An Algebraic Approach to Test Primality

Every 10 minutes, the amount of human generated data expands by more than 10 petabyes. This is equivalent to nearly one third of all literature in all languages from the beginning of recorded history. Such vast amounts of data necessitate effective techniques for data integrity, identity verification and data security. Cryptography aims to satisfy these needs. Many modern cryptographic schemes depend on generating prime numbers. Consequently, one must develop efficient tests to check whether or not a given integer is prime. Many of these tests use the properties of mathematical structures called groups. However, there are cases where non-prime numbers, called pseudoprimes, pass these tests for primality. We investigate several types of pseudoprimes based on primality tests associated to Lucas groups and Elliptic curve groups. In each case, we study the existence of and relationships among these different types of pseudoprimes

Astro2020 APC White Paper. 2020 Vision: Towards a Sustainable OIR System

Open-access telescopes of all apertures are needed to operate a competitive and efficient national science program. While larger facilities contribute light-gathering power and angular resolution, smaller ones dominate for field of view, time-resolution, and especially, total available observing time, thereby enabling our entire, diversely-expert community. Smaller aperture telescopes therefore play a critical and indispensable role in advancing science. Thus, the divestment of NSF support for modest-aperture (1 – 4 m) public telescopes poses a serious threat to U.S. scientific leadership, which is compounded by the unknown consequences of the shift from observations driven by individual investigators to survey-driven science. Given the much higher cost efficiency and dramatic science returns for investments in modest aperture telescopes, it is hard to justify funding only the most expensive facilities. We therefore urge the Astro2020 panel to explicitly make the case for modest aperture facilities, and to recommend enhancing this funding stream to support and grow this critical component of the OIR System. Further study is urgently needed to prioritize the numerous exciting potential capabilities of smaller facilities,and to establish sustainable, long-term planning for the System

2020 Vision: Towards a Sustainable OIR System

Open-access telescopes of all apertures are needed to operate a competitive and efficient national science program. While larger facilities contribute light-gathering power and angular resolution, smaller ones dominate for field of view, time-resolution, and especially, total available observing time, thereby enabling our entire, diversely-expert community. Smaller aperture telescopes therefore play a critical and indispensable role in advancing science. Thus, the divestment of NSF support for modest-aperture (1 - 4 m) public telescopes poses a serious threat to U.S. scientific leadership, which is compounded by the unknown consequences of the shift from observations driven by individual investigators to survey-driven science. Given the much higher cost efficiency and dramatic science returns for investments in modest aperture telescopes, it is hard to justify funding only the most expensive facilities. We therefore urge the Astro2020 panel to explicitly make the case for modest aperture facilities, and to recommend enhancing this funding stream to support and grow this critical component of the OIR System. Further study is urgently needed to prioritize the numerous exciting potential capabilities of smaller facilities,and to establish sustainable, long-term planning for the System.Comment: Astro2020 APC White Pape

Status of our scientific understanding of lodgepole pine and mountain pine beetles: a focus on forest ecology and fire behavior, The

A synthesis of our current knowledge about the effects of the mountain pine beetle epidemic on lodgepole pine forests and fire behavior, with a geographic focus on Colorado and southern Wyoming.A synthesis of our current knowledge about the effects of the mountain pine beetle epidemic on lodgepole pine forests and fire behavior, with a geographic focus on Colorado and southern Wyoming