For each standard affine data satisfying some condition on the coroots, we define a group functor on the category of all rings which is a subgroup of some group functor R 7→ G(R[t, t−1])o T (R), where G is a Chevalley scheme and T is a torus. This functor is then shown to satisfy the conditions of the five axioms required by [Ti4] to be a ‘minimal’ Kac-Moody group.

We employed a pyramidal training model (PTM) to teach staff to correctly implement and collect data for trial-based functional analysis (TBFA) in simulated situations. First, we trained four behavioral consultants (BCs) in a group format, who each trained one behavior technician (BT) in an individual format. We utilized a non-concurrent multiple baseline design to evaluate the effect of the tra...

Aim Food Allergy may have an impact on socioeconomic (SE) aspects of life. The Europrevall study (EU FP6, 2005-2009) developed and validated a SE questionnaire to measure the direct, indirect and intangible costs of food allergy. This measure takes up to 1 hour to complete as participants are required to respond to 70 to 170 questions, depending on response choice. We aimed to develop a brief, ...

This paper compares and contrasts financial strength ratings assigned by Value Line, Standard and Poor's, and Moody's. All of these rating agencies use modified ratings. When modifiers are considered, these agencies agree between 85 97 percent of the time. A model using stock market information as well as liquidity, leverage, activity and profitability ratios is presented. Cronbach's alpha, a m...

We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, whi...

Interpretation: Past, Present and Future

Research suggests that inexperienced individuals cannot accurately implement stimulus preference assessments given written instructions alone. Training that includes written instructions supplemented with feedback from a professional with expertise in conducting preference assessments has proven effective; unfortunately, expert-facilitated direct training may not be widely available. In the cur...

Let X be the Dynkin diagram of a symmetrizable Kac-Moody algebra, and X0 a subgraph with all vertices of degree 1 or 2. Using the crystal structure on the components of quiver varieties for X , we show that if we expand X by extending X0, the branching multiplicities and tensor product multiplicities stabilize, provided the weights involved satisfy a condition which we call “depth” and are supp...

Moody’s KMV method is a popular commercial implementation of the structural credit risk model pioneered by Merton (1974). It is an algorithm for estimating the unobserved asset value and the unknown parameters required for implementing such a model. This estimation method has found its way to the recent academic literature, but it has not yet been formally analyzed to assess its statistical pro...

Compactification can control chaotic Mixmaster behavior in gravitational systems with p–form matter: we consider this in light of the connection between supergravity models and Kac–Moody algebras. We show that different compactifications define “mutations” of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems ...