Related papers: An informal introduction to quantitative stochasti…
The real-space renormalization group technique is introduced to evaluate the effective diffusion constant for diffusion in inhomogeneous media, which has been obtained by singular perturbation methods. Our method is formulated on a…
We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of…
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…
An asymmetric variant of the contact process where the activity spreads with different and independent random rates to the left and to the right is introduced. A real space renormalization scheme is formulated for model by means of which it…
We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…
Molecular dynamics simulations are widely used across chemistry, physics, and biology, providing quantitative insight into complex processes with atomic detail. However, their limited timescale of a few microseconds is a significant…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
Meta-analysis can be formulated as combining $p$-values across studies into a joint $p$-value function, from which point estimates and confidence intervals can be derived. We extend the meta-analytic estimation framework based on combined…
This paper aims to systematically solve stochastic team optimization of large-scale system, in a rather general framework. Concretely, the underlying large-scale system involves considerable weakly-coupled cooperative agents for which the…
We present a pedagogical treatment of the formalism of continuous quantum measurement. Our aim is to show the reader how the equations describing such measurements are derived and manipulated in a direct manner. We also give elementary…
Operator-type estimates of homogenization are obtained for elliptic operators of arbitrary even order equal or greater than two. Operators under consideration are non-selfadjoint with lower-order terms.
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
The technique known as group averaging provides powerful machinery for the study of constrained systems. However, it is likely to be well defined only in a limited set of cases. Here, we investigate the possibility of using a `renormalized'…
With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…
A new class of stochastic variables, governed by a specifice set of rules, is introduced. These rules force them to loose some properties usually assumed for this kind of variables. We demonstrate that stochastic processes driven by these…
We study homogenization it its most basic form $$-\left(a\left(\frac{x}{\varepsilon}\right) u_{\varepsilon}'(x)\right)' = f(x) \quad \mbox{for} ~x \in (0,1),$$ where $a(\cdot)$ is a positive $1-$periodic continuous function, $f$ is smooth…
With many pretreatment covariates and treatment factors, the classical factorial experiment often fails to balance covariates across multiple factorial effects simultaneously. Therefore, it is intuitive to restrict the randomization of the…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density.…
Variational inequalities have gained significant attention in machine learning and optimization research. While stochastic methods for solving these problems typically assume independent data sampling, we investigate an alternative approach…