Hidden unity in the quantum description of matter

We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity behind seemingly unrelated physical phenomena, thus establishing exact connections between them. This leads to the fundamental concept of {\it universality} of physical phenomena, a general concept not restricted to the domain of critical behavior. Key to our framework is the concept of {\it languages} and the construction of {\it dictionaries} relating them.Comment: 10 pages 2 psfigures. Appeared in Recent Progress in Many-Body Theorie

Mosaicking with cosmic microwave background interferometers

Measurements of cosmic microwave background (CMB) anisotropies by interferometers offer several advantages over single-dish observations. The formalism for analyzing interferometer CMB data is well developed in the flat-sky approximation, valid for small fields of view. As the area of sky is increased to obtain finer spectral resolution, this approximation needs to be relaxed. We extend the formalism for CMB interferometry, including both temperature and polarization, to mosaics of observations covering arbitrarily large areas of the sky, with each individual pointing lying within the flat-sky approximation. We present a method for computing the correlation between visibilities with arbitrary pointing centers and baselines and illustrate the effects of sky curvature on the l-space resolution that can be obtained from a mosaic.Comment: 9 pages; submitted to Ap

Optimal Image Reconstruction in Radio Interferometry

We introduce a method for analyzing radio interferometry data which produces maps which are optimal in the Bayesian sense of maximum posterior probability density, given certain prior assumptions. It is similar to maximum entropy techniques, but with an exact accounting of the multiplicity instead of the usual approximation involving Stirling's formula. It also incorporates an Occam factor, automatically limiting the effective amount of detail in the map to that justified by the data. We use Gibbs sampling to determine, to any desired degree of accuracy, the multi-dimensional posterior density distribution. From this we can construct a mean posterior map and other measures of the posterior density, including confidence limits on any well-defined function of the posterior map.Comment: 41 pages, 11 figures. High resolution figures 8 and 9 available at http://www.astro.uiuc.edu/~bwandelt/SuttonWandelt200

Calibration of Low-Frequency, Wide-Field Radio Interferometers Using Delay/Delay-Rate Filtering

We present a filtering technique that can be applied to individual baselines of wide-bandwidth, wide-field interferometric data to geometrically select regions on the celestial sphere that contain primary calibration sources. The technique relies on the Fourier transformation of wide-band frequency spectra from a given baseline to obtain one-dimensional "delay images", and then the transformation of a time-series of delay images to obtain two-dimensional "delay/delay-rate images." Source selection is possible in these images given appropriate combinations of baseline, bandwidth, integration time and source location. Strong and persistent radio frequency interference (RFI) limits the effectiveness of this source selection owing to the removal of data by RFI excision algorithms. A one-dimensional, complex CLEAN algorithm has been developed to compensate for RFI-excision effects. This approach allows CLEANed, source-isolated data to be used to isolate bandpass and primary beam gain functions. These techniques are applied to data from the Precision Array for Probing the Epoch of Reionization (PAPER) as a demonstration of their value in calibrating a new generation of low-frequency radio interferometers with wide relative bandwidths and large fields-of-view.Comment: 17 pages, 6 figures, 2009AJ....138..219

Station-Keeping Requirements for Constellations of Free-Flying Collectors Used for Astronomical Imaging in Space

The accuracy requirements on station-keeping for constellations of free-flying collectors coupled as (future) imaging arrays in space for astrophysics applications are examined. The basic imaging element of these arrays is the two-element interferometer. Accurate knowledge of two quantities is required: the \textit{projected baseline length}, which is the distance between the two interferometer elements projected on the plane tranverse to the line of sight to the target; and the \textit{optical path difference}, which is the difference in the distances from that transverse plane to the beam combiner. ``Rules-of-thumb'' are determined for the typical accuracy required on these parameters. The requirement on the projected baseline length is a \textit{knowledge} requirement and depends on the angular size of the targets of interest; it is generally at a level of half a meter for typical stellar targets, decreasing to perhaps a few centimeters only for the widest attainable fields of view. The requirement on the optical path difference is a \textit{control} requirement and is much tighter, depending on the bandwidth of the signal; it is at a level of half a wavelength for narrow (few %) signal bands, decreasing to $\approx 0.2 \lambda$ for the broadest bandwidths expected to be useful. Translation of these requirements into engineering requirements on station-keeping accuracy depends on the specific details of the collector constellation geometry. Several examples are provided to guide future application of the criteria presented here. Some implications for the design of such collector constellations and for the methods used to transform the information acquired into images are discussed.Comment: 13 pages, 6 figures, accepted 6/29/07 for the August 2007 issue of PAS

