Equiangular lines in Euclidean spaces

We obtain several new results contributing to the theory of real equiangular line systems. Among other things, we present a new general lower bound on the maximum number of equiangular lines in d dimensional Euclidean space; we describe the two-graphs on 12 vertices; and we investigate Seidel matrices with exactly three distinct eigenvalues. As a result, we improve on two long-standing upper bounds regarding the maximum number of equiangular lines in dimensions d=14, and d=16. Additionally, we prove the nonexistence of certain regular graphs with four eigenvalues, and correct some tables from the literature.Comment: 24 pages, to appear in JCTA. Corrected an entry in Table

On quaternary complex Hadamard matrices of small orders

One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete enumeration of the objects is possible, there is no apparent way how to study them in details, store them efficiently, or generate a particular one rapidly. In this paper we propose a novel method to deal with these difficulties, and illustrate it by presenting the classification of quaternary complex Hadamard matrices up to order 8. The obtained matrices are members of only a handful of parametric families, and each inequivalent matrix, up to transposition, can be identified through its fingerprint.Comment: 7 page

A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6

We exhibit an infinite family of {\it triplets} of mutually unbiased bases (MUBs) in dimension 6. These triplets involve the Fourier family of Hadamard matrices, $F(a,b)$. However, in the main result of the paper we also prove that for any values of the parameters $(a,b)$, the standard basis and $F(a,b)$ {\it cannot be extended to a MUB-quartet}. The main novelty lies in the {\it method} of proof which may successfully be applied in the future to prove that the maximal number of MUBs in dimension 6 is three.Comment: 32 pages (with Appendix A and B

Damage and fluctuations induce loops in optimal transport networks

Leaf venation is a pervasive example of a complex biological network, endowing leaves with a transport system and mechanical resilience. Transport networks optimized for efficiency have been shown to be trees, i.e. loopless. However, dicotyledon leaf venation has a large number of closed loops, which are functional and able to transport fluid in the event of damage to any vein, including the primary veins. Inspired by leaf venation, we study two possible reasons for the existence of a high density of loops in transport networks: resilience to damage and fluctuations in load. In the first case, we seek the optimal transport network in the presence of random damage by averaging over damage to each link. In the second case, we seek the network that optimizes transport when the load is sparsely distributed: at any given time most sinks are closed. We find that both criteria lead to the presence of loops in the optimum state

Interspecific transfer of parasites following a range-shift in Ficedula flycatchers

Human‐induced climate change is expected to cause major biotic changes in species distributions and thereby including escalation of novel host‐parasite associations. Closely related host species that come into secondary contact are especially likely to exchange parasites and pathogens. Both the Enemy Release Hypothesis (where invading hosts escape their original parasites) and the Novel Weapon Hypothesis (where invading hosts bring new parasites that have detrimental effects on native hosts) predict that the local host will be most likely to experience a disadvantage. However, few studies evaluate the occurrence of interspecific parasite transfer by performing wide‐scale geographic sampling of pathogen lineages, both within and far from host contact zones. In this study, we investigate how haemosporidian (avian malaria) prevalence and lineage diversity vary in two, closely related species of passerine birds; the pied flycatcher Ficedula hypoleuca and the collared flycatcher F. albicollis in both allopatry and sympatry. We find that host species is generally a better predictor of parasite diversity than location, but both prevalence and diversity of parasites vary widely among populations of the same bird species. We also find a limited and unidirectional transfer of parasites from pied flycatchers to collared flycatchers in a recent contact zone. This study therefore rejects both the Enemy Release Hypothesis and the Novel Weapon Hypothesis and highlights the complexity and importance of studying host‐parasite relationships in an era of global climate change and species range shifts.</p

Discrete molecular dynamics can predict helical prestructured motifs in disordered proteins.

Intrinsically disordered proteins (IDPs) lack a stable tertiary structure, but their short binding regions termed Pre-Structured Motifs (PreSMo) can form transient secondary structure elements in solution. Although disordered proteins are crucial in many biological processes and designing strategies to modulate their function is highly important, both experimental and computational tools to describe their conformational ensembles and the initial steps of folding are sparse. Here we report that discrete molecular dynamics (DMD) simulations combined with replica exchange (RX) method efficiently samples the conformational space and detects regions populating alpha-helical conformational states in disordered protein regions. While the available computational methods predict secondary structural propensities in IDPs based on the observation of protein-protein interactions, our ab initio method rests on physical principles of protein folding and dynamics. We show that RX-DMD predicts alpha-PreSMos with high confidence confirmed by comparison to experimental NMR data. Moreover, the method also can dissect alpha-PreSMos in close vicinity to each other and indicate helix stability. Importantly, simulations with disordered regions forming helices in X-ray structures of complexes indicate that a preformed helix is frequently the binding element itself, while in other cases it may have a role in initiating the binding process. Our results indicate that RX-DMD provides a breakthrough in the structural and dynamical characterization of disordered proteins by generating the structural ensembles of IDPs even when experimental data are not available

