A Bayesian Approach to Inverse Quantum Statistics

A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over potentials implemented in form of stochastic processes. Its specific advantages are the possibilities to deal with heterogeneous data and to express a priori information explicitly, i.e., directly in terms of the potential of interest. A numerical solution in maximum a posteriori approximation was feasible for one--dimensional problems. Using correct a priori information turned out to be essential.Comment: 4 pages, 6 figures, revte

Semiclassical Quantisation Using Diffractive Orbits

Diffraction, in the context of semiclassical mechanics, describes the manner in which quantum mechanics smooths over discontinuities in the classical mechanics. An important example is a billiard with sharp corners; its semiclassical quantisation requires the inclusion of diffractive periodic orbits in addition to classical periodic orbits. In this paper we construct the corresponding zeta function and apply it to a scattering problem which has only diffractive periodic orbits. We find that the resonances are accurately given by the zeros of the diffractive zeta function.Comment: Revtex document. Submitted to PRL. Figures available on reques

Chaotic wave functions and exponential convergence of low-lying energy eigenvalues

We suggest that low-lying eigenvalues of realistic quantum many-body hamiltonians, given, as in the nuclear shell model, by large matrices, can be calculated, instead of the full diagonalization, by the diagonalization of small truncated matrices with the exponential extrapolation of the results. We show numerical data confirming this conjecture. We argue that the exponential convergence in an appropriate basis may be a generic feature of complicated ("chaotic") systems where the wave functions are localized in this basis.Comment: 4 figure

Likelihood Geometry

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its maximum likelihood degree. We present an introduction to this theory and its statistical motivations. Many favorite objects from combinatorial algebraic geometry are featured: toric varieties, A-discriminants, hyperplane arrangements, Grassmannians, and determinantal varieties. Several new results are included, especially on the likelihood correspondence and its bidegree. These notes were written for the second author's lectures at the CIME-CIRM summer course on Combinatorial Algebraic Geometry at Levico Terme in June 2013.Comment: 45 pages; minor changes and addition

Collisional Damping of Nuclear Collective Vibrations in a Non-Markovian Transport Approach

A detailed derivation of the collisional widths of collective vibrations is presented in both quantal and semi-classical frameworks by considering the linearized limits of the extended TDHF and the BUU model with a non-Markovian binary collision term. Damping widths of giant dipole and giant quadrupole excitations are calculated by employing an effective Skyrme force, and the results are compared with GDR measurements in Lead and Tin nuclei at finite temperature.Comment: 23 pages, 6 Figure

Health professionals, their medical interventions and uncertainty : a study focusing on women at midlife

Health professionals face a tension between focusing on the individual and attending to health issues for the population as a whole. This tension is intrinsic to medicine and gives rise to medical uncertainty, which here is explored through accounts of three medical interventions focused on women at midlife: breast screening, hormone replacement therapy and bone densitometry. The accounts come from interviews with UK health professionals using these medical interventions in their daily work. Drawing on the analysis of Fox [(2002). Health and Healing: The public/private divide (pp. 236–253). London: Routledge] we distinguish three aspects of medical uncertainty and explore each one of them in relation to one of the interventions. First is uncertainty about the balance between the individual and distributive ethic of medicine, explored in relation to breast screening. Second is the dilemma faced by health professionals when using medicial evidence generated through studies of populations and applying this to individuals. We explore this dilemma for hormone replacement therapy. Thirdly there is uncertainty because of the lack of a conceptual framework for understanding how new micro knowledge, such as human genetic information, can be combined with knowledge of other biological and social dimensions of health. The accounts from the bone denistometry clinic indicate the beginnings of an understanding of the need for such a framework, which would acknowledge complexity, recognising that factors from many different levels of analysis, from heredity through to social factors, interact with each other and influence the individual and their health. However, our analysis suggests biomedicine continues to be dominated by an individualised, context free, concept of health and health risk with individuals alone responsible for their own health and for the health of the population. This may continue to dominate how we perceive responsibilities for health until we establish a conceptual framework that recognises the complex interaction of many factors at macro and micro level affecting health

Binary Models for Marginal Independence

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach taken is graphical and draws on analogies to multivariate Gaussian models for marginal independence. For the graphical model representation we use bi-directed graphs, which are in the tradition of path diagrams. We show how the models can be parameterized in a simple fashion, and how maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. Finally we consider combining these models with symmetry restrictions

Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

The selectivity, voltage-dependence and acid sensitivity of the tandem pore potassium channel TASK-1 : contributions of the pore domains

We have investigated the contribution to ionic selectivity of residues in the selectivity filter and pore helices of the P1 and P2 domains in the acid sensitive potassium channel TASK-1. We used site directed mutagenesis and electrophysiological studies, assisted by structural models built through computational methods. We have measured selectivity in channels expressed in Xenopus oocytes, using voltage clamp to measure shifts in reversal potential and current amplitudes when Rb+ or Na+ replaced extracellular K+. Both P1 and P2 contribute to selectivity, and most mutations, including mutation of residues in the triplets GYG and GFG in P1 and P2, made channels nonselective. We interpret the effects of these—and of other mutations—in terms of the way the pore is likely to be stabilised structurally. We show also that residues in the outer pore mouth contribute to selectivity in TASK-1. Mutations resulting in loss of selectivity (e.g. I94S, G95A) were associated with slowing of the response of channels to depolarisation. More important physiologically, pH sensitivity is also lost or altered by such mutations. Mutations that retained selectivity (e.g. I94L, I94V) also retained their response to acidification. It is likely that responses both to voltage and pH changes involve gating at the selectivity filter