Related papers: Regularisation of functional determinants using bo…
Normalization techniques play an important role in supporting efficient and often more effective training of deep neural networks. While conventional methods explicitly normalize the activations, we suggest to add a loss term instead. This…
We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space $L_{2}(0,b).$ In contrast to the classical convolution, the introduced convolution…
We show that boundary contributions of BCFW recursions can be interpreted as the form factors of some composite operators which we call 'boundary operators'. The boundary operators can be extracted from the operator product expansion of…
Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions…
The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1+1)-dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary…
In this note we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems and the corresponding Euler-Lagrange and Hamilton equations are analyzed.…
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
We study functional determinants for Dirac operators on manifolds with boundary. We give, for local boundary conditions, an explicit formula relating these determinants to the corresponding Green functions. We finally apply this result to…
The many-normal-means problem is a classic example that motivates the development of many important inferential procedures in the history of statistics. In this short note, we consider a further special case of the problem, which involves…
We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of…
Differential operators usually result in derivatives expressed as a ratio of differentials. For all but the simplest derivatives, these ratios are typically not algebraically manipulable, but must be held together as a unit in order to…
Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
We show the well-posed variational principle in constraint systems. In a naive procedure of the variational principle with constraints, the proper number of boundary conditions does not match with that of physical degrees of freedom…
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…
We study two types of regularizations of the determinant of Laplacian on Riemann manifold from the viewpoint of resurgence theory. One is the formal logarithmic derivative of the determinant, and the other is its exponential deformation.…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
The standard formula for the change in the effective action under a conformal transformation is extended to the case when the boundary is piecewise smooth. We then find the functional determinants of the scalar Laplacian on regions of the…
Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in…