Cambridge Philosophical Society Research Articles

A work in progress: William Bateson's vibratory theory of repetition of parts.

In 1891 Cambridge biologist William Bateson (1861-1926) announced his idea that the symmetrical segmentation in living organisms resulted from energy peaks of some vibratory force acting on tissues during morphogenesis. He also demonstrated topographically how folding a radially symmetric organism could produce another with bilateral symmetry. Bateson attended many lectures at the Cambridge Philosophical Society and viewed mechanical models prepared by eminent physicists that illustrated how vibrations affected materials. In his subsequent research, Bateson utilized analogies and metaphors based upon his observations of nature to build a thought model on the effects of vibrations on living tissue, because he realized that the chemistry and biology of his day lacked technologies to perform actual experiments on the subject. He concluded the production of organic segmentation was both a chemical and mechanical phenomenon. By the time of his death Bateson had incorporated new ideas about embryonic organizer regions to suggest a center from which a rhythmic force emanated and then produced the observed repetitive segmentation as a common feature in living organisms.

Constructions and equivalence of Sidon spaces

Sidon spaces have been introduced by Bachoc et al. (in: Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 2017) as the q-analogue of Sidon sets. The interest on Sidon spaces has increased quickly, especially after the work of Roth et al. (IEEE Trans Inform Theory 64(6):4412–4422, 2017), in which they highlighted the correspondence between Sidon spaces and cyclic subspace codes. Up to now, the known constructions of Sidon Spaces may be divided in three families: the ones contained in the sum of two multiplicative cosets of a fixed subfield of mathbb {F}_{q^n}, the ones contained in the sum of more than two multiplicative cosets of a fixed subfield of mathbb {F}_{q^n} and finally the ones obtained as the kernel of subspace polynomials. In this paper, we will mainly focus on the first class of examples, for which we provide characterization results and we will show some new examples, arising also from some well-known combinatorial objects. Moreover, we will give a quite natural definition of equivalence among Sidon spaces, which relies on the notion of equivalence of cyclic subspace codes and we will discuss about the equivalence of the known examples.

Lgrgtest: Lagrange multiplier test after constrained maximum-likelihood estimation

Besides the Wald and likelihood-ratio tests, the Lagrange multiplier test (Rao, 1948, Mathematical Proceedings of the Cambridge Philosophical Society 44: 50–57; Aitchison and Silvey, 1958, Annals of Mathematical Statistics 29: 813–828; Silvey, 1959, Annals of Mathematical Statistics 30: 389–407) is the third canonical approach to testing hypotheses after maximum likelihood estimation. While the Stata commands test and lrtest implement the first two, Stata does not have an official command for implementing the third. The community-contributed boottest package (Roodman et al., 2019, Stata Journal 19: 4–60) focuses on methods of bootstrap inference and also implements the Lagrange multiplier test functionality. In this article, I introduce the new community-contributed postestimation command lgrgtest, which allows for straightforwardly using the Lagrange multiplier test after constrained maximum-likelihood estimation. lgrgtest is intended to be compatible with all Stata estimation commands that use maximum likelihood and allow for the options constraints(), iterate(), and from(). lgrgtest can also be used after cnsreg.

Static Spherically Symmetric Einstein-Vlasov Bifurcations of the Schwarzschild Spacetime

We construct a one-parameter family of static and spherically symmetric solutions to the Einstein-Vlasov system bifurcating from the Schwarzschild spacetime. The constructed solutions have the property that the spatial support of the matter is a finite, spherically symmetric shell located away from the black hole. Our proof is mostly based on the analysis of the set of trapped timelike geodesics and of the effective potential energy for static spacetimes close to Schwarzschild. This provides an alternative approach to the construction of static solutions to the Einstein-Vlasov system in a neighbourhood of black hole vacuum spacetimes made in Rein (in Mathematical proceedings of the cambridge philosophical society. Cambridge University Press, Cambridge, vol 115, pp 559–570, 1994).

