A note on products of Relative Difference Sets

Relative Difference Sets with the parameters k = nλ have been constructed many ways (see (Davis, forthcoming; Elliot and Butson 1966; and Jungnickel 1982)). This paper proves a result on building new RDS by taking products of others (much like (Dillon 1985)), and this is applied to several new examples (primarily involving (pi, pj, pi, pi-j))

Convexity of the class of currents with finite relative energy

We prove the convexity of the class of currents with finite relative energy. A key ingredient is an integration by parts formula for relative non-pluripolar products which is of independent interest.Comment: 10 page

Constructions of biangular tight frames and their relationships with equiangular tight frames

We study several interesting examples of Biangular Tight Frames (BTFs) - basis-like sets of unit vectors admitting exactly two distinct frame angles (ie, pairwise absolute inner products) - and examine their relationships with Equiangular Tight Frames (ETFs) - basis-like systems which admit exactly one frame angle. We demonstrate a smooth parametrization BTFs, where the corresponding frame angles transform smoothly with the parameter, which "passes through" an ETF answers two questions regarding the rigidity of BTFs. We also develop a general framework of so-called harmonic BTFs and Steiner BTFs - which includes the equiangular cases, surprisingly, the development of this framework leads to a connection with the famous open problem(s) regarding the existence of Mersenne and Fermat primes. Finally, we construct a (chordally) biangular tight set of subspaces (ie, a tight fusion frame) which "Pl\"ucker embeds" into an ETF.Comment: 19 page

Generating global products of LAI and FPAR from SNPP-VIIRS data: theoretical background and implementation

Leaf area index (LAI) and fraction of photosynthetically active radiation (FPAR) absorbed by vegetation have been successfully generated from the Moderate Resolution Imaging Spectroradiometer (MODIS) data since early 2000. As the Visible Infrared Imaging Radiometer Suite (VIIRS) instrument onboard, the Suomi National Polar-orbiting Partnership (SNPP) has inherited the scientific role of MODIS, and the development of a continuous, consistent, and well-characterized VIIRS LAI/FPAR data set is critical to continue the MODIS time series. In this paper, we build the radiative transfer-based VIIRS-specific lookup tables by achieving minimal difference with the MODIS data set and maximal spatial coverage of retrievals from the main algorithm. The theory of spectral invariants provides the configurable physical parameters, i.e., single scattering albedos (SSAs) that are optimized for VIIRS-specific characteristics. The effort finds a set of smaller red-band SSA and larger near-infraredband SSA for VIIRS compared with the MODIS heritage. The VIIRS LAI/FPAR is evaluated through comparisons with one year of MODIS product in terms of both spatial and temporal patterns. Further validation efforts are still necessary to ensure the product quality. Current results, however, imbue confidence in the VIIRS data set and suggest that the efforts described here meet the goal of achieving the operationally consistent multisensor LAI/FPAR data sets. Moreover, the strategies of parametric adjustment and LAI/FPAR evaluation applied to SNPP-VIIRS can also be employed to the subsequent Joint Polar Satellite System VIIRS or other instruments.Accepted manuscrip

The phase transition in random catalytic sets

The notion of (auto) catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems. Here we study catalytic random networks with respect to the final outcome diversity of products. We show that an analytical treatment of this longstanding problem is possible by mapping the problem onto a set of non-linear recurrence equations. The solution of these equations show a crucial dependence of the final number of products on the initial number of products and the density of catalytic production rules. For a fixed density of rules we can demonstrate the existence of a phase transition from a practically unpopulated regime to a fully populated and diverse one. The order parameter is the number of final products. We are able to further understand the origin of this phase transition as a crossover from one set of solutions from a quadratic equation to the other.Comment: 7 pages, ugly eps files due to arxiv restriction

Motivation crowding in real consumption decisions: Who is messing with my groceries?

We present evidence of crowding out of intrinsic motivation in real purchasing decisions from a field experiment in a large supermarket chain. We compare three instruments, a label, a subsidy and a neutral price change, in their ability to induce consumers to switch from dirty to clean products. Interestingly a subsidy framed as an intervention is less effective than either a label or a neutrally framed price change. We argue that this provides a new explanation for crowding behaviour: consumers are resistant to having the line of demarcation between public and private decision making moved - in either direction