Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst-Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.Comment: 21 pages, To appear in Compositio Mathematic

It’s not the model that doesn’t fit, it’s the controller! The role of cognitive skills in understanding the links between natural mapping, performance, and enjoyment of console video games

This study examines differences in performance, frustration, and game ratings of individuals playing first person shooter video games using two different controllers (motion controller and a traditional, pushbutton controller) in a within-subjects, randomized order design. Structural equation modeling was used to demonstrate that cognitive skills such as mental rotation ability and eye/hand coordination predicted performance for both controllers, but the motion control was significantly more frustrating. Moreover, increased performance was only related to game ratings for the traditional controller input. We interpret these data as evidence that, contrary to the assumption that motion controlled interfaces are more naturally mapped than traditional push-button controllers, the traditional controller was more naturally mapped as an interface for gameplay

Abnormal flowers and pattern formation in floral

“From our acquaintance with this abnormal enabled to unveil the secrets that normal us, and to see distinctly what, from the regular we can only infer.” - J. W. von Goethe (1790

Parametric Euler Sum Identities

We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables generate reduction formulae for these sums.Comment: 12 page

Genetic interactions among floral homeotic genes of Arabidopsis

We describe allelic series for three loci, mutations in which result in homeotic conversions in two adjacent whorls in the Arabidopsis thaliana flower. Both the structure of the mature flower and its development from the initial primordium are described by scanning electron microscopy. New mutations at the APETALA2 locus, ap2-2, ap2-8 and ap2-9, cause homeotic conversions in the outer two whorls: sepals to carpels (or leaves) and petals to stamens. Two new mutations of PISTILLATA, pi-2 and pi-3, cause second and third whorl organs to differentiate incorrectly. Homeotic conversions are petals to sepals and stamens to carpels, a pattern similar to that previously described for the apetala3-1 mutation. The AGAMOUS mutations, ag-2 and ag-3, affect the third and fourth whorls and cause petals to develop instead of stamens and another flower to arise in place of the gynoecium. In addition to homeotic changes, mutations at the APETALA2, APETALA3 and PISTILLATA loci may lead to reduced numbers of organs, or even their absence, in specific whorls. The bud and flower phenotypes of doubly and triply mutant strains, constructed with these and previously described alleles, are also described. Based on these results, a model is proposed that suggests that the products of these homeotic genes are each active in fields occupying two adjacent whorls, AP2 in the two outer whorls, PI and AP3 in whorls two and three, and AG in the two inner whorls. In combination, therefore, the gene products in these three concentric, overlapping fields specify the four types of organs in the wild-type flower. Further, the phenotypes of multiple mutant lines indicate that the wild-type products of the AGAMOUS and APETALA2 genes interact antagonistically. AP2 seems to keep the AG gene inactive in the two outer whorls while the converse is likely in the two inner whorls. This field model successfully predicts the phenotypes of all the singly, doubly and triply mutant flowers described

Multi-wavelength holography with a single spatial light modulator for ultracold atom experiments

The authors acknowledge funding from the Leverhulme Trust Research Project Grant RPG-2013-074 and from the EPSRC grant GR/T08272/01.We demonstrate a method to independently and arbitrarily tailor the spatial profile of light of multiple wavelengths and we show possible applications to ultracold atoms experiments. A single spatial light modulator is programmed to create a pattern containing multiple spatially separated structures in the Fourier plane when illuminated with a single wavelength. When the modulator is illuminated with overlapped laser beams of different wavelengths, the position of the structures is wavelength-dependent. Hence, by designing their separations appropriately, a desired overlap of different structures at different wavelengths is obtained. We employ regional phase calculation algorithms and demonstrate several possible experimental scenarios by generating light patterns with 670 nm, 780 nm and 1064 nm laser light which are accurate to the level of a few percent. This technique is easily integrated into cold atom experiments, requiring little optical access.PostprintPeer reviewe

Editorial: Video Games as Demanding Technologies

From the middle-20th century to today, video games have grown from an idiosyncratic interest of computer programmers and engineers to a globally dominant form of media entertainment. Advances in technology and creativity have combined to present players with interactive experience that vary in their cognitive, emotional, physical, and social complexity. That video games constitute co-authored experiences - dialogues between the player and the system - is at least one explanation for their appeal, but this co-authorship brings with it an enhanced set of requirements for the player’s attention. For this thematic issue, researchers were invited to debate and examine the cognitive, emotional, physical, and social demands of video games; their work (as well as the impetus for this work) is summarized below