Audaciously Hopeful: How President Obama Can Help Restore the Pro-Trade Consensus

There is reason for grave concern about the direction of U.S. trade policy. The bipartisan, pro-trade consensus that served U.S. economic and diplomatic interests so well for so long collapsed during the final two years of the Bush administration. Trade skeptics have increased their ranks in the new Congress, a majority of Americans perceive trade as threatening, and grim economic news has made the political climate inhospitable to arguments in support of trade. But restoring the pro-trade consensus must be a priority of the Obama administration. If the United States indulges misplaced fears, restrains economic freedoms, and attempts to retreat from the global economy, the country will suffer slower economic growth and have greater difficulty facing future economic and foreign policy challenges. America's trade skepticism is largely the product of a top-down process. Perceptions have been shaped overwhelmingly by relentless political rhetoric that relies on three myths. Congress and the media have spoken for years about the decline of U.S. manufacturing as though it were fact, when the overwhelming evidence points to a sector that, until the onset of the current recession, was robust and setting performance records. Both lament the U.S. trade deficit without attempting to convey or even understand its causes, meaning, or implications. And both attribute these alleged failures of policy to lax enforcement of existing trade agreements. President Obama should reexamine these premises. He will find that they are long on fallacy and short on fact. Meanwhile, the president will find it necessary to rein in the congressional leadership's increasingly provocative approach to trade policy if he is to have success repairing America's foreign policy credibility. The determination of the president to arrest and reverse America's misguided and metastasizing aversion to trade could dramatically improve prospects for restoring the pro-trade consensus

BosonSampling with Lost Photons

BosonSampling is an intermediate model of quantum computation where linear-optical networks are used to solve sampling problems expected to be hard for classical computers. Since these devices are not expected to be universal for quantum computation, it remains an open question of whether any error-correction techniques can be applied to them, and thus it is important to investigate how robust the model is under natural experimental imperfections, such as losses and imperfect control of parameters. Here we investigate the complexity of BosonSampling under photon losses---more specifically, the case where an unknown subset of the photons are randomly lost at the sources. We show that, if $k$ out of $n$ photons are lost, then we cannot sample classically from a distribution that is $1/n^{\Theta(k)}$-close (in total variation distance) to the ideal distribution, unless a $\text{BPP}^{\text{NP}}$ machine can estimate the permanents of Gaussian matrices in $n^{O(k)}$ time. In particular, if $k$ is constant, this implies that simulating lossy BosonSampling is hard for a classical computer, under exactly the same complexity assumption used for the original lossless case.Comment: 12 pages. v2: extended concluding sectio

Taylor's Theorem for Functionals on BMO with Application to BMO Local Minimizers

In this note two results are established for energy functionals that are given by the integral of $W(\mathbf x,\nabla \mathbf u(\mathbf x))$ over $\Omega \subset\mathbb{R}^n$ with $\nabla \mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$, the space of functions of Bounded Mean Oscillation of John & Nirenberg. A version of Taylor's theorem is first shown to be valid provided the integrand $W$ has polynomial growth. This result is then used to demonstrate that, for the Dirichlet, Neumann, and mixed problems, every Lipschitz-continuous solution of the corresponding Euler-Lagrange equations at which the second variation of the energy is uniformly positive is a strict local minimizer of the energy in $W^{1,BMO}(\Omega;\mathbb{R}^N)$, the subspace of the Sobolev space $W^{1,1}(\Omega;\mathbb{R}^N)$ for which the weak derivative $\nabla\mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$.Comment: 8 page

The yeast F1-ATPase beta subunit precursor contains functionally redundant mitochondrial protein import information

The NH2 terminus of the yeast F1-ATPase beta subunit precursor directs the import of this protein into mitochondria. To define the functionally important components of this import signal, oligonucleotide-directed mutagenesis was used to introduce a series of deletion and missense mutations into the gene encoding the F1-beta subunit precursor. Among these mutations were three nonoverlapping deletions, two within the 19-amino-acid presequence (delta 5-12 and delta 16-19) and one within the mature protein (delta 28-34). Characterization of the mitochondrial import properties of various mutant F1-beta subunit proteins containing different combinations of these deletions showed that import was blocked only when all three deletions were combined. Mutant proteins containing all possible single and pairwise combinations of these deletions were found to retain the ability to direct mitochondrial import of the F1-beta subunit. These data suggest that the F1-beta subunit contains redundant import information at its NH2 terminus. In fact, we found that deletion of the entire F1-beta subunit presequence did not prevent import, indicating that a functional mitochondrial import signal is present near the NH2 terminus of the mature protein. Furthermore, by analyzing mitochondrial import of the various mutant proteins in [rho-] yeast, we obtained evidence that different segments of the F1-beta subunit import signal may act in an additive or cooperative manner to optimize the import properties of this protein