Related papers: Multiset permutation generation by transpositions

By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are…

In this paper, we give a polynomial (O(n^8)) algorithm for finding a longest common pattern between two permutations of size n given that one is separable. We also give an algorithm for general permutations whose complexity depends on the…

Creating large-scale datasets for training high-performance generative models is often prohibitively expensive, especially when associated attributes or annotations must be provided. As a result, merging existing datasets has become a…

The construction of low-discrepancy sets, used for uniform sampling and numerical integration, has recently seen great improvements based on optimization and machine learning techniques. However, these methods are computationally expensive,…

We introduce a compressed representation of sets of sets that exploits how much they differ from each other. Our representation supports access, membership, predecessor and successor queries on the sets within logarithmic time. In addition,…

Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…

We initiate the study of sorting permutations using prefix block-interchanges, which exchange any prefix of a permutation with another non-intersecting interval. The goal is to transform a given permutation into the identity permutation…

Finding the minimum distance of linear codes is an NP-hard problem. Traditionally, this computation has been addressed by means of the design of algorithms that find, by a clever exhaustive search, a linear combination of some generating…

We study the problem of learning permutation invariant representations that can capture "flexible" notions of containment. We formalize this problem via a measure theoretic definition of multisets, and obtain a theoretically-motivated…

Morphology in unbalanced languages remains a big challenge in the context of machine translation. In this paper, we propose to de-couple machine translation from morphology generation in order to better deal with the problem. We investigate…

Consider a finite sequence of permutations of the elements 1,...,n, with the property that each element changes its position by at most 1 from any permutation to the next. We call such a sequence a tangle, and we define a move of element i…

The problem of inhomogeneous cluster densities has been a long-standing issue for distance-based and density-based algorithms in clustering and anomaly detection. These algorithms implicitly assume that all clusters have approximately the…

Machine learning algorithms have difficulties to generalize over a small set of examples. Humans can perform such a task by exploiting vast amount of background knowledge they possess. One method for enhancing learning algorithms with…

We solve the problem of designing an O(1) time algorithm for generating adjacent multiset combinations in a different approach from Walsh. By the word adjacent, we mean that two adjacent multiset combinations are different at two places by…

The reconstruction problem for permutations on $n$ elements from their erroneous patterns which are distorted by transpositions is presented in this paper. It is shown that for any $n \geq 3$ an unknown permutation is uniquely…

We describe a new algorithm, termed subspace evolution and transfer (SET), for solving low-rank matrix completion problems. The algorithm takes as its input a subset of entries of a low-rank matrix, and outputs one low-rank matrix…

Using the approach suggested in [arXiv:1002.2761] we present below a sufficient condition guaranteeing that two collections of patterns of permutations have the same exponential generating functions for the number of permutations avoiding…

Generating as diverse molecules as possible with desired properties is crucial for drug discovery research, which invokes many approaches based on deep generative models today. Despite recent advancements in these models, particularly in…

Transposed convolution is crucial for generating high-resolution outputs, yet has received little attention compared to convolution layers. In this work we revisit transposed convolution and introduce a novel layer that allows us to place…

Some genes can change their relative locations in a genome. Thus for different individuals of the same species, the orders of genes might be different. Such jumping genes are called transposons. A practical problem is to determine…