This paper is concerned with certain connections between the ensemble of n × n unitary matrices—specifically the characteristic function of the random variable tr(U)—and combinatorics—specifically Ulam’s problem concerning the distribution of the length of the longest increasing subsequence in permutation groups—and the appearance of Painlevé functions in the answers to apparently unrelated que...

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium (or ti...

Stereo-transparency is an intriguing, but not well-understood, phenomenon. In the present experiment, we simultaneously manipulated the number of overlaid planes, density of elements, and depth separation between the planes in random dot stereograms to evaluate the constraints on stereoscopic transparency. We used a novel task involving identification of patterned planes among the planes consti...

There has been an increasing interest in all-optical analogues of electromagnetically induced transparency and Autler-Townes splitting. Despite the differences in their underlying physics, both electromagnetically induced transparency and Autler-Townes splitting are quantified by a transparency window in the absorption or transmission spectrum, which often leads to a confusion about its origin....

in this paper, an exchange of letters between the philosopher jacques derrida and architect peter eisenman is used as a catalyst to discuss the material qualities of glass and its relationship with the concept of transparency in architecture. in his criticism of an architecture devoid of human qualities, derrida uses glass, defined through walter benjamin’s writings, as a hard and cold material...

Sellers increasingly compete with innovative Internet-based selling mechanisms, revealing or concealing market information. Transparency strategy involves design choices by firms that influence the availability and accessibility of information about products and prices. We develop decision support models for suppliers to set prices for online mechanisms with different transparency levels. We th...