Search results for "Statistical"

Ancestral processes in population genetics-the coalescent.

2000

A special stochastic process, called the coalescent, is of fundamental interest in population genetics. For a large class of population models this process is the appropriate tool to analyse the ancestral structure of a sample of n individuals or genes, if the total number of individuals in the population is sufficiently large. A corresponding convergence theorem was first proved by Kingman in 1982 for the Wright-Fisher model and the Moran model. Generalizations to a large class of exchangeable population models and to models with overlying mutation processes followed shortly later. One speaks of the "robustness of the coalescent, as this process appears in many models as the total populati…

Statistical inference as a decision problem: the choice of sample size

1997

Estimating regression models with unknown break-points.

2003

This paper deals with fitting piecewise terms in regression models where one or more break-points are true parameters of the model. For estimation, a simple linearization technique is called for, taking advantage of the linear formulation of the problem. As a result, the method is suitable for any regression model with linear predictor and so current software can be used; threshold modelling as function of explanatory variables is also allowed. Differences between the other procedures available are shown and relative merits discussed. Simulations and two examples are presented to illustrate the method.

Global stability of protein folding from an empirical free energy function

2013

The principles governing protein folding stand as one of the biggest challenges of Biophysics. Modeling the global stability of proteins and predicting their tertiary structure are hard tasks, due in part to the variety and large number of forces involved and the difficulties to describe them with sufficient accuracy. We have developed a fast, physics-based empirical potential, intended to be used in global structure prediction methods. This model considers four main contributions: Two entropic factors, the hydrophobic effect and configurational entropy, and two terms resulting from a decomposition of close-packing interactions, namely the balance of the dispersive interactions of folded an…

Generalized Riesz systems and orthonormal sequences in Krein spaces

2018

We analyze special classes of bi-orthogonal sets of vectors in Hilbert and in Krein spaces, and their relations with generalized Riesz systems. In this way, the notion of the first/second type sequences is introduced and studied. We also discuss their relevance in some concrete quantum mechanical system driven by manifestly non self-adjoint Hamiltonians.

Implementability of Liouville Evolution, Koopman and Banach-Lamperti Theorems in Classical and Quantum Dynamics

2002

We extend the concept of implementability of semigroups of evolution operators associated with dynamical systems to quantum case. We show that such an extension can be properly formulated in terms of Jordan morphisms and isometries on non-commutative Lp spaces. We focus our attention on a non-commutative analog of the Banach-Lamperti theorem.

Gabor-like systems in ${cal L}^2({bf R}^d)$ and extensions to wavelets

2008

In this paper we show how to construct a certain class of orthonormal bases in starting from one or more Gabor orthonormal bases in . Each such basis can be obtained acting on a single function with a set of unitary operators which operate as translation and modulation operators in suitable variables. The same procedure is also extended to frames and wavelets. Many examples are discussed.

Non-self-adjoint Hamiltonians with complex eigenvalues

2016

Motivated by what one observes dealing with PT-symmetric quantum mechanics, we discuss what happens if a physical system is driven by a diagonalizable Hamiltonian with not all real eigenvalues. In particular, we consider the functional structure related to systems living in finite-dimensional Hilbert spaces, and we show that certain intertwining relations can be deduced also in this case if we introduce suitable antilinear operators. We also analyze a simple model, computing the transition probabilities in the broken and in the unbroken regime.

Explicit near-symplectic mappings of Hamiltonian systems with Lie-generating functions

2008

The construction of explicit near-symplectic mappings for generic Hamiltonian systems with the utilization of Lie transforms is presented. The method is mathematically rigorous and systematically extended to high order with respect to a perturbation parameter. The explicit mappings are compared to their implicit counterparts, which use mixed-variable generating functions, in terms of conservation of invariant quantities, calculation speed and accurate construction of Poincare surfaces of sections. The comparative study considers a wide range of parameters and initial conditions for which different time scales are involved due to large differences between internal and external frequencies of…

Gibbs states defined by biorthogonal sequences

2016

Motivated by the growing interest on PT-quantum mechanics, in this paper we discuss some facts on generalized Gibbs states and on their related KMS-like conditions. To achieve this, we first consider some useful connections between similar (Hamiltonian) operators and we propose some extended version of the Heisenberg algebraic dynamics, deducing some of their properties, useful for our purposes.