energy expenditure) in human subjects and animals. The errors inherent to this classical technique can stem from various sources: 1) model of calculation and assumptions, 2) calorimetric factors used, 3) technical factors and 4) human factors. The physiological and biochemical factors influencing the interpretation of calorimetric data include a change in the size of the bicarbonate and urea pools and the accumulation or loss (via breath, urine or sweat) of intermediary metabolites (gluconeogenesis, ketogenesis). More recently, respiratory gas exchange data have been used to estimate substrate utilization rates in various physiological and metabolic situations (fasting, post-prandial state, etc.). It should be recalled that indirect calorimetry provides an index of overall substrate disappearance rates. This is incorrectly assumed to be equivalent to substrate "oxidation" rates. Unfortunately, there is no adequate golden standard to validate whole body substrate "oxidation" rates, and this contrasts to the "validation" of heat production by indirect calorimetry, through use of direct calorimetry under strict thermal equilibrium conditions. Tracer techniques using stable (or radioactive) isotopes, represent an independent way of assessing substrate utilization rates. When carbohydrate metabolism is measured with both techniques, indirect calorimetry generally provides consistent glucose "oxidation" rates as compared to isotopic tracers, but only when certain metabolic processes (such as gluconeogenesis and lipogenesis) are minimal or / and when the respiratory quotients are not at the extreme of the physiological range. However, it is believed that the tracer techniques underestimate true glucose "oxidation" rates due to the failure to account for glycogenolysis in the tissue storing glucose, since this escapes the systemic circulation. A major advantage of isotopic techniques is that they are able to estimate (given certain assumptions) various metabolic processes (such as gluconeogenesis) in a noninvasive way. Furthermore when, in addition to the 3 macronutrients, a fourth substrate is administered (such as ethanol), isotopic quantification of substrate "oxidation" allows one to eliminate the inherent assumptions made by indirect calorimetry. In conclusion, isotopic tracers techniques and indirect calorimetry should be considered as complementary techniques, in particular since the tracer techniques require the measurement of carbon dioxide production obtained by indirect calorimetry. However, it should be kept in mind that the assessment of substrate oxidation by indirect calorimetry may involve large errors in particular over a short period of time. By indirect calorimetry, energy expenditure (heat production) is calculated with substantially less error than substrate oxidation rates.

The yellow fever 17D vaccine virus as a vector for the expression of foreign proteins: development of new live flavivirus vaccines

The Flaviviridae is a family of about 70 mostly arthropod-borne viruses many of which are major public health problems with members being present in most continents. Among the most important are yellow fever (YF), dengue with its four serotypes and Japanese encephalitis virus. A live attenuated virus is used as a cost effective, safe and efficacious vaccine against YF but no other live flavivirus vaccines have been licensed. The rise of recombinant DNA technology and its application to study flavivirus genome structure and expression has opened new possibilities for flavivirus vaccine development. One new approach is the use of cDNAs encopassing the whole viral genome to generate infectious RNA after in vitro transcription. This methodology allows the genetic mapping of specific viral functions and the design of viral mutants with considerable potential as new live attenuated viruses. The use of infectious cDNA as a carrier for heterologous antigens is gaining importance as chimeric viruses are shown to be viable, immunogenic and less virulent as compared to the parental viruses. The use of DNA to overcome mutation rates intrinsic of RNA virus populations in conjunction with vaccine production in cell culture should improve the reliability and lower the cost for production of live attenuated vaccines. The YF virus despite a long period ignored by researchers probably due to the effectiveness of the vaccine has made a come back, both in nature as human populations grow and reach endemic areas as well as in the laboratory being a suitable model to understand the biology of flaviviruses in general and providing new alternatives for vaccine development through the use of the 17D vaccine strain.

Population genetic structure of the major malaria vector Anopheles darlingi (Diptera: Culicidae) from the Brazilian Amazon, using microsatellite markers

The population genetic structure of Anopheles darlingi, the major human malaria vector in the Neotropics, was examined using seven microsatellite loci from nine localities in central and western Amazonian Brazil. High levels of genetic variability were detected (5-25 alleles per locus; H E = 0.519-0.949). There was deviation from Hardy-Weinberg Equilibrium for 59.79% of the tests due to heterozygote deficits, while the analysis of linkage disequilibrium was significant for only two of 189 (1.05%) tests, most likely caused by null alleles. Genetic differentiation (F ST = 0.001-0.095; Nm = 4.7-363.8) indicates that gene flow is extensive among locations < 152 km apart (with two exceptions) and reduced, but not absent, at a larger geographic scale. Genetic and geographic distances were significantly correlated (R² = 0.893, P < 0.0002), supporting the isolation by distance (IBD) model. The overall estimate of Ne was 202.4 individuals under the linkage disequilibrium model, and 8 under the heterozygote excess model. Analysis of molecular variance showed that nearly all variation (~ 94%) was within sample locations. The UPGMA phenogram clustered the samples geographically, with one branch including 5/6 of the state of Amazonas localities and the other branch the Acre, Rondônia, and remaining Amazonas localities. Taken together, these data suggest little genetic structure for An. darlingi from central and western Amazonian Brazil. These findings also imply that the IBD model explains nearly all of the differentiation detected. In practical terms, populations of An. darlingi at distances < 152 km should respond similarly to vector control measures, because of high gene flow.

