Synpolydactyly phenotypes correlate with size of expansions in HOXD13 polyalanine tract

Synpolydactyly (SPD) is a dominantly inherited congenital limb malformation. Typical cases have 3/4 finger and 4/5 toe syndactyly, with a duplicated digit in the syndactylous web, but incomplete penetrance and variable expressivity are common. The condition has recently been shown to be caused by expansions of an imperfect trinucleotide repeat sequence encoding a 15-residue polyalanine tract in HOXD13. We have studied 16 new and 4 previously published SPD families, with between 7 and 14 extra residues in the tract, to analyze the molecular basis for the observed variation in phenotype. Although there is no evidence of change in expansion size within families, even over six generations, there is a highly significant increase in the penetrance and severity of phenotype with increasing expansion size, affecting both hands (P = 0.012) and feet (P < 0.00005). Affected individuals from a family with a 14-alanine expansion, the largest so far reported, all have a strikingly similar and unusually severe limb phenotype, involving the first digits and distal carpals. Affected males from this family also have hypospadias, not previously described in SPD, but consistent with HOXD13 expression in the developing genital tubercle. The remarkable correlation between phenotype and expansion size suggests that expansion of the tract leads to a specific gain of function in the mutant HOXD13 protein, and has interesting implications for the role of polyalanine tracts in the control of transcription.

The asymptotic distribution of canonical correlations and vectors in higher-order cointegrated models

The study of the large-sample distribution of the canonical correlations and variates in cointegrated models is extended from the first-order autoregression model to autoregression of any (finite) order. The cointegrated process considered here is nonstationary in some dimensions and stationary in some other directions, but the first difference (the “error-correction form”) is stationary. The asymptotic distribution of the canonical correlations between the first differences and the predictor variables as well as the corresponding canonical variables is obtained under the assumption that the process is Gaussian. The method of analysis is similar to that used for the first-order process.

Evolution of vertebrate steroid receptors from an ancestral estrogen receptor by ligand exploitation and serial genome expansions

The evolution of novelty in tightly integrated biological systems, such as hormones and their receptors, seems to challenge the theory of natural selection: it has not been clear how a new function for any one part (such as a ligand) can be selected for unless the other members of the system (e.g., a receptor) are already present. Here I show—based on identification and phylogenetic analysis of steroid receptors in basal vertebrates and reconstruction of the sequences and functional attributes of ancestral proteins—that the first steroid receptor was an estrogen receptor, followed by a progesterone receptor. Genome mapping and phylogenetic analyses indicate that the full complement of mammalian steroid receptors evolved from these ancient receptors by two large-scale genome expansions, one before the advent of jawed vertebrates and one after. Specific regulation of physiological processes by androgens and corticoids are relatively recent innovations that emerged after these duplications. These findings support a model of ligand exploitation in which the terminal ligand in a biosynthetic pathway is the first for which a receptor evolves; selection for this hormone also selects for the synthesis of intermediates despite the absence of receptors, and duplicated receptors then evolve affinity for these substances. In this way, novel hormone-receptor pairs are created, and an integrated system of increasing complexity elaborated. This model suggests that ligands for some “orphan” receptors may be found among intermediates in the synthesis of ligands for phylogenetically related receptors.

One-sided asymptotic inferences for a proportion.

Two-sided asymptotic confidence intervals for an unknown proportion p have been the subject of a great deal of literature. Surprisingly, there are very few papers devoted, like this article, to the case of one tail, despite its great importance in practice and the fact that its behavior is usually different from that of the case with two tails. This paper evaluates 47 methods and concludes that (1) the optimal method is the classic Wilson method with a correction for continuity and (2) a simpler option, almost as good as the first, is the new adjusted Wald method (Wald's classic method applied to the data increased in the values proposed by Borkowf: adding a single imaginary failure or success).

Nonequilibrium expansions of air with coupled chemical reactions

Caption title.

Asymptotic properties of stationary sequences.

Bibliography: p. 146.

Asymptotic bifurcation results for quasilinear elliptic operators

We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.

Asymptotic theory of time varying networks with memory and heterogeneous activation pattern

In this thesis work we develop a new generative model of social networks belonging to the family of Time Varying Networks. The importance of correctly modelling the mechanisms shaping the growth of a network and the dynamics of the edges activation and inactivation are of central importance in network science. Indeed, by means of generative models that mimic the real-world dynamics of contacts in social networks it is possible to forecast the outcome of an epidemic process, optimize the immunization campaign or optimally spread an information among individuals. This task can now be tackled taking advantage of the recent availability of large-scale, high-quality and time-resolved datasets. This wealth of digital data has allowed to deepen our understanding of the structure and properties of many real-world networks. Moreover, the empirical evidence of a temporal dimension in networks prompted the switch of paradigm from a static representation of graphs to a time varying one. In this work we exploit the Activity-Driven paradigm (a modeling tool belonging to the family of Time-Varying-Networks) to develop a general dynamical model that encodes fundamental mechanism shaping the social networks' topology and its temporal structure: social capital allocation and burstiness. The former accounts for the fact that individuals does not randomly invest their time and social interactions but they rather allocate it toward already known nodes of the network. The latter accounts for the heavy-tailed distributions of the inter-event time in social networks. We then empirically measure the properties of these two mechanisms from seven real-world datasets and develop a data-driven model, analytically solving it. We then check the results against numerical simulations and test our predictions with real-world datasets, finding a good agreement between the two. Moreover, we find and characterize a non-trivial interplay between burstiness and social capital allocation in the parameters phase space. Finally, we present a novel approach to the development of a complete generative model of Time-Varying-Networks. This model is inspired by the Kaufman's adjacent possible theory and is based on a generalized version of the Polya's urn. Remarkably, most of the complex and heterogeneous feature of real-world social networks are naturally reproduced by this dynamical model, together with many high-order topological properties (clustering coefficient, community structure etc.).

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Asymptotic theory of wall-attached convection in a horizontal fluid layer with a vertical magnetic field

A horizontal fluid layer heated from below in the presence of a vertical magnetic field is considered. A simple asymptotic analysis is presented which demonstrates that a convection mode attached to the side walls of the layer sets in at Rayleigh numbers much below those required for the onset of convection in the bulk of the layer. The analysis complements an earlier analysis by Houchens [J. Fluid Mech. 469, 189 (2002)] which derived expressions for the critical Rayleigh number for the onset of convection in a vertical cylinder with an axial magnetic field in the cases of two aspect ratios. © 2008 American Institute of Physics.

On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

This work was presented in part at the 8th International Conference on Finite Fields and Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.