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# National Institute for Mathematical and Biological Synthesis

I just got this invitation. Can anyone think of a good way for the Azimuth Project to take advantage of this? Of course I could try to organize something on network theory and biology, but maybe there's a more 'environmentalist' or 'Azimuthy' thing we could do.

Dear Dr. Baez,

I am writing to you in my capacity as Associate Director for Scientific Activities at the National Institute for Mathematical and Biological Synthesis (NIMBioS, http://www.nimbios.org). Our Institute is a relatively recent addition to a network of synthesis centers supported by the NSF and other funding agencies. We've already had more than 2,700 people participating in different scientific and educational activities here but we also continuously look into expanding into new research areas at the interface of mathematics and biology.

Our Board of Advisers believes that you might potentially be interested in and be a very suitable person for organizing one of our activities, e.g. a working group (http://www.nimbios.org/workinggroups/) or an investigative workshop (http://www.nimbios.org/workshops/). Organizing such an activity doesn't require too much effort but could be tremendously beneficial from a number of different angles (personal, scientific, societal, etc.).

I would like to encourage you to seriously consider such a possibility. Our next deadline is March 1, 2013. I would be happy to answer any questions you might have.

Best regards,

Sergey

Sergey Gavrilets

Distinguished Professor

Arts and Science Excellence Professor

Department of Ecology and Evolutionary Biology

Department of Mathematics

Associate Director for Scientific Activities

National Institute for Mathematical and Biological Synthesis (NIMBioS)

University of Tennessee

Knoxville, TN 37996

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edited January 2013

If nobody has better suggestions, I might try to use this opportunity to run a workshop on stability and tipping points for food webs, climate systems and economic systems. The constraints, I believe, are that:

1) the workshop needs to be about math 2) the workshop needs to be about biology 3) it needs to 'synthesize' these topics

and my own constraint is that

4) I really want to push toward doing things that can help the environment.

Detecting tipping points, and knowing general strategies for stopping them or making them less catastrophic, seems to meet all these criteria, since biologists have done a lot of work on this subject.

Of course the big problem is that I haven't myself done any work on this yet! But I'm hoping I could round up some people who have.

Comment Source:If nobody has better suggestions, I might try to use this opportunity to run a workshop on stability and tipping points for food webs, climate systems and economic systems. The constraints, I believe, are that: 1) the workshop needs to be about math 2) the workshop needs to be about biology 3) it needs to 'synthesize' these topics and my own constraint is that 4) I really want to push toward doing things that can help the environment. Detecting tipping points, and knowing general strategies for stopping them or making them less catastrophic, seems to meet all these criteria, since biologists have done a lot of work on this subject. Of course the big problem is that I haven't myself done any work on this yet! But I'm hoping I could round up some people who have.
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edited January 2013

I guess I should ask Sergey Gavrilets about this. Since he invited me to apply, that's a good sign. But maybe he wants me to propose a workshop that deals with work of mine he's seen - I guess that's typically how it works! I've worked on "network theory" and also "biodiversity and information theory", so this is probably what he expects.

In short, I have to really think about the extra constraint:

5) the workshop should be about something where I can convince people I'll do a good job.

Of course I'm convinced I'll do a good job of anything I attempt, but this enthusiasm is not universally contagious.

Comment Source:I guess I should ask Sergey Gavrilets about this. Since he invited me to apply, that's a good sign. But maybe he wants me to propose a workshop that deals with work of mine he's seen - I guess that's typically how it works! I've worked on "network theory" and also "biodiversity and information theory", so this is probably what he expects. In short, I have to really think about the extra constraint: 5) the workshop should be about something where I can convince people I'll do a good job. Of course _I'm_ convinced I'll do a good job of anything I attempt, but this enthusiasm is not universally contagious.
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3.

NIMBioS Working Groups are chosen to focus on major scientific questions at the interface between biology and mathematics that require insights from diverse researchers. The questions to be addressed may be either fundamental, applied or both, and may be focused around a particular biological topic, or one from mathematics that is driven by biological insight. We are particularly interested in questions that integrate diverse fields, require synthesis at multiple scales, and/or make use of or require development of new mathematical/computational approaches.

