Rank, trace, eigenvalues and norms of a structured matrix

The paper deals with rank, trace, eigenvalues and norms of the matrix [Formula: see text], where [Formula: see text] are ith components of any real sequence [Formula: see text]. A result in this paper is that the Euclidean and spectral norms of the matrix [Formula: see text] is [Formula: see text]. This is a generalization of the main result by Solak [Appl. Math. Comput. 232 (2014) 919–921], with the proof based on a simple property of norms of real matrices.

Complementary Information and Learning Traps*

We develop a model of social learning from complementary information: short-lived agents sequentially choose from a large set of flexibly correlated information sources for prediction of an unknown state, and information is passed down across periods. Will the community collectively acquire the best kinds of information? Long-run outcomes fall into one of two cases: (i) efficient information aggregation, where the community eventually learns as fast as possible; (ii) “learning traps,” where the community gets stuck observing suboptimal sources and information aggregation is inefficient. Our main results identify a simple property of the underlying informational complementarities that determines which occurs. In both regimes, we characterize which sources are observed in the long run and how often.

On Strategyproof Conference Peer Review

We consider peer review under a conference setting where there are conflicts between the reviewers and the submissions. Under such conflicts, reviewers can manipulate their reviews in a strategic manner to influence the final rankings of their own papers. Present-day peer-review systems are not designed to guard against such strategic behavior, beyond minimal (and insufficient) checks such as not assigning a paper to a conflicted reviewer. In this work, we address this problem through the lens of social choice, and present a theoretical framework for strategyproof and efficient peer review. Given the conflict graph which satisfies a simple property, we first present and analyze a flexible framework for reviewer-assignment and aggregation for the reviews that guarantees not only strategyproofness but also a natural efficiency property (unanimity). Our framework is based on the so-called partitioning method, and can be treated as a generalization of this type of method to conference peer review settings. We then empirically show that the requisite property on the (authorship) conflict graph is indeed satisfied in the ICLR-17 submissions data, and further demonstrate a simple trick to make the partitioning method more practically appealing under conference peer-review settings. Finally, we complement our positive results with negative theoretical results where we prove that under slightly stronger requirements, it is impossible for any algorithm to be both strategyproof and efficient.

Breakable Semihypergroups

In this paper, we introduce and characterize the breakable semihypergroups, a natural generalization of breakable semigroups, defined by a simple property: every nonempty subset of them is a subsemihypergroup. Then, we present and discuss on an extended version of Rédei’s theorem for semi-symmetric breakable semihypergroups, proposing a different proof that improves also the theorem in the classical case of breakable semigroups.

A NOTE ON POSITIVE OPERATORS

We show that positive absolutely norm attaining operators can be characterised by a simple property of their spectra. This result clarifies and simplifies a result of Ramesh. As an application we characterise weighted shift operators which are absolutely norm attaining.

Truth in British Idealism and its Analytic Critics

Arguments about truth were central to the debates between British idealists such as Bradley and their analytic critics such as Russell. Bradley’s thesis of the “unreality” of relations led him to the holistic monism of the Absolute, within which truth is no relation between judgment and fact but the expansion of judgment until it becomes reality. Russell argued that this idealist monism rests on the mistaken assumption that all relations are internal, and should be replaced by a realist pluralism of facts. Initially Russell followed Moore in holding that truth is a simple property of judgments which are facts. But that position cannot deal sensibly with falsehood, so Russell then moved to his multiple-relation theory of judgment. But having been persuaded by Wittgenstein that this was not a tenable position, he adopted the semantic correspondence theory of logical atomism.

Alternating adjectives

The paper describes a puzzle in the semantics of a class of English adjectives which alternate systematically in meaning. We know from the literature on adjectival meanings that the STIMULUS vs. EXPERIENCER pair of roles forms the basis of two kinds of adjectives in English depending on whether the STIMULUS or the EXPERIENCER is the one who holds the property. Our puzzle adjectives alternate between these two readings in a way parallel to the morphologically marked adjectival participles (in -ed vs. -ing) of Object Experiencer verbs. I argue further that there are reasons to think that the relationship between these two roles in this alternation is a stative version of causation, with the STIMULUS reading of the adjective being derived from the Psych EXPERIENCER reading. The existence of this alternation shows that within simple property ascriptions (of which adjectival predication is a prototypical expression) a distinction is made between Holders of properties simpliciter, and Holders of causational-properties. Thus, in analysing this adjectival puzzle as a parallel to verbal diathesis, the paper contributes to the debate on the similarities and differences between states and dynamic events.