相关论文: Long-range mutual information and topological unce…
"Topological ordered" phases such as gapped quantum spin-liquids and fractional quantum Hall states possess ground state degeneracy on a torus. We show that the topological nature of this degeneracy has interesting consequences for the…
This paper considers the identification of large-scale 1D networks consisting of identical LTI dynamical systems. A new subspace identification method is developed that only uses local input-output information and does not rely on knowledge…
Understanding phases of matter is of both fundamental and practical importance. Prior to the widespread appreciation and acceptance of topological order, the paradigm of spontaneous symmetry breaking, formulated along the…
We demonstrate the existence of an extended non-equilibrium critical phase, characterized by sub-exponential decay of conditional mutual information (CMI), in the surface code subject to heralded random Pauli measurement channels. By…
This paper proposes a novel distributed interval observer design for linear time-invariant (LTI) discrete-time systems subject to bounded disturbances. In the proposed observer algorithm, each agent in a networked group exchanges…
Model-based clustering is a powerful tool that is often used to discover hidden structure in data by grouping observational units that exhibit similar response values. Recently, clustering methods have been developed that permit…
The Typical Medium Theory provides conceptually the simplest order parameter description of Anderson localization by self-consistently calculating the geometrically-averaged (typical) local density of states (LDOS). Here we show how spatial…
We consider linear time invariant systems with exogenous stochastic disturbances, and in feedback with structured stochastic uncertainties. This setting encompasses linear systems with both additive and multiplicative noise. Our concern is…
Renormalization is an essential technique in field-theoretic descriptions of natural phenomena, where the absence of a UV-complete description yields an abundance of divergent quantities. While the renormalization prescription has been…
Feature selection methods are usually evaluated by wrapping specific classifiers and datasets in the evaluation process, resulting very often in unfair comparisons between methods. In this work, we develop a theoretical framework that…
Estimating mutual information between continuous random variables is often intractable and extremely challenging for high-dimensional data. Recent progress has leveraged neural networks to optimize variational lower bounds on mutual…
Topological phases of matter are primarily studied in systems with short-range interactions. In nature, however, non-relativistic quantum systems often exhibit long-range interactions. Under what conditions topological phases survive such…
Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. In order to compute the various topological descriptors commonly used to characterize the structure of…
Information-theoretic quantities reveal dependencies among variables in the structure of joint, marginal, and conditional entropies, but leave some fundamentally different systems indistinguishable. Furthermore, there is no consensus on how…
Topologically ordered phases in $2+1$ dimensions are generally characterized by three mutually-related features: fractionalized (anyonic) excitations, topological entanglement entropy, and robust ground state degeneracy that does not…
Continuous spin models with long-range interactions of the form $r^{-\sigma}$, where $r$ is the distance between two spins and $\sigma$ controls the decay of the interaction, exhibit enhanced order that competes with thermal disturbances,…
Quantum many-body systems divide into a variety of phases with very different physical properties. The question of what kind of phases exist and how to identify them seems hard especially for strongly interacting systems. Here we make an…
We propose predictive information, that is information between a long past of duration T and the entire infinitely long future of a time series, as a universal order parameter to study phase transitions in physical systems. It can be used,…
Linear time-translation-invariant (LTI) models offer simple, yet powerful, abstractions of complex classical dynamical systems. Quantum versions of such models have so far relied on assumptions of Markovianity or an internal state-space…
We consider the problem of learning predictive models from longitudinal data, consisting of irregularly repeated, sparse observations from a set of individuals over time. Such data often exhibit {\em longitudinal correlation} (LC)…