Related papers: Functional Covering of Point Processes

Charge balance functions provide insight into critical issues concerning hadronization and transport in heavy-ion collisions by statistically isolating charge/anti-charge pairs which are correlated by charge conservation. However,…

A scenario involving a source, a channel, and a destination, where the destination is interested in {\em both} reliably reconstructing the message transmitted by the source and estimating with a fidelity criterion the state of the channel,…

The high-pressure compaction of three dimensional granular packings is simulated using a bonded particle model (BPM) to capture linear elastic deformation. In the model, grains are represented by a collection of point particles connected by…

In recent years, a number of functional inequalities have been derived for Poisson random measures, with a wide range of applications. In this paper, we prove that such inequalities can be extended to the setting of marked temporal point…

We identify an issue in multi-task learnable compression, in which a representation learned for one task does not positively contribute to the rate-distortion performance of a different task as much as expected, given the estimated amount…

We consider the semantic rate-distortion problem motivated by task-oriented video compression. The semantic information corresponding to the task, which is not observable to the encoder, shows impacts on the observations through a joint…

Heuristics indicate that point processes exhibiting clustering of points have larger critical radius $r_c$ for the percolation of their continuum percolation models than spatially homogeneous point processes. It has already been shown, and…

Fitting models for non-Poisson point processes is complicated by the lack of tractable models for much of the data. By using large samples of independent and identically distributed realizations and statistical learning, it is possible to…

This paper is concerned with the lossy compression of general random variables, specifically with rate-distortion theory and quantization of random variables taking values in general measurable spaces such as, e.g., manifolds and fractal…

Recent years have seen a tremendous growth in both the capability and popularity of automatic machine analysis of images and video. As a result, a growing need for efficient compression methods optimized for machine vision, rather than…

Focal loss has recently gained significant popularity, particularly in tasks like object detection where it helps to address class imbalance by focusing more on hard-to-classify examples. This work proposes the focal loss as a distortion…

We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet…

We consider a Poisson process $\eta$ on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of $\eta$. As a consequence we…

There are some papers which describe the use of bootstrap techniques in point process statistics. The aim of the present paper is to show that the form in which bootstrap is used there is dubious. In case of variance estimation of pair…

Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…

Mutually uncorrelated random discrete events, manifesting a common basic process, are examined often in terms of their occurrence rate as a function of one or more of their distinguishing attributes, such as measurements of photon spectrum…

We use a stochastic approach to show how Taylor dispersion is affected by kinetic processes of adsorption and desorption onto surfaces. A general theory is developed, from which we derive explicitly the dispersion coefficients of canonical…

For the HB problem with the CR constraint, the rate-distortion function is derived under the assumption that the side information sequences are (stochastically) degraded. The rate-distortion function is also calculated explicitly for three…

In this paper we relate the partition function to the max-statistics of random variables. In particular, we provide a novel framework for approximating and bounding the partition function using MAP inference on randomly perturbed models. As…

The commonly used radial distortion model for camera calibration is in fact an assumption or a restriction. In practice, camera distortion could happen in a general geometrical manner that is not limited to the radial sense. This paper…