Aberrant Mitochondrial tRNA Genes Appear Frequently in Animal Evolution.

Mitochondrial tRNAs have acquired a diverse portfolio of aberrant structures throughout metazoan evolution. With the availability of more than 12,500 mitogenome sequences, it is essential to compile a comprehensive overview of the pattern changes with regard to mitochondrial tRNA repertoire and structural variations. This, of course, requires reanalysis of the sequence data of more than 250,000 mitochondrial tRNAs with a uniform workflow.

Non-uniqueness of Admissible Solutions for the 2D Euler Equation with Vortex Data.

For any we prove that there exists an initial velocity field with vorticity for which there are infinitely many bounded admissible solutions to the 2D Euler equation. This shows sharpness of the weak-strong uniqueness principle, as well as sharpness of Yudovich's proof of uniqueness in the class of bounded admissible solutions. The initial data are truncated power-law vortices.

Spaces of mathematical chemistry.

In an effort to expand the domain of mathematical chemistry and inspire research beyond the realms of graph theory and quantum chemistry, we explore five mathematical chemistry spaces and their interconnectedness. These spaces comprise the chemical space, which encompasses substances and reactions; the space of reaction conditions, spanning the physical and chemical aspects involved in chemical reactions; the space of reaction grammars, which encapsulates the rules for creating and breaking chemical bonds; the space of substance properties, covering all documented measurements regarding substances; and the space of substance representations, composed of the various ontologies for characterising substances.

Oscillatory-Quality of sleep spindles links brain state with sleep regulation and function.

Here, we characterized the dynamics of sleep spindles, focusing on their damping, which we estimated using a metric called oscillatory-Quality (o-Quality), derived by fitting an autoregressive model to electrophysiological signals, recorded from the cortex in mice. The o-Quality of sleep spindles correlates weakly with their amplitude, shows marked laminar differences and regional topography across cortical regions, reflects the level of synchrony within and between cortical networks, is strongly modulated by sleep-wake history, reflects the degree of sensory disconnection, and correlates with the strength of coupling between spindles and slow waves. As most spindle events are highly localized and not detectable with conventional low-density recording approaches, o-Quality thus emerges as a valuable metric that allows us to infer the spread and dynamics of spindle activity across the brain and directly links their spatiotemporal dynamics with local and global regulation of brain states, sleep regulation, and function.

Evolution of neuropeptide Y/RFamide-like receptors in nematodes.

The Neuropeptide Y/RFamide-like receptors belong to the Rhodopsin-like G protein-coupled receptors G protein-coupled receptors (GPCRs) and are involved in functions such as locomotion, feeding and reproduction. With 41 described receptors they form the best-studied group of neuropeptide GPCRs in . In order to understand the expansion of the Neuropeptide Y/RFamide-like receptor family in nematodes, we started from the sequences of selected receptor paralogs in as query and surveyed the corresponding orthologous sequences in another 159 representative nematode target genomes.

Lengths of factorizations of integer-valued polynomials on Krull domains with prime elements.

Let be a Krull domain admitting a prime element with finite residue field and let be its quotient field. We show that for all positive integers and , there exists an integer-valued polynomial on , that is, an element of , which has precisely essentially different factorizations into irreducible elements of whose lengths are exactly . Using this, we characterize lengths of factorizations when is a unique factorization domain and therefore also in case is a discrete valuation domain.

Identifiability of Level-1 Species Networks from Gene Tree Quartets.

When hybridization or other forms of lateral gene transfer have occurred, evolutionary relationships of species are better represented by phylogenetic networks than by trees. While inference of such networks remains challenging, several recently proposed methods are based on quartet concordance factors-the probabilities that a tree relating a gene sampled from the species displays the possible 4-taxon relationships. Building on earlier results, we investigate what level-1 network features are identifiable from concordance factors under the network multispecies coalescent model.

Reaction rebalancing: a novel approach to curating reaction databases.

Purpose: Reaction databases are a key resource for a wide variety of applications in computational chemistry and biochemistry, including Computer-aided Synthesis Planning (CASP) and the large-scale analysis of metabolic networks. The full potential of these resources can only be realized if datasets are accurate and complete. Missing co-reactants and co-products, i.

Phylogenetic and Chemical Probing Information as Soft Constraints in RNA Secondary Structure Prediction.

Extrinsic, experimental information can be incorporated into thermodynamics-based RNA folding algorithms in the form of pseudo-energies. Evolutionary conservation of RNA secondary structure elements is detectable in alignments of phylogenetically related sequences and provides evidence for the presence of certain base pairs that can also be converted into pseudo-energy contributions. We show that the centroid base pairs computed from a consensus folding model such as RNAalifold result in a substantial improvement of the prediction accuracy for single sequences.

Comparative RNA Genomics.

