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 origin of the λ\lambda-transition in liquid Sulphur

Developing a novel experimental technique, we applied photon correlation spectroscopy using infrared radiation in liquid Sulphur around $T_\lambda$, i.e. in the temperature range where an abrupt increase in viscosity by four orders of magnitude is observed upon heating within few degrees. This allowed us - overcoming photo-induced and absorption effects at visible wavelengths - to reveal a chain relaxation process with characteristic time in the ms range. These results do rehabilitate the validity of the Maxwell relation in Sulphur from an apparent failure, allowing rationalizing the mechanical and thermodynamic behavior of this system within a viscoelastic scenario.Comment: 5 pages, 4 eps figures, accepted in Phys. Rev. Let

Parameterized complexity of DPLL search procedures

We study the performance of DPLL algorithms on parameterized problems. In particular, we investigate how difficult it is to decide whether small solutions exist for satisfiability and other combinatorial problems. For this purpose we develop a Prover-Delayer game which models the running time of DPLL procedures and we establish an information-theoretic method to obtain lower bounds to the running time of parameterized DPLL procedures. We illustrate this technique by showing lower bounds to the parameterized pigeonhole principle and to the ordering principle. As our main application we study the DPLL procedure for the problem of deciding whether a graph has a small clique. We show that proving the absence of a k-clique requires n steps for a non-trivial distribution of graphs close to the critical threshold. For the restricted case of tree-like Parameterized Resolution, this result answers a question asked in [11] of understanding the Resolution complexity of this family of formulas

Brief report: how adolescents with ASD process social information in complex scenes. Combining evidence from eye movements and verbal descriptions

We investigated attention, encoding and processing of social aspects of complex photographic scenes. Twenty-four high-functioning adolescents (aged 11–16) with ASD and 24 typically developing matched control participants viewed and then described a series of scenes, each containing a person. Analyses of eye movements and verbal descriptions provided converging evidence that both groups displayed general interest in the person in each scene but the salience of the person was reduced for the ASD participants. Nevertheless, the verbal descriptions revealed that participants with ASD frequently processed the observed person’s emotion or mental state without prompting. They also often mentioned eye-gaze direction, and there was evidence from eye movements and verbal descriptions that gaze was followed accurately. The combination of evidence from eye movements and verbal descriptions provides a rich insight into the way stimuli are processed overall. The merits of using these methods within the same paradigm are discussed

Predicting vaccine effectiveness against severe COVID-19 over time and against variants: a meta-analysis

Vaccine protection from symptomatic SARS-CoV-2 infection has been shown to be strongly correlated with neutralising antibody titres; however, this has not yet been demonstrated for severe COVID-19. To explore whether this relationship also holds for severe COVID-19, we performed a systematic search for studies reporting on protection against different SARS-CoV-2 clinical endpoints and extracted data from 15 studies. Since matched neutralising antibody titres were not available, we used the vaccine regimen, time since vaccination and variant of concern to predict corresponding neutralising antibody titres. We then compared the observed vaccine effectiveness reported in these studies to the protection predicted by a previously published model of the relationship between neutralising antibody titre and vaccine effectiveness against severe COVID-19. We find that predicted neutralising antibody titres are strongly correlated with observed vaccine effectiveness against symptomatic (Spearman ρ = 0.95, p < 0.001) and severe (Spearman ρ = 0.72, p < 0.001 for both) COVID-19 and that the loss of neutralising antibodies over time and to new variants are strongly predictive of observed vaccine protection against severe COVID-19

Paradoxical interactions among estrogen receptors,

Abstract The phenomenon of mutual annihilation of action between 17b estradiol (E 2 ) and a selective estrogen receptor modulator (SERM), previously described in prepubertal rat diaphysis, epiphysis and uterus, has been investigated in ROS 17/2.8 rat osteoblastic cells and in transiently co-transfected cells in culture. In ROS 17/2.8 cells, the estrogen-induced marker enzyme creatine kinase B (CKB) was stimulated by raloxifene, tamoxifen and tamoxifen methiodide to a specific activity equal to or greater than that induced by 10 nM E 2 . However, when a fully inhibitory dose of any of these SERMS was given simultaneously with E 2 , no stimulation of CK activity resulted. Therefore, SERMS can be full agonists when acting alone, but complete antagonists to a super-physiological dose of estrogen. It is expected that excess tamoxifen would prevent the action of a SERM, but that the agonist activity of a SERM is abolished by 1000-fold less estrogen is a phenomenon without obvious explanation by classical pharmacology of competitive inhibition. To probe the mechanism of this interaction further, a ckb-CAT reporter plasmid, plus the human receptor expression plasmid, HEO, was transfected transiently into several cell types. In MCF-7 cells, a 1:10 ratio of E 2 to tamoxifen produced mutual annihilation, but the same ratio in ROS 17/2.8 or HeLa cells led to synergistic stimulation. In HeLa cells, co-transfected with the more efficient wild-type estrogen receptor plasmid, HEGO, synergy was demonstrated only at sub-saturation levels of HEGO. We speculate that, in the presence of estradiol and a SERM, not only active homodimers would be formed, but also hetero-dimers of estrogen-liganded and tamoxifen-liganded receptor monomers, depending on the molar ratio of their ligands and their relative affinities. The resulting hetero-dimer conformation would change the specific receptor surface for interactions with the growing number of co-activators and co-repressors, structural changes which could help to explain the mutual annihilation and synergy phenomena and their cell selectivity

Linear-Time Arguments with Sublinear Verification from Tensor Codes

Minimizing the computational cost of the prover is a central goal in the area of succinct arguments. In particular, it remains a challenging open problem to construct a succinct argument where the prover runs in linear time and the verifier runs in polylogarithmic time. We make progress towards this goal by presenting a new linear-time probabilistic proof. For any fixed $\epsilon > 0$, we construct an interactive oracle proof (IOP) that, when used for the satisfiability of an $N$-gate arithmetic circuit, has a prover that uses $O(N)$ field operations and a verifier that uses $O(N^{\epsilon})$ field operations. The sublinear verifier time is achieved in the holographic setting for every circuit (the verifier has oracle access to a linear-size encoding of the circuit that is computable in linear time). When combined with a linear-time collision-resistant hash function, our IOP immediately leads to an argument system where the prover performs $O(N)$ field operations and hash computations, and the verifier performs $O(N^{\epsilon})$ field operations and hash computations (given a short digest of the $N$-gate circuit)