The capacity of a channel with arbitrarily varying channel probability functions and binary output alphabet

1970 ◽  
Vol 15 (3) ◽  
pp. 186-194 ◽  
Author(s):  
R. Ahlswede ◽  
J. Wolfowitz
Keyword(s):  
Probability Functions ◽  
Binary Output ◽  
Output Alphabet

An Introduction to Uncertain Futures

2018 ◽  
Author(s):  
Jens Beckert ◽  
Richard Bronk
Keyword(s):  
Optimal Strategies ◽  
Theoretical Framework ◽  
Objective Probability ◽  
Political Debate ◽  
Probability Functions ◽  
Market Economies ◽  
Socially Constructed ◽  
The Future ◽  
Radical Uncertainty ◽  
Calculative Practices

This chapter provides a theoretical framework for considering how imaginaries and narratives interact with calculative devices to structure expectations and beliefs in the economy. It analyses the nature of uncertainty in innovative market economies and examines how economic actors use imaginaries, narratives, models, and calculative practices to coordinate and legitimize action, determine value, and establish sufficient conviction to act despite the uncertainty they face. Placing the themes of the volume in the context of broader trends in economics and sociology, the chapter argues that, in conditions of widespread radical uncertainty, there is no uniquely rational set of expectations, and there are no optimal strategies or objective probability functions; instead, expectations are often structured by contingent narratives or socially constructed imaginaries. Moreover, since expectations are not anchored in a pre-existing future reality but have an important role in creating the future, they become legitimate objects of political debate and crucial instruments of power in markets and societies.

The calculation of single inclusion probability functions

1987 ◽  
Vol 86 (2) ◽  
pp. 1010-1019
Author(s):  
Gregory J. Gillette ◽  
John J. McCoy
Keyword(s):  
Inclusion Probability ◽  
Probability Functions ◽  
Single Inclusion

scholarly journals THE THEORY OF SPECTRUM EXCHANGEABILITY

2014 ◽  
Vol 8 (1) ◽  
pp. 108-130
Author(s):  
E. HOWARTH ◽  
J. B. PARIS
Keyword(s):  
Probability Function ◽  
Inductive Logic ◽  
Probability Functions ◽  
Homogeneous Functions ◽  
Finite Structures ◽  
Spectrum Exchangeability

AbstractSpectrum Exchangeability, Sx, is an irrelevance principle of Pure Inductive Logic, and arguably the most natural (but not the only) extension of Atom Exchangeability to polyadic languages. It has been shown1 that all probability functions which satisfy Sx are comprised of a mixture of two essential types of probability functions; heterogeneous and homogeneous functions. We determine the theory of Spectrum Exchangeability, which for a fixed language L is the set of sentences of L which must be assigned probability 1 by every probability function satisfying Sx, by examining separately the theories of heterogeneity and homogeneity. We find that the theory of Sx is equal to the theory of finite structures, i.e., those sentences true in all finite structures for L, and it emerges that Sx is inconsistent with the principle of Super-Regularity (Universal Certainty). As a further consequence we are able to characterize those probability functions which satisfy Sx and the Finite Values Property.

A Modified Supervaluationist Framework for Decision-Making

2021 ◽  
Vol 12 (2) ◽  
pp. 175-191
Author(s):  
Jonas Karge ◽  
Keyword(s):  
Decision Making ◽  
Probability Function ◽  
Imprecise Probabilities ◽  
Adequate Account ◽  
Alternative Account ◽  
Semantic Approach ◽  
Probability Functions ◽  
Degree Of Belief ◽  
The Way

How strongly an agent beliefs in a proposition can be represented by her degree of belief in that proposition. According to the orthodox Bayesian picture, an agent's degree of belief is best represented by a single probability function. On an alternative account, an agent’s beliefs are modeled based on a set of probability functions, called imprecise probabilities. Recently, however, imprecise probabilities have come under attack. Adam Elga claims that there is no adequate account of the way they can be manifested in decision-making. In response to Elga, more elaborate accounts of the imprecise framework have been developed. One of them is based on supervaluationism, originally, a semantic approach to vague predicates. Still, Seamus Bradley shows that some of those accounts that solve Elga’s problem, have a more severe defect: they undermine a central motivation for introducing imprecise probabilities in the first place. In this paper, I modify the supervaluationist approach in such a way that it accounts for both Elga’s and Bradley’s challenges to the imprecise framework.

scholarly journals GenMap: ultra-fast computation of genome mappability

2020 ◽  
Vol 36 (12) ◽  
pp. 3687-3692 ◽  
Author(s):  
Christopher Pockrandt ◽  
Mai Alzamel ◽  
Costas S Iliopoulos ◽  
Knut Reinert
Keyword(s):  
Source Code ◽  
Probe Design ◽  
Fast Method ◽  
Biological Applications ◽  
Fast Computation ◽  
Genomic Position ◽  
Guide Rna ◽  
Binary Output ◽  
A Genome ◽  
Reciprocal Value

Abstract Motivation Computing the uniqueness of k-mers for each position of a genome while allowing for up to e mismatches is computationally challenging. However, it is crucial for many biological applications such as the design of guide RNA for CRISPR experiments. More formally, the uniqueness or (k, e)-mappability can be described for every position as the reciprocal value of how often this k-mer occurs approximately in the genome, i.e. with up to e mismatches. Results We present a fast method GenMap to compute the (k, e)-mappability. We extend the mappability algorithm, such that it can also be computed across multiple genomes where a k-mer occurrence is only counted once per genome. This allows for the computation of marker sequences or finding candidates for probe design by identifying approximate k-mers that are unique to a genome or that are present in all genomes. GenMap supports different formats such as binary output, wig and bed files as well as csv files to export the location of all approximate k-mers for each genomic position. Availability and implementation GenMap can be installed via bioconda. Binaries and C++ source code are available on https://github.com/cpockrandt/genmap.

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