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Christopher Griffin

Publications and source records attributed to Christopher Griffin.

At least 19 recordsLinked to original sources
arXiv2026

New Families and Operations on Integrable Graphs

In this paper, we investigate the integrability of Lotka-Volterra (replicator) systems arising from interaction matrices generated from corresponding graph structures, continuing work started by Visomirski and Griffin [J. Phys. A., 58:015701, 2025] and Evripidou et al. [J. Phys. A., 55:325201, 2022] (among others). In particular, we define a new family of graphs, the spoked graphs, and show that all dynamics generated from this family are integrable. In reference to Evripidou et al. (2022), we define a new anti-cloning operator and show that its action on balanced tournament graphs (with odd vertex count) generates new graphs whose dynamics are integrable. Interestingly, we provide numerical evidence that this anti-cloning operation leads to chaotic behaviour when applied to other graph families (e.g., the directed cycles that generate the classically integrable Volterra lattice). This work completes a taxonomy of all integrable dynamics generated by directed graphs with up to six vertices started by Visomirski and Griffin (2025), and suggests several future directions of study on this topic.

nlin.SI↗
arXiv2026

Human-AI Collaboration for Estimating Scientific Replicability

Determining whether published scientific findings can successfully be replicated is a long-standing challenge in the empirical sciences. Existing approaches for replicability assessment typically rely either on human judgment, i.e., creative assembly of human experts, or on machine learning models trained on paper content metadata. While both approaches have demonstrated value, each also has important limitations. Human forecasts can be influenced by cognitive biases and narrow exposure to the research literature, while automated assessments often struggle to capture contextual cues and subtle signals of credibility. In this paper, we examine a hybrid approach. Specifically, we introduce a hybrid prediction market in which algorithmic agents trade alongside human participants to jointly estimate the likelihood that a published scientific finding will be corroborated via the outcome of a controlled replication study. Agents are trained on outcomes from hundreds of prior replication studies while human participants contribute domain knowledge through real-time trading. We evaluate this hybrid approach through multiple live experiments involving participants from different academic disciplines and compare its performance to artificial-only and human-only baselines. Our results show that, except for a few cases, hybrid markets match or outperform artificial prediction markets, producing more accurate and reliable replication forecasts.

cs.CY↗
arXiv2026

Classical and Quantum Dynamics in an Information Theoretic Space

We study elementary classical and quantum dynamics in an information geometric space corresponding to a Bernoulli random variable, extending work by Goehle and Griffin [Chaos, Solitons & Fractals, 188, 115535, (2024)], who study the information theoretic analog of the spring-mass system. Information geometric constructions are useful in both statistical physics and in physical interpretations of Friston's free energy principle, a form of the Bayesian brain hypothesis. In this letter, we derive the spectrum for the Laplace-Beltrami operator in Bernoulli space and find Green's functions for the Helmholtz equation, which provides solutions to the wave, heat, and Poisson equations. We then show how to quantize momentum in Bernoulli space and obtain energies and wavefunctions for both a free particle and a variety of quantum (harmonic) oscillators in this space. In particular, we show that quadratic approximation of the Kullback-Leibler potential used by Goehle and Griffin results in a quantum oscillator in information space that is equivalent to a quantum pendulum in Euclidean space.

quant-ph↗
arXiv2026

Coherent Structures and Travelling Waves in Spatial Replicators from a Biased Volterra Lattice

The Volterra lattice is a well-known integrable family that is also a special class of replicator dynamics and whose members can be put in one-to-one correspondence with the directed cycle graphs. In this paper, we study a variation of the Volterra lattice by introducing a bias term in the replicator interaction matrix. The resulting system can still be put into one-to-one correspondence with the directed cycles, and the dynamics offer one generalisation of the classic rock-paper-scissors evolutionary game. We study the resulting spatial dynamics of this family, showing that travelling wave solutions are present in those dynamics corresponding to the directed 5- and 6-cycles, but not the 4-cycle. Instead, the 4-cycle exhibits a set of stationary solutions that we call `frozen waves' that are similar to but distinct from Turing patterns. This type of solution is also found in the dynamics generated from the directed 6- and 8-cycles. We discuss how these stationary solutions can represent naturally emergent ecological niches in these systems, and offer generalizing conjectures for the existence of both travelling wave solutions and frozen wave solutions in this family of dynamics as a potential program of future investigation.

