Iterative min-sum decoding of tail-biting codes

By invoking a form of the Perron-Frobenius theorem for the “min-sum” semi-ring, we obtain a union bound on the performance of iterative decoding of tail-biting codes. This bound shows that for the Gaussian channel, iterative decoding will be optimum, at least for high SNRs, if and only if the minimum “pseudo-distance” of the code is larger than the ordinary minimum distance

Trade Agreements as Endogenously Incomplete Contracts

We propose a model of trade agreements in which contracting is costly, and as a consequence the optimal agreement may be incomplete. In spite of its simplicity, the model yields rich predictions on the structure of the optimal trade agreement and how this depends on the fundamentals of the contracting environment. We argue that taking contracting costs explicitly into account can help explain a number of key features of real trade agreements.

A Study of Music Education In The Senior High Schools of Western Kansas

The purpose of this thesis is to present the following specific facts regarding music education in the State of Kansas. (1) To survey the general status of music in the senior high schools of Western Kansas; (2) To ascertain the professional preparation and teaching experience of the music teachers in these schools; (3) To make a survey of the teaching load of the music teacher; (4) To learn the equipment of the music departments; (5) To study the finance and financing of the music departments; (6) To survey the music courses of the senior high schools; (7) To learn of the music activities; (8) To compare the status of music education in Western Kansas with the music education as outlined by the different state courses of study, and; (9) To aid in bringing about a reorganization of the music departments of the schools of Western Kansas and show the need for music in the high schools of Kansas and especially those of Western Kansas

Chicago’s Shifting Attitude Toward Concentrations of Business Power (1934–1962)

The postwar Chicago School is commonly associated with a pro-corporate standpoint because of its position toward antitrust law and business monopoly. For example, starting in the 1950s, Aaron Director—who is often considered the father of Chicago law and economics—and his students, such as John McGee, defended the practices of the Standard Oil Company, arguing that the Supreme Court’s holding against the company in 1911 was erroneous. Since that time, Chicago has been associated with the position that competition has a self-correcting power, ensuring that monopoly power is short-lived. Members of the Chicago School did not always take a pro-corporate position. In the 1930s, for example, the respected University of Chicago professor and self-identified classical liberal, Henry Simons, described monopoly in all its forms, including “gigantic corporations” and “other agencies for price control,” as “the great enemy of democracy.” For Simons, concentrations of power undermined the necessary condition for democracy to flourish, namely, a competitive market. Besides Simons, Jacob Viner, the infamous Chicago price-theory guru and self-proclaimed classical liberal, also opposed concentrations of business power. Viner’s views on business monopoly in the late 1930s can be gleaned from his correspondence with Laird Bell, a distinguished attorney and public benefactor of Chicago. In writing Bell, Viner acknowledged that big business had some benefits, but emphasized, “[T]he mere size of business units tends almost inevitably to result in attempts to escape the impact of competition which have important—and in my opinion highly desirable—consequences for the operation of the economic system.” Viner considered this to be “the most important economic issue of our day” because “‘bigness’ . . . is the essential element in the faulty working . . . of our economic system.” This Essay traces the development of the Chicago School’s changing position toward concentrations of business power. In Parts II and III, the Essay details the Chicago School’s early position of broad hostility toward concentrations of business power and its belief that such concentrations of power needed to be eradicated by vigorous antitrust enforcement and radical corporate reform. Then, in Part IV, the Essay charts the Chicago School’s shift during the Free Market Study toward a broad acceptance of concentrations of power and a position that large corporations and industrial monopoly were relatively benign. This Essay argues that the Chicago School’s shift toward concentrations of power was a product of the postwar Chicago School’s effort to reconstitute liberalism as a bulwark against collectivist challenges and increasing government regulation of business