On Maltsev Digraphs

This is an Open Access article, first published by E-CJ on 25 February 2015.We study digraphs preserved by a Maltsev operation: Maltsev digraphs. We show that these digraphs retract either onto a directed path or to the disjoint union of directed cycles, showing in this way that the constraint satisfaction problem for Maltsev digraphs is in logspace, L. We then generalize results from Kazda (2011) to show that a Maltsev digraph is preserved not only by a majority operation, but by a class of other operations (e.g., minority, Pixley) and obtain a O(|VG|4)-time algorithm to recognize Maltsev digraphs. We also prove analogous results for digraphs preserved by conservative Maltsev operations which we use to establish that the list homomorphism problem for Maltsev digraphs is in L. We then give a polynomial time characterisation of Maltsev digraphs admitting a conservative 2-semilattice operation. Finally, we give a simple inductive construction of directed acyclic digraphs preserved by a Maltsev operation, and relate them with series parallel digraphs.Peer reviewedFinal Published versio

Improved Optimal and Approximate Power Graph Compression for Clearer Visualisation of Dense Graphs

Drawings of highly connected (dense) graphs can be very difficult to read. Power Graph Analysis offers an alternate way to draw a graph in which sets of nodes with common neighbours are shown grouped into modules. An edge connected to the module then implies a connection to each member of the module. Thus, the entire graph may be represented with much less clutter and without loss of detail. A recent experimental study has shown that such lossless compression of dense graphs makes it easier to follow paths. However, computing optimal power graphs is difficult. In this paper, we show that computing the optimal power-graph with only one module is NP-hard and therefore likely NP-hard in the general case. We give an ILP model for power graph computation and discuss why ILP and CP techniques are poorly suited to the problem. Instead, we are able to find optimal solutions much more quickly using a custom search method. We also show how to restrict this type of search to allow only limited back-tracking to provide a heuristic that has better speed and better results than previously known heuristics.Comment: Extended technical report accompanying the PacificVis 2013 paper of the same nam

Congruence modularity implies cyclic terms for finite algebras

An n-ary operation f : A(n) -> A is called cyclic if it is idempotent and f(a(1), a(2), a(3), ... , a(n)) = f(a(2), a(3), ... , a(n), a(1)) for every a(1), ... , a(n) is an element of A. We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than vertical bar A vertical bar

Affecting Effects on Affect: The Impact of Protocol Permutations on Affective Responses to Sprint Interval Exercise; A Systematic Review and Meta-Analysis of Pooled Individual Participant Data

Responses to sprint interval exercise (SIE) are hypothesized to be perceived as unpleasant, but SIE protocols are diverse, and moderating effects of various SIE protocol parameters on affective responses are unknown. We performed a systematic search to identify studies (up to 01/05/2021) measuring affective valence using the Feeling Scale during acute SIE in healthy adults. Thirteen studies involving 18 unique trials and 316 unique participant (142 women and 174 men) affective responses to SIE were eligible for inclusion. We received individual participant data for all participants from all studies. All available end-of-sprint affect scores from each trial were combined in a linear mixed model with sprint duration, mode, intensity, recovery duration, familiarization and baseline affect included as covariates. Affective valence decreased significantly and proportionally with each additional sprint repetition, but this effect was modified by sprint duration: affect decreased more during 30 s (0.84 units/sprint; 95% CI: 0.74–0.93) and 15–20 s sprints (1.02 units/sprint; 95% CI: 0.93–1.10) compared with 5–6 s sprints (0.20 units/sprint; 95% CI: 0.18–0.22) (both p < 0.0001). Although the difference between 15–20 s and 30 s sprints was also significant (p = 0.02), the effect size was trivial (d = −0.12). We observed significant but trivial effects of mode, sprint intensity and pre-trial familiarization, whilst there was no significant effect of recovery duration. We conclude that affective valence declines during SIE, but the magnitude of the decrease for an overall SIE session strongly depends on the number and duration of sprints. This information can be applied by researchers to design SIE protocols that are less likely to be perceived as unpleasant in studies of real-world effectiveness