aFold – using polynomial uncertainty modelling for differential gene expression estimation from RNA sequencing data

Data normalization and identification of significant differential expression represent crucial steps in RNA-Seq analysis. Many available tools rely on assumptions that are often not met by real data, including the common assumption of symmetrical distribution of up- and down-regulated genes, the presence of only few differentially expressed genes and/or few outliers. Moreover, the cut-off for selecting significantly differentially expressed genes for further downstream analysis often depend on arbitrary choices

The DSUBmm Approximation Scheme for the Coupled Cluster Method and Applications to Quantum Magnets

A new approximate scheme, DSUB$m$, is described for the coupled cluster method. We then apply it to two well-studied (spin-1/2 Heisenberg antiferromagnet) spin-lattice models, namely: the $XXZ$ and the $XY$ models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the sublattice magnetization and the quantum critical point. They are in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods and those from the CCM using the LSUB$m$ scheme.Comment: 18 pages, 10 figure

Independent magnon states on magnetic polytopes

For many spin systems with constant isotropic antiferromagnetic next-neighbour Heisenberg coupling the minimal energies E_{min}(S) form a rotational band, i.e. depend approximately quadratically on the total spin quantum number S, a property which is also known as Lande interval rule. However, we find that for certain coupling topologies, including recently synthesised icosidodecahedral structures this rule is violated for high total spins. Instead the minimal energies are a linear function of total spin. This anomaly results in a corresponding jump of the magnetisation curve which otherwise would be a regular staircase.Comment: 11 pages, 4 figures, submitted to Eur. Phys. J.

Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices

For a class of frustrated spin lattices including the kagome lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the kagome lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.Comment: 4 pages, 4 figures, accepted by Phys.Rev.Let

Community assembly of the native C. elegans microbiome is influenced by time, substrate and individual bacterial taxa

Summary Microbiome communities are complex assemblages of bacteria. The dissection of their assembly dynamics is challenging because it requires repeated sampling of both host and source communities. We used the nematode Caenorhabditis elegans as a model to study these dynamics. We characterized microbiome variation from natural worm populations and their substrates for two consecutive years using 16S rDNA amplicon sequencing. We found conservation in microbiome composition across time at the genus, but not amplicon sequencing variant (ASV) level. Only three ASVs were consistently present across worm samples (Comamonas ASV10859, Pseudomonas ASV7162 and Cellvibrio ASV9073). ASVs were more diverse in worms from different rather than the same substrates, indicating an influence of the source community on microbiome assembly. Surprisingly, almost 50% of worm-associated ASVs were absent in corresponding substrates, potentially due to environmental filtering. Ecological network analysis revealed strong effects of bacteria–bacteria interactions on community composition: While a dominant Erwinia strain correlated with decreased alpha-diversity, predatory bacteria of the Bdellovibrio and like organisms associated with increased alpha-diversity. High alpha-diversity was further linked to high worm population growth, especially on species-poor substrates. Our results highlight that microbiomes are individually shaped and sensitive to dramatic community shifts in response to particular competitive species

Quantum J1J_1--J2J_2 antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering

Using the coupled-cluster method (CCM) and the rotation-invariant Green's function method (RGM), we study the influence of the interlayer coupling $J_\perp$ on the magnetic ordering in the ground state of the spin-1/2 $J_1$-$J_2$ frustrated Heisenberg antiferromagnet ($J_1$-$J_2$ model) on the stacked square lattice. In agreement with known results for the $J_1$-$J_2$ model on the strictly two-dimensional square lattice ($J_\perp=0$) we find that the phases with magnetic long-range order at small $J_2< J_{c_1}$ and large $J_2> J_{c_2}$ are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling $J_\perp>0$ the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small $J_\perp \sim 0.2 ... 0.3 J_1$.Comment: 4 pages, 3 figure

