Fast Fourier Optimization: Sparsity Matters

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier transform} (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursive, it is difficult to embed into a linear optimization problem. In this paper, we explain the main idea behind the fast Fourier transform and show how to adapt it in such a manner as to make it encodable as constraints in an optimization problem. We demonstrate a real-world problem from the field of high-contrast imaging. On this problem, dramatic improvements are translated to an ability to solve problems with a much finer grid of discretized points. As we shall show, in general, the "fast Fourier" version of the optimization constraints produces a larger but sparser constraint matrix and therefore one can think of the fast Fourier transform as a method of sparsifying the constraints in an optimization problem, which is usually a good thing.Comment: 16 pages, 8 figure

Diversity and productivity of photosynthetic picoeukaryotes in biogeochemically distinct regions of the South East Pacific Ocean

© The Author(s), 2016. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Limnology and Oceanography 61 (2016): 806–824, doi:10.1002/lno.10255.Picophytoplankton, including photosynthetic picoeukaryotes (PPE) and unicellular cyanobacteria, are important contributors to plankton biomass and primary productivity. In this study, phytoplankton composition and rates of carbon fixation were examined across a large trophic gradient in the South East Pacific Ocean (SEP) using a suite of approaches: photosynthetic pigments, rates of 14C-primary productivity, and phylogenetic analyses of partial 18S rRNA genes PCR amplified and sequenced from flow cytometrically sorted cells. While phytoplankton >10 μm (diatoms and dinoflagellates) were prevalent in the upwelling region off the Chilean coast, picophytoplankton consistently accounted for 55–92% of the total chlorophyll a inventories and >60% of 14C-primary productivity throughout the sampling region. Estimates of rates of 14C-primary productivity derived from flow cytometric sorting of radiolabeled cells revealed that the contributions of PPE and Prochlorococcus to euphotic zone depth-integrated picoplankton productivity were nearly equivalent (ranging 36–57%) along the transect, with PPE comprising a larger share of picoplankton productivity than cyanobacteria in the well-lit (>15% surface irradiance) region compared with in the lower regions (1–7% surface irradiance) of the euphotic zone. 18S rRNA gene sequence analyses revealed the taxonomic identities of PPE; e.g., Mamiellophyceae (Ostreococcus) were the dominant PPE in the upwelling-influenced waters, while members of the Chrysophyceae, Prymnesiophyceae, Pelagophyceae, and Prasinophyceae Clades VII and IX flourished in the oligotrophic South Pacific Subtropical Gyre. Our results suggest that, despite low numerical abundance in comparison to cyanobacteria, diverse members of PPE are significant contributors to carbon cycling across biogeochemically distinct regions of the SEP.Support for this work derived from U.S. National Science Foundation grants to C-MORE (EF-0424599; DMK) and OCE-1241263 (MJC). Additional support was received from the University of Hawai'i Denise B. Evans Research Fellowship in Oceanography (YMR), the Gordon and Betty Moore Foundation (DMK), and the Simons Foundation via the Simons Collaboration on Ocean Processes and Ecology (SCOPE: DJR, MJC, and DMK)

An ERP Investigation on Visuotactile Interactions in Peripersonal and Extrapersonal Space: Evidence for the Spatial Rule

The spatial rule of multisensory integration holds that cross-modal stimuli presented from the same spatial location result in enhanced multisensory integration. The present study investigated whether processing within the somatosensory cortex reflects the strength of cross-modal visuotactile interactions depending on the spatial relationship between visual and tactile stimuli. Visual stimuli were task-irrelevant and were presented simultaneously with touch in peripersonal and extrapersonal space, in the same or opposite hemispace with respect to the tactile stimuli. Participants directed their attention to one of their hands to detect infrequent tactile target stimuli at that hand while ignoring tactile targets at the unattended hand, all tactile nontarget stimuli, and any visual stimuli. Enhancement of ERPs recorded over and close to the somatosensory cortex was present as early as 100 msec after onset of stimuli (i.e., overlapping with the P100 component) when visual stimuli were presented next to the site of tactile stimulation (i.e., perihand space) compared to when these were presented at different locations in peripersonal or extrapersonal space. Therefore, this study provides electrophysiological support for the spatial rule of visual–tactile interaction in human participants. Importantly, these early cross-modal spatial effects occurred regardless of the locus of attention. In addition, and in line with previous research, we found attentional modulations of somatosensory processing only to be present in the time range of the N140 component and for longer latencies with an enhanced negativity for tactile stimuli at attended compared to unattended locations. Taken together, the pattern of the results from this study suggests that visuotactile spatial effects on somatosensory processing occur prior and independent of tactile–spatial attention

