On the theta number of powers of cycle graphs

We give a closed formula for Lovasz theta number of the powers of cycle graphs and of their complements, the circular complete graphs. As a consequence, we establish that the circular chromatic number of a circular perfect graph is computable in polynomial time. We also derive an asymptotic estimate for this theta number.Comment: 17 page

Can Dark Energy emerge from quantum effects in compact extra dimension ?

The origin of the observed acceleration of the expansion of the universe is a major problem of modern cosmology and theoretical physics. Simple estimations of the contribution of vacuum to the density energy of the universe in quantum field theory are known to lead to catastrophic large values compared to observations. Such a contribution is therefore generally not regarded as a viable source for the acceleration of the expansion. In this letter we propose that the vacuum contribution actually provides a small positive value to the density energy of the universe. The underlying mechanism is a manifestation of the quantum nature of the gravitational field, through a Casimir-like effect from an additional compact dimension of space. A key ingredient is to assume that only modes with wavelength shorter than the Hubble length contribute to the vacuum. Such a contribution gives a positive energy density, has a Lorentz invariant equation of state in the usual 4D spacetime and hence can be interpreted as a cosmological constant. Its value agrees with observations for a radius of a 5th extra dimension given by $35\,\mu$m. This implies a modification of the gravitational inverse square law around this scale, close but below existing limits from experiments testing gravity at short range.Comment: To be published in A\&

Incompatibility boundaries for properties of community partitions

We prove the incompatibility of certain desirable properties of community partition quality functions. Our results generalize the impossibility result of [Kleinberg 2003] by considering sets of weaker properties. In particular, we use an alternative notion to solve the central issue of the consistency property. (The latter means that modifying the graph in a way consistent with a partition should not have counterintuitive effects). Our results clearly show that community partition methods should not be expected to perfectly satisfy all ideally desired properties. We then proceed to show that this incompatibility no longer holds when slightly relaxed versions of the properties are considered, and we provide in fact examples of simple quality functions satisfying these relaxed properties. An experimental study of these quality functions shows a behavior comparable to established methods in some situations, but more debatable results in others. This suggests that defining a notion of good partition in communities probably requires imposing additional properties.Comment: 17 pages, 3 figure

Equality of Opportunity: Definitions and testable conditions, with an application to income in France

We offer a model of equality of opportunity that encompasses different conceptions expressed in the public debate. In addition to circumstances whose effect on outcome should be compensated and effort which represents a legitimate source of inequality, we introduce a third factor, luck, that captures the non-responsibility factors whose impact on outcome should be even-handed for equality of opportunity to be satisfied. Then, we analyse how the various definitions of equality of opportunity can be empirically identified, given data limitations and provide testable conditions. Definitions and conditions resort to standard stochastic dominance tools. Lastly, we develop an empirical analysis of equality of opportunity for income acquisition in France over the period 1979-2000 which reveals that the degree of inequality of opportunity tends to decrease and that the risk of social lotteries appears very similar across the different groups of social origin.Equality of Opportunity, Income distribution, Luck, Stochastic dominance

Equality of opportunity and luck: Denitions and testable conditions, with an application to income in France

We oer a model of equality of opportunity that encompasses dierent conceptions expressed in the public and philosophical debates. In addition to circumstances whose eect on outcome should be compensated and eort which represents a legitimate source of inequality, we introduce a third factor, luck, that captures the random factors whose impact on outcome should be even-handed for equality of opportunity to be satised. Then, we analyse how the various denitions of equality of opportunity can be empirically identied, given data limitations and provide testable conditions. Denitions and conditions resort to standard stochastic dominance tools. Lastly, we develop an empirical analysis of equality of opportunity for income acquisition in France over the period 1979-2000 which reveals that the degree of inequality of opportunity tends to decrease and that the degree of risk of income distributions, conditional on social origin, appears very similar across all groups of social origins.Equality of opportunity, Luck, Stochastic dominance, Income distribution.

Equality of opportunity: Definitions and testable conditions, with an application to income in France

We offer a model of equality of opportunity that encompasses different conceptions expressed in the public debate. In addition to circumstances whose effect on outcome should be compensated and eort which represents a legitimate source of inequality, we introduce a third factor, luck, that captures the non-responsibility factors whose impact on outcome should be even-handed for equality of opportunity to be satisfied. Then, we analyse how the various definitions of equality of opportunity can be empirically identified, given data limitations and provide testable conditions. Definitions and conditions resort to standard stochastic dominance tools. Lastly, we develop an empirical analysis of equality of opportunity for income acquisition in France over the period 1979-2000 which reveals that the degree of inequality of opportunity tends to decrease and that the risk of social lotteries appears very similar across the different groups of social origin.Equality of opportunity, Income distribution, Luck, Stochastic dominance.

Inequality of opportunities vs. inequality of outcomes: Are Western societies all alike?

This paper analyzes the relationship between income inequality and inequality of opportunities for income acquisition in nine developed countries during the nineties. We develop a new definition of equality of opportunity and show how it can be implemented empirically. Equality of opportunity is defined as the situation where income distributions conditional on social origin cannot be ranked according to stochastic dominance criteria. Stochastic dominance is assessed using non-parametric statistical tests. We measure social origin by parental education and occupation and use national household surveys to assess inequality of income and opportunities. USA and Italy show up as the most unequal countries both in terms of outcome and opportunity. At the opposite extreme, income distributions conditional on social origin are very close in Scandinavian countries even before any redistributive policy. The analysis highlights that inequality of outcome and inequality of opportunity can sometimes lead to different pictures. For instance, France and Germany experience a similar level of inequality of income but the former country is much more unequal than the latter from the point of view of equality of opportunity. Differences in rankings according to inequality of outcome and inequality of opportunity underscore the importance of the policymaker's choice of the conception of equality to promote.Equality of opportunity, Income inequality, Income distribution, Lorenz dominance.

Effect of steam, lactic acid and combined treatments for inactivating Campylobacter jejuni inoculated on chicken skin

International audienceno abstrac

Dark sectors of the Universe: A Euclid survey approach

In this paper we study the consequences of relaxing the hypothesis of the pressureless nature of the dark matter component when determining constraints on dark energy. To this aim we consider simple generalized dark matter models with constant equation of state parameter. We find that present-day low-redshift probes (type-Ia supernovae and baryonic acoustic oscillations) lead to a complete degeneracy between the dark energy and the dark matter sectors. However, adding the cosmic microwave background (CMB) high-redshift probe restores constraints similar to those on the standard $\Lambda$CDM model. We then examine the anticipated constraints from the galaxy clustering probe of the future Euclid survey on the same class of models, using a Fisher forecast estimation. We show that the Euclid survey allows us to break the degeneracy between the dark sectors, although the constraints on dark energy are much weaker than with standard dark matter. The use of CMB in combination allows us to restore the high precision on the dark energy sector constraints.Comment: 10 pages, 6 figure