On the weights of nations: assigning voting weights in a heterogenous union

Consider a voting procedure where countries, states, or districts comprising a union each elect representatives who then participate in later votes at the union level on their behalf. The countries, provinces, and states may vary in their populations and composition. If we wish to maximize the total expected utility of all agents in the union, how to weight the votes of the representatives of the different countries, states or districts at the union level? We provide a simple characterization of the efficient voting rule in terms of the weights assigned to different districts and the voting threshold (how large a qualified majority is needed to induce change versus the status quo). Next, in the context of a model of the correlation structure of agents preferences, we analyze how voting weights relate to the population size of a country. We then analyze the voting weights in Council of the European Union under the Nice Treaty and the recently proposed constitution, and contrast them under different versions of our model.

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.

Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

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.

Job accessibility and employment probability

The objective of this paper is to estimate the impact of residential job accessibility on female employment probability in the metropolitan areas of Barcelona and Madrid. Following a “spatial mismatch” framework, we estimate a female employment probability equation where variables controlling for personal characteristics, residential segregation and employment potential on public transport network are included. Data used come from Microcensus 2001 of INE (National Institute of Statistics). The research focuses on the treatment of endogeneity problems and the measurement of accessibility variables. Our results show that low job accessibility in public transport negatively affects employment probability. The intensity of this effect tends to decrease with individual’s educational attainment. A higher degree of residential segregation also reduces job probability in a significant way..

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Export-market dynamics and the probability of firm closure: Evidence for the UK

This study presents the first empirical analysis of the determinants of firm closure in the UK with an emphasis on the role of export-market dynamics, using panel data for a nationally representative group of firms operating in all-market based sectors during 1997-2003. Our findings show that the probability of closure is (cet. par.) significantly lower for exporters, particularly those experiencing export-market entry and exit. Having controlled for other attributes associated with productivity (such as size and export status), the following factors are found to increase the firm’s survival prospects: higher capital intensity and TFP, foreign ownership, young age, displacement effects (through relatively high rates of entry of firms in each industry), and belonging to certain industries. Interestingly, increased import penetration (a proxy for lower trade costs) leads to a lower hazard rate for exporting entrants and continuous exporters, whilst inducing a higher hazard rate for domestic producers or those that quit exporting.

Estimation of the Spatial Weights Matrix under Structural Constraints

While estimates of models with spatial interaction are very sensitive to the choice of spatial weights, considerable uncertainty surrounds de nition of spatial weights in most studies with cross-section dependence. We show that, in the spatial error model the spatial weights matrix is only partially identi ed, and is fully identifi ed under the structural constraint of symmetry. For the spatial error model, we propose a new methodology for estimation of spatial weights under the assumption of symmetric spatial weights, with extensions to other important spatial models. The methodology is applied to regional housing markets in the UK, providing an estimated spatial weights matrix that generates several new hypotheses about the economic and socio-cultural drivers of spatial di¤usion in housing demand.

Separating Myth from Probability: the Origins and Evolution of QWERTY

We use basic probability theory and simple replicable electronic search experiments to evaluate some reported “myths” surrounding the origins and evolution of the QWERTY standard. The resulting evidence is strongly supportive of arguments put forward by Paul A. David (1985) and W. Brian Arthur (1989) that QWERTY was path dependent with its course of development strongly influenced by specific historical circumstances. The results also include the unexpected finding that QWERTY was as close to an optimal solution to a serious but transient problem as could be expected with the resources at the disposal of its designers in 1873.

