Characterization and Inference of Graph Diffusion Processes from Observations of Stationary Signals

Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph signal processing tools cannot be used anymore. Researchers have proposed approaches to infer a graph topology from observations of signals on its nodes. Since the problem is ill-posed, these approaches make assumptions, such as smoothness of the signals on the graph, or sparsity priors. In this paper, we propose a characterization of the space of valid graphs, in the sense that they can explain stationary signals. To simplify the exposition in this paper, we focus here on the case where signals were i.i.d. at some point back in time and were observed after diffusion on a graph. We show that the set of graphs verifying this assumption has a strong connection with the eigenvectors of the covariance matrix, and forms a convex set. Along with a theoretical study in which these eigenvectors are assumed to be known, we consider the practical case when the observations are noisy, and experimentally observe how fast the set of valid graphs converges to the set obtained when the exact eigenvectors are known, as the number of observations grows. To illustrate how this characterization can be used for graph recovery, we present two methods for selecting a particular point in this set under chosen criteria, namely graph simplicity and sparsity. Additionally, we introduce a measure to evaluate how much a graph is adapted to signals under a stationarity assumption. Finally, we evaluate how state-of-the-art methods relate to this framework through experiments on a dataset of temperatures.Comment: Submitted to IEEE Transactions on Signal and Information Processing over Network

Land O' Lakes

The case begins with an examination of Land O' Lakes' diversified portfolio of businesses. The business had undergone significant changes since 1998 - it dominated market share in butter and deli cheese, had become the largest crop protection, plant nutrient, and feed manufacturer in the US, and was the fourth largest US seed company. Land O'Lakes used mergers, joint ventures, acquisitions of public and private firms, and divestitures/closing of assets to restructure its portfolio to build its portfolio. The main issue was to evaluate its diversified portfolio of businesses and find ways to improve future performance.Dairy, Agribusiness, Portfolio, Cooperative, Agribusiness, Livestock Production/Industries,

Rapid Metabolic Recovery Following Vigorous Exercise in Burrow-Dwelling Larval Sea Lampreys (\u3cem\u3ePetromyzon marinus\u3c/em\u3e)

Although the majority of the sea lamprey’s (Petromyzon marinus) life cycle is spent as a burrow-dwelling larva, or ammocoete, surprisingly little is known about intermediary metabolism in this stage of the lamprey’s life history. In this study, larval sea lampreys (ammocoetes) were vigorously exercised for 5 min, and their patterns of metabolic fuel depletion and replenishment and oxygen consumption, along with measurements of net whole-body acid and ion movements, were followed during a 4–24-h postexercise recovery period. Exercise led to initial five- to sixfold increases in postexercise oxygen consumption, which remained significantly elevated by 1.5–2.0 times for the next 3 h. Exercise also led to initial 55% drops in whole-body phosphocreatine, which was restored by 0.5 h, but no significant changes in whole-body adenosine triphosphate were observed. Whole-body glycogen concentrations dropped by 70% immediately following exercise and were accompanied by a simultaneous ninefold increase in lactate. Glycogen and lactate were quickly restored to resting levels after 0.5 and 2.0 h, respectively. The presence of an associated metabolic acidosis was supported by very high rates of metabolic acid excretion, which approached 1,000 nmol g-1 during the first 2 h of postexercise recovery. Exercise-induced ion imbalances were also rapidly alleviated, as initially high rates of net Na+ and Cl- loss (—1,200 nmol g-1h-1 and —1,800 nmol g-1h-1 respectively) were corrected within 1–2 h. Although larval sea lampreys spend most of their time burrowed, they are adept at performing and recovering from vigorous anaerobic exercise. Such attributes could be important when these animals are vigorously swimming or burrowing as they evade predators or forage

Improving mass conservation in FE approximations of the Navier Stokes equations using continuous velocity fields: A connection between grad-div stabilization and Scott--Vogelius elements

This article studies two methods for obtaining excellent mass conservation in finite element computations of the Navier-Stokes equations using continuous velocity fields. Under mild restrictions, the Scott-Vogelius element pair has recently been shown to be inf-sup stable and have optimal approximation properties, while also providing pointwise mass conservation. We present herein the first numerical tests of this element pair for the time dependent Navier-Stokes equations. We also prove that, again under these mild restrictions, the limit of the grad-div stabilized Taylor-Hood solutions to the Navier-Stokes problem converges to the Scott-Vogelius solution as the stabilization parameter tends to infinity. That is, in this setting, we provide theoretical justification that choosing the parameter large does not destroy the solution. A limiting result is also proven for the general case. Numerical tests are provided which verify the theory, and show how both Scott-Vogelius and grad-div stabilized Taylor-Hood (with large stabilization parameter) elements can provide accurate results with excellent mass conservation for Navier-Stokes approximations

Bottled Water Logistics and Forecasting

CASE OVERVIEW This case presents an interesting and very real dilemma: In 2005, Walmart committed to selling “products that sustain people and the environment.” However, despite environmental and social concerns of the category that include energy required for transport and storage, the plastic used for bottling, the potential lack of purity due to chemicals leeching from the plastic, massive waste, and the cost relative to tap water, consumers want and continue to buy bottled water. Thus the espoused goals of the company are in seeming conflict with its business model. Bottled water is an item under public scrutiny, and producers were already working on solutions such as less plastic in bottles. But what responsibility does Walmart have? Lee Scott provided the answer to this dilemma in his interview with the Wall Street Journal when he said that as long as consumers demanded bottled water, Walmart would sell it. With that backdrop, what can managers do? Overall, the case implies four possible approaches to this challenge: discontinue selling all bottled water products; change consumer demand; redesign the supply network; or Improve forecasting

Bottled Water Mini Case

CASE OVERVIEW This case presents an interesting and very real dilemma: In 2005, Walmart committed to selling “products that sustain people and the environment.” However, despite environmental and social concerns of the category that include energy required for transport and storage, the plastic used for bottling, the potential lack of purity due to chemicals leeching from the plastic, massive waste, and the cost relative to tap water, consumers want and continue to buy bottled water. Thus the espoused goals of the company are in seeming conflict with its business model. Bottled water is an item under public scrutiny, and producers were already working on solutions such as less plastic in bottles. But what responsibility does Walmart have? Lee Scott provided the answer to this dilemma in his interview with the Wall Street Journal when he said that as long as consumers demanded bottled water, Walmart would sell it. With that backdrop, what can managers do? Overall, the case implies four possible approaches to this challenge: discontinue selling all bottled water products; change consumer demand; redesign the supply network; or improve forecasting. This case is not designed for full forecasting analysis

Creating traveling waves from standing waves from the gyrotropic paramagnetic properties of Fe3+^{3+} ions in a high-Q whispering gallery mode sapphire resonator

We report observations of the gyrotropic change in magnetic susceptibility of the Fe$^{3+}$ electron paramagnetic resonance at 12.037GHz (between spin states $|1/2>$ and $|3/2>$) in sapphire with respect to applied magnetic field. Measurements were made by observing the response of the high-Q Whispering Gallery doublet (WGH$_{\pm17,0,0}$) in a Hemex sapphire resonator cooled to 5 K. The doublets initially existed as standing waves at zero field and were transformed to traveling waves due to the gyrotropic response.Comment: Accepted for publication in Phys. Rev.