Saari's homographic conjecture for planar equal-mass three-body problem in Newton gravity

Saari's homographic conjecture in N-body problem under the Newton gravity is the following; configurational measure \mu=\sqrt{I}U, which is the product of square root of the moment of inertia I=(\sum m_k)^{-1}\sum m_i m_j r_{ij}^2 and the potential function U=\sum m_i m_j/r_{ij}, is constant if and only if the motion is homographic. Where m_k represents mass of body k and r_{ij} represents distance between bodies i and j. We prove this conjecture for planar equal-mass three-body problem. In this work, we use three sets of shape variables. In the first step, we use \zeta=3q_3/(2(q_2-q_1)) where q_k \in \mathbb{C} represents position of body k. Using r_1=r_{23}/r_{12} and r_2=r_{31}/r_{12} in intermediate step, we finally use \mu itself and \rho=I^{3/2}/(r_{12}r_{23}r_{31}). The shape variables \mu and \rho make our proof simple

Dynamics of Macrosystems; Proceedings of a Workshop, September 3-7, 1984

There is an increasing awareness of the important and persuasive role that instability and random, chaotic motion play in the dynamics of macrosystems. Further research in the field should aim at providing useful tools, and therefore the motivation should come from important questions arising in specific macrosystems. Such systems include biochemical networks, genetic mechanisms, biological communities, neutral networks, cognitive processes and economic structures. This list may seem heterogeneous, but there are similarities between evolution in the different fields. It is not surprising that mathematical methods devised in one field can also be used to describe the dynamics of another. IIASA is attempting to make progress in this direction. With this aim in view this workshop was held at Laxenburg over the period 3-7 September 1984. These Proceedings cover a broad canvas, ranging from specific biological and economic problems to general aspects of dynamical systems and evolutionary theory

Voriconazole and fluconazole increase the exposure to oral diazepam

Conclusion Both voriconazole and fluconazole considerably increase the exposure to diazepam. Recurrent administration of diazepam increases the risk of clinically significant interactions during voriconazole or fluconazole treatment, because the elimination of diazepam is impaired significantly

Effect of voriconazole and fluconazole on the pharmacokinetics of intravenous fentanyl

Conclusion Both voriconazole and fluconazole delay the elimination of fentanyl significantly. Caution should be exercised, especially in patients who are given voriconazole or fluconazole during long-lasting fentanyl treatment, because insidiously elevated fentanyl concentration may lead to respiratory depression

When night never falls : female sexual signalling in a nocturnal insect along a latitudinal gradient

The environment can play an important role in animal communication by affecting signal transmission and detection. Variation in the signalling environment is expected to be especially pronounced in widely distributed species, potentially affecting how their signals are detected. Such environmental variability is presumably relevant for sedentary females of a nocturnal capital breeder, the European common glow-worm (Lampyris noctiluca), which produce green light during the night to attract flying males to mate. Being widely distributed in Europe, glow-worm populations are exposed to both rapidly descending, darker summer nights in the south, and slowly dimming, brighter summer nights further north, with the latter potentially posing challenges to the visibility of the female glow. To test how female signalling is affected by latitude, we sampled glowing females during summer nights along a latitudinal gradient in Finland, Northern Europe, and used a novel apparatus to measure the intensity and peak wavelength (hue/colour) of their glow. Surprisingly, females at higher latitudes, similar to those at lower latitudes, were commonly glowing during the brightest (and hence the shortest) nights of the year. Females also glowed brighter in more northern areas, partly due to their larger body size, whereas the colour of their glow was not associated with latitude. Since females glow even during midsummer, independent of latitude, the increase in glow intensity at higher latitudes presumably serves to maintain signal visibility in brighter signalling conditions. Overall, these findings highlight the influence of environmental conditions on the evolution of sexual signals, especially in the context of species distribution range. Significance statement When environmental conditions impact signal transmission and perception, local conditions can have a crucial role in shaping animal communication and signal evolution. To analyse how dark-dependant common glow-worm females cope with variable nocturnal light environments, we used a novel apparatus, presumably not applied to living animals before, to measure female glow intensity at various latitudes along a latitudinal gradient. Interestingly, females did not avoid signalling during the brightest summer nights, but instead, their glow intensity and body size both increased with latitude. These findings suggest that females can ensure visibility to mate-searching males over a range of local conditions. Our study therefore shows how females can adapt to environmental constraints on signal visibility, and how the expression of sexual signals is shaped not only by social interactions but also by the signalling environment.Peer reviewe

Voting and the Cardinal Aggregation of Judgments

The paper elaborates the idea that voting is an instance of the aggregation of judgments, this being a more general concept than the aggregation of preferences. To aggregate judgments one must first measure them. I show that such aggregation has been unproblematic whenever it has been based on an independent and unrestricted scale. The scales analyzed in voting theory are either context dependent or subject to unreasonable restrictions. This is the real source of the diverse 'paradoxes of voting' that would better be termed 'voting pathologies'. The theory leads me to advocate what I term evaluative voting. It can also be called utilitarian voting as it is based on having voters express their cardinal preferences. The alternative that maximizes the sum wins. This proposal operationalizes, in an election context, the abstract cardinal theories of collective choice due to Fleming and Harsanyi. On pragmatic grounds, I argue for a three valued scale for general elections

Modularity and Optimality in Social Choice

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M^3 logM) time (where M is the number of social outcomes).Comment: 42 pages, 4 figures, 8 tables, 1 algorithm