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A rapidly increasing portion of internet traffic is dominated by requests from mobile devices with limited and metered bandwidth constraints. To satisfy these requests, it has become standard practice for websites to transmit small and…
We develop a theory of probabilistic coherence spaces equipped with an additional extensional structure and apply it to approximating probability of convergence of ground type programs of probabilistic PCF whose free variables are of ground…
An algebraic approximation, of order $K$, of a polyhedron correlation function (CF) can be obtained from $\gamma\pp(r)$, its chord-length distribution (CLD), considering first, within the subinterval $[D_{i-1},\, D_i]$ of the full range of…
Given the widespread use of lossless compression algorithms to approximate algorithmic (Kolmogorov-Chaitin) complexity, and that lossless compression algorithms fall short at characterizing patterns other than statistical ones not different…
Probabilistic quantum error correction is an error-correcting procedure which uses postselection to determine if the encoded information was successfully restored. In this work, we deeply analyze probabilistic version of the…
The Karhunen-Lo\`eve transform (KLT) is often used for data decorrelation and dimensionality reduction. Because its computation depends on the matrix of covariances of the input signal, the use of the KLT in real-time applications is…
The quantification of visual aesthetics and complexity have a long history, the latter previously operationalized via the application of compression algorithms. Here we generalize and extend the compression approach beyond simple complexity…
Consider a random graph G in G(n,p) and the graph property: G contains a copy of a specific graph H. (Note: H depends on n; a motivating example: H is a Hamiltonian cycle.) Let q be the minimal value for which the expected number of copies…
In this paper, we propose a new protocol for a data compression task, blind quantum data compression, with finite local approximations. The rate of blind data compression is susceptible to approximations even when the approximations are…
Given a compact semialgebraic set S of R^n and a polynomial map f from R^n to R^m, we consider the problem of approximating the image set F = f(S) in R^m. This includes in particular the projection of S on R^m for n greater than m. Assuming…
If one assumes there is probability of perception in quantum mechanics, then unitarity dictates that it must have the coefficient squared form, in agreement with experiment.
The existence of probability in the sense of the frequency interpretation, i.e. probability as "long term relative frequency," is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the…
In this paper, we propose to enhance learned image compression systems with a richer probability model for the latent variables. Previous works model the latents with a Gaussian or a Laplace distribution. Inspired by binary arithmetic…
Rapid growth in the field of quantitative digital image analysis is paving the way for researchers to make precise measurements about objects in an image. To compute quantities from the image such as the density of compressed materials or…
We report an algorithm, based on quantum optics formulation, where a coherent state is used as the elementary quantum resource for the image representation. We provide an architecture with constituent optical elements in linear order with…
This paper presents an achievability bound that evaluates the exact probability of error of an ensemble of random codes that are decoded by a minimum distance decoder. Compared to the state-of-the-art which demands exponential computation…
Theoretical investigations into the deflection angle caused by microlenses offer a direct path to uncovering principles of the cosmological microlensing effect. This work specifically concentrates on the the probability density function…
Learning the parameters of graphical models using the maximum likelihood estimation is generally hard which requires an approximation. Maximum composite likelihood estimations are statistical approximations of the maximum likelihood…
A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…
We propose a new simple approach for image compression: instead of storing the RGB values for each pixel of an image, we store the weights of a neural network overfitted to the image. Specifically, to encode an image, we fit it with an MLP…