scholarly journals A Third Strike Against Perfect Phylogeny

2019 ◽  
Vol 68 (5) ◽  
pp. 814-827 ◽  
Author(s):  
Leo Van Iersel ◽  
Mark Jones ◽  
Steven Kelk
Keyword(s):  
Open Problem ◽  
Efficient Algorithm ◽  
Classical Result ◽  
Input Data ◽  
Fixed Number ◽  
Evolutionary Trees ◽  
Perfect Phylogeny ◽  
Fixed Size ◽  
Algorithm Development ◽  
Negative Results

Abstract Perfect phylogenies are fundamental in the study of evolutionary trees because they capture the situation when each evolutionary trait emerges only once in history; if such events are believed to be rare, then by Occam’s Razor such parsimonious trees are preferable as a hypothesis of evolution. A classical result states that 2-state characters permit a perfect phylogeny precisely if each subset of 2 characters permits one. More recently, it was shown that for 3-state characters the same property holds but for size-3 subsets. A long-standing open problem asked whether such a constant exists for each number of states. More precisely, it has been conjectured that for any fixed number of states $r$ there exists a constant $f(r)$ such that a set of $r$-state characters $C$ has a perfect phylogeny if and only if every subset of at most $f(r)$ characters has a perfect phylogeny. Informally, the conjecture states that checking fixed-size subsets of characters is enough to correctly determine whether input data permits a perfect phylogeny, irrespective of the number of characters in the input. In this article, we show that this conjecture is false. In particular, we show that for any constant $t$, there exists a set $C$ of $8$-state characters such that $C$ has no perfect phylogeny, but there exists a perfect phylogeny for every subset of at most $t$ characters. Moreover, there already exists a perfect phylogeny when ignoring just one of the characters, independent of which character you ignore. This negative result complements the two negative results (“strikes”) of Bodlaender et al. (1992,2000). We reflect on the consequences of this third strike, pointing out that while it does close off some routes for efficient algorithm development, many others remain open.

scholarly journals Culling a Set of Points for Roundness or Cylindricity Evaluations

2003 ◽  
Vol 13 (03) ◽  
pp. 231-240 ◽  
Author(s):  
Olivier Devillers ◽  
Franco P. Preparata
Keyword(s):  
Cross Sections ◽  
Input Data ◽  
Linear Time ◽  
Programming Approach ◽  
Fixed Size ◽  
Recent Approach ◽  
Data Points ◽  
Surface Measurements ◽  
Computational Metrology ◽  
Set Of Points

Roundness and cylindricity evaluations are among the most important problems in computational metrology, and are based on sets of surface measurements (input data points). A recent approach to such evaluations is based on a linear-programming approach yielding a rapidly converging solution. Such a solution is determined by a fixed-size subset of a large input set. With the intent to simplify the main computational task, it appears desirable to cull from the input any point that cannot provably define the solution. In this note we present an analysis and an efficient solution to the problem of culling the input set. For input data points arranged in cross-sections under mild conditions of uniformity, this algorithm runs in linear time.

scholarly journals Experimenting with Segmentation in ITK

2007 ◽  
Author(s):  
Cemal Cagatay Bilgin
Keyword(s):  
Open Problem ◽  
Input Data ◽  
Source Code ◽  
Output Data

This document describes some experiments for segmentation using the Insight Toolkit ITK . The code of the experiment is written following the ITK CodingStyle as described in the directory .Segmentation is still an open problem and there are quite a lot of algorithms specific to application domains and data being used. In this experiment I’ve used a 3-D MRA scan of Brain retrieved from MIDAS website. This paper is accompanied with the source code, input data, parameters and output data that the author used for experimenting with the algorithm.

The influence of age structure on total productivity in breeding flocks of Merino sheep. I. Flocks with a fixed number of breeding ewes, producing their own replacements

1968 ◽  
Vol 19 (3) ◽  
pp. 443 ◽  
Author(s):  
HN Turner ◽  
GH Brown ◽  
GH Ford
Keyword(s):  
Age Structure ◽  
Age Groups ◽  
Fixed Number ◽  
Reproduction Rate ◽  
Fixed Size ◽  
Young Stock ◽  
Merino Sheep ◽  
Total Productivity ◽  
Two Age Groups

In a flock of breeding ewes of fixed size, the number of age groups of rams and ewes influences the annual rate of genetic gain in any character under selection. The number of ewe age groups also influences the number of surplus stock aged 1½ years, and the number cast for age, as well as the amount and quality of wool obtained. The latter is also influenced by the proportion of ewes which rear no lambs, one, or two, as well as the proportion themselves born in multiple births or as the progeny of young ewes. In this paper, all these influences are considered in determining the age structure of the breeding flock which gives the greatest number of surplus stock and the greatest relative wool return. To combine the two, relative weights have to be given to wool and surplus stock. One such set of weights has been used, and the conclusion has been drawn that two age groups of rams, with either five or six age groups of ewes, give optimal return, the number of ewe groups depending on the level of reproduction rate. This conclusion depends on the relative weights used. In cases where numbers of animals are of supreme importance, such as after a drought or at a time of increasing pasture improvement, then retaining ewes to an older age would increase the number of surplus young stock.

