A Sensitivity and Array-Configuration Study for Measuring the Power Spectrum of 21cm Emission from Reionization

Telescopes aiming to measure 21cm emission from the Epoch of Reionization must toe a careful line, balancing the need for raw sensitivity against the stringent calibration requirements for removing bright foregrounds. It is unclear what the optimal design is for achieving both of these goals. Via a pedagogical derivation of an interferometer's response to the power spectrum of 21cm reionization fluctuations, we show that even under optimistic scenarios, first-generation arrays will yield low-SNR detections, and that different compact array configurations can substantially alter sensitivity. We explore the sensitivity gains of array configurations that yield high redundancy in the uv-plane -- configurations that have been largely ignored since the advent of self-calibration for high-dynamic-range imaging. We first introduce a mathematical framework to generate optimal minimum-redundancy configurations for imaging. We contrast the sensitivity of such configurations with high-redundancy configurations, finding that high-redundancy configurations can improve power-spectrum sensitivity by more than an order of magnitude. We explore how high-redundancy array configurations can be tuned to various angular scales, enabling array sensitivity to be directed away from regions of the uv-plane (such as the origin) where foregrounds are brighter and where instrumental systematics are more problematic. We demonstrate that a 132-antenna deployment of the Precision Array for Probing the Epoch of Reionization (PAPER) observing for 120 days in a high-redundancy configuration will, under ideal conditions, have the requisite sensitivity to detect the power spectrum of the 21cm signal from reionization at a 3\sigma level at k<0.25h Mpc^{-1} in a bin of \Delta ln k=1. We discuss the tradeoffs of low- versus high-redundancy configurations.Comment: 34 pages, 5 figures, 2 appendices. Version accepted to Ap

Hydrodynamical and radio evolution of young supernova remnant G1.9+0.3 based on the model of diffusive shock acceleration

The radio evolution of, so far the youngest known, Galactic supernova remnant (SNR) G1.9+0.3 is investigated by using three-dimensional (3D) hydrodynamic modelling and non-linear kinetic theory of cosmic ray (CR) acceleration in SNRs. We include consistent numerical treatment of magnetic field amplification (MFA) due to resonant streaming instability. Under the assumption that SNR G1.9+0.3 is the result of a Type Ia supernova explosion located near the Galactic Centre, using widely accepted values for explosion energy 10$^{51}$ erg and ejecta mass 1.4 $M_{\odot}$, the non-thermal continuum radio emission is calculated. The main purpose of this paper is to explain radio flux brightening measured over recent decades and also predict its future temporal evolution. We estimate that the SNR is now $\sim$ 120 yr old, expanding in an ambient density of 0.02 cm$^{-3}$, and explain its steep radio spectral index only by means of efficient non-linear diffusive shock acceleration (NLDSA). We also make comparison between simulations and observations of this young SNR, in order to test the models and assumptions suggested. Our model prediction of a radio flux density increase of $\sim$ 1.8 per cent yr$^{-1}$ during the past two decades agrees well with the measured values. We synthesize the synchrotron spectrum from radio to X-ray and it fits well the VLA, MOST, Effelsberg, Chandra and NuSTAR measurements. We also propose a simplified evolutionary model of the SNR in gamma rays and suggest it may be a promising target for gamma-ray observations at TeV energies with the future generation of instruments like Cherenkov Telescope Array. SNR G1.9+0.3 is the only known Galactic SNR with the increasing flux density and we present here the prediction that the flux density will start to decrease approximately 500 yr from now. We conclude that this is a general property of SNRs in free expansion phase.Comment: 16 pages, 11 figures, 1 table; corrected typos, updated reference

Search-based Model-driven Loop Optimizations for Tensor Contractions

Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. The Tensor Contraction Engine (TCE) is a high-level program synthesis system that facilitates the generation of high-performance parallel programs from tensor contraction equations. We are developing a new software infrastructure for the TCE that is designed to allow experimentation with optimization algorithms for modern computing platforms, including for heterogeneous architectures employing general-purpose graphics processing units (GPGPUs). In this dissertation, we present improvements and extensions to the loop fusion optimization algorithm, which can be used with cost models, e.g., for minimizing memory usage or for minimizing data movement costs under a memory constraint. We show that our data structure and pruning improvements to the loop fusion algorithm result in significant performance improvements that enable complex cost models being use for large input equations. We also present an algorithm for optimizing the fused loop structure of handwritten code. It determines the regions in handwritten code that are safe to be optimized and then runs the loop fusion algorithm on the dependency graph of the code. Finally, we develop an optimization framework for generating GPGPU code consisting of loop fusion optimization with a novel cost model, tiling optimization, and layout optimization. Depending on the memory available on the GPGPU and the sizes of the tensors, our framework decides which processor (CPU or GPGPU) should perform an operation and where the result should be moved. We present extensive measurements for tuning the loop fusion algorithm, for validating our optimization framework, and for measuring the performance characteristics of GPGPUs. Our measurements demonstrate that our optimization framework outperforms existing general-purpose optimization approaches both on multi-core CPUs and on GPGPUs

The Thermodynamics of Network Coding, and an Algorithmic Refinement of the Principle of Maximum Entropy

