Related papers: Principles Weaker than BD-N

The demiclosedness principle is one of the key tools in nonlinear analysis and fixed point theory. In this note, this principle is extended and made more flexible by two mutually orthogonal affine subspaces. Versions for finitely many…

It is argued that a weak value of an observable is a robust property of a single pre- and post-selected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affects other systems…

We investigate the Whyburn and weakly Whyburn property in the class of $P$-spaces, that is spaces where every countable intersection of open sets is open. We construct examples of non-weakly Whyburn $P$-spaces of size continuum, thus giving…

The minimum classical extension S$^{+g}$ of a classically sound theory S based on intuitionistic logic, defined by adding to S the Gentzen negative interpretations of its mathematical axioms, contains a faithful translation S$^g$ of the…

We study an analogue of the Brauer-Manin obstruction to the local-global principle for embedding problems over global fields. We will prove the analogues of several fundamental structural results. In particular we show that the (algebraic)…

A Nikishin-Maurey characterization is given for bounded subsets of weak-type Lebesgue spaces. New factorizations for linear and multilinear operators are shown to follow.

The P versus NP problem is addressed in a context of provability and limitations on the possibility of finding sound axioms for formal theories. It is shown that if the term "constructible theory" is defined in a way which satisfies certain…

Lecture notes on Weak Topologies: We discuss about the weak and weak star topologies on a normed linear space. Our aim is to prove the well known Banach-Alaouglu theorem and discuss some of its consequences, in particular, characterizations…

We provides some new equivalent forms of collection principle over some very weak set theories after reviewing the existing ones.

We construct a denotational model of linear logic, whose objects are all the locally convex and separated topological vector spaces endowed with their weak topology. The negation is interpreted as the dual, linear proofs are interpreted as…

Motivated by recent disagreements in the context of AdS/CFT, we study the non-planar sector of the BMN correspondence. In particular, we reconsider the energy shift of states with two stringy excitations in light-cone string field theory…

Adversarial examples have been shown to cause neural networks to fail on a wide range of vision and language tasks, but recent work has claimed that Bayesian neural networks (BNNs) are inherently robust to adversarial perturbations. In this…

We propose a notion of a generalized order, which can be used for the notion of a strict partial order. We introduce a weak order to replace the usual weak order defined from a strict partial order. In a constructive setting, that usual…

We show quantifier elimination theorems for real closed valued fields with separated analytic structure and overconvergent analytic structure in their natural one-sorted languages and deduce that such structures are weakly o-minimal. We…

Kedem's Comment [arXiv:1402.1352] on our Letter [PRL 112, 040406 (2014)] contains only the criticism that we did not consider complex weak values. We point out follow-up work which uses the same analysis as in our Letter, includes any type…

In Reverse Mathematics, the axiom system DNR, asserting the existence of diagonally non-recursive functions, is strictly weaker than WWKL$_0$ (weak weak K\"onig's Lemma).

We introduce a notion of "weak model category" which is a weakening of the notion of Quillen model category, still sufficient to define a homotopy category, Quillen adjunctions, Quillen equivalences and most of the usual construction of…

We prove that every Banach space containing a subspace isomorphic to $\co$ fails the fixed point property. The proof is based on an amalgamation approach involving a suitable combination of known results and techniques, including James's…

In this note we deduce a strengthening of the Orlicz-Pettis theorem from the It\^o-Nisio theorem. The argument shows that given any series in a Banach space which isn't summable (or more generally unconditionally summable), we can construct…

Research has shown that widely used deep neural networks are vulnerable to carefully crafted adversarial perturbations. Moreover, these adversarial perturbations often transfer across models. We hypothesize that adversarial weakness is…