Natural Density of Rectangular Unimodular Integer Matrices

In this paper, we compute the natural density of the set of k x n integer matrices that can be extended to an invertible n x n matrix over the integers. As a corollary, we find the density of rectangular matrices with Hermite normal form [O Id]. Connections with Cesaro's Theorem on the density of coprime integers and Quillen-Suslin's Theorem are also presented.Comment: 8 page

Public Key Cryptography based on Semigroup Actions

A generalization of the original Diffie-Hellman key exchange in $(\Z/p\Z)^*$ found a new depth when Miller and Koblitz suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build interesting semigroup actions using finite (simple) semirings. The practicality of the proposed extensions rely on the orbit sizes of the semigroup actions and at this point it is an open question how to compute the sizes of these orbits in general and also if there exists a square root attack in general. In Section 2 a concrete practical semigroup action built from simple semirings is presented. It will require further research to analyse this system.Comment: 20 pages. To appear in Advances in Mathematics of Communication

Weight-Preserving Simulated Tempering

Simulated tempering is popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\pi}. One problem with simulated tempering for multimodal targets is that the weights of the various modes change for different inverse-temperature values, sometimes dramatically so. In this paper, we provide a fix to overcome this problem, by adjusting the mode weights to be preserved (i.e., constant) over different inverse-temperature settings. We then apply simulated tempering algorithms to multimodal targets using our mode weight correction. We present simulations in which our weight-preserving algorithm mixes between modes much more successfully than traditional tempering algorithms. We also prove a diffusion limit for an version of our algorithm, which shows that under appropriate assumptions, our algorithm mixes in time O(d [log d]^2)

Representing Native Peoples: Native Narratives of Indigenous History and Culture

Together, the articles in this special issue of the American Indian Culture and Research Journal offer a discussion of how Indigenous peoples have represented themselves and their communities in different periods and contexts, as well as through various media. Ranging across anthropology, art history, cartography, film studies, history, and literature, the authors examine how Native people negotiate with prominent images and ideas that represented Indians in the dominant culture and society in the United States and the Americas. These essays go beyond the problems of cultural appropriation by non-Indians to probe the myriad ways Native Americans and Indigenous people have challenged, reinforced, shifted, and overturned those representations

This is Indian Country

For most of the past century, a migration has been taking place within the United States: Native Americans have been moving from tribal and rural lands to America’s cities. But Native Americans have not abandoned reservations for urban life. Instead, they’ve built a network that joins reservations, rural lands, suburban communities and urban centers, with Los Angeles as the “urban Indian capital of the United States.

Painting Native America in Public: American Indian Artists and the New Deal

The New Deal represents a critical period in the development of American Indian art. Shifts in policy created opportunities for American Indians to study art, and New Deal commissions for murals in post offices and other public spaces enabled artists to develop skills, establish their reputations, and make a living. American Indian artists also faced challenges in the form of dominant expectations for Native art and paternalism from officials and administrators. The benefits of New Deal commissions and the struggles with their limitations nonetheless formed a foundation for subsequent generations of Native artists who claimed more control over their art