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

What does the local structure of a planar graph tell us about its global structure?

The local k-neighborhood of a vertex v in an unweighted graph G = (V,E) with vertex set V and edge set E is the subgraph induced by all vertices of distance at most k from v. The rooted k-neighborhood of v is also called a k-disk around vertex v. If a graph has maximum degree bounded by a constant d, and k is also constant, the number of isomorphism classes of k-disks is constant as well. We can describe the local structure of a bounded-degree graph G by counting the number of isomorphic copies in G of each possible k-disk. We can summarize this information in form of a vector that has an entry for each isomorphism class of k-disks. The value of the entry is the number of isomorphic copies of the corresponding k-disk in G. We call this vector frequency vector of k-disks. If we only know this vector, what does it tell us about the structure of G? In this paper we will survey a series of papers in the area of Property Testing that leads to the following result (stated informally): There is a k = k(ε,d) such that for any planar graph G its local structure (described by the frequency vector of k-disks) determines G up to insertion and deletion of at most εd n edges (and relabelling of vertices)

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

Cube Testers and Key Recovery Attacks On Reduced-Round MD6 and Trivium

CRYPTO 2008 saw the introduction of the hash function MD6 and of cube attacks, a type of algebraic attack applicable to cryptographic functions having a low-degree algebraic normal form over GF(2). This paper applies cube attacks to reduced round MD6, finding the full 128-bit key of a 14-round MD6 with complexity 2^22 (which takes less than a minute on a single PC). This is the best key recovery attack announced so far for MD6. We then introduce a new class of attacks called cube testers, based on efficient property-testing algorithms, and apply them to MD6 and to the stream cipher Trivium. Unlike the standard cube attacks, cube testers detect nonrandom behavior rather than performing key extraction, but they can also attack cryptographic schemes described by nonrandom polynomials of relatively high degree. Applied to MD6, cube testers detect nonrandomness over 18 rounds in 2^17 complexity; applied to a slightly modified version of the MD6 compression function, they can distinguish 66 rounds from random in 2^24 complexity. Cube testers give distinguishers on Trivium reduced to 790 rounds from random with 2^30 complexity and detect nonrandomness over 885 rounds in 2^27, improving on the original 767-round cube attack

Raising rivals’ fixed costs

This article demonstrates that raising fixed costs can serve as a credible mechanism for a well placed firm to exclude its rivals. We identify a number of credible avenues, such as increased regulation, vexatious litigation and increased prices for essential inputs, through which such a firm can raise fixed costs. We show that for a wide range of oligopoly models this may be a profitable strategy, even if the firm’s own fixed costs are affected as much (or even more) than its rivals and even if it is less efficient. The resulting reduction in the number of firms in the market is detrimental to consumer welfare and hence worthy of scrutiny by competition and regulatory authorities

Budesonide/formoterol and formoterol provide similar rapid relief in patients with acute asthma showing refractoriness to salbutamol

BACKGROUND: To compare the efficacy and safety of budesonide/formoterol (Symbicort(®)) with formoterol (Oxis(®)) in the treatment of patients with acute asthma who showed evidence of refractoriness to short-acting β(2)-agonist therapy. METHODS: In a 3 hour, randomized, double-blind study, a total of 115 patients with acute asthma (mean FEV(1 )40% of predicted normal) and a refractory response to salbutamol (mean reversibility 2% of predicted normal after inhalation of 400 μg), were randomized to receive either budesonide/formoterol (320/9 μg, 2 inhalations at t = -5 minutes and 2 inhalations at 0 minutes [total dose 1280/36 μg]) or formoterol (9 μg, 2 inhalations at t = -5 minutes and 2 inhalations at 0 minutes [total dose 36 μg]). The primary efficacy variable was the average FEV(1 )from the first intake of study medication to the measurement at 90 minutes. Secondary endpoints included changes in FEV(1 )at other timepoints and change in respiratory rate at 180 minutes. Treatment success, treatment failure and patient assessment of the effectiveness of the study medication were also measured. RESULTS: FEV(1 )increased after administration of the study medication in both treatment groups. No statistically significant difference between the treatment groups was apparent for the primary outcome variable, or for any of the other efficacy endpoints. There were no statistically significant between-group differences for treatment success, treatment failure or patient assessment of medication effectiveness. Both treatments were well tolerated. CONCLUSION: Budesonide/formoterol and formoterol provided similarly rapid relief of acute bronchoconstriction in patients with asthma who showed evidence of refractoriness to a short-acting β(2)-agonist

A study of patent thickets

Report analysing whether entry of UK enterprises into patenting in a technology area is affected by patent thickets in the technology area

Wnt expression is not correlated with β-catenin dysregulation in Dupuytren's Disease

BACKGROUND: Dupuytren's contracture or disease (DD) is a fibro-proliferative disease of the hand that results in finger flexion contractures. Increased cellular β-catenin levels have been identified as characteristic of this disease. As Wnts are the most widely recognized upstream regulators of cellular β-catenin accumulation, we have examined Wnt gene expression in surgical specimens and in DD-derived primary cell cultures grown in two-dimensional monolayer culture or in three-dimensional FPCL collagen lattice cultures. RESULTS: The Wnt expression profile of patient-matched DD and unaffected control palmar fascia tissue was determined by a variety of complimentary methods; Affymetrix Microarray analysis, specific Wnt and degenerative primer-based Reverse Transcriptase (RT)-PCR, and Real Time PCR. Microarray analysis identified 13 Wnts associated with DD and control tissues. Degenerate Wnt RT-PCR analysis identified Wnts 10b and 11, and to a lesser extent 5a and 9a, as the major Wnt family members expressed in our patient samples. Competitive RT-PCR analysis identified significant differences between the levels of expression of Wnts 9a, 10b and 11 in tissue samples and in primary cell cultures grown as monolayer or in FPCL, where the mRNA levels in tissue > FPCL cultures > monolayer cultures. Real Time PCR data confirmed the down-regulation of Wnt 11 mRNA in DD while Wnt 10b, the most frequently isolated Wnt in DD and control palmar fascia, displayed widely variable expression between the methods of analysis. CONCLUSION: These data indicate that changes in Wnt expression per se are unlikely to be the cause of the observed dysregulation of β-catenin expression in DD

The Leukemia-Associated Mllt10/Af10-Dot1l Are Tcf4/β-Catenin Coactivators Essential for Intestinal Homeostasis

The leukemia-associated Mllt10/Af10 and its partner the histone methyltransferase Dot1l are identified as Tcf4/β-catenin co-activators and shown to be essential for Wnt-driven endogenous gene expression, intestinal development and homeostasis