A new characterization of abduction and induction is proposed, which is based on the idea that the various aspects of the two kinds of inference rest on the essential features of increment of (so to speak, extensionalized) comprehension and, respectively, of extension of the terms involved. These two essential features are in a reciprocal relation of duality, whence the highlighting of the dual...

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for finite eigenvalues are obtained by using analyticity and monotonicity properties (rather than variational principles) and they are general enough to include ...

A general parameter process defined by a continuum of random variables is not jointly measurable with respect to the usual product σ-algebra. For the case of independent random variables, a one-way Fubini extension of the product space was constructed in [11] to satisfy a limited form of joint measurability. For the general case we show that this extension exists if and only if there is a count...

The planar cell polarity (PCP) signaling pathway is essential for a wide variety of celland tissue-level morphogenetic events in developing embryos. PCP research has been predominantly directed at the role played by a small number of core proteins, including Dishevelled and Frizzled. Much less is known about how these proteins signal downstream to direct the execution of such diverse cell behav...

The planar cell polarity (PCP) signaling pathway is essential for a wide variety of celland tissue-level morphogenetic events in developing embryos. PCP research has been predominantly directed at the role played by a small number of core proteins, including Dishevelled and Frizzled. Much less is known about how these proteins signal downstream to direct the execution of such diverse cell behav...

The planar cell polarity (PCP) signaling pathway is essential for a wide variety of celland tissue-level morphogenetic events in developing embryos. PCP research has been predominantly directed at the role played by a small number of core proteins, including Dishevelled and Frizzled. Much less is known about how these proteins signal downstream to direct the execution of such diverse cell behav...