Subspace-Invariant AC0^0 Formulas

We consider the action of a linear subspace $U$ of $\{0,1\}^n$ on the set of AC$^0$ formulas with inputs labeled by literals in the set $\{X_1,\overline X_1,\dots,X_n,\overline X_n\}$, where an element $u \in U$ acts on formulas by transposing the $i$th pair of literals for all $i \in [n]$ such that $u_i=1$. A formula is {\em $U$-invariant} if it is fixed by this action. For example, there is a well-known recursive construction of depth $d+1$ formulas of size $O(n{\cdot}2^{dn^{1/d}})$ computing the $n$-variable PARITY function; these formulas are easily seen to be $P$-invariant where $P$ is the subspace of even-weight elements of $\{0,1\}^n$. In this paper we establish a nearly matching $2^{d(n^{1/d}-1)}$ lower bound on the $P$-invariant depth $d+1$ formula size of PARITY. Quantitatively this improves the best known $\Omega(2^{\frac{1}{84}d(n^{1/d}-1)})$ lower bound for {\em unrestricted} depth $d+1$ formulas, while avoiding the use of the switching lemma. More generally, for any linear subspaces $U \subset V$, we show that if a Boolean function is $U$-invariant and non-constant over $V$, then its $U$-invariant depth $d+1$ formula size is at least $2^{d(m^{1/d}-1)}$ where $m$ is the minimum Hamming weight of a vector in $U^\bot \setminus V^\bot$

Thamnophis proximus

Number of Pages: 3Integrative BiologyGeological Science

Thamnophis sauritus

Number of Pages: 2Integrative BiologyGeological Science

Alterations of membrane curvature during influenza virus budding

Influenza A virus belongs to the Orthomyxoviridae family. It is an enveloped virus that contains a segmented and negative-sense RNA genome. Influenza A viruses cause annual epidemics and occasional major pandemics, are a major cause of morbidity and mortality worldwide, and have a significant financial impact on society. Assembly and budding of new viral particles are a complex and multi-step process involving several host and viral factors. Influenza viruses use lipid raft domains in the apical plasma membrane of polarized epithelial cells as sites of budding. Two viral glycoproteins, haemagglutinin and neuraminidase, concentrate in lipid rafts, causing alterations in membrane curvature and initiation of the budding process. Matrix protein 1 (M1), which forms the inner structure of the virion, is then recruited to the site followed by incorporation of the viral ribonucleoproteins and matrix protein 2 (M2). M1 can alter membrane curvature and progress budding, whereas lipid raft-associated M2 stabilizes the site of budding, allowing for proper assembly of the virion. In the later stages of budding, M2 is localized to the neck of the budding virion at the lipid phase boundary, where it causes negative membrane curvature, leading to scission and virion release

Who Killed the Travelin' Soldier: Elites, Masses, and Blacklisting of Critical Speakers

Several studies have shown the influence of ownership on media content in routine contexts but none has quantitatively tested it in the theoretically important context of a crisis. Recently the country musicians the Dixie Chicks were blacklisted from the radio for criticizing the president in wartime. I use this event to test the role of media ownership in a crisis. Through analyzing airplay from a national sample of radio stations, this paper finds that contrary to prominent allegations grounded in the political economy tradition of media sociology, this backlash did not come from owners of large chains. Rather, I find that opposition to the Dixie Chicks represents grassroots conservative sentiment, which may be exacerbated by the ideological connotations of country music or tempered by tolerance for dissent.