'Cum' Revisited: Preliminaries to Thinking the Interval

In the name of “the community,” humanity - in particular in 20th century Europe - has shown an unexpected capacity to destroy itself. This destruction has been quantitative - mass extermination on such a scale that the very concept of quantity and of quantification was perverted and inverted into a quality: the quality of the unquantifiable, numbers becoming innumerable, becoming absolute, infinite figures. And at the same time this autodestruction has been qualitative, for the idea and the value of “humanity” and of “human nature” itself was destroyed, and its fragile texture being torn up; precisely because of this, human singularities were reduced to numbers, quality being perverted and inverted into quantity. Nevertheless, the multiform history of the community, whether in its universal, global, or in its particular, local shape, should not be seen as some evil, disastrous deviation from the course of civilization; however stained it may have become, it is not an aberrance from normality but rather humanity’s and humanism’s less innocent, less ethereal side. One of the compelling questions of our time is whether the community is a place, a topos, of self-destruction humanity cannot avoid or eliminate. At least this presupposes that we must think the community as a “groundform” and not a side-effect of human existence. As soon as people are exposed to one another in a plurality – and what else could humanity be than precisely this reciprocal exposition of people and peoples? – “there is community”. But this fundamental form of community is not simply their product, nor their operation or “oeuvre”; it is not just the sum of individuals having something in common. It is a place where they, inadvertently, are in common, only to discover that this “in-common” cannot be controlled by them and so eludes them. Consequently, anything can happen, can take place in this strange place of the “inoperative community” (of “that” in a community which remains inoperative): peace and violence, order and disorder, cohesion and destruction

Ramanujan and Extensions and Contractions of Continued Fractions

If a continued fraction $K_{n=1}^{\infty} a_{n}/b_{n}$ is known to converge but its limit is not easy to determine, it may be easier to use an extension of $K_{n=1}^{\infty}a_{n}/b_{n}$ to find the limit. By an extension of $K_{n=1}^{\infty} a_{n}/b_{n}$ we mean a continued fraction $K_{n=1}^{\infty} c_{n}/d_{n}$ whose odd or even part is $K_{n=1}^{\infty} a_{n}/b_{n}$. One can then possibly find the limit in one of three ways: (i) Prove the extension converges and find its limit; (ii) Prove the extension converges and find the limit of the other contraction (for example, the odd part, if $K_{n=1}^{\infty}a_{n}/b_{n}$ is the even part); (ii) Find the limit of the other contraction and show that the odd and even parts of the extension tend to the same limit. We apply these ideas to derive new proofs of certain continued fraction identities of Ramanujan and to prove a generalization of an identity involving the Rogers-Ramanujan continued fraction, which was conjectured by Blecksmith and Brillhart.Comment: 16 page

Evidence for differential effects of reduced and oxidised nitrogen deposition on vegetation independent of nitrogen load

Nitrogen (N) deposition impacts natural and semi-natural ecosystems globally. The responses of vegetation to N deposition may, however, differ strongly between habitats and may be mediated by the form of N. Although much attention has been focused on the impact of total N deposition, the effects of reduced and oxidised N, independent of the total N deposition, have received less attention. In this paper, we present new analyses of national monitoring data in the UK to provide an extensive evaluation of whether there are differences in the effects of reduced and oxidised N deposition across eight habitat types (acid, calcareous and mesotrophic grasslands, upland and lowland heaths, bogs and mires, base-rich mires, woodlands). We analysed data from 6860 plots in the British Countryside Survey 2007 for effects of total N deposition and N form on species richness, Ellenberg N values and grass:forb ratio. Our results provide clear evidence that that N deposition affects species richness in all habitats except base-rich mires, after factoring out correlated explanatory variables (climate and sulphur deposition). In addition, the form of N in deposition appears important for the biodiversity of grasslands and woodlands but not mires and heaths. Ellenberg N increased more in relation to NHx deposition than NOy deposition in all but one habitat type. Relationships between species richness and N form were habitat-specific: acid and mesotrophic grasslands appear more sensitive to NHx deposition while calcareous grasslands and woodlands appeared more responsive to NOy deposition. These relationships are likely driven by the preferences of the component plant species for oxidised or reduced forms of N, rather than by soil acidification