Detection of Optimal Models in Parameter Space with Support Vector Machines

The paper proposes an approach aimed at detecting optimal model parameter combinations to achieve the most representative description of uncertainty in the model performance. A classification problem is posed to find the regions of good fitting models according to the values of a cost function. Support Vector Machine (SVM) classification in the parameter space is applied to decide if a forward model simulation is to be computed for a particular generated model. SVM is particularly designed to tackle classification problems in high-dimensional space in a non-parametric and non-linear way. SVM decision boundaries determine the regions that are subject to the largest uncertainty in the cost function classification, and, therefore, provide guidelines for further iterative exploration of the model space. The proposed approach is illustrated by a synthetic example of fluid flow through porous media, which features highly variable response due to the parameter values' combination.

Implicit collusion on wide spreads

Recent empirical findings suggest that spreads quoted in dealershipmarkets might be uncompetitive. This paper analyzes theoretically if pricecompetition between risk--averse market--makers leaves room for implicitcollusive behavior. We compare the spread and risk--sharing efficiencyarising in several market structures differing in terms of i) the priorityrule followed in case of ties, and ii) the type of schedules market makersmay use, namely: general schedules, linear schedules, or limit orders. Ingeneral, competitive pricing does not arise in equilibrium, and there isa conflict between risk sharing efficiency and the tightness of the spread.This conflict can be mitigated by an appropriate market structure design.The limit order market is the only market structure in which the competitiveequilibrium is the unique equilibrium.

Building a Social Accounting Matrix within the ESA95 Framework: Obtaining a Dataset for Applied General Equilibrium Modelling

This research provides a description of the process followed in order to assemble a "Social Accounting Matrix" for Spain corresponding to the year 2000 (SAMSP00). As argued in the paper, this process attempts to reconcile ESA95 conventions with requirements of applied general equilibrium modelling. Particularly, problems related to the level of aggregation of net taxation data, and to the valuation system used for expressing the monetary value of input-output transactions have deserved special attention. Since the adoption of ESA95 conventions, input-output transactions have been preferably valued at basic prices, which impose additional difficulties on modellers interested in computing applied general equilibrium models. This paper addresses these difficulties by developing a procedure that allows SAM-builders to change the valuation system of input-output transactions conveniently. In addition, this procedure produces new data related to net taxation information.

Computational problems in perfect phylogeny haplotyping: typing without calling the allele.

A haplotype is an m-long binary vector. The XOR-genotype of two haplotypes is the m-vector of their coordinate-wise XOR. We study the following problem: Given a set of XOR-genotypes, reconstruct their haplotypes so that the set of resulting haplotypes can be mapped onto a perfect phylogeny (PP) tree. The question is motivated by studying population evolution in human genetics, and is a variant of the perfect phylogeny haplotyping problem that has received intensive attention recently. Unlike the latter problem, in which the input is "full" genotypes, here we assume less informative input, and so may be more economical to obtain experimentally. Building on ideas of Gusfield, we show how to solve the problem in polynomial time, by a reduction to the graph realization problem. The actual haplotypes are not uniquely determined by that tree they map onto, and the tree itself may or may not be unique. We show that tree uniqueness implies uniquely determined haplotypes, up to inherent degrees of freedom, and give a sufficient condition for the uniqueness. To actually determine the haplotypes given the tree, additional information is necessary. We show that two or three full genotypes suffice to reconstruct all the haplotypes, and present a linear algorithm for identifying those genotypes.

Building a Social Accounting Matrix within the ESA95 Framework: Obtaining a Dataset for Applied General Equilibrium Modelling

This research provides a description of the process followed in order to assemble a "Social Accounting Matrix" for Spain corresponding to the year 2000 (SAMSP00). As argued in the paper, this process attempts to reconcile ESA95 conventions with requirements of applied general equilibrium modelling. Particularly, problems related to the level of aggregation of net taxation data, and to the valuation system used for expressing the monetary value of input-output transactions have deserved special attention. Since the adoption of ESA95 conventions, input-output transactions have been preferably valued at basic prices, which impose additional difficulties on modellers interested in computing applied general equilibrium models. This paper addresses these difficulties by developing a procedure that allows SAM-builders to change the valuation system of input-output transactions conveniently. In addition, this procedure produces new data related to net taxation information.

Financial reforms and capital flows: Insights from general equilibrium

As a result of debt enforcement problems, many high-productivity firms in emergingeconomies are unable to pledge enough future profits to their creditors and this constrains thefinancing they can raise. Many have argued that, by relaxing these credit constraints, reformsthat strengthen enforcement institutions would increase capital flows to emerging economies. Thisargument is based on a partial equilibrium intuition though, which does not take into account theorigin of any additional resources that flow to high-productivity firms after the reforms. We showthat some of these resources do not come from abroad, but instead from domestic low-productivityfirms that are driven out of business as a result of the reforms. Indeed, the resources released bythese low-productivity firms could exceed those absorbed by high-productivity ones so that capitalflows to emerging economies might actually decrease following successful reforms. This resultprovides a new perspective on some recent patterns of capital flows in industrial and emergingeconomies.