Quantum Chromodynamics and the Precision Phenomenology of Heavy Quarks

This thesis was funded by an STFC studentship with assistance from the Cambridge Philosophical Society.

Macroevolution and phylogenomics in the adaptive radiation of Heliconiini butterflies

This author of this work was supported by Herchel Smith funds (Harvard College), Balfour Studentship (Department of Zoology, University of Cambridge), External Research Scholarship (Emmanuel College, University of Cambridge), Smithsonian Tropical Research Institution short fellowship and a grant from the Cambridge Philosophical Society. The research costs were covered by the Leverhulme Trust award and the BBSRC grant H01439X/1 to prof. Chris D. Jiggins, as well as the Panton Trust grant and the Systematics Research Fund (Systematics Association) to KMK.

How the Weak Variance of Momentum Can Turn Out to be Negative

Weak values are average quantities,therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as possible, building primarily on material from Moyal (Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, Cambridge, 1949) and Sonego (Found Phys 21(10):1135, 1991) . The weak variance is defined in terms of the Wigner function, using a standard construction from probability theory. We show this corresponds to a measurable quantity, which is not itself a weak value. It also leads naturally to a connection between the imaginary part of the weak value of momentum and the quantum potential. We study how the negativity of the Wigner function causes negative weak variances, and the implications this has on a class of `subquantum' theories. We also discuss the role of weak variances in studying determinism, deriving the classical limit from a variational principle.

A Natural History of Mathematics: George Peacock and the Making of English Algebra

In a series of papers read to the Cambridge Philosophical Society through the 1820s, the Cambridge mathematician George Peacock laid the foundation for a natural history of arithmetic that would tell a story of human progress from counting to modern arithmetic. The trajectory of that history, Peacock argued, established algebraic analysis as a form of universal reasoning that used empirically warranted operations of mind to think with symbols on paper. The science of counting would suggest arithmetic, arithmetic would suggest arithmetical algebra, and, finally, arithmetical algebra would suggest symbolic algebra. This philosophy of suggestion provided the foundation for Peacock's "principle of equivalent forms," which justified the practice of nineteenth-century English symbolic algebra. Peacock's philosophy of suggestion owed a considerable debt to the early Cambridge Philosophical Society culture of natural history. The aim of this essay is to show how that culture of natural history was constitutively significant to the practice of nineteenth-century English algebra.

Dragonfly larval polarization sensitivity as a contrast enhancer in turbid water

Dragonfly larval polarization sensitivity as a contrast enhancer in turbid water

Natural models for evolution on networks

Evolutionary dynamics has been traditionally studied in the context of homogeneous populations, mainly described by the Moran process [P. Moran, Random processes in genetics, Proceedings of the Cambridge Philosophical Society 54 (1) (1958) 60–71]. Recently, this approach has been generalized in [E. Lieberman, C. Hauert, M.A. Nowak, Evolutionary dynamics on graphs, Nature 433 (2005) 312–316] by arranging individuals on the nodes of a network (in general, directed). In this setting, the existence of directed arcs enables the simulation of extreme phenomena, where the fixation probability of a randomly placed mutant (i.e., the probability that the offspring of the mutant eventually spread over the whole population) is arbitrarily small or large. On the other hand, undirected networks (i.e., undirected graphs) seem to have a smoother behavior, and thus it is more challenging to find suppressors/amplifiers of selection, that is, graphs with smaller/greater fixation probability than the complete graph (i.e., the homogeneous population). In this paper we focus on undirected graphs. We present the first class of undirected graphs which act as suppressors of selection, by achieving a fixation probability that is at most one half of that of the complete graph, as the number of vertices increases. Moreover, we provide some generic upper and lower bounds for the fixation probability of general undirected graphs. As our main contribution, we introduce the natural alternative of the model proposed in [E. Lieberman, C. Hauert, M.A. Nowak, Evolutionary dynamics on graphs, Nature 433 (2005) 312–316]. In our new evolutionary model, all individuals interact simultaneously and the result is a compromise between aggressive and non-aggressive individuals. We prove that our new model of mutual influences admits a potential function, which guarantees the convergence of the system for any graph topology and any initial fitness vector of the individuals. Furthermore, we prove fast convergence to the stable state for the case of the complete graph, as well as we provide almost tight bounds on the limit fitness of the individuals. Apart from being important on its own, this new evolutionary model appears to be useful also in the abstract modeling of control mechanisms over invading populations in networks. We demonstrate this by introducing and analyzing two alternative control approaches, for which we bound the time needed to stabilize to the “healthy” state of the system.

