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The learning speed of feed-forward neural networks is notoriously slow and has presented a bottleneck in deep learning applications for several decades. For instance, gradient-based learning algorithms, which are used extensively to train neural networks, tend to work slowly when all of the network parameters must be iteratively tuned. To counter this, both researchers and practitioners have tried introducing randomness to reduce the learning requirement. Based on the original construction of Igelnik and Pao, single layer neural-networks with random input-to-hidden layer weights and biases have seen success in practice, but the necessary theoretical justification is lacking. In this paper, we begin to fill this theoretical gap. We provide a (corrected) rigorous proof that the Igelnik and Pao construction is a universal approximator for continuous functions on compact domains, with approximation error decaying asymptotically like $O(1/\sqrt{n})$ for the number $n$ of network nodes. We then extend this result to the non-asymptotic setting, proving that one can achieve any desired approximation error with high probability provided $n$ is sufficiently large. We further adapt this randomized neural network architecture to approximate functions on smooth, compact submanifolds of Euclidean space, providing theoretical guarantees in both the asymptotic and non-asymptotic forms. Finally, we illustrate our results on manifolds with numerical experiments., Comment: 40 pages, 1 figure

We study the problem of approximately recovering signals on a manifold from one-bit linear measurements drawn from either a Gaussian ensemble, partial circulant ensemble, or bounded orthonormal ensemble and quantized using Sigma-Delta or distributed noise shaping schemes. We assume we are given a Geometric Multi-Resolution Analysis, which approximates the manifold, and we propose a convex optimization algorithm for signal recovery. We prove an upper bound on the recovery error which outperforms prior works that use memoryless scalar quantization, requires a simpler analysis, and extends the class of measurements beyond Gaussians. Finally, we illustrate our results with numerical experiments.

Adrenal insufficiency is divided into three types based on the etiology of its development. In primary adrenal insufficiency, pathology resides in end-organ failure at the level of the adrenal cortex, while in secondary and tertiary adrenal insufficiency, impairment rests in the pituitary gland and hypothalamus, respectively. Regardless of etiology, adrenal insufficiency results in a hypocortisolemic condition. While the relationship between neuropsychiatric symptoms, especially psychosis, and hypercortisolemia has been extensively documented, the development of hypocortisolemia-induced psychosis is less common. We present a case of secondary adrenal insufficiency caused by a pituitary tumor. During the course of evaluation and treatment, the patient developed a psychotic episode. We will briefly review the condition of adrenal insufficiency and propose how hypocortisolemia can result in psychosis.

In this chapter, we present a simple classification scheme that utilizes only 1-bit measurements of the training and testing data. Our method is intended to be efficient in terms of computation and storage while also allowing for a rigorous mathematical analysis. After providing some motivation, we present our method and analyze its performance for a simple data model. We also discuss extensions of the method to the hierarchical data setting, and include some further implementation considerations. Experimental evidence provided in this chapter demonstrates that our methods yield accurate classification on a variety of synthetic and real data.

The objective of this study was to assess the ability of a quantitative software-aided approach to improve the diagnostic accuracy of 18F FDG PET for Alzheimer’s dementia over visual analysis alone. Twenty normal subjects (M:F-12:8; mean age 80.6 years) and twenty mild AD subjects (M:F-12:8; mean age 70.6 years) with 18F FDG PET scans were obtained from the ADNI database. Three blinded readers interpreted these PET images first using a visual qualitative approach and then using a quantitative software-aided approach. Images were classified on two five-point scales based on normal/abnormal (1-definitely normal; 5-definitely abnormal) and presence of AD (1-definitely not AD; 5-definitely AD). Diagnostic sensitivity, specificity, and accuracy for both approaches were compared based on the aforementioned scales. The sensitivity, specificity, and accuracy for the normal vs. abnormal readings of all readers combined were higher when comparing the software-aided vs. visual approach (sensitivity 0.93 vs. 0.83 P = 0.0466; specificity 0.85 vs. 0.60 P = 0.0005; accuracy 0.89 vs. 0.72 P

A recent report postulated that the mast cell population is a significant reservoir for persistent HIV infection. Our study attempted to validate this hypothesis by quantitatively comparing the distribution of mast cells and cells expressing the HIV protein p24 in HIV infected patients. Consecutive sections of paraffin-embedded human tissues from various tissue sites were subjected to immunohistochemistry with monoclonal antibodies to mast cell tryptase, viral protein p24, and other molecules. The sub-cellular distribution of these molecules was examined, to determine whether immunoreactivities to these molecules would be co-localized within the same cells. Our study revealed that, in two immediate adjacent sections immunostained for mast cell tryptase and p24, respectively, all or nearly all tryptase and p24 expressing cells were distributed at different areas. In the single section double immunostained for mast cell tryptase and p24, 5 (1.1%) of 460 large p24 expressing cell clusters encountered showed a single or few mast cells within or adjacent to p24 expressing cell clusters, but no distinct co-localization of these two proteins was observed. Similarly, no distinct co-localization was observed in any of over 500 isolated individual mast cells and p24 expressing cells. In contrast, macrophages were consistently intermixed with or adjacent to p24 expressing cells, and p24 immunostaining were seen in the cytoplasm of a subset of macrophages. These findings suggest that tissue mast cells do not show evidence for active virus replication by the techniques employed.

Publication in the conference proceedings of SampTA, Bremen, Germany, 2013

CHDS State/Local The thesis suggests that homeland security personnel lack a uniform method to make sound and defensible ethical decisions. Building on a foundation of classical ethical thought, it is established that ethics are essential to the work of homeland security. Philosophical underpinnings include virtue ethics, deontology, utilitarianism, decision-making practices, and values common to the homeland security enterprise. Real-world case studies were examined in an attempt to understand and demonstrate what can happen if ethics are neglected, considered incompletely or incorrectly, or thoughtfully applied. Case studies include the response to Hurricane Katrina, motivation and thought behind terrorism, and the discussion on torture. Examples of good ethics programs were analyzed, including the Canadian Defense Ethics Program and the Wildfire Fire Leadership Development Program. From this research, a conceptual framework for understanding was developed. The DRIVE framework (Duty, Respect, Integrity, Vision, Ends/Expected outcomes) is proposed to give homeland security personnel the tools necessary to evaluate a situation, make a decision, and review it retrospectively. The framework is easy to remember, flexible to allow for individual differences, yet comprehensive enough to encompass classical ethical thought, common values, and decision-making. The thesis recommends developing an ethics-training program for homeland security, using DRIVE as a foundation. http://archive.org/details/ethicaldecisionm1094537684 Captain, Unified Fire Authority of Greater Salt Lake, Salt Lake City, Utah

Proceedings of the Western Farm Economics Association Thirty-sixth Annual Meeting, Laramie, WY, July 24-26, 1963