nlin.PS↗
arXiv2025

Binary Option Market Manipulation by Influencing Belief Dynamics

Using techniques from information geometry, we construct a semi-Hamiltonian system modelling trader beliefs in a binary asset market and study the impact of inequality or asymmetry in beliefs, information, and power on price dynamics. We show that in a market with no inequality and $N$ completely symmetric traders, the resulting dynamics evolve on a $2N + 1$ dimensional manifold consisting of a $2N-2$ dimensional centre manifold, a $2$ dimensional stable manifold and a $1$ dimensional slow manifold. Introducing asymmetry into the traders has the potential to decrease the dimension of the centre manifold, which we prove using a parameter analysis. Using the belief model, we also study the impact of inter-agent communication, exogenous information and asymmetric purchasing power on price dynamics, showing that market bubbles can emerge when powerful traders produce outsize influence in the market, thus impacting other traders' beliefs as well as the price. This process is exacerbated when back-channel communication is permitted. The impact of areas of high curvature in belief space is also discussed.

physics.soc-ph↗
arXiv2025

Multi-Group Dynamics with Tolerant Switching in the Kolkata Paise Restaurant Problem with Dining Clubs

We study the Kolkata Paise Restaurant Problem (KPRP) with multiple dining clubs, extending work in [A. Harlalka, A. Belmonte and C. Griffin, \textit{Physica A}, 620:128767, 2023]. In classical KPRP, $N$ agents chose among $N$ restaurants at random. If multiple users choose the same restaurant, only one will eat. In a dining club, agents coordinate to avoid choosing the same restaurant, but may collide with users outside the club. We consider a dynamic in which agents switch among clubs or the unaffiliated (free agent) group based on their comparative probability of eating. Agents' affiliations are sticky in the sense that they are insensitive (tolerate) to differences in eating probability below a threshold $\tau$ without switching groups. We study the tendency of one group (dining club or free agent group) to become dominant as a function of tolerance by studying the mean-field dynamics of group proportion. We then show empirically that the mean-field group dynamic (assuming infinite populations) differs from the finite population group dynamic. We derive a mathematical approximation in the latter case, showing good agreement with the data. The paper concludes by studying the impact of (food) taxation, redistribution and freeloading in the finite population case. We show that a group that redistributes food tends to become dominant more often as a function of increasing tolerance to a point, at which point agents do not switch frequently enough to enable group dynamics to emerge. This is negatively affected by freeloaders from the non-redistributing group.

physics.soc-ph↗
arXiv2024

Integrability of Generalised Skew-Symmetric Replicator Equations via Graph Embeddings

It is known that there is a one-to-one mapping between oriented directed graphs and zero-sum replicator dynamics (Lotka-Volterra equations) and that furthermore these dynamics are Hamiltonian in an appropriately defined nonlinear Poisson bracket. In this paper, we investigate the problem of determining whether these dynamics are Liouville-Arnold integrable, building on prior work graph in graph decloning by Evripidou et al. [J. Phys. A., 55:325201, 2022] and graph embedding by Paik and Griffin [Phys. Rev. E. 107(5): L052202, 2024]. Using the embedding procedure from Paik and Griffin, we show (with certain caveats) that when a graph producing integrable dynamics is embedded in another graph producing integrable dynamics, the resulting graph structure also produces integrable dynamics. We also construct a new family of graph structures that produces integrable dynamics that does not arise either from embeddings or decloning. We use these results, along with numerical methods, to classify the dynamics generated by almost all oriented directed graphs on six vertices, with three hold-out graphs that generate integrable dynamics and are not part of a natural taxonomy arising from known families and graph operations. These hold-out graphs suggest more structure is available to be found. Moreover, the work suggests that oriented directed graphs leading to integrable dynamics may be classifiable in an analogous way to the classification of finite simple groups, creating the possibility that there is a deep connection between integrable dynamics and combinatorial structures in graphs.

nlin.SI↗
arXiv2024

Dynamics of An Information Theoretic Analog of Two Masses on a Spring

In this short communication we investigate an information theoretic analogue of the classic two masses on spring system, arising from a physical interpretation of Friston's free energy principle in the theory of learning in a system of agents. Using methods from classical mechanics on manifolds, we define a kinetic energy term using the Fisher metric on distributions and a potential energy function defined in terms of stress on the agents' beliefs. The resulting Lagrangian (Hamiltonian) produces a variation of the classic DeGroot dynamics. In the two agent case, the potential function is defined using the Jeffrey's divergence and the resulting dynamics are characterized by a non-linear spring. These dynamics produce trajectories that resemble flows on tori but are shown numerically to produce chaos near the boundary of the space. We then investigate persuasion as an information theoretic control problem where analysis indicates that manipulating peer pressure with a fixed target is a more stable approach to altering an agent's belief than providing a slowly changing belief state that approaches the target.

