Fast eigenspace decomposition of correlated images

Includes bibliographical references.We present a computationally efficient algorithm for the eigenspace decomposition of correlated images. Our approach is motivated by the fact that for a planar rotation of a two-dimensional (2-D) image, analytical expressions can be given for the eigendecomposition, based on the theory of circulant matrices. These analytical expressions turn out to be good first approximations of the eigendecomposition, even for three-dimensional (3-D) objects rotated about a single axis. In addition, the theory of circulant matrices yields good approximations to the eigendecomposition for images that result when objects are translated and scaled. We use these observations to automatically determine the dimension of the subspace required to represent an image with a guaranteed user-specified accuracy, as well as to quickly compute a basis for the subspace. Examples show that the algorithm performs very well on a number of test cases ranging from images of 3-D objects rotated about a single axis to arbitrary video sequences.This work was supported by the Sze Tsao Chang Memorial Engineering Fund, the National Imagery and Mapping Agency under Contract NMA201-00-1-1003, and by the Office of Naval Research under Contract N00014-97-1-0640

Fast eigenspace decomposition of correlated images

Includes bibliographical references.We present a computationally efficient algorithm for the eigenspace decomposition of correlated images. Our approach is motivated by the fact that for a planar rotation of a two-dimensional image, analytical expressions can be given for the eigendecomposition, based on the theory of circulant matrices. These analytical expressions turn out to be good first approximations of the eigendecomposition, even for three-dimensional objects rotated about a single axis. We use this observation to automatically determine the dimension of the subspace required to represent an image with a guaranteed user-specified accuracy, as well as to quickly compute a basis for the subspace. Examples show that the algorithm performs very well on a range of test images composed of three-dimensional objects rotated about a single axis.This work was supported by the Sze Tsao Chang Memorial Engineering Fund and by the Office of Naval Research under contract no. N00014-97-1-0540

Meridional Transport in the Stratosphere of Jupiter

The Cassini measurements of C$_2$H$_2$ and C$_2$H$_6$ at $\sim$5 mbar provide a constraint on meridional transport in the stratosphere of Jupiter. We performed a two-dimensional photochemical calculation coupled with mass transport due to vertical and meridional mixing. The modeled profile of C$_2$H$_2$ at latitudes less than 70$^\circ$ follows the latitude dependence of the solar insolation, while that of C$_2$H$_6$ shows little latitude dependence, consistent with the measurements. In general, our model study suggests that the meridional transport timescale above 5-10 mbar altitude level is $\gtrsim$1000 years and the time could be as short as 10 years below 10 mbar level, in order to fit the Cassini measurements. The derived meridional transport timescale above the 5 mbar level is a hundred times longer than that obtained from the spreading of gas-phase molecules deposited after the impact of Shoemaker-Levy 9 comet. There is no explanation at this time for this discrepancy.Comment: 11 pages, 3 figures, 1 table. ApJL in pres

Quadtree-based eigendecomposition for pose estimation in the presence of occlusion and background clutter

Includes bibliographical references (pages 29-30).Eigendecomposition-based techniques are popular for a number of computer vision problems, e.g., object and pose estimation, because they are purely appearance based and they require few on-line computations. Unfortunately, they also typically require an unobstructed view of the object whose pose is being detected. The presence of occlusion and background clutter precludes the use of the normalizations that are typically applied and significantly alters the appearance of the object under detection. This work presents an algorithm that is based on applying eigendecomposition to a quadtree representation of the image dataset used to describe the appearance of an object. This allows decisions concerning the pose of an object to be based on only those portions of the image in which the algorithm has determined that the object is not occluded. The accuracy and computational efficiency of the proposed approach is evaluated on 16 different objects with up to 50% of the object being occluded and on images of ships in a dockyard

