Creating the Royal Society's Sylvester Medal

Following the death of James Joseph Sylvester in 1897, contributions were collected in order to mark his life and work by a suitable memorial. This initiative resulted in the Sylvester Medal, which is awarded triennially by the Royal Society for the encouragement of research into pure mathematics. Ironically the main advocate for initiating this medal was not a fellow mathematician but the chemist and naturalist Raphael Meldola. Religion, not mathematics, provided the link between Meldola and Sylvester; they were among the very few Jewish Fellows of the Royal Society. This paper focuses primarily on the politics of the Anglo-Jewish community and why it, together with a number of scientists and mathematicians, supported Meldola in creating the Sylvester Medal

Quaker responses to Darwin

[FIRST PARAGRAPH] In his seminal work Darwin and the General Reader (1958), Alvar Ellegird surveyed the British periodical press over the period 1859 to 1872 in order to discover how Darwin's theory had been received in a hundred publications reflecting a wide range of social, religious, and political opinion. He paid attention both to the amount of space devoted to Darwinian topics and also to each periodical's stance with respect to such issues as the theory of natural selection and the naturalistic account of the formation of humankind. In each case he summarized his findings using a numerical scale. Among the journals he examined were two Quaker periodicals- the Friend and the Friends' Quarterly Examiner-from which he concluded that Quakers paid little attention to Darwin's theory and that the few references that appeared were generally antagonistic to the new theory. The quotations Ellegird selected confirmed this judgment: for example, in characterizing the Friend as anti-Darwinian he cited an 1861 entry in which a reviewer regretted the large number of converts to Darwinism, exclaiming, "Alas, their name is legion." Despite the somewhat higher scores achieved by the Friends' Quarterly Examiner, Ellegird did not adequately distinguish between these two periodicals, which reflected significantly different sections within the British Quaker community. Rather surprisingly, he also lumped Quakers with Congregationalists, Baptists, and certain other dissenting groups that appear to have responded similarly to Darwin's theory but shared little of religious significance with Quakers. In contrast to these denominations, Unitarians scored higher but Methodists were lower still on Elleglrd's scale

Charles Singer and the founding of the British Society for the History of Science

[FIRST PARAGRAPHS] Presidential addresses offer an opportunity to reflect on the history of our subject and where the history of science stands in our own day. Such reflections are particularly appropriate with the fiftieth anniversary of the founding of the British Society for the History of Science (BSHS) which is marked in 1997. Some may consider that looking back over our past is either an unacceptable luxury or an occasion for the kind of celebration that can all too easily degenerate into hagiography and an excuse to rake over the past in a thoroughly uncritical manner." This address - and I trust the events of 1997 - will try to avoid such excesses and instead contribute to the historiography of our subject. This paper contains an all-too-sketchy account of the role of the first president, Charles Singer (1876±1960), in the founding of the BSHS. My main theme is Singer's commitment to a form of internationalism that appeared so necessary and so appealing after Europe had been shattered by Fascism and a devastating war. I shall be exploring the ways in which his background and the political events of the 1930s and 1940s shaped his vision for the history of science in the post-war era and especially his concern to found a specifically British society that would, through encouraging study of the history of science, contribute to international peace and stability. I should make clear at the outset that by focusing on Singer I will doubtless undervalue the roles of the many other people who were active in the early years of this Society. There are, without doubt, other contending narratives and ones that I hope will soon be heard. I also approach this subject with some trepidation in the realization that some of my readers will have known Singer and may themselves have been actors in the events I am discussing

Cyclic Universe and Infinite Past

We address two questions about the past for infinitely cyclic cosmology. The first is whether it can contain an infinite length null geodesic into the past in view of the Borde-Guth-Vilenkin (BGV) "no-go" theorem, The second is whether, given that a small fraction of spawned universes fail to cycle, there is an adequate probability for a successful universe after an infinite time. We give positive answers to both questions then show that in infinite cyclicity the total number of universes has been infinite for an arbitrarily long time.Comment: 7 pages. Clarification in discussion of infinite pas

Measure Recognition Problem

This is an article in mathematics, specifically in set theory. On the example of the Measure Recognition Problem (MRP) the article highlights the phenomenon of the utility of a multidisciplinary mathematical approach to a single mathematical problem, in particular the value of a set-theoretic analysis. MRP asks if for a given Boolean algebra \algB and a property $\Phi$ of measures one can recognize by purely combinatorial means if \algB supports a strictly positive measure with property $\Phi$. The most famous instance of this problem is MRP(countable additivity), and in the first part of the article we survey the known results on this and some other problems. We show how these results naturally lead to asking about two other specific instances of the problem MRP, namely MRP(nonatomic) and MRP(separable). Then we show how our recent work D\v zamonja and Plebanek (2006) gives an easy solution to the former of these problems, and gives some partial information about the latter. The long term goal of this line of research is to obtain a structure theory of Boolean algebras that support a finitely additive strictly positive measure, along the lines of Maharam theorem which gives such a structure theorem for measure algebras

A variational principle for stationary, axisymmetric solutions of Einstein's equations

Stationary, axisymmetric, vacuum, solutions of Einstein's equations are obtained as critical points of the total mass among all axisymmetric and $(t,\phi)$ symmetric initial data with fixed angular momentum. In this variational principle the mass is written as a positive definite integral over a spacelike hypersurface. It is also proved that if absolute minimum exists then it is equal to the absolute minimum of the mass among all maximal, axisymmetric, vacuum, initial data with fixed angular momentum. Arguments are given to support the conjecture that this minimum exists and is the extreme Kerr initial data.Comment: 21 page

Cloned mouse cells with natural killer function and cloned suppressor T cells express ultrastructural and biochemical features not shared by cloned inducer T cells.

