Cramér-Rao sensitivity limits for astronomical instruments: implications for interferometer design

Multiple-telescope interferometry for high-angular-resolution astronomical imaging in the optical–IR–far-IR bands is currently a topic of great scientific interest. The fundamentals that govern the sensitivity of direct-detection instruments and interferometers are reviewed, and the rigorous sensitivity limits imposed by the Cramér–Rao theorem are discussed. Numerical calculations of the Cramér–Rao limit are carried out for a simple example, and the results are used to support the argument that interferometers that have more compact instantaneous beam patterns are more sensitive, since they extract more spatial information from each detected photon. This argument favors arrays with a larger number of telescopes, and it favors all-on-one beam-combining methods as compared with pairwise combination

Systematic Framework for Reflectarray Synthesis Based on Phase Optimization

A new systematic synthesis framework for reflectarray antennas is discussed. Optimization based on the Levenberg-Marquardt algorithm is used to obtain the phase distribution of the reflection coefficients required on the reflectarray surface, in order to achieve the pattern specifications. A Local Multipoint Distribution System (LMDS) base station working in the 24.5–26.5 GHz frequency band has been proposed to evaluate the method. The 3D requirements are defined by the combination of the elevation and templates and considering a maximum acceptable ripple in the beam shaping. Some illustrative results are obtained

Analysis and Synthesis of the Dynamic Response of Retinal Neurons

theory of linear systems analysis is developed in a form directly applicable to the treatment of the Limulus retina. The dynamics of the retina may conveniently be characterized by means of a spatiotemporal transfer function, which summarizes the response of the system to moving sinusoidal gratings ( analysis ). The response of the retina to an arbitrary stimulus may then be calculated by addition of the response to suitably weighted sinusoidal stimuli ( synthesis ). Responses were obtained from the in-situ retina by means of extracellular recording of impulse activity in single optic nerve fibers. Test ommatidia were chosen in the interior of the retina, to avoid asymmetries introduced by the edge of the retina. Stimuli which varied in both space and time were produced under computer control on the screen of a display oscilloscope, and were conveyed to the Limulus eye by means of a fiber-optic taper. Transfer functions were measured using counterphase modulation of cosine gratings according to a sum-of-sinusoids temporal signal, a procedure equivalent to the use of moving gratings, for ommatidia with symmetrical receptive fields. By means of these transfer functions, the responses of the Limulus eye to visual stimuli moving at various velocities were predicted in a parameter-free Fourier synthesis calculation. There was good agreement between these predictions and the measured responses to these stimuli. A quantitative model for the dynamic, integrative action of the Limulus retina is developed, based on the original formulation for the steady state given by the Hartline- Ratliff equations. The model comprises an excitatory generator potential, and dynamic processes of self and lateral inhibition. An explicit expression for the spatiotemporal transfer function is obtained in terms of transfer functions for the generator potential, self-inhibitory, and lateral-inhibitory transductions, and spatial transforms of the lateral inhibitory kernel and the point-spread characteristic of the experimental and physiological optics. Explicit functional forms for these component transductions are adopted. The parameters which occur in these expressions serve to incorporate information about the subcellular physiology of retinal neurons into the quantitative description of the function of the retina as a whole. Procedures are described for the estimation of these parameters from empirical transfer function data. Transfer functions calculated from the model on the basis of parameters obtained with these procedures show good agreement with the corresponding empirical transfer functions. The parameter values obtained in this way are, in general, quite consistent with the results of many more direct (and frequently more invasive) measurements reported in the literature. In particular, the inhibitory kernel, as determined from our transfer function measurements, shows a small crater in the vicinity of the test-ommatidium. The dynamical model can be used to describe the response of the retina in the vicinity of its boundary, as well as in the interior. An analysis, based on the Wiener-Hopf technique, is given for the response of peripheral retinal neurons. The predictions derived from this theory were compared with experiment through the use of illumination patterns in which one half of the retina was kept in darkness, while the remaining half was presented with a moving stimulus. This procedure permitted the calibration of model transfer functions by means of methods appropriate only for interior ommatidia, while simulating the neural environment at the edge of a homogeneous retina. Significant differences between the responses to stimuli which moved toward and away from the simulated edge were observed experimentally, in good agreement with the predictions of the theory. Similar behavior was also observed at the actual anatomical boundary of the eye

