Maximal determinants and saturated D-optimal designs of orders 19 and 37

A saturated D-optimal design is a {+1,-1} square matrix of given order with maximal determinant. We search for saturated D-optimal designs of orders 19 and 37, and find that known matrices due to Smith, Cohn, Orrick and Solomon are optimal. For order 19 we find all inequivalent saturated D-optimal designs with maximal determinant, 2^30 x 7^2 x 17, and confirm that the three known designs comprise a complete set. For order 37 we prove that the maximal determinant is 2^39 x 3^36, and find a sample of inequivalent saturated D-optimal designs. Our method is an extension of that used by Orrick to resolve the previously smallest unknown order of 15; and by Chadjipantelis, Kounias and Moyssiadis to resolve orders 17 and 21. The method is a two-step computation which first searches for candidate Gram matrices and then attempts to decompose them. Using a similar method, we also find the complete spectrum of determinant values for {+1,-1} matrices of order 13.Comment: 28 pages, 4 figure

Critical behaviour of the two-dimensional Ising susceptibility

We report computations of the short-distance and the long-distance (scaling) contributions to the square-lattice Ising susceptibility in zero field close to T_c. Both computations rely on the use of nonlinear partial difference equations for the correlation functions. By summing the correlation functions, we give an algorithm of complexity O(N^6) for the determination of the first N series coefficients. Consequently, we have generated and analysed series of length several hundred terms, generated in about 100 hours on an obsolete workstation. In terms of a temperature variable, \tau, linear in T/T_c-1, the short-distance terms are shown to have the form \tau^p(ln|\tau|)^q with p>=q^2. To O(\tau^14) the long-distance part divided by the leading \tau^{-7/4} singularity contains only integer powers of \tau. The presence of irrelevant variables in the scaling function is clearly evident, with contributions of distinct character at leading orders |\tau|^{9/4} and |\tau|^{17/4} being identified.Comment: 11 pages, REVTex

Student Movement on Climate Action at UC San Diego: How College and Students Can Combat Climate Change

The effect of climate disruption is arguably the most imminent threat facing ourgeneration. If we continue down the same “business as usual” model, we will be exposed tounforeseen climate disasters as early as the next decade1. The University of California's Bendingthe Curve2 report outlines the ways in which we can significantly mitigate the threat of climatedisruption through ten scalable solutions that fall into six clusters: Science, Technology,Governance Solutions, Societal Transformation, Market-Based Solutions, and EcosystemRestoration. Since climate change is such an imminent issue, mitigation on a global scale isnecessary in order to bend the curve before unprecedented disruption. However, this call toaction is rarely ever motivated through moral conviction alone.3Most governments exist tosatisfy the people within their constituencies, so the voice calling for climate action needs tocome directly from the people. In this report, we find that students are key actors in climateaction because of their youthful passion, access to education and technology, and incentive to getinvolved in their communities. Our report advocates for a global student movement againstclimate disruption. In this paper, we will analyze the current movement against climate changethat is active at our university (University of California, San Diego), suggest solutions that clubson campuses can take in order to strengthen the numbers and initiatives of the movement, andfinally, propose ways in which students can get involved with climate action in the city of SanDiego