We have examined the morphology, cytochemistry, and biochemistry of mouse leukocyte subsets by analyzing cloned leukocyte populations specialized to perform different immunologic functions. Cloned cells expressing high-affinity plasma membrane receptors for IgE and mediating natural killer (NK) lysis and cloned antigen-specific suppressor T cells contained prominent osmiophilic cytoplasmic granules similar by ultrastructure to those of mouse basophils. Both clones also incorporated 35SO4 into granule-associated sulfated glycosaminoglycans, expressed a characteristic ultrastructural pattern of nonspecific esterase activity, incorporated exogenous [3H]5-hydroxytryptamine, and contained cytoplasmic deposits of particulate glycogen. By contrast, cloned inducer T cells lacked cytoplasmic granules and glycogen, incorporated neither 35SO4 nor [3H]5-hydroxytryptamine, and differed from the other clones in pattern of nonspecific esterase activity. These findings establish that certain cloned cells with NK activity and cloned suppressor T cells express morphologic and biochemical characteristics heretofore associated with basophilic granulocytes. However, these clones differ in surface glycoprotein expression and immunologic function, and the full extent of the similarities and differences among these populations and basophils remains to be determined

Reachability in Parametric Interval Markov Chains using Constraints

Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are labeled with parametric intervals of probabilities. In this work, we study the difference between pIMCs and other Markov Chain abstractions models and investigate the two usual semantics for IMCs: once-and-for-all and at-every-step. In particular, we prove that both semantics agree on the maximal/minimal reachability probabilities of a given IMC. We then investigate solutions to several parameter synthesis problems in the context of pIMCs -- consistency, qualitative reachability and quantitative reachability -- that rely on constraint encodings. Finally, we propose a prototype implementation of our constraint encodings with promising results

Mast cell clones: a model for the analysis of cellular maturation.

Cloned mouse mast cells resemble, by ultrastructure, immature mast cells observed in vivo. These mast cell clones can be grown in the absence of any other cells, facilitating direct investigations of their biochemistry and function. We find that cloned mast cells express plasma membrane receptors (Fc epsilon R) that bind mouse IgE with an equilibrium constant (KA) similar to that of normal mouse peritoneal mast cells. In addition, cloned mast cells do not display detectable la antigens and cannot enhance lg secretion when added to lymphocyte cultures or mediate natural killer lysis. In the presence of 1 mM sodium butyrate, cloned mast cells stop dividing and acquire abundant electron-dense cytoplasmic granules similar to those of mature mast cells. Their histamine content increases concomitant with cytoplasmic granule maturation and may exceed that of untreated mast cells by 50-fold. Unlike peritoneal mast cells, cloned mast cells incorporate 35SO4 into chondroitin sulfates rather than heparin. These findings demonstrate that, unlike fully differentiated mouse peritoneal mast cells, cloned immature mouse mast cells contain no heparin and low levels of histamine. In addition, they establish that high-affinity Fc epsilon R are expressed early in mast cell maturation, well before completion of cytoplasmic granule synthesis and mediator storage

Stretching Semiflexible Polymer Chains: Evidence for the Importance of Excluded Volume Effects from Monte Carlo Simulation

Semiflexible macromolecules in dilute solution under very good solvent conditions are modeled by self-avoiding walks on the simple cubic lattice ($d=3$ dimensions) and square lattice ($d=2$ dimensions), varying chain stiffness by an energy penalty $\epsilon_b$ for chain bending. In the absence of excluded volume interactions, the persistence length $\ell_p$ of the polymers would then simply be $\ell_p=\ell_b(2d-2)^{-1}q_b^{-1}$ with $q_b= \exp(-\epsilon_b/k_BT)$, the bond length $\ell_b$ being the lattice spacing, and $k_BT$ is the thermal energy. Using Monte Carlo simulations applying the pruned-enriched Rosenbluth method (PERM), both $q_b$ and the chain length $N$ are varied over a wide range $(0.005 \leq q_b \leq 1, \; N \leq 50000$), and also a stretching force $f$ is applied to one chain end (fixing the other end at the origin). In the absence of this force, in $d=2$ a single crossover from rod-like behavior (for contour lengths less than $\ell_p$) to swollen coils occurs, invalidating the Kratky-Porod model, while in $d=3$ a double crossover occurs, from rods to Gaussian coils (as implied by the Kratky-Porod model) and then to coils that are swollen due to the excluded volume interaction. If the stretching force is applied, excluded volume interactions matter for the force versus extension relation irrespective of chain stiffness in $d=2$, while theories based on the Kratky-Porod model are found to work in $d=3$ for stiff chains in an intermediate regime of chain extensions. While for $q_b \ll 1$ in this model a persistence length can be estimated from the initial decay of bond-orientational correlations, it is argued that this is not possible for more complex wormlike chains (e.g. bottle-brush polymers). Consequences for the proper interpretation of experiments are briefly discussed.Comment: 23 pages, 17 figures, 2 tables, to be published in J. Chem. Phys. (2011