HR: A System for Machine Discovery in Finite Algebras

We describe the HR concept formation program which invents mathematical definitions and conjectures in finite algebras such as group theory and ring theory. We give the methods behind and the reasons for the concept formation in HR, an evaluation of its performance in its training domain, group theory, and a look at HR in domains other than group theory

Reallocation Problems in Scheduling

In traditional on-line problems, such as scheduling, requests arrive over time, demanding available resources. As each request arrives, some resources may have to be irrevocably committed to servicing that request. In many situations, however, it may be possible or even necessary to reallocate previously allocated resources in order to satisfy a new request. This reallocation has a cost. This paper shows how to service the requests while minimizing the reallocation cost. We focus on the classic problem of scheduling jobs on a multiprocessor system. Each unit-size job has a time window in which it can be executed. Jobs are dynamically added and removed from the system. We provide an algorithm that maintains a valid schedule, as long as a sufficiently feasible schedule exists. The algorithm reschedules only a total number of O(min{log^* n, log^* Delta}) jobs for each job that is inserted or deleted from the system, where n is the number of active jobs and Delta is the size of the largest window.Comment: 9 oages, 1 table; extended abstract version to appear in SPAA 201

Lower Bounds for Structuring Unreliable Radio Networks

In this paper, we study lower bounds for randomized solutions to the maximal independent set (MIS) and connected dominating set (CDS) problems in the dual graph model of radio networks---a generalization of the standard graph-based model that now includes unreliable links controlled by an adversary. We begin by proving that a natural geographic constraint on the network topology is required to solve these problems efficiently (i.e., in time polylogarthmic in the network size). We then prove the importance of the assumption that nodes are provided advance knowledge of their reliable neighbors (i.e, neighbors connected by reliable links). Combined, these results answer an open question by proving that the efficient MIS and CDS algorithms from [Censor-Hillel, PODC 2011] are optimal with respect to their dual graph model assumptions. They also provide insight into what properties of an unreliable network enable efficient local computation.Comment: An extended abstract of this work appears in the 2014 proceedings of the International Symposium on Distributed Computing (DISC

Compressive Inverse Scattering II. SISO Measurements with Born scatterers

Inverse scattering methods capable of compressive imaging are proposed and analyzed. The methods employ randomly and repeatedly (multiple-shot) the single-input-single-output (SISO) measurements in which the probe frequencies, the incident and the sampling directions are related in a precise way and are capable of recovering exactly scatterers of sufficiently low sparsity. For point targets, various sampling techniques are proposed to transform the scattering matrix into the random Fourier matrix. The results for point targets are then extended to the case of localized extended targets by interpolating from grid points. In particular, an explicit error bound is derived for the piece-wise constant interpolation which is shown to be a practical way of discretizing localized extended targets and enabling the compressed sensing techniques. For distributed extended targets, the Littlewood-Paley basis is used in analysis. A specially designed sampling scheme then transforms the scattering matrix into a block-diagonal matrix with each block being the random Fourier matrix corresponding to one of the multiple dyadic scales of the extended target. In other words by the Littlewood-Paley basis and the proposed sampling scheme the different dyadic scales of the target are decoupled and therefore can be reconstructed scale-by-scale by the proposed method. Moreover, with probes of any single frequency \om the coefficients in the Littlewood-Paley expansion for scales up to \om/(2\pi) can be exactly recovered.Comment: Add a new section (Section 3) on localized extended target

Automatic Invention of Integer Sequences

We report on the application of the HR program (Colton, Bundy, & Walsh 1999) to the problem of automatically inventing integer sequences. Seventeen sequences invented by HR are interesting enough to have been accepted into the Encyclopedia of Integer Sequences (Sloane 2000) and all were supplied with interesting conjectures about their nature, also discovered by HR. By extending HR, we have enabled it to perform a two stage process of invention and investigation. This involves generating both the definition and terms of a new sequence, relating it to sequences already in the Encyclopedia and pruning the output to help identify the most surprising and interesting results