Working Groups are relatively small (10-12 participants), focus on a well-defined topic and have well-defined goals and metrics of success (e.g., publications, database, software). Selection of Working Groups is based upon the potential scientific impact and inclusion of participants with a diversity of backgrounds and expertise that match the scientific needs of the effort. Organizers are responsible for identifying and confirming participants with demonstrated accomplishments and skills to contribute to the Working Group. Given this emphasis, working group activities rarely involve recently-trained researchers such as postdocs and graduate students. Participation by international researchers is encouraged, though generally there will not be more than 2-3 individuals from outside North America in a Working Group. Note that, typically, no more than 2 participants can be from the same institution. Working Groups typically meet 2-4 times over a two year period, with each meeting lasting 3-5 days; however the number of participants, number of meetings, and duration of each meeting is flexible, depending on the needs and goals of the Group. Plans can include visits to NIMBioS for subsets of Working Group members to collaborate with NIMBioS IT staff and researchers on Working Group needs.

Comment Source:More information on NIMBios working groups: > NIMBioS Working Groups are chosen to focus on major scientific questions at the interface between biology and mathematics that require insights from diverse researchers. The questions to be addressed may be either fundamental, applied or both, and may be focused around a particular biological topic, or one from mathematics that is driven by biological insight. We are particularly interested in questions that integrate diverse fields, require synthesis at multiple scales, and/or make use of or require development of new mathematical/computational approaches. > Working Groups are relatively small (10-12 participants), focus on a well-defined topic and have well-defined goals and metrics of success (e.g., publications, database, software). Selection of Working Groups is based upon the potential scientific impact and inclusion of participants with a diversity of backgrounds and expertise that match the scientific needs of the effort. Organizers are responsible for identifying and confirming participants with demonstrated accomplishments and skills to contribute to the Working Group. Given this emphasis, working group activities rarely involve recently-trained researchers such as postdocs and graduate students. Participation by international researchers is encouraged, though generally there will not be more than 2-3 individuals from outside North America in a Working Group. Note that, typically, no more than 2 participants can be from the same institution. Working Groups typically meet 2-4 times over a two year period, with each meeting lasting 3-5 days; however the number of participants, number of meetings, and duration of each meeting is flexible, depending on the needs and goals of the Group. Plans can include visits to NIMBioS for subsets of Working Group members to collaborate with NIMBioS IT staff and researchers on Working Group needs.
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4.

NIMBioS Investigative Workshops differ from Working Groups in that they focus on a broader topic or set of related topics at the interface of biology and mathematics and have relatively large size (30-40 participants). Workshops attempt to summarize/synthesize the state of the art and identify future directions, and they have potential for leading to one or more future Working Groups. Organizers invite 15-20 key participants, and the remaining 15-20 participants are filled through open application from the scientific community. Those selected to attend are notified by NIMBioS within two weeks of the application deadline. Participants can include post-docs and graduate students with less experience in the particular topic than those participating in Working Groups. Workshops meet at NIMBioS just once for 2-3 days.

Click here for instructions for organizers and a description of best practices for conducting a successful NIMBioS Investigative Workshop.

NIMBioS support includes travel, accommodation, and per diem for meals. No salary support is provided, and no overhead is allowed.

Development of new experimental or observational data is outside the scope of NIMBioS Workshops, though Workshop results may provide justification for new empirical research and suggest priorities for such research.

A goal of NIMBioS is to enhance the cadre of researchers capable of interdisciplinary efforts across mathematics and biology. As part of this goal, NIMBioS is committed to promoting diversity in all its activities. Diversity is considered in all its aspects, social and scientific, including gender, ethnicity, scientific field, career stage, geography and type of home institution. Requests for support are required to provide an explicit diversity statement describing how the proposed list of participants achieves a broad level of diversity. Questions regarding diversity issues should be directed to Dr. Suzanne Lenhart, the NIMBioS Associate Director for Outreach, Education, and Diversity (diversity@nimbios.org).

Comment Source:More information on NIMBIoS workshops: > NIMBioS Investigative Workshops differ from Working Groups in that they focus on a broader topic or set of related topics at the interface of biology and mathematics and have relatively large size (30-40 participants). Workshops attempt to summarize/synthesize the state of the art and identify future directions, and they have potential for leading to one or more future Working Groups. Organizers invite 15-20 key participants, and the remaining 15-20 participants are filled through open application from the scientific community. Those selected to attend are notified by NIMBioS within two weeks of the application deadline. Participants can include post-docs and graduate students with less experience in the particular topic than those participating in Working Groups. Workshops meet at NIMBioS just once for 2-3 days. > Click here for instructions for organizers and a description of best practices for conducting a successful NIMBioS Investigative Workshop. > NIMBioS support includes travel, accommodation, and per diem for meals. No salary support is provided, and no overhead is allowed. > Development of new experimental or observational data is outside the scope of NIMBioS Workshops, though Workshop results may provide justification for new empirical research and suggest priorities for such research. > A goal of NIMBioS is to enhance the cadre of researchers capable of interdisciplinary efforts across mathematics and biology. As part of this goal, NIMBioS is committed to promoting diversity in all its activities. Diversity is considered in all its aspects, social and scientific, including gender, ethnicity, scientific field, career stage, geography and type of home institution. Requests for support are required to provide an explicit diversity statement describing how the proposed list of participants achieves a broad level of diversity. Questions regarding diversity issues should be directed to Dr. Suzanne Lenhart, the NIMBioS Associate Director for Outreach, Education, and Diversity (diversity@nimbios.org).
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edited February 2013

