Related papers: Compression of enumerations and gain
For different classes of measure preserving transformations, we investigate collections of sets that exhibit the property of lightly mixing. Lightly mixing is a stronger property than topological mixing, and requires that a lim inf is…
We study in which way Kolmogorov complexity and instance complexity affect properties of r.e. sets. We show that the well-known 2log n upper bound on the Kolmogorov complexity of initial segments of r.e.\ sets is optimal and characterize…
This paper studies direct limits of full upper triangular matrix algebras with embeddings which are not *-extendible. A representation of the limit algebra is found so that the generated C*-algebra is the C*-envelope. Some examples are…
We consider the problem of learned transform compression where we learn both, the transform as well as the probability distribution over the discrete codes. We utilize a soft relaxation of the quantization operation to allow for…
We discuss the applicability of compressed sensing theory. We take a genuine look at both experimental results and theoretical works. We answer the following questions: 1) What can compressed sensing really do? 2) More importantly, why?
We analyze the computational complexity of the problem of deciding whether, for a given simple game, there exists the possibility of rearranging the participants in a set of $j$ given losing coalitions into a set of $j$ winning coalitions.…
A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change…
The problem of interpreting or aggregating multiple rankings is common to many real-world applications. Perhaps the simplest and most common approach is a weighted rank aggregation, wherein a (convex) weight is applied to each input ranking…
We consider iterative (`turbo') algorithms for compressed sensing. First, a unified exposition of the different approaches available in the literature is given, thereby enlightening the general principles and main differences. In particular…
A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…
This work continues the study of the relationship between sample compression schemes and statistical learning, which has been mostly investigated within the framework of binary classification. The central theme of this work is establishing…
We analyze the effect of lossy compression in the processing of sensor signals that must be used to detect anomalous events in the system under observation. The intuitive relationship between the quality loss at higher compression and the…
Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by a probability assignment to each argument. There are various interpretations that can be ascribed…
When inclusions in a composite are separated by a very small gap, high contrast between the inclusion and matrix properties can induce strong amplification of the underlying field inside the narrow region. Quantifying this field…
We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy this…
Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term…
Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities. As this new technology permeated through…
In this paper some links between the density of a set of integers and the density of its sumset, product set and set of subset sums are presented.
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…