It is well known that on arbitrary metric measure spaces, the notion of minimal p-weak upper gradient may depend p. In this paper we investigate how a first-order condition metric-measure structure, call Bounded Interpolation Property, guarantees in fact such dependence not present. We also show Property stable for pointed Gromov Hausdorff convergence and holds large class spaces satisfying cur...

For small involutive and integral quantaloids Q it is shown that covariant presheaves on symmetric Q-categories are equivalent to certain subalgebras of a speci c monad on the category of symmetric Q-categories. This construction is related to a weakening of the subobject classi er axiom which does not require the classi cation of all subalgebras, but only guarantees that classi able subalgebra...

Radial convolution operators on free groups with non-negative kernel of weak type (2, 2) and of restricted weak type (2, 2) are characterized. Estimates of weak type (p, p) are obtained as well for 1 < p < 2.

we start this article by rebuilding higher operads of weak higher transformations, and correct those in cite{cambat}. as in cite{cambat} we propose an operadic approach for weak higher $n$-transformations, for each $ninmathbb{n}$, where such weak higher $n$-transformations are seen as algebras for specific contractible higher operads. the last chapter of this article asserts that, up to precise...

We recall two previously-proposed notions of asymptotic calibration for a forecaster making a sequence of probability predictions. We note that the existence of efficient algorithms for calibrated forecasting holds only in the case of binary outcomes. We pose the question: do there exist such efficient algorithms for the general (non-binary) case? Review of Calibrated Forecasting Glenn Brier, w...

We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 ± 7 kHz/√Hz with only 2 mW of continuous-wave, single-mode input power. We describe the measurement of a weak value and show how even higher-frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as preci...