MicroRNA precursors are not structurally robust but plastic

Robustness is considered a ubiquitous property of living systems at all levels of organization, and small noncoding RNA (sncRNA) is a genuine model for its study at the molecular level. In this communication, we question whether microRNA precursors (pre-miRNAs) are actually structurally robust, as previously suggested. We found that natural pre-miRNAs are not more robust than expected under an appropriate null model. On the contrary, we found that eukaryotic pre-miRNAs show a significant enrichment in conformational flexibility at the thermal equilibrium of the molecule, that is, in their plasticity. Our results further support the selection for functional diversification and evolvability in sncRNAs.The authors thank R. B. R. Azevedo for useful comments. This work was supported by an EMBO long-term fellowship co-funded by Marie Curie actions (ALTF-1177-2011) to G. R. and by grant BFU2012-30805 from the Spanish Secretaria de Estado de Investigacion, Desarrollo e Innovacion, to S.F.E.Rodrigo Tarrega, G.; Elena Fito, SF. (2013). MicroRNA precursors are not structurally robust but plastic. Genome Biology and Evolution. 5(1):181-186. https://doi.org/10.1093/gbe/evs132S18118651Ancel, L. W., & Fontana, W. (2000). Plasticity, evolvability, and modularity in RNA. Journal of Experimental Zoology, 288(3), 242-283. doi:10.1002/1097-010x(20001015)288:33.0.co;2-oBorenstein, E., & Ruppin, E. (2006). Direct evolution of genetic robustness in microRNA. Proceedings of the National Academy of Sciences, 103(17), 6593-6598. doi:10.1073/pnas.0510600103CLOTE, P. (2005). Structural RNA has lower folding energy than random RNA of the same dinucleotide frequency. RNA, 11(5), 578-591. doi:10.1261/rna.7220505Draghi, J. A., Parsons, T. L., Wagner, G. P., & Plotkin, J. B. (2010). Mutational robustness can facilitate adaptation. 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Diversity, Loss, and Gain of Malaria Parasites in a Globally Invasive Bird

Invasive species can displace natives, and thus identifying the traits that make aliens successful is crucial for predicting and preventing biodiversity loss. Pathogens may play an important role in the invasive process, facilitating colonization of their hosts in new continents and islands. According to the Novel Weapon Hypothesis, colonizers may out-compete local native species by bringing with them novel pathogens to which native species are not adapted. In contrast, the Enemy Release Hypothesis suggests that flourishing colonizers are successful because they have left their pathogens behind. To assess the role of avian malaria and related haemosporidian parasites in the global spread of a common invasive bird, we examined the prevalence and genetic diversity of haemosporidian parasites (order Haemosporida, genera Plasmodium and Haemoproteus) infecting house sparrows (Passer domesticus). We sampled house sparrows (N = 1820) from 58 locations on 6 continents. All the samples were tested using PCR-based methods; blood films from the PCR-positive birds were examined microscopically to identify parasite species. The results show that haemosporidian parasites in the house sparrows' native range are replaced by species from local host-generalist parasite fauna in the alien environments of North and South America. Furthermore, sparrows in colonized regions displayed a lower diversity and prevalence of parasite infections. Because the house sparrow lost its native parasites when colonizing the American continents, the release from these natural enemies may have facilitated its invasion in the last two centuries. Our findings therefore reject the Novel Weapon Hypothesis and are concordant with the Enemy Release Hypothesis

Assessing the Effects of Climate on Host-Parasite Interactions: A Comparative Study of European Birds and Their Parasites

[Background] Climate change potentially has important effects on distribution, abundance, transmission and virulence of parasites in wild populations of animals. [Methodology/Principal Finding] Here we analyzed paired information on 89 parasite populations for 24 species of bird hosts some years ago and again in 2010 with an average interval of 10 years. The parasite taxa included protozoa, feather parasites, diptera, ticks, mites and fleas. We investigated whether change in abundance and prevalence of parasites was related to change in body condition, reproduction and population size of hosts. We conducted analyses based on the entire dataset, but also on a restricted dataset with intervals between study years being 5–15 years. Parasite abundance increased over time when restricting the analyses to datasets with an interval of 5–15 years, with no significant effect of changes in temperature at the time of breeding among study sites. Changes in host body condition and clutch size were related to change in temperature between first and second study year. In addition, changes in clutch size, brood size and body condition of hosts were correlated with change in abundance of parasites. Finally, changes in population size of hosts were not significantly related to changes in abundance of parasites or their prevalence. [Conclusions/Significance] Climate change is associated with a general increase in parasite abundance. Variation in laying date depended on locality and was associated with latitude while body condition of hosts was associated with a change in temperature. Because clutch size, brood size and body condition were associated with change in parasitism, these results suggest that parasites, perhaps mediated through the indirect effects of temperature, may affect fecundity and condition of their hosts. The conclusions were particularly in accordance with predictions when the restricted dataset with intervals of 5–15 years was used, suggesting that short intervals may bias findings.The Academy of Finland is acknowledged for a grant to TE (project 8119367) and EK (project 250709). PLP was supported by a research grant (TE_291/2010) offered by the Romanian Ministry of Education and Science. T. Szép received funding from OTKA K69068 and JT from OTKA 75618. JMP was supported by a JAE grant from Consejo Superior de Investigaciones Científicas. SM-JM, FdL-AM, JF, JJS and FV were respectively supported by projects CGL2009-09439, CGL2012-36665, CGL2009- 11445, CGL2010-19233-C03-01 and CGL2008-00562 by the Spanish Ministry of Science and Innovation and FEDER and project EVITAR by the Spanish Ministry of Health. FV was also supported by the European Regional Development Fund. MACT was funded by a predoctoral FPU grant from the Spanish Ministry of Education (AP20043713). PM was supported by grant from the Polish Ministry of Science and Higher Education (project 2P04F07030), and the Foundation for Polish Science