Over the last quarter of a century it has become clear that RNA is much more than just a boring intermediate in protein expression. Ancient RNAs still appear in the core information metabolism and comprise a surprisingly large component in bacterial gene regulation. A common theme with these types of mostly small RNAs is their reliance of conserved secondary structures.

The Theory of Gene Family Histories.

Most genes are part of larger families of evolutionary-related genes. The history of gene families typically involves duplications and losses of genes as well as horizontal transfers into other organisms. The reconstruction of detailed gene family histories, i.

Assessing the Quality of Cotranscriptional Folding Simulations.

Structural changes in RNAs are an important contributor to controlling gene expression not only at the posttranscriptional stage but also during transcription. A subclass of riboswitches and RNA thermometers located in the 5' region of the primary transcript regulates the downstream functional unit - usually an ORF - through premature termination of transcription. Not only such elements occur naturally, but they are also attractive devices in synthetic biology.

Quantifying synergy and redundancy between networks.

Understanding how different networks relate to each other is key for understanding complex systems. We introduce an intuitive yet powerful framework to disentangle different ways in which networks can be (dis)similar and complementary to each other. We decompose the shortest paths between nodes as uniquely contributed by one source network, or redundantly by either, or synergistically by both together.

Cavity approach for the approximation of spectral density of graphs with heterogeneous structures.

Graphs have become widely used to represent and study social, biological, and technological systems. Statistical methods to analyze empirical graphs were proposed based on the graph's spectral density. However, their running time is cubic in the number of vertices, precluding direct application to large instances.

Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals.

We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the standard model in dimensional regularization. After highlighting issues in the textbook treatment of Landau singularities, we develop an algorithm for classifying and computing them using techniques from computational algebraic geometry. We introduce an algebraic variety called the principal Landau determinant, which captures the singularities even in the presence of massless particles or UV/IR divergences.

Diversity begets stability: Sublinear growth and competitive coexistence across ecosystems.

The worldwide loss of species diversity brings urgency to understanding how diverse ecosystems maintain stability. Whereas early ecological ideas and classic observations suggested that stability increases with diversity, ecological theory makes the opposite prediction, leading to the long-standing "diversity-stability debate." Here, we show that this puzzle can be resolved if growth scales as a sublinear power law with biomass (exponent <1), exhibiting a form of population self-regulation analogous to models of individual ontogeny.

Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA.

The monogamy property of entanglement is an intriguing feature of multipartite quantum entanglement. Most entanglement measures satisfying the monogamy inequality have turned out to be convex. Whether nonconvex entanglement measures obey the monogamy inequalities remains less known at present.

Relativistic Perturbation Theory for Black-Hole Boson Clouds.

We develop a relativistic perturbation theory for scalar clouds around rotating black holes. We first introduce a relativistic product and corresponding orthogonality relation between modes, extending a recent result for gravitational perturbations. We then derive the analog of time-dependent perturbation theory in quantum mechanics, and apply it to calculate self-gravitational frequency shifts.

Taking identity-by-descent analysis into the wild: Estimating realized relatedness in free-ranging macaques.

Biological relatedness is a key consideration in studies of behavior, population structure, and trait evolution. Except for parent-offspring dyads, pedigrees capture relatedness imperfectly. The number and length of DNA segments that are identical-by-descent (IBD) yield the most precise estimates of relatedness.

IDENTIFIABILITY OF LEVEL-1 SPECIES NETWORKS FROM GENE TREE QUARTETS.

When hybridization or other forms of lateral gene transfer have occurred, evolutionary relationships of species are better represented by phylogenetic networks than by trees. While inference of such networks remains challenging, several recently proposed methods are based on quartet concordance factors - the probabilities that a tree relating a gene sampled from the species displays the possible 4-taxon relationships. Building on earlier results, we investigate what level-1 network features are identifiable from concordance factors under the network multispecies coalescent model.

Geometry and convergence of natural policy gradient methods.

We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular policy parametrizations. For a variety of NPGs and reward functions we show that the trajectories in state-action space are solutions of gradient flows with respect to Hessian geometries, based on which we obtain global convergence guarantees and convergence rates. In particular, we show linear convergence for unregularized and regularized NPG flows with the metrics proposed by Kakade and Morimura and co-authors by observing that these arise from the Hessian geometries of conditional entropy and entropy respectively.

Proteinortho6: pseudo-reciprocal best alignment heuristic for graph-based detection of (co-)orthologs.

Proteinortho is a widely used tool to predict (co)-orthologous groups of genes for any set of species. It finds application in comparative and functional genomics, phylogenomics, and evolutionary reconstructions. With a rapidly increasing number of available genomes, the demand for large-scale predictions is also growing.

Conditioning in Tropical Probability Theory.

We define a natural operation of conditioning of tropical diagrams of probability spaces and show that it is Lipschitz continuous with respect to the asymptotic entropy distance.