The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the rest of the elements in the distribution. Because classical entropy-based Maxent collapses cases confounding all distinct degrees of randomness and pseudo-randomness, here we take into consideration the generative mechanism of the systems considered in the ensemble to separate objects that may comply with the principle under some restriction and whose entropy is maximal but may be generated recursively from those that are actually algorithmically random offering a refinement to classical Maxent. We take advantage of a causal algorithmic calculus to derive a thermodynamic-like result based on how difficult it is to reprogram a computer code. Using the distinction between computable and algorithmic randomness we quantify the cost in information loss associated with reprogramming. To illustrate this we apply the algorithmic refinement to Maxent on graphs and introduce a Maximal Algorithmic Randomness Preferential Attachment (MARPA) Algorithm, a generalisation over previous approaches. We discuss practical implications of evaluation of network randomness. Our analysis provides insight in that the reprogrammability asymmetry appears to originate from a non-monotonic relationship to algorithmic probability. Our analysis motivates further analysis of the origin and consequences of the aforementioned asymmetries, reprogrammability, and computation.Comment: 30 page

Analysis techniques for complex-field radiation pattern measurements

Complex field measurements are increasingly becoming the standard for state-of-the-art astronomical instrumentation. Complex field measurements have been used to characterize a suite of ground, airborne, and space-based heterodyne receiver missions [1], [2], [3], [4], [5], [6], and a description of how to acquire coherent field maps for direct detector arrays was demonstrated in Davis et. al. 2017. This technique has the ability to determine both amplitude and phase radiation patterns from individual pixels on an array. Phase information helps to better characterize the optical performance of the array (as compared to total power radiation patterns) by constraining the fit in an additional plane [4]. Here we discuss the mathematical framework used in an analysis pipeline developed to process complex field radiation pattern measurements. This routine determines and compensates misalignments of the instrument and scanning system. We begin with an overview of Gaussian beam formalism and how it relates to complex field pattern measurements. Next we discuss a scan strategy using an offset in z along the optical axis that allows first-order optical standing waves between the scanned source and optical system to be removed in post-processing. Also discussed is a method by which the co- and cross-polarization fields can be extracted individually for each pixel by rotating the two orthogonal measurement planes until the signal is the co-polarization map is maximized (and the signal in the cross-polarization field is minimized). We detail a minimization function that can fit measurement data to an arbitrary beam shape model. We conclude by discussing the angular plane wave spectral (APWS) method for beam propagation, including the near-field to far-field transformation

Searches for Large-Scale Anisotropies of Cosmic Rays: Harmonic Analysis and Shuffling Technique

The measurement of large scale anisotropies in cosmic ray arrival directions is generally performed through harmonic analyses of the right ascension distribution as a function of energy. These measurements are challenging due to the small expected anisotropies and meanwhile the relatively large modulations of observed counting rates due to experimental effects. In this paper, we present a procedure based on the shuffling technique to carry out these measurements, applicable to any cosmic ray detector without any additional corrections for the observed counting rates.Comment: 22 pages, 10 figures, to appear in Astroparticle Physic

Conceptual roles of data in program: analyses and applications

Program comprehension is the prerequisite for many software evolution and maintenance tasks. Currently, the research falls short in addressing how to build tools that can use domain-specific knowledge to provide powerful capabilities for extracting valuable information for facilitating program comprehension. Such capabilities are critical for working with large and complex program where program comprehension often is not possible without the help of domain-specific knowledge.;Our research advances the state-of-art in program analysis techniques based on domain-specific knowledge. The program artifacts including variables and methods are carriers of domain concepts that provide the key to understand programs. Our program analysis is directed by domain knowledge stored as domain-specific rules. Our analysis is iterative and interactive. It is based on flexible inference rules and inter-exchangeable and extensible information storage. We designed and developed a comprehensive software environment SeeCORE based on our knowledge-centric analysis methodology. The SeeCORE tool provides multiple views and abstractions to assist in understanding complex programs. The case studies demonstrate the effectiveness of our method. We demonstrate the flexibility of our approach by analyzing two legacy programs in distinct domains

Compiling Programs for Nonshared Memory Machines

Nonshared-memory parallel computers promise scalable performance for scientific computing needs. Unfortunately, these machines are now difficult to program because the message-passing languages available for them do not reflect the computational models used in designing algorithms. This introduces a semantic gap in the programming process which is difficult for the programmer to fill. The purpose of this research is to show how nonshared-memory machines can be programmed at a higher level than is currently possible. We do this by developing techniques for compiling shared-memory programs for execution on those architectures. The heart of the compilation process is translating references to shared memory into explicit messages between processors. To do this, we first define a formal model for distribution data structures across processor memories. Several abstract results describing the messages needed to execute a program are immediately derived from this formalism. We then develop two distinct forms of analysis to translate these formulas into actual programs. Compile-time analysis is used when enough information is available to the compiler to completely characterize the data sent in the messages. This allows excellent code to be generated for a program. Run-time analysis produces code to examine data references while the program is running. This allows dynamic generation of messages and a correct implementation of the program. While the over-head of the run-time approach is higher than the compile-time approach, run-time analysis is applicable to any program. Performance data from an initial implementation show that both approaches are practical and produce code with acceptable efficiency

The Tree Inclusion Problem: In Linear Space and Faster

Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML databases. Kilpel\"ainen and Mannila [\emph{SIAM J. Comput. 1995}] presented the first polynomial time algorithm using quadratic time and space. Since then several improved results have been obtained for special cases when $P$ and $T$ have a small number of leaves or small depth. However, in the worst case these algorithms still use quadratic time and space. Let $n_S$, $l_S$, and $d_S$ denote the number of nodes, the number of leaves, and the %maximum depth of a tree $S \in \{P, T\}$. In this paper we show that the tree inclusion problem can be solved in space $O(n_T)$ and time: O(\min(l_Pn_T, l_Pl_T\log \log n_T + n_T, \frac{n_Pn_T}{\log n_T} + n_{T}\log n_{T})). This improves or matches the best known time complexities while using only linear space instead of quadratic. This is particularly important in practical applications, such as XML databases, where the space is likely to be a bottleneck.Comment: Minor updates from last tim