Identifying genetic marker sets associated with phenotypes via an efficient adaptive score test

In recent years, genome-wide association studies (GWAS) and gene-expression profiling have generated a large number of valuable datasets for assessing how genetic variations are related to disease outcomes. With such datasets, it is often of interest to assess the overall effect of a set of genetic markers, assembled based on biological knowledge. Genetic marker-set analyses have been advocated as more reliable and powerful approaches compared with the traditional marginal approaches (Curtis and others, 2005. Pathways to the analysis of microarray data. TRENDS in Biotechnology 23, 429-435; Efroni and others, 2007. Identification of key processes underlying cancer phenotypes using biologic pathway analysis. PLoS One 2, 425). Procedures for testing the overall effect of a marker-set have been actively studied in recent years. For example, score tests derived under an Empirical Bayes (EB) framework (Liu and others, 2007. Semiparametric regression of multidimensional genetic pathway data: least-squares kernel machines and linear mixed models. Biometrics 63, 1079-1088; Liu and others, 2008. Estimation and testing for the effect of a genetic pathway on a disease outcome using logistic kernel machine regression via logistic mixed models. BMC bioinformatics 9, 292-2; Wu and others, 2010. Powerful SNP-set analysis for case-control genome-wide association studies. American Journal of Human Genetics 86, 929) have been proposed as powerful alternatives to the standard Rao score test (Rao, 1948. Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Mathematical Proceedings of the Cambridge Philosophical Society, 44, 50-57). The advantages of these EB-based tests are most apparent when the markers are correlated, due to the reduction in the degrees of freedom. In this paper, we propose an adaptive score test which up- or down-weights the contributions from each member of the marker-set based on the Z-scores of their effects. Such an adaptive procedure gains power over the existing procedures when the signal is sparse and the correlation among the markers is weak. By combining evidence from both the EB-based score test and the adaptive test, we further construct an omnibus test that attains good power in most settings. The null distributions of the proposed test statistics can be approximated well either via simple perturbation procedures or via distributional approximations. Through extensive simulation studies, we demonstrate that the proposed procedures perform well in finite samples. We apply the tests to a breast cancer genetic study to assess the overall effect of the FGFR2 gene on breast cancer risk.

Stationarity of the transition probabilities in the Markov chain formulation of owner payments on projects

Stationarity of the transition probabilities in the Markov chain formulation of owner payments on projects

Institutions and innovation: experimental zoology and the creation of theBritish Journal of Experimental Biologyand the Society for Experimental Biology

AbstractThis paper throws light on the development of experimental zoology in Britain by focusing on the establishment of theBritish Journal of Experimental Biology(BJEB) and the Society for Experimental Biology (SEB) in 1923. The key actors in this story were Lancelot T. Hogben, Julian S. Huxley and Francis A.E. Crew, who started exploring the possibility of establishing an experimentally oriented zoological journal in 1922. In order to support theBJEBand further the cause of the experimental approach, Hogben, Crew, Huxley and their colleagues decided to found a society, which led to the formation of the SEB. From its inception the journal was plagued with difficulties that led to the merger of theBJEBand theBiological Proceedingsof the Cambridge Philosophical Society in the autumn of 1925. Also discussed are the views that the leading proponents of experimental zoology in Britain in the 1920s expressed towards morphology and how their views further complicate the already much modified ‘revolt from morphology’ thesis.

