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Related Concept Videos

Probability Laws01:49

Probability Laws

Overview
Arithmetic Sequences01:30

Arithmetic Sequences

An arithmetic sequence is a structured arrangement of numbers where each term is derived by adding a constant value, known as the common difference, to the previous term. This consistent pattern allows for the efficient computation of any term within the sequence as well as the cumulative sum of multiple terms. The formula for finding the nth term of an arithmetic sequence is:Here, aₙ represents the nth term of the sequence, a is the first term, d is the common difference, and n is the term...
Probability in Statistics01:14

Probability in Statistics

Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
Random Variables01:09

Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Combining Functions01:16

Combining Functions

Functions can be combined to form new mathematical models that describe interactions between variables. These combinations are fundamental in understanding relationships between changing quantities and are commonly encountered in scientific and engineering contexts. The combination methods—addition, subtraction, multiplication, division, and composition—each have unique implications for the resulting function’s domain and behavior.When combining functions through arithmetic operations, such...

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Related Experiment Videos

Probabilistic arithmetic automata and their applications.

Tobias Marschall1, Inke Herms, Hans-Michael Kaltenbach

  • 1Life Sciences Group, Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG Amsterdam, TheNetherlands. T.Marschall@cwi.nl

IEEE/ACM Transactions on Computational Biology and Bioinformatics
|August 8, 2012
PubMed
Summary
This summary is machine-generated.

Probabilistic arithmetic automata (PAAs) offer a unified framework for analyzing probabilistic computations. This review details PAAs and algorithms for computing probabilistic results across various applications, including bioinformatics.

Related Experiment Videos

Area of Science:

  • Computational Biology
  • Theoretical Computer Science
  • Algorithm Analysis

Background:

  • Probabilistic calculations are common in computational biology and other fields.
  • Existing methods for analyzing these calculations can be fragmented.
  • A unifying framework is needed to simplify the analysis of probabilistic operations.

Purpose of the Study:

  • To present probabilistic arithmetic automata (PAAs) as a general model for probabilistic computations.
  • To introduce algorithms for numerically computing the distribution of results from probabilistic calculations.
  • To demonstrate the broad applicability of PAAs through diverse examples.

Main Methods:

  • Developed probabilistic arithmetic automata (PAAs) as a unifying framework.
  • Designed two algorithms for numerical computation of probabilistic result distributions.
  • Introduced deterministic arithmetic automata (DAAs) as a method to simplify PAA construction.
  • Applied the PAA framework to five distinct computational problems.

Main Results:

  • PAAs provide a flexible and unifying approach to analyzing probabilistic calculations.
  • The proposed algorithms efficiently compute distributions of results for complex probabilistic operations.
  • Demonstrated PAA utility in pattern matching statistics, sequence alignment, peptide analysis, and sequencing read length statistics.
  • A simplified PAA construction method using DAAs was successfully applied across all examples.

Conclusions:

  • Probabilistic arithmetic automata (PAAs) offer a powerful and versatile framework for computational problems involving chance.
  • The presented algorithms and construction methods facilitate the analysis of complex probabilistic systems.
  • The MoSDi package provides implementations, enabling rapid development of new applications based on the PAA framework.