About Phase: Synthetic Aperture Radar and the Phase Retrieval Problem

Synthetic aperture radar (SAR) uses relative motion to produce fine resolution images from microwave frequencies and is a useful tool for regular monitoring and mapping applications. Unfortunately, if target distance is estimated poorly, then phase errors are incurred in the data, producing a blurry reconstruction of the image. In this thesis, we introduce a new multistatic methodology for determining these phase errors from interferometry-inspired combinations of signals. To motivate this, we first consider a more general problem called phase retrieval, in which a signal is reconstructed from linear measurements whose phases are either unreliable or unavailable. We make significant theoretical progress on the phase retrieval problem, to include characterizing injectivity in the complex case, devising the theory of almost injectivity, and performing a stability analysis. We then apply certain ideas from phase retrieval to resolve phase errors in SAR. Specifically, we use bistatic techniques to measure relative phases, and then we apply a graph-theoretic phase retrieval algorithm to recover the phase errors. We conclude by devising an image reconstruction procedure based on this algorithm, and we provide simulations that demonstrate stability to noise

Phase retrieval from very few measurements

In many applications, signals are measured according to a linear process, but the phases of these measurements are often unreliable or not available. To reconstruct the signal, one must perform a process known as phase retrieval. This paper focuses on completely determining signals with as few intensity measurements as possible, and on efficient phase retrieval algorithms from such measurements. For the case of complex M-dimensional signals, we construct a measurement ensemble of size 4M-4 which yields injective intensity measurements; this is conjectured to be the smallest such ensemble. For the case of real signals, we devise a theory of "almost" injective intensity measurements, and we characterize such ensembles. Later, we show that phase retrieval from M+1 almost injective intensity measurements is NP-hard, indicating that computationally efficient phase retrieval must come at the price of measurement redundancy.Comment: 18 pages, 1 figur

Saving phase: Injectivity and stability for phase retrieval

Recent advances in convex optimization have led to new strides in the phase retrieval problem over finite-dimensional vector spaces. However, certain fundamental questions remain: What sorts of measurement vectors uniquely determine every signal up to a global phase factor, and how many are needed to do so? Furthermore, which measurement ensembles lend stability? This paper presents several results that address each of these questions. We begin by characterizing injectivity, and we identify that the complement property is indeed a necessary condition in the complex case. We then pose a conjecture that 4M-4 generic measurement vectors are both necessary and sufficient for injectivity in M dimensions, and we prove this conjecture in the special cases where M=2,3. Next, we shift our attention to stability, both in the worst and average cases. Here, we characterize worst-case stability in the real case by introducing a numerical version of the complement property. This new property bears some resemblance to the restricted isometry property of compressed sensing and can be used to derive a sharp lower Lipschitz bound on the intensity measurement mapping. Localized frames are shown to lack this property (suggesting instability), whereas Gaussian random measurements are shown to satisfy this property with high probability. We conclude by presenting results that use a stochastic noise model in both the real and complex cases, and we leverage Cramer-Rao lower bounds to identify stability with stronger versions of the injectivity characterizations.Comment: 22 page

Development of a SimpleProbe real-Time PCR Assay for rapid detection and identification of the US novel urethrotropic clade of Neisseria meningitidis ST-11 (US_NmUC)

Urethritis, or inflammation of the urethra, is one of the most common reasons men seek clinical care. Sexually transmitted pathogens including Neisseria gonorrhoeae are responsible for over half of the symptomatic urethritis cases in U.S. men. Recently, clinics in Indianapolis, Columbus, Atlanta, and other U.S. cities began to note increasing numbers of men presenting with urethritis and Gram-negative intracellular diplococci in their urethral smears who test negative for N. gonorrhoeae. Many of these discordant cases, which have periodically reached highs of more than 25% of presumed gonococcal cases in some sexually transmitted infection clinics in the U.S. Midwest, are infected with strains in a novel urethrotropic clade of Neisseria meningitidis ST-11 (US_NmUC). However, no cultivation-independent tests are available for the US_NmUC strains, and prior studies relied on microbial culture and genome sequencing to identify them. Here, we describe a PCR test that can identify the US_NmUC strains and distinguish them from commensal and invasive N. meningitidis strains as well as N. gonorrhoeae. Our SimpleProbe®-based real-time PCR assay targets a conserved nucleotide substitution in a horizontally acquired region of US_NmUC strain genomes. We applied the assay to 241 urine specimens whose microbial compositions had previously been determined by deep shotgun metagenomic sequencing. The assay detected the single US_NmUC positive case in this cohort, with no false positives. Overall, our simple and readily adaptable assay could facilitate investigation of the pathogenesis and epidemiology of the US_NmUC clade

Nonlinear terahertz metamaterials via field-enhanced carrier dynamics in GaAs

We demonstrate nonlinear metamaterial split ring resonators (SRRs) on GaAs at terahertz frequencies. For SRRs on doped GaAs films, incident terahertz radiation with peak fields of ~20 - 160 kV/cm drives intervalley scattering. This reduces the carrier mobility and enhances the SRR LC response due to a conductivity decrease in the doped thin film. Above ~160 kV/cm, electric field enhancement within the SRR gaps leads to efficient impact ionization, increasing the carrier density and the conductivity which, in turn, suppresses the SRR resonance. We demonstrate an increase of up to 10 orders of magnitude in the carrier density in the SRR gaps on semi-insulating GaAs substrate. Furthermore, we show that the effective permittivity can be swept from negative to positive values with increasing terahertz field strength in the impact ionization regime, enabling new possibilities for nonlinear metamaterials.Comment: 5 pages, 4 figure