Origin and Characteristics of the Spray Patterns Generated by Planing Hulls

Analytical and experimental studies were made of the origin and characteristics of the two distinctly different appearing spray patterns associated with prismatic planing hulls. It was found that these two spray patterns, identified as "whisker spray" and "main spray," are a consequence of the same basic hydrodynamic flow phenomenon and transform seamlessly from one into the other. Similar to the analytical treatment developed for swept-wing aircraft, where the oncoming free stream velocity is divided into components normal to and along the leading edge of the swept wing, the free stream velocity for the planing surface is divided into components normal to and along the stagnation line. Combining this orientation of velocity components with the results of analytical studies of Wagner (Uber stoss-und gleitoorgauge an der oberflache von flussiglaseiten. Z.f.a.M.M., 2, 4, 1932) for two-dimensional planing of infinitely long flat planing surfaces with those of Green (The gliding of a flat plate on a stream of finite depth, Proceedings of the Cambridge Philosophical Society, 31, 1935) for planing of a two-dimensional, finite length surface, explains the origin and characteristics of both the whisker and main spray patterns. It is shown that the main spray originates in a small local area at the intersection of the stagnation line with the chine. Relatively simplistic equations that define the three-dimensional location of the spray apex are developed, and the results presented in three graphs. An illustrative example is presented that demonstrates the ease of application of the method to define the main spray geometry of a typical planing craft. Model tests were conducted to define the maximum height of the main spray and its lateral and longitudinal positions relative to the hull as a function of deadrise angle, trim angle, and speed coefficient. These data substantiate the analytical results.

How to determine sapling buckling risk with only a few measurements

Tree buckling risk (actual height/critical buckling height) is an important biomechanical trait of plant growth strategies, and one that contributes to species coexistence. To estimate the diversity of this trait among wide samples, a method that minimizes damage to the plants is necessary. On the basis of the rarely used, complete version of Greenhill's model (1881, Proceedings of the Cambridge Philosophical Society 4(2): 65-73), we precisely measured all the necessary parameters on a sample of 236 saplings of 16 species. Then, using sensitivity (variance) analysis, regressions between successive models for risk factors and species ranks and the use of these models on samples of self- and nonself-supporting saplings, we tested different degrees of simplification up to the most simple and widely used formula that assumes that the tree is a cylindrical homogeneous pole. The size factor had the greatest effect on buckling risk, followed by the form factor and the modulus of elasticity of the wood. Therefore, estimates of buckling risk must consider not only the wood properties but especially the form factor. Finally, we proposed a simple but accurate method of assessing tree buckling risk that is applicable to a wide range of samples and that requires mostly nondestructive measurements.

Some relationships between the generalized Apostol–Bernoulli polynomials and Hurwitz–Lerch Zeta functions

The main object of this paper is to further investigate the generalized Apostol–Bernoulli polynomials of higher order, which were introduced and studied recently by Luo and Srivastava [2005, Journal of Mathematical Analysis and Applications, 308, 290–302; 2006, Computers and Mathematics with Applications, 51, 631–642]. Here, we first derive an explicit representation of these generalized Apostol–Bernoulli polynomials of higher order in terms of a generalization of the Hurwitz–Lerch Zeta function and then proceed to establish a functional relationship between the generalized Apostol–Bernoulli polynomials of rational arguments and the Hurwitz (or generalized) Zeta function. Our results would provide extensions of those given earlier by (for example) Apostol [1951, Pacific Journal of Mathematics, 1, 161–167] and Srivastava [2000, Mathematical Proceedings of the Cambridge Philosophical Society, 129, 77–84].

