A Bunched Logic for Conditional Independence

Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle conditional independence. We extend the logic of bunched implications (BI) with a non-commutative conjunction and provide a model based on Markov kernels; conditional independence can be directly captured as a logical formula in this model. Noting that Markov kernels are Kleisli arrows for the distribution monad, we then introduce a second model based on the powerset monad and show how it can capture join dependency, a non-probabilistic analogue of conditional independence from database theory. Finally, we develop a program logic for verifying conditional independence in probabilistic programs

Generalist genes analysis of DNA markers associated with mathematical ability and disability reveals shared influence across ages and abilities

Background The Generalist Genes Hypothesis is based upon quantitative genetic findings which indicate that many of the same genes influence diverse cognitive abilities and disabilities across age. In a recent genome-wide association study of mathematical ability in 10-year-old children, 43 SNP associations were nominated from scans of pooled DNA, 10 of which were validated in an individually genotyped sample. The 4927 children in this genotyped sample have also been studied at 7, 9 and 12 years of age on measures of mathematical ability, as well as on other cognitive and learning abilities. Results Using these data we have explored the Generalist Genes Hypothesis by assessing the association of the available measures of ability at age 10 and other ages with two composite 'SNP-set' scores, formed from the full set of 43 nominated SNPs and the sub-set of 10 SNPs that were previously found to be associated with mathematical ability at age 10. Both SNP sets yielded significant associations with mathematical ability at ages 7, 9 and 12, as well as with reading and general cognitive ability at age 10. Conclusions Although effect sizes are small, our results correspond with those of quantitative genetic research in supporting the Generalist Genes Hypothesis. SNP sets identified on the basis of their associations with mathematical ability at age 10 show associations with mathematical ability at earlier and later ages and show associations of similar magnitude with reading and general cognitive ability. With small effect sizes expected in such complex traits, future studies may be able to capitalise on power by searching for 'generalist genes' using longitudinal and multivariate approaches

Partially Observable Concurrent Kleene Algebra

We introduce partially observable concurrent Kleene algebra (POCKA), an algebraic framework to reason about concurrent programs with variables as well as control structures, such as conditionals and loops, that depend on those variables. We illustrate the use of POCKA through concrete examples. We prove that POCKA is a sound and complete axiomatisation of a model of partial observations, and show the semantics passes an important check for sequential consistency

The Role of Ageing and Parenchymal Senescence on Macrophage Function and Fibrosis

In this review, we examine senescent cells and the overlap between the direct biological impact of senescence and the indirect impact senescence has via its effects on other cell types, particularly the macrophage. The canonical roles of macrophages in cell clearance and in other physiological functions are discussed with reference to their functions in diseases of the kidney and other organs. We also explore the translational potential of different approaches based around the macrophage in future interventions to target senescent cells, with the goal of preventing or reversing pathologies driven or contributed to in part by senescent cell load in vivo

An interpretation of Robinson-Trautman type N solutions

The Robinson-Trautman type N solutions, which describe expanding gravitational waves, are investigated for all possible values of the cosmological constant Lambda and the curvature parameter epsilon. The wave surfaces are always (hemi-)spherical, with successive surfaces displaced in a way which depends on epsilon. Explicit sandwich waves of this class are studied in Minkowski, de Sitter or anti-de Sitter backgrounds. A particular family of such solutions which can be used to represent snapping or decaying cosmic strings is considered in detail, and its singularity and global structure is presented.Comment: 13 pages, 3 figures. To appear in Class. Quantum Gra

Partially Observable Concurrent Kleene Algebra

We introduce partially observable concurrent Kleene algebra (POCKA), an algebraic framework to reason about concurrent programs with variables as well as control structures, such as conditionals and loops, that depend on those variables. We illustrate the use of POCKA through concrete examples. We prove that POCKA is a sound and complete axiomatisation of a model of partial observations, and show the semantics passes an important check for sequential consistency

Generalised Kundt waves and their physical interpretation

We present the complete family of space-times with a non-expanding, shear-free, twist-free, geodesic principal null congruence (Kundt waves) that are of algebraic type III and for which the cosmological constant ($\Lambda_c$) is non-zero. The possible presence of an aligned pure radiation field is also assumed. These space-times generalise the known vacuum solutions of type N with arbitrary $\Lambda_c$ and type III with $\Lambda_c=0$. It is shown that there are two, one and three distinct classes of solutions when $\Lambda_c$ is respectively zero, positive and negative. The wave surfaces are plane, spherical or hyperboloidal in Minkowski, de Sitter or anti-de Sitter backgrounds respectively, and the structure of the family of wave surfaces in the background space-time is described. The weak singularities which occur in these space-times are interpreted in terms of envelopes of the wave surfaces.Comment: 16 pages including 2 figures. To appear in Classical and Quantum Gra