Development of an Indirect ELISA, Blocking ELISA, Fluorescent Microsphere Immunoassay and Fluorescent Focus Neutralization Assay for Serologic Evaluation of Exposure to North American Strains of Porcine Epidemic Diarrhea Virus

Recent, severe outbreaks of porcine epidemic diarrhea virus (PEDV) in Asia and North America highlight the need for well-validated diagnostic tests for the identification of PEDV infected animals and evaluation of their immune status to this virus. PEDV was first detected in the U.S. in May 2013 and spread rapidly across the country. Some serological assays for PEDV have been previously described, but few were readily available in the U.S. Several U.S. laboratories quickly developed indirect fluorescent antibody (IFA) assays for the detection of antibodies to PEDV in swine serum, indicating prior exposure. However, the IFA has several disadvantages, including low throughput and relatively subjective interpretation. Different serologic test formats have advantages and disadvantages, depending on the questions being asked, so a full repertoire of tests is useful. Therefore, the objective of this study was to develop and validate multiple improved serological assays for PEDV, including an indirect ELISA (iELISA); a highly specific monoclonal antibody-based blocking ELISA (bELISA); fluorescent microsphere immunoassays (FMIA) that can be multiplexed to monitor exposure to multiple antigens and pathogens simultaneously; and a fluorescent focus neutralization assay (FFN) to measure functional virus neutralizing antibodies

An Evaluation of Porcine Epidemic Diarrhea Virus Survival in Individual Feed Ingredients in the Presence or Absence of a Liquid Antimicrobial

Background: Contaminated complete feed and porcine plasma are risk factors for PEDV introduction to farms and a liquid antimicrobial has been proven useful for reducing risk. This study provides information on the survivability of PEDV across common swine feed ingredients in the presence or absence of the liquid antimicrobial.Results: Eighteen ingredients commonly included in commercial swine diets were selected, including 3 grain sources (corn, soybean meal (SBM), dried distillers grains with solubles (DDGS)), 5 porcine by-products (spray-dried plasma, purified plasma, intestinal mucosa, meat and bone meal and red blood cells (RBCs)), 3 vitamin/trace mineral (VTM) mixes (sow, nursery, finishing), 2 fat sources (choice white grease and soy oil), 3 synthetic amino acids (lysine HCL, D/L methionine, threonine), as well as limestone and dry choline chloride. Complete feed and stock PEDV served as controls. Thirty grams of each ingredient were inoculated with 2 mL PEDV. A matched set of samples were treated with the formaldehyde-based liquid antimicrobial SalCURB® (LA). All samples (n = 320) were stored outdoors under winter time ambient conditions for 30 days. Samples were submitted on 1, 7, 14 and 30 days post-inoculation (DPI) and tested by PCR and virus isolation (VI). All VI-negative samples were tested by swine bioassay. Viable PEDV was detected by VI or swine bioassay at 1, 7, 14 and 30 DPI from SBM, DDGS, meat & bone meal, RBCs, lysine HCL, D/L methionine, choice white grease, choline chloride, complete feed and stock virus control and at 7 DPI in limestone and at 14 DPI in threonine. Supplementary testing of complete feed and SBM indicated viable virus out to 45 and 180 DPI, respectively. All other samples were negative by VI and bioassay. In contrast, treatment with LA inactivated PEDV across all ingredients on 1 DPI and induced RNA reduction over time.Conclusions: Under the conditions of this study, PEDV viability in feed was influenced by ingredient with extended survival in SBM. Furthermore, LA treatment rendered virus inactive, independent of ingredient type

You’re Having Fun When Time Flies: The Hedonic Consequences of Subjective Time Progression

Seven studies tested the hypothesis that people use subjective time progression in hedonic evaluation. When people believe that time has passed unexpectedly quickly, they rate tasks as more engaging, noises as less irritating, and songs as more enjoyable. We propose that felt time distortion operates as a metacognitive cue that people implicitly attribute to their enjoyment of an experience (i.e., time flew, so the experience must have been fun). Consistent with this attribution account, the effects of felt time distortion on enjoyment ratings were moderated by the need for attribution, the strength of the “time flies” naive theory, and the presence of an alternative attribution. These findings suggest a previously unexplored process through which subjective time progression can influence the hedonic evaluation of experiences

Photoperiod Manipulation Reveals a Light-Driven Component to Daily Patterns of Ventilation in Male C57Bl/6J Mice

Obstructive sleep apnea is a common sleep disorder that increases risk for cardiovascular disease and mortality. The severity of sleep-disordered breathing in obstructive sleep apnea patients fluctuates with the seasons, opening the possibility that seasonal changes in light duration, or photoperiod, can influence mechanisms of breathing. Photoperiod can have profound effects on internal timekeeping and can reshape metabolic rhythms in mammals. While the daily rhythm in ventilation is largely shaped by the metabolic rate, less is known about whether ventilatory rhythms are altered in accordance with metabolism under different photoperiods. Here, we investigate the relationship between ventilation and metabolism under different photoperiods using whole-body plethysmography and indirect calorimetry. We find that the daily timing of ventilation is chiefly synchronized to dark onset and that light cues are important for maintaining daily ventilatory rhythms. Moreover, changes in ventilatory patterns are not paralleled by changes in oxygen consumption, energy expenditure, or respiratory exchange rate under different photoperiods. We conclude that ventilatory patterns are not only shaped by the metabolic rate and circadian timing but are also influenced by other light-driven factors. Collectively, these findings have clinical implications for the seasonal variations in sleep-disordered breathing found in individuals with obstructive sleep apnea