12,051 research outputs found
Psychophysiological modelling and the measurement of fear conditioning
Quantification of fear conditioning is paramount to many clinical and translational studies on aversive learning. Various measures of fear conditioning co-exist, including different observables and different methods of pre-processing. Here, we first argue that low measurement error is a rational desideratum for any measurement technique. We then show that measurement error can be approximated in benchmark experiments by how closely intended fear memory relates to measured fear memory, a quantity that we term retrodictive validity. From this perspective, we discuss different approaches commonly used to quantify fear conditioning. One of these is psychophysiological modelling (PsPM). This builds on a measurement model that describes how a psychological variable, such as fear memory, influences a physiological measure. This model is statistically inverted to estimate the most likely value of the psychological variable, given the measured data. We review existing PsPMs for skin conductance, pupil size, heart period, respiration, and startle eye-blink. We illustrate the benefit of PsPMs in terms of retrodictive validity and translate this into sample size required to achieve a desired level of statistical power. This sample size can differ up to a factor of three between different observables, and between the best, and the current standard, data pre-processing methods
A vanishing theorem for operators in Fock space
We consider the bosonic Fock space over the Hilbert space of transversal
vector fields in three dimensions. This space carries a canonical
representation of the group of rotations. For a certain class of operators in
Fock space we show that rotation invariance implies the absence of terms which
either create or annihilate only a single particle. We outline an application
of this result in an operator theoretic renormalization analysis of Hamilton
operators, which occur in non-relativistic qed.Comment: 14 page
Uniqueness of the ground state in the Feshbach renormalization analysis
In the operator theoretic renormalization analysis introduced by Bach,
Froehlich, and Sigal we prove uniqueness of the ground state.Comment: 10 page
An O(M(n) log n) algorithm for the Jacobi symbol
The best known algorithm to compute the Jacobi symbol of two n-bit integers
runs in time O(M(n) log n), using Sch\"onhage's fast continued fraction
algorithm combined with an identity due to Gauss. We give a different O(M(n)
log n) algorithm based on the binary recursive gcd algorithm of Stehl\'e and
Zimmermann. Our implementation - which to our knowledge is the first to run in
time O(M(n) log n) - is faster than GMP's quadratic implementation for inputs
larger than about 10000 decimal digits.Comment: Submitted to ANTS IX (Nancy, July 2010
Ground States in the Spin Boson Model
We prove that the Hamiltonian of the model describing a spin which is
linearly coupled to a field of relativistic and massless bosons, also known as
the spin-boson model, admits a ground state for small values of the coupling
constant lambda. We show that the ground state energy is an analytic function
of lambda and that the corresponding ground state can also be chosen to be an
analytic function of lambda. No infrared regularization is imposed. Our proof
is based on a modified version of the BFS operator theoretic renormalization
analysis. Moreover, using a positivity argument we prove that the ground state
of the spin-boson model is unique. We show that the expansion coefficients of
the ground state and the ground state energy can be calculated using regular
analytic perturbation theory
Ground State and Resonances in the Standard Model of Non-relativistic QED
We prove existence of a ground state and resonances in the standard model of
the non-relativistic quantum electro-dynamics (QED). To this end we introduce a
new canonical transformation of QED Hamiltonians and use the spectral
renormalization group technique with a new choice of Banach spaces.Comment: 50 pages change
Kramers degeneracy theorem in nonrelativistic QED
Degeneracy of the eigenvalues of the Pauli-Fierz Hamiltonian with spin 1/2 is
proven by the Kramers degeneracy theorem. The Pauli-Fierz Hamiltonian at fixed
total momentum is also investigated.Comment: LaTex, 11 page
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