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We analyze the renormalization of systems whose effective degrees of freedom are described in terms of fluctuations which are ``environment'' dependent. Relevant environmental parameters considered are: temperature, system size, boundary…
We develop a tensor network-based method for calculating disorder-averaged expectation values in random spin chains without having to explicitly sample over disorder configurations. The algorithm exploits statistical translation invariance…
The nonperturbative renormalization group has been considered as a solid framework to investigate fixed point and critical exponents for matrix and tensor models, expected to correspond with the so-called double scaling limit. In this…
The Renormalisation Group is a versatile tool for the study of many systems where scale-dependent behaviour is important. Its functional formulation can be cast into the form of an exact flow equation for the scale-dependent effective…
The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case,…
Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This helps to avoid the staircasing effect of Total Variation…
We consider the random transverse-field Ising model in $d=3$ dimensions with long-range ferromagnetic interactions which decay as a power $\alpha > d$ with the distance. Using a variant of the strong disorder renormalization group method we…
Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work…
We include spontaneous symmetry breaking into the functional renormalization group (RG) equations for the irreducible vertices of Ginzburg-Landau theories by augmenting these equations by a flow equation for the order parameter, which is…
On the example of the three-dimensional Ising model, we show that nonperturbative renormalization group equations allow one to obtain very accurate critical exponents. Implementing the order $\partial^4$ of the derivative expansion leads to…
We explain the recent numerical successes obtained by Tao Xiang's group, who developed and applied Tensor Renormalization Group methods for the Ising model on square and cubic lattices, by the fact that their new truncation method sharply…
We study the 3d Ising universality class using the functional renormalisation group. With the help of background fields and a derivative expansion up to fourth order we compute the leading index, the subleading symmetric and anti-symmetric…
We discuss the errors introduced by level truncation in the study of boundary renormalisation group flows by the Truncated Conformal Space Approach. We show that the TCSA results can have the qualitative form of a sequence of RG flows…
We investigate the parameter recovery of Markov-switching ordinary differential processes from discrete observations, where the differential equations are nonlinear additive models. This framework has been widely applied in biological…
Dependence on the gauge parameters is an important issue in gauge theories: physical quantities have to be independent. Extending BRS transformations by variation of the gauge parameter into a Grassmann variable one can control gauge…
Modern deep learning models employ considerably more parameters than required to fit the training data. Whereas conventional statistical wisdom suggests such models should drastically overfit, in practice these models generalize remarkably…
Extraneous variables are variables that are irrelevant for a certain task, but heavily affect the distribution of the available data. In this work, we show that the presence of such variables can degrade the performance of deep-learning…
In this paper, a way of generalizing the tensor renormalization group(TRG) is proposed. Mathematically, the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is…
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…
In a disordered system one can either consider a microcanonical ensemble, where there is a precise constraint on the random variables, or a canonical ensemble where the variables are chosen according to a distribution without constraints.…