89,568 research outputs found
Functional programming framework for GRworkbench
The software tool GRworkbench is an ongoing project in visual, numerical
General Relativity at The Australian National University. Recently, the
numerical differential geometric engine of GRworkbench has been rewritten using
functional programming techniques. By allowing functions to be directly
represented as program variables in C++ code, the functional framework enables
the mathematical formalism of Differential Geometry to be more closely
reflected in GRworkbench . The powerful technique of `automatic
differentiation' has replaced numerical differentiation of the metric
components, resulting in more accurate derivatives and an order-of-magnitude
performance increase for operations relying on differentiation
Developments in GRworkbench
The software tool GRworkbench is an ongoing project in visual, numerical
General Relativity at The Australian National University. Recently, GRworkbench
has been significantly extended to facilitate numerical experimentation in
analytically-defined space-times. The numerical differential geometric engine
has been rewritten using functional programming techniques, enabling objects
which are normally defined as functions in the formalism of differential
geometry and General Relativity to be directly represented as function
variables in the C++ code of GRworkbench. The new functional differential
geometric engine allows for more accurate and efficient visualisation of
objects in space-times and makes new, efficient computational techniques
available. Motivated by the desire to investigate a recent scientific claim
using GRworkbench, new tools for numerical experimentation have been
implemented, allowing for the simulation of complex physical situations.Comment: 14 pages. To appear A. Moylan, S.M. Scott and A.C. Searle,
Developments in GRworkbench. Proceedings of the Tenth Marcel Grossmann
Meeting on General Relativity, editors M. Novello, S. Perez-Bergliaffa and R.
Ruffini. Singapore: World Scientific 200
Convex Geometry and its Applications
The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of other algorithms in computer science. High-dimensional geometry is an extremely active area of research: the participation of a considerable number of talented young mathematicians at this meeting is testament to the fact that the field is flourishing
Convex Geometry and its Applications (hybrid meeting)
The geometry of convex domains in Euclidean space plays a central role
in several branches of mathematics: functional and harmonic analysis, the
theory of PDE, linear programming and, increasingly, in the study of
algorithms in computer science.
The purpose
of this meeting was to bring together researchers from the analytic, geometric and probabilistic
groups who have contributed to these developments
The game semantics of game theory
We use a reformulation of compositional game theory to reunite game theory
with game semantics, by viewing an open game as the System and its choice of
contexts as the Environment. Specifically, the system is jointly controlled by
noncooperative players, each independently optimising a real-valued
payoff. The goal of the system is to play a Nash equilibrium, and the goal of
the environment is to prevent it. The key to this is the realisation that
lenses (from functional programming) form a dialectica category, which have an
existing game-semantic interpretation.
In the second half of this paper, we apply these ideas to build a compact
closed category of `computable open games' by replacing the underlying
dialectica category with a wave-style geometry of interaction category,
specifically the Int-construction applied to the cartesian monoidal category of
directed-complete partial orders
Structural optimization: Challenges and opportunities
A review of developments in structural optimization techniques and their interface with growing computer capabilities is presented. Structural design steps comprise functional definition of an object, an evaluation phase wherein external influences are quantified, selection of the design concept, material, object geometry, and the internal layout, and quantification of the physical characteristics. Optimization of a fully stressed design is facilitated by use of nonlinear mathematical programming which permits automated definition of the physics of a problem. Design iterations terminate when convergence is acquired between mathematical and physical criteria. A constrained minimum algorithm has been formulated using an Augmented Lagrangian approach and a generalized reduced gradient to obtain fast convergence. Various approximation techniques are mentioned. The synergistic application of all the methods surveyed requires multidisciplinary teamwork during a design effort
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