Related papers: Diffraction of Random Noble Means Words
We review recent developments of slow/fast stochastic differential equations, and also present a new result on Diffusion Homogenisation Theory with fractional and non-strong-mixing noise and providing new examples. The emphasise of the…
In this work, we systematically investigate how well current models of coherence can capture aspects of text implicated in discourse organisation. We devise two datasets of various linguistic alterations that undermine coherence and test…
Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the…
We consider systems of slow--fast diffusions with small noise in the slow component. We construct provably logarithmic asymptotically optimal importance schemes for the estimation of rare events based on the moderate deviations principle.…
Interpretability benefits the theoretical understanding of representations. Existing word embeddings are generally dense representations. Hence, the meaning of latent dimensions is difficult to interpret. This makes word embeddings like a…
Recent measurements of the diffractive deep-inelastic cross section are used to extract diffractive parton densities of the proton. These are subsequently applied in models to predict the production of jets and open charm in the final…
Statistical models of word-sense disambiguation are often based on a small number of contextual features or on a model that is assumed to characterize the interactions among a set of features. Model selection is presented as an alternative…
Information valuable words are the strings with the significant deviation of real frequency from the expected one. The expected frequency is determined through the maximum entropy principle of the reconstructed (extended) frequency…
This work considers the notion of random tensors and reviews some fundamental concepts in statistics when applied to a tensor based data or signal. In several engineering fields such as Communications, Signal Processing, Machine learning,…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
Using the Palm measure notion, we prove the existence of the diffraction measure of all stationary and ergodic point processes. We get precise expressions of those measures in the case of specific processes : stochastic subsets of Z^d, sets…
This paper studies ergodic properties of certain measures arising in the dynamics of holomorphic correspondences. These measures, in general, are not invariant in the classical sense of ergodic theory. We define a notion of ergodicity, and…
In this note, we discuss the uniform ergodicity of a diffusion process given by an It\^o stochastic differential equation. We present an integral condition in terms of the drift and diffusion coefficients that ensures the uniform ergodicity…
Word embeddings allow natural language processing systems to share statistical information across related words. These embeddings are typically based on distributional statistics, making it difficult for them to generalize to rare or unseen…
We consider random walks on a non-elementary hyperbolic group endowed with a word distance. To a probability measure on the group are associated two numerical quantities, the rate of escape and the entropy. On the set of admissible…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
Higher-order exceptional points have attracted increased attention in recent years due to their enhanced sensitivity and distinct topological features. Here, we show that nonlocal acoustic metagratings that enable precise and simultaneous…
We take another look at the general problem of selecting a preferred probability measure among those that comply with some given constraints. The dominant role that entropy maximization has obtained in this context is questioned by arguing…
A one-dimensional system of masses with nearest-neighbor interactions and periodic boundary conditions is used to study mode decay and ergodicity in nonlinear, disordered systems. The system is given an initial periodic displacement, and…
We present a new proof of an Ergodic theorem for Wide-Sense Stationary Random Processes added with a new canonical sampling theorem of mine for finite time duration signals in the frequency domain (periodograms) which is free from the…