Related papers: Signal detection in nearly continuous spectra and …
Renormalization group techniques are widely used in modern physics to describe the low energy relevant aspects of systems involving a large number of degrees of freedom. Those techniques are thus expected to be a powerful tool to address…
Signal detection is one of the main challenges of data science. As it often happens in data analysis, the signal in the data may be corrupted by noise. There is a wide range of techniques aimed at extracting the relevant degrees of freedom…
This review paper uses renormalization group techniques for signal detection in nearly-continuous positive spectra. We highlight universal aspects of the analogue field-theory approach. The first aim is to present an extended…
The tensorial principal component analysis is a generalization of ordinary principal component analysis, focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative…
We establish a correspondence between anomaly detection in high-noise regimes and the renormalization group flow of non-equilibrium field theories. We provide a physical grounding for this framework by proving that the detection of phase…
Consider a network consisting of two subnetworks (communities) connected by some external edges. Given the network topology, the community detection problem can be cast as a graph partitioning problem that aims to identify the external…
Signal detection in high dimensions is a critical challenge in data science. While standard methods based on random matrix theory provide sharp detection thresholds for finite-rank perturbations, such as the known Baik-Ben Arous-P\'ech\'e…
If supersymmetric particles are discovered, an important problem will be to determine how supersymmetry has been broken. At collider energies, supersymmetry breaking can be parameterised by soft supersymmetry breaking parameters. Several…
In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, in a recent paper some general sufficient conditions for these phenomena in $\mathbb{Z}_2$-symmetric systems (i.e.…
Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…
The spontaneous breaking of a $Z_2$ symmetry typically gives rise to emergent excitations possessing the same symmetry with a renormalized mass. Contrary to this conventional wisdom, we present a theory in which the low-lying excitation in…
We present a physical interpretation of machine learning functions, opening up the possibility to control properties of statistical systems via the inclusion of these functions in Hamiltonians. In particular, we include the predictive…
The collective mode spectrum of a symmetry-breaking state, such as a superconductor, provides crucial insight into the nature of the order parameter. In this context, we present a microscopic weak-coupling theory for the collective modes of…
We consider a group synchronization problem with multiple frequencies which involves observing pairwise relative measurements of group elements on multiple frequency channels, corrupted by Gaussian noise. We study the computational phase…
Financial stock return correlations have been analyzed through the lens of random matrix theory to differentiate the underlying signal from spurious correlations. The continuous spectrum of the eigenvalue distribution derived from the stock…
Anomalous global symmetries, which can be realized on the boundary of symmetry-protected topological phases, brings new phases and phase transitions to condensed matter physics. In this work, we study a one dimensional model with an…
We demonstrate a novel feature of certain phase transitions in theories with large rank symmetry group that exhibit specific types of non-local interactions. A typical example of such a theory is a large-$N$ gauge theory where by `non-local…
We consider the dynamics of bodies with "active" microstructure described by vector-valued phase fields. For waves with time-varying amplitude, the associated evolution equation involves a matrix that can be non-normal, depending on the…
In this paper, we study the phase transition behavior emerging from the interactions among multiple agents in the presence of noise. We propose a simple discrete-time model in which a group of non-mobile agents form either a fixed connected…
The functional renormalization group (FRG) has been used widely to investigate phase diagrams, in particular the one of the two-dimensional Hubbard model. So far, the study of one-dimensional models has not attracted as much attention. We…