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WPM package manager version 1.0 : software documentation
WPM is a command-line tool designed to support build and installation facilities. It is implemented as a collection of script files, written in Bourne shell syntax. For the sake of portability the code takes care of the common pitfalls of shell programming.
On Tetrahedralisations Containing Knotted and Linked Line Segments
This paper considers a set of twisted line segments in 3d such that they form a knot (a closed curve) or a link of two closed curves. Such line segments appear on the boundary of a family of 3d indecomposable polyhedra (like the Schönhardt polyhedron) whose interior cannot be tetrahedralised without additional vertices added. On the other hand, a 3d (non-convex) polyhedron whose boundary contains such line segments may still be decomposable as long as the twist is not too large. It is therefore interesting to consider the question: when there exists a tetrahedralisation contains a given set of knotted or linked line segments? In this paper, we studied a simplified question with the assumption that all vertices of the line segments are in convex position. It is straightforward to show that no tetrahedralisation of 6 vertices (the three-line-segments case) can contain a trefoil knot. Things become interesting when the number of line segments increases. Since it is necessary to create new interior edges to form a tetrahedralisation. We provided a detailed analysis for the case of a set of 4 line segments. This leads to a crucial condition on the orientation of pairs of new interior edges which determines whether this set is decomposable or not. We then prove a new theorem about the decomposability for a set of n (n ≥ 3) knotted or linked line segments. This theorem implies that the family of polyhedra generalised from the Schonhardt polyhedron by Rambau [1] are all indecomposable.
Statistical parametric maps for functional MRI experiments in R: The package fmri
The purpose of the package fmri is the analysis of single subject functional magnetic resonance imaging (fMRI) data. It provides fMRI analysis from time series modeling by a linear model to signal detection and publication quality images. Specifically, it implements structural adaptive smoothing methods with signal detection for adaptive noise reduction which avoids blurring of activation areas. Within this paper we describe the complete pipeline for fMRI analysis using fmri. We describe data reading from various medical imaging formats and the linear modeling used to create the statistical parametric maps. We review the rationale behind the structural adaptive smoothing algorithms and explain their usage from the package fmri. We demonstrate the results of such analysis using two experimental datasets. Finally, we report on the usage of a graphical user interface for some of the package functions.
Maximally dissipative solutions for incompressible fluid dynamics
We introduce the new concept of maximally dissipative solutions for a general class of isothermal GENERIC systems. Under certain assumptions, we show that maximally dissipative solutions are well-posed as long as the bigger class of dissipative solutions is non-empty. Applying this result to the Navier–Stokes and Euler equations, we infer global well-posedness of maximally dissipative solutions for these systems. The concept of maximally dissipative solutions coincides with the concept of weak solutions as long as the weak solutions inherits enough regularity to be unique.
Ground reaction forces and external hip joint moments predict in vivo hip contact forces during gait
Younger patients increasingly receive total hip arthroplasty (THA) as therapy for end-stage osteoarthritis. To maintain the long-term success of THA in such patients, avoiding extremely high hip loads, i.e., in vivo hip contact force (HCF), is considered essential. However, in vivo HCFs are difficult to determine and their direct measurement is limited to instrumented joint implants. It remains unclear whether external measurements of ground reaction forces (GRFs), a non-invasive, markerless and clinic-friendly measure can estimate in vivo HCFs. Using data from eight patients with instrumented hip implants, this study determined whether GRF time series data, alone or combined with other scalar variables such as hip joint moments (HJMs) and lean muscle volume (LMV), could predict the resultant HCF (rHCF) impulse using a functional linear modeling approach. Overall, single GRF time series data did not predict in vivo rHCF impulses. However, when GRF time series data were combined with LMV of the gluteus medius or sagittal HJM using a functional linear modeling approach, the in vivo rHCF impulse could be predicted from external measures only. Accordingly, this approach can predict in vivo rHCF impulses, and thus provide patients with useful insight regarding their gait behavior to avoid hip joint overloading.
