Research interests
Our work focuses on the statistical physics of complex systems, in particular stochastic processes out of equilibrium. I am mainly interested in the development of analytical theory, but naturally most of our work also involves simulations. I have also collaborated with a number of colleagues in other disciplines, most notably in evolutionary and developmental biology, with linguists, economists and social scientists.
If you are a (prospective) student you may be interested in the methods we use:
- theory of stochastic processes (e.g. master and Fokker-Planck equations, van Kampen or Kramers-Moyal expansions)
- nonlinear dynamics, chaos, pattern formation
- field theory, path integrals and generating functionals (Martin-Siggia-Rose formalism), replica theory, random matrix theory
- piecewise deterministic Markov processes
- WKB method and rare events
- population dynamics, in particular invasion, fixation and extinction events
- ...
Principal research topics (partially overlapping):
Stochastic populations and individual-based models
This is really the main topic of my work. We use methods from statistical physics to study populations consisting of discrete individuals. Our main interest is in the effects of noise. Applications include social and biological populations.
Key papers
Evolutionary dynamics, intrinsic noise, and cycles of cooperation
AJ Bladon, T Galla, AJ McKane
Physical Review E 81 (6), 066122
Mixing times in evolutionary game dynamics
AJ Black, A Traulsen, T Galla
Physical Review Letters 109 (2), 028101
Consensus and diversity in multistate noisy voter models
F Herrerías-Azcué, T Galla
Physical Review E 100 (2), 022304
Stochastic waves in a Brusselator model with nonlocal interaction
T Biancalani, T Galla, AJ McKane
Physical Review E 84 (2), 026201
Competition for resources can explain patterns of social and individual learning in nature
M Smolla, RT Gilman, T Galla, S Shultz
Proceedings of the Royal Society B: Biological Sciences 282 (1815), 20151405
L De Sanctis, T Galla
Disordered systems, random matrices and models of complex ecosystems
I did my PhD with David Sherrington, one of the fathers of spin glass physics, so naturally I have an interest in disordered systems. Recent work focuses on the statistical physics of random Lotka-Volterra systems, and how the spectra of random matrices can be used to characterise the stability of `feasible' equilibria. The AI (actual investigator) for most of our recent papers is Joseph W. Baron.
Key papers
Dispersal-induced instability in complex ecosystems
JW Baron, T Galla
Nature communications 11 (1), 6032
Breakdown of random-matrix universality in persistent Lotka-Volterra communities
JW Baron, TJ Jewell, C Ryder, T Galla
Physical Review Letters 130 (13), 137401
Eigenvalues of random matrices with generalized correlations: A path integral approach
JW Baron, TJ Jewell, C Ryder, T Galla
Physical Review Letters 128 (12), 120601
Dynamically evolved community size and stability of random Lotka-Volterra ecosystems
T Galla
Europhysics Letters 123 (4), 48004
Stochastic systems in switching environments
Many biological systems are subject to changing external environments. In this line of worl we study the statistical physics of individual-based models for which the rules of engagement switch from time to time, often stochastically. We have developed a method to systematically approximate the stationary states of sysems with intrinsic noise in switching environments, and we work on fixation of mutants in changing external conditions. Applications include the evolution of anti-microbial resistance (collaboration with Danna Gifford), and the evolution of mating types (collaboration with George Constable).
Selected papers
Intrinsic noise in systems with switching environments
PG Hufton, YT Lin, T Galla, AJ McKane
Physical Review E 93 (5), 052119
Fixation in finite populations evolving in fluctuating environments
P Ashcroft, PM Altrock, T Galla
Journal of The Royal Society Interface 11 (100), 20140663
Switching environments, synchronous sex, and the evolution of mating types
E Berríos-Caro, T Galla, GWA Constable
Theoretical population biology 138, 28-42
Competition delays multi-drug resistance evolution during combination therapy
E Berríos-Caro, DR Gifford, T Galla
Journal of Theoretical Biology 509, 110524
Systems with delay and applications in biology
I'm interested in non-Markovian stochastic systems (systems with delay), and in particular noise-induced effects in these systems. We have come up with systematic Gaussian approximations for individual-based systems with delay. These methods can be used to study for example gene regulatory circuits. I have collaborated with Nancy Papalopulu and her lab (Jochen Kursawe in particular) on genetic oscillators and cell differentiation in developmental biology.
Selected papers
T Galla
Physical Review E 80 (2), 021909
T Brett, T Galla
Physical Review Letters 110 (25), 250601
M Goodfellow, NE Phillips, C Manning, T Galla, N Papalopulu
Nature communications 5 (1), 3399
NE Phillips, CS Manning, T Pettini, V Biga, E Marinopoulou, P Stanley, ...
Elife 5, e16118
Network Meta-Analysis
A few years ago Annabel Davies (then first year PhD student) and I decided to jump on a ship with unknown destination and to start working on Network Meta-Analysis, a technique in medical statistics. We started collaborating with Gerta Rücker and her group, and we have established some analogies of NMA and random walks on networks. We have also written an introduction to NMA for physicists.
Papers
Network meta-analysis: a statistical physics perspective
AL Davies, T Galla
Journal of Statistical Mechanics: Theory and Experiment 2022 (11), 11R001
Network meta‐analysis and random walks
AL Davies, T Papakonstantinou, A Nikolakopoulou, G Rücker, T Galla
Statistics in Medicine 41 (12), 2091-2114
Degree irregularity and rank probability bias in network meta‐analysis
AL Davies, T Galla
Research Synthesis Methods 12 (3), 316-332
Dynamics of language features
This is a collaboration with Henri Kauhanen, Ricardo Bermúdez-Otero and Deepthi Gopal. We use an individual-based model of the evolution of language features and its statistical physics solution to introduce `linguistic temperature' -- a dimensionless measure of the propensity of language features to undergo change. Using data from the World Atlas of Language Structures, we show that temperature estimates correlate well with conventional measures of instability, obtained for example from phylogenetic analyses.
Paper
Geospatial distributions reflect temperatures of linguistic features
H Kauhanen, D Gopal, T Galla, R Bermúdez-Otero
Science advances 7 (1), eabe6540
Game learning
We are interested in what happens when players learn how to play a game by trial and error. They try out strategies and then use a learning model to decide which strategies work well and which ones don't. This is in contrast to the fully rational players with full information in conventional game theory. With Doyne Farmer I have shown that realistic learning models lead to unpredictable outcome when the number of strategies in the game is large. Thus, the player's actions do not converge to a Nash equilibrium. We have also worked on the influence of noise (imperfect observations) on the outcome of game learning.
Key papers
Complex dynamics in learning complicated games
T Galla, JD Farmer
Proceedings of the National Academy of Sciences 110 (4), 1232-1236
The prevalence of chaotic dynamics in games with many players
JBT Sanders, JD Farmer, T Galla
Scientific reports 8 (1), 4902
Intrinsic noise in game dynamical learning
T Galla
Physical review letters 103 (19), 198702