Related papers: Missing levels in intermediate spectra
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…
Along the line of thoughts of Berry and Robnik\cite{[1]}, we investigated the gap distribution function of systems with infinitely many independent components, and discussed the level-spacing distribution of classically integrable quantum…
We study the statistics of level spacing of geometric resonances in the disordered binary networks. For a definite concentration $p$ within the interval $[0.2,0.7]$, numerical calculations indicate that the unfolded level spacing…
Spectral properties of random matrices play an important role in statistics, machine learning, communications, and many other areas. Engaging results regarding the convergence of the empirical spectral distribution (ESD) and the…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…
The mixed spherical models were recently found to violate long-held assumptions about mean-field glassy dynamics. In particular, the threshold energy, where most stationary points are marginal and that in the simpler pure models attracts…
Complete spectroscopy (measurements of a complete sequence of consecutive levels) is often considered as a prerequisite to extract fluctuation properties of spectra. It is shown how this goal can be achieved even if only a fraction of…
We obtain analytic formulae for the spacing between conductance peaks in the Coulomb blockade regime, based on the universal Hamiltonian model of quantum dots. New random matrix theory results are developed in order to treat correlations…
Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c(w,x) as well as the distributions…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
Many body localization (MBL) is a phenomena that allows for the preservation of quantum information for long times. We study a variation of the disordered-Heisenberg model, which is known to exhibit an MBL phase [5][6], known as the…
Level statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between…
Background: Data preparation, such as missing values imputation and transformation, is the first step in any data analysis and requires crucial attention. Particularly, analysis of metabolites demands more preparation since those small…
We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…
Mutual Information (MI) is a crucial measure for capturing dependencies between variables, but exact computation is challenging in high dimensions with intractable likelihoods, impacting accuracy and robustness. One idea is to use an…
Simulations often involve the use of model parameters which are unknown or uncertain. For this reason, simulation experiments are often repeated for multiple combinations of parameter values, often iterating through parameter values lying…
We consider an ensemble of $2\times 2$ normal matrices with complex entries representing operators in the quantum mechanics of 2 - level parity-time reversal (PT) symmetric systems. The randomness of the ensemble is endowed by obtaining…
We calculate an analytical expression for the terrace-width distribution $P(s)$ for an interacting step system with nearest and next nearest neighbor interactions. Our model is derived by mapping the step system onto a statistically…
We calculate the condensate fraction and the condensate and non-condensate spatial and momentum distribution of the Bose-Hubbard model in a trap. From our results, it is evident that using approximate distributions can lead to erroneous…
We study high-dimensional sample covariance matrices based on independent random vectors with missing coordinates. The presence of missing observations is common in modern applications such as climate studies or gene expression…