A PCP Characterization of AM

We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP Theorem for NP. Similar characterizations have been given for higher levels of the Polynomial Hierarchy, and for PSPACE; however, we suggest that the result for AM might be of particular significance for attempts to derandomize this class. To test this notion, we pose some `Randomized Optimization Hypotheses' related to our stochastic CSPs that (in light of our result) would imply collapse results for AM. Unfortunately, the hypotheses appear over-strong, and we present evidence against them. In the process we show that, if some language in NP is hard-on-average against circuits of size 2^{Omega(n)}, then there exist hard-on-average optimization problems of a particularly elegant form. All our proofs use a powerful form of PCPs known as Probabilistically Checkable Proofs of Proximity, and demonstrate their versatility. We also use known results on randomness-efficient soundness- and hardness-amplification. In particular, we make essential use of the Impagliazzo-Wigderson generator; our analysis relies on a recent Chernoff-type theorem for expander walks.Comment: 18 page

On the Power of Many One-Bit Provers

We study the class of languages, denoted by \MIP[k, 1-\epsilon, s], which have $k$-prover games where each prover just sends a \emph{single} bit, with completeness $1-\epsilon$ and soundness error $s$. For the case that $k=1$ (i.e., for the case of interactive proofs), Goldreich, Vadhan and Wigderson ({\em Computational Complexity'02}) demonstrate that \SZK exactly characterizes languages having 1-bit proof systems with"non-trivial" soundness (i.e., $1/2 < s \leq 1-2\epsilon$). We demonstrate that for the case that $k\geq 2$, 1-bit $k$-prover games exhibit a significantly richer structure: + (Folklore) When $s \leq \frac{1}{2^k} - \epsilon$, \MIP[k, 1-\epsilon, s] = \BPP; + When $\frac{1}{2^k} + \epsilon \leq s < \frac{2}{2^k}-\epsilon$, \MIP[k, 1-\epsilon, s] = \SZK; + When $s \ge \frac{2}{2^k} + \epsilon$, \AM \subseteq \MIP[k, 1-\epsilon, s]; + For $s \le 0.62 k/2^k$ and sufficiently large $k$, \MIP[k, 1-\epsilon, s] \subseteq \EXP; + For $s \ge 2k/2^{k}$, \MIP[k, 1, 1-\epsilon, s] = \NEXP. As such, 1-bit $k$-prover games yield a natural "quantitative" approach to relating complexity classes such as \BPP,\SZK,\AM, \EXP, and \NEXP. We leave open the question of whether a more fine-grained hierarchy (between \AM and \NEXP) can be established for the case when $s \geq \frac{2}{2^k} + \epsilon$

Competitive adsorption of phenolic compounds from aqueous solution using sludge‐based activated carbon.

Preparation of activated carbon from sewage sludge is a promising approach to produce cheap and efficient adsorbent for pollutants removal as well as to dispose of sewage sludge. The first objective of this study was to investigate the physical and chemical properties (BET surface area, ash and elemental content, surface functional groups by Boehm titration and weight loss by thermogravimetric analysis) of the sludge‐based activated carbon (SBAC) so as to give a basic understanding of its structure and to compare to those of two commercial activated carbons, PICA S23 and F22. The second and main objective was to evaluate the performance of SBAC for single and competitive adsorption of four substituted phenols (p‐nitrophenol, p‐chlorophenol, p‐hydroxy benzoic acid and phenol) from their aqueous solutions. The results indicated that, despite moderate micropore and mesopore surface areas, SBAC had remarkable adsorption capacity for phenols, though less than PICA carbons. Uptake of the phenolic compound was found to be dependent on both the porosity and surface chemistry of the carbons. Furthermore, the electronegativity and the hydrophobicity of the adsorbate have significant influence on the adsorption capacity. The Langmuir and Freundlich models were used for the mathematical description of the adsorption equilibrium for single‐solute isotherms. Moreover, the Langmuir–Freundlich model gave satisfactory results for describing multicomponent system isotherms. The capacity of the studied activated carbons to adsorb phenols from a multi‐solute system was in the following order: p‐nitrophenol > p‐chlorophenol > PHBA > phenol

A Hypergraph Dictatorship Test with Perfect Completeness

A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based \PCP construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are $o(1).$ Their test makes $q\geq3$ queries and has amortized query complexity $1+O(\frac{\log q}{q})$ but has an inherent loss of perfect completeness. In this paper we give an adaptive hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity $1+O(\frac{\log q}{q})$.Comment: Some minor correction

Mining microbial genomes for new natural products and biosynthetic pathways

Analyses of microbial genome sequences have revealed numerous examples of ‘cryptic’ or ‘orphan’ biosynthetic gene clusters, with the potential to direct the production of novel, structurally complex natural products. This article summarizes the various methods that have been developed for discovering the products of cryptic biosynthetic gene clusters in microbes and gives an account of my group's discovery of the products of two such gene clusters in the model actinomycete Streptomyces coelicolor M145. These discoveries hint at new mechanisms, roles and specificities for natural product biosynthetic enzymes. Our efforts to elucidate these are described. The identification of new secondary metabolites of S. coelicolor raises the question: what is their biological function? Progress towards answering this question is also summarized

Interaction of the phencyclidine model of schizophrenia and nicotine on total and categorized ultrasonic vocalizations in rats

Patients with schizophrenia smoke cigarettes at a higher rate than the general population. We hypothesized that a factor in this comorbidity is sensitivity to the reinforcing and reinforcement- enhancement effects of nicotine. Phencyclidine (PCP) was used to model behavioral changes resembling negative symptoms of schizophrenia in rats. USVs in rats have been used to measure emotional states, with 50 kHz USVs indicating positive states and 22 kHz indicating negative. Total and categorized numbers of 22 and 50 kHz ultrasonic vocalizations (USVs) and USVs during a visual stimulus (e.g. a potential measure of reinforcement-enhancement) were examined in rats following .injection ofh PCP (2.0 mg/kg), and/or nicotine (0.2 or 0.4 mg/kg) daily for 7 days. PCP was then discontinued and all rats received nicotine (0.2 mg/kg and 0.4 mg/kg) and PCP (2.0 mg/kg) on 3 challenge days. PCP acutely decreased 50 kHz vocalizations while repeated nicotine potentiated rates of vocalizations, with similar patterns during light presentations. Rats in the PCP and nicotine combination groups made more 50 kHz vocalizations compared to control groups on challenge days. We conclude that PCP may produce a reward deficit that is shown by decreased 50 kHz USVs, and behaviors post-PCP exposure may best model the comorbidity between schizophrenia and nicotine