On the Characterization of Borderline Cases

This chapter was originally written for Gary Ostertag’s edition of the festschrift for Stephen Schiffer, Meanings and Other Things (Oxford University Press, 2016). It centres on Schiffer’s treatment of the characterization problem: the problem of saying what being a borderline case of a concept expressed by a vague expression consists in. While broadly sympathetic to Schiffer’s approach, the chapter takes issue with two aspects of it. Schiffer endorses Verdict Exclusion: the doctrine that a ‘polar verdict’ about a borderline case cannot be an expression of knowledge. This endorsement comes at too high a cost: among other things, it conflicts with the entitlement intuition—the intuition that there will be no point in a Sorites sequence at which it is mandatory to return neither of the polar verdicts. The chapter argues for agnosticism about Verdict Exclusion (‘Liberalism’). It also rejects Schiffer’s idea that a special genre of partial belief—vagueness-related partial belief—plays an essential role in characterizing the possession conditions for vague concepts.

Lie polynomials in an algebra defined by a linearly twisted commutation relation

We present an elementary approach to characterizing Lie polynomials on the generators [Formula: see text] of an algebra with a defining relation in the form of a twisted commutation relation [Formula: see text]. Here, the twisting map [Formula: see text] is a linear polynomial with a slope parameter, which is not a root of unity. The class of algebras defined as such encompasses [Formula: see text]-deformed Heisenberg algebras, rotation algebras, and some types of [Formula: see text]-oscillator algebras, the deformation parameters of which, are not roots of unity. Thus, we have a general solution for the Lie polynomial characterization problem for these algebras.

Parallelization in Characterization of Digital Cells Libraries

Various aspects (starting tasks, monitoring execution, collecting data, visualizing, forming final tables) of the problem of characterization of digital elements libraries used in the process of creating and manufacturing integrated circuits are considered. The analysis of parallelization application at various stages of the characterization problem is carried out. The implementation of the proposed methods is described using the example of developing a web-based characterization system for digital cell libraries.

A Forward-Reverse Brascamp-Lieb Inequality: Entropic Duality and Gaussian Optimality

Inspired by the forward and the reverse channels from the image-size characterization problem in network information theory, we introduce a functional inequality which unifies both the Brascamp-Lieb inequality and Barthe's inequality, which is a reverse form of the Brascamp-Lieb inequality. For Polish spaces, we prove its equivalent entropic formulation using the Legendre-Fenchel duality theory. Capitalizing on the entropic formulation, we elaborate on a "doubling trick" used by Lieb and Geng-Nair to prove the Gaussian optimality in this inequality for the case of Gaussian reference measures.