ON THE EXISTENCE OF LOOKAHEAD DELEGATORS FOR NFA

2007 ◽  
Vol 18 (05) ◽  
pp. 949-973 ◽  
Author(s):  
BALA RAVIKUMAR ◽  
NICOLAE SANTEAN
Keyword(s):  
Open Problem ◽  
Finite Automata ◽  
Fixed Number ◽  
Buffer Size ◽  
Membership Problem ◽  
Web Services Composition ◽  
Deterministic Finite Automata ◽  
Practical Applications ◽  
Services Composition ◽  
The Right

We investigate deterministically simulating (i.e., solving the membership problem for) nondeterministic finite automata (NFA), relying solely on the NFA's resources (states and transitions). Unlike the standard NFA simulation, involving an algorithm which stores at each step all the states reached nondeterministically while reading the input, we consider deterministic finite automata (DFA) with lookahead, which choose the “right” NFA transitions based on a fixed number of input symbols read ahead. This concept, known as lookahead delegation, arose in a formal study of web services composition and its subsequent practical applications. Here we answer several related questions, such as “when is lookahead delegation possible?” and “how hard is it to find a delegator with a given lookahead buffer size?”. In particular, we show that only finite languages have the property that all their NFA have delegators. This implies, among others, that delegation is a machine property, rather than a language property. We also prove that the existence of lookahead delegators for unambiguous NFA is decidable, thus partially solving an open problem. Finally, we show that finding delegators (even for a given buffer size) is hard in general, and is more efficient for unambiguous NFA, and we give an algorithm and a compact characterization for NFA delegation in general.

scholarly journals Stabilizer extent is not multiplicative

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 400
Author(s):  
Arne Heimendahl ◽  
Felipe Montealegre-Mora ◽  
Frank Vallentin ◽  
David Gross
Keyword(s):  
Open Problem ◽  
Efficient Algorithm ◽  
Tensor Products ◽  
Affirmative Answer ◽  
The State ◽  
Quantum Circuits ◽  
Classical Simulation ◽  
Important Open Problem ◽  
Classical Computer ◽  
Stabilizer States

The Gottesman-Knill theorem states that a Clifford circuit acting on stabilizer states can be simulated efficiently on a classical computer. Recently, this result has been generalized to cover inputs that are close to a coherent superposition of logarithmically many stabilizer states. The runtime of the classical simulation is governed by the stabilizer extent, which roughly measures how many stabilizer states are needed to approximate the state. An important open problem is to decide whether the extent is multiplicative under tensor products. An affirmative answer would yield an efficient algorithm for computing the extent of product inputs, while a negative result implies the existence of more efficient classical algorithms for simulating largescale quantum circuits. Here, we answer this question in the negative. Our result follows from very general properties of the set of stabilizer states, such as having a size that scales subexponentially in the dimension, and can thus be readily adapted to similar constructions for other resource theories.

scholarly journals Efficient Search for Optimal Diffusion Layers of Generalized Feistel Networks

2019 ◽  
pp. 218-240
Author(s):  
Patrick Derbez ◽  
Pierre-Alain Fouque ◽  
Baptiste Lambin ◽  
Victor Mollimard
Keyword(s):  
Lower Bound ◽  
Open Problem ◽  
Building Block ◽  
Efficient Algorithm ◽  
Main Idea ◽  
Diffusion Layers ◽  
Round Function ◽  
Feistel Networks ◽  
Impossibility Proof

The Feistel construction is one of the most studied ways of building block ciphers. Several generalizations were then proposed in the literature, leading to the Generalized Feistel Network, where the round function first applies a classical Feistel operation in parallel on an even number of blocks, and then a permutation is applied to this set of blocks. In 2010 at FSE, Suzaki and Minematsu studied the diffusion of such construction, raising the question of how many rounds are required so that each block of the ciphertext depends on all blocks of the plaintext. They thus gave some optimal permutations, with respect to this diffusion criteria, for a Generalized Feistel Network consisting of 2 to 16 blocks, as well as giving a good candidate for 32 blocks. Later at FSE’19, Cauchois et al. went further and were able to propose optimal even-odd permutations for up to 26 blocks.In this paper, we complete the literature by building optimal even-odd permutations for 28, 30, 32, 36 blocks which to the best of our knowledge were unknown until now. The main idea behind our constructions and impossibility proof is a new characterization of the total diffusion of a permutation after a given number of rounds. In fact, we propose an efficient algorithm based on this new characterization which constructs all optimal even-odd permutations for the 28, 30, 32, 36 blocks cases and proves a better lower bound for the 34, 38, 40 and 42 blocks cases. In particular, we improve the 32 blocks case by exhibiting optimal even-odd permutations with diffusion round of 9. The existence of such a permutation was an open problem for almost 10 years and the best known permutation in the literature had a diffusion round of 10. Moreover, our characterization can be implemented very efficiently and allows us to easily re-find all optimal even-odd permutations for up to 26 blocks with a basic exhaustive search

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