13 research outputs found

    Subject Index Volumes 1–200

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    International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

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    The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

    Bifurcation analysis of the Topp model

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    In this paper, we study the 3-dimensional Topp model for the dynamicsof diabetes. We show that for suitable parameter values an equilibrium of this modelbifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests thatnear this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arisethrough period doubling cascades of limit cycles.Keywords Dynamics of diabetes · Topp model · Reduced planar quartic Toppsystem · Singular point · Limit cycle · Hopf-saddle-node bifurcation · Perioddoubling bifurcation · Shilnikov homoclinic orbit · Chao

    Subject index volumes 1–92

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    Problems in Signal Processing and Inference on Graphs

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    Modern datasets are often massive due to the sharp decrease in the cost of collecting and storing data. Many are endowed with relational structure modeled by a graph, an object comprising a set of points and a set of pairwise connections between them. A ``signal on a graph'' has elements related to each other through a graph---it could model, for example, measurements from a sensor network. In this dissertation we study several problems in signal processing and inference on graphs. We begin by introducing an analogue to Heisenberg's time-frequency uncertainty principle for signals on graphs. We use spectral graph theory and the standard extension of Fourier analysis to graphs. Our spectral graph uncertainty principle makes precise the notion that a highly localized signal on a graph must have a broad spectrum, and vice versa. Next, we consider the problem of detecting a random walk on a graph from noisy observations. We characterize the performance of the optimal detector through the (type-II) error exponent, borrowing techniques from statistical physics to develop a lower bound exhibiting a phase transition. Strong performance is only guaranteed when the signal to noise ratio exceeds twice the random walk's entropy rate. Monte Carlo simulations show that the lower bound is quite close to the true exponent. Next, we introduce a technique for inferring the source of an epidemic from observations at a few nodes. We develop a Monte Carlo technique to simulate the infection process, and use statistics computed from these simulations to approximate the likelihood, which we then maximize to locate the source. We further introduce a logistic autoregressive model (ALARM), a simple model for binary processes on graphs that can still capture a variety of behavior. We demonstrate its simplicity by showing how to easily infer the underlying graph structure from measurements; a technique versatile enough that it can work under model mismatch. Finally, we introduce the exact formula for the error of the randomized Kaczmarz algorithm, a linear system solver for sparse systems, which often arise in graph theory. This is important because, as we show, existing performance bounds are quite loose.Engineering and Applied Sciences - Engineering Science

    27th Annual European Symposium on Algorithms: ESA 2019, September 9-11, 2019, Munich/Garching, Germany

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    Deep Learning in Medical Image Analysis

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    The accelerating power of deep learning in diagnosing diseases will empower physicians and speed up decision making in clinical environments. Applications of modern medical instruments and digitalization of medical care have generated enormous amounts of medical images in recent years. In this big data arena, new deep learning methods and computational models for efficient data processing, analysis, and modeling of the generated data are crucially important for clinical applications and understanding the underlying biological process. This book presents and highlights novel algorithms, architectures, techniques, and applications of deep learning for medical image analysis
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