I find some of the existing NIMBioS working groups and workshops interesting, like these:

• Food web dynamics and stoichiometric constraints in meta-ecosystems- "Ecological stoichiometry and meta-community/-ecosystem theory are two recent approaches that have had success in explaining large-scale ecological dynamics and patterns. However they have developed independently and have addressed different aspects of ecology. This working group will synthesize these two approaches to food web/ecosystem dynamics and address important questions at the community/ecosystem interface. Interactions between stoichiometry and metacommunity processes are likely because the movement of organisms among patches involves the transfer of materials as well as changing the identity of species and their ecological traits. Although some consequences of this process have been identified in models with only a single limiting nutrient we know of no theory that links these two fundamental aspects of dispersal involving more than one nutrient (and thus addressing stoichiometric dynamics)."

• Multi-scale analysis of cortical networks - "We present the use of statistical network theory as a unifying mathematical model that enables the analysis of neuroscientific data across multiple levels of abstraction, ranging from single neuron to whole brain. There are three basic steps in our approach. The first is to convert the cortical spatio-temporal measurements into a functional graph-based representation, where the nodes are cortical elements, and the edges represent correlations or other specific relations such as causality between their activities. The second step extracts basic network properties based on building blocks called motifs. The third step examines properties of the network as characterized by the distribution of motifs. We will analyze the differences in motifs as a function of the state of the subject and the task being performed. This analysis will allow us to determine whether functional network features can be used as bio-markers of the state of the brain. This may prove useful in distinguishing diseased brains from normal ones, such as in the case of Alzheimer's."

• Disturbance Regimes and Climate-Carbon Feedback - "Disturbances have been recognized as a key factor affecting terrestrial biogeochemical processes but can be easily misinterpreted without considering the context of disturbance regimes. Many studies have been conducted to quantify impacts of individual disturbance events on ecosystem carbon processes. In general, one disturbance event, such as wildfire, usually triggers release of a large amount of carbon and then follows by recovery processes. It is important to recognize that any disturbance events happen in a context of disturbance regime in a region. If the disturbance regime does not change over time in a region (i.e. stationary), recovery processes after one disturbance event result in net carbon uptake that can fully compensate the carbon loss triggered by the disturbance event, leading to no net change in carbon balance over time. Similarly over space, the carbon loss triggered by the disturbance event in one area can be fully compensated by carbon gain by recovery in other areas in a region if regional disturbance regimes are stationary. Thus, disturbance impacts on biogeochemical cycles have to be interpreted in the context of disturbance regimes and their responses to global change. Disturbance regimes can usually be characterized by disturbance frequency, severity, and extensity, and differ in different regions of the world. So far, the quantitative relationship between carbon-climate feedback and disturbance regimes has not yet been carefully explored. Climate change likely alters disturbance regimes (i.e. nonstationary). The nonstationary disturbance regimes trigger either net carbon releases from or uptake by terrestrial ecosystems, feeding back to climate change. Mathematical models are needed to quantify stationarity of disturbance regimes and their feedback to global carbon cycles and climate change."