A sequential protocol combining dual neuroanatomical tract-tracing with the visualization of local circuit neurons within the striatum

We describe here an experimental approach designed to aid in the identification of complex brain circuits within the rat corpus striatum. Our aim was to characterize in a single section (i) striatal thalamic afferents, (ii) striatopallidal projection neurons and (iii) striatal local circuit interneurons. To this end, we have combined anterograde tracing using biotinylated dextran amine and retrograde neuroanatomical tracing with Fluoro-Gold. This dual tracing protocol was further implemented with the visualization of different subpopulations of striatal interneurons. The subsequent use of three different peroxidase substrates enabled us to unequivocally detect structures that were labeled within a three-color paradigm

Thalamic innervation of the direct and indirect basal ganglia pathways in the rat: Ipsi- and contralateral projections

The present study describes the thalamic innervation coming from the rat parafascicular nucleus (PF) onto striatal and subthalamic efferent neurons projecting either to the globus pallidus (GP) or to the substantia nigra pars reticulata (SNr) by using a protocol for multiple neuroanatomical tracing. Both striatofugal neurons targeting the ipsilateral SNr (direct pathway) as well as striatal efferent neurons projecting to the ipsilateral GP (indirect pathway) were located within the terminal fields of the thalamostriatal afferents. In the subthalamic nucleus (STN), both neurons projecting to ipsilateral GP as well as neurons projecting to ipsilateral SNr also appear to receive thalamic afferents. Although the projections linking the caudal intralaminar nuclei with the ipsilateral striatum and STN are far more prominent, we also noticed that thalamic axons could gain access to the contralateral STN. Furthermore, a small number of STN neurons were seen to project to both the contralateral GP and PF nuclei. These ipsi- and contralateral projections enable the caudal intralaminar nuclei to modulate the activity of both the direct and the indirect pathway

Complex brain circuits studied via simultaneous and permanent detection of three transported neuroanatomical tracers in the same histological section.

Experimental neuroanatomical tracing methods lie at the basis of the study of the nervous system. When the scientific question is relatively straightforward, it may be sufficient to derive satisfactory answers from experiments in which a single neuroanatomical tracing method is applied. In various scientific paradigms however, for instance when the degree of convergence of two different projections on a particular cortical area or subcortical nucleus is the subject of study, the application of single tracing methods can be either insufficient or uneconomical to solve the questions asked. In cases where chains of projections are the subjects of study, the simultaneous application of two tracing methods or even more may be compulsory. The present contribution focuses on combinations of several neuroanatomical tract-tracing strategies, enabling in the end the simultaneous, unambiguous and permanent detection of three transported markers according to a three-color paradigm. A number of combinations of three tracers or of two tracers plus the immunocytochemical detection of a neuroactive substance can be conceived; we describe several of these combinations implemented by us using the present multitracer protocol

Gaming motivation and problematic video gaming: The role of needs frustration

Motivation is often used as a predictor of a problematic style of video game engagement, implying that individuals' gaming undermines optimal functioning. Drawing from recent advances in Self-Determination Theory (SDT), the present study explores the links between gaming motivations, the daily frustration of basic psychological needs, and reports of problematic video gaming (PVG). A sample of 1029 participants (72.8% male; M = 22.96 years; SD = 4.13 years) completed items regarding their gaming engagement and gaming motivation as well as their experience of needs frustration and PVG symptoms. Results revealed positive associations between gaming motivations and PVG, and between daily needs frustration and PVG. Finally, after comparing several competing models, a mediational model whereby needs frustration explained the association between individuals' gaming motivation and PVG emerged as best fitting the data. The discussion addresses the theoretical and practical implications of these findings in the context of recent research