Longitudinal dynamics of semiconductor lasers
We investigate the longitudinal dynamics of semiconductor lasers using a model which couples a hyperbolic linear system of partial differential equations nonlinearly with ordinary differential equations. We prove the global existence and uniqueness of solutions using the theory of strongly continuous semigroups. Subsequently, we analyse the long-time behavior of the solutions in two steps. First, we find attracting invariant manifolds of low dimension benefitting from the fact that the system is singularly perturbed, i. e., the optical and the electronic variables operate on differente time-scales. The flow on these manifolds can be approximated by the so-called mode approximations. The dimension of these mode approximations depends on the number of critical eigenvalues of the linear hyperbolic operator. Next, we perform a detailed numerical and analytic bifurcation analysis for the two most common constellations. Starting from known results for the single-mode approximation, we investigate the two-mode approximation in the special case of a rapidly rotating phase difference between the two optical components. In this case, the first-order averaged model unveils the mechanisms for various phenomena observed in simulations of the complete system. Moreover, it predicts the existence of a more complex spatio-temporal behavior. In the scope of the averaged model, this is a bursting regime.
Convective Nozaki-Bekki holes in a long cavity OCT laser
We show, both experimentally and theoretically, that the loss of coherence of a long cavity optical coherence tomography (OCT) laser can be described as a transition from laminar to turbulent flows. We demonstrate that in this strongly dissipative system, the transition happens either via an absolute or a convective instability depending on the laser parameters. In the latter case, the transition occurs via formation of localised structures in the laminar regime, which trigger the formation of growing and drifting puffs of turbulence. Experimentally, we demonstrate that these turbulent bursts are seeded by appearance of Nozaki-Bekki holes, characterised by the zero field amplitude and π phase jumps. Our experimental results are supported with numerical simulations based on the delay differential equations model.
TetGen: A quality tetrahedral mesh generator and a 3D Delaunay triangulator (Version 1.5 — User’s Manual)
TetGen is a software for tetrahedral mesh generation. Its goal is to generate good quality tetrahedral meshes suitable for numerical methods and scientific computing. It can be used as either a standalone program or a library component integrated in other software. The purpose of this document is to give a brief explanation of the kind of tetrahedralizations and meshing problems handled by TetGen and to give a fairly detailed documentation about the usage of the program. Readers will learn how to create tetrahedral meshes using input files from the command line. Furthermore, the programming interface for calling TetGen from other programs is explained.
Death and rebirth of neural activity in sparse inhibitory networks
Inhibition is a key aspect of neural dynamics playing a fundamental role for the emergence of neural rhythms and the implementation of various information coding strategies. Inhibitory populations are present in several brain structures, and the comprehension of their dynamics is strategical for the understanding of neural processing. In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of neural activity, as expected, but can also promote neural re-activation. In particular, for globally coupled systems, the number of firing neurons monotonically reduces upon increasing the strength of inhibition (neuronal death). However, the random pruning of connections is able to reverse the action of inhibition, i.e. in a random sparse network a sufficiently strong synaptic strength can surprisingly promote, rather than depress, the activity of neurons (neuronal rebirth). Thus, the number of firing neurons reaches a minimum value at some intermediate synaptic strength. We show that this minimum signals a transition from a regime dominated by neurons with a higher firing activity to a phase where all neurons are effectively sub-threshold and their irregular firing is driven by current fluctuations. We explain the origin of the transition by deriving a mean field formulation of the problem able to provide the fraction of active neurons as well as the first two moments of their firing statistics. The introduction of a synaptic time scale does not modify the main aspects of the reported phenomenon. However, for sufficiently slow synapses the transition becomes dramatic, and the system passes from a perfectly regular evolution to irregular bursting dynamics. In this latter regime the model provides predictions consistent with experimental findings for a specific class of neurons, namely the medium spiny neurons in the striatum.
First-Order Methods for Convex Optimization
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories reported in various applications, including most importantly machine learning, signal processing, imaging and control theory. First-order methods have the potential to provide low accuracy solutions at low computational complexity which makes them an attractive set of tools in large-scale optimization problems. In this survey, we cover a number of key developments in gradient-based optimization methods. This includes non-Euclidean extensions of the classical proximal gradient method, and its accelerated versions. Additionally we survey recent developments within the class of projection-free methods, and proximal versions of primal-dual schemes. We give complete proofs for various key results, and highlight the unifying aspects of several optimization algorithms.