Testing formula satisfaction

We study the query complexity of testing for properties defined by read once formulae, as instances of massively parametrized properties, and prove several testability and non-testability results. First we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries exponential in \epsilon and independent of all other parameters. When the gates are limited to being monotone, we prove that there is an estimation algorithm, that outputs an approximation of the distance of the input from satisfying the property. For formulae only involving And/Or gates, we provide a more efficient test whose query complexity is only quasi-polynomial in \epsilon. On the other hand we show that such testability results do not hold in general for formulae over non-Boolean alphabets; specifically we construct a property defined by a read-once arity 2 (non-Boolean) formula over alphabets of size 4, such that any 1/4-test for it requires a number of queries depending on the formula size

Midazolam Versus Diazepam for the Treatment of Status Epilepticus in Children and Young Adults: A Meta-analysis

Rapid treatment of status epilepticus (SE) is associated with better outcomes. Diazepam and midazolam are commonly used, but the optimal agent and administration route is unclear.The objective was to determine by systematic review if nonintravenous (non-IV) midazolam is as effective as diazepam, by any route, in terminating SE seizures in children and adults. Time to seizure cessation and respiratory complications was examined.We performed a search of PubMed, Web of Knowledge, Embase, Cochrane Database of Systematic Reviews, Database of Abstracts of Reviews of Effects, American College of Physicians Journal Club, Cochrane Central Register of Controlled Trials, the Cumulative Index to Nursing and Allied Health Literature, and International Pharmaceutical Abstracts for studies published January 1, 1950, through July 4, 2009. English language quasi-experimental or randomized controlled trials comparing midazolam and diazepam as first-line treatment for SE, and meeting the Consolidated Standards of Reporting Trials (CONSORT)-based quality measures, were eligible. Two reviewers independently screened studies for inclusion and extracted outcomes data. Administration routes were stratified as non-IV (buccal, intranasal, intramuscular, rectal) or IV. Fixed-effects models generated pooled statistics.Six studies with 774 subjects were included. For seizure cessation, midazolam, by any route, was superior to diazepam, by any route (relative risk [RR] = 1.52; 95% confidence interval [CI] = 1.27 to 1.82). Non-IV midazolam is as effective as IV diazepam (RR = 0.79; 95% CI = 0.19 to 3.36), and buccal midazolam is superior to rectal diazepam in achieving seizure control (RR = 1.54; 95% CI = 1.29 to 1.85). Midazolam was administered faster than diazepam (mean difference = 2.46 minutes; 95% CI = 1.52 to 3.39 minutes) and had similar times between drug administration and seizure cessation. Respiratory complications requiring intervention were similar, regardless of administration route (RR = 1.49; 95% CI = 0.25 to 8.72).Non-IV midazolam, compared to non-IV or IV diazepam, is safe and effective in treating SE. Comparison to lorazepam, evaluation in adults, and prospective confirmation of safety and efficacy is needed.ACADEMIC EMERGENCY MEDICINE 2010; 17:575–582 © 2010 by the Society for Academic Emergency MedicinePeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79121/1/j.1553-2712.2010.00751.x.pd

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