Bijections for Entringer families

Andr\'e proved that the number of alternating permutations on $\{1, 2, \dots, n\}$ is equal to the Euler number $E_n$. A refinement of Andr\'e's result was given by Entringer, who proved that counting alternating permutations according to the first element gives rise to Seidel's triangle $(E_{n,k})$ for computing the Euler numbers. In a series of papers, using generating function method and induction, Poupard gave several further combinatorial interpretations for $E_{n,k}$ both in alternating permutations and increasing trees. Kuznetsov, Pak, and Postnikov have given more combinatorial interpretations of $E_{n,k}$ in the model of trees. The aim of this paper is to provide bijections between the different models for $E_{n,k}$ as well as some new interpretations. In particular, we give the first explicit one-to-one correspondence between Entringer's alternating permutation model and Poupard's increasing tree model.Comment: 19 page

Everything, and then some

On its intended interpretation, logical, mathematical and metaphysical discourse sometimes seems to involve absolutely unrestricted quantification. Yet our standard semantic theories do not allow for interpretations of a language as expressing absolute generality. A prominent strategy for defending absolute generality, influentially proposed by Timothy Williamson in his paper ‘Everything’ (2003), avails itself of a hierarchy of quantifiers of ever increasing orders to develop non-standard semantic theories that do provide for such interpretations. However, as emphasized by Øystein Linnebo and Agustín Rayo (2012), there is pressure on this view to extend the quantificational hierarchy beyond the finite level, and, relatedly, to allow for a cumulative conception of the hierarchy. In his recent book, Modal Logic as Metaphysics (2013), Williamson yields to that pressure. I show that the emerging cumulative higher-orderist theory has implications of a strongly generality-relativist flavour, and consequently undermines much of the spirit of generality absolutism that Williamson set out to defend

The effects of belongingness on the Simultaneous Lightness Contrast: A virtual reality study

Simultaneous Lightness Contrast (SLC) is the phenomenon whereby a grey patch on a dark background appears lighter than an equal patch on a light background. Interestingly, the lightness difference between these patches undergoes substantial augmentation when the two backgrounds are patterned, thereby forming the articulated-SLC display. There are two main interpretations of these phenomena: The midlevel interpretation maintains that the visual system groups the luminance within a set of contiguous frameworks, whilst the high-level one claims that the visual system splits the luminance into separate overlapping layers corresponding to separate physical contributions. This research aimed to test these two interpretations by systematically manipulating the viewing distance and the horizontal distance between the backgrounds of both the articulated and plain SLC displays. An immersive 3D Virtual Reality system was employed to reproduce identical alignment and distances, as well as isolating participants from interfering luminance. Results showed that reducing the viewing distance resulted in increased contrast in both the plain- and articulated-SLC displays and that, increasing the horizontal distance between the backgrounds resulted in decreased contrast in the articulated condition but increased contrast in the plain condition. These results suggest that a comprehensive lightness theory should combine the two interpretations

(WP 2018-03) Comment on White on the Relationship between Economics and Ethics

This short comment on Mark White’s comment on the relationship of economics and ethics focuses on the nature of economics and ethics as an emergent field of investigation. It discusses different types of between-discipline fields, and compares crossdisciplinary and transdisciplinary interpretations of economics and ethics. The ‘domestication’ thesis associated with borrowing across disciplines is examined in terms of the idea of a metaphorical transfers. Institutional constraints on between-discipline developments are evaluated relative to increasing specialization within and across disciplines. The transdisciplinary interpretation of economics and ethics is given a complexity theory explanation

Editorialising practices, competitive marketablility and James Thomson's 'The seasons'

The lapse of Andrew Millar's copyright for James Thomson's The Seasons in 1765 resulted in an increasing number of new editions of the poem being published in the late eighteenth century. This article compares the print-cultural make-ups of three editions of The Seasons that were issued in the 1790s. An examination of the print-cultural differences between these publishing ventures reveals distinct editorial practices and marketing strategies. In an attempt to increase the attractiveness of their editions with visual and textual paraphernalia, the producers developed their own versions' of The Seasons and, in the process, fashioned new interpretations of Thomson's poem