Modeling, Analysis, and Optimization Issues for Large Space Structures

Topics concerning the modeling, analysis, and optimization of large space structures are discussed including structure-control interaction, structural and structural dynamics modeling, thermal analysis, testing, and design

Kinetic Intersections as a Source of Information on Rate Coefficients

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Automating Program Verification and Repair Using Invariant Analysis and Test Input Generation

Software bugs are a persistent feature of daily life---crashing web browsers, allowing cyberattacks, and distorting the results of scientific computations. One approach to improving software uses program invariants---mathematical descriptions of program behaviors---to verify code and detect bugs. Current invariant generation techniques lack support for complex yet important forms of invariants, such as general polynomial relations and properties of arrays. As a result, we lack the ability to conduct precise analysis of programs that use this common data structure. This dissertation presents DIG, a static and dynamic analysis framework for discovering several useful classes of program invariants, including (i) nonlinear polynomial relations, which are fundamental to many scientific applications; disjunctive invariants, (ii) which express branching behaviors in programs; and (iii) properties about multidimensional arrays, which appear in many practical applications. We describe theoretical and empirical results showing that DIG can efficiently and accurately find many important invariants in real-world uses, e.g., polynomial properties in numerical algorithms and array relations in a full AES encryption implementation. Automatic program verification and synthesis are long-standing problems in computer science. However, there has been a lot of work on program verification and less so on program synthesis. Consequently, important synthesis tasks, e.g., generating program repairs, remain difficult and time-consuming. This dissertation proves that certain formulations of verification and synthesis are equivalent, allowing for direct applications of techniques and tools between these two research areas. Based on these ideas, we develop CETI, a tool that leverages existing verification techniques and tools for automatic program repair. Experimental results show that CETI can have higher success rates than many other standard program repair methods

Design of Radio-Frequency Arrays for Ultra-High Field MRI

Magnetic Resonance Imaging (MRI) is an indispensable, non-invasive diagnostic tool for the assessment of disease and function. As an investigational device, MRI has found routine use in both basic science research and medicine for both human and non-human subjects. Due to the potential increase in spatial resolution, signal-to-noise ratio (SNR), and the ability to exploit novel tissue contrasts, the main magnetic field strength of human MRI scanners has steadily increased since inception. Beginning in the early 1980’s, 0.15 T human MRI scanners have steadily risen in main magnetic field strength with ultra-high field (UHF) 8 T MRI systems deemed to be insignificant risk by the FDA (as of 2016). However, at UHF the electromagnetic fields describing the collective behaviour of spin dynamics in human tissue assume ‘wave-like’ behaviour due to an increase in the processional frequency of nuclei at UHF. At these frequencies, the electromagnetic interactions transition from purely near-field interactions to a mixture of near- and far-field mechanisms. Due to this, the transmission field at UHF can produce areas of localized power deposition – leading to tissue heating – as well as tissue-independent contrast in the reconstructed images. Correcting for these difficulties is typically achieved via multi-channel radio-frequency (RF) arrays. This technology allows multiple transmitting elements to synthesize a more uniform field that can selectively minimize areas of local power deposition and remove transmission field weighting from the final reconstructed image. This thesis provides several advancements in the design and construction of these arrays. First, in Chapter 2 a general framework for modeling the electromagnetic interactions occurring inside an RF array is adopted from multiply-coupled waveguide filters and applied to a subset of decoupling problems encountered when constructing RF arrays. It is demonstrated that using classic filter synthesis, RF arrays of arbitrary size and geometry can be decoupled via coupling matrix synthesis. Secondly, in Chapters 3 and 4 this framework is extended for designing distributed filters for simple decoupling of RF arrays and removing the iterative tuning portion of utilizing decoupling circuits when constructing RF arrays. Lastly, in Chapter 5 the coupling matrix synthesis framework is applied to the construction of a conformal transmit/receive RF array that is shape optimized to minimize power deposition in the human head during any routine MRI examination