Related papers: Laplacian Renormalization Group for heterogeneous …
We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph…
We set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The…
We analyze renormalization group (RG) flows in two-dimensional quantum field theories in the presence of redundant directions. We use the operator picture in which redundant operators are total derivatives. Our analysis has three levels of…
The renormalization group equations for large-scale structure (RG-LSS) describe how the bias and stochastic (noise) parameters -- both of matter and biased tracers such as galaxies -- evolve as a function of the cutoff $\Lambda$ of the…
Based on the Renormalization Group method, a reduction of non integrable multi-dimensional hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density, and for the…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…
Renormalization group (RG) methods are emerging as tools in biology and computer science to support the search for simplifying structure in distributions over high-dimensional spaces. We show that mixture models can be thought of as having…
This paper studies a generalization of the standard continuous-time consensus protocol, obtained by replacing the Laplacian matrix of the communication graph with the so-called deformed Laplacian. The deformed Laplacian is a second-degree…
We develop an algorithmic, system-specific renormalization group (RG) procedure that is adapted from model reductions techniques from engineering control theory. The resulting "generalized" RG is a consistent generalization of the Wilsonian…
Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is…
The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very…
Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and…
Various aspects of the Exact Renormalization Group (ERG) are explored, starting with a review of the concepts underpinning the framework and the circumstances under which it is expected to be useful. A particular emphasis is placed on the…
Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric…
Using the example of configurations generated with the worm algorithm for the two-dimensional Ising model, we propose renormalization group (RG) transformations, inspired by the tensor RG, that can be applied to sets of images. We relate…
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…
The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…
The Wilsonian renormalization group approach to matrix models is outlined and applied to multitrace matrix models with emphasis on the computation of the fixed points which could describe the phase structure of noncommutative scalar…
Renormalization group method is applied to the study of vibrational energy transfer in protein molecule. An effective Lagrangian and associated equations of motion to describe the resonant energy transfer are analyzed in terms of the…