Abstraction and Simulation

By Eric Cruet

 

Complex computational models typically require large amounts of processing power to produce highly detailed output difficult for users to understand. Building abstracted simulation and visualization systems that simplify both computation and output can help overcome this barrier.

Furthermore, the output of such simulations, which often consists of an agonizingly detailed trace of system events, can be difficult to understand at a global or intuitive level. These two considerations, economy of resources (time, cycles) and intelligibility, argue for the development of abstracted simulation systems of reduced complexity that ignore certain interactions or collapse over some dimensions. Abstracting a detailed simulation can simplify both computation and output, providing an accurate picture of events and efficient utilization of resources.

Since W. S. Gosset, a brewer at Guiness and considered the “father of statistics”, used simulation to prove his elucidation of the t-statistic [2], simulation and visualization in scientific research have been driven by interaction between the following:

1. Inspiration, which may be motivated by sheer curiosity as well as specific theoretical or practical problems

2. Intuition, which may guide the search for a problem solution or lead to new discoveries when reasoning alone is insufficient to ensure continued progress

3. Abstraction, which encompasses the modeling and analysis techniques required to build a simulation model, design experiments using that model, and draw appropriate conclusions from the observed results

4. Experimentation, which is computer based and thus differs fundamentally from other empirical scientific work because of the efficiency improvements that are achievable using Monte Carlo methods

Henri Poincare, was a polymath, and in mathematics also known as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime.  In his text, Mathematical Discovery [1], he stated on inspiration and detailed verification (emphasis added)— “I have spoken of the feeling of absolute certainty which accompanies the inspiration; in the cases quoted this feeling was not deceptive, and more often than not this will be the case. But we must beware of thinking that this is a rule without exceptions. Often the feeling deceives us without being any less distinct on that account, and we only detect it when we attempt to establish the demonstration

From the opposite perspective, abstraction encompasses both simulation modeling and the simulation analysis required to do the following:

•Build a model

•Design experiments using that model

•Draw appropriate conclusions from the observed results.

Simulation-based experimentation differs fundamentally from all other types of empirical scientific work by the large potential efficiency improvements that are achievable because we have complete control of the experimental conditions under which each alternative scenario is simulated.

Examples:

NEURON

NEURON is a simulation environment for modeling individual neurons and networks of neurons. As of version 7.3, Neuron is capable of handling diffusion-reaction models, and integrating diffusion functions into models of synapses and cellular networks.

NEURON [3] models individual neurons via the use of sections which are subdivided into individual compartments by the program, instead of requiring the user to manually create the compartments. The primary scripting language that is used to interact with it is hoc but a Python interface is also available. The programs for it can be written interactively in a shell, or loaded from a file. NEURON supports parallelization via the MPI protocol. Also, starting with NEURON 7.0 parallelization is possible via internal multithreaded routines, for use on computers with multiple cores. 

Currently, NEURON is used as the basis for instruction in computational neuroscience in many courses and laboratories around the world.

GENESIS

Generative E-Social Science for Socio-Spatial Simulation (GENESIS) [6]

Generative social science is widely regarded as one of the grand  challenges of the social sciences. The term was popularised by  Epstein and Axtell of the Brookings Institution in the book (1996) Growing Artificial Societies: Social Science from the Bottom Up who define it as simulation that “… allows us to grow social  structures in silico demonstrating that certain sets of micro-specifications are sufficient to  generate the macro-phenomena of interest”. It is consistent with the  development of the complexity sciences, with the development of decentralised  and distributed agent-based simulation, and with ideas about social and spatial  emergence. It requires large-scale data bases for its execution as well as  powerful techniques of visualisation for its understanding and dissemination. It  provides experimental conditions under which key policy initiatives can be  tested on large-scale populations simulated at individual level. It is entirely  coincident with the development of e-social science which provides the infrastructure  on which such modelling must take place.

In closing, advances in simulation are driven by the continuous interplay of the following:

Our sources of inspiration—both internal and external—for the discovery of solutions to practical problems as well as the theory and methodology required to attack those problems;

The intuition that we acquire from careful experimentation with well-designed simulation models, from intense scrutiny of the results, and from allowing the unconscious to work on the results

The conscious follow-up work in which the emerging flashes of insight into the problem at hand are expressed precisely, verified completely, and connected to other simulation work.

http://youtu.be/JqMpGrM5ECo

References:

[1] Poincaré, Henri. (1914) 1952. “Mathematical Discovery.” In Science and Method, 46–63. Translated by Francis Maitland, with a preface by Bertrand Russell. London: Thomas Nelson and Sons. Reprint, New York: Dover Publications.

[2] http://www.lib.ncsu.edu/specialcollections/simulation/collections.php

[3] Brette R., Rudolph M., Carnevale T., Hines M., Beeman D., Bower J., et al.  (2007). Simulation of networks of spiking neurons: a review of tools and strategies. J. Comput. Neurosci. 23, 349–398. doi: 10.1007/s10827-007-0038-6. [PMC free article]  [PubMed] [Cross Ref]

[4] Drewes R. (2005). Brainlab: a Toolkit to Aid in the Design, Simulation, and Analysis of Spiking Neural Networks with the NCS Environment. Master’s thesis, University of Nevada, Reno. [PMC free article]  [PubMed]

[5] Drewes R., Zou Q., Goodman P. (2009). Brainlab: a python toolkit to aid in the design, simulation, and analysis of spiking neural networks with the neocortical simulator. Front. Neuroinform. 3:16. doi: 10.3389/neuro.11.016.2009. [PMC free article]  [PubMed] [Cross Ref]

http://www.genesis.ucl.ac.uk/