The integral as an average on a group of translations in a subinvariant measure space

Thesis (Ph.D.)--Boston University.If for each i the sequence of points is a finite group if G1 C Gi+l for all i we call the sequence a monotonic sequence of finite groups. Given a measurable group (X,S,1l) with summable on X and a monotonic sequence of finite groups in X, then as Maker has shown, (1) Limit exists a.e. (almost everywhere) and is denoted by f(x) (2) f(x+an)=f(x) for all n (3) f(x) is summable [TRUNCATED

Post-Retirement Adjustments of Pension Benefits

This paper examines why pension plans increased their liabflities by giving benefit increases to persons no longer working even though almost al lof them were not required to do so by any legally enforceable contract. In our model workers and firms have implicit contracts under which post-retirement increases in benefits are purchased by workers through lower wages or initial benefits. Such arrangements permit both plans and workersto share the risk of uncertain rates of return. They also allow beneficiaries to invest at a higher net rate of return than they could obtain elsewhere because of tax advantages and, in large plans, economies of scale. We also discuss how post-retirement adjustments can be used to influence turnover. Some empirical implications of the model are tested over a sample of beneficiaries of defined benefit plans. The major empirical findings are:(1) There is strong evidence of compensating differentials in final salary and initial pension benefits for beneficiaries receiving post-retirement adjustments.(2) Regardless of how the size of pension plans is measured(beneficiaries, participants, amount of benefits paid), large pension plans provide larger post-retirement benefit increases.(3) Beneficiaries of collectively bargained plans are more likelyto receive benefit increases and, among those receiving benefit increases, receive larger increases.(4) Benefit increases are larger in percentage terms for those who have been retired the longest and for those with the most years of service.

Emergence of integrated institutions in a large population of self-governing communities

Most aspects of our lives are governed by large, highly developed institutions that integrate several governance tasks under one authority structure. But theorists differ as to the mechanisms that drive the development of such concentrated governance systems from rudimentary beginnings. Is the emergence of integrated governance schemes a symptom of consolidation of authority by small status groups? Or does integration occur because a complex institution has more potential responses to a complex environment? Here we examine the emergence of complex governance regimes in 5,000 sovereign, resource-constrained, self-governing online communities, ranging in scale from one to thousands of users. Each community begins with no community members and no governance infrastructure. As communities grow, they are subject to selection pressures that keep better managed servers better populated. We identify predictors of community success and test the hypothesis that governance complexity can enhance community fitness. We find that what predicts success depends on size: changes in complexity predict increased success with larger population servers. Specifically, governance rules in a large successful community are more numerous and broader in scope. They also tend to rely more on rules that concentrate power in administrators, and on rules that manage bad behavior and limited server resources. Overall, this work is consistent with theories that formal integrated governance systems emerge to organize collective responses to interdependent resource management problems, especially as factors such as population size exacerbate those problems.Comment: contains supplemen

Spatial processing is frequency-specific in auditory cortex but not in the midbrain

The cochlea behaves like a bank of band-pass filters, segregating information into different frequency channels. Some aspects of perception reflect processing within individual channels, but others involve the integration of information across them. One instance of this is sound localization, which improves with increasing bandwidth. The processing of binaural cues for sound location has been extensively studied. However, while the advantage conferred by bandwidth is clear we currently know little about how this additional information is combined to form our percept of space. We investigated the ability of cells in the auditory system of guinea pigs to compare interaural level differences (ILDs), a key localization cue, between tones of disparate frequencies in each ear. Cells in auditory cortex, believed to be integral to ILD processing (Excitatory from one ear, Inhibitory from the other: EI cells), separately compare ILDs over restricted frequency ranges, not consistent with their monaural tuning. In contrast, cortical EE (Excitatory from both ears) cells showed no evidence of frequency-specific processing. Both cell types are explained by a model in which ILDs are computed within separate frequency channels and subsequently combined in a single cortical cell. Interestingly, ILD processing in all inferior colliculus cell types (EE and EI) is largely consistent with processing within single matched frequency channels from each ear. Our data suggests a clear constraint on the way that localisation cues are integrated: cortical ILD tuning to broadband sounds is a composite of separate frequency-specific binaurally sensitive channels. This frequency-specific processing appears after the midbrain