The{dollar}p{dollar}-Norm Generalization of the LMS Algorithm for Adaptive Filtering

Peer reviewe

On-line PCA with Optimal Regrets

We carefully investigate the on-line version of PCA, where in each trial a learning algorithm plays a k-dimensional subspace, and suffers the compression loss on the next instance when projected into the chosen subspace. In this setting, we analyze two popular on-line algorithms, Gradient Descent (GD) and Exponentiated Gradient (EG). We show that both algorithms are essentially optimal in the worst-case. This comes as a surprise, since EG is known to perform sub-optimally when the instances are sparse. This different behavior of EG for PCA is mainly related to the non-negativity of the loss in this case, which makes the PCA setting qualitatively different from other settings studied in the literature. Furthermore, we show that when considering regret bounds as function of a loss budget, EG remains optimal and strictly outperforms GD. Next, we study the extension of the PCA setting, in which the Nature is allowed to play with dense instances, which are positive matrices with bounded largest eigenvalue. Again we can show that EG is optimal and strictly better than GD in this setting

Looking at Vector Space and Language Models for IR using Density Matrices

In this work, we conduct a joint analysis of both Vector Space and Language Models for IR using the mathematical framework of Quantum Theory. We shed light on how both models allocate the space of density matrices. A density matrix is shown to be a general representational tool capable of leveraging capabilities of both VSM and LM representations thus paving the way for a new generation of retrieval models. We analyze the possible implications suggested by our findings.Comment: In Proceedings of Quantum Interaction 201

Spectroscopic analysis of interaction between an EIT wave and a coronal upflow region

We report a spectroscopic analysis of an EIT wave event that occurred in active region 11081 on 2010 June 12 and was associated with an M2.0 class flare. The wave propagated near circularly. The south-eastern part of the wave front passed over an upflow region nearby a magnetic bipole. Using EIS raster observations for this region, we studied the properties of plasma dynamics in the wave front, as well as the interaction between the wave and the upflow region. We found a weak blueshift for the Fe XII {\lambda}195.12 and Fe XIII {\lambda}202.04 lines in the wave front. The local velocity along the solar surface, which is deduced from the line of sight velocity in the wave front and the projection effect, is much lower than the typical propagation speed of the wave. A more interesting finding is that the upflow and non-thermal velocities in the upflow region are suddenly diminished after the transit of the wave front. This implies a significant change of magnetic field orientation when the wave passed. As the lines in the upflow region are redirected, the velocity along the line of sight is diminished as a result. We suggest that this scenario is more in accordance with what was proposed in the field-line stretching model of EIT waves.Comment: 13 pages, 7 figures, accepted for publication in Ap

Open Problem: Online Sabotaged Shortest Path

Abstract There has been much work on extending the prediction with expert advice methodology to the case when experts are composed of components and there are combinatorially many such experts. One of the core examples is the Online Shortest Path problem where the components are edges and the experts are paths. In this note we revisit this online routing problem in the case where in each trial some of the edges or components are sabotaged / blocked. In the vanilla expert setting a known method can solve this extension where experts are now awake or asleep in each trial. We ask whether this technology can be upgraded efficiently to the case when at each trial every component can be awake or asleep. It is easy get to get an initial regret bound by using combinatorially many experts. However it is open whether there are efficient algorithms achieving the same regret

Coronal Shock Waves, EUV Waves, and Their Relation to CMEs. III. Shock-Associated CME/EUV Wave in an Event with a Two-Component EUV Transient

On 17 January 2010, STEREO-B observed in extreme ultraviolet (EUV) and white light a large-scale dome-shaped expanding coronal transient with perfectly connected off-limb and on-disk signatures. Veronig et al. (2010, ApJL 716, 57) concluded that the dome was formed by a weak shock wave. We have revealed two EUV components, one of which corresponded to this transient. All of its properties found from EUV, white light, and a metric type II burst match expectations for a freely expanding coronal shock wave including correspondence to the fast-mode speed distribution, while the transient sweeping over the solar surface had a speed typical of EUV waves. The shock wave was presumably excited by an abrupt filament eruption. Both a weak shock approximation and a power-law fit match kinematics of the transient near the Sun. Moreover, the power-law fit matches expansion of the CME leading edge up to 24 solar radii. The second, quasi-stationary EUV component near the dimming was presumably associated with a stretched CME structure; no indications of opening magnetic fields have been detected far from the eruption region.Comment: 18 pages, 10 figures. Solar Physics, published online. The final publication is available at http://www.springerlink.co

