Related papers: Functional Covering of Point Processes
Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In this paper we consider two such likelihood ratios. The first one is an…
In the focus of our attention is the asymptotic properties of the sequence of convex hulls which arise as a result of a peeling procedure applied to the convex hull generated by a Poisson point process. Processes of the considered type are…
Recent advances in machine learning-aided lossy compression are incorporating perceptual fidelity into the rate-distortion theory. In this paper, we study the rate-distortion-perception trade-off when the perceptual quality is measured by…
We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…
We examine the coordinated and universal rate-efficient sampling of a subset of correlated discrete memoryless sources followed by lossy compression of the sampled sources. The goal is to reconstruct a predesignated subset of sources within…
In this paper, we study the computation of the rate-distortion-perception function (RDPF) for discrete memoryless sources subject to a single-letter average distortion constraint and a perception constraint that belongs to the family of…
In this presentation, we obtain the corresponding universal function to the diffractive process and show the cross section exhibits the geometrical scaling. It is observed the diffractive theory according to the color dipole approach at…
This paper deals with the intersection point process of a stationary and isotropic Poisson hyperplane process in $\mathbb{R}^d$ of intensity $t>0$, where only hyperplanes that intersect a centred ball of radius $R>0$ are considered. Taking…
Diffusion models have emerged as powerful generative models, inspiring extensive research into their underlying mechanisms. One of the key questions in this area is the loss functions these models shall train with. Multiple formulations…
The physical processes affecting the thermalization of cosmic microwave background spectral distortions are very simple and well understood. This allows us to make precise predictions for the distortions signals caused by various energy…
Deriving exact density functions for Gibbs point processes has been challenging due to their general intractability, stemming from the intractability of their normalising constants/partition functions. This paper offers a solution to this…
This paper studies the minimum achievable source coding rate as a function of blocklength $n$ and probability $\epsilon$ that the distortion exceeds a given level $d$. Tight general achievability and converse bounds are derived that hold at…
Deep learning has been shown to achieve impressive results in several domains like computer vision and natural language processing. A key element of this success has been the development of new loss functions, like the popular cross-entropy…
The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$.…
Ordinary fracture functions, describing hadrons production in the deep inelastic scattering target fragmentation region, are generalized to account for the production of hadrons in arbitrary number, thus offering a renewed framework for…
The notion of statistical depth has been extensively studied in multivariate and functional data over the past few decades. In contrast, the depth on temporal point process is still under-explored. The problem is challenging because a point…
The robustness of object detection algorithms plays a prominent role in real-world applications, especially in uncontrolled environments due to distortions during image acquisition. It has been proven that the performance of object…
The preservation of stochastic orders by distortion functions has become a topic of increasing interest in the reliability analysis of coherent systems. The reason of this interest is that the reliability function of a coherent system with…
Fissile nuclei with small shape distortion relative to the ground-state deformation and with low angular momentum were produced in peripheral heavy-ion collisions. Under the conditions of small shape distortions and low angular momentum,…
Consider two independent Poisson point processes of unit intensity in the Euclidean space of dimension $d$ at least 3. We construct a perfect matching between the two point sets that is a factor (i.e., an equivariant measurable function of…