physics.soc-ph↗
arXiv2023

Spatial Dynamics of Higher Order Rock-Paper-Scissors and Generalisations

We introduce and study the spatial replicator equation with higher order interactions and both infinite (spatially homogeneous) populations and finite (spatially inhomogeneous) populations. We show that in the special case of three strategies (rock-paper-scissors) higher order interaction terms allow travelling waves to emerge in non-declining finite populations. We show that these travelling waves arise from diffusion stabilisation of an unstable interior equilibrium point that is present in the aspatial dynamics. Based on these observations and prior results, we offer two conjectures whose proofs would fully generalise our results to all odd cyclic games, both with and without higher order interactions, assuming a spatial replicator dynamic. Intriguingly, these generalisations for $N \geq 5$ strategies seem to require declining populations, as we show in our discussion.

nlin.PS↗
arXiv2023

Free Entropy Minimizing Persuasion in a Predictor-Corrector Dynamic

Persuasion is the process of changing an agent's belief distribution from a given (or estimated) prior to a desired posterior. A common assumption in the acceptance of information or misinformation as fact is that the (mis)information must be consistent with or familiar to the individual who accepts it. We model the process as a control problem in which the state is given by a (time-varying) belief distribution following a predictor-corrector dynamic. Persuasion is modeled as the corrector control signal with the performance index defined using the Fisher-Rao information metric, reflecting a fundamental cost associated to altering the agent's belief distribution. To compensate for the fact that information production arises naturally from the predictor dynamic (i.e., expected beliefs change) we modify the Fisher-Rao metric to account just for information generated by the control signal. The resulting optimal control problem produces non-geodesic paths through distribution space that are compared to the geodesic paths found using the standard free entropy minimizing Fisher metric in several example belief models: a Kalman Filter, a Boltzmann distribution and a joint Kalman/Boltzmann belief system.

physics.soc-ph↗
arXiv2023

A Multidimensional Fourier Approximation of Optimal Control Surfaces

This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control problem into an unconstrained optimization one is proposed and two problems are solved: a quadratic control problem in the context of Newtonian mechanics, and a control problem arising from an odd-circulant game ruled by the replicator dynamics. Various computational results are presented. Use of automatic differentiation is explored to circumvent the elaborated gradient computation in the first-order optimization procedure. Furthermore, mean square error bounds are derived for the case of one and two-dimensional Fourier series approximations, inducing a general bound for problems of $n$ dimensions.

math.OC↗
arXiv2023

Consensus in Complex Networks with Noisy Agents and Peer Pressure

In this paper we study a discrete time consensus model on a connected graph with monotonically increasing peer-pressure and noise perturbed outputs masking a hidden state. We assume that each agent maintains a constant hidden state and a presents a dynamic output that is perturbed by random noise drawn from a mean-zero distribution. We show consensus is ensured in the limit as time goes to infinity under certain assumptions on the increasing peer-pressure term and also show that the hidden state cannot be exactly recovered even when model dynamics and outputs are known. The exact nature of the distribution is computed for a simple two vertex graph and results found are shown to generalize (empirically) to more complex graph structures.

physics.soc-ph↗
arXiv2023

Approximation of Optimal Control Surfaces for the Bass Model with Stochastic Dynamics

The Bass diffusion equation is a well-known and established modeling approach for describing new product adoption in a competitive market. This model also describes diffusion phenomena in various contexts: infectious disease spread modeling and estimation, rumor spread on social networks, prediction of renewable energy technology markets, among others. Most of these models, however, consider a deterministic trajectory of the associated state variable (e.g., market-share). In reality, the diffusion process is subject to noise, and a stochastic component must be added to the state dynamics. The stochastic Bass model has also been studied in many areas, such as energy markets and marketing. Exploring the stochastic version of the Bass diffusion model, we propose in this work an approximation of (stochastic) optimal control surfaces for a continuous-time problem arising from a $2\times2$ skew symmetric evolutionary game, providing the stochastic counter-part of the Fourier-based optimal control approximation already existent in the literature.

