Infinite partition monoids

Let $\mathcal P_X$ and $\mathcal S_X$ be the partition monoid and symmetric group on an infinite set $X$. We show that $\mathcal P_X$ may be generated by $\mathcal S_X$ together with two (but no fewer) additional partitions, and we classify the pairs $\alpha,\beta\in\mathcal P_X$ for which $\mathcal P_X$ is generated by $\mathcal S_X\cup\{\alpha,\beta\}$. We also show that $\mathcal P_X$ may be generated by the set $\mathcal E_X$ of all idempotent partitions together with two (but no fewer) additional partitions. In fact, $\mathcal P_X$ is generated by $\mathcal E_X\cup\{\alpha,\beta\}$ if and only if it is generated by $\mathcal E_X\cup\mathcal S_X\cup\{\alpha,\beta\}$. We also classify the pairs $\alpha,\beta\in\mathcal P_X$ for which $\mathcal P_X$ is generated by $\mathcal E_X\cup\{\alpha,\beta\}$. Among other results, we show that any countable subset of $\mathcal P_X$ is contained in a $4$-generated subsemigroup of $\mathcal P_X$, and that the length function on $\mathcal P_X$ is bounded with respect to any generating set

Mathematically optimized cryoprotectant equilibration procedures for cryopreservation of human oocytes

Background Simple and effective cryopreservation of human oocytes would have an enormous impact on the financial and ethical constraints of human assisted reproduction. Recently, studies have demonstrated the potential for cryopreservation in an ice-free glassy state by equilibrating oocytes with high concentrations of cryoprotectants (CPAs) and rapidly cooling to liquid nitrogen temperatures. A major difficulty with this approach is that the high concentrations required for the avoidance of crystal formation (vitrification) also increase the risk of osmotic and toxic damage. We recently described a mathematical optimization approach for designing CPA equilibration procedures that avoid osmotic damage and minimize toxicity, and we presented optimized procedures for human oocytes involving continuous changes in solution composition. Methods Here we adapt and refine our previous algorithm to predict piecewise-constant changes in extracellular solution concentrations in order to make the predicted procedures easier to implement. Importantly, we investigate the effects of using alternate equilibration endpoints on predicted protocol toxicity. Finally, we compare the resulting procedures to previously described experimental methods, as well as mathematically optimized procedures involving continuous changes in solution composition. Results For equilibration with CPA, our algorithm predicts an optimal first step consisting of exposure to a solution containing only water and CPA. This is predicted to cause the cells to initially shrink and then swell to the maximum cell volume limit. To reach the target intracellular CPA concentration, the cells are then induced to shrink to the minimum cell volume limit by exposure to a high CPA concentration. For post-thaw equilibration to remove CPA, the optimal procedures involve exposure to CPA-free solutions that are predicted to cause swelling to the maximum volume limit. The toxicity associated with these procedures is predicted to be much less than that of conventional procedures and comparable to that of the corresponding procedures with continuous changes in solution composition. Conclusions The piecewise-constant procedures described in this study are experimentally facile and are predicted to be less toxic than conventional procedures for human oocyte cryopreservation. Moreover, the mathematical optimization approach described here will facilitate the design of cryopreservation procedures for other cell types.This work was supported by a National Science Foundation grant (#1150861) to Adam Higgins. This article is made openly accessible in part by an award from the Northern Illinois University Libraries’ Open Access Publishing Fund

The Robertson v. Princeton Case: Too Important to Be Left to the Lawyers

Offers comments from eleven contributors on the Robertson family's donor rights suit against the Woodrow Wilson School of Public and International Affairs for violation of donor intent. Explores its effects on and implications for the nonprofit sector

