Related papers: Perspective from Micro-Macro Duality -- Towards no…
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…
We consider the signal reconstruction problem under the case of the signals sampled in the multichannel way and with the presence of noise. Observing that if the samples are inexact, the rigorous enforcement of multichannel interpolation is…
We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed…
Renormalization schemes for tan(beta) are discussed in view of their gauge dependence. It is shown that several common renormalization schemes lead to a gauge-dependent definition of tan(beta), whereas two classes of gauge-independent…
A renormalization group study of a scalar theory coupled to gravity through a general functional dependence on the Ricci scalar in the action is discussed. A set of non-perturbative flow equations governing the evolution of the new…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
An elementary introduction to the non-perturbative renormalization group is presented mainly in the context of statistical mechanics. No prior knowledge of field theory is necessary. The aim is this article is not to give an extensive…
Macroprogramming refers to the theory and practice of conveniently expressing the macro(scopic) behaviour of a system using a single program. Macroprogramming approaches are motivated by the need of effectively capturing global/system-level…
This review provides a detailed introduction to chiral gauge theories, renormalization theory, and the application of dimensional regularization with the non-anticommuting BMHV scheme for $\gamma_5$. One goal is to show how chiral gauge…
I briefly review the three nonperturbative methods for the treatment of disordered systems -- supersymmetry, replicas and dynamics -- with a parallel presentation that highlights their connections and differences.
We discuss a renormalization scheme for relativistic baryon chiral perturbation theory which provides a simple and consistent power counting for renormalized diagrams. The method involves finite subtractions of dimensionally regularized…
The explorations of models beyond the Standard Model (BSM) naturally involve scans over the unknown BSM parameters. On the other hand, high precision predictions require calculations at the loop-level and thus a renormalization of (some of)…
Starting from a well defined local Lagrangian, we analyze the renormalization group equations in terms of the two different arbitrary scales associated with the regularization procedure and with the physical renormalization of the bare…
In this paper we consider a general, challenging distributed optimization set-up arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local…
Imposing T-duality in the renormalisation process of entanglement entropy leads to new relations between entanglement entropy counter-terms. T-duality is made explicit by means of the generalised metric of double field theory in the context…
This is a copy of the 2009 Princeton University thesis which examined various aspects of gauge/gravity duality, including renormalization group flows, phase transitions of the holographic entanglement entropy, and instabilities associated…
A proper version of the proto renormalization-group scheme is presented to derive amplitude equations in striped pattern formation with conserved and nonconserved order parameter. In the conserved case, the result preserves the conservation…
In the calculation of quantum-mechanical singular-potential scattering, one encounters divergence. We suggest three renormalization schemes, dimensional renormalization, analytic continuation approach, and minimal-subtraction scheme to…