math.OC↗
arXiv2023

A prototype hybrid prediction market for estimating replicability of published work

We present a prototype hybrid prediction market and demonstrate the avenue it represents for meaningful human-AI collaboration. We build on prior work proposing artificial prediction markets as a novel machine-learning algorithm. In an artificial prediction market, trained AI agents buy and sell outcomes of future events. Classification decisions can be framed as outcomes of future events, and accordingly, the price of an asset corresponding to a given classification outcome can be taken as a proxy for the confidence of the system in that decision. By embedding human participants in these markets alongside bot traders, we can bring together insights from both. In this paper, we detail pilot studies with prototype hybrid markets for the prediction of replication study outcomes. We highlight challenges and opportunities, share insights from semi-structured interviews with hybrid market participants, and outline a vision for ongoing and future work.

cs.HC↗
arXiv2023

Stability of Dining Clubs in the Kolkata Paise Problem with and without Cheating

We introduce the idea of a dining club to the Kolkata Paise Restaurant Problem. In this problem, $N$ agents choose (randomly) among $N$ restaurants, but if multiple agents choose the same restaurant, only one will eat. Agents in the dining club will coordinate their restaurant choice to avoid choice collision and increase their probability of eating. We model the problem of deciding whether to join the dining club as an evolutionary game and show that the strategy of joining the dining club is evolutionarily stable. We then introduce an optimized member tax to those individuals in the dining club, which is used to provide a safety net for those group members who don't eat because of collision with a non-dining club member. When non-dining club members are allowed to cheat and share communal food within the dining club, we show that a new unstable fixed point emerges in the dynamics. A bifurcation analysis is performed in this case. To conclude our theoretical study, we then introduce evolutionary dynamics for the cheater population and study these dynamics. Numerical experiments illustrate the behaviour of the system with more than one dining club and show several potential areas for future research.

physics.soc-ph↗
arXiv2023

Topological Learning in Multi-Class Data Sets

We specialize techniques from topological data analysis to the problem of characterizing the topological complexity (as defined in the body of the paper) of a multi-class data set. As a by-product, a topological classifier is defined that uses an open sub-covering of the data set. This sub-covering can be used to construct a simplicial complex whose topological features (e.g., Betti numbers) provide information about the classification problem. We use these topological constructs to study the impact of topological complexity on learning in feedforward deep neural networks (DNNs). We hypothesize that topological complexity is negatively correlated with the ability of a fully connected feedforward deep neural network to learn to classify data correctly. We evaluate our topological classification algorithm on multiple constructed and open source data sets. We also validate our hypothesis regarding the relationship between topological complexity and learning in DNN's on multiple data sets.

cs.LG↗
arXiv2023

On a Finite Population Variation of the Fisher-KPP Equation

In this paper, we formulate a finite population variation of the Fisher-KPP equation using the fact that the reaction term can be generated from the replicator dynamic using a two-player two-strategy skew-symmetric game. We use prior results from Ablowitz and Zeppetella to show that the resulting system of partial differential equations admits a travelling wave solution, and that there are closed form solutions for this travelling wave. Interestingly, the closed form solution is constructed from a sign-reversal of the known closed form solution of the classic Fisher equation. We also construct a closed form solution approximation for the corresponding equilibrium problem on a finite interval with Dirichlet and Neumann boundary conditions. Two conjectures on these corresponding equilibrium problems are presented and analysed numerically.

nlin.PS↗
arXiv2023

Higher Order Dynamics in the Replicator Equation Produce a Limit Cycle in Rock-Paper-Scissors

Recent work has shown that pairwise interactions may not be sufficient to fully model ecological dynamics in the wild. In this letter, we consider a replicator dynamic that takes both pairwise and triadic interactions into consideration using a rank-three tensor. We study {these} new nonlinear dynamics using a generalized rock-paper-scissors game whose dynamics are well understood in the {standard} replicator sense. We show that the addition of higher-order dynamics leads to the creation of a subcritical Hopf bifurcation and consequently an unstable limit cycle. It is known that this kind of behaviour cannot occur in the pairwise replicator in any three strategy games, showing the effect higher-order interactions can have on the resulting dynamics of the system. We numerically characterize parameter regimes in which limit cycles exist and discuss possible ways to generalize this approach to studying higher-order interactions.

nlin.AO↗