Post-processing partitions to identify domains of modularity optimization

We introduce the Convex Hull of Admissible Modularity Partitions (CHAMP) algorithm to prune and prioritize different network community structures identified across multiple runs of possibly various computational heuristics. Given a set of partitions, CHAMP identifies the domain of modularity optimization for each partition ---i.e., the parameter-space domain where it has the largest modularity relative to the input set---discarding partitions with empty domains to obtain the subset of partitions that are "admissible" candidate community structures that remain potentially optimal over indicated parameter domains. Importantly, CHAMP can be used for multi-dimensional parameter spaces, such as those for multilayer networks where one includes a resolution parameter and interlayer coupling. Using the results from CHAMP, a user can more appropriately select robust community structures by observing the sizes of domains of optimization and the pairwise comparisons between partitions in the admissible subset. We demonstrate the utility of CHAMP with several example networks. In these examples, CHAMP focuses attention onto pruned subsets of admissible partitions that are 20-to-1785 times smaller than the sets of unique partitions obtained by community detection heuristics that were input into CHAMP.Comment: http://www.mdpi.com/1999-4893/10/3/9

Repeated boundary slopes for 2-bridge knots

We investigate the question of when distinct branched surfaces in the complement of a 2-bridge knot support essential surfaces with identical boundary slopes. We determine all instances in which this occurs and identify an infinite family of knots for which no boundary slopes are repeated

PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison

The selection, development, or comparison of machine learning methods in data mining can be a difficult task based on the target problem and goals of a particular study. Numerous publicly available real-world and simulated benchmark datasets have emerged from different sources, but their organization and adoption as standards have been inconsistent. As such, selecting and curating specific benchmarks remains an unnecessary burden on machine learning practitioners and data scientists. The present study introduces an accessible, curated, and developing public benchmark resource to facilitate identification of the strengths and weaknesses of different machine learning methodologies. We compare meta-features among the current set of benchmark datasets in this resource to characterize the diversity of available data. Finally, we apply a number of established machine learning methods to the entire benchmark suite and analyze how datasets and algorithms cluster in terms of performance. This work is an important first step towards understanding the limitations of popular benchmarking suites and developing a resource that connects existing benchmarking standards to more diverse and efficient standards in the future.Comment: 14 pages, 5 figures, submitted for review to JML

A Peptide Core Motif for Binding to Heterotrimeric G Protein α Subunits

Recently, in vitro selection using mRNA display was used to identify a novel peptide sequence that binds with high affinity to G{alpha}i1. The peptide was minimized to a 9-residue sequence (R6A-1) that retains high affinity and specificity for the GDP-bound state of G{alpha}i1 and acts as a guanine nucleotide dissociation inhibitor (GDI). Here we demonstrate that the R6A-1 peptide interacts with G{alpha} subunits representing all four G protein classes, acting as a core motif for G{alpha} interaction. This contrasts with the consensus G protein regulatory(GPR) sequence, a 28-mer peptide GDI derived from the GoLoco (G{alpha}i/0-Loco interaction)/GPR motif that shares no homology with R6A-1 and binds only to G{alpha}i1-3 in this assay. Binding of R6A-1 is generally specific to the GDP-bound state of the G{alpha} subunits and excludes association with G{beta}{gamma}. R6A-G{alpha}i1 complexes are resistant to trypsin digestion and exhibit distinct stability in the presence of Mg2+, suggesting that the R6A and GPR peptides exert their activities using different mechanisms. Studies using G{alpha}i1/G{alpha}s chimeras identify two regions of G{alpha}i1 (residues 1–35 and 57–88) as determinants for strong R6A-Gi{alpha}1 interaction. Residues flanking the R6A-1 peptide confer unique binding properties, indicating that the core motif could be used as a starting point for the development of peptides exhibiting novel activities and/or specificity for particular G protein subclasses or nucleotide-bound states

Anti-cancer Action of Metal Complexes: Electron Transfer and Oxidative Stress?

Evidence is presented in support of an electron transfer mechanism for various metal complexes possessing anti-neoplastic properties. Cyclic voltammetry was performed on several metallocenes, bis(acetato)bis(imidazole)Cu(II), and coordination compounds (Cu or Fe) of the anti-tumor agents, bipyridine, phenanthroline, hydroxyurea, diethyldithiocarbamate, and α, α1-bis(8-hydroxyquinolin-7-yl)-4-methoxytoluene. The favorable reduction potentials ranged from +0.5 to -0.5 V. Electrochemical behavior is correlated in some cases with structure and physiological activity. Relevant literature data are discussed

Digital zero noise extrapolation for quantum error mitigation

Zero-noise extrapolation (ZNE) is an increasingly popular technique for mitigating errors in noisy quantum computations without using additional quantum resources. We review the fundamentals of ZNE and propose several improvements to noise scaling and extrapolation, the two key components in the technique. We introduce unitary folding and parameterized noise scaling. These are digital noise scaling frameworks, i.e. one can apply them using only gate-level access common to most quantum instruction sets. We also study different extrapolation methods, including a new adaptive protocol that uses a statistical inference framework. Benchmarks of our techniques show error reductions of 18X to 24X over non-mitigated circuits and demonstrate ZNE effectiveness at larger qubit numbers than have been tested previously. In addition to presenting new results, this work is a self-contained introduction to the practical use of ZNE by quantum programmers.Comment: 11 pages, 7 figure