The excedances and descents of bi-increasing permutations

Starting from some considerations we make about the relations between certain difference statistics and the classical permutation statistics we study permutations whose inversion number and excedance difference coincide. It turns out that these (so-called bi-increasing) permutations are just the 321-avoiding ones. The paper investigates their excedance and descent structure. In particular, we find some nice combinatorial interpretations for the distribution coefficients of the number of excedances and descents, respectively, and their difference analogues over the bi-increasing permutations in terms of parallelogram polyominoes and 2-Motzkin paths. This yields a connection between restricted permutations, parallelogram polyominoes, and lattice paths that reveals the relations between several well-known bijections given for these objects (e.g. by Delest-Viennot, Billey-Jockusch-Stanley, Francon-Viennot, and Foata-Zeilberger). As an application, we enumerate skew diagrams according to their rank and give a simple combinatorial proof for a result concerning the symmetry of the joint distribution of the number of excedances and inversions, respectively, over the symmetric group.Comment: 36 page

Ideology is theft: Thoughts on the legitimacy of a Maori psychology

‘War, in fact, can be seen as a process of achieving equilibrium among unequal technologies’ (McLuhan, 1964) We are at war. As Western science and its accompanying technology expands the frontiers of knowledge at an ever-increasing rate, ‘indigenous’ perspectives of knowledge are exiled into the borderlands of special interest groups and localized research programmes. Mainstream scientific thought lays claim to objective interpretations of experience at the expense of alternative realities offered by emerging theories of knowledge. Furthermore, as localized worldviews (i.e., those derived from ancestral knowledge bases and pre-industrial or non-scientific premises) challenge existing paradigms, the inevitable interactions threaten to undermine the fidelity of this knowledge. One such arena where this ideological conflict is apparent is the growing field of Maori psychology

Effect of pressure on the polarized infrared optical response of quasi-one-dimensional LaTiO3.41_{3.41}

The pressure-induced changes in the optical properties of the quasi-one-dimensional conductor LaTiO$_{3.41}$ were studied by polarization-dependent mid-infrared micro-spectroscopy at room temperature. For the polarization of the incident radiation parallel to the conducting direction, the optical conductivity spectrum shows a pronounced mid-infrared absorption band, exhibiting a shift to lower frequencies and an increase in oscillator strength with increasing pressure. On the basis of its pressure dependence, interpretations of the band in terms of electronic transitions and polaronic excitations are discussed. Discontinuous changes in the optical response near 15 GPa are in agreement with a recently reported pressure-induced structural phase transition and indicate the onset of a dimensional crossover in this highly anisotropic system.Comment: 7 pages, 7 figure

Attention training through gaze-contingent feedback: effects on reappraisal and negative emotions

Reappraisal is central to emotion regulation but its mechanisms are unclear. This study tested the theoretical prediction that emotional attention bias is linked to reappraisal of negative emotion-eliciting stimuli and subsequent emotional responding using a novel attentional control training. Thirty-six undergraduates were randomly assigned to either the control or the attention training condition and were provided with different task instructions while they performed an interpretation task. Whereas control participants freely created interpretations, participants in the training condition were instructed to allocate attention toward positive words to efficiently create positive interpretations (i.e., recruiting attentional control) while they were provided with gaze-contingent feedback on their viewing behavior. Transfer to attention bias and reappraisal success was evaluated using a dot-probe task and an emotion regulation task which were administered before and after the training. The training condition was effective at increasing attentional control and resulted in beneficial effects on the transfer tasks. Analyses supported a serial indirect effect with larger attentional control acquisition in the training condition leading to negative attention bias reduction, in turn predicting greater reappraisal success which reduced negative emotions. Our results indicate that attentional mechanisms influence the use of reappraisal strategies and its impact on negative emotions. The novel attention training highlights the importance of tailored feedback to train attentional control. The findings provide an important step toward personalized delivery of attention training