Birth of a Learning Law

Defense Advanced Research Projects Agency; Office of Naval Research (N00014-95-1-0409, N00014-95-1-0657, N00014-92-J-1309

Radar signal categorization using a neural network

Neural networks were used to analyze a complex simulated radar environment which contains noisy radar pulses generated by many different emitters. The neural network used is an energy minimizing network (the BSB model) which forms energy minima - attractors in the network dynamical system - based on learned input data. The system first determines how many emitters are present (the deinterleaving problem). Pulses from individual simulated emitters give rise to separate stable attractors in the network. Once individual emitters are characterized, it is possible to make tentative identifications of them based on their observed parameters. As a test of this idea, a neural network was used to form a small data base that potentially could make emitter identifications

On Submodularity and Controllability in Complex Dynamical Networks

Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem is sensor and actuator placement: choose a subset from a finite set of possible placements to optimize some real-valued controllability and observability metrics of the network. Surprisingly little is known about the structure of such combinatorial optimization problems. In this paper, we show that several important classes of metrics based on the controllability and observability Gramians have a strong structural property that allows for either efficient global optimization or an approximation guarantee by using a simple greedy heuristic for their maximization. In particular, the mapping from possible placements to several scalar functions of the associated Gramian is either a modular or submodular set function. The results are illustrated on randomly generated systems and on a problem of power electronic actuator placement in a model of the European power grid.Comment: Original arXiv version of IEEE Transactions on Control of Network Systems paper (Volume 3, Issue 1), with a addendum (located in the ancillary documents) that explains an error in a proof of the original paper and provides a counterexample to the corresponding resul

Subjective Evaluations with Performance Feedback

This paper models two key roles of subjective performance evaluations: their incentive role and their feedback role. The paper shows that the feedback role makes subjective pay feasible even without repeated interaction, as long as there exists some verifiable measure of performance. It also shows that while subjective pay is helpful, it cannot achieve full efficiency. However, fully efficient incentives are achievable if the firm can commit to a forced distribution of evaluations and employs a continuum of workers. With a small number of workers, a forced distribution is valuable only if the verifiable measure is poor.Subjective Evaluations, Performance Feedback, Optimal Contracts

A String-Inspired Model for the Low-ℓ\ell CMB

We present a semi--analytic exploration of some low--$\ell$ angular power spectra inspired by "Brane Supersymmetry Breaking". This mechanism splits Bose and Fermi excitations in String Theory, leaving behind an exponential potential that is just too steep for the inflaton to emerge from the initial singularity while descending it. As a result, the scalar generically bounces against the exponential wall, which typically introduces an infrared depression and a pre--inflationary peak in the power spectrum of scalar perturbations. We elaborate on a possible link between this phenomenon and the low--$\ell$ CMB. For the first 32 multipoles, combining the hard exponential with a milder one leading to $n_s\simeq 0.96$ and with a small gaussian bump we have attained a reduction of $\chi^{\,2}$ to about 46% of the standard $\Lambda$CDM setting, with both WMAP9 and PLANCK 2013 data. This result corresponds to a $\chi^{\,2}/DOF$ of about 0.45, to be compared with a $\Lambda$CDM value of about 0.85. The preferred choices combine naturally quadrupole depression, a first peak around $\ell=5$ and a wide minimum around $\ell=20$. We have also gathered some evidence that similar spectra emerge if the hard exponential is combined with more realistic models of inflation. A problem of the preferred examples is their slow convergence to an almost scale--invariant profile.Comment: 12 pages, latex, 7 figures. Power and limitations of the models and of the semi-analytic approach stressed, misprints corrected. Final version to appear in Mod. Phys. Lett.