Ambient noise tomography reveals basalt and sub-basalt velocity structure beneath the Faroe Islands, North Atlantic

© 2017 Elsevier B.V. Ambient noise tomography is applied to seismic data recorded by a portable array of seismographs deployed throughout the Faroe Islands in an effort to illuminate basalt sequences of the North Atlantic Igneous Province, as well as underlying sedimentary layers and Precambrian basement. Rayleigh wave empirical Green's functions between all station pairs are extracted from the data via cross-correlation of long-term recordings, with phase weighted stacking implemented to boost signal-to-noise ratio. Dispersion analysis is applied to extract inter-station group travel-times in the period range 0.5–15 s, followed by inversion for period-dependent group velocity maps. Subsequent inversion for 3-D shear wave velocity reveals the presence of significant lateral heterogeneity (up to 25%) in the crust. Main features of the final model include: (i) a near-surface low velocity layer, interpreted to be the Malinstindur Formation, which comprises subaerial compound lava flows with a weathered upper surface; (ii) a sharp velocity increase at the base of the Malinstindur Formation, which may mark a transition to the underlying Beinisvørð Formation, a thick laterally extensive layer of subaerial basalt sheet lobes; (iii) a low velocity layer at 2.5–7.0 km depth beneath the Beinisvørð Formation, which is consistent with hyaloclastites of the Lopra Formation; (iv) an upper basement layer between depths of 5–9 km and characterized by S wave velocities of approximately 3.2 km/s, consistent with low-grade metamorphosed sedimentary rocks; (v) a high velocity basement, with S wave velocities in excess of 3.6 km/s. This likely reflects the presence of a crystalline mid-lower crust of Archaean continental origin. Compared to previous interpretations of the geological structure beneath the Faroe Islands, our new results point to a more structurally complex and laterally heterogeneous crust, and provide constraints which may help to understand how continental fragments are rifted from the margins of newly forming ocean basins

Grey matter volume correlates with virtual water maze task performance in boys with androgen excess

Major questions remain about the specific role of testosterone in human spatial navigation. We tested 10 boys (mean age 11.65 years) with an extremely rare disorder of androgen excess (Familial Male Precocious Puberty, FMPP) and 40 healthy boys (mean age 12.81 years) on a virtual version of the Morris Water Maze task. In addition, anatomical magnetic resonance images were collected for all patients and a subsample of the controls (n=21) after task completion. Behaviourally, no significant differences were found between both groups. However, in the MRI analyses, grey matter volume (GMV) was correlated with performance using voxel-based morphometry (VBM). Group differences in correlations of performance with GMV were apparent in medial regions of the prefrontal cortex as well as the middle occipital gyrus and the cuneus. By comparison, similar correlations for both groups were found in the inferior parietal lobule. These data provide novel insight into the relation between testosterone and brain development and suggest that morphological differences in a spatial navigation network covary with performance in spatial ability. Published by Elsevier Ltd on behalf of IBRO

Displacement- and Timing-Noise Free Gravitational-Wave Detection

Motivated by a recently-invented scheme of displacement-noise-free gravitational-wave detection, we demonstrate the existence of gravitational-wave detection schemes insusceptible to both displacement and timing (laser) noises, and are thus realizable by shot-noise-limited laser interferometry. This is possible due to two reasons: first, gravitational waves and displacement disturbances contribute to light propagation times in different manners; second, for an N-detector system, the number of signal channels is of the order O(N^2), while the total number of timing- and displacement-noise channels is of the order O(N).Comment: 4 pages, 3 figures; mistake correcte

Obstructions to Lagrangian concordance

We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in R3. In particular, we give obstructions to a concordance from an arbitrary knot to the standard Legendrian unknot, in terms of normal rulings. We also place strong restrictions on knots that have concordances both to and from the unknot and construct an infinite family of knots with nonreversible concordances from the unknot. Finally, we use our obstructions to present a complete list of knots with up to 14 crossings that have Legendrian representatives that are Lagrangian slice

