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The General Linear Model

2015
This article provides an introduction into the statistical analysis of neuroimaging data using the general linear model. The analysis allows a flexible use of various models offering a wide range of statistical tests for the analysis of typical neuroimaging experiments. A short introduction to the general linear model is provided using simple examples.
Kiebel, S.   +1 more
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Linear Orders on General Algebras

Order, 2005
A characterization of partially ordered algebraic structures \((A,F,r)\) having a compatible linear extension of \(r\) is given. As a consequence, it is proved that a partial order \(r\) can be linearly extended if and only if it can be extended on every finitely generated subalgebra. A few further results are obtained.
Radeleczki, Sándor, Szigeti, Jenő
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Linearity and plan generation

New Generation Computing, 1987
The paper deals with the intuitive linearity concept and its weak points. This concept is commonly used at plan generation using theorem proving in which deduction of a goal statement is proved from the initial situation and rules describing the actions.
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General Linear Models

2007
This chapter presents the general linear model as an extension to the two-sample t-test, analysis of variance (ANOVA), and linear regression. We illustrate the general linear model using two-way ANOVA as a prime example. The underlying principle of ANOVA, which is based on the decomposition of the value of an observed variable into grand mean, group ...
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LINEAR LAYOUT OF GENERALIZED HYPERCUBES

International Journal of Foundations of Computer Science, 1994
This paper deals with two kinds of generalized hypercubes: a d-dimensional c-ary clique [Formula: see text] and a d-dimensional c-ary array [Formula: see text]. A d-dimensional c-ary clique [Formula: see text] has nodes labeled by cdintegers from 0 to cd- 1 and two nodes are connected by an edge if and only if the c-ary representations of their labels ...
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Generating Linear Extensions Fast

SIAM Journal on Computing, 1994
Summary: One of the most important sets associated with a poset \(\mathcal P\) is its set of linear extensions, \(E({\mathcal P})\). This paper presents an algorithm to generate all of the linear extensions of a poset in constant amortized time, that is, in time \(O(e({\mathcal P}))\), where \(e({\mathcal P})= | E({\mathcal P})|\).
Gara Pruesse, Frank Ruskey
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On the Linear Complexity of the Power Generator

Designs, Codes and Cryptography, 2001
Let \(\vartheta, m\) and \(e\) be integers such that \(\text{gcd}(\vartheta,m) = 1\). Then one can define the sequence \((u_n)\) by \[ u_n \equiv u_{n-1}^e (\bmod m), \quad 0 \leq u_n \leq m-1, n = 1,2,\dots,\tag{pg} \] with the initial value \(u_0 = \vartheta\). This sequence is known as the power generator, and in the two special cases \(\text{gcd}(e,
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Generalized linear models

American Journal of Orthodontics and Dentofacial Orthopedics, 2023
Tomasz Burzykowski   +3 more
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Linear Equality Constraints in the General Linear Mixed Model

Biometrics, 2001
Scientists may wish to analyze correlated outcome data with constraints among the responses. For example, piecewise linear regression in a longitudinal data analysis can require use of a general linear mixed model combined with linear parameter constraints.
Edwards, Lloyd J.   +3 more
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Linear models for keystream generators

IEEE Transactions on Computers, 1996
Consider a keystream generator (KSG) with \(M\) bits of memory. For dimensional reasons, there exists at least one linear function \(L\) of any \(M+1\) consecutive output bits that is not balanced. Under reasonable hypotheses, \(L\) is independent of time, so \(L\) (essentially an \(| M+1| \times 1\) matrix) is a function of the initial state vector ...
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