Local Intrinsic Dimensionality, Entropy and Statistical Divergences.

Properties of data distributions can be assessed at both global and local scales. At a highly localized scale, a fundamental measure is the local intrinsic dimensionality (LID), which assesses growth rates of the cumulative distribution function within a restricted neighborhood and characterizes properties of the geometry of a local neighborhood. In this paper, we explore the connection of LID to other well known measures for complexity assessment and comparison, namely, entropy and statistical distances or divergences. In an asymptotic context, we develop analytical new expressions for these quantities in terms of LID. This reveals the fundamental nature of LID as a building block for characterizing and comparing data distributions, opening the door to new methods for distributional analysis at a local scale.

Rank-Based Similarity Search: Reducing the Dimensional Dependence.

This paper introduces a data structure for k-NN search, the Rank Cover Tree (RCT), whose pruning tests rely solely on the comparison of similarity values; other properties of the underlying space, such as the triangle inequality, are not employed. Objects are selected according to their ranks with respect to the query object, allowing much tighter control on the overall execution costs. A formal theoretical analysis shows that with very high probability, the RCT returns a correct query result in time that depends very competitively on a measure of the intrinsic dimensionality of the data set. The experimental results for the RCT show that non-metric pruning strategies for similarity search can be practical even when the representational dimension of the data is extremely high. They also show that the RCT is capable of meeting or exceeding the level of performance of state-of-the-art methods that make use of metric pruning or other selection tests involving numerical constraints on distance values.

Expansion of the APC superfamily of secondary carriers.

The amino acid-polyamine-organoCation (APC) superfamily is the second largest superfamily of secondary carriers currently known. In this study, we establish homology between previously recognized APC superfamily members and proteins of seven new families. These families include the PAAP (Putative Amino Acid Permease), LIVCS (Branched Chain Amino Acid:Cation Symporter), NRAMP (Natural Resistance-Associated Macrophage Protein), CstA (Carbon starvation A protein), KUP (K⁺ Uptake Permease), BenE (Benzoate:H⁺ Virginia Symporter), and AE (Anion Exchanger). The topology of the well-characterized human Anion Exchanger 1 (AE1) conforms to a UraA-like topology of 14 TMSs (12 α-helical TMSs and 2 mixed coil/helical TMSs). All functionally characterized members of the APC superfamily use cation symport for substrate accumulation except for some members of the AE family which frequently use anion:anion exchange. We show how the different topologies fit into the framework of the common LeuT-like fold, defined earlier (Proteins. 2014 Feb;82(2):336-46), and determine that some of the new members contain previously undocumented topological variations. All new entries contain the two 5 or 7 TMS APC superfamily repeat units, sometimes with extra TMSs at the ends, the variations being greatest within the CstA family. New, functionally characterized members transport amino acids, peptides, and inorganic anions or cations. Except for anions, these are typical substrates of established APC superfamily members. Active site TMSs are rich in glycyl residues in variable but conserved constellations. This work expands the APC superfamily and our understanding of its topological variations.

Identification of distant Agouti-like sequences and re-evaluation of the evolutionary history of the Agouti-related peptide (AgRP).

The Agouti-like peptides including AgRP, ASIP and the teleost-specific A2 (ASIP2 and AgRP2) peptides have potent and diverse functional roles in feeding, pigmentation and background adaptation mechanisms. There are contradictory theories about the evolution of the Agouti-like peptide family as well the nomenclature. Here we performed comprehensive mining and annotation of vertebrate Agouti-like sequences. We identified A2 sequences from salmon, trout, seabass, cod, cichlid, tilapia, gilt-headed sea bream, Antarctic toothfish, rainbow smelt, common carp, channel catfish and interestingly also in lobe-finned fish. Moreover, we surprisingly found eight novel homologues from the kingdom of arthropods and three from fungi, some sharing the characteristic C-x(6)-C-C motif which are present in the Agouti-like sequences, as well as approximate sequence length (130 amino acids), positioning of the motif sequence and sharing of exon-intron structures that are similar to the other Agouti-like peptides providing further support for the common origin of these sequences. Phylogenetic analysis shows that the AgRP sequences cluster basally in the tree, suggesting that these sequences split from a cluster containing both the ASIP and the A2 sequences. We also used a novel approach to determine the statistical evidence for synteny, a sinusoidal Hough transform pattern recognition technique. Our analysis shows that the teleost AgRP2 resides in a chromosomal region that has synteny with Hsa 8, but we found no convincing synteny between the regions that A2, AgRP and ASIP reside in, which would support that the Agouti-like peptides were formed by whole genome tetraplodization events. Here we suggest that the Agouti-like peptide genes were formed through classical subsequent gene duplications where the AgRP is the most distantly related to the three other members of that group, first splitting from a common ancestor to ASIP and A2, and then later the A2 split from ASIP followed by a split resulting in ASIP2 and AgRP2.