Convection during the Late Stages of Simmering in Type Ia Supernovae

Following unstable ignition of carbon, but prior to explosion, a white dwarf (WD) in a Type Ia supernova (SN Ia) undergoes a simmering phase. During this time, a central convective region grows and encompasses ~1 Msun of the WD over a timescale of ~1000 yrs, which sets the thermal and turbulent profile for the subsequent explosion. We study this time-dependent convection and summarize some of the key features that differ from the traditional, steady-state case. We show that the long conductive timescale above the convective zone and the extraction of energy to heat the WD core leads to a decrease of the convective luminosity and characteristic velocities near the convective zone's top boundary. In addition, differences in the composition between the convective core and the conductive exterior will significantly alter the location of this boundary. In this respect, we find the biggest effect due to complete 22Ne sedimentation prior to carbon ignition. These effects add diversity to the possible WD models, which may alter the properties of the SN Ia explosion.Comment: Accepted for publication in The Astrophysical Journal, 7 pages, 3 figure

Effect of selective serotonin reuptake inhibitor treatment following diagnosis of depression on suicidal behaviour risk: a target trial emulation

There is concern regarding the impact of selective serotonin reuptake inhibitors (SSRIs) on suicidal behaviour. Using the target trial framework, we investigated the effect on suicidal behaviour of SSRI treatment following a depression diagnosis. We identified 162,267 individuals receiving a depression diagnosis aged 6–59 years during 2006–2018 in Stockholm County, Sweden, after at least 1 year without antidepressant dispensation. Individuals who initiated an SSRI within 28 days of the diagnosis were assigned as SSRI initiators, others as non-initiators. Intention-to-treat and per-protocol effects were estimated; for the latter, individuals were censored when they ceased adhering to their assigned treatment strategy. We applied inverse probability weighting (IPW) to account for baseline confounding in the intention-to-treat analysis, and additionally for treatment non-adherence and time-varying confounding in the per-protocol analysis. The suicidal behaviour risk difference (RD), and risk ratio (RR) between SSRI initiators and non-initiators were estimated at 12 weeks. In the overall cohort, we found an increased risk of suicidal behaviour among SSRI initiators (intention-to-treat RR = 1.50, 95% CI = 1.25, 1.80; per-protocol RR = 1.69, 95% CI = 1.20, 2.36). In age strata, we only found evidence of an increased risk among individuals under age 25, with the greatest risk among 6–17-year-olds (intention-to-treat RR = 2.90, 95% CI = 1.72, 4.91; per-protocol RR = 3.34, 95% CI = 1.59, 7.00). Our finding of an increased suicidal behaviour risk among individuals under age 25 reflects evidence from RCTs. We found no evidence of an effect in the high-risk group of individuals with past suicidal behaviour. Further studies with information on a wider array of confounders are called for

Noninflammatory Changes of Microglia Are Sufficient to Cause Epilepsy.

Microglia are well known to play a critical role in maintaining brain homeostasis. However, their role in epileptogenesis has yet to be determined. Here, we demonstrate that elevated mTOR signaling in mouse microglia leads to phenotypic changes, including an amoeboid-like morphology, increased proliferation, and robust phagocytosis activity, but without a significant induction of pro-inflammatory cytokines. We further provide evidence that these noninflammatory changes in microglia disrupt homeostasis of the CNS, leading to reduced synapse density, marked microglial infiltration into hippocampal pyramidal layers, moderate neuronal degeneration, and massive proliferation of astrocytes. Moreover, the mice thus affected develop severe early-onset spontaneous recurrent seizures (SRSs). Therefore, we have revealed an epileptogenic mechanism that is independent of the microglial inflammatory response. Our data suggest that microglia could be an opportune target for epilepsy prevention

Spanning tree generating functions and Mahler measures

We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when differentiated. By making use of known results for logarithmic Mahler measures of certain Laurent polynomials, and proving new results, we express the STGFs as hypergeometric functions for all regular two and three dimensional lattices (and one higher-dimensional lattice). This gives closed form expressions for the spanning tree constants for all such lattices, which were previously largely unknown in all but one three-dimensional case. We show for all lattices that these can also be represented as Dirichlet $L$-series. Making the connection between spanning tree generating functions and lattice Green functions produces integral identities and hypergeometric connections, some of which appear to be new.Comment: 26 pages. Dedicated to F Y Wu on the occasion of his 80th birthday. This version has additional references, additional calculations, and minor correction

Cosmic Radiation Reduced Photo-Thermal Dispersion in Silicon Micro-Ring Resonators

We show post-spaceflight results for a silicon photonic integrated circuit micro-ring resonator. The free-carrier lifetime reduced by factor of 2 after radiation damage events in space