If not empty, NP — P is topologically large

AbstractIn the classical Cantor topology or in the superset topology, NP and, consequently, classes included in NP are meagre. However, in a natural combination of the two topologies, we prove that NP — P, if not empty, is a second category class, while NP-complete sets form a first category class. These results are extended to different levels in the polynomial hierarchy and to the low and high hierarchies. P-immune sets in NP, NP-simple sets, P-bi-immune sets and NP-effectively simple sets are all second category (if not empty). It is shown that if C is any of the above second category classes, then for all B∈NP there exists an A∈C such that A is arbitrarily close to B infinitely often

Evolutionary algorithms for robust methods

A drawback of robust statistical techniques is the increased computational effort often needed compared to non robust methods. Robust estimators possessing the exact fit property, for example, are NP-hard to compute. This means thatunder the widely believed assumption that the computational complexity classes NP and P are not equalthere is no hope to compute exact solutions for large high dimensional data sets. To tackle this problem, search heuristics are used to compute NP-hard estimators in high dimensions. Here, an evolutionary algorithm that is applicable to different robust estimators is presented. Further, variants of this evolutionary algorithm for selected estimatorsmost prominently least trimmed squares and least median of squaresare introduced and shown to outperform existing popular search heuristics in difficult data situations. The results increase the applicability of robust methods and underline the usefulness of evolutionary computation for computational statistics. --Evolutionary algorithms,robust regression,least trimmed squares (LTS),least median of squares (LMS),least quantile of squares (LQS),least quartile difference (LQD)

Finding Near-Optimal Independent Sets at Scale

The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in huge sparse networks. A recent exact algorithm has shown that large networks can be solved exactly by employing a branch-and-reduce technique that recursively kernelizes the graph and performs branching. However, one major drawback of their algorithm is that, for huge graphs, branching still can take exponential time. To avoid this problem, we recursively choose vertices that are likely to be in a large independent set (using an evolutionary approach), then further kernelize the graph. We show that identifying and removing vertices likely to be in large independent sets opens up the reduction space---which not only speeds up the computation of large independent sets drastically, but also enables us to compute high-quality independent sets on much larger instances than previously reported in the literature.Comment: 17 pages, 1 figure, 8 tables. arXiv admin note: text overlap with arXiv:1502.0168

Formation of an ordered phase in neutron star matter

In this work, we explore the possible formation of ordered phases in hadronic matter, related to the presence of hyperons at high densities. We analyze a microscopic mechanism which can lead to the crystallization of the hyperonic sector by the confinement of the hyperons on the nodes of a lattice. For this purpose, we introduce a simplified model of the hadronic plasma, in which the nuclear interaction between protons, neutrons and hyperons is mediated by meson fields. We find that, for some reasonable sets of values of the model parameters, such ordered phases are energetically favoured as density increases beyond a threshold value.Comment: 16 pages, 14 figures, submitted to NP

High-precision covariant one-boson-exchange potentials for np scattering below 350 MeV

All realistic potential models for the two-nucleon interaction are to some extent based on boson exchange. However, in order to achieve an essentially perfect fit to the scattering data, characterized by a chi2/Ndata ~ 1, previous potentials have abandoned a pure one boson-exchange mechanism (OBE). Using a covariant theory, we have found a OBE potential that fits the 2006 world np data below 350 MeV with a chi2/Ndata = 1.06 for 3788 data. Our potential has fewer adjustable parameters than previous high-precision potentials, and also reproduces the experimental triton binding energy without introducing additional irreducible three-nucleon forces.Comment: 4 pages; revised version with augmented data sets; agrees with published versio

Evolutionary algorithms for robust methods

A drawback of robust statistical techniques is the increased computational effort often needed compared to non robust methods. Robust estimators possessing the exact fit property, for example, are NP-hard to compute. This means that — under the widely believed assumption that the computational complexity classes NP and P are not equal — there is no hope to compute exact solutions for large high dimensional data sets. To tackle this problem, search heuristics are used to compute NP-hard estimators in high dimensions. Here, an evolutionary algorithm that is applicable to different robust estimators is presented. Further, variants of this evolutionary algorithm for selected estimators — most prominently least trimmed squares and least median of squares—are introduced and shown to outperform existing popular search heuristics in difficult data situations. The results increase the applicability of robust methods and underline the usefulness of evolutionary computation for computational statistics

Three human cell types respond to multi-walled carbon nanotubes and titanium dioxide nanobelts with cell-specific transcriptomic and proteomic expression patterns

The growing use of engineered nanoparticles (NPs) in commercial and medical applications raises the urgent need for tools that can predict NP toxicity. We conducted global transcriptome and proteome analyses of three human cell types, exposed to two high aspect ratio NP types, to identify patterns of expression that might indicate high vs. low NP toxicity. Three cell types representing the most common routes of human exposure to NPs, including macrophage like (THP-1), small airway epithelial (SAE), and intestinal (Caco-2/HT29-MTX) cells, were exposed to TiO2 nanobelts (TiO2-NB; high toxicity) and multi-walled carbon nanotubes (MWCNT; low toxicity) at low (10 μg/ml) and high (100 μg/ml) concentrations for 1 and 24 h. Unique patterns of gene and protein expressions were identified for each cell type, with no differentially expressed (p<0.05, 1.5-fold change) genes or proteins overlapping across all three cell types. While unique to each cell-type, the early response was primarily independent of NP type, showing similar expression patterns in response to both TiO2-NB and MWCNT. The early response might therefore indicate a general response to insult. In contrast, the 24 h response was unique to each NP type. The most significantly (p<0.05) enriched biological processes in THP-1 cells indicated TiO2-NB regulation of pathways associated with inflammation, apoptosis, cell cycle arrest, DNA replication stress and genomic instability, while MWCNT regulated pathways indicating increased cell proliferation, DNA repair and anti-apoptosis. These two distinct sets of biological pathways might therefore underlie cellular responses to high and low NP toxicity, respectively