Chomp on numerical semigroups

We consider the two-player game chomp on posets associated to numerical semigroups and show that the analysis of strategies for chomp is strongly related to classical properties of semigroups. We characterize, which player has a winning-strategy for symmetric semigroups, semigroups of maximal embedding dimension and several families of numerical semigroups generated by arithmetic sequences. Furthermore, we show that which player wins on a given numerical semigroup is a decidable question. Finally, we extend several of our results to the more general setting of subsemigroups of $\mathbb{N} \times T$, where $T$ is a finite abelian group.Comment: 22 pages, 14 figures, 1 table (improved exposition

Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence

Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a latent vector $w^* \in \mathbb{R}^d$ that represents the "qualities" of the $d$ items being compared; this class of models includes the two most widely used parametric models--the Bradley-Terry-Luce (BTL) and the Thurstone models. Working within a standard minimax framework, we provide tight upper and lower bounds on the optimal error in estimating the quality score vector $w^*$ under this class of models. The bounds depend on the topology of the comparison graph induced by the subset of pairs being compared via its Laplacian spectrum. Thus, in settings where the subset of pairs may be chosen, our results provide principled guidelines for making this choice. Finally, we compare these error rates to those under cardinal measurement models and show that the error rates in the ordinal and cardinal settings have identical scalings apart from constant pre-factors.Comment: 39 pages, 5 figures. Significant extension of arXiv:1406.661

Menstrual cycle and competitive bidding

In an experiment using two-bidder first-price sealed bid auctions with symmetric independent private values, we collected information on the female participants' menstrual cycles. We find that women bid significantly higher than men in their menstrual and premenstrual phase but do not bid significantly different in other phases of the menstrual cycle. We suggest an evolutionary hypothesis according to which women are genetically predisposed by hormones to generally behave more riskily during their fertile phase of their menstrual cycle in order to increase the probability of conception, quality of offspring, and genetic variety. Our finding is in contrast to results by Chen, Katuscak and Ozdenoren (2005, 2009).hormones; menstrual cycle; gender; likelihood of conception; first price auction; risk behavior; competition; bidding; endocrinological economics

Design for the contact zone. Knowledge management software and the structures of indigenous knowledges

This article examines the design of digital indigenous knowledge archives. In a discussion of the distinction between indigenous knowledge and western science, a decentred perspective is developed, in which the relationship between different local knowledges is explored. The particular characteristics of indigenous knowledges raise questions about if and how these knowledges can be managed. The role of technology in managing indigenous knowledges is explored with examples from fieldwork in India and Kenya and from web-based databases and digital archives. The concept of contact zone is introduced to explore the space in which different knowledges meet and are performed, such as indigenous knowledge and the technoscientific knowledge of the database. Design for the contact zone, this article proposes, is an intra-active and adaptive process for in creating databases that are meaningful for indigenous knowers. The meta-design approach is introduced as a methodology, which may provide indigenous knowers tools for self-representation and self-organisation through design

Three-point bounds for energy minimization

Three-point semidefinite programming bounds are one of the most powerful known tools for bounding the size of spherical codes. In this paper, we use them to prove lower bounds for the potential energy of particles interacting via a pair potential function. We show that our bounds are sharp for seven points in RP^2. Specifically, we prove that the seven lines connecting opposite vertices of a cube and of its dual octahedron are universally optimal. (In other words, among all configurations of seven lines through the origin, this one minimizes energy for all potential functions that are completely monotonic functions of squared chordal distance.) This configuration is the only known universal optimum that is not distance regular, and the last remaining universal optimum in RP^2. We also give a new derivation of semidefinite programming bounds and present several surprising conjectures about them.Comment: 30 page

Beach users’ perceptions of coastal regeneration projects as an adaptation strategy in the western Mediterranean

Some coastal environments facing climate change risks are starting to be managed with nature-based solutions (NBS). Strategies based on the rehabilitation of green infrastructures in coastal municipalities, such as renaturalization of seafronts, are considered adaptive to the effects of climate change but may cause misconceptions that could lead to social conflicts between the tourist sector and the society. A survey was carried out to study user perceptions on the effects of climate change, preferences for adaptation strategies, and the assessment of projects of dune reconstruction. We find that while beach users recognize the benefits of NBS for environmental conservation and storm protection, they show little concern about possible effects of climate change on recreational activity and have limited understanding about the protective capacity of NBS. Thus, a greater effort must be made to better explain the effects of climate change and the potential benefits of NBS in coastal risk management.Peer ReviewedPostprint (author's final draft

Bracketing effects in categorized survey questions and the measurement of economic quantities

In households surveys, quantities of interest are frequently elicited using categorized (range-card) formats rather than open-ended questions. One advantage of this format is that is typically reduces item non-response. Unfortunately, results from research in social psychology suggest that the choice of bracket values in range-card questions is likely to influence responses. As yet, there is not much known about the effects of bracketing bias on the measurement of economic quantities and regression analysis. This paper reports evidence on existence and size of bracketing bias based on data from controlled survey experiments. I also discuss strategies for avoiding bracketing bias in household surveys.