Current: Influence Maximization in Ising Systems

introexample4In network science and machine learning, a fundamental problem is influence maximization: Given a social network that describes the interactions between individuals in a population, which individuals should be influenced to maximize the collective effect on the entire population? Traditionally, influence maximization has been studied in the context of contagion models which treat marketing as a viral spreading process. While the viral paradigm accurately describes out-of-equilibrium phenomena, it fails to capture scenarios where stochastic opinions yield complex, reverberant opinion patterns, as, for instance, is the case in the formation of political opinions.

Statistical mechanics is particularly well-suited to describe stochastic opinions, and in the context of the Ising model, influence maximization has a natural physical interpretation as maximizing the magnetization given a budget of external magnetic field. Remarkably, the optimal external field solution undergoes a phase transition from focusing on high-degree individuals at high temperatures to focusing on low-degree individuals at low temperatures. Thus, stochastic noise in a social system plays a vital role in determining the optimal control strategy, a result not observed in viral models.

Since the Ising model has found widespread use in machine learning under names such as the Boltzmann machine and pair-wise Markov random fields, this work opens the door for many potential research directions. For instance, Boltzmann machine learning techniques could be used to formulate a data-based influence maximization algorithm. Furthermore, the wealth of approximation techniques (mean-field, TAP, backprop) could yield a number of efficient influence maximization algorithms.


Christopher W. Lynn and Daniel D. Lee. Maximizing Activity in Ising Networks via the TAP Approximation. Association for the Advancement of Artificial Intelligence (AAAI). 2018. (

Christopher W. Lynn and Daniel D. Lee. Statistical Mechanics of Influence Maximization with Thermal Noise. EPL (Europhysics Letters) 117.6: 66001. 2017.

Christopher W. Lynn and Daniel D. Lee. Maximizing Influence in an Ising Network: A Mean-Field Optimal Solution. Advances in Neural Information Processing Systems (NIPS). 2016. (


Past: Simulating Channeling Radiation at Fermilab

linacpicI spent the summer of 2013 at Fermilab working with Tanaji Sen. Together, we developed simulation software to predict the results of electron-channeling experiments at the LINAC at Fermilab (previously named ASTA). In the experiments, a tight beam of electrons is fired parallel to the carbon planes of a diamond. Once the electrons enter the diamond, they become trapped in the inter-planar potential and hop between the induced quantum excited states. When electrons hop from high- to low-energy states, they release radiation that is Lorentz-boosted into the X-ray spectrum in the direction of the electron beam. Given the structure of the beam and the diamond crystal, our simulations were able to accurately predict the spectrum of the resulting channeling radiation from first-principles.


Tanaji Sen and Christopher LynnSpectral Brilliance of Channeling Radiation at the ASTA Photoinjector. Journal of Modern Physics A 29.30: 1450179. 2014.

Ben Blomberg, Daniel Mihalcea, Harsha Panuganti, Philippe Piot, Charles Brau, Bo Choi, William Gabella, Borislav Ivanov, Marcus Mendenhall, Christopher Lynn, Tanaji Sen, Wolfgang Wagner. Planned High-brightness Channeling Radiation Experiment at Fermilab’s Advanced Superconducting Test Accelerator. International Particle Accelerator Conference (IPAC). 2014.


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