Thamnophis proximus

Number of Pages: 3Integrative BiologyGeological Science

Thamnophis sauritus

Number of Pages: 2Integrative BiologyGeological Science

Clonophis, C. kirtlandii

Number of Pages: 2Integrative BiologyGeological Science

An average-case depth hierarchy theorem for Boolean circuits

We prove an average-case depth hierarchy theorem for Boolean circuits over the standard basis of $\mathsf{AND}$, $\mathsf{OR}$, and $\mathsf{NOT}$ gates. Our hierarchy theorem says that for every $d \geq 2$, there is an explicit $n$-variable Boolean function $f$, computed by a linear-size depth-$d$ formula, which is such that any depth-$(d-1)$ circuit that agrees with $f$ on $(1/2 + o_n(1))$ fraction of all inputs must have size $\exp({n^{\Omega(1/d)}}).$ This answers an open question posed by H{\aa}stad in his Ph.D. thesis. Our average-case depth hierarchy theorem implies that the polynomial hierarchy is infinite relative to a random oracle with probability 1, confirming a conjecture of H{\aa}stad, Cai, and Babai. We also use our result to show that there is no "approximate converse" to the results of Linial, Mansour, Nisan and Boppana on the total influence of small-depth circuits, thus answering a question posed by O'Donnell, Kalai, and Hatami. A key ingredient in our proof is a notion of \emph{random projections} which generalize random restrictions

Defining the International Accounting Standard Board\u27s governance network

There is little empirical research identifying the structural forces influencing the International Accounting Standards Board (IASB). The purpose of this study was to analyze the structural forces underlying international accounting regulation to contribute insights useable by the public, politicians, and scholars to conceptualize the processes of international accounting regulation. Based on stakeholder theory, legitimacy theory, and social network theory it was posited that this network is rationally created to serve certain stakeholder groups in the face of divergent stakeholder interests. The research questions for this study addressed the organizations which constituted the IASB\u27s governance network, the professional and geographic perspectives represented, and the extent to which the governance network was structurally embedded. Social network methodology was utilized within a case study design. All data consisted of publically available existing data. Social network analysis including graphic notations, density, comembership overlap, and co-organizational overlap were employed to produce a representation of the governance network and to measure the extent to which the network was structurally embedded. To provide supplementary detail, the professional perspectives and geographic representations of the actors were measured. The results indicated that the network forms a definable hierarchy that exhibits qualities of structural embeddedness. Banking interests were more embedded within the governance network than any other professional, academic, or social group. Also, a strong Western influence was detected. The societal benefit of this effort was to engage society in general and accounting researchers in particular in hopes of encouraging diverse representation in regulatory processes with both macro and micro-consequences