Starts 17 May 2017 15:00
Ends 17 May 2017 16:00
Central European Time
QLS Seminar: Extracting information from simple statistical laws in complex component systems
ICTP
Central Area, 2nd floor, old SISSA building, Via Beirut
Several complex systems in various fields can be described as component systems, i.e. sets of objects (genomes, books, or LEGO toys) composed of elementary components (genes, words, or LEGO bricks). Several emerging statistical laws regarding the statistics of components can be empirically observed in such diverse systems. These laws may be the consequence of the underlying architectural constrains, thus in principle can provide information about the system properties.
Our work tackles the general questions of what can be learned from these simple statistical laws about what laws are a "universal" property of very different component system and what are instead specific of the system in analysis, how and if these laws are related to each other, and what simple stochastic processes can be used to understand their origins.
In this presentation I will focus on two specific examples. The first example concerns the "U"-shaped distribution of shared genes across genomes, which is central to the current debate in evolutionary genomics. We show that its characteristic shape can be obtained by a null model simply based on the empirical heterogeneity of the component abundances. This implies that the distribution of shared genes is mainly a statistical consequence of other known system properties. This result shows that to extract the relevant biological information it is necessary to build null models. In this way it is possible to take into account general emerging features and thus extract the systems specific properties.
The second example considers the growth of the book/object "vocabulary" (i.e. how many distinct words/components are present) as a function of its "size" (i.e. the total number of components), a law known in linguistics as Heaps’ law. We focused on how the vocabulary fluctuations scale with its average value, showing a non-trivial and general behavior across different systems. Specifically, the standard deviation grows linearly with the average (Taylor’s law). We have found that the minimal stochastic growth processes that can reproduce this scaling belong to a class of models that includes the Chinese Restaurant process. This suggests a general rich-gets-richer mechanism in the innovation dynamics of thus component systems, leading to interesting system-specific interpretations.
In this presentation I will focus on two specific examples. The first example concerns the "U"-shaped distribution of shared genes across genomes, which is central to the current debate in evolutionary genomics. We show that its characteristic shape can be obtained by a null model simply based on the empirical heterogeneity of the component abundances. This implies that the distribution of shared genes is mainly a statistical consequence of other known system properties. This result shows that to extract the relevant biological information it is necessary to build null models. In this way it is possible to take into account general emerging features and thus extract the systems specific properties.
The second example considers the growth of the book/object "vocabulary" (i.e. how many distinct words/components are present) as a function of its "size" (i.e. the total number of components), a law known in linguistics as Heaps’ law. We focused on how the vocabulary fluctuations scale with its average value, showing a non-trivial and general behavior across different systems. Specifically, the standard deviation grows linearly with the average (Taylor’s law). We have found that the minimal stochastic growth processes that can reproduce this scaling belong to a class of models that includes the Chinese Restaurant process. This suggests a general rich-gets-richer mechanism in the innovation dynamics of thus component systems, leading to interesting system-specific interpretations.