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

Certain Canine Weakly β-Hemolytic Intestinal Spirochetes Are Phenotypically and Genotypically Related to Spirochetes Associated with Human and Porcine Intestinal Spirochetosis

Four canine weakly β-hemolytic intestinal spirochetes associated with intestinal spirochetosis (IS-associated WBHIS) were compared with IS-associated human and porcine WBHIS and the type species for Serpulina hyodysenteriae and S. innocens by using phenotypic and genotypic parameters. The IS-associated canine, human, and porcine WBHIS belonged to a phyletic group distinct from but related to previously described Serpulina type species

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

‘‘Cooling by Heating’’- Demonstrating the Significance of the Longitudinal Specific Heat

Heating a solid sphere at its surface induces mechanical stresses inside the sphere. If a finite amount of heat is supplied, the stresses gradually disappear as temperature becomes homogeneous throughout the sphere. We show that before this happens, there is a temporary lowering of pressure and density in the interior of the sphere, inducing a transient lowering of the temperature here. For ordinary solids this effect is small because c_{p}≅c_{V}. For fluent liquids the effect is negligible because their dynamic shear modulus vanishes. For a liquid at its glass transition, however, the effect is generally considerably larger than in solids. This paper presents analytical solutions of the relevant coupled thermoviscoelastic equations. In general, there is a difference between the isobaric specific heat c_{p} measured at constant isotropic pressure and the longitudinal specific heat c_{l} pertaining to mechanical boundary conditions that confine the associated expansion to be longitudinal. In the exact treatment of heat propagation, the heat-diffusion constant contains c_{l} rather than c_{p}. We show that the key parameter controlling the magnitude of the “cooling-by-heating“ effect is the relative difference between these two specific heats. For a typical glass-forming liquid, when the temperature at the surface is increased by 1 K, a lowering of the temperature at the sphere center of the order of 5 mK is expected if the experiment is performed at the glass transition. The cooling-by-heating effect is confirmed by measurements on a glucose sphere at the glass transition

Illusory perceptions of space and time preserve cross-saccadic perceptual continuity

When voluntary saccadic eye movements are made to a silently ticking clock, observers sometimes think that the second hand takes longer than normal to move to its next position. For a short period, the clock appears to have stopped (chronostasis). Here we show that the illusion occurs because the brain extends the percept of the saccadic target backwards in time to just before the onset of the saccade. This occurs every time we move the eyes but it is only perceived when an external time reference alerts us to the phenomenon. The illusion does not seem to depend on the shift of spatial attention that accompanies the saccade. However, if the target is moved unpredictably during the saccade, breaking perception of the target's spatial continuity, then the illusion disappears. We suggest that temporal extension of the target's percept is one of the mechanisms that 'fill in' the perceptual 'gap' during saccadic suppression. The effect is critically linked to perceptual mechanisms that identify a target's spatial stability

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