Related papers: On calculating response functions via their Lorent…
Neutron reflectometry analysis is an inherently ill-posed, which is to say that there are many possible solutions which agree equally well with the measured data. This leads to the application of model-dependent analysis, where information…
The inverse of the error function, $\operatorname{inverf}(x),$ has applications in diffusion problems, chemical potentials, ultrasound imaging, etc. We analyze the derivatives $\frac{d^{n}}{dz^{n}} \operatorname*{inverf}(z) |_{z=0}$, as…
The correlation between a random sequence and its transformed sequences is studied. In the case of a permutation operation or, in other word, the shuffling operation, it is shown that the correlation can be so small that the sequences can…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
We study calibration in question answering, estimating whether model correctly predicts answer for each question. Unlike prior work which mainly rely on the model's confidence score, our calibrator incorporates information about the input…
Energy-dependent sum rules are useful tools in many fields of physics. In nuclear physics, they typically involve an integration of the response function over the nuclear spectrum with a weight function composed of integer powers of the…
Convex functionals are ubiquitous in applied analysis, appearing as value functions, risk measures, super-hedging prices, and loss functionals in machine learning. In many applications, however, the functional is only observed through…
We derive exact reconstruction methods for cracks consisting of unions of Lipschitz hypersurfaces in the context of Calder\'on's inverse conductivity problem. Our first method obtains upper bounds for the unknown cracks, bounds that can be…
In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from the theories of groups, automata, and inverse semigroups.…
Trained transformer models have been found to implement interpretable procedures for tasks like arithmetic and associative recall, but little is understood about how the circuits that implement these procedures originate during training. To…
In this paper a new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function $f(t)$ is continuous with (known) compact support. An…
Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
Blurring of a photographic image by a wrong focus can be modeled by convolution. Is inversion a possible answer? This paper adds complements to a foregoing paper discussing convolution-inversion of some measures.
In this paper we investigate an indirect regression model characterized by the Radon transformation. This model is useful for recovery of medical images obtained by computed tomography scans. The indirect regression function is estimated…
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…
Machine learning (ML) in its current form implies that an answer to any problem can be well approximated by a function of a very peculiar form: a specially adjusted iteration of Heavyside theta-functions. It is natural to ask if the answers…
The image reconstruction of partially coherent light is interpreted as the quantum state reconstruction. The efficient method based on maximum-likelihood estimation is proposed to acquire information from registered intensity measurements…
We present a consistent \emph{ab initio} computation of the longitudinal response function $R_L$ in $^{40}$Ca using the coupled-cluster and Lorentz integral transform methods starting from chiral nucleon-nucleon and three-nucleon…
We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the…