We employ tools from the fields of symbolic computation and satisfiability checking— namely, computer algebra systems and SAT solvers—to study the Williamson conjecture from combinatorial design theory and increase the bounds to which Williamson matrices have been enumerated. In particular, we completely enumerate all Williamson matrices of even order up to and including 70 which gives us deepe...

It is shown that if q is a prime power then there are Williamson-type matrices of order (i) 1/2q2(q + 1) when q ≡ 1 (mod 4), (ii)1/4q2(q + 1) when q ≡ 3 (mod 4) and there are Williamson-type matrices of order l/4(q + 1). This gives Williamson-type matrices for the new orders 363, 1183, 1805, 2601, 3174, 5103. The construction can be combined with known results on orthogonal designs to give an H...

Neuroimmune Signaling in the Hippocampus: Mechanisms of Risk and Resilience by Lauren Leshen Williamson Department of Psychology & Neuroscience Duke University Date: _______________________ Approved: ___________________________ Staci D. Bilbo, Supervisor ___________________________ Christina L. Williams ___________________________ Henry Yin ___________________________ Cagla Eroglu _____________...

This chapter will focus on the first two questions. The last question is equally important — of course we need to know the best way to make predictions, perform diagnoses and make strategic decisions — but in the absence of a well-entrenched mathematical calculus of causality, the answers given to the last question tend to depend on the answers provided to the first two questions. Standard resp...

I do not propose this evening to delve into the age-old argument concerning the discoverer of anesthesia. It is doubtful if any here assembled have, to any very great extent, witnessed surgery without anesthesia, yet only 100 years ago the screams of agony issuing from the operating room would have chilled the blood of the hardiest among us. The important point of this contribution is not which...

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