相关论文: Time Series Correlations and Kolmogorov Complexity…
Future observations of the large-scale structure have the potential to investigate cosmological models with a high degree of complexity, including the properties of gravity on large scales, the presence of a complicated dark energy…
Recently, tensor data (or multidimensional array) have been generated in many modern applications, such as functional magnetic resonance imaging (fMRI) in neuroscience and videos in video analysis. Many efforts are made in recent years to…
Kolmogorov complexity measures the algorithmic complexity of a finite binary string $\sigma$ in terms of the length of the shortest description $\sigma^*$ of $\sigma$. Traditionally, the length of a string is taken to measure the amount of…
Performing likelihood ratio based detection with high dimensional multimodal data is a challenging problem since the computation of the joint probability density functions (pdfs) in the presence of inter-modal dependence is difficult. While…
Any positive word comprised of random sequence of tokens form a finite alphabet can be reduced (without change of length) using an appropriate size Braid group relationships. Surprisingly the Braid relations dramatically reduce the…
Time series data arising in many applications nowadays are high-dimensional. A large number of parameters describe features of these time series. We propose a novel approach to modeling a high-dimensional time series through several…
The fast growing field of compressed sensing is founded on the fact that if a signal is 'simple' and has some 'structure', then it can be reconstructed accurately with far fewer samples than its ambient dimension. Many different plausible…
Randomness extraction is the process of constructing a source of randomness of high quality from one or several sources of randomness of lower quality. The problem can be modeled using probability distributions and min-entropy to measure…
Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from high-dimensional distributions in Statistics and Machine learning. HMC is known to run very efficiently in practice and its popular second-order "leapfrog"…
We consider a problem of superconductivity coexistence with the spin-density-wave order in disordered multiband metals. It is assumed that random variations of the disorder potential on short length scales render the interactions between…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
We consider the (smoothed) average correlation between the density of energy levels of a disordered system, in which the Hamiltonian is equal to the sum of a deterministic H0 and of a random potential $\varphi$. Remarkably, this correlation…
In this article, we investigate posterior convergence in nonparametric regression models where the unknown regression function is modeled by some appropriate stochastic process. In this regard, we consider two setups. The first setup is…
The linear response is investigated in a long-range Hamiltonian system from the view point of dynamics, which is described by the Vlasov equation in the limit of large population. Due to existence of the Casimir invariants of the Vlasov…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
We consider a system of stochastic interacting particles with general diffusion coefficient and drift functions and we study the types of collisions that arise in them. In particular, interactions between particles are inversely…
Complex systems often involve random fluctuations for which self-similar properties in space and time play an important role. Fractional Brownian motions, characterized by a single scaling exponent, the Hurst exponent $H$, provide a…
We perform time series analysis of small networks where every node is the slow-fast version of the denatured Morris--Lecar neuron proposed by Schaeffer and Cain. We choose popular coupling strategies from the literature and provide a…
We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or log-periodicity) is found in a time series. We investigate general situations with non-Gaussian…
We propose a general method for constructing a minimal cover of high-dimensional chaotic attractors by embedded unstable recurrent patterns. By minimal cover we mean a subset of available patterns such that the approximation of chaotic…