Related papers: Negative spherical perceptron
In this work, a scattering process of quantum particles through a potential barrier is considered. The statistical complexity and the Fisher-Shannon information are calculated for this problem. The behaviour of these entropy-information…
It is common for researchers to record long, multiple time series from experiments or calculations. But sometimes there are no good models for the systems or no applicable mathematical theorems that can tell us when there are basic…
These lectures introduce the non-specialist to the evaluation of spin structure functions from asymmetries measured in polarized deep-inelastic scattering experiments. The various steps leading from apparatus dependent counting rate…
Noise contrastive learning is a popular technique for unsupervised representation learning. In this approach, a representation is obtained via reduction to supervised learning, where given a notion of semantic similarity, the learner tries…
We investigate in a $2$D setting the scattering of time-harmonic electromagnetic waves by a plasmonic device, represented as a non dissipative bounded and penetrable obstacle with a negative permittivity. Using the $\textrm{T}$-coercivity…
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…
In this paper, we address the problem of how many randomly labeled patterns can be correctly classified by a single-layer perceptron when the patterns are correlated with each other. In order to solve this problem, two analytical schemes…
Reservoir computing is a recently introduced machine learning paradigm that has been shown to be well-suited for the processing of spatiotemporal data. Rather than training the network node connections and weights via backpropagation in…
Factor models are widely used across diverse areas of application for purposes that include dimensionality reduction, covariance estimation, and feature engineering. Traditional factor models can be seen as an instance of linear embedding…
We pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of…
Statistical mechanics is applied to lossy compression using multilayer perceptrons for unbiased Boolean messages. We utilize a tree-like committee machine (committee tree) and tree-like parity machine (parity tree) whose transfer functions…
The concept of negative refraction is attracting a lot of attention. The initial ideas and the misconceptions that have arisen are discussed in sufficient detail to understand the conceptual structure that binds negative refraction to the…
We discuss a method that employs a multilayer perceptron to detect deviations from a reference model in large multivariate datasets. Our data analysis strategy does not rely on any prior assumption on the nature of the deviation. It is…
The scan statistic is widely used in spatial cluster detection applications of inhomogeneous Poisson processes. However, real data may present substantial departure from the underlying Poisson process. One of the possible departures has to…
We study the dynamics of a macroscopic object interacting with a dissipative stochastic environment using an adiabatic perturbation theory. The perturbation theory reproduces known expressions for the friction coefficient and, surprisingly,…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
Reservoir computing has repeatedly been shown to be extremely successful in the prediction of nonlinear time-series. However, there is no complete understanding of the proper design of a reservoir yet. We find that the simplest popular…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
Compactness is one of the core notions of analysis: it connects local properties to global ones and makes limits well-behaved. We study the computational properties of the compactness of Cantor space $2^{\mathbb{N}}$ for uncountable covers.…