The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study

We investigate the ground-state magnetic order of the spin-1/2 J1-J2 Heisenberg model on the square lattice with ferromagnetic nearest-neighbor exchange J1<0 and frustrating antiferromagnetic next-nearest neighbor exchange J2>0. We use the coupled-cluster method to high orders of approximation and Lanczos exact diagonalization of finite lattices of up to N=40 sites in order to calculate the ground-state energy, the spin-spin correlation functions, and the magnetic order parameter. We find that the transition point at which the ferromagnetic ground state disappears is given by J2^{c1}=0.393|J1| (exact diagonalization) and J2^{c1}=0.394|J1| (coupled-cluster method). We compare our results for ferromagnetic J1 with established results for the spin-1/2 J1-J2 Heisenberg model with antiferromagnetic J1. We find that both models (i.e., ferro- and antiferromagnetic J1) behave similarly for large J2, although significant differences between them are observed for J2/|J1| \lesssim 0.6. Although the semiclassical collinear magnetic long-range order breaks down at J2^{c2} \approx 0.6J1 for antiferromagnetic J1, we do not find a similar breakdown of this kind of long-range order until J2 \sim 0.4|J1| for the model with ferromagnetic J1. Unlike the case for antiferromagnetic J1, if an intermediate disordered phase does occur between the phases exhibiting semiclassical collinear stripe order and ferromagnetic order for ferromagnetic J1 then it is likely to be over a very small range below J2 \sim 0.4|J1|.Comment: 15 pages, 7 figures, 2 table

Modeling host-associating microbes under selection

The concept of fitness is often reduced to a single component, such as the replication rate in a given habitat. For species with multi-step life cycles, this can be an unjustified oversimplification, as every step of the life cycle can contribute to the overall reproductive success in a specific way. In particular, this applies to microbes that spend part of their life cycles associated to a host. In this case, there is a selection pressure not only on the replication rates, but also on the phenotypic traits associated to migrating from the external environment to the host and vice-versa (i.e., the migration rates). Here, we investigate a simple model of a microbial lineage living, replicating, migrating and competing in and between two compartments: a host and an environment. We perform a sensitivity analysis on the overall growth rate to determine the selection gradient experienced by the microbial lineage. We focus on the direction of selection at each point of the phenotypic space, defining an optimal way for the microbial lineage to increase its fitness. We show that microbes can adapt to the two-compartment life cycle through either changes in replication or migration rates, depending on the initial values of the traits, the initial distribution across the two compartments, the intensity of competition, and the time scales involved in the life cycle versus the time scale of adaptation (which determines the adequate probing time to measure fitness). Overall, our model provides a conceptual framework to study the selection on microbes experiencing a host-associated life cycle

On the evolutionary origins of host–microbe associations

Animals can provide benefits to their associated microbes—}and these can, in turn, positively affect their hosts. But how do such mutually beneficial associations arise in the first place? In particular, when animal and microbe initially have independent lifestyles, this is not clear. By developing a model of animal and microbial life cycles on patchy habitats, we show how their overlapping ecologies of development and dispersal can lead to the enrichment of certain microbes in the dispersing animals, even in the absence of specific mutualistic benefits. This enrichment can then set the stage for the evolution of more specific host{–}microbe associations, which also implies that host enrichment per se is not an indicator of a beneficial host{–}microbe symbiosis.Many microorganisms with high prevalence in host populations are beneficial to the host and maintained by specialized transmission mechanisms. Although microbial promotion of host fitness and specificity of the associations undoubtedly enhance microbial prevalence, it is an open question whether these symbiotic traits are also a prerequisite for the evolutionary origin of prevalent microbial taxa. To address this issue, we investigate how processes without positive microbial effects on host fitness or host choice can influence the prevalence of certain microbes in a host population. Specifically, we develop a theoretical model to assess the conditions under which particular microbes can become enriched in animal hosts even when they are not providing a specific benefit to a particular host. We find increased prevalence of specific microbes in a host when both show some overlap in their lifecycles, and especially when both share dispersal routes across a patchy habitat distribution. Our results emphasize that host enrichment per se is not a reliable indicator of beneficial host{–microbe interactions. The resulting increase in time spent associated with a host may nevertheless give rise to new selection conditions, which can favor microbial adaptations toward a host-associated lifestyle, and, thus, it could be the foundation for subsequent evolution of mutually beneficial coevolved symbioses.A Python implementation of the model underlying the results in this paper has been deposited in GitHub (https://github.com/misieber/patchbiota)