Image Sampling with Quasicrystals

We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image. Their self-similar structure can be attractive for creating sampling patterns endowed with a decorative symmetry. We present a brief general overview of the algebraic theory of cut-and-project quasicrystals based on the geometry of the golden ratio. To assess the practical utility of quasicrystal sampling, we evaluate the visual effects of a variety of non-adaptive image sampling strategies on photorealistic image reconstruction and non-photorealistic image rendering used in multiresolution image representations. For computer visualization of point sets used in image sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary materials, please visit at http://www.Eyemaginary.com/Portfolio/Publications.htm

CMB power spectra from cosmic strings: predictions for the Planck satellite and beyond

We present a significant improvement over our previous calculations of the cosmic string contribution to cosmic microwave background (CMB) power spectra, with particular focus on sub-WMAP angular scales. These smaller scales are relevant for the now-operational Planck satellite and additional sub-orbital CMB projects that have even finer resolutions. We employ larger Abelian Higgs string simulations than before and we additionally model and extrapolate the statistical measures from our simulations to smaller length scales. We then use an efficient means of including the extrapolations into our Einstein-Boltzmann calculations in order to yield accurate results over the multipole range 2 < l 3000 in the case of the temperature power spectrum, which then allows cautious extrapolation to even smaller scales. We find that a string contribution to the temperature power spectrum making up 10% of power at l=10 would be larger than the Silk-damped primary adiabatic contribution for l > 3500. Astrophysical contributions such as the Sunyaev-Zeldovich effect also become important at these scales and will reduce the sensitivity to strings, but these are potentially distinguishable by their frequency-dependence.Comment: 18 pages, 16 figure

Abelian Higgs Cosmic Strings: Small Scale Structure and Loops

Classical lattice simulations of the Abelian Higgs model are used to investigate small scale structure and loop distributions in cosmic string networks. Use of the field theory ensures that the small-scale physics is captured correctly. The results confirm analytic predictions of Polchinski & Rocha [1] for the two-point correlation function of the string tangent vector, with a power law from length scales of order the string core width up to horizon scale with evidence to suggest that the small scale structure builds up from small scales. An analysis of the size distribution of string loops gives a very low number density, of order 1 per horizon volume, in contrast with Nambu-Goto simulations. Further, our loop distribution function does not support the detailed analytic predictions for loop production derived by Dubath et al. [2]. Better agreement to our data is found with a model based on loop fragmentation [3], coupled with a constant rate of energy loss into massive radiation. Our results show a strong energy loss mechanism which allows the string network to scale without gravitational radiation, but which is not due to the production of string width loops. From evidence of small scale structure we argue a partial explanation for the scale separation problem of how energy in the very low frequency modes of the string network is transformed into the very high frequency modes of gauge and Higgs radiation. We propose a picture of string network evolution which reconciles the apparent differences between Nambu-Goto and field theory simulations.Comment: 16 pages, 17 figure

CMB power spectrum contribution from cosmic strings using field-evolution simulations of the Abelian Higgs model

We present the first field-theoretic calculations of the contribution made by cosmic strings to the temperature power spectrum of the cosmic microwave background (CMB). Unlike previous work, in which strings were modeled as idealized one-dimensional objects, we evolve the simplest example of an underlying field theory containing local U(1) strings, the Abelian Higgs model. Limitations imposed by finite computational volumes are overcome using the scaling property of string networks and a further extrapolation related to the lessening of the string width in comoving coordinates. The strings and their decay products, which are automatically included in the field theory approach, source metric perturbations via their energy-momentum tensor, the unequal-time correlation functions of which are used as input into the CMB calculation phase. These calculations involve the use of a modified version of CMBEASY, with results provided over the full range of relevant scales. We find that the string tension $\mu$ required to normalize to the WMAP 3-year data at multipole $\ell = 10$ is $G\mu = [2.04\pm0.06\textrm{(stat.)}\pm0.12\textrm{(sys.)}] \times 10^{-6}$, where we have quoted statistical and systematic errors separately, and $G$ is Newton's constant. This is a factor 2-3 higher than values in current circulation.Comment: 23 pages, 14 figures; further optimized figures for 1Mb size limit, appendix added before submission to journal, matches accepted versio

Distinguishing the “Truly National” From the “Truly Local”: Customary Allocation, Commercial Activity, and Collective Action