Determining the shape of defects in non-absorbing inhomogeneous media from far-field measurements

International audienceWe consider non-absorbing inhomogeneous media represented by some refraction index. We have developed a method to reconstruct, from far-field measurements, the shape of the areas where the actual index differs from a reference index. Following the principle of the Factorization Method, we present a fast reconstruction algorithm relying on far field measurements and near field values, easily computed from the reference index. Our reconstruction result is illustrated by several numerical test cases

Principles of proteome allocation are revealed using proteomic data and genome-scale models

Integrating omics data to refine or make context-specific models is an active field of constraint-based modeling. Proteomics now cover over 95% of the Escherichia coli proteome by mass. Genome-scale models of Metabolism and macromolecular Expression (ME) compute proteome allocation linked to metabolism and fitness. Using proteomics data, we formulated allocation constraints for key proteome sectors in the ME model. The resulting calibrated model effectively computed the "generalist" (wild-type) E. coli proteome and phenotype across diverse growth environments. Across 15 growth conditions, prediction errors for growth rate and metabolic fluxes were 69% and 14% lower, respectively. The sector-constrained ME model thus represents a generalist ME model reflecting both growth rate maximization and "hedging" against uncertain environments and stresses, as indicated by significant enrichment of these sectors for the general stress response sigma factor σS. Finally, the sector constraints represent a general formalism for integrating omics data from any experimental condition into constraint-based ME models. The constraints can be fine-grained (individual proteins) or coarse-grained (functionally-related protein groups) as demonstrated here. This flexible formalism provides an accessible approach for narrowing the gap between the complexity captured by omics data and governing principles of proteome allocation described by systems-level models

Near-Unity Unselective Absorption in Sparse InP Nanowire Arrays

We experimentally demonstrate near-unity, unselective absorption, broadband, angle-insensitive, and polarization-independent absorption, in sparse InP nanowire arrays, embedded in flexible polymer sheets via geometric control of waveguide modes in two wire motifs: (i) arrays of tapered wires and (ii) arrays of nanowires with varying radii. Sparse arrays of these structures exhibit enhanced absorption due to strong coupling into the first order azimuthal waveguide modes of individual nanowires; wire radius thus controls the spectral region of the absorption enhancement. Whereas arrays of cylindrical wires with uniform radius exhibit narrowband absorption, arrays of tapered wires and arrays with multiple wire radii expand this spectral region and achieve broadband absorption enhancement. Herein, we present an economic, top-down lithographic/etch fabrication method that enables fabrication of multiple InP nanowire arrays from a single InP wafer with deliberate control of nanowire radius and taper. Using this method, we create sparse tapered and multiradii InP nanowire arrays and demonstrate optical absorption that is broadband (450–900 nm), angle-insensitive, and near-unity (>90%) in roughly 100 nm planar equivalence of InP. These highly absorbing sparse nanowire arrays represent a promising approach to flexible, high efficiency optoelectronic devices, such as photodetectors, solar cells, and photoelectrochemical devices

High Spectral Resolution Plasmonic Color Filters with Subwavelength Dimensions

Rapid advances in image sensor technology have generated a mismatch between the small size of image sensor pixels and the achievable filter spectral resolution. This mismatch has prevented the realization of chip-based image sensors with simultaneously high spatial and spectral resolution. We report here a concept that overcomes this trade-off, enabling high spectral resolution (transmission FWHM <31 nm) filters with subwavelength dimensions operating at optical and near-infrared wavelengths. An inverse design methodology was used to realize a new type of plasmonic cavity that efficiently couples an in-plane Fabry–Perot resonator to a single plasmonic slit that supports surface plasmon polaritons. This design principle, combined with a new metal imprinting method that yields metallic nanostructures with both top and bottom surfaces that are extremely smooth, enabled demonstration of high spectral resolution transmission filters with smaller area than any previously reported