Large-scale Bright Fronts in the Solar Corona: A Review of "EIT waves"

``EIT waves" are large-scale coronal bright fronts (CBFs) that were first observed in 195 \AA\ images obtained using the Extreme-ultraviolet Imaging Telescope (EIT) onboard the \emph{Solar and Heliospheric Observatory (SOHO)}. Commonly called ``EIT waves", CBFs typically appear as diffuse fronts that propagate pseudo-radially across the solar disk at velocities of 100--700 km s$^{-1}$ with front widths of 50-100 Mm. As their speed is greater than the quiet coronal sound speed ($c_s\leq$200 km s$^{-1}$) and comparable to the local Alfv\'{e}n speed ($v_A\leq$1000 km s$^{-1}$), they were initially interpreted as fast-mode magnetoacoustic waves ($v_{f}=(c_s^2 + v_A^2)^{1/2}$). Their propagation is now known to be modified by regions where the magnetosonic sound speed varies, such as active regions and coronal holes, but there is also evidence for stationary CBFs at coronal hole boundaries. The latter has led to the suggestion that they may be a manifestation of a processes such as Joule heating or magnetic reconnection, rather than a wave-related phenomena. While the general morphological and kinematic properties of CBFs and their association with coronal mass ejections have now been well described, there are many questions regarding their excitation and propagation. In particular, the theoretical interpretation of these enigmatic events as magnetohydrodynamic waves or due to changes in magnetic topology remains the topic of much debate.Comment: 34 pages, 19 figure

Coronal Shock Waves, EUV waves, and Their Relation to CMEs. I. Reconciliation of "EIT waves", Type II Radio Bursts, and Leading Edges of CMEs

We show examples of excitation of coronal waves by flare-related abrupt eruptions of magnetic rope structures. The waves presumably rapidly steepened into shocks and freely propagated afterwards like decelerating blast waves that showed up as Moreton waves and EUV waves. We propose a simple quantitative description for such shock waves to reconcile their observed propagation with drift rates of metric type II bursts and kinematics of leading edges of coronal mass ejections (CMEs). Taking account of different plasma density falloffs for propagation of a wave up and along the solar surface, we demonstrate a close correspondence between drift rates of type II bursts and speeds of EUV waves, Moreton waves, and CMEs observed in a few known events.Comment: 30 pages, 15 figures. Solar Physics, published online. The final publication is available at http://www.springerlink.co

Radio Bursts Associated with Flare and Ejecta in the 13 July 2004 Event

We investigate coronal transients associated with a GOES M6.7 class flare and a coronal mass ejection (CME) on 13 July 2004. During the rising phase of the flare, a filament eruption, loop expansion, a Moreton wave, and an ejecta were observed. An EIT wave was detected later on. The main features in the radio dynamic spectrum were a frequency-drifting continuum and two type II bursts. Our analysis shows that if the first type II burst was formed in the low corona, the burst heights and speed are close to the projected distances and speed of the Moreton wave (a chromospheric shock wave signature). The frequency-drifting radio continuum, starting above 1 GHz, was formed almost two minutes prior to any shock features becoming visible, and a fast-expanding piston (visible as the continuum) could have launched another shock wave. A possible scenario is that a flare blast overtook the earlier transient, and ignited the first type II burst. The second type II burst may have been formed by the same shock, but only if the shock was propagating at a constant speed. This interpretation also requires that the shock-producing regions were located at different parts of the propagating structure, or that the shock was passing through regions with highly different atmospheric densities. This complex event, with a multitude of radio features and transients at other wavelengths, presents evidence for both blast-wave-related and CME-related radio emissions.Comment: 14 pages, 6 figures; Solar Physics Topical Issue, in pres