**Guided Local Search (GLS)**

Guided Local Search is a metaheuristic search method. A meta-heuristic method is a method that sits on top of a local search algorithm to change its behavior. Guided Local Search builds up penalties during a search. It uses penalties to help local search algorithms escape from local minimal and plateaus. When the given local search algorithm settles in a local optimum, GLS modifies the objective function using a specific scheme (explained below). Then the local search will operate using an augmented objective function, which is designed to bring the search out of the local optimum. The key is in the way that the objective function is modified. … **Projective Sparse Latent Space Network Models**

In typical latent-space network models, nodes have latent positions, which are all drawn independently from a common distribution. As a consequence, the number of edges in a network scales quadratically with the number of nodes, resulting in a dense graph sequence as the number of nodes grows. We propose an adjustment to latent-space network models which allows the number edges to scale linearly with the number of nodes, to scale quadratically, or at any intermediate rate. Our models also form projective families, making statistical inference and prediction well-defined. Built through point processes, our models are related to both the Poisson random connection model and the graphex framework. … **Renyi Entropy**

In information theory, the Rényi entropy generalizes the Hartley entropy, the Shannon entropy, the collision entropy and the min entropy. Entropies quantify the diversity, uncertainty, or randomness of a system. The Rényi entropy is named after Alfréd Rényi. In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of Generalized dimensions. The Rényi entropy is important in ecology and statistics as index of diversity. The Rényi entropy is also important in quantum information, where it can be used as a measure of entanglement. In the Heisenberg XY spin chain model, the Rényi entropy as a function of a can be calculated explicitly by virtue of the fact that it is an automorphic function with respect to a particular subgroup of the modular group. In theoretical computer science, the min-entropy is used in the context of randomness extractors. …

# If you did not already know

**26**
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Mar 2018

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