scholarly journals Generalized Householder Transformations

2021 ◽  
Author(s):  
Karl Svozil
Keyword(s):  
Spectral Decomposition ◽  
Householder Transformation ◽  
Functional Relations ◽  
Negative Eigenvalues ◽  
State Dependent ◽  
Generalized Operator ◽  
Householder Transformations

The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. Dichotomy is modulated by allowing more than one negative eigenvalues, or by abandoning it altogether, yielding generalized operator valued arguments for contextuality. We also discuss a form of state-dependent contextuality by variation of the functional relations of the operators; in particular, by additivity.

Case Formulation and Design of Behavioral Treatment Programs

2003 ◽  
Vol 19 (3) ◽  
pp. 164-174 ◽  
Author(s):  
Stephen N. Haynes ◽  
Andrew E. Williams
Keyword(s):  
Functional Analysis ◽  
Behavior Problems ◽  
Behavioral Treatment ◽  
Clinical Case ◽  
Relative Magnitude ◽  
Mechanisms Of Action ◽  
Treatment Programs ◽  
Case Formulation ◽  
Functional Relations ◽  
Causal Variables

Summary: We review the rationale for behavioral clinical case formulations and emphasize the role of the functional analysis in the design of individualized treatments. Standardized treatments may not be optimally effective for clients who have multiple behavior problems. These problems can affect each other in complex ways and each behavior problem can be influenced by multiple, interacting causal variables. The mechanisms of action of standardized treatments may not always address the most important causal variables for a client's behavior problems. The functional analysis integrates judgments about the client's behavior problems, important causal variables, and functional relations among variables. The functional analysis aids treatment decisions by helping the clinician estimate the relative magnitude of effect of each causal variable on the client's behavior problems, so that the most effective treatments can be selected. The parameters of, and issues associated with, a functional analysis and Functional Analytic Clinical Case Models (FACCM) are illustrated with a clinical case. The task of selecting the best treatment for a client is complicated because treatments differ in their level of specificity and have unequally weighted mechanisms of action. Further, a treatment's mechanism of action is often unknown.

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