Comment Source:I find some of the existing NIMBioS working groups and workshops interesting, like these: * [Food web dynamics and stoichiometric constraints in meta-ecosystems](http://www.nimbios.org/workinggroups/WG_FoodWebs)- &quot;Ecological stoichiometry and meta-community/-ecosystem theory are two recent approaches that have had success in explaining large-scale ecological dynamics and patterns. However they have developed independently and have addressed different aspects of ecology. This working group will synthesize these two approaches to food web/ecosystem dynamics and address important questions at the community/ecosystem interface. Interactions between stoichiometry and metacommunity processes are likely because the movement of organisms among patches involves the transfer of materials as well as changing the identity of species and their ecological traits. Although some consequences of this process have been identified in models with only a single limiting nutrient we know of no theory that links these two fundamental aspects of dispersal involving more than one nutrient (and thus addressing stoichiometric dynamics).&quot; * [Multi-scale analysis of cortical networks](http://www.nimbios.org/workinggroups/WG_CorticalNetworks) - &quot;We present the use of statistical network theory as a unifying mathematical model that enables the analysis of neuroscientific data across multiple levels of abstraction, ranging from single neuron to whole brain. There are three basic steps in our approach. The first is to convert the cortical spatio-temporal measurements into a functional graph-based representation, where the nodes are cortical elements, and the edges represent correlations or other specific relations such as causality between their activities. The second step extracts basic network properties based on building blocks called motifs. The third step examines properties of the network as characterized by the distribution of motifs. We will analyze the differences in motifs as a function of the state of the subject and the task being performed. This analysis will allow us to determine whether functional network features can be used as bio-markers of the state of the brain. This may prove useful in distinguishing diseased brains from normal ones, such as in the case of Alzheimer's.&quot; * [Disturbance Regimes and Climate-Carbon Feedback ](http://www.nimbios.org/workshops/WS_carbon) - &quot;Disturbances have been recognized as a key factor affecting terrestrial biogeochemical processes but can be easily misinterpreted without considering the context of disturbance regimes. Many studies have been conducted to quantify impacts of individual disturbance events on ecosystem carbon processes. In general, one disturbance event, such as wildfire, usually triggers release of a large amount of carbon and then follows by recovery processes. It is important to recognize that any disturbance events happen in a context of disturbance regime in a region. If the disturbance regime does not change over time in a region (i.e. stationary), recovery processes after one disturbance event result in net carbon uptake that can fully compensate the carbon loss triggered by the disturbance event, leading to no net change in carbon balance over time. Similarly over space, the carbon loss triggered by the disturbance event in one area can be fully compensated by carbon gain by recovery in other areas in a region if regional disturbance regimes are stationary. Thus, disturbance impacts on biogeochemical cycles have to be interpreted in the context of disturbance regimes and their responses to global change. Disturbance regimes can usually be characterized by disturbance frequency, severity, and extensity, and differ in different regions of the world. So far, the quantitative relationship between carbon-climate feedback and disturbance regimes has not yet been carefully explored. Climate change likely alters disturbance regimes (i.e. nonstationary). The nonstationary disturbance regimes trigger either net carbon releases from or uptake by terrestrial ecosystems, feeding back to climate change. Mathematical models are needed to quantify stationarity of disturbance regimes and their feedback to global carbon cycles and climate change.&quot;
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edited February 2013

Hi John. I must apologize for not responding to your question regarding a previous question of mine on the graph transformations thread, which I thought had gotten lost in the forum flow (I'll continue that discussion there soon).

This does look like an interesting opportunity. I'm not sure if what I am interested in would satisfy criterion

4) I really want to push toward doing things that can help the environment

in a direct way.

I think we could attempt to push forward our preliminary discussion about graph transformations, which could also be related to food webs. I don't know about climate systems or economic systems, but I would like to learn much more about both of them.

For the general understanding of biological systems, I think it would be helpful to develop a better theory of the way in which information is intrinsically represented in networks of molecular interactions. It could be nice to attempt to abstract from something akin to an operationalist framework. This could be developed on abstract representations of such networks, which would then basically tie all of these ideas into the general network theory that you've been working on and, by extension, to the graph transformations stuff, but using examples of molecular biological networks as intuition pumps to satisfy criterion

2) the workshop needs to be about biology.

Comment Source:Hi John. I must apologize for not responding to your question regarding a previous question of mine on the graph transformations thread, which I thought had gotten lost in the forum flow (I'll continue that discussion there soon). This does look like an interesting opportunity. I'm not sure if what I am interested in would satisfy criterion > 4) I really want to push toward doing things that can help the environment in a direct way. I think we could attempt to push forward our preliminary discussion about graph transformations, which could also be related to food webs. I don't know about climate systems or economic systems, but I would like to learn much more about both of them. For the general understanding of biological systems, I think it would be helpful to develop a better theory of the way in which information is intrinsically represented in networks of molecular interactions. It could be nice to attempt to abstract from something akin to an operationalist framework. This could be developed on abstract representations of such networks, which would then basically tie all of these ideas into the general network theory that you've been working on and, by extension, to the graph transformations stuff, but using examples of molecular biological networks as intuition pumps to satisfy criterion > 2) the workshop needs to be about biology.
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Comment Source:Hi! I'll think about this a little and then say something...
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edited March 2013

I decided not to apply by March 1st. I will try to apply for the next round by 1 September 2013, for programs starting in the summer or fall of 2014. Right now I'm thinking a program on entropy and biology might be fun. I sent emails to these people to see if they could be interested:

They're all interested in biology and entropy.

