Beyond collective intelligence: Collective adaptation

We develop a conceptual framework for studying collective adaptation: the process of iterative co-adaptation of cognitive strategies, social environments, and problem structures. Going beyond searching for “intelligent” collectives, we integrate research from different disciplines to show how collective adaptation perspective can help explain why similar collectives can follow very different and sometimes counter-intuitive trajectories. We further discuss how this perspective explains why successful collectives appear to have a general collective intelligence factor, why collectives rarely optimize their behaviour for a single problem, why their behaviours can appear myopic, and why playful exploration of alternative social systems can be useful. We describe different approaches for the study of collective adaptation, including computational models inspired by evolution and statistical physics. The framework of collective adaptation enables the integration and formalization of knowledge about human collective phenomena and opens doors to a rigorous transdisciplinary pursuit of important outstanding questions about human sociality.

Mean exit time in irregularly-shaped annular and composite disc domains

Calculating the mean exit time (MET) for models of diffusion is a classical problem in statistical physics, with various applications in biophysics, economics and heat and mass transfer. While many exact results for MET are known for diffusion in simple geometries involving homogeneous materials, calculating MET for diffusion in realistic geometries involving heterogeneous materials is typically limited to repeated stochastic simulations or numerical solutions of the associated boundary value problem (BVP). In this work we derive exact solutions for the MET in irregular annular domains, including some applications where diffusion occurs in heterogenous media. These solutions are obtained by taking the exact results for MET in an annulus, and then constructing various perturbation solutions to account for the irregular geometries involved. These solutions, with a range of boundary conditions, are implemented symbolically and compare very well with averaged data from repeated stochastic simulations and with numerical solutions of the associated BVP. Software to implement the exact solutions is available on \href{https://github.com/ProfMJSimpson/Exit_time}{GitHub}.

Machine learning of phase transitions in nonlinear polariton lattices

Polaritonic lattices offer a unique testbed for studying nonlinear driven-dissipative physics. They show qualitative changes of their steady state as a function of system parameters, which resemble non-equilibrium phase transitions. Unlike their equilibrium counterparts, these transitions cannot be characterised by conventional statistical physics methods. Here, we study a lattice of square-arranged polariton condensates with nearest-neighbour coupling, and simulate the polarisation (pseudospin) dynamics of the polariton lattice, observing regions with distinct steady-state polarisation patterns. We classify these patterns using machine learning methods and determine the boundaries separating different regions. First, we use unsupervised data mining techniques to sketch the boundaries of phase transitions. We then apply learning by confusion, a neural network-based method for learning labels in a dataset, and extract the polaritonic phase diagram. Our work takes a step towards AI-enabled studies of polaritonic systems.

Classical and Quantum Statistical Physics

Statistical physics examines the collective properties of large ensembles of particles, and is a powerful theoretical tool with important applications across many different scientific disciplines. This book provides a detailed introduction to classical and quantum statistical physics, including links to topics at the frontiers of current research. The first part of the book introduces classical ensembles, provides an extensive review of quantum mechanics, and explains how their combination leads directly to the theory of Bose and Fermi gases. This allows a detailed analysis of the quantum properties of matter, and introduces the exotic features of vacuum fluctuations. The second part discusses more advanced topics such as the two-dimensional Ising model and quantum spin chains. This modern text is ideal for advanced undergraduate and graduate students interested in the role of statistical physics in current research. 140 homework problems reinforce key concepts and further develop readers' understanding of the subject.

Independent sets of a given size and structure in the hypercube

We determine the asymptotics of the number of independent sets of size $\lfloor \beta 2^{d-1} \rfloor$ in the discrete hypercube $Q_d = \{0,1\}^d$ for any fixed $\beta \in (0,1)$ as $d \to \infty$ , extending a result of Galvin for $\beta \in (1-1/\sqrt{2},1)$ . Moreover, we prove a multivariate local central limit theorem for structural features of independent sets in $Q_d$ drawn according to the hard-core model at any fixed fugacity $\lambda>0$ . In proving these results we develop several general tools for performing combinatorial enumeration using polymer models and the cluster expansion from statistical physics along with local central limit theorems.

A statistical physics approach to a multi-channel Wigner spiked model

In this letter we present a finite temperature approach to a high-dimensional inference problem, the Wigner spiked model, with group dependent signal-to-noise ratios. For two classes of convex and non-convex network architectures the error in the reconstruction is described in terms of the solution of a mean-field spin-glass on the Nishimori line. In the cases studied the order parameters do not fluctuate and are the solution of finite dimensional variational problems. The deep architecture is optimized in order to confine the high temperature phase where reconstruction fails.

Chemical Differentiation of Planets: A Core Issue

By plotting empirical chemical element abundances on Earth relative to the Sun and normalized to silicon versus their first ionization potentials, we confirm the existence of a correlation reported earlier. To explain this, we develop a model based on principles of statistical physics that predicts differentiated relative abundances for any planetary body in a solar system as a function of its orbital distance. This simple model is successfully tested against available chemical composition data from CI chondrites and surface compositional data of Mars, Earth, the Moon, Venus, and Mercury. We show, moreover, that deviations from the proposed law for a given planet correspond to later surface segregation of elements driven both by gravity and chemical reactions. We thus provide a new picture for the distribution of elements in the solar system and inside planets, with important consequences for their chemical composition. Particularly, a 4 wt% initial hydrogen content is predicted for bulk early Earth. This converges with other works suggesting that the interior of the Earth could be enriched with hydrogen.

The Buffon needle problem for Lévy distributed spacings and renewal theory

What is the probability that a needle dropped at random on a set of points scattered on a line segment does not fall on any of them? We compute the exact scaling expression of this hole probability when the spacings between the points are independent identically distributed random variables with a power-law distribution of index less than unity, implying that the average spacing diverges. The theoretical framework for such a setting is renewal theory, to which the present study brings a new contribution. The question posed here is also related to the study of some correlation functions of simple models of statistical physics.

Modeling of probable maximum values in autonomous driving

In this paper, we approximate the probable maximum (very rare, extremal) values of highly autonomous driving sensor signals by reviewing two methods based on dynamic time series scaling and multifractal statistics.The article is a significantly revised and modified version of the conference material ("Determination of extreme values ​​in autonomous driving based on multifractals and dynamic scaling") presented at the conference "2021 IEEE 15th International Symposium on Applied Computational Intelligence and Informatics, SACI". The method of dynamic scaling is originally derived from statistical physics and approximates the critical interface phenomena. The time series of the vibration signal of the corner radar can be considered as a fractal surface and grow appropriately for a given scale-inverse dynamic equation. In the second method we initiate, that multifractal statistics can be useful in searching for statistical analog time series that have a similar multifractal spectrum as the original sensor time series.