Reconstructing a Graph from Path Traces

This paper considers the problem of inferring the structure of a network from indirect observations. Each observation (a "trace") is the unordered set of nodes which are activated along a path through the network. Since a trace does not convey information about the order of nodes within the path, there are many feasible orders for each trace observed, and thus the problem of inferring the network from traces is, in general, illposed. We propose and analyze an algorithm which inserts edges by ordering each trace into a path according to which pairs of nodes in the path co-occur most frequently in the observations. When all traces involve exactly 3 nodes, we derive necessary and sufficient conditions for the reconstruction algorithm to exactly recover the graph. Finally, for a family of random graphs, we present expressions for reconstruction error probabilities (false discoveries and missed detections)

Reconstruction of Causal Networks by Set Covering

We present a method for the reconstruction of networks, based on the order of nodes visited by a stochastic branching process. Our algorithm reconstructs a network of minimal size that ensures consistency with the data. Crucially, we show that global consistency with the data can be achieved through purely local considerations, inferring the neighbourhood of each node in turn. The optimisation problem solved for each individual node can be reduced to a Set Covering Problem, which is known to be NP-hard but can be approximated well in practice. We then extend our approach to account for noisy data, based on the Minimum Description Length principle. We demonstrate our algorithms on synthetic data, generated by an SIR-like epidemiological model.Comment: Under consideration for the ECML PKDD 2010 conferenc

Localization for Anchoritic Sensor Networks

We introduce a class of anchoritic sensor networks, where communications between sensor nodes is undesirable or infeasible, e.g., due to harsh environment, energy constraints, or security considerations

Bessel beam illumination reduces random and systematic errors in quantitative functional studies using light-sheet microscopy

Light-sheet microscopy (LSM), in combination with intrinsically transparent zebrafish larvae, is a choice method to observe brain function with high frame rates at cellular resolution. Inherently to LSM, however, residual opaque objects cause stripe artifacts, which obscure features of interest and, during functional imaging, modulate fluorescence variations related to neuronal activity. Here, we report how Bessel beams reduce streaking artifacts and produce high-fidelity quantitative data demonstrating a fivefold increase in sensitivity to calcium transients and a 20 fold increase in accuracy in the detection of activity correlations in functional imaging. Furthermore, using principal component analysis, we show that measurements obtained with Bessel beams are clean enough to reveal in one-shot experiments correlations that can not be averaged over trials after stimuli as is the case when studying spontaneous activity. Our results not only demonstrate the contamination of data by systematic and random errors through conventional Gaussian illumination and but,furthermore, quantify the increase in fidelity of such data when using Bessel beams

Structure and Properties of Traces for Functional Programs

The tracer Hat records in a detailed trace the computation of a program written in the lazy functional language Haskell. The trace can then be viewed in various ways to support program comprehension and debugging. The trace was named the augmented redex trail. Its structure was inspired by standard graph rewriting implementations of functional languages. Here we describe a model of the trace that captures its essential properties and allows formal reasoning. The trace is a graph constructed by graph rewriting but goes beyond simple term graphs. Although the trace is a graph whose structure is independent of any rewriting strategy, we define the trace inductively, thus giving us a powerful method for proving its properties