Rademacher's infinite partial fraction conjecture is (almost certainly) false

In his book \emph{Topics in Analytic Number Theory}, Hans Rademacher conjectured that the limits of certain sequences of coefficients that arise in the ordinary partial fraction decomposition of the generating function for partitions of integers into at most $N$ parts exist and equal particular values that he specified. Despite being open for nearly four decades, little progress has been made toward proving or disproving the conjecture, perhaps in part due to the difficulty in actually computing the coefficients in question. In this paper, we provide a fast algorithm for calculating the Rademacher coefficients, a large amount of data, direct formulas for certain collections of Rademacher coefficients, and overwhelming evidence against the truth of the conjecture. While the limits of the sequences of Rademacher coefficients do not exist (the sequences oscillate and attain arbitrarily large positive and negative values), the sequences do get very close to Rademacher's conjectured limits for certain (predictable) indices in the sequences

Hearing without listening: attending to a quiet audiobook

Careful systematic tests of hearing ability may miss the cognitive consequences of sub-optimal hearing when listening in the real world. In Experiment One, sub-optimal hearing is simulated by presenting an audiobook at a quiet but discriminable level over 50 minutes. Recall of facts, words and inferences are assessed and performance compared to another group at a comfortable listening volume. At the quiet intensity, participants are able to detect, discriminate and identify spoken words but do so at a cost to sequential accuracy and fact recall when attention must be sustained over time. To exclude other interpretations, the effects are studied in Experiment Two by comparing recall to the same sentences presented in isolation. Here, the differences disappear. The results demonstrate that the cognitive consequences of listening at low volume arise when sustained attention is demanded over time

The incidence of scarring on the dorsum of the hand

When undertaking image comparison of the hand between accused and perpetrator, it is not unusual for scars to be identified on the back of the hand. To investigate the occurrence of scarring in a discreet sample, a database of 238 individuals was examined, and the dorsum of the right and left hands was gridded for each individual. The position, size and type of scar were recorded within each grid. It was found that, in general, males exhibited a higher incidence of scarring than females. However, males were more likely to show scarring on their left hand whereas females were more likely to exhibit scarring on their right hand. Contrary to the literature, scarring was not most prevalent along the borders of the hand but occurred more frequently in association with the index and middle finger corridor regions. Surgical scars were rare as were large scars whereas linear scars smaller than 6 mm were the most frequently identified. Close to half of the sample did not exhibit scarring on one hand. The importance of understanding the pattern of scarring on the back of the hand is discussed in the light of forensic image comparison analysis

Quantum Cryptography

Quantum cryptography is a new method for secret communications offering the ultimate security assurance of the inviolability of a Law of Nature. In this paper we shall describe the theory of quantum cryptography, its potential relevance and the development of a prototype system at Los Alamos, which utilises the phenomenon of single-photon interference to perform quantum cryptography over an optical fiber communications link.Comment: 36 pages in compressed PostScript format, 10 PostScript figures compressed tar fil

On being a good Bayesian

Bayesianism is fast becoming the dominant paradigm in archaeological chronology construction. This paradigm shift has been brought about in large part by widespread access to tailored computer software which provides users with powerful tools for complex statistical inference with little need to learn about statistical modelling or computer programming. As a result, we run the risk that such software will be reduced to the status of black boxes. This would be a dangerous position for our community since good, principled use of Bayesian methods requires mindfulness when selecting the initial model, defining prior information, checking the reliability and sensitivity of the software runs and interpreting the results obtained. In this article, we provide users with a brief review of the nature of the care required and offer some comments and suggestions to help ensure that our community continues to be respected for its philosophically rigorous scientific approach

The new enclosures: critical perspectives on corporate land deals

The contributions to this collection use the tools of agrarian political economy to explore the rapid growth and complex dynamics of large-scale land deals in recent years, with a special focus on the implications of big land deals for property and labour regimes, labour processes and structures of accumulation. The first part of this introductory essay examines the implications of this agrarian political economy perspective. First we explore the continuities and contrasts between historical and contemporary land grabs, before examining the core underlying debate around large- versus small-scale farming futures. Next, we unpack the diverse contexts and causes of land grabbing today, highlighting six overlapping mechanisms. The following section turns to assessing the crisis narratives that frame the justifications for land deals, and the flaws in the argument around there being excess, empty or idle land available. Next the paper turns to an examination of the impacts of land deals, and the processes of inclusion and exclusion at play, before looking at patterns of resistance and constructions of alternatives. The final section introduces the papers in the collection.ESR