This gives complete freedom to answer if the input is close to having property P but does not exactly have this property. It is natural to think of property testing algorithms for which the input queries might have a very small probability of error. In this case it would be good to be able to separate inputs that are ε-far from having property P from those that are ε′-close to having property P...

Phospholipase C-ε (PLC-ε) is a unique PLC isoform that can be regulated by multiple signaling inputs from both Ras family GTPases and heterotrimeric G proteins and has primary sites of expression in the heart and lung. Whereas the role of PLC-ε in cardiac function and pathology has been documented, its relevance in acute lung injury (ALI) is unclear. We used PLC-ε(-/-) mice to address the role ...

We break the convexity bound in the t–aspect for L–functions attached to cuspforms f for GL2(k) over arbitrary number fields k. The argument uses asymptotics with error term with a power saving, for second integral moments over spectral families of twists L(s, f ⊗χ) by grossencharacters χ, from our previous paper [Di-Ga]. §0. Introduction In many instances, for cuspidal automorphic forms f on r...

The dependence of single-molecule photoluminescence intermittency (PI) or "blinking" on the local dielectric constant (ε) is examined for nile red (NR) in thin films of poly(vinylidene fluoride) (PVDF). In previous studies, variation of the local dielectric constant was accomplished by studying luminophores in chemically and structurally different hosts. In contrast, the NR/PVDF guest-host pair...

A system of semilinear parabolic stochastic partial differential equations with additive space-time noise is considered on the union of thin bounded tubular domains D1,ε := Γ× (0, ε) and D2,ε := Γ× (−ε, 0) joined at the common base Γ ⊂ Rd, where d ≥ 1. The equations are coupled by an interface condition on Γ which involves a reaction intensity k(x′, ε), where x = (x′, xd+1) ∈ Rd+1 with x′ ∈ Γ a...

We answer a recent question of Bienvenu, Muchnik, Shen, and Vereshchagin. In particular, we prove an effective version of the standard fact from analysis which says that, for any ε > 0 and any Lebesgue-measurable subset of Cantor space, X ⊆ 2, there is an open set Uε ⊆ 2, Uε ⊇ X, such that μ(Uε) ≤ μ(X) + ε, where μ(Z) denotes the Lebesgue measure of Z ⊆ 2. More specifically, our main result sho...

The following is a proof which is independent of this characterisation. First assume that ‖ ‖ is non-archimedean. Let x, y ∈ K. Using that ‖ ‖ extends | | we then obtain |x + y| = ‖x + y‖ ≤ max{‖x‖, ‖y‖} = max{|x|, |y|} which shows that | | is non-archimedean. Now assume that | | is non-archimedean. Let x, y ∈ K̂. Let ε > 0. Since K is dense in K̂ there exist u, v ∈ K such that ‖x − u‖ < ε and ‖y...

A temporal constraint language Γ is a set of relations with first-order definitions in (Q;<). Let CSP(Γ) denote the set of constraint satisfaction problem instances with relations from Γ. CSP(Γ) admits robust approximation if, for any ε ≥ 0, given a (1 − ε)-satisfiable instance of CSP(Γ), we can compute an assignment that satisfies at least a (1−f(ε))-fraction of constraints in polynomial time....

A quantile summary is a data structure that approximates to ε-relative error the order statistics of a much larger underlying dataset. In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses O( ε log 1 ε ) words of memory. This improves upon the previous best upper bound of O( ε log 3/2 1 ε ) by Agarwal et a...