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The random field Ising model with Gaussian disorder is studied using a new Monte Carlo algorithm. The algorithm combines the advantanges of the replica exchange method and the two-replica cluster method and is much more efficient than the…
We have provided a concise introduction to the Ising model as one of the most important models in statistical mechanics and in studying the phenomenon of phase transition. The required theoretical background and derivation of the…
We propose a statistical framework to quantify location and co-location associations of economic activities using information-theoretic measures. We relate the resulting measures to existing measures of revealed comparative advantage,…
Machine learning has become a central technique for modeling in science and engineering, either complementing or as surrogates to physics-based models. Significant efforts have recently been devoted to models capable of predicting field…
The spatial heterogeneity of cities -- the uneven distribution of population and activities -- is fundamental to urban dynamics and related to critical issues such as infrastructure overload, housing affordability, and social inequality.…
In the past decade, cities have experienced rapid growth, expansion, and changes in their community structure. Many aspects of critical urban infrastructure are closely coupled with the human communities that they serve. Urban communities…
We study the problem of learning the structure and parameters of the Ising model, a fundamental model of high-dimensional data, when observing the evolution of an associated Markov chain. A recent line of work has studied the natural…
Iterative geostatistical seismic inversion integrates seismic and well data to infer the spatial distribution of subsurface elastic properties. These methods provide limited assessment to the spatial uncertainty of the inverted elastic…
Hard-to-predict bursts of COVID-19 pandemic revealed significance of statistical modeling which would resolve spatio-temporal correlations over geographical areas, for example spread of the infection over a city with census tract…
Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms…
Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for…
In this work we consider the problem of extracting a set of interaction parameters from an high-dimensional dataset describing T independent configurations of a complex system composed of N binary units. This problem is formulated in the…
The recent availability of digital traces from Information and Communications Technologies (ICT) has facilitated the study of both individual- and population-level movement with unprecedented spatiotemporal resolution, enabling us to better…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…
We introduce a subclass of Lie symmetries, called parameter-state symmetries, to analyse the local structural identifiability and observability of mechanistic models consisting of state-dependent ODEs with observed outputs. These symmetries…
The evolution of many dynamical systems that describe relationships or interactions between objects can be effectively modeled by temporal networks, which are typically represented as a sequence of static network snapshots. In this paper,…
This work develops a powerful and versatile framework for determining acceptance ratios in Metropolis-Hastings type Markov kernels widely used in statistical sampling problems. Our approach allows us to derive new classes of kernels which…
Coupled Ising models are studied in a discrete choice theory framework, where they can be understood to represent interdependent choice making processes for homogeneous populations under social influence. Two different coupling schemes are…
This discussion serves as an introduction to the use of Monte Carlo simulations as a useful way to evaluate the observables of a ferromagnet. Key background is given about the relevance and effectiveness of this stochastic approach and in…