McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions

Evidence is presented to suggest that, in three dimensions, spherical 6-designs with N points exist for N=24, 26, >= 28; 7-designs for N=24, 30, 32, 34, >= 36; 8-designs for N=36, 40, 42, >= 44; 9-designs for N=48, 50, 52, >= 54; 10-designs for N=60, 62, >= 64; 11-designs for N=70, 72, >= 74; and 12-designs for N=84, >= 86. The existence of some of these designs is established analytically, while others are given by very accurate numerical coordinates. The 24-point 7-design was first found by McLaren in 1963, and -- although not identified as such by McLaren -- consists of the vertices of an "improved" snub cube, obtained from Archimedes' regular snub cube (which is only a 3-design) by slightly shrinking each square face and expanding each triangular face. 5-designs with 23 and 25 points are presented which, taken together with earlier work of Reznick, show that 5-designs exist for N=12, 16, 18, 20, >= 22. It is conjectured, albeit with decreasing confidence for t >= 9, that these lists of t-designs are complete and that no others exist. One of the constructions gives a sequence of putative spherical t-designs with N= 12m points (m >= 2) where N = t^2/2 (1+o(1)) as t -> infinity.Comment: 16 pages, 1 figur

Bidirectional syntactic priming across cognitive domains: from arithmetic to language and back

Scheepers et al. (2011) showed that the structure of a correctly solved mathematical equation affects how people subsequently complete sentences containing high vs. low relative-clause attachment ambiguities. Here we investigated whether such effects generalise to different structures and tasks, and importantly, whether they also hold in the reverse direction (i.e., from linguistic to mathematical processing). In a questionnaire-based experiment, participants had to solve structurally left- or right-branching equations (e.g., 5 × 2 + 7 versus 5 + 2 × 7) and to provide sensicality ratings for structurally left- or right-branching adjective-noun-noun compounds (e.g., alien monster movie versus lengthy monster movie). In the first version of the experiment, the equations were used as primes and the linguistic expressions as targets (investigating structural priming from maths to language). In the second version, the order was reversed (language-to-maths priming). Both versions of the experiment showed clear structural priming effects, conceptually replicating and extending the findings from Scheepers et al. (2011). Most crucially, the observed bi-directionality of cross-domain structural priming strongly supports the notion of shared syntactic representations (or recursive procedures to generate and parse them) between arithmetic and language

A new class of random processes with application to helicopter noise

The concept of dividing random processes into classes (e.g., stationary, locally stationary, periodically correlated, and harmonizable) has long been employed. A new class of random processes is introduced which includes many of these processes as well as other interesting processes which fall into none of the above classes. Such random processes are denoted as linearly correlated. This class is shown to include the familiar stationary and periodically correlated processes as well as many other, both harmonizable and non-harmonizable, nonstationary processes. When a process is linearly correlated for all t and harmonizable, its two-dimensional power spectral density S(x)(omega 1, omega 2) is shown to take a particularly simple form, being non-zero only on lines such that omega 1 to omega 2 = + or - r(k) where the r(k's) are (not necessarily equally spaced) roots of a characteristic function. The relationship of such processes to the class of stationary processes is examined. In addition, the application of such processes in the analysis of typical helicopter noise signals is described

On a class of nonstationary stochastic processes

A new class of nonstationary stochastic processes is introduced and some of the essential properties of its members are investigated. This class is richer than the class of stationary processes and has the potential of modeling some nonstationary time series. The relation between these newly defined processes with other important classes of nonstationary processes is investigated. Several examples of linearly correlated processes which are not stationary, periodically correlated, or harmonizable are given

Mesh ratios for best-packing and limits of minimal energy configurations

For $N$-point best-packing configurations $\omega_N$ on a compact metric space $(A,\rho)$, we obtain estimates for the mesh-separation ratio $\gamma(\omega_N,A)$, which is the quotient of the covering radius of $\omega_N$ relative to $A$ and the minimum pairwise distance between points in $\omega_N$. For best-packing configurations $\omega_N$ that arise as limits of minimal Riesz $s$-energy configurations as $s\to \infty$, we prove that $\gamma(\omega_N,A)\le 1$ and this bound can be attained even for the sphere. In the particular case when N=5 on $S^2$ with $\rho$ the Euclidean metric, we prove our main result that among the infinitely many 5-point best-packing configurations there is a unique configuration, namely a square-base pyramid $\omega_5^*$, that is the limit (as $s\to \infty$) of 5-point $s$-energy minimizing configurations. Moreover, $\gamma(\omega_5^*,S^2)=1$

Development of a Translator from LLVM to ACL2

In our current work a library of formally verified software components is to be created, and assembled, using the Low-Level Virtual Machine (LLVM) intermediate form, into subsystems whose top-level assurance relies on the assurance of the individual components. We have thus undertaken a project to build a translator from LLVM to the applicative subset of Common Lisp accepted by the ACL2 theorem prover. Our translator produces executable ACL2 formal models, allowing us to both prove theorems about the translated models as well as validate those models by testing. The resulting models can be translated and certified without user intervention, even for code with loops, thanks to the use of the def::ung macro which allows us to defer the question of termination. Initial measurements of concrete execution for translated LLVM functions indicate that performance is nearly 2.4 million LLVM instructions per second on a typical laptop computer. In this paper we overview the translation process and illustrate the translator's capabilities by way of a concrete example, including both a functional correctness theorem as well as a validation test for that example.Comment: In Proceedings ACL2 2014, arXiv:1406.123

Incivility in the Workplace: The Experiences of Female Sport Management Faculty in Higher Education

Access to higher education for women has dramatically increased in the United States during the past 50 years. Female college graduates have reversed the figures and gone from being outnumbered by their male counterparts 3 to 2 in the 1970s, to now outnumbering male college graduates 3 to 2. Women also graduate from masters and doctoral programs at a higher rate than men. However, increases in the number of women obtaining college and advanced degrees has not translated to comparable representation in faculty positions or leadership roles in higher education. This lack of women in leadership positions, as well as perceived discrimination against female faculty, may be even more of a concern in sport management programs. Sport is considered a male domain, and women are often seen as intruders in this realm. The purpose of this study was to examine the manifestation of incivility from colleagues and superiors experienced within a sample of female sport management faculty members utilizing social identity theory as a guiding framework. Incivility was conceptualized for the current study as deviant behavior that is not necessarily intended to physically harm the target (e.g., belittling others, showing disdain to someone while they are talking, engaging in outside tasks during meetings)