Related papers: Granger causality and the inverse Ising problem
The kinetic Glauber-Ising spin chain is one of the very few exactly solvable models of non-equilibrium statistical mechanics. Nevertheless, existing solutions do not yield tractable expressions for two-time correlation and response…
Clustering is an unsupervised learning technique that is useful when working with a large volume of unlabeled data. Complex dynamical systems in real life often entail data streaming from a large number of sources. Although it is desirable…
In the present paper, we examine Ising systems on d-dimensional hypercube lattices and solve an inverse problem where we have to determine interaction constants of an Ising connection matrix when we know a spectrum of it eigenvalues. In…
Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of…
Ising models are a simple generative approach to describing interacting binary variables. They have proven useful in a number of biological settings because they enable one to represent observed many-body correlations as the separable…
Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns.…
The causal connectivity of a network is often inferred to understand the network function. It is arguably acknowledged that the inferred causal connectivity relies on causality measure one applies, and it may differ from the network's…
We study the scaling of the Renyi and entanglement entropy of two disjoint blocks of critical Ising models, as function of their sizes and separations. We present analytic results based on conformal field theory that are quantitatively…
Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data.…
We study two Heisenberg spin-1/2 chains coupled by a frustrating ``zigzag'' interaction. We are particularly interested in the regime of weak interchain coupling, which is difficult to analyse by either numerical or analytical methods.…
We establish a general perturbative method to prove entropic Ricci curvature bounds for interacting stochastic particle systems. We apply this method to obtain curvature bounds in several examples, namely: Glauber dynamics for a class of…
The Granger framework is useful for discovering causal relations in time-varying signals. However, most Granger causality (GC) methods are developed for densely sampled timeseries data. A substantially different setting, particularly common…
We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of…
Systems of interacting particles or agents have wide applications in many disciplines such as Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from…
In a large transverse field, there is an energy cost associated with flipping spins along the axis of the field. This penalty can be employed to relate the transverse-field Ising model in a large field to the XY model in no field (when…
Granger Causality (GC) offers an elegant statistical framework to study the association between multivariate time series data. Vector autoregressive models (VAR) are simple and easy to fit, but have limited application because of their…
Small-world networks provide an interesting framework for studying the interplay between regular and random graphs, where links are located in a regular and random way, respectively. On one hand, the random links make the model to obey some…
We study Granger causality in the context of wide-sense stationary time series, where our focus is on the topological aspects of the underlying causality graph. We establish sufficient conditions (in particular, we develop the notion of a…
Spin networks appear in a number of areas, for instance in lattice gauge theories and in quantum gravity. They describe the contraction of intertwiners according to the underlying network. We show that a certain generating function of…
Inferring the connectivity of neural circuits from incomplete observations is a fundamental challenge in neuroscience. We present a covariance-based method for estimating the weight matrix of a recurrent neural network from sparse, partial…