Related papers: The decimation process in random k-SAT
In Analog-to-digital (A/D) conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one couples signal decimation with the $\Sigma\Delta$ quantization scheme, the…
Realisation of experiments even on small and medium-scale quantum computers requires an optimisation of several parameters to achieve high-fidelity operations. As the size of the quantum register increases, the characterisation of quantum…
We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of…
Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…
By taking the need for quantum reference frames into account, it is shown that Hilbert-space factorization is a dissipative process requiring on the order of kT to reduce by one bit an observer's uncertainty in the provenance of a…
Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim…
We consider the K-satisfiability problem on a regular d-ary rooted tree. For this model, we demonstrate how we can calculate in closed form, the moments of the total number of solutions as a function of d and K, where the average is over…
We propose a new algorithm for k-means clustering in a distributed setting, where the data is distributed across many machines, and a coordinator communicates with these machines to calculate the output clustering. Our algorithm guarantees…
The problem of P vs. NP is very serious, and solutions to the problem can help save lives. This article is an attempt at solving the problem using a computer algorithm. It is presented in a fashion that will hopefully allow for easy…
A set of programs for the numerical simulation of the diffusion decomposition processes was developed by using simulation methods, kinetic and particle method. The complex has been validated on the model system Ni-Al by the growth of -phase…
In this paper we study biased random K-SAT problems in which each logical variable is negated with probability $p$. This generalization provides us a crossover from easy to hard problems and would help us in a better understanding of the…
It is found that the statistical level fluctuations of the AQC 3-SAT problem undergo a transition from a poisson (regular) fluctuation form to a form consistent with the predictions of Random Matrix Theory. We present data which suggests…
Signal processing techniques will lean on blind methods in the near future, where no redundant, resource allocating information will be transmitted through the channel. To achieve a proper decision, however, it is essential to know at least…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
A simple statistical model for the effects of dephasing on electron transport in one-dimensional quantum systems is introduced, which allows to adjust the degree of phase and momentum randomization independently. Hence, the model is able to…
Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…
The foraging problem asks how a collective of particles with limited computational, communication and movement capabilities can autonomously compress around a food source and disperse when the food is depleted or shifted, which may occur at…
We consider transformations of deterministic and random signals governed by simple dynamical mappings. It is shown that the resulting signal can be a random process described in terms of fractal distributions and fractal domain integrals.…
Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…
A novel approach is suggested for improving the accuracy of fault detection in distribution networks. This technique combines adaptive probability learning and waveform decomposition to optimize the similarity of features. Its objective is…