Climate change vulnerability for species—Assessing the assessments

Climate change vulnerability assessments are commonly used to identify species at risk from global climate change, but the wide range of methodologies available makes it difficult for end users, such as conservation practitioners or policymakers, to decide which method to use as a basis for decision-making. In this study, we evaluate whether different assessments consistently assign species to the same risk categories and whether any of the existing methodologies perform well at identifying climate threatened species. We compare the outputs of 12 climate change vulnerability assessment methodologies, using both real and simulated species, and validate the methods using historic data for British birds and butterflies (i.e. using historical data to assign risks and more recent data for validation). Our results show that the different vulnerability assessment methods are not consistent with one another; different risk categories are assigned for both the real and simulated sets of species. Validation of the different vulnerability assessments suggests that methods incorporating historic trend data into the assessment perform best at predicting distribution trends in subsequent time periods. This study demonstrates that climate change vulnerability assessments should not be used interchangeably due to the poor overall agreement between methods when considering the same species. The results of our validation provide more support for the use of trend-based rather than purely trait-based approaches, although further validation will be required as data become available

Ferromagnetism in laser deposited anatase Ti1−x_{1-x}Cox_{x}O_{2-\delta} films

Pulsed laser deposited films of Co doped anatase TiO2 are examined for Co substitutionality, ferromagnetism, transport, magnetotransport and optical properties. Our results show limited solubility (up to ~ 2 %) of Co in the as-grown films and formation of Co clusters thereafter. For Ti0.93Co0.07O2-d sample, which exhibits a Curie temperature (Tc) over 1180 K, we find the presence of 20-50 nm Co clusters as well as a small concentration of Co incorporated into the remaining matrix. After being subjected to the high temperature anneal during the first magnetization measurement, the very same sample shows a Tc ~ 650 K and almost full matrix incorporation of Co. This Tc is close to that of as-grown Ti0.99Co0.01O2-d sample (~ 700 K). The transport, magnetotransport and optical studies also reveal interesting effects of the matrix incorporation of Co. These results are indicative of an intrinsic Ti1-xCoxO2-d diluted magnetic semiconductor with Tc of about 650-700 K.Comment: 14 pages + 9 figure

Measurement of molecular mixing at a conjugated polymer interface by specular and off-specular neutron scattering

Measurements have been performed on thermally equilibrated conjugated-polymer/insulating-polymer bilayers, using specular and off-specular neutron reflectivity. While specular reflectivity is only sensitive to the structure normal to the sample, off-specular measurements can probe the structure of the buried polymer/polymer interface in the plane of the sample. Systematic analysis of the scattering from a set of samples with varying insulating-polymer-thickness, using the distorted-wave Born approximation (DWBA), has allowed a robust determination of the intrinsic width at the buried polymer/polymer interface. The quantification of this width (12 Å ± 4 Å) allows us to examine aspects of the conjugated polymer conformation at the interface, by appealing to self-consistent field theory (SCFT) predictions for equilibrium polymer/polymer interfaces in the cases of flexible and semi-flexible chains. This analysis enables us to infer that mixing at this particular interface cannot be described in terms of polymer chain segments that adopt conformations similar to a random walk. Instead, a more plausible explanation is that the conjugated polymer chain segments become significantly oriented in the plane of the interface. It is important to point out that we are only able to reach this conclusion following the extensive analysis of reflectivity data, followed by comparison with SCFT predictions. It is not simply the case that conjugated polymers would be expected to adopt this kind of oriented conformation at the interface, because of their relatively high chain stiffness. It is the combination of a high stiffness and a relatively narrow intrinsic interfacial width that results in a deviation from flexible chain behaviour

Analysis of the recombination landscape of hexaploid bread wheat reveals genes controlling recombination and gene conversion frequency

Background: Sequence exchange between homologous chromosomes through crossing over and gene conversion is highly conserved among eukaryotes, contributing to genome stability and genetic diversity. A lack of recombination limits breeding efforts in crops; therefore, increasing recombination rates can reduce linkage drag and generate new genetic combinations. Results: We use computational analysis of 13 recombinant inbred mapping populations to assess crossover and gene conversion frequency in the hexaploid genome of wheat (Triticum aestivum). We observe that high-frequency crossover sites are shared between populations and that closely related parents lead to populations with more similar crossover patterns. We demonstrate that gene conversion is more prevalent and covers more of the genome in wheat than in other plants, making it a critical process in the generation of new haplotypes, particularly in centromeric regions where crossovers are rare. We identify quantitative trait loci for altered gene conversion and crossover frequency and confirm functionality for a novel RecQ helicase gene that belongs to an ancient clade that is missing in some plant lineages including Arabidopsis. Conclusions: This is the first gene to be demonstrated to be involved in gene conversion in wheat. Harnessing the RecQ helicase has the potential to break linkage drag utilizing widespread gene conversions

Association of Previous Measles Infection With Markers of Acute Infectious Disease Among 9- to 59-Month-Old Children in the Democratic Republic of the Congo.

