Intelligent encoding and economical communication in the visual stream.

The theory of computational complexity is used to underpin a recent model of neocortical sensory processing. We argue that encoding into reconstruction networks is appealing for communicating agents using Hebbian learning and working on hard combinatorial problems, which are easy to verify. Computational definition of the concept of intelligence is provided. Simulations illustrate the idea

The algebraic combinatorial approach for low-rank matrix completion

We propose an algebraic combinatorial framework for the problem of completing partially observed low-rank matrices. We show that the intrinsic properties of the problem, including which entries can be reconstructed, and the degrees of freedom in the reconstruction, do not depend on the values of the observed entries, but only on their position. We associate combinatorial and algebraic objects, differentials and matroids, which are descriptors of the particular reconstruction task, to the set of observed entries, and apply them to obtain reconstruction bounds. We show how similar techniques can be used to obtain reconstruction bounds on general compressed sensing problems with algebraic compression constraints. Using the new theory, we develop several algorithms for low-rank matrix completion, which allow to determine which set of entries can be potentially reconstructed and which not, and how, and we present algorithms which apply algebraic combinatorial methods in order to reconstruct the missing entries

Sensor Selection and Random Field Reconstruction for Robust and Cost-effective Heterogeneous Weather Sensor Networks for the Developing World

We address the two fundamental problems of spatial field reconstruction and sensor selection in heterogeneous sensor networks: (i) how to efficiently perform spatial field reconstruction based on measurements obtained simultaneously from networks with both high and low quality sensors; and (ii) how to perform query based sensor set selection with predictive MSE performance guarantee. For the first problem, we developed a low complexity algorithm based on the spatial best linear unbiased estimator (S-BLUE). Next, building on the S-BLUE, we address the second problem, and develop an efficient algorithm for query based sensor set selection with performance guarantee. Our algorithm is based on the Cross Entropy method which solves the combinatorial optimization problem in an efficient manner.Comment: Presented at NIPS 2017 Workshop on Machine Learning for the Developing Worl

Error Graphs and the Reconstruction of Elements in Groups

Packing and covering problems for metric spaces, and graphs in particular, are of essential interest in combinatorics and coding theory. They are formulated in terms of metric balls of vertices. We consider a new problem in graph theory which is also based on the consideration of metric balls of vertices, but which is distinct from the traditional packing and covering problems. This problem is motivated by applications in information transmission when redundancy of messages is not sufficient for their exact reconstruction, and applications in computational biology when one wishes to restore an evolutionary process. It can be defined as the reconstruction, or identification, of an unknown vertex in a given graph from a minimal number of vertices (erroneous or distorted patterns) in a metric ball of a given radius r around the unknown vertex. For this problem it is required to find minimum restrictions for such a reconstruction to be possible and also to find efficient reconstruction algorithms under such minimal restrictions. In this paper we define error graphs and investigate their basic properties. A particular class of error graphs occurs when the vertices of the graph are the elements of a group, and when the path metric is determined by a suitable set of group elements. These are the undirected Cayley graphs. Of particular interest is the transposition Cayley graph on the symmetric group which occurs in connection with the analysis of transpositional mutations in molecular biology. We obtain a complete solution of the above problems for the transposition Cayley graph on the symmetric group.Comment: Journal of Combinatorial Theory A 200

Charged particle tracking with quantum annealing-inspired optimization

At the High Luminosity Large Hadron Collider (HL-LHC), traditional track reconstruction techniques that are critical for analysis are expected to face challenges due to scaling with track density. Quantum annealing has shown promise in its ability to solve combinatorial optimization problems amidst an ongoing effort to establish evidence of a quantum speedup. As a step towards exploiting such potential speedup, we investigate a track reconstruction approach by adapting the existing geometric Denby-Peterson (Hopfield) network method to the quantum annealing framework and to HL-LHC conditions. Furthermore, we develop additional techniques to embed the problem onto existing and near-term quantum annealing hardware. Results using simulated annealing and quantum annealing with the D-Wave 2X system on the TrackML dataset are presented, demonstrating the successful application of a quantum annealing-inspired algorithm to the track reconstruction challenge. We find that combinatorial optimization problems can effectively reconstruct tracks, suggesting possible applications for fast hardware-specific implementations at the LHC while leaving open the possibility of a quantum speedup for tracking