Using Augmented Feedback to Decrease Patellofemoral Pain in Runners: A Pilot study

Objective: Patellofemoral pain (PFP) is a common injury in running. The cause of patellofemoral pain is multifactorial in nature, which results varied treatment approaches for this disorder. Many studies have examined the effect of using strengthening protocols targeted at subjects’ hip and quadriceps strength. Although these studies have resulted in a reduction in short-term PFP for runners, many continue to experience PFP after undergoing these treatment strategies. A more recent theory regarding the treatment of PFP in runners involves the use of augmented verbal and visual feedback. This treatment strategy involves giving the runner scheduled visual feedback to adapt their running strategies in hopes of reducing their PFP. Much of this research has been done with experienced runners in the age range of 18-22 years old. The purpose of this study was to examine the effects of augmented verbal and real-time visual feedback on patellofemoral pain. The hypothesis was that training with the use of auditory and visual feedback would improve patellofemoral pain in this runner. In clinical practice, auditory and visual feedback to change hip and knee mechanics while running may be used as a treatment strategy for patellofemoral pain. Design and Setting: The study was conducted in a controlled laboratory setting and was an experimental design including a single-subject. Participants: The subject was a recreational female runner that was 22 years of age. The subject was recruited via a flyer distributed on campus. Once the individual agreed to participate, they were given a date to begin the study. This study was approved by the Institutional Review Board at the institution. When the subject arrived at the first meeting, the informed consent was reviewed and signed by the subject. Intervention: At the first visit, the subject was given a PFP questionnaire to determine if they were eligible for the study. For this study, the subject was classified as having PFP if they had pre-patellar or retropatellar knee pain while running that was an insidious onset, and knee pain that has lasted for at least three months. The subject also needed these symptoms to occur during two of the following functional activities: ascending/descending stairs, squatting, kneeling, jumping, and long periods of sitting. Subjects were excluded from the study if they exhibited any type of neurological disorder, injury to the lower extremity, previous surgeries involving the lower extremity, rheumatoid arthritis, heart conditions, or any other knee pathologies including patellar instability, patellofemoral dysplasia, meniscal or ligament tears, osteoarthritis, or tendinopathies. Once the subject met the inclusion criteria, they completed a visual analog scale (VAS) and a lower extremity functional scale survey (LEFS) to assess their function. The subject completed 2 training sessions per week for a total of 8 training sessions on a treadmill. During the run, an iPad was used to capture an anterior view of the subject. This image was mirrored to a television monitor to provide the subject with real time visual feedback of their running. For each session, the subject was given a five-minute warm-up at their self-selected running speed and was then asked to move to a speed that they were comfortable with running 25 minutes. This speed was constant throughout the entire study. The augmented verbal and visual feedback was given based on a schedule of “on” times and “off” times. The “on” times for the feedback stayed at a constant one minute where the “off” times became progressively longer. Main Outcome Measurement: The VAS and the LEFS served as the dependent variables in this study. The subject completed these questionnaires at the first test session and after completion of the training protocol. Results: The subject completed a four-week, eight session, verbal and real-time visual feedback training. The subject demonstrated a small improvement in LEFS scores from a pre-test score of 68 points to a post-test score of 73 points. The subject demonstrated an improvement in VAS scores from 21 millimeters (mm) to 6 mm. Conclusion: The subject’s pre- and post- training VAS scores exceeded the 14 mm minimal clinically important difference (MCID) which is important for determining improvement with PFP. However, although the subject experienced an increase in their LEFS score, this change was below the threshold of the MCID. The results from this case study design support the use of verbal and real-time visual feedback to improve the short-term perceived symptoms from PFP in recreational runners. Further research should be conducted to determine if the effects of this type of training protocol promote long-term relief of PFP, or if the need for “retraining” is necessary. Additionally, including dependent variables that actually measure hip and knee kinematics before and after this type of training may be of interest. Key words: Patellofemoral pain, lower extremity functional scale, visual analog scale, augmented feedbac