Suppressors of selection

Inspired by recent works on evolutionary graph theory, an area of growing interest in mathematical and computational biology, we present the first known examples of undirected structures acting as suppressors of selection for any fitness value $r > 1$. This means that the average fixation probability of an advantageous mutant or invader individual placed at some node is strictly less than that of this individual placed in a well-mixed population. This leads the way to study more robust structures less prone to invasion, contrary to what happens with the amplifiers of selection where the fixation probability is increased on average for advantageous invader individuals. A few families of amplifiers are known, although some effort was required to prove it. Here, we use computer aided techniques to find an exact analytical expression of the fixation probability for some graphs of small order (equal to $6$, $8$ and $10$) proving that selection is effectively reduced for $r > 1$. Some numerical experiments using Monte Carlo methods are also performed for larger graphs.Comment: New title, improved presentation, and further examples. Supporting Information is also include

Fast and asymptotic computation of the fixation probability for Moran processes on graphs

Evolutionary dynamics has been classically studied for homogeneous populations, but now there is a growing interest in the non-homogenous case. One of the most important models has been proposed by Lieberman, Hauert and Nowak, adapting to a weighted directed graph the classical process described by Moran. The Markov chain associated with the graph can be modified by erasing all non-trivial loops in its state space, obtaining the so-called Embedded Markov chain (EMC). The fixation probability remains unchanged, but the expected time to absorption (fixation or extinction) is reduced. In this paper, we shall use this idea to compute asymptotically the average fixation probability for complete bipartite graphs. To this end, we firstly review some recent results on evolutionary dynamics on graphs trying to clarify some points. We also revisit the 'Star Theorem' proved by Lieberman, Hauert and Nowak for the star graphs. Theoretically, EMC techniques allow fast computation of the fixation probability, but in practice this is not always true. Thus, in the last part of the paper, we compare this algorithm with the standard Monte Carlo method for some kind of complex networks.Comment: Corrected typo

Banchoff’s sphere and branched covers over the trefoil

A filling Dehn surface in a 3-manifold M is a generically immersed surface in M that induces a cellular decomposition of M. Given a tame link L in M, there is a filling Dehn sphere of M that “trivializes” (diametrically splits) it. This allows to construct filling Dehn surfaces in the coverings of M branched over L. It is shown that one of the simplest filling Dehn spheres of S3 (Banchoff’s sphere) diametrically splits the trefoil knot. Filling Dehn spheres, and their Johansson diagrams, are constructed for the coverings of S3 branched over the trefoil. The construction is explained in detail. Johansson diagrams for generic cyclic coverings and for the simplest locally cyclic and irregular ones are constructed explicitly, providing new proofs of known results about cyclic coverings and the 3-fold irregular covering over the trefoil

Is it possible to discriminate the body weight loss?

Most studies have described how the weight loss is when different treatments are compared (1-3), while others have also compared the weight loss by sex (4), or have taken into account psychosocial (5) and lifestyle (6, 7) variables. However, no studies have examined the interaction of different variables and the importance of them in the weight loss

Authoritarianism versus participation in innovation decisions

Why do innovation projects fail? The most common answers are (A) the implementation differs from what was planned; (B) despite positive expected payoffs, there is an ex-ante positive probability that payoff can be negative (risk). As a third option, we consider the fallibility of individuals who evaluate innovation projects using their limited information-processing capabilities (bounded rationality). Furthermore, we compare the overall organizational performance of two decision mechanisms. First, an informal Collective Decision as an unanimity participative mechanism to decide on technological innovation adoption and, second, a centralized Authority decision. Authority-based decision-making results in higher commission errors (acceptance of projects that an unbounded rational decision-maker would reject) and lower omission errors (rejection of projects that an unbounded rational decision-maker would accept) than Collective Decision. In a dynamic technological adoption process where a sequence of randomly generated innovation projects is evaluated using the two mechanisms, the simulations show that, in the short-term, omission errors dominate and Authority is preferred to Collective Decision; however, in the mid and long terms, commission errors dominate and Collective Decision is preferred to Authority, especially if Collective Decision does not incorporate social influence. With Collective Decision, the ratio of projects that fail is lower, more innovation projects are rejected, and fewer innovation projects are accepted, which can be interpreted as resistance to innovation