Optimal control of information epidemics modeled as Maki Thompson rumors

We model the spread of information in a homogeneously mixed population using the Maki Thompson rumor model. We formulate an optimal control problem, from the perspective of single campaigner, to maximize the spread of information when the campaign budget is fixed. Control signals, such as advertising in the mass media, attempt to convert ignorants and stiflers into spreaders. We show the existence of a solution to the optimal control problem when the campaigning incurs non-linear costs under the isoperimetric budget constraint. The solution employs Pontryagin's Minimum Principle and a modified version of forward backward sweep technique for numerical computation to accommodate the isoperimetric budget constraint. The techniques developed in this paper are general and can be applied to similar optimal control problems in other areas. We have allowed the spreading rate of the information epidemic to vary over the campaign duration to model practical situations when the interest level of the population in the subject of the campaign changes with time. The shape of the optimal control signal is studied for different model parameters and spreading rate profiles. We have also studied the variation of the optimal campaigning costs with respect to various model parameters. Results indicate that, for some model parameters, significant improvements can be achieved by the optimal strategy compared to the static control strategy. The static strategy respects the same budget constraint as the optimal strategy and has a constant value throughout the campaign horizon. This work finds application in election and social awareness campaigns, product advertising, movie promotion and crowdfunding campaigns. (C) 2014 Elsevier B.V. All rights reserved.

William Francis Thompson (1888–1965): a Preeminent Fishery Biologist of the Early and Mid Twentieth Century

William Francis Thompson (1888–1965) was a preeminent fishery scientist of the early to mid twentieth century. Educated at Stanford University in California (B.A. 1911, Ph.D. 1930), Thompson conducted pioneering research on the Pacific halibut, Hippoglossus stenolepis, from 1914 to 1917 for the British Columbia Provincial Fisheries Department. He then directed marine fisheries research for the State of California from 1917 to 1924, was Director of Investigations for the International Fisheries Commission from 1924 to 1939, and Director of the International Pacific Salmon Fisheries Commission from 1937 to 1942. He was also Director of the School of Fisheries, University of Washing-ton, Seattle, from 1930 to 1947. Thompson was the founding director in 1947 of the Fisheries Research Institute at the University of Washington and served in that capacity until his retirement in 1958. He was a dominant figure in fisheries research of the Pacific Northwest and influenced a succession of fishery scientists with his yield-based analysis of fishery stocks, as opposed to studying the fishes’environment. Will Thompson was also a major figure in education, and many of his former students attained leadership positions in fisheries research and administration.

William Francis Thompson (1888–1965) and His Pioneering Studies of the Pacific Halibut, Hippoglossus stenolepis

William Francis Thompson (1888–1965), as a temporary employee of the British Columbia Provincial Fisheries Department, was assigned in 1914 to under-take full-time studies of the Pacific halibut, Hippoglossus stenolepis. The fishery was showing signs of depletion, so Thompson undertook the inquiry into this resource, the first intensive study on the Pacific halibut. Three years later, Thompson, working alone, had provided a basic foundation of knowledge for the subsequent management of this resource. He published seven land-mark papers on this species, and this work marked the first phase of a career in fisheries science that was to last nearly 50 years.

William Francis Thompson (1888–1965) and the Dawn of Marine Fisheries Research in Californ

William Francis Thompson (1888–1965), an early fishery biologist, joined the California Fish and Game Commission in 1917 with a mandate to investigate the marine fisheries of the state. He initiated studies on the albacore tuna, Thunnus alalunga, and the Pacific sardine, Sardinops sagax, as well as studies on other economically important marine organisms. Thompson built up a staff of fishery scientists, many of whom later attained considerable renown in their field, and he helped develop, and then direct, the commission’s first marine fisheries laboratory. During his tenure in California, he developed a personal philosophy of research that he outlined in several publications. Thompson based his approach on the yield-based analysis of the fisheries as opposed to large-scale environmental studies. He left the state agency in 1925 to direct the newly formed International Fisheries Commission (now the International Pacific Halibut Commission). William Thompson became a major figure in fisheries research in the United States, and particularly in the Pacific Northwest and Alaska, during the first half of the 20th cent

