Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization

We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity operator with respect to the non-smooth term. We show that both the basic proximal-gradient method and the accelerated proximal-gradient method achieve the same convergence rate as in the error-free case, provided that the errors decrease at appropriate rates.Using these rates, we perform as well as or better than a carefully chosen fixed error level on a set of structured sparsity problems.Comment: Neural Information Processing Systems (2011

Minimizing Finite Sums with the Stochastic Average Gradient

We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in the sum. However, by incorporating a memory of previous gradient values the SAG method achieves a faster convergence rate than black-box SG methods. The convergence rate is improved from O(1/k^{1/2}) to O(1/k) in general, and when the sum is strongly-convex the convergence rate is improved from the sub-linear O(1/k) to a linear convergence rate of the form O(p^k) for p \textless{} 1. Further, in many cases the convergence rate of the new method is also faster than black-box deterministic gradient methods, in terms of the number of gradient evaluations. Numerical experiments indicate that the new algorithm often dramatically outperforms existing SG and deterministic gradient methods, and that the performance may be further improved through the use of non-uniform sampling strategies.Comment: Revision from January 2015 submission. Major changes: updated literature follow and discussion of subsequent work, additional Lemma showing the validity of one of the formulas, somewhat simplified presentation of Lyapunov bound, included code needed for checking proofs rather than the polynomials generated by the code, added error regions to the numerical experiment

Implementation strategies for hyperspectral unmixing using Bayesian source separation

Bayesian Positive Source Separation (BPSS) is a useful unsupervised approach for hyperspectral data unmixing, where numerical non-negativity of spectra and abundances has to be ensured, such in remote sensing. Moreover, it is sensible to impose a sum-to-one (full additivity) constraint to the estimated source abundances in each pixel. Even though non-negativity and full additivity are two necessary properties to get physically interpretable results, the use of BPSS algorithms has been so far limited by high computation time and large memory requirements due to the Markov chain Monte Carlo calculations. An implementation strategy which allows one to apply these algorithms on a full hyperspectral image, as typical in Earth and Planetary Science, is introduced. Effects of pixel selection, the impact of such sampling on the relevance of the estimated component spectra and abundance maps, as well as on the computation times, are discussed. For that purpose, two different dataset have been used: a synthetic one and a real hyperspectral image from Mars.Comment: 10 pages, 6 figures, submitted to IEEE Transactions on Geoscience and Remote Sensing in the special issue on Hyperspectral Image and Signal Processing (WHISPERS

VoodooFlash: authoring across physical and digital form

Design tools that integrate hardware and software components facilitate product design work across aspects of physical form and user interaction, but at the cost of requiring designers to work with other than their accustomed programming tools. In this paper we introduce VoodooFlash, a tool designed to build on the widespread use of Flash while facilitating design work across physical and digital components. VoodooFlash extends the existing practice of authoring interactive applications in terms of arranging components on a virtual stage, and provides a physical stage on which controls can be arranged, linked to software components, and appropriated with other physical design materials

Direct photon production and flow at low transverse momenta in pp, p-Pb and Pb-Pb collisions

Low transverse momentum direct photon measurements have been carried out by the ALICE experiment at the CERN LHC in small collision systems (pp, $\sqrt{s}=2.76$ and 8 TeV and p--Pb, $\sqrt{s_\text{NN}}=5.02$ TeV) as well as in heavy-ion collisions (Pb--Pb, $\sqrt{s_\text{NN}}=2.76$ TeV). For the first time, also the multiplicity dependence of direct photon production was investigated in p--Pb collisions. Whereas in the small systems no significant thermal photon signal was observed, a $\sim15\%$ excess has been measured in central Pb--Pb collisions in the region of $p_{\rm T}<3$ GeV/$c$. A signal of prompt photon production at high transverse momentum consistent with binary scaling has been observed in all collision systems following NLO pQCD predictions. Direct photon flow has been measured in central and semi-central Pb--Pb collisions and found to be of similar size as the charged hadron and decay photon flow.Comment: Proceedings of Hard Probes 2018, 30 September - 5 October, Aix-Les-Bains, Franc

Endeavors 2004-05

Research, discovery for Nebraskans; Tallow key to new cholesterol fighter; Exploring genetics of potential biological threat; Creating wearable corn – husks, that is; Tracking helps predict landslide sites; Assessing foot-and-mouth test kits; New mapping system tracks livestock diseases; Remote images could predict crop health; Exploring genetics behind obesity; Team seeks lower cost ways to reduce arsenic; Larger, softer kernels boost feed value; Alternative crops could aid Panhandle; Analysis examines impact of GM crops; Better understanding servant-leadership; Simulation tool aids corn growers; Devising ways to predict livestock odors; Local produce could help growers, chefs; Using corn for ethanol makes energy sense; Sensors should reveal soil differences; IDing safe levels of manure for growing crop

Light meson nuclear modification factor in p-Pb collisions over an unprecedented pTp_\mathrm{T} range with ALICE

Light neutral meson differential invariant cross section and nuclear modification factor measurements have been carried out with the ALICE detector at the CERN LHC in pp collisions at $\sqrt{s}=8$ TeV and p--Pb collisions at $\sqrt{s_\mathrm{NN}}=8.16$ TeV. The analysis combines results from several partially independent reconstruction techniques where the $\pi^0$ and $\eta$ meson decay photons were detected with the electromagnetic calorimeter, EMCal, the photon spectrometer, PHOS, or via reconstruction of $e^+e^-$ pairs from conversions in the ALICE detector material using the central tracking system. The neutral pion measurement reaching a $p_\mathrm{T}$ of 200 GeV/$c$ poses as the highest measured identified particle spectrum to date while the $\eta$ meson is measured to an unprecedented $p_\mathrm{T}$ of 50 GeV/$c$. The spectra are found to be generally overestimated by NLO pQCD calculations. The nuclear modification factors of both mesons exhibit a suppression for $p_\mathrm{T}<10$ GeV/$c$ which is stronger compared to previous measurements at $\sqrt{s_\mathrm{NN}}=5.02$ TeV and consistent with CGC and cold nuclear matter energy loss calculations. For $p_\mathrm{T}>10$ GeV/$c$, $R_\mathrm{pPb}$ is consistent with unity and theory predictions.Comment: Proceedings of the 10th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions, Hard Probes 202