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Article
Functional Equivariance and Conservation Laws in Numerical Integration
Preservation of linear and quadratic invariants by numerical integrators has been well studied. However, many systems have linear or quadratic observables that are not invariant, but which satisfy evolution eq...
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Article
Frequency, morbidity and equity — the case for increased research on male fertility
Currently, most men with infertility cannot be given an aetiology, which reflects a lack of knowledge around gamete production and how it is affected by genetics and the environment. A failure to recognize the...
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Article
Open AccessDiverse monogenic subforms of human spermatogenic failure
Non-obstructive azoospermia (NOA) is the most severe form of male infertility and typically incurable. Defining the genetic basis of NOA has proven challenging, and the most advanced classification of NOA subf...
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Article
Analysing ‘Simple’ Image Registrations
Processes such as growth and atrophy cause changes through time that can be visible in a series of medical images, following the hypothesis that form follows function. As was hypothesised by D’Arcy Thompson mo...
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Article
Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation
We show that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that non-symplectic integrators do not. We provide a universal description of the breaking of umbilic bifurc...
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Article
Parallelization, initialization, and boundary treatments for the diamond scheme
We study a class of general purpose linear multisymplectic integrators for Hamiltonian wave equations based on a diamond-shaped mesh. On each diamond, the PDE is discretized by a symplectic Runge–Kutta method....
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Article
Multisymplecticity of Hybridizable Discontinuous Galerkin Methods
In this paper, we prove necessary and sufficient conditions for a hybridizable discontinuous Galerkin method to satisfy a multisymplectic conservation law, when applied to a canonical Hamiltonian system of par...
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Article
Currents and Finite Elements as Tools for Shape Space
The nonlinear spaces of shapes (unparameterized immersed curves or submanifolds) are of interest for many applications in image analysis, such as the identification of shapes that are similar modulo the action...
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Article
Symplectic integration of boundary value problems
Symplectic integrators can be excellent for Hamiltonian initial value problems. Reasons for this include their preservation of invariant sets like tori, good energy behaviour, nonexistence of attractors, and g...
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Article
Open AccessCryopreservation of reproductive material before cancer treatment: a qualitative study of health care professionals’ views about ways to enhance clinical care
Cancer treatment can diminish fertility in women and men. The need for fertility preservation is growing as increasing numbers of people survive cancer. Cryostorage of reproductive material to preserve potenti...
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Article
Geometry of Discrete-Time Spin Systems
Classical Hamiltonian spin systems are continuous dynamical systems on the symplectic phase space \((S^2)^n\) ...
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Article
B-series methods are exactly the affine equivariant methods
Butcher series, also called B-series, are a type of expansion, fundamental in the analysis of numerical integration. Numerical methods that can be expanded in B-series are defined in all dimensions, so they co...
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Reference Work Entry In depth
Composition Methods
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Article
Geometric Generalisations of shake and rattle
A geometric analysis of the shake and rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relat...
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Article
Geodesic Warps by Conformal Map**s
In recent years there has been considerable interest in methods for diffeomorphic war** of images, with applications in e.g. medical imaging and evolutionary biology. The original work generally cited is tha...
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Article
Energy-Preserving Integrators and the Structure of B-series
B-series are a powerful tool in the analysis of Runge–Kutta numerical integrators and some of their generalizations (“B-series methods”). A general goal is to understand what structure-preservation can be achi...
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Article
Preservation and destruction of periodic orbits by symplectic integrators
We investigate what happens to periodic orbits and lower-dimensional tori of Hamiltonian systems under discretisation by a symplectic one-step method where the system may have more than one degree of freedom. ...
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Article
Open AccessDeterminants of male reproductive health disorders: the Men in Australia Telephone Survey (MATeS)
The relationship between reproductive health disorders and lifestyle factors in middle-aged and older men is not clear. The aim of this study is to describe lifestyle and biomedical associations as possible ca...
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Article
Hypogonadotropism with elevated serum testosterone: reversible causes of secondary infertility
Background A 33-year-old man presented with secondary infertility, increased libido, and extreme oligospermia. Testicular volumes were reduced, but no gynecomastia was apparent and androgen abuse was denied.
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Article
The Discrete Moser–Veselov Algorithm for the Free Rigid Body, Revisited
In this paper we revisit the Moser–Veselov description of the free rigid body in body coordinates, which, in the 3 × 3 case, can be implemented as an explicit, second-order, integrable approximation of...
