Related papers: Covering Point Patterns
An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbol-wise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…
A prescription to calculate the minimum number of bits needed for binary strip detector readout is presented. This permits a systematic analysis of the readout efficiency relative to this theoretical minimum number of bits. Different level…
An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbolwise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…
Spatial point patterns are a commonly recorded form of data in ecology, medicine, astronomy, criminology, epidemiology and many other application fields. One way to understand their second order dependence structure is via their spectral…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
A likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on the soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering…
This paper formalizes a latent variable inference problem we call {\em supervised pattern discovery}, the goal of which is to find sets of observations that belong to a single ``pattern.'' We discuss two versions of the problem and prove…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
We consider the problem of encoding a set of vectors into a minimal number of bits while preserving information on their Euclidean geometry. We show that this task can be accomplished by applying a Johnson-Lindenstrauss embedding and…
Universal compression of patterns of sequences generated by independently identically distributed (i.i.d.) sources with unknown, possibly large, alphabets is investigated. A pattern is a sequence of indices that contains all consecutive…
We define an algorithm that parses multidimensional arrays sequentially into mainly unrepeated but nested multidimensional sub-arrays of increasing size, and show that the resulting sub-block pointer encoder compresses almost every…
Given partial information about a set, we are interested in fully recovering the original set from what is given. If a set encodes itself robustly, any partial information about the set suffices to fully recover the information about the…
We present an algorithm for generating Poisson-disc patterns taking O(N) time to generate $N$ points. The method is based on a grid of regions which can contain no more than one point in the final pattern, and uses an explicit model of…
Point patterns are characterized by their density and correlation. While spatial variation of density is well-understood, analysis and synthesis of spatially-varying correlation is an open challenge. No tools are available to intuitively…
Object detection in point clouds is an important aspect of many robotics applications such as autonomous driving. In this paper we consider the problem of encoding a point cloud into a format appropriate for a downstream detection pipeline.…
This study investigates a multiplicative integer system using a method that was developed for studying pattern generation problems. The entropy and the Minkowski dimensions of general multiplicative systems can thus be computed. A…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
Given a permutation w, we look at the range of how often a simple reflection s_k appears in reduced decompositions of w. We compute the minimum and give a sharp upper bound on the maximum. That bound is in terms of 321- and 3412-patterns in…
Given a database, a common problem is to find the pairs or $k$-tuples of items that frequently co-occur. One specific problem is to create a small space "sketch" of the data that records which $k$-tuples appear in more than an $\epsilon$…
A method for bounding the rate of bit-stuffing encoders for 2-D constraints is presented. Instead of considering the original encoder, we consider a related one which is quasi-stationary. We use the quasi-stationary property in order to…