This paper is the answer to the paper by Kastner [ Found. Phys. to be published, quant-ph/9807037] in which she continued the criticism of the counterfactual usage of the Aharonov-Bergman-Lebowitz rule in the framework of the time-symmetrized quantum theory, in particular, by analyzing the three-box “paradox”. It is argued that the criticism is not sound. Paradoxical features of the three-box e...

Fermion N -loops with an arbitrary number of density vertices N > d + 1 in d spatial dimensions can be expressed as a linear combination of (d + 1)-loops with coefficients that are rational functions of external momentum and energy variables. A theorem on symmetrized products then implies that divergencies of single loops for low energy and small momenta cancel each other when loops with permut...

Given a decomposable graph, we characterize and enumerate the set of pairs of vertices whose connection or disconnection results in a new graph that is also decomposable. We discuss the relevance of this results to Markov chain Monte Carlo methods that sample or optimize over the space of decomposable graphical models according to probabilities determined by a posterior distribution given obser...

We prove induced Ramsey theorems in which the monochromatic induced subgraph satisfies that all members of a prescribed set of its partial isomorphisms extend to automorphisms of the colored graph (without requirement of preservation of colors). We consider vertex and edge colorings, and extensions of partial isomorphisms in the set of all partial isomorphisms between singletons as considered b...

We prove induced Ramsey theorems in which the induced monochromatic subgraph satisfies that some of its partial automorphisms extend to automorphisms of the colored graph.

A characterization of module alphabets with the Hamming weight EP (abbreviation for Extension Property) had been settled. A thoughtfully constructed piece-of-art example by J.A.Wood ([7]) finished the tour. In 2009, in [8], Frobenius bimodules were proved to satisfy the EP with respect to symmetrized weight compositions. In [4], the embeddability in the character group of the ambient ring R was...