Fecundity, parity, and adult feeding relationships among Nyssorhynchus malaria vectors from Venezuela

Relative to their pre-engorgement weights, nulliparous Anopheles nuneztovari consumed significantly smaller blood meals than A. marajoara, A. triannulatus or A. aquasalis. When females were deprived of sugar before blood feeding, only one-quarter of A. nuneztovari, but more than two-thirds of A. marajoara, A. triannulatus and A. aquasalis matured eggs. Sugar feeding before blood, or two sucessive blood meals by sugar-deprived females, increased the proportion of nulliparous a. nuneztovari which developed eggs, but not significantly so. Nearly all individuals of nulliparous, sugar-fed A. marajoara, A. triannulatus and A. aquasalis matured eggs after one blood feeding. Among A. nuneztovari, A. marajoara and A. aquasalis that matured some eggs in the laboratory, there were no positive correlations between the number of eggs developed and relative vlood mealsize. However, blood meals larger than the mean size significantly increased the chance that A. nuneztovari would develop some eggs. Mean fecundities of gravid A. nuneztovari and A. marajoara reared in the laboratory were significantly lower than those of the same species captured at human bait in nature. Post-engorgement access to sugar by A. nuneztovari (captured at human bait) did not influence fecundity, but significantly enhanced survivorship and the proporticon of individuals which retained eggs. Release-recapture experiments revealed that relatively small blood meals are typical of A. nuneztovari only during the first gonotrophic cycle. We suggest that multiple blood feeding, seemingly necessary for most A. nuneztovari to develop a first clutch of eggs, may increase the probability of infection with Plasmodium vivax where this mosquito species is a primary vector.

Theoretical estimates of consumable food and probability of acquiring food in larvae of Chrysomya putoria (Diptera: Calliphoridae)

An indirect estimate of consumable food and probability of acquiring food in a blowfly species, Chrysomya putoria, is presented. This alternative procedure combines three distinct models to estimate consumable food in the context of the exploitative competition experienced by immature individuals in blowfly populations. The relevant parameters are derived from data for pupal weight and survival and estimates of density-independent larval mortality in twenty different larval densities. As part of this procedure, the probability of acquiring food per unit of time and the time taken to exhaust the food supply are also calculated. The procedure employed here may be valuable for estimations in insects whose immature stages develop inside the food substrate, where it is difficult to partial out confounding effects such as separation of faeces. This procedure also has the advantage of taking into account the population dynamics of immatures living under crowded conditions, which are particularly characteristic of blowflies and other insects as well.

Progesterone down-regulates the open probability of the amiloride-sensitive epithelial sodium channel via a Nedd4-2-dependent mechanism.

Activation of the mitogen-activated protein (MAP) kinase cascade by progesterone in Xenopus oocytes leads to a marked down-regulation of activity of the amiloride-sensitive epithelial sodium channel (ENaC). Here we have studied the signaling pathways involved in progesterone effect on ENaC activity. We demonstrate that: (i) the truncation of the C termini of the alphabetagammaENaC subunits results in the loss of the progesterone effect on ENaC; (ii) the effect of progesterone was also suppressed by mutating conserved tyrosine residues in the Pro-X-X-Tyr (PY) motif of the C termini of the beta and gamma ENaC subunits (beta(Y618A) and gamma(Y628A)); (iii) the down-regulation of ENaC activity by progesterone was also suppressed by co-expression ENaC subunits with a catalytically inactive mutant of Nedd4-2, a ubiquitin ligase that has been previously demonstrated to decrease ENaC cell-surface expression via a ubiquitin-dependent internalization/degradation mechanism; (iv) the effect of progesterone was significantly reduced by suppression of consensus sites (beta(T613A) and gamma(T623A)) for ENaC phosphorylation by the extracellular-regulated kinase (ERK), a MAP kinase previously shown to facilitate the binding of Nedd4 ubiquitin ligases to ENaC; (v) the quantification of cell-surface-expressed ENaC subunits revealed that progesterone decreases ENaC open probability (whole cell P(o), wcP(o)) and not its cell-surface expression. Collectively, these results demonstrate that the binding of active Nedd4-2 to ENaC is a crucial step in the mechanism of ENaC inhibition by progesterone. Upon activation of ERK, the effect of Nedd4-2 on ENaC open probability can become more important than its effect on ENaC cell-surface expression.

Multimodel inference and multimodel averaging in empirical modeling of occupational exposure levels.

