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The Bak Sneppen (BS) model is a very simple model that exhibits all the richness of self-organized criticality theory. At the thermodynamic limit, the BS model converges to a situation where all particles have a fitness that is uniformly…
Many mathematical models of statistical physics in two dimensions are either known or conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions of various exponents describing the behavior of these models.…
Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors. Exact analytic BFB conditions are known only in simple cases. In this work, we present…
While sliding mode observers (SMOs) using discontinuous relays are widely analyzed, most SMOs are implemented computationally using a continuous approximation of the discontinuous relays. This approximation results in the formation of a…
For normal canonical models, and more generally a vast array of general spherically symmetric location-scale models with a residual vector, we consider estimating the (univariate) location parameter when it is lower bounded. We provide…
In this paper, we solve a North-type Energy Balance Model (EBM) using an analytical method, the Boundary Integral Method. This approach is discussed in light of existing analytical techniques for this type of equation. We use the method to…
This paper proposes the asymmetric linear double autoregression, which jointly models the conditional mean and conditional heteroscedasticity characterized by asymmetric effects. A sufficient condition is established for the existence of a…
We study the $c=-2$ model of logarithmic conformal field theory in the presence of a boundary using symplectic fermions. We find boundary states with consistent modular properties. A peculiar feature of this model is that the vacuum…
We consider applications of the Boundary Control (BC) method to generalized spectral estimation problems and to inverse source problems. We derive the equations of the BC method for this problems and show that solvability of this equations…
Boundary condition changing operators in conformal field theory describe various types of "sudden switching" problems in condensed matter physics such as the X-ray edge singularity. We review this subject and give two extensions of previous…
Traditional variable selection methods could fail to be sign consistent when irrepresentable conditions are violated. This is especially critical in high-dimensional settings when the number of predictors exceeds the sample size. In this…
The 15-vertex model of Statistical Mechanics is studied on a square domain with partially oriented boundary. With DWBC the model would reduce to the six-vertex model, but more general boundary configurations are available. After…
We study minimax testing in a statistical inverse problem when the associated operator is unknown. In particular, we consider observations from an inverse Gaussian regression model where the associated operator is unknown but contained in a…
Quantum dynamics, typically expressed in the form of a time-dependent Schr\"odinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, when simulating quantum dynamics that involves the emission…
We introduce and analyze a penalty-free formulation of the Shifted Boundary Method (SBM), inspired by the asymmetric version of the Nitsche method. We prove its stability and convergence for arbitrary order finite element interpolation…
Simulation-based inference (SBI) methods such as approximate Bayesian computation (ABC), synthetic likelihood, and neural posterior estimation (NPE) rely on simulating statistics to infer parameters of intractable likelihood models.…
Approximate Bayesian computation (ABC) is a popular likelihood-free inference method for models with intractable likelihood functions. As ABC methods usually rely on comparing summary statistics of observed and simulated data, the choice of…
Several improvements in numerical methods and gauge choice are presented that make it possible now to perform simulations of the merger and ringdown phases of "generic" binary black-hole evolutions using the pseudo-spectral evolution code…
We propose a novel technique for analyzing adaptive sampling called the {\em Simulator}. Our approach differs from the existing methods by considering not how much information could be gathered by any fixed sampling strategy, but how…
The linear PDE ${\mathbf B} {\mathbf L} (\frac{\partial}{\partial x}) u ={\mathbf L}_1(\frac{\partial}{\partial x})u +f(x)$ with nonclassic conditions on boundary $\partial \Omega$ is considered. Here ${\mathbf B}$ is linear noninvertible…