This is a technical paper devoted to the investigation of collapsing of Alexandrov spaces with lower curvature bound. In a previous paper, the author defined a canonical stratification of an Alexandrov space by the so-called extremal subsets. It is likely that if the limit of a collapsing sequence has no proper extremal subsets, then the collapsing spaces are fiber bundles over the limit space....

Methods that collapse information across genetic markers when searching for association signals are gaining momentum in the literature. Although originally developed to achieve a better balance between retaining information and controlling degrees of freedom when performing multimarker association analysis, these methods have recently been proven to be a powerful tool for identifying rare varia...

We investigate the post-quantum security of hash functions based on the sponge construction. A crucial property for hash functions in the post-quantum setting is the collapsing property (a strengthening of collision-resistance). We show that the sponge construction is collapsing (and in consequence quantum collision-resistant) under suitable assumptions about the underlying block function. In p...

The purpose of this paper is to introduce a variant of the geometric collapsing theory for Riemannian manifolds contained in the joint work of J. Cheeger, K. Fukaya and M. Gromov (henceforth called the “C-F-G-theory”). The authors make important use of this variant geometric collapsing theory in Farrell and Jones, 1998(2), to develop a theory for collapsing foliated Riemannian manifolds and the...

We investigate the band-gap modiication by collapsing deformation in C, BN, and BC3 nanotubes through rst-principles pseudopotential calculations. Semiconductor-metal transitions occur when zigzag C and armchair BC3 nanotubes undergo collapsing deformation, while in zigzag BN tubes, a variation of band gaps from 5 to 2 eV is found. On the other hand, the band gaps of armchair BN and zigzag BC3 ...

We investigate the post-quantum security of hash functions based on the sponge construction. A crucial property for hash functions in the post-quantum setting is the collapsing property (a strengthening of collision-resistance). We show that the sponge construction is collapsing (and in consequence quantum collision-resistant) under suitable assumptions about the underlying block function. In p...

Analysis of longitudinal family data is challenging because of 2 sources of correlations: correlations across longitudinal measurements and correlations among related individuals. We investigated whether analysis using long-term average (average of all 3 visits) can enhance gene discovery compared with a single-visit analysis. We analyzed all 200 replicates of simulated systolic blood pressure ...

A word w over a finite alphabet Σ is n-collapsing if for an arbitrary deterministic finite automaton A = 〈Q,Σ, δ〉, the inequality |δ(Q,w)| ≤ |Q| − n holds provided that |δ(Q, u)| ≤ |Q| − n for some word u ∈ Σ (depending on A ). We prove that the the property of being n-collapsing is algorithmically recognizable for any given positive integer n. We also prove that the language of all n-collapsin...