This Essay makes two claims about different methods of defining the expanse and limits of the Commerce Clause. My first claim is that approaches that privilege traditional subjects of state regulation are unworkable and undesirable. These approaches are unworkable in light of the frequency with which the federal government and the states regulate the same subject matter in our world of largely overlapping federal and state legislative jurisdiction. The approaches are undesirable because the question of customary allocation is unrelated to the principal reason why Congress possesses the power to regulate interstate commerce: solving collective action problems involving multiple states. These problems are evident in the way that some federal judges invoked regulatory custom in litigation over the constitutionality of the minimum coverage provision in the Patient Protection and Affordable Care Act. The areas of health insurance and health care are not of exclusive state concern, and it is impossible to lose—or to win—a competition requiring skillful lawyers or judges to describe them as more state than federal, or more federal than state. Nor is it most important what the answer is. More promising are the approaches that view congressional authority as turning on either commercial activity or collective action problems facing the states. My second claim is that these two approaches have advantages and disadvantages, and that the choice between them exemplifies the more general tension between applying rules and applying their background justifications. I have previously defended a collective action approach to Article I, Section 8. My primary purpose in this Essay is to clarify the jurisprudential stakes in adopting one method or the other and to identify the problems that advocates of each approach must address

Age‐related trends in cardiometabolic disease among adults with cerebral palsy

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/148228/1/dmcn13777_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148228/2/dmcn13777.pd

Causal Modifications of Gravity and Their Observational Bounds

Since general relativity is the unique theory of massless spin 2 particles at large distances, the most reasonable way to have significant modifications is to introduce one or more light scalars that mediate a new long-range force. Most existing studies of such scalars invoke models that exhibit some kind of "screening" at short distances to hide the force from solar system tests. However, as is well known, such modifications also exhibit superluminality, which can be interpreted as a form of acausality. In this work we explore explicitly subluminal and causal scalar field models. In particular, we study a conformally coupled scalar $\phi$, with a small coupling to matter to obey solar system bounds, and a non-canonical kinetic term $K(X)$ ($X=(\partial\phi)^2/2$) that obeys all subluminality constraints and is hyperbolic. We consider $K(X)$ that is canonical for small $X$, but beyond some nonlinear scale enters a new scaling regime of power $p$, with $1/2<p<1$ (the DBI kinetic term is the limit $p=1/2$ and a canonical scalar is $p=1$). As opposed to screening (and superluminality), this new force becomes more and more important in the regime of high densities (and subluminality). We then turn to the densest environments to put bounds on this new interaction. We compute constraints from precession in binary systems such as Hulse-Taylor, we compute corrections to neutron star hydrostatic equilibrium, and we compute power in radiation, both tensor mode corrections and the new scalar mode, which can be important during mergers.Comment: 43 pages, 5 figures. V3: Small update

Exciton Energy Transfer in Pairs of Single-Walled Carbon Nanotubes

We studied the exciton energy transfer in pairs of semiconducting nanotubes using high-resolution optical microscopy and spectroscopy on the nanoscale. Photoluminescence from large band gap nanotubes within bundles is observed with spatially varying intensities due to distance-dependent internanotube transfer. The range of efficient energy transfer is found to be limited to a few nanometers because of competing fast nonradiative relaxation responsible for low photoluminescence quantum yield

Commercially Hosted Government Payloads: Lessons from Recent Programs

In a commercially hosted operational mode, a scientific instrument or operational device is attached to a spacecraft but operates independently from the spacecraft s primary mission. Despite the expected benefits of this arrangement, there are few examples of hosted payload programs actually being executed by government organizations. The lack of hosted payload programs is largely driven by programmatic challenges, both real and perceived, rather than by technical challenges. Partly for these reasons, NASA has not sponsored a hosted payload program, in spite of the benefits and visible community interest in doing so. In the interest of increasing the use of hosted payloads across the space community, this paper seeks to alleviate concerns about hosted payloads by identifying these programmatic challenges and presenting ways in which they can be avoided or mitigated. Despite the challenges, several recent hosted payload programs have been successfully completed or are currently in progress. This paper presents an assessment of these programs, with a focus on acquisition, costs, schedules, risks, and other programmatic aspects. The hosted payloads included in this study are the Federal Aviation Administration's Wide Area Augmentation System (WAAS) payloads, United States Coast Guard's Automatic Identification System (AIS) demonstration payload, Department of Defense's IP Router In Space (IRIS) demonstration payload, the United States Air Force's Commercially Hosted Infrared Payload (CHIRP), and the Australian Defence Force's Ultra High Frequency (UHF) payload. General descriptions of each of these programs are presented along with issues that have been encountered and lessons learned from those experiences. A set of recommended approaches for future hosted payload programs is presented, with a focus on addressing risks or potential problem areas through smart and flexible contracting up front. This set of lessons and recommendations is broadly applicable to future hosted payload programs, whether they are technology demonstrations, communications systems, or operational sensors. Additionally, we present a basic cost model for commercial access to space for hosted payloads as a function of payload mas