Related papers: How to recover a permutation group amidst errors
Permutation tests date back nearly a century to Fisher's randomized experiments, and remain an immensely popular statistical tool, used for testing hypotheses of independence between variables and other common inferential questions. Much of…
The sequence reconstruction problem asks for the recovery of a sequence from multiple noisy copies, where each copy may contain up to $r$ errors. In the case of permutations on \(n\) letters under the Hamming metric, this problem is closely…
Let $X=(X_1,X_2, X_3)$ be a Gaussian random vector such that $X\sim \mathcal{N} (0,\Sigma)$. We consider the problem of determining the matrix $\Sigma$, up to permutation, based on the knowledge of the distribution of…
When a subgroup is identified from the data, it must be evaluated in a replicable way. The usual in-sample approach, which evaluates the post-hoc identified subgroup as predefined, might suffer from selection bias. This issue of in-sample…
We stress the potential usefulness of renormalization group invariants. Especially particular combinations thereof could for instance be used as probes into patterns of supersymmetry breaking in the MSSM at inaccessibly high energies. We…
Identification of defective members of large populations has been widely studied in the statistics community under the name of group testing. It involves grouping subsets of items into different pools and detecting defective members based…
Consider a query-based data acquisition problem that aims to recover the values of $k$ binary variables from parity (XOR) measurements of chosen subsets of the variables. Assume the response model where only a randomly selected subset of…
Frequently, randomly organized data is needed to avoid an anomalous operation of other algorithms and computational processes. An analogy is that a deck of cards is ordered within the pack, but before a game of poker or solitaire the deck…
In this paper, we introduce a novel approach for generating random elements of a finite group given a set of generators of that. Our method draws upon combinatorial group theory and automata theory to achieve this objective. Furthermore, we…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…
A generalized numerical semigroup is a submonoid $S$ of $\mathbb{N}^d$ with finite complement in it. We characterize isomorphisms between these monoids in terms of permutation of coordinates. Considering the equivalence relation that…
Let $\Gamma$ be the fundamental group of a closed orientable surface of genus at least two. Consider the composition of a uniformly random element of $\mathrm{Hom}(\Gamma,S_n)$ with the $(n-1)$-dimensional irreducible representation of…
Graph shotgun assembly refers to the problem of reconstructing a graph from a collection of local neighborhoods. In this paper, we consider shotgun assembly of \ER random graphs $G(n, p_n)$, where $p_n = n^{-\alpha}$ for $0 < \alpha < 1$.…
We discuss uniform sampling algorithms that are based on stochastic growth methods, using sampling of extreme configurations of polymers in simple lattice models as a motivation. We shall show how a series of clever enhancements to a…
The problem of recovering (count and sum) range queries over multidimensional data only on the basis of aggregate information on such data is addressed. This problem can be formalized as follows. Suppose that a transformation T producing a…
We consider the problem of spatiotemporal sampling in a discrete infinite dimensional spatially invariant evolutionary process $x^{(n)}=A^nx$ to recover an unknown convolution operator $A$ given by a filter $a \in \ell^1(\mathbb{Z})$ and an…
In the mixture models problem it is assumed that there are $K$ distributions $\theta_{1},\ldots,\theta_{K}$ and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances…
Many machine learning tasks, such as learning with invariance and policy evaluation in reinforcement learning, can be characterized as problems of learning from conditional distributions. In such problems, each sample $x$ itself is…
We give a 1-sided randomised algorithm to detect when a permutation group of degree n, given by generators, contains the alternating group of degree n. This improves on standard methods, and on an algorithm of P. Cameron and J. Cannon.
We give an efficient algorithm which can obtain a relative error approximation to the spectral norm of a matrix, combining the power iteration method with some techniques from matrix reconstruction which use random sampling.