Publications related to Parity of a permutation

Revisiting the Indifferentiability of the Sum of Permutations

The sum of two n-bit pseudorandom permutations is known to behave like a pseudorandom function with n bits of security. A recent line of research has investigated the security of two public n-bit permutations and its degree of indifferentiability. Mandal e ...

Springer2023

From Trees to Barcodes and Back Again: A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view. Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...

EPFL2022

Optimizing Quantum Circuit Synthesis for Permutations Using Recursion

Bruno Schmitt Antunes

We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth. In each case we combine a scalable heuristic with a nonscalabl ...

ASSOC COMPUTING MACHINERY2022

Efficient Preparation of Cyclic Quantum States

Giovanni De Micheli, Fereshte Mozafari Ghoraba

Universal quantum algorithms that prepare arbitrary n-qubit quantum states require O(2n) gate complexity. The complexity can be reduced by considering specific families of quantum states depending on the task at hand. In particular, multipartite quantum st ...

IEEE2022

A Large, Finite Permutation of Specific, Discrete Variants: Dan Graham's Children's Pavilion at Chambres d'Amis (1986)

Christophe van Gerrewey

In 1986, Dan Graham participated in Chambres d'Amis in Ghent, Belgium, curated by Jan Hoet as an art exhibition outside of the museum, in individual houses. With the help of a local architect, Graham constructed a glass and steel pavilion in a private gard ...

ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD2021

Swap and Rotate: Lightweight Linear Layers for SPN-based Blockciphers

Serge Vaudenay, Francesco Regazzoni, Subhadeep Banik, Muhammed Fatih Balli

In CHES 2017, Jean et al. presented a paper on "Bit-Sliding" in which the authors proposed lightweight constructions for SPN based block ciphers like AES, PRESENT and SKINNY. The main idea behind these constructions was to reduce the length of the datapath ...

2020

Unique decomposition of homogeneous languages and application to isothetic regions

Nicolas René Jean Ninin

A language is said to be homogeneous when all its words have the same length. Homogeneous languages thus form a monoid under concatenation. It becomes freely commutative under the simultaneous actions of every permutation group G(n) on the collection of ho ...

2019

Permutation-based Decoding of Reed-Muller Codes in Binary Erasure Channel

Rüdiger Urbanke, Kirill Ivanov

In this paper, we consider the problem of decoding Reed-Muller (RM) codes in binary erasure channel. We propose a novel algorithm, which exploits several techniques, such as list recursive (successive cancellation) decoding based on Plotkin decomposition, ...

IEEE2019

Enumeration of reversible functions and its application to circuit complexity

Giovanni De Micheli, Mathias Soeken, Nabila Abdessaied

We review combinational results to enumerate and classify reversible functions and investigate the application to circuit complexity. In particularly, we consider the effect of negating and permuting input and output variables and the effect of applying li ...

Springer2016

Structural cluster analysis of chemical reactions in solution

Fabio Pietrucci

We introduce a simple and general approach to the problem of clustering structures from atomic trajectories of chemical reactions in solution. By considering distance metrics which are invariant under permutation of identical atoms or molecules, we demonst ...

Amer Inst Physics2013

Graph Theory Meets Ab Initio Molecular Dynamics: Atomic Structures and Transformations at the Nanoscale

Wanda Andreoni, Fabio Pietrucci

Social permutation invariant coordinates are introduced describing the bond network around a given atom. They originate from the largest eigenvalue and the corresponding eigenvector of the contact matrix, are invariant under permutation of identical atoms, ...

2011

Sorting signed permutations by inversions in O(nlogn) time

Bernard Moret, Yu Lin, Vaibhav Rajan, Krister Swenson

The study of genomic inversions (or reversals) has been a mainstay of computational genomics for nearly 20 years. After the initial breakthrough of Hannenhalli and Pevzner, who gave the first polynomial-time algorithm for sorting signed permutations by inv ...

2010

Polar Codes: Characterization of Exponent, Bounds, and Constructions

Rüdiger Urbanke, Satish Babu Korada, Eren Sasoglu

Polar codes were recently introduced by Arikan. They achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code construction is closely rel ...

2010

The Metropolized Partial Importance Sampling MCMC mixes slowly on minimal reversal rearrangement paths

Krister Swenson

Markov chain Monte Carlo has been the standard technique for inferring the posterior distribution of genome rearrangement scenarios under a Bayesian approach. We present here a negative result on the rate of convergence of the generally used Markov chains. ...

2010

Maximum independent sets of commuting and noninterfering inversions

Bernard Moret, Krister Swenson

Background: Given three signed permutations, an inversion median is a fourth permutation that minimizes the sum of the pairwise inversion distances between it and the three others. This problem is NP-hard as well as hard to approximate. Yet median-based ap ...

2009

Polar Codes: Characterization of Exponent, Bounds, and Constructions

Rüdiger Urbanke, Satish Babu Korada, Eren Sasoglu

Polarization codes were recently introduced by Ar\i kan. They are explicit code constructions which achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels (and even extensions thereof) under a low complexity successive decodi ...

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