On Tractable Convex Relaxations of Standard Quadratic Optimization Problems under Sparsity Constraints.

Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex relaxations of sparse StQPs arising from a mixed-binary quadratic formulation, namely, the linear optimization relaxation given by the reformulation-linearization technique, the Shor relaxation, and the relaxation resulting from their combination.

Conic formulation of QPCCs applied to truly sparse QPs.

We study (nonconvex) quadratic optimization problems with complementarity constraints, establishing an exact completely positive reformulation under-apparently new-mild conditions involving only the constraints, not the objective. Moreover, we also give the conditions for strong conic duality between the obtained completely positive problem and its dual. Our approach is based on purely continuous models which avoid any branching or use of large constants in implementation.

Uncover: Toward Interpretable Models for Detecting New Star Cluster Members.

In this design study, we present Uncover, an interactive tool aimed at astronomers to find previously unidentified member stars in stellar clusters. We contribute data and task abstraction in the domain of astronomy and provide an approach for the non-trivial challenge of finding a suitable hyper-parameter set for highly flexible novelty detection models. We achieve this by substituting the tedious manual trial and error process, which usually results in finding a small subset of passable models with a five-step workflow approach.

Building a completely positive factorization.

A symmetric matrix of order is called if it has a symmetric factorization by means of a rectangular matrix with columns and no negative entries (a so-called ), i.e., if it can be interpreted as a Gram matrix of directions in the positive orthant of another Euclidean space of possibly different dimension.

One-third rules with equality: Second-order evolutionary stability conditions in finite populations.

The one-third law of evolutionary dynamics [Nowak et al. 2004. Emergence of cooperation and evolutionary stability in finite populations.

Approximating the maximum weight clique using replicator dynamics.

Given an undirected graph with weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having the largest total weight.

The role of Mendelian genetics in strategic models on animal behaviour.

The authors combine known models for the evolution of (a) strategies in animal conflicts, and (b) gene frequencies for differential fecundity in order to relate the sociobiological notion of evolutionarily stable strategy with the genetic mechanism of Mendelian populations.