Suppose X ∼ N(μ, σ) ∈ R. We want to test if μ = 0 or μ > 0, and say we know σ. Then noting that Y = X/σ ∼ N(0, 1) under the null, we suggest the test I(X/σ > zα) which has error rate P1(X/σ ≤ zα) = Φ(zα − μ/σ) Hence everything depends on SNR μ/σ. Getting an observation from X ∼ N(μ, σ) is exactly like getting an observation Y ∼ N(μ/σ, 1). Similarly, suppose we get M measurements, calculating X̄ ...

We consider the distribution of argζ (σ + it) on fixed lines σ > 1 2 , and in particular the density d(σ) = lim T→+∞ 1 2T |{t ∈ [−T,+T ] : |argζ (σ + it)|> π/2}| , and the closely related density d−(σ) = lim T→+∞ 1 2T |{t ∈ [−T,+T ] : Rζ (σ + it) < 0}| . Using classical results of Bohr and Jessen, we obtain an explicit expression for the characteristic function ψσ (x) associated with argζ (σ + ...

In this Perspective article, we seek the origin of scaling laws developing turbulent boundary layers over a flat plate from perspective phenomenological theory turbulence. The boundary-layer thickness and shear stress in rough smooth flows are established. flow, (scaled with roughness) dynamic pressure) obey “2/(1− σ)” “(1+ σ)/(1− laws, respectively, streamwise distance roughness). Here, σ is s...

The human auditory system is capable of perceiving the direction of a sound source despite reeections oo of walls, ceiling and other interfering objects. This phenomenon, the precedence eeect, has been previously modeled only for synthetic click stimuli. This paper presents a biologically plausible computer simulation for speech, that combines a cross-correlation model with an onset enhancement...

Recent work has studied the fragmentability and σ-fragmentability properties of Banach spaces. Here examples are given that justify the definitions that have been used. The fragmentability and σ-fragmentability properties of the spaces `∞ and `c (Γ ), with Γ uncountable, are determined.

A field K is 0-Hilbertian if K 6= ⋃ni=1 φi(K) for any collection of rational functions φi of degree at least 2, i = 1, . . . ,m. Corvaja and Zannier [CoZ] give an elementary construction for a 0-Hilbertian field that isn’t Hilbertian. There is an obvious generalization of the notion of 0-Hilbertian to g-Hilbertian. Guralnick-Thompson and Liebeck-Saxl have given a partial classification of monod...