Empirical modeling of exposure levels has been popular for identifying exposure determinants in occupational hygiene. Traditional data-driven methods used to choose a model on which to base inferences have typically not accounted for the uncertainty linked to the process of selecting the final model. Several new approaches propose making statistical inferences from a set of plausible models rather than from a single model regarded as 'best'. This paper introduces the multimodel averaging approach described in the monograph by Burnham and Anderson. In their approach, a set of plausible models are defined a priori by taking into account the sample size and previous knowledge of variables influent on exposure levels. The Akaike information criterion is then calculated to evaluate the relative support of the data for each model, expressed as Akaike weight, to be interpreted as the probability of the model being the best approximating model given the model set. The model weights can then be used to rank models, quantify the evidence favoring one over another, perform multimodel prediction, estimate the relative influence of the potential predictors and estimate multimodel-averaged effects of determinants. The whole approach is illustrated with the analysis of a data set of 1500 volatile organic compound exposure levels collected by the Institute for work and health (Lausanne, Switzerland) over 20 years, each concentration having been divided by the relevant Swiss occupational exposure limit and log-transformed before analysis. Multimodel inference represents a promising procedure for modeling exposure levels that incorporates the notion that several models can be supported by the data and permits to evaluate to a certain extent model selection uncertainty, which is seldom mentioned in current practice.

Probability of achieving optimal molecular response to imatinib in chronic myeloid leukemia (CML) patients: Pharmacokinetic/Pharmacodynamic (PK/PD) relationships observed under field-conditions

Objectives: Imatinib has been increasingly proposed for therapeutic drug monitoring (TDM), as trough concentrations (Cmin) correlate with response rates in CML patients. This analysis aimed to evaluate the impact of imatinib exposure on optimal molecular response rates in a large European cohort of patients followed by centralized TDM.¦Methods: Sequential PK/PD analysis was performed in NONMEM 7 on 2230 plasma (PK) samples obtained along with molecular response (PD) data from 1299 CML patients. Model-based individual Bayesian estimates of exposure, parameterized as to initial dose adjusted and log-normalized Cmin (log-Cmin) or clearance (CL), were investigated as potential predictors of optimal molecular response, while accounting for time under treatment (stratified at 3 years), gender, CML phase, age, potentially interacting comedication, and TDM frequency. PK/PD analysis used mixed-effect logistic regression (iterative two-stage method) to account for intra-patient correlation.¦Results: In univariate analyses, CL, log-Cmin, time under treatment, TDM frequency, gender (all p<0.01) and CML phase (p=0.02) were significant predictors of the outcome. In multivariate analyses, all but log-Cmin remained significant (p<0.05). Our model estimates a 54.1% probability of optimal molecular response in a female patient with a median CL of 14.4 L/h, increasing by 4.7% with a 35% decrease in CL (percentile 10 of CL distribution), and decreasing by 6% with a 45% increased CL (percentile 90), respectively. Male patients were less likely than female to be in optimal response (odds ratio: 0.62, p<0.001), with an estimated probability of 42.3%.¦Conclusions: Beyond CML phase and time on treatment, expectedly correlated to the outcome, an effect of initial imatinib exposure on the probability of achieving optimal molecular response was confirmed in field-conditions by this multivariate analysis. Interestingly, male patients had a higher risk of suboptimal response, which might not exclusively derive from their 18.5% higher CL, but also from reported lower adherence to the treatment. A prospective longitudinal study would be desirable to confirm the clinical importance of identified covariates and to exclude biases possibly affecting this observational survey.

Constitutive activity and inverse agonism at the α(₁a) and α(₁b) adrenergic receptor subtypes.

The α(1b)-adrenergic receptor (AR) was, after rhodopsin, the first G protein-coupled receptor (GPCR) in which point mutations were shown to trigger constitutive (agonist-independent) activity. Constitutively activating mutations have been found in other AR subtypes as well as in several GPCRs. This chapter briefly summarizes the main findings on constitutively active mutants of the α(1a)- and α(1b)-AR subtypes and the methods used to predict activating mutations, to measure constitutive activity of Gq-coupled receptors and to investigate inverse agonism. In addition, it highlights the implications of studies on constitutively active AR mutants on elucidating the molecular mechanisms of receptor activation and drug action.