BackgroundTransient immunosuppression and increased susceptibility to other infections after measles infection is well known, but recent studies have suggested the occurrence of an "immune amnesia" that could have long-term immunosuppressive effects.MethodsWe examined the association between past measles infection and acute episodes of fever, cough, and diarrhea among 2350 children aged 9 to 59 months whose mothers were selected for interview in the 2013-2014 Democratic Republic of the Congo (DRC) Demographic and Health Survey (DHS). Classification of children who had had measles was completed using maternal recall and measles immunoglobulin G serostatus obtained via dried-blood-spot analysis with a multiplex immunoassay. The association with time since measles infection and fever, cough, and diarrhea outcomes was also examined.ResultsThe odds of fever in the previous 2 weeks were 1.80 (95% confidence interval [CI], 1.25-2.60) among children for whom measles was reported compared to children with no history of measles. Measles vaccination demonstrated a protective association against selected clinical markers of acute infectious diseases.ConclusionOur results suggest that measles might have a long-term effect on selected clinical markers of acute infectious diseases among children aged 9 to 59 months in the DRC. These findings support the immune-amnesia hypothesis suggested by others and underscore the need for continued evaluation and improvement of the DRC's measles vaccination program

Acoustic Energy and Momentum in a Moving Medium

By exploiting the mathematical analogy between the propagation of sound in a non-homogeneous potential flow and the propagation of a scalar field in a background gravitational field, various wave ``energy'' and wave ``momentum'' conservation laws are established in a systematic manner. In particular the acoustic energy conservation law due to Blokhintsev appears as the result of the conservation of a mixed co- and contravariant energy-momentum tensor, while the exchange of relative energy between the wave and the mean flow mediated by the radiation stress tensor, first noted by Longuet-Higgins and Stewart in the context of ocean waves, appears as the covariant conservation of the doubly contravariant form of the same energy-momentum tensor.Comment: 25 Pages, Late

1976 Research Progress Reports; Fruit and Vegetable Processing and Food Technology

Evaluation of tomato cultivars for processing / W. A. Gould, R. Stillabower and D. Grindell -- Using tomato seeds / J. R. Geisman -- Evaluation of snap bean cultivars for processing / W. A. Gould and R. Stillabower -- Flame sterilization of canned green beans / J. R. Mount and W. A. Gould -- Flame sterilization of canned peas / J. R. Ice, J. R. Mount and W. A. Gould -- Flame sterilization of other canned products / John Mount and W. A. Gould -- Determination of factors affecting heat penetration in flame sterilized canned whole kernel sweet corn / R. Joseph and W. A. Gould -- Geotrichum candidum: the new FDA indicator of plant sanitation for the food processing industry / J. G. Fox and W. A. Gould -- Recycling spent pickling brines ; Uses for the outer green leaves of cabbage / J. R. Geisman -- The development of a fish spread by the utilization of freshwater drum from Lake Erie / J. D. Morgan and W. A. Gould -- Development of a sausage product from Lake Erie freshwater drum / S. Hauck and W. A. Gould -- Utilization of Lake Erie freshwater drum for fish sticks / W. Stone and W. A. Gould -- Acidification and thermal processing of tripolyphosphate treated freshwater drum fillets / T. F. Chin and W. A. Gould -- Effect of lipid and fatty acid composition on keeping quality / Andrew C. Peng -- Grape lipids / P. A. Higgins and A. C. Peng -- The effect of maturation on the lipid content of 'Concord' grapes / John A. Bauman and James F. Gallander -- Stability of ascorbic acid in fortified apple juice / M. I. Mahmoud and W. A. Gould -- Wine deacidification with mixed cultures of Schizosaccharomyces pombe and Saccharomyces cerevisiae ; The effect of bacterial inoculum on malo-lactic fermentation in wines ; Concentrations of tartaric and malic acids of several wine varieties grown in Ohio / J. F. Gallander and J. F. Stetso