Uncovering Ramanujan's "Lost" Notebook: An Oral History

Here we weave together interviews conducted by the author with three prominent figures in the world of Ramanujan's mathematics, George Andrews, Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the "lost" notebook, Andrews and Berndt's effort of proving and editing Ramanujan's notes, and recent breakthroughs by Ono and others carrying certain important aspects of the Indian mathematician's work into the future. Also presented are historical details related to Ramanujan and his mathematics, perspectives on the impact of his work in contemporary mathematics, and a number of interesting personal anecdotes from Andrews, Berndt and Ono

Infinite spin particles

We show that Wigner's infinite spin particle classically is described by a reparametrization invariant higher order geometrical Lagrangian. The model exhibit unconventional features like tachyonic behaviour and momenta proportional to light-like accelerations. A simple higher order superversion for half-odd integer particles is also derived. Interaction with external vector fields and curved spacetimes are analyzed with negative results except for (anti)de Sitter spacetimes. We quantize the free theories covariantly and show that the resulting wave functions are fields containing arbitrary large spins. Closely related infinite spin particle models are also analyzed.Comment: 43 pages, Late

Novel plant–frugivore network on Mauritius is unlikely to compensate for the extinction of seed dispersers

Insular communities are particularly vulnerable to anthropogenic extinctions and introductions. Changes in composition of island frugivore communities may affect seed dispersal within the native plant community, risking ecological shifts and ultimately co-extinction cascades. Introduced species could potentially mitigate these risks by replacing ecological functions of extinct species, but conclusive evidence is lacking. Here, we investigate changes in plant–frugivore interactions involving frugivorous birds, mammals and reptiles in Mauritius, an oceanic island with an exceptionally well-specified frugivore community and well-described species introduction history. We demonstrate substantial losses of binary interaction partnerships (at the species level) resulting from native species extinctions, but also gains of equal numbers of novel interactions with introduced species, potentially supporting the idea that non-native species might compensate for lost seed dispersal. However, closer investigation of animal seed handling behaviour reveals that most interactions with seed dispersers are replaced by ecologically different interactions with seed predators. Therefore, restoration of seed dispersal functionality in this novel plant–frugivore community is unlikely

Charactering taper junction wear helps understand the mechanism of failure of metal on metal hip replacements.

Introduction: Taper junction material loss is the result of corrosion and mechanical wear. The significance of the taper junction material loss is highlighted by studies that compared resurfacing and total hip replacements of the same type and size. High volumes of material loss are reported, especially from the head taper, but the pattern of wear is unknown. One report characterized the material loss pattern of five tapers (n=5) into axisymmetrical and asymmetrical, along the long axis of the taper. We noticed more than two patterns on our retrievals and we set out to characterize these types and relate them to clinical variables. Methods: We retrospectively analysed retrieved cobalt-chromium tapers (n=146) using a roundness measurement machine. We also performed a corrosion classification and collected clinical data (metal ion levels, time to revision, component sizes). A non-blinded author devised a four-group classification (table). Two blinded authors classified the material loss patterns derived from the roundness measurement machine. Results: The four groups of material loss patterns Low wear (n= 62), Open-end band (n=29), Stripped material loss (n=51) and Coup-Countercoup (n=4). Kappa was 0.78 (p<0.001) in the assessment of interobserver reliability. Kruskal-Wallis test revealed: - Significantly higher volumes of wear on the taper of Stripped material loss compared to Low wear (p<0.001) and Open-end band compared to Low wear (p<0.001) groups. - Significantly higher chromium ion blood levels in the open-end band compared to the Stripped material loss group. - Significantly higher Cobalt ion blood levels in the Stripped material loss compared to the Low wear group - Significantly higher Cobalt/Chromium ration in the Open-end band compared to the Low wear group One-way ANOVA analysis revealed: - Significant difference between in the head sizes between the groups (p=0.01). Post-hoc analysis located the difference between the Low wear (median=40, range=20) and Open-end band (median=49, range=20) groups (p<0.001). - Significantly higher time to revision in the Stripped material loss compared to the Low wear group (p=0.05), in the post-hoc analysis. - Significantly higher corrosion scores in the Stripped material loss compared to the Low wear group (p<0.001) and the Open-end band compared to the Low wear group (p<0.001). Discussion: The results suggests that corrosion becomes worse over time and that the material loss pattern evolves gradually from the Low wear to Open-end band and finally to Stripped. Further analysis is required to assess the factors that affect the Coup-countercoup group

Development of an operational high refractive index resist for 193nm immersion lithography

Generation-three (Gen-3) immersion lithography offers the promise of enabling the 32nm half-pitch node. For Gen-3 lithography to be successful, however, there must be major breakthroughs in materials development: The hope of obtaining numerical aperture imaging 1.70 is dependent on a high index lens, fluid, and resist. Assuming that a fluid and a lens will be identified, this paper focuses on a possible path to a high index resist. Simulations have shown that the index of the resist should be 1.9 with any index higher than 1.9 leading to an increased process latitude. Creation of a high index resist from conventional chemistry has been shown to be unrealistic. The answer may be to introduce a high index, polarizable material into a resist that is inert relative to the polymer behavior, but will this too degrade the performance of the overall system? The specific approach is to add very high index (~2.9) nanoparticles to an existing resist system. These nanoparticles have a low absorbance; consequently the imaging of conventional 193nm resists does not degrade. Further, the nanoparticles are on the order of 3nm in diameter, thus minimizing any impact on line edge roughness (LER)

Case study: Treatment of oral and locomotory stereotypic behaviors in a mature sow

