Related papers: How to partition or count an abstract simplicial c…
As improved versions of successive cancellation (SC) decoding algorithm, successive cancellation list (SCL) decoding and successive cancellation stack (SCS) decoding are used to improve the finite-length performance of polar codes. Unified…
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…
In this paper, we consider the problem of partitioning a small data sample drawn from a mixture of $k$ product distributions. We are interested in the case that individual features are of low average quality $\gamma$, and we want to use as…
Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…
Successive-cancellation list (SCL) decoding is an algorithm that provides very good error-correction performance for polar codes. However, its hardware implementation requires a large amount of memory, mainly to store intermediate results.…
Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…
Although the successive cancelation (SC) algorithm works well for very long polar codes, its error performance for shorter polar codes is much worse. Several SC based list decoding algorithms have been proposed to improve the error…
Given a complete graph with positive weights on its edges, we define the weight of a subset of edges as the product of weights of the edges in the subset and consider sums (partition functions) of weights over subsets of various kinds:…
Simplicial partitions are a fundamental structure in computational geometry, as they form the basis of optimal data structures for range searching and several related problems. Current algorithms are built on very specific spatial…
Graphs are ubiquitous to model the irregular (non-Euclidean) structure of complex data, but they are limited to pairwise relationships and fail to model the complexities of the datasets exhibiting higher-order interactions. In that context,…
For a subspace arrangement over a finite field we study the evaluation code defined on the arrangement's set of points. The length of this code is given by the subspace arrangement's characteristic polynomial. For coordinate subspace…
Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie…
In this paper we introduce a novel method for segmentation that can benefit from general semantics of Convolutional Neural Network (CNN). Our segmentation proposes visually and semantically coherent image segments. We use binary encoding of…
In the field of mathematics, a purely combinatorial equivalent to a simplicial complex, or more generally, a down-set, is an abstract structure known as a family of sets. This family is closed under the operation of taking subsets, meaning…
We consider closed simplicial and cubical $n$-complexes in terms of link of their $(n-2)$-faces. Especially, we consider the case, when this link has size 3 or 4, i.e., every $(n-2)$-face is contained in 3 or 4 $n$-faces. Such simplicial…
Analyzing a distributed computation is a hard problem in general due to the combinatorial explosion in the size of the state-space with the number of processes in the system. By abstracting the computation, unnecessary explorations can be…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
Segmentation-based image coding methods provide high compression ratios when compared with traditional image coding approaches like the transform and sub band coding for low bit-rate compression applications. In this paper, a…
This paper introduces a data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored in a trie whose nodes are in bijection with the faces of the…
We outline a novel clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex. The method is inspired by, and can be seen as a higher-dimensional version of,…