scholarly journals Improved design and analysis of practical minimizers

2020 ◽  
Author(s):  
Hongyu Zheng ◽  
Carl Kingsford ◽  
Guillaume Marçais
Keyword(s):  
Randomized Algorithm ◽  
Necessary And Sufficient Condition ◽  
Optimal Density ◽  
Asymptotically Optimal ◽  
The Core ◽  
Computation Efficiency ◽  
Bioinformatics Software ◽  
Reference Implementation ◽  
Improved Design ◽  
Necessary And Sufficient

AbstractMotivationMinimizers are methods to sample k-mers from a sequence, with the guarantee that similar set of k-mers will be chosen on similar sequences. It is parameterized by the k-mer length k, a window length w and an order on the k-mers. Minimizers are used in a large number of softwares and pipelines to improve computation efficiency and decrease memory usage. Despite the method’s popularity, many theoretical questions regarding its performance remain open. The core metric for measuring performance of a minimizer is the density, which measures the sparsity of sampled k-mers. The theoretical optimal density for a minimizer is 1/w, provably not achievable in general. For given k and w, little is known about asymptotically optimal minimizers, that is minimizers with density O(1/w).ResultsWe derive a necessary and sufficient condition for existence of asymptotically optimal minimizers. We also provide a randomized algorithm, called the Miniception, to design minimizers with the best theoretical guarantee to date on density in practical scenarios. Constructing and using the Miniception is as easy as constructing and using a random minimizer, which allows the design of efficient minimizers that scale to the values of k and w used in current bioinformatics software programs.AvailabilityReference implementation of the Miniception and the codes for analysis can be found at https://github.com/kingsford-group/[email protected]

scholarly journals Improved design and analysis of practical minimizers

2020 ◽  
Vol 36 (Supplement_1) ◽  
pp. i119-i127
Author(s):  
Hongyu Zheng ◽  
Carl Kingsford ◽  
Guillaume Marçais
Keyword(s):  
Randomized Algorithm ◽  
Supplementary Information ◽  
Necessary And Sufficient Condition ◽  
Asymptotically Optimal ◽  
The Core ◽  
Computation Efficiency ◽  
Bioinformatics Software ◽  
Reference Implementation ◽  
Improved Design ◽  
Necessary And Sufficient

Abstract Motivation Minimizers are methods to sample k-mers from a string, with the guarantee that similar set of k-mers will be chosen on similar strings. It is parameterized by the k-mer length k, a window length w and an order on the k-mers. Minimizers are used in a large number of softwares and pipelines to improve computation efficiency and decrease memory usage. Despite the method’s popularity, many theoretical questions regarding its performance remain open. The core metric for measuring performance of a minimizer is the density, which measures the sparsity of sampled k-mers. The theoretical optimal density for a minimizer is 1/w, provably not achievable in general. For given k and w, little is known about asymptotically optimal minimizers, that is minimizers with density O(1/w). Results We derive a necessary and sufficient condition for existence of asymptotically optimal minimizers. We also provide a randomized algorithm, called the Miniception, to design minimizers with the best theoretical guarantee to date on density in practical scenarios. Constructing and using the Miniception is as easy as constructing and using a random minimizer, which allows the design of efficient minimizers that scale to the values of k and w used in current bioinformatics software programs. Availability and implementation Reference implementation of the Miniception and the codes for analysis can be found at https://github.com/kingsford-group/miniception. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Convexity of b-matching Games

2020 ◽  
Author(s):  
Soh Kumabe ◽  
Takanori Maehara
Keyword(s):  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Kidney Exchange ◽  
The Core ◽  
Emptiness Problem ◽  
Matching Games ◽  
Matching Game ◽  
Necessary And Sufficient

The b-matching game is a cooperative game defined on a graph. The game generalizes the matching game to allow each individual to have more than one partner. The game has several applications, such as the roommate assignment, the multi-item version of the seller-buyer assignment, and the international kidney exchange. Compared with the standard matching game, the b-matching game is computationally hard. In particular, the core non-emptiness problem and the core membership problem are co-NP-hard. Therefore, we focus on the convexity of the game, which is a sufficient condition of the core non-emptiness and often more tractable concept than the core non-emptiness. It also has several additional benefits. In this study, we give a necessary and sufficient condition of the convexity of the b-matching game. This condition also gives an O(n log n + m α(n)) time algorithm to determine whether a given game is convex or not, where n and m are the number of vertices and edges of a given graph, respectively, and α(・) is the inverse-Ackermann function. Using our characterization, we also give a polynomial-time algorithm to compute the Shapley value of a convex b-matching game.

Stackelberg Oligopoly TU-Games: Characterization and Nonemptiness of the Core

2017 ◽  
Vol 19 (04) ◽  
pp. 1750020 ◽  
Author(s):  
Dongshuang Hou ◽  
Aymeric Lardon ◽  
T. S. H. Driessen
Keyword(s):  
Demand Function ◽  
Necessary And Sufficient Condition ◽  
Function Form ◽  
Tu Games ◽  
Marginal Costs ◽  
The Core ◽  
Dynamic Setting ◽  
Necessary And Sufficient ◽  
Second Period ◽  
Characteristic Function Form

In this paper, we consider the dynamic setting of Stackelberg oligopoly TU-games in [Formula: see text]-characteristic function form. Any deviating coalition produces an output at a first period as a leader and then, outsiders simultaneously and independently play a quantity at a second period as followers. We assume that the inverse demand function is linear and that firms operate at constant but possibly distinct marginal costs. First, we show that the core of any Stackelberg oligopoly TU-game always coincides with the set of imputations. Second, we provide a necessary and sufficient condition, depending on the heterogeneity of firms’ marginal costs, under which the core is nonempty.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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