Integrating Theoretical Algorithmic Ideas in Empirical Biological Study Amos Korman In collaboration with Ofer Feinerman (Weizmann Institute) 1 / 31
Scientific frameworks Outline Scientific frameworks 1 How can an algorithmic perspective contribute? 2 A novel scientific framework 3 Searching for a nearby treasure 4 Information lower bounds for probabilistic search (DISC 2012) 5 Conclusions 6 2 / 31
Scientific frameworks Classical scientific frameworks in biology Experimental framework: Preprocessing stage: observe and analyze 1 “Guess” a mathematical model 2 Data analysis: tune the parameters 3 3 / 31
Scientific frameworks Example: the Albatross (Nature 1996, 2007) Pr ( l =d) ¡≈ ¡1/d α ¡ The Albatross is performing a Lévy flight 4 / 31
Scientific frameworks Example: the Albatross (Nature 1996, 2007) Pr ( l =d) ¡≈ ¡1/d α ¡ The Albatross is performing a Lévy flight What is α ? do statistics on experiments and obtain e.g., α = 2 4 / 31
Scientific frameworks Theoretical framework: Guess an abstract mathematical model 1 Analyze the model 2 5 / 31
Scientific frameworks Theoretical framework: Guess an abstract mathematical model 1 Analyze the model 2 Find parameters maximizing a utility function 5 / 31
Scientific frameworks Theoretical framework: Guess an abstract mathematical model 1 Analyze the model 2 Find parameters maximizing a utility function Example: if you perform a Lévy flight search under some certain food distribution then α = 2 is optimal [Viswanathan et al. Nature 1999] 5 / 31
Scientific frameworks Theoretical framework: Guess an abstract mathematical model 1 Analyze the model 2 Find parameters maximizing a utility function Example: if you perform a Lévy flight search under some certain food distribution then α = 2 is optimal [Viswanathan et al. Nature 1999] “Explain” a known phenomena Example: Kleinberg’s analysis of the greedy routing algorithm in small world networks “explains” Milgram’s experiment [Nature 2000] 5 / 31
How can an algorithmic perspective contribute? Outline Scientific frameworks 1 How can an algorithmic perspective contribute? 2 A novel scientific framework 3 Searching for a nearby treasure 4 Information lower bounds for probabilistic search (DISC 2012) 5 Conclusions 6 6 / 31
How can an algorithmic perspective contribute? An algorithmic perspective Recently, CS theoreticians have tried to contribute from an algorithmic perspective [Alon, Chazelle, Kleinberg, Papadimitriou, Valiant, etc.]. 7 / 31
How can an algorithmic perspective contribute? An algorithmic perspective Recently, CS theoreticians have tried to contribute from an algorithmic perspective [Alon, Chazelle, Kleinberg, Papadimitriou, Valiant, etc.]. Guiding principle Algorithms’ people are good at: 7 / 31
How can an algorithmic perspective contribute? An algorithmic perspective Recently, CS theoreticians have tried to contribute from an algorithmic perspective [Alon, Chazelle, Kleinberg, Papadimitriou, Valiant, etc.]. Guiding principle Algorithms’ people are good at: Formulating sophisticated guesses (algorithms) 1 Analyzing the algorithms 2 7 / 31
How can an algorithmic perspective contribute? Algorithmic perspective in classical frameworks Experimental framework: Preprocessing stage: observe and analyze 1 Guess a mathematical model [Afek et al., Science’11] 2 Data analysis: tune the parameters 3 Theoretical framework: Guess a mathematical model 1 Analyze the model 2 Maximize a utility function [Papadimitriou et al., PNAS 2008] Explain a known phenomena [Kleinberg, Nature, 2000] 8 / 31
How can an algorithmic perspective contribute? Algorithmic perspective in classical frameworks Experimental framework: Preprocessing stage: observe and analyze 1 Guess a mathematical model [Afek et al., Science’11] 2 Data analysis: tune the parameters 3 Theoretical framework: Guess a mathematical model 1 Analyze the model 2 Maximize a utility function [Papadimitriou et al., PNAS 2008] Explain a known phenomena [Kleinberg, Nature, 2000] Can an algorithmic perspective contribute otherwise? 8 / 31
How can an algorithmic perspective contribute? Systems biology Biology is lacking tools for dealing with large, complex and interactive systems. 9 / 31
How can an algorithmic perspective contribute? Systems biology Biology is lacking tools for dealing with large, complex and interactive systems. Early 90’s – Systems Biology (a holistic approach) 9 / 31
How can an algorithmic perspective contribute? Systems biology Biology is lacking tools for dealing with large, complex and interactive systems. Early 90’s – Systems Biology (a holistic approach) Mathematics tools: differential equations. 9 / 31