Comment Source:I decided not to apply by March 1st. I will try to apply for the next round by 1 September 2013, for programs starting in the summer or fall of 2014. Right now I'm thinking a program on entropy and biology might be fun. I sent emails to these people to see if they could be interested: * [Marc Harper](http://johncarlosbaez.wordpress.com/2011/05/26/information-geometry-part-8/) * [John Harte](http://johncarlosbaez.wordpress.com/2013/02/21/maximum-entropy-and-ecology/) * [Tom Leinster](http://johncarlosbaez.wordpress.com/2011/11/07/measuring-biodiversity/) * [Chris Lee](http://potentialinfo.blogspot.com/) * [Romain Brasselet](http://johncarlosbaez.wordpress.com/2012/07/14/the-mathematics-of-biodiversity-part-8/) They're all interested in biology and entropy.
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John Harte wrote:

Dear John,

I would be very interested!

Ethan White would be a good participant, as would Roderick Dewar from Australia. They are both very familiar with the nuances of MaxEnt and are also familiar with my theory. Rod Dewar is also very involved at the frontier of what is called the theory of maximum entropy production.

I am attaching pdfs of two of my papers because I note that some of the responders to your blog seemed to have trouble accessing them. My Oxford Press book "Maximum Entropy and Ecology: A Theory of Abundance, Distribution and Energetics" is unfortunately only available thru Amazon or the publisher or libraries…I can't send a pdf of the manuscript.

Cheers,

John

If anyone wants those pdfs, let me know!

So, I'll add to the list

Roderick Dewar's page includes some interesting things about the highly controversial 'maximum entropy production' principle.

Comment Source:John Harte wrote: > Dear John, > I would be very interested! > Ethan White would be a good participant, as would Roderick Dewar from Australia. They are both very familiar with the nuances of MaxEnt and are also familiar with my theory. Rod Dewar is also very involved at the frontier of what is called the theory of maximum entropy production. > I am attaching pdfs of two of my papers because I note that some of the responders to your blog seemed to have trouble accessing them. My Oxford Press book "Maximum Entropy and Ecology: A Theory of Abundance, Distribution and Energetics" is unfortunately only available thru Amazon or the publisher or libraries…I can't send a pdf of the manuscript. > Cheers, > John If anyone wants those pdfs, let me know! So, I'll add to the list * [Ethan White](http://whitelab.weecology.org/publications) * [Roderick Dewar](http://biology.anu.edu.au/roderick_dewar/) Roderick Dewar's page includes some interesting things about the highly controversial 'maximum entropy production' principle.
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Romain Brasselet wrote:

Of relevance to this workshop in the neuroscience community, the first person I know who comes to mind is William Bialek (http://www.princeton.edu/~wbialek/wbialek.html) who has an impressive bibliography on (among others) entropy-based methods to study biological systems. In the field of information theory applied to neural coding, among others, Jonathan Victor (http://www-users.med.cornell.edu/~jdvicto/jdvonweb.html) and Stefano Panzeri (http://www.nature.com/nrn/journal/v10/n3/full/nrn2578.html) made some important contributions and are considered experts in the domain.

So, I need to check out

Comment Source:Romain Brasselet wrote: > Of relevance to this workshop in the neuroscience community, the first person I know who comes to mind is William Bialek ([http://www.princeton.edu/~wbialek/wbialek.html](http://www.princeton.edu/~wbialek/wbialek.html)) who has an impressive bibliography on (among others) entropy-based methods to study biological systems. In the field of information theory applied to neural coding, among others, Jonathan Victor ([http://www-users.med.cornell.edu/~jdvicto/jdvonweb.html](http://www-users.med.cornell.edu/~jdvicto/jdvonweb.html)) and Stefano Panzeri ([http://www.nature.com/nrn/journal/v10/n3/full/nrn2578.html](http://www.nature.com/nrn/journal/v10/n3/full/nrn2578.html)) made some important contributions and are considered experts in the domain. So, I need to check out * [William Bialek](http://www.princeton.edu/~wbialek/wbialek.html) * [Jonathan Victor](http://www-users.med.cornell.edu/~jdvicto/jdvonweb.html) * [Stefano Panzeri](http://www.nature.com/nrn/journal/v10/n3/full/nrn2578.html)
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edited March 2013

Marc Harper wrote:

Hi John,

I am definitely interested! Here are some people that I think would be good (with example papers):

David Koslicki, Ohio State, Topological entropy of DNA sequences. David has a very interesting method applying topological entropy to genomic data.