On finite matroids with two more hyperplanes than points

One of the most interesting results about finite matroids of finite rank and generalized projective spaces is the result of Basterfield, Kelly and Green (1968/1970) (J.G. Basterfield, L.M. Kelly, A characterization of sets of n points which determine n hyperplanes, in: Proceedings of the Cambridge Philosophical Society, vol. 64, 1968, pp. 585–588; C. Greene, A rank inequality for finite geometric lattices, J. Combin Theory 9 (1970) 357–364) affirming that any matroid contains at least as many hyperplanes as points, with equality in the case of generalized projective spaces. Consequently, the goal is to characterize and classify all matroids containing more hyperplanes than points. In 1996, I obtained the classification of all finite matroids containing one more hyperplane than points. In this paper a complete classification of finite matroids with two more hyperplanes than points is obtained. Moreover, a partial contribution to the classification of those matroids containing a certain number of hyperplanes more than points is presented.

An experimental and theoretical analysis on the application of stress-based forming limit criterion

In this paper, a detailed study on the stress-based forming limit criterion (FLSD) during linear and complex strain paths is developed. The calculation of stress-based forming limits based on experimental strain data is performed by using the method proposed by Stoughton [A general forming limit criterion for sheet metal forming. International Journal of Mechanical Sciences 2000;42:1–27]. By applying several combinations of different constitutive equations on the required plastic calculation, an analysis on the experimental forming stress limits is performed. The necking phenomenon is simulated by Marciniack–Kuczinsky (M–K) model using a more general code for predicting the forming limits. The selected materials are a bake-hardened steel (BH steel) and an AA6016-T4 aluminium alloy. Several yield criteria such as Von Mises isotropic yield function, quadratic and non-quadratic criterion of Hill (A theory of the yielding and plastic flow of anisotropic metals. Proceedings of the Royal Society of London 1948;A193:281–97; Theoretical plasticity of textured aggregates. Mathematical Proceedings of the Cambridge Philosophical Society 1979;85:179–91) and the advanced Barlat Yld96 yield function are used to show the influence of the constitutive law incorporated in the analysis on the stress-based forming limits. The effect of the hardening model on the FLSD is analysed by using two hardening laws, namely Swift law and Voce law. The influence of work hardening coefficient, strain rate sensitivity and the balanced biaxial yield stress on the theoretical FLSD is also presented. The effect of strain path changes on the stress-based forming limits is analysed. Some relevant remarks about stress-based forming limit criterion concept are presented.

On the parameter β=Re/KC= D2/ νT

This brief communication is a summary of the facts regarding the universalization in 1976 of a parameter β to fully nonlinear unsteady separated flows about bluff bodies nearly 125 years after its first appearance in a linearized analysis of unseparated viscous flow with very slow oscillations about a cylindrical rod and sphere by Sir George Gabriel Stokes [1851. On the effect of the internal friction of fluids on the motion of pendulums. Transactions of the Cambridge Philosophical Society 9(II), 8–106]. The primary purpose of Stokes was to show that “ the index of friction” (the kinematic viscosity), in the equations of motion may be deduced from experiments for the vindication of the heuristic reasoning that went into the derivation by Navier [1827. Mémoire sur les lois du movement des fluides. Mémoires de l’Académie de Sciences 6, 389–416.], Poisson [1831. Nouvelle théorie de l’action capillaire Bachelier, Paris.], de Saint-Venant [1843. Note á joindre un memoire sur la dynamique des fluides. Comptes Rendus 17, 1240–1244.] and Stokes [1845. On the theories of internal friction of fluids in motion. Transactins of the Cambridge Philosophical Society 8, 287–305.] of what are now called the Navier–Stokes equations.

On the connection between Stokes drift and Darwin drift

Stokes and Darwin drift, for irrotational waves and flow past rigid bodies, are analysed in a general framework and shown to be fundamentally the same thing. © 1999 Cambridge Philosophical Society.