How can an algorithmic perspective contribute? Systems biology Biology is lacking tools for dealing with large, complex and interactive systems. Early 90’s – Systems Biology (a holistic approach) Mathematics tools: differential equations. Distributed computing: closer to mainstream CS than to physics. 9 / 31
How can an algorithmic perspective contribute? Systems biology Biology is lacking tools for dealing with large, complex and interactive systems. Early 90’s – Systems Biology (a holistic approach) Mathematics tools: differential equations. Distributed computing: closer to mainstream CS than to physics. How can a distributed algorithmic perspective contribute to biology? 9 / 31
How can an algorithmic perspective contribute? The big challenge: reduce the parameter space 10 / 31
How can an algorithmic perspective contribute? The big challenge: reduce the parameter space In physics: rules of nature Obtain equation (or connection) between parameters. E.g., E = MC 2 , ∆ U = Q + W , σ x · σ p ≥ � , etc. 10 / 31
How can an algorithmic perspective contribute? The big challenge: reduce the parameter space In physics: rules of nature Obtain equation (or connection) between parameters. E.g., E = MC 2 , ∆ U = Q + W , σ x · σ p ≥ � , etc. What about biology? 1st solution: borrow connections from physics. 2nd solution: ignore seemingly negligable parameters. 10 / 31
How can an algorithmic perspective contribute? The big challenge: reduce the parameter space In physics: rules of nature Obtain equation (or connection) between parameters. E.g., E = MC 2 , ∆ U = Q + W , σ x · σ p ≥ � , etc. What about biology? 1st solution: borrow connections from physics. 2nd solution: ignore seemingly negligable parameters. We propose: obtain connections between parameters using an algorithmic approach . Tradeoffs: use lower bounds from CS to show that, e.g., any algorithm that runs in time T must use x amount of resources ( x > f ( T ) ). 10 / 31
A novel scientific framework Outline Scientific frameworks 1 How can an algorithmic perspective contribute? 2 A novel scientific framework 3 Searching for a nearby treasure 4 Information lower bounds for probabilistic search (DISC 2012) 5 Conclusions 6 11 / 31
A novel scientific framework Connecting parameters using an algorithmic perspective Ants ¡ Food ¡ Measurements ¡ ¡ Algorithmic ¡tradeoff ¡ ¡ Time ¡ Time ¡vs. ¡ Informa4on ¡capacity ¡ Lower ¡bound ¡on ¡ Informa4on ¡capacity ¡ 12 / 31
A novel scientific framework Remarks: simplified experimental verifications • ¡ Simple ¡ Se7ng ¡ • ¡ Realis+c ¡ Requires ¡ verifica+on ¡ Algorithmic ¡tradeoff ¡ ¡ Measurements ¡ ¡ 100% ¡correct ¡ ¡ Biological ¡bound ¡ ◦ Tradeoffs are invariant of the algorithm = ⇒ Instead of verifying setting+algorithm, only need to verify the setting! 13 / 31
A novel scientific framework A proof of concept This talk Introduce the model (semi-realistic) Discuss the theoretical tradeoffs Experimental part: on-going 14 / 31
A novel scientific framework A proof of concept This talk Introduce the model (semi-realistic) Discuss the theoretical tradeoffs Experimental part: on-going Remark The work is not complete. This presentation is a proof of concept 14 / 31
Searching for a nearby treasure Outline Scientific frameworks 1 How can an algorithmic perspective contribute? 2 A novel scientific framework 3 Searching for a nearby treasure 4 Information lower bounds for probabilistic search (DISC 2012) 5 Conclusions 6 15 / 31
Searching for a nearby treasure Inspiration: the Cataglyphis niger and Honey bee The Cataglyphis niger: 16 / 31
Searching for a nearby treasure Inspiration: the Cataglyphis niger and Honey bee The Cataglyphis niger: Desert ant– does not leave traces, more individual 16 / 31
Searching for a nearby treasure Inspiration: the Cataglyphis niger and Honey bee The Cataglyphis niger: Desert ant– does not leave traces, more individual Relatively smart– big brain, good navigation abilities 16 / 31
Searching for a nearby treasure Good distance and location estimations [Wehner et al.] 17 / 31
Searching for a nearby treasure Goal: find nearby treasures fast Reasons for proximity Increasing the rate of food collection in case a large quantity of food is found [Orians and Pearson, 1979], Decreasing predation risk [Krebs, 1980], The ease of navigating back after collecting the food using familiar landmarks [Collett et al., 1992], etc. 18 / 31
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