William Francis Thompson (1888–1965) and His Pioneering Studies of the Pacific Halibut, Hippoglossus stenolepis

William Francis Thompson (1888–1965), as a temporary employee of the British Columbia Provincial Fisheries Department, was assigned in 1914 to under-take full-time studies of the Pacific halibut, Hippoglossus stenolepis. The fishery was showing signs of depletion, so Thompson undertook the inquiry into this resource, the first intensive study on the Pacific halibut. Three years later, Thompson, working alone, had provided a basic foundation of knowledge for the subsequent management of this resource. He published seven land-mark papers on this species, and this work marked the first phase of a career in fisheries science that was to last nearly 50 years.

High-resolution natural recording systems: intercomparisons of the response to interannual climatic variability [abstract]

The goal of this work is to examine the properties of recording mechanisms which are common to continuously recording high-resolution natural systems in which climatic signals are imprinted and preserved as proxy records. These systems produce seasonal structures as an indirect response to climatic variability over the annual cycle. We compare the proxy records from four different high-resolution systems: the Quelccaya ice cap of the Peruvian Andes; composite tree ring growth from southern California and the southwestern United States; and the marine varve sedimentation systems in the Santa Barbara basin (off California, United States) and in the Gulf of California, Mexico. An important focus of this work is to indicate how the interannual climatic signal is recorded in a variety of different natural systems with vastly different recording mechanisms and widely separated in space. These high-resolution records are the products of natural processes which should be comparable, to some degree, to human-engineered systems developed to transmit and record physical quantities. We therefore present a simple analogy of a data recording system as a heuristic model to provide some unifying concepts with which we may better understand the formation of the records. This analogy assumes special significance when we consider that natural proxy records are the principal means to extend our knowledge of climatic variability into the past, beyond the limits of instrumentally recorded data.

John Thompson: Seeing through China

In 1848, Karl Marx predicted that a flow of cheap commodities would be the heavy artillery which would batter down all Chinese walls and open up the country to the west (Marx, 1978, p. 477). The Scottish photographer John Thomson (1837-1921) was both chronicler of and participant in the early moments of this process. Thomson was a commercial photographer who first arrived in the Far East in 1862. He earned the moniker of 'China' in a decade-long stay during which he photographed what he considered to be the key aspects of its culture and landscape. In this body of work, Illustrations of China and its People (first published in 1874) is perhaps the most comprehensive. It explores, through two hundred photographs and accompanying texts, a series of phenomena from the macro-scale of landscape, infrastructure and industry to the smaller scales of streetscapes, domestic spaces, individual portraits, and other details of everyday life. Despite his own description of the volumes as encyclopedic, Illustrations is geographically quite limited. Thomson's explorations into the hinterland proceed up the country’s principal rivers from those coastal ports which had already been wrested into western hands during the Opium Wars (of the 1840s) and subsequently opened up to trade. This is perhaps one of the reasons why Illustrations has been described as an explicitly colonial text, a guide-book for the prospective settler whose content offered the strategic knowledge of land, culture and natural resources necessary if the territorial advantages of the coastal periphery were to extended to the interior (Jeffrey, 1981, p. 64). It can also be argued, however, that Thomson’s volume offered justification for a potential colonial presence. Faced with a civilization whose history was as sophisticated as the west, it depicts a culture that is static and moribund, its addiction to traditional values an impediment to progress. While this is perhaps most explicit in the texts of Illustrations of China, it can also be seen in the images whose uniform chemical rendering also serves to make an essentially diverse culture seem homogenous. Yet it is these images that distinguish Illustrations from previous attempts to collate China’s culture and landscape. Here, the mechanical precision of his camera captures a reality that often subverts the colonial narrative, confounding stereotypes as Thomson’s mass-produced images allow another China to emerge.

Noon Recital, Joel Salsman, pianist, Music of Alan Hovhaness, February 11, 1966

Concert program for Noon Recital, Joel Salsman, pianist, Music of Alan Hovhaness, February 11, 1966