Information
- Talks can be given in English or German
- Structure of the presentation:
- ~20-30 mins Talk with slides (I'll bring laptop and projector; PDF files will work, everything else has to be tested before-hand)
- ~10-20 mins Visualisation in a simple simulation program + code presentation
- ~10-20 mins Discussion
- It might be useful to recycle (parts of) the simulation programs used in previous talks if they were in the same programming language, e.g. if one wants to compare one approach to another. Feel free to collaborate on the programming projects where that seems helpful.
- If you need discussion, or want help finding/understanding the literature on your subject, or have specific questions, (at least one of these will usually be the case!), then please come and see me at least 2-3 weeks before your talk is scheduled.
- In any case I would like to briefly discuss your almost finalised slides/program ~one week before your talk (possibly after the previous talk if the room is still available).
General references
Topics and dates
Here you can find the listing and schedule of the topics we distributed in the first week. I have added a few bullet points for each topic to give an idea of the content I had in mind. Also, I have indicated ideas for the simple example programs. Please use these only as suggestions and if you have other ideas feel free to bring them up!
21.10. Frank Siegert:
Applications of Monte-Carlo methods in particle physics
28.10. David Meisel:
Random numbers
- Classification: random vs. pseudo-random vs. quasi-random
- Criteria for pseudo-random numbers
- Algorithms
- Example program: Implementation of a few algorithms and test of their properties, comparison to built-in random number generators
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4.11. Max Hils:
Without Monte-Carlo methods: integration by numerical quadrature
- Classification of algorithms
- Error estimate and its scaling with the number of dimensions
- Example program: Implement a few algorithms and compare their results for an analytically known 1D integral with the expected error estimates with fixed number of evaluations
- Reference: Computational Physics http://www.comp-phys.tu-dresden.de/cp2013/
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11.11. Lukas Schröder:
Monte-Carlo integration basics
- Motivation and basic idea
- Law of large numbers
- Error estimate
- Example program: Volume of a d-dimensional sphere in MC vs. (simple) classical integration. Estimate the (statistical) uncertainty of each result. Compare the runtime (= number of points N) necessary to reach a given accuracy target (e.g. 1%). Plot the scaling of the MC result with N for some fixed values of d. Discuss the scaling with d.
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18.11. Fabian Heisse:
Improving Monte-Carlo integration: Stratified sampling
- Motivation
- Introduction to stratified sampling
- Example program: Demonstrate improvement from stratified sampling for different suitably chosen (1D?) integrals
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18.11. Christian Bartzsch:
Improving Monte-Carlo integration: Importance sampling
- Motivation
- Introduction to importance sampling
- Example program: Demonstrate improvement from importance sampling for different suitably chosen (1D?) integrals
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2.12. Jonas Golde:
Monte-Carlo integration: Adaptive methods (VEGAS)
- Motivation and basic idea
- Algorithm in 1D and nD
- Limitations/assumptions for efficient usage
- Relations to importance sampling
- Example program: VEGAS implementation to integrate spontaneously selected 1D-functions
- References:
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9.12. Johannes Krause:
Monte-Carlo integration with the multi-channel method
- Motivation and basic idea
- Automatic adaptation of weights
- Example program: Demonstrate improvement from a multi-channel for a suitably chosen integral (e.g. with double-peak structure)
- Original reference: http://arxiv.org/abs/hep-ph/9405257
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16.12. Philipp Horn:
Monte-Carlo sampling basics
- Motivation
- Inverse transform method
- Hit-or-miss method
- Example program: reproduce a given distribution function using inverse-transform and hit-or-miss including a comparison of different hit-or-miss input distributions
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13.1. Martin Rehwald:
Particle collision phase space with the RAMBO algorithm
- Phase space for n massless particles
- RAMBO algorithm
- Example program: Generate 10000 events for a 2->4 scattering of massless particles, with a fixed configuration of incoming momenta of p_{0,1}=(E, px, py, pz)=(1000, 0, 0, +-1000) and a uniform distribution of the outgoing momenta. Plot their distribution in the theta variable. (Display some of them in 3D. ?)
- Original reference: http://dx.doi.org/10.1016/0010-4655(86)90119-0 (only from TUD)
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20.1. Alexander Melzer:
Sampling generalised radioactive decay type distributions
- Motivation
- Parton branching probabilities and the analogy to radioactive decay
- Veto algorithm
- Example program: Simplified parton cascade: One splitting function, simplified splitting kernel
- Reference: http://arxiv.org/abs/hep-ph/0603175 Section 4, in particular 4.2
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27.1. Robert Wolff:
Monte-Carlo sampling with the Metropolis/Hastings algorithm
- Introduction to Metropolis algorithm, Markov chains
- Extension to arbitrary distribution functions (Metropolis-Hastings)
- Markov-Chain-Monte-Carlo (MCMC) methods
- Example program:
- References:
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