Sum of Two Squares - Pair Correlation and Distribution in Short Intervals

In this work we show that based on a conjecture for the pair correlation of integers representable as sums of two squares, which was first suggested by Connors and Keating and reformulated here, the second moment of the distribution of the number of representable integers in short intervals is consistent with a Poissonian distribution, where "short" means of length comparable to the mean spacing between sums of two squares. In addition we present a method for producing such conjectures through calculations in prime power residue rings and describe how these conjectures, as well as the above stated result, may by generalized to other binary quadratic forms. While producing these pair correlation conjectures we arrive at a surprising result regarding Mertens' formula for primes in arithmetic progressions, and in order to test the validity of the conjectures, we present numericalz computations which support our approach.Comment: 3 figure

Treatment of falciparum malaria in the age of drug-resistance

The growing problem of drug resistance has greatly complicated the treatment for falciparum malaria. Whereaschloroquine and sulfadoxine/ pyrimethamine could once cure most infections, this is no longer true and requiresexamination of alternative regimens. Not all treatment failures are drug resistant and other issues such asexpired antimalarials and patient compliance need to be considered. Continuation of a failing treatment policyafter drug resistance is established suppresses infections rather than curing them, leading to increasedtransmission of malaria, promotion of epidemics and loss of public confidence in malaria control programs.Antifolate drug resistance (i.e. pyrimethamine) means that new combinations are urgently needed particularlybecause addition of a single drug to an already failing regimen is rarely effective for very long. Atovaquone/proguanil and mefloquine have been used against multiple drug resistant falciparum malaria with resistance toeach having been documented soon after drug introduction. Drug combinations delay further transmission ofresistant parasites by increasing cure rates and inhibiting formation of gametocytes. Most currentlyrecommended drug combinations for falciparum malaria are variants of artemisinin combination therapy wherea rapidly acting artemisinin compound is combined with a longer half-life drug of a different class. Artemisininsused include dihydroartemisinin, artesunate, artemether and companion drugs include mefloquine, amodiaquine,sulfadoxine/ pyrimethamine, lumefantrine, piperaquine, pyronaridine, chlorproguanil/dapsone. The standard ofcare must be to cure malaria by killing the last parasite. Combination antimalarial treatment is vital not only tothe successful treatment of individual patients but also for public health control of malaria

Baby-Step Giant-Step Algorithms for the Symmetric Group

We study discrete logarithms in the setting of group actions. Suppose that $G$ is a group that acts on a set $S$. When $r,s \in S$, a solution $g \in G$ to $r^g = s$ can be thought of as a kind of logarithm. In this paper, we study the case where $G = S_n$, and develop analogs to the Shanks baby-step / giant-step procedure for ordinary discrete logarithms. Specifically, we compute two sets $A, B \subseteq S_n$ such that every permutation of $S_n$ can be written as a product $ab$ of elements $a \in A$ and $b \in B$. Our deterministic procedure is optimal up to constant factors, in the sense that $A$ and $B$ can be computed in optimal asymptotic complexity, and $|A|$ and $|B|$ are a small constant from $\sqrt{n!}$ in size. We also analyze randomized "collision" algorithms for the same problem

Mary Shanks

Dr. Shanks graduated from Illinois Wesleyan University in 1947 and served as the School of Nursing Director from 1960-1976. She was the first Caroline F. Rupert Endowed Chair of Nursing when it was established in 1967

Measurement and Compensation of Horizontal Crabbing at the Cornell Electron Storage Ring Test Accelerator

In storage rings, horizontal dispersion in the rf cavities introduces horizontal-longitudinal (xz) coupling, contributing to beam tilt in the xz plane. This coupling can be characterized by a "crabbing" dispersion term {\zeta}a that appears in the normal mode decomposition of the 1-turn transfer matrix. {\zeta}a is proportional to the rf cavity voltage and the horizontal dispersion in the cavity. We report experiments at the Cornell Electron Storage Ring Test Accelerator (CesrTA) where xz coupling was explored using three lattices with distinct crabbing properties. We characterize the xz coupling for each case by measuring the horizontal projection of the beam with a beam size monitor. The three lattice configurations correspond to a) 16 mrad xz tilt at the beam size monitor source point, b) compensation of the {\zeta}a introduced by one of two pairs of RF cavities with the second, and c) zero dispersion in RF cavities, eliminating {\zeta}a entirely. Additionally, intrabeam scattering (IBS) is evident in our measurements of beam size vs. rf voltage.Comment: 5 figures, 10 page