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Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel…
This paper presents a Transformer-based image compression system that allows for a variable image quality objective according to the user's preference. Optimizing a learned codec for different quality objectives leads to reconstructed…
Alice and Bob are given two correlated n-bit strings x_1 and, respectively, x_2, which they want to losslessly compress and send to Zack. They can either collaborate by sharing their strings, or work separately. We show that there is no…
We consider the problem of {\em restructuring} compressed texts without explicit decompression. We present algorithms which allow conversions from compressed representations of a string $T$ produced by any grammar-based compression…
Time series account for a large proportion of the data stored in financial, medical and scientific databases. The efficient storage of time series is important in practical applications. In this paper, we propose a novel compression scheme…
Neural network compression methods have enabled deploying large models on emerging edge devices with little cost, by adapting already-trained models to the constraints of these devices. The rapid development of AI-capable edge devices with…
We introduce a simple recurrent variational auto-encoder architecture that significantly improves image modeling. The system represents the state-of-the-art in latent variable models for both the ImageNet and Omniglot datasets. We show that…
We introduce a variation of the scheduling with precedence constraints problem that has applications to molecular folding and production management. We are given a bipartite graph $H=(B,S)$. Vertices in $B$ are thought of as goods or…
We present an effective method for computing parametric primary decomposition via comprehensive Gr\"obner systems. In general, it is very difficult to compute a parametric primary decomposition of a given ideal in the polynomial ring with…
A word-representable graph is a simple graph $G$ which can be represented by a word $w$ over the vertices of $G$ such that any two vertices are adjacent in $G$ if and only if they alternate in $w$. It is known that the class of…
Our starting point is the observation that if graphs in a class C have low descriptive complexity in first order logic, then the isomorphism problem for C is solvable by a fast parallel algorithm (essentially, by a simple combinatorial…
A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For…
A decision list is an ordered list of rules. Each rule is specified by a term, which is a conjunction of literals, and a value. Given an input, the output of a decision list is the value corresponding to the first rule whose term is…
In the procedure of constraining the cosmological parameters with the observational Hubble data and the type Ia supernova data, the combination of Masked Autoregressive Flow and Denoising Autoencoder can perform a good result. The above…
For an ideal $I\subseteq\mathbb{R}[x]$ given by a set of generators, a new semidefinite characterization of its real radical $I(V_\mathbb{R}(I))$ is presented, provided it is zero-dimensional (even if $I$ is not). Moreover we propose an…
Cadences are structurally maximal arithmetic progressions of indices corresponding to equal characters in an underlying string. This paper provides a polynomial time detection algorithm for 3-cadences in grammar-compressed binary strings.…
Network alignment is useful for multiple applications that require increasingly large graphs to be processed. Existing research approaches this as an optimization problem or computes the similarity based on node representations. However,…
Let G be a bipartite graph with positive integer weights on the edges and without isolated nodes. Let n, N and W be the node count, the largest edge weight and the total weight of G. Let k(x,y) be log(x)/log(x^2/y). We present a new…
We present a data compression and dimensionality reduction scheme for data fusion and aggregation applications to prevent data congestion and reduce energy consumption at network connecting points such as cluster heads and gateways. Our…
A graph $G$ with vertex set $V(G)$ and edge set $E(G)$ is said to be word-representable if there exists a word $w$ over the alphabet $V(G)$ such that, for any two distinct letters $x,y \in V(G)$, the letters $x$ and $y$ alternate in $w$ if…