A 32-month-old female 225-kg nonpregnant cross-bred Newsham sow presented a 6-week history of stereotypic behaviors when housed in a laboratory research facility. A behavioral examination over 12 daylight hours revealed 3 main stereotypic motor patterns, namely (1) oral-nasal gate manipulation defined as placement of the snout between the bars of the pen gate with repetitive, forceful up and down movement; (2) head weaving defined as repetitive lateral head and snout movement toward the pen gates while rocking back and forth on her forequarters with hooves remaining on ground at all times; and (3) body weaving defined as repetitive shifting of body weight from one side to the other with front hooves lifting alternately off the ground. The sow performed the oral-nasal gate manipulation and head and body weaving 4.0%, 12.4%, and 6.8% of her total baseline time budget, respectively. The presumptive diagnosis was oral-nasal and locomotory stereotypies. Three treatments were used to mitigate the duration and frequency of these stereotypic behaviors. Treatment 1—Social treatment (change social stimuli by providing visual and nose-to-nose contact with different neighboring sows); Treatment 2—Forage treatment (change foraging substrates by providing peat moss as a rooting substrate); and Treatment 3—Space treatment (change pen configuration by increasing space). The sow performed the oral-nasal gate manipulation and head and body weaving 0%, 0.4%, and 0.1% of her total time budget, respectively; social treatment: the sow performed the oral-nasal gate manipulation and head and body weaving 0.9%, 15.3%, and 11.3% of her total time budget, respectively; and forage treatment: the sow performed the oral-nasal gate manipulation and head and body weaving 0.5%, 28.0%, and 15.5% of her total time budget, respectively. This study is one of the first reports to evaluate the treatment of established stereotypies in a mature sow. Results suggest the promise of environmental enrichment as an effective treatment strategy. Further research is needed to evaluate the persistence of these behavioral changes and relative importance of different environmental manipulations provided

Damage patterns at the head-stem taper junction helps understand the mechanisms of material loss

Background: Material loss at the taper junction of metal-on-metal total hip replacements (MOM THRs) has been implicated in their early failure. The mechanisms of material loss are not fully understood; analysis of the patterns of damage at the taper can help us better understand why material loss occurs at this junction. Methods: We mapped the patterns of material loss in a series of 155 MOM-THRs received at our centre by scanning the taper surface using a roundness-measuring machine. We examined these material loss maps to develop a five-tier classification system based on visual differences between different patterns. We correlated these patterns to surgical, implant and patient factors known to be important for head-stem taper damage. Results: We found that 63 implants had ‘minimal damage’ at the taper (material loss <1mm3 ) and the remaining 92 implants could be categorised by four distinct patterns of taper material loss. We found that (1) head diameter and (2) time to revision were key significant variables separating the groups. Conclusion: These material loss maps allow us to suggest different mechanisms that dominate the cause of the material loss in each pattern: (a) corrosion, (b) mechanically assisted corrosion or (c) intra-operative damage or poor size tolerances leading to toggling of trunnion in taper

Marine Phytoplankton Temperature versus Growth Responses from Polar to Tropical Waters – Outcome of a Scientific Community-Wide Study

"It takes a village to finish (marine) science these days" Paraphrased from Curtis Huttenhower (the Human Microbiome project) The rapidity and complexity of climate change and its potential effects on ocean biota are challenging how ocean scientists conduct research. One way in which we can begin to better tackle these challenges is to conduct community-wide scientific studies. This study provides physiological datasets fundamental to understanding functional responses of phytoplankton growth rates to temperature. While physiological experiments are not new, our experiments were conducted in many laboratories using agreed upon protocols and 25 strains of eukaryotic and prokaryotic phytoplankton isolated across a wide range of marine environments from polar to tropical, and from nearshore waters to the open ocean. This community-wide approach provides both comprehensive and internally consistent datasets produced over considerably shorter time scales than conventional individual and often uncoordinated lab efforts. Such datasets can be used to parameterise global ocean model projections of environmental change and to provide initial insights into the magnitude of regional biogeographic change in ocean biota in the coming decades. Here, we compare our datasets with a compilation of literature data on phytoplankton growth responses to temperature. A comparison with prior published data suggests that the optimal temperatures of individual species and, to a lesser degree, thermal niches were similar across studies. However, a comparison of the maximum growth rate across studies revealed significant departures between this and previously collected datasets, which may be due to differences in the cultured isolates, temporal changes in the clonal isolates in cultures, and/or differences in culture conditions. Such methodological differences mean that using particular trait measurements from the prior literature might introduce unknown errors and bias into modelling projections. Using our community-wide approach we can reduce such protocol-driven variability in culture studies, and can begin to address more complex issues such as the effect of multiple environmental drivers on ocean biota.EL and MKT were in part supported by the National Science Foundation (NSF) grants DEB-0845932 and OCE-0928819. TAR and KAW were supported by NSF grant OCE-0727227. UP was supported by NSF grants OCE-0926711 and OCE-1041038. PWB and RS were supported by the New Zealand Royal Society Marsden Fund and the Ministry of Science and Innovation. RMK and KH were in part supported by National Oceanic and Atmospheric Administration (NOAA) Monitoring and Event Response for Harmful Algal Blooms (MERHAB) grant NA04NOS4780239 and NSF grant OCE-0238347. DAH and FX-F were supported by NSF grants OCE-0942379, OCE-0962309, and OCE-117030687. MRM was partially supported by NSF grant OCE-0722395 and a NOAA The Ecology and Oceanography of Harmful Algal Blooms (ECOHAB) grant NA06NO54780246. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript