A Class of Minimal Generically Universally Rigid Frameworks

Following a review of related results in rigidity theory, we provide a construction to obtain generically universally rigid frameworks with the minimum number of edges, for any given set of n nodes in two or three dimensions. When a set of edge-lengths is compatible with only one configuration in d-dimensions, the framework is globally rigid. When that configuration is unique even if embedded in a higher dimensional space, the framework is universally rigid. In case of generic configurations, where the nodal coordinates are algebraically independent, the minimum number of edges required is equal to dn-d(d+1)/2+1, that is, 2n-2 for d=2, and 3n-5 for d=3. Our contribution is a specific construction for this case by introducing a class of frameworks generalizing that of Gr\"{u}nbaum polygons. The construction applies also to nongeneric configurations, although in this case the number of edges is not necessarily the minimum. One straightforward application is the design of wireless sensor networks or multi-agent systems with the minimum number of communication links.Comment: 8 page

Depletion effects and loop formation in self-avoiding polymers

Langevin dynamics is employed to study the looping kinetics of self-avoiding polymers both in ideal and crowded solutions. A rich kinetics results from the competition of two crowding-induced effects: the depletion attraction and the enhanced viscous friction. For short chains, the enhanced friction slows down looping, while, for longer chains, the depletion attraction renders it more frequent and persistent. We discuss the possible relevance of the findings for chromatin looping in living cells.Comment: 4 pages, 3 figure

Role of Secondary Motifs in Fast Folding Polymers: A Dynamical Variational Principle

A fascinating and open question challenging biochemistry, physics and even geometry is the presence of highly regular motifs such as alpha-helices in the folded state of biopolymers and proteins. Stimulating explanations ranging from chemical propensity to simple geometrical reasoning have been invoked to rationalize the existence of such secondary structures. We formulate a dynamical variational principle for selection in conformation space based on the requirement that the backbone of the native state of biologically viable polymers be rapidly accessible from the denatured state. The variational principle is shown to result in the emergence of helical order in compact structures.Comment: 4 pages, RevTex, 4 eps figure

Intrafamily and intragenomic conflicts in human warfare

A.J.C.M. is supported by a Ph.D. studentship from the School of Biology, University of St Andrews, and A.G. is supported by a Natural Environment Research Council Independent Research Fellowship (NE/K009524/1).Recent years have seen an explosion of multidisciplinary interest in ancient human warfare. Theory has emphasised a key role for kin-selected cooperation, modulated by sex-specific demography, in explaining intergroup violence. However, conflicts of interest remain a relatively underexplored factor in the evolutionary-ecological study of warfare, with little consideration given to which parties influence the decision to go to war and how their motivation may differ. We develop a mathematical model to investigate the interplay between sex-specific demography and human warfare, showing that: the ecology of warfare drives the evolution of sex-biased dispersal; sex-biased dispersal modulates intrafamily and intragenomic conflicts in relation to warfare; intragenomic conflict drives parent-of-origin-specific patterns of gene expression – i.e. 'genomic imprinting' – in relation to warfare phenotypes; and an ecological perspective of conflicts at the levels of the gene, individual and social group yields novel predictions as to pathologies associated with mutations and epimutations at loci underpinning human violence.Publisher PDFPeer reviewe

A Coarse Grained Model for DNA and Polymer Packaging: Statics and Dynamics

We present a numerical characterization of the statics and dynamics of the packaging of a semi-flexible polymer inside a sphere. The study is motivated by recent experiments on the packaging of DNA inside viral capsids. It is found that the force required to confine the coarse-grained polymer is in fair agreement with that found in experiments for the packaging of the phi29 bacteriophage genome. Despite its schematic nature, the model is capable of reproducing the most salient dynamical features of packaging experiments such as the presence of pauses during individual packaging processes and the trend of the resisting force as a function of chain packed fraction

The demography of human warfare can drive sex differences in altruism

Funding from a Ph.D. studentship from the School of Biology, University of St Andrews (A.J.C.M.), a Natural Environment Research Council Independent Research Fellowship (A.G., grant number NE/K009524/1), a European Research Council Consolidator Grant (A.G., A.J.C.M., grant number 771387), the French Agence Nationale de la Recherche (under the Investissement d’Avenir programme, ANR 17-EURE-0010) (A.J.C.M.) is gratefully acknowledged.Recent years have seen great interest in the suggestion that between-group aggression and within-group altruism have coevolved. However, these efforts have neglected the possibility that warfare – via its impact on demography – might influence human social behaviours more widely, not just those directly connected to success in war. Moreover, the potential for sex differences in the demography of warfare to translate into sex differences in social behaviour more generally has remained unexplored. Here, we develop a kin-selection model of altruism performed by men and women for the benefit of their groupmates in a population experiencing intergroup conflict. We find that warfare can promote altruistic, helping behaviours as the additional reproductive opportunities winners obtain in defeated groups decrease harmful competition between kin. Furthermore, we find that sex can be a crucial modulator of altruism, with there being a tendency for the sex that competes more intensely with relatives to behave more altruistically and for the sex that competes more intensely with non-relatives in defeated groups to receive more altruism. In addition, there is also a tendency for the less-dispersing sex to both give and receive more altruism. We discuss implications for our understanding of observed sex differences in cooperation in human societies.Publisher PDFPeer reviewe

Farmland Use Transitions After the CAP Greening: a Preliminary Analysis Using Markov Chains Approach

This paper represents a preliminary attempt to evaluate ex-post impact of the CAP greening payment on farmland use changes, testing by a Markov Chain approach whether farmland use transitions dynamics changed after the introduction of this new policy instrument. Unlike previous contributions, relying on ex-ante simulations, this analysis is based on the actual behaviour of farmers over the period immediately after the last CAP reform. Such ex-post assessment was based on real georeferenced data on farmland allocation, collected in the Lombardy Region, in Northern Italy, over the period 2011-2016. As the current CAP has recently entered in force (in 2015), the present analysis covers the \ufb01rst two years of implementation of the new rules along with the previous four years. Results are in line with previous ex-ante simulations in the same region, detecting a deep discontinuity for those farmland uses characterised by monoculture before the introduction of the greening. They show a signi\ufb01cant discontinuity of farmland use transitions in the reference area after the introduction of greening rules, pointing to a decrease in maize monoculture, in favour of other cereals and legume crops like soybean and alfalfa. Unlike some critical opinions that see current greening rules as a \u201clow pro\ufb01le\u201d compromise, the present analysis points to a strong e\ufb00ect of such rules on regions with high-intensity agriculture