Weighted Spectral Embedding of Graphs

We present a novel spectral embedding of graphs that incorporates weights assigned to the nodes, quantifying their relative importance. This spectral embedding is based on the first eigenvectors of some properly normalized version of the Laplacian. We prove that these eigenvectors correspond to the configurations of lowest energy of an equivalent physical system, either mechanical or electrical, in which the weight of each node can be interpreted as its mass or its capacitance, respectively. Experiments on a real dataset illustrate the impact of weighting on the embedding

Robust Multi-Cellular Developmental Design

This paper introduces a continuous model for Multi-cellular Developmental Design. The cells are fixed on a 2D grid and exchange "chemicals" with their neighbors during the growth process. The quantity of chemicals that a cell produces, as well as the differentiation value of the cell in the phenotype, are controlled by a Neural Network (the genotype) that takes as inputs the chemicals produced by the neighboring cells at the previous time step. In the proposed model, the number of iterations of the growth process is not pre-determined, but emerges during evolution: only organisms for which the growth process stabilizes give a phenotype (the stable state), others are declared nonviable. The optimization of the controller is done using the NEAT algorithm, that optimizes both the topology and the weights of the Neural Networks. Though each cell only receives local information from its neighbors, the experimental results of the proposed approach on the 'flags' problems (the phenotype must match a given 2D pattern) are almost as good as those of a direct regression approach using the same model with global information. Moreover, the resulting multi-cellular organisms exhibit almost perfect self-healing characteristics

The Effects of Transmission Uncertainty on the Flexibility-Credibility Tradeoff in Monetary Policy

In this paper we address the issue of how parameter uncertainty affects the optimal degree of central bank conservatism. The analysis is conducted in the standard macroeconomic model of a monetary policy game embedding an expectational Phillips-curve. Multiplicative "Brainard" uncertainty is added to the model. This means that the central bank's policy instrument has a stochastic impact on inflation. This type of uncertainty is particularly interesting, since it affects the credibility–flexibility tradeoff in monetary policymaking. We show that if the flexibility problem dominates, an increase in uncertainty reduces optimal conservatism. However, increases in uncertainty can also require increases in the optimal degree of conservatism. This happens when the central bank has a sufficiently large credibility problem. This is particularly clear in the case of the introduction of uncertainty at the margin. Furthermore, the coefficient of variation of inflation appears to contain useful information about the relative size of the credibility problem and, hence, about how incipient uncertainty can affect optimal conservatism in actual economies.credibility; flexibility; monetary policy; conservatism; uncertainty

Streaming, Memory Limited Algorithms for Community Detection

In this paper, we consider sparse networks consisting of a finite number of non-overlapping communities, i.e. disjoint clusters, so that there is higher density within clusters than across clusters. Both the intra- and inter-cluster edge densities vanish when the size of the graph grows large, making the cluster reconstruction problem nosier and hence difficult to solve. We are interested in scenarios where the network size is very large, so that the adjacency matrix of the graph is hard to manipulate and store. The data stream model in which columns of the adjacency matrix are revealed sequentially constitutes a natural framework in this setting. For this model, we develop two novel clustering algorithms that extract the clusters asymptotically accurately. The first algorithm is {\it offline}, as it needs to store and keep the assignments of nodes to clusters, and requires a memory that scales linearly with the network size. The second algorithm is {\it online}, as it may classify a node when the corresponding column is revealed and then discard this information. This algorithm requires a memory growing sub-linearly with the network size. To construct these efficient streaming memory-limited clustering algorithms, we first address the problem of clustering with partial information, where only a small proportion of the columns of the adjacency matrix is observed and develop, for this setting, a new spectral algorithm which is of independent interest.Comment: NIPS 201