718,139 research outputs found
Bijections for Entringer families
Andr\'e proved that the number of alternating permutations on is equal to the Euler number . 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 for computing
the Euler numbers. In a series of papers, using generating function method and
induction, Poupard gave several further combinatorial interpretations for
both in alternating permutations and increasing trees. Kuznetsov,
Pak, and Postnikov have given more combinatorial interpretations of
in the model of trees. The aim of this paper is to provide bijections between
the different models for 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
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
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
(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 LaTiO
The pressure-induced changes in the optical properties of the
quasi-one-dimensional conductor LaTiO 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
Anderson localization through Polyakov loops: lattice evidence and Random matrix model
We investigate low-lying fermion modes in SU(2) gauge theory at temperatures
above the phase transition. Both staggered and overlap spectra reveal
transitions from chaotic (random matrix) to integrable (Poissonian) behavior
accompanied by an increasing localization of the eigenmodes. We show that the
latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong"
Polyakov loops can therefore be viewed as defects leading to Anderson
localization in gauge theories. We find strong similarities in the spatial
profile of these localized staggered and overlap eigenmodes. We discuss
possible interpretations of this finding and present a sparse random matrix
model that reproduces these features.Comment: 11 pages, 23 plots in 11 figures; some comments and references added,
some axis labels corrected; journal versio
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