Michael Lachmann, Max Planck institute, The fitness value of information (and his collaborators?).

Chris Strelioff, UC Davis, Evolutionary dynamics, epistatic interactions, and biological information

The authors of this paper might be good: Stability and diversity in collective adaptation. They are information geometers that have studied agent-based evolutionary dynamics in a similar manner to my work on the replicator equation.

Leibler, of KL-divergence, wrote a relevant paper a few years back: Phenotypic diversity, population growth, and information in fluctuating environments with Edo Kussell on applying information divergences to biology.

You could also add Dashiell Fryer, my collaborator at Pomona College, and perhaps Georgy P. Karev.

Do you need more? I could find others. Chris may know of others on the bioinformatics side.

Best,

Marc

Comment Source:Marc Harper wrote: > Hi John, > I am definitely interested! Here are some people that I think would be good (with example papers): > David Koslicki, Ohio State, [Topological entropy of DNA sequences](http://bioinformatics.oxfordjournals.org/content/27/8/1061.full). David has a very interesting method applying topological entropy to genomic data. > Michael Lachmann, Max Planck institute, [The fitness value of information](http://onlinelibrary.wiley.com/doi/10.1111/j.1600-0706.2009.17781.x/abstract) (and his collaborators?). > Chris Strelioff, UC Davis, [Evolutionary dynamics, epistatic interactions, and biological information](http://www.sciencedirect.com/science/article/pii/S0022519310003826) > The authors of this paper might be good: [Stability and diversity in collective adaptation](https://www.sciencedirect.com/science/article/pii/S0167278905002708). They are information geometers that have studied agent-based evolutionary dynamics in a similar manner to my work on the replicator equation. > Leibler, of KL-divergence, wrote a relevant paper a few years back: [Phenotypic diversity, population growth, and information in fluctuating environments](http://www.sciencemag.org/content/309/5743/2075.full) with Edo Kussell on applying information divergences to biology. > You could also add Dashiell Fryer, my collaborator at Pomona College, and perhaps Georgy P. Karev. > Do you need more? I could find others. Chris may know of others on the bioinformatics side. > Best, > Marc
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edited March 2013

Marc Harper also wrote:

Hi John,

I remembered another good potential participant. Jeremy England, MIT Physics, wrote an interesting paper last year:

"Statistical Physics of Self-Replication"

Self-replication is a capacity common to every species of living thing, and simple physical intuition dictates that such a process must invariably be fueled by the production of entropy. Here, we undertake to make this intuition rigorous and quantitative by deriving a lower bound for the amount of heat that is produced during a process of self-replication in a system coupled to a thermal bath. We find that the minimum value for the physically allowed rate of heat production is determined by the growth rate, internal entropy, and durability of the replicator, and we discuss the implications of this finding for bacterial cell division, as well as for the pre-biotic emergence of self-replicating nucleic acids.

http://arxiv.org/abs/1209.1179

This is the paper that found that E. coli and self-replicating RNA molecules replicate at a rate close to the thermodynamic limit.

Comment Source:Marc Harper also wrote: > Hi John, > I remembered another good potential participant. Jeremy England, MIT Physics, wrote an interesting paper last year: > "Statistical Physics of Self-Replication" > Self-replication is a capacity common to every species of living thing, and simple physical intuition dictates that such a process must invariably be fueled by the production of entropy. Here, we undertake to make this intuition rigorous and quantitative by deriving a lower bound for the amount of heat that is produced during a process of self-replication in a system coupled to a thermal bath. We find that the minimum value for the physically allowed rate of heat production is determined by the growth rate, internal entropy, and durability of the replicator, and we discuss the implications of this finding for bacterial cell division, as well as for the pre-biotic emergence of self-replicating nucleic acids. > [http://arxiv.org/abs/1209.1179](http://arxiv.org/abs/1209.1179) > This is the paper that found that E. coli and self-replicating RNA molecules replicate at a rate close to the thermodynamic limit.