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Trace formulae for d-regular graphs are derived and used to express the spectral density in terms of the periodic walks on the graphs under consideration. The trace formulae depend on a parameter w which can be tuned continuously to assign different weights to different periodic orbit contributions. At the special value w = 1, the only periodic orbits which(More)
The autism susceptibility candidate 2 gene (AUTS2) has been associated with multiple neurological diseases including autism spectrum disorders (ASDs). Previous studies showed that AUTS2 has an important neurodevelopmental function and is a suspected master regulator of genes implicated in ASD-related pathways. However, the regulatory role and targets of(More)
We study the distribution of the number of (non-backtracking) periodic walks on large regular graphs. We propose a formula for the ratio between the variance of the number of t-periodic walks and its mean, when the cardinality of the vertex set V and the period t approach ∞ with t/V → τ for any τ. This formula is based on the conjecture that the spectral(More)
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