Beyond PCSP(1-in-3, NAE)

The promise constraint satisfaction problem (PCSP) is a recently introduced vast generalisation of the constraint satisfaction problem (CSP) that captures approximability of satisfiable instances. A PCSP instance comes with two forms of each constraint: a strict one and a weak one. Given the promise that a solution exists using the strict constraints, the task is to find a solution using the weak constraints. While there are by now several dichotomy results for fragments of PCSPs, they all consider (in some way) symmetric PCSPs. 1-in-3-SAT and Not-All-Equal-3-SAT are classic examples of Boolean symmetric (non-promise) CSPs. While both problems are NP-hard, Brakensiek and Guruswami showed [SODA\u2718] that given a satisfiable instance of 1-in-3-SAT one can find a solution to the corresponding instance of (weaker) Not-All-Equal-3-SAT. In other words, the PCSP template (?-in-?,NAE) is tractable. We focus on non-symmetric PCSPs. In particular, we study PCSP templates obtained from the Boolean template (?-in-?, NAE) by either adding tuples to ?-in-? or removing tuples from NAE. For the former, we classify all templates as either tractable or not solvable by the currently strongest known algorithm for PCSPs, the combined basic LP and affine IP relaxation of Brakensiek and Guruswami [SODA\u2720]. For the latter, we classify all templates as either tractable or NP-hard

Communication, leadership and coordination failure

We investigate the limits of communication and leadership in avoiding coordination failure in minimum effort games. Our environment is challenging, with low benefits of coordination relative to the effort cost. We consider two leader types: cheap-talk leader-communicators who suggest an effort level, and first-mover leaders who lead by example. Both types of leadership have some ability to increase effort in groups with no history, but are insufficient in groups with a history of low effort. Using the strategy method for followers’ responses, we attribute the persistence of coordination failure to the presence of followers who do not follow the leader

Volumes of Hyperbolic Three-Manifolds Associated with Modular Links

Periodic geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle PSL₂(ℤ)\PSL₂(ℝ). A finite collection of such orbits is a collection of disjoint closed curves in a 3-manifold, in other words a link. The complement of those links is always a hyperbolic 3-manifold, and hence has a well-defined volume. We present strong numerical evidence that, in the case of the set of geodesics corresponding to the ideal class group of a real quadratic field, the volume has linear asymptotics in terms of the total length of the geodesics. This is not the case for general sets of geodesics.Science, Faculty ofNon UBCMathematics, Department ofReviewedFacult

The dynamics of functional classes of plant genes in rediploidized ancient polyploids

BACKGROUND:To understand the particular evolutionary patterns of plant genomes, there is a need to systematically survey the fate of the subgenomes of polyploids fixed as whole genome duplicates, including patterns of retention of duplicate, triplicate, etc. genes.RESULTS:We measure the simultaneous dynamics of duplicate orthologous gene loss in rosids, in asterids, and in monocots, as influenced by biological functional class. This pan-angiosperm view confirms common tendencies and consistency through time for both ancient and more recent whole genome polyploidization events.CONCLUSIONS:The gene loss analysis represents an assessment of post-polyploidization evolution, at the level of individual gene families within and across sister genomes. Functional analysis confirms universal trends previously reported for more recent plant polyploidy events: genes involved with regulation and responses were retained in multiple copies, while genes involved with metabolic and catalytic processes tended to lose copies, across all three groups of plants.This item is part of the UA Faculty Publications collection. For more information this item or other items in the UA Campus Repository, contact the University of Arizona Libraries at [email protected]