Influence of hand position on the near-effect in 3D attention

Voluntary reorienting of attention in real depth situations is characterized by an attentional bias to locations near the viewer once attention is deployed to a spatially cued object in depth. Previously this effect (initially referred to as the ‘near-effect’) was attributed to access of a 3D viewer-centred spatial representation for guiding attention in 3D space. The aim of this study was to investigate whether the near-bias could have been associated with the position of the response-hand, always near the viewer in previous studies investigating endogenous attentional shifts in real depth. In Experiment 1, the response-hand was placed at either the near or far target depth in a depth cueing task. Placing the response-hand at the far target depth abolished the near-effect, but failed to bias spatial attention to the far location. Experiment 2 showed that the response-hand effect was not modulated by the presence of an additional passive hand, whereas Experiment 3 confirmed that attentional prioritization of the passive hand was not masked by the influence of the responding hand on spatial attention in Experiment 2. The pattern of results is most consistent with the idea that response preparation can modulate spatial attention within a 3D viewer-centred spatial representation

Biases in the perceived timing of perisaccadic perceptual and motor events

Subjects typically experience the temporal interval immediately following a saccade as longer than a comparable control interval. One explanation of this effect is that the brain antedates the perceptual onset of a saccade target to around the time of saccade initiation. This could explain the apparent continuity of visual perception across eye movements. Thisantedating account was tested in three experiments in which subjects made saccades of differing extents and then judged either the duration or the temporal order of key events. Postsaccadic stimuli underwent subjective temporal lengthening and had early perceived onsets. A temporally advanced awareness of saccade completion was also found, independently of antedating effects. These results provide convergent evidence supporting antedating and differentiating it from other temporal biases

Response of CsI(Tl) scintillators over a large range in energy and atomic number of ions (Part I): recombination and delta -- electrons

A simple formalism describing the light response of CsI(Tl) to heavy ions, which quantifies the luminescence and the quenching in terms of the competition between radiative transitions following the carrier trapping at the Tl activator sites and the electron-hole recombination, is proposed. The effect of the delta rays on the scintillation efficiency is for the first time quantitatively included in a fully consistent way. The light output expression depends on four parameters determined by a procedure of global fit to experimental data.Comment: 28 pages, 6 figures, submitted to Nucl. Inst. Meth.

Multifragmentation process for different mass asymmetry in the entrance channel around the Fermi energy

The influence of the entrance channel asymmetry upon the fragmentation process is addressed by studying heavy-ion induced reactions around the Fermi energy. The data have been recorded with the INDRA 4pi array. An event selection method called the Principal Component Analysis is presented and discussed. It is applied for the selection of central events and furthermore to multifragmentation of single source events. The selected subsets of data are compared to the Statistical Multifragmentation Model (SMM) to check the equilibrium hypothesis and get the source characteristics. Experimental comparisons show the evidence of a decoupling between thermal and compresional (radial flow) degrees of freedom in such nuclear systems.Comment: 28 pages, 15 figures, article sumitted to Nuclear Physics

Measurements of sideward flow around the balance energy

Sideward flow values have been determined with the INDRA multidetector for Ar+Ni, Ni+Ni and Xe+Sn systems studied at GANIL in the 30 to 100 A.MeV incident energy range. The balance energies found for Ar+Ni and Ni+Ni systems are in agreement with previous experimental results and theoretical calculations. Negative sideward flow values have been measured. The possible origins of such negative values are discussed. They could result from a more important contribution of evaporated particles with respect to the contribution of promptly emitted particles at mid-rapidity. But effects induced by the methods used to reconstruct the reaction plane cannot be totally excluded. Complete tests of these methods are presented and the origins of the ``auto-correlation'' effect have been traced back. For heavy fragments, the observed negative flow values seem to be mainly due to the reaction plane reconstruction methods. For light charged particles, these negative values could result from the dynamics of the collisions and from the reaction plane reconstruction methods as well. These effects have to be taken into account when comparisons with theoretical calculations are done.Comment: 27 pages, 15 figure

Effect of the intermediate velocity emissions on the quasi-projectile properties for the Ar+Ni system at 95 A.MeV

The quasi-projectile (QP) properties are investigated in the Ar+Ni collisions at 95 A.MeV taking into account the intermediate velocity emission. Indeed, in this reaction, between 52 and 95 A.MeV bombarding energies, the number of particles emitted in the intermediate velocity region is related to the overlap volume between projectile and target. Mean transverse energies of these particles are found particularly high. In this context, the mass of the QP decreases linearly with the impact parameter from peripheral to central collisions whereas its excitation energy increases up to 8 A.MeV. These results are compared to previous analyses assuming a pure binary scenario

Study of intermediate velocity products in the Ar+Ni collisions between 52 and 95 A.MeV

Intermediate velocity products in Ar+Ni collisions from 52 to 95 A.MeV are studied in an experiment performed at the GANIL facility with the 4$\pi$ multidetector INDRA. It is shown that these emissions cannot be explained by statistical decays of the quasi-projectile and the quasi-target in complete equilibrium. Three methods are used to isolate and characterize intermediate velocity products. The total mass of these products increases with the violence of the collision and reaches a large fraction of the system mass in mid-central collisions. This mass is found independent of the incident energy, but strongly dependent on the geometry of the collision. Finally it is shown that the kinematical characteristics of intermediate velocity products are weakly dependent on the experimental impact parameter, but strongly dependent on the incident energy. The observed trends are consistent with a participant-spectator like scenario or with neck emissions and/or break-up.Comment: 37 pages, 13 figure