A robust parallel algorithm for combinatorial compressed sensing

In previous work two of the authors have shown that a vector $x \in \mathbb{R}^n$ with at most $k < n$ nonzeros can be recovered from an expander sketch $Ax$ in $\mathcal{O}(\mathrm{nnz}(A)\log k)$ operations via the Parallel-$\ell_0$ decoding algorithm, where $\mathrm{nnz}(A)$ denotes the number of nonzero entries in $A \in \mathbb{R}^{m \times n}$. In this paper we present the Robust-$\ell_0$ decoding algorithm, which robustifies Parallel-$\ell_0$ when the sketch $Ax$ is corrupted by additive noise. This robustness is achieved by approximating the asymptotic posterior distribution of values in the sketch given its corrupted measurements. We provide analytic expressions that approximate these posteriors under the assumptions that the nonzero entries in the signal and the noise are drawn from continuous distributions. Numerical experiments presented show that Robust-$\ell_0$ is superior to existing greedy and combinatorial compressed sensing algorithms in the presence of small to moderate signal-to-noise ratios in the setting of Gaussian signals and Gaussian additive noise

Self-Specifying Machines

We study the computational power of machines that specify their own acceptance types, and show that they accept exactly the languages that \manyonesharp-reduce to NP sets. A natural variant accepts exactly the languages that \manyonesharp-reduce to P sets. We show that these two classes coincide if and only if \psone = \psnnoplusbigohone, where the latter class denotes the sets acceptable via at most one question to \sharpp followed by at most a constant number of questions to \np.Comment: 15 pages, to appear in IJFC

Different perceptions of adaptation to climate change: a mental model approach applied to the evidence from expert interviews

We argue that differences in the perception and governance of adaptation to climate change and extreme weather events are related to sets of beliefs and concepts through which people understand the environment and which are used to solve the problems they face (mental models). Using data gathered in 31 in-depth interviews with adaptation experts in Europe, we identify five basic stakeholder groups whose divergent aims and logic can be related to different mental models they use: advocacy groups, administration, politicians, researchers, and media and the public. Each of these groups uses specific interpretations of climate change and specifies how to deal with climate change impacts. We suggest that a deeper understanding and follow-up of the identified mental models might be useful for the design of any stakeholder involvement in future climate impact research processes. It might also foster consensus building about adequate adaptation measures against climate threats in a society

On the Power of Probabilistic Polynomial Time: PNP[log] ⊆ PP

We show that every set in the ΘP2 level of the polynomial hierarchy -- that is, every set polynomial-time truth-table reducible to SAT -- is accepted by a probabilistic polynomialtime Turing machine: PNP[log] ⊆ PP