Operator Coproduct-Realization of Quantum Group Transformations in Two Dimensional Gravity, I.

A simple connection between the universal $R$ matrix of $U_q(sl(2))$ (for spins \demi and $J$) and the required form of the co-product action of the Hilbert space generators of the quantum group symmetry is put forward. This gives an explicit operator realization of the co-product action on the covariant operators. It allows us to derive the quantum group covariance of the fusion and braiding matrices, although it is of a new type: the generators depend upon worldsheet variables, and obey a new central extension of $U_q(sl(2))$ realized by (what we call) fixed point commutation relations. This is explained by showing that the link between the algebra of field transformations and that of the co-product generators is much weaker than previously thought. The central charges of our extended $U_q(sl(2))$ algebra, which includes the Liouville zero-mode momentum in a nontrivial way are related to Virasoro-descendants of unity. We also show how our approach can be used to derive the Hopf algebra structure of the extended quantum-group symmetry U_q(sl(2))\odot U_{\qhat}(sl(2)) related to the presence of both of the screening charges of 2D gravity.Comment: 33 pages, latex, no figure

The Quantum Group Structure of 2D Gravity and Minimal Models II: The Genus-Zero Chiral Bootstrap

The F and B matrices associated with Virasoro null vectors are derived in closed form by making use of the operator-approach suggested by the Liouville theory, where the quantum-group symmetry is explicit. It is found that the entries of the fusing and braiding matrices are not simply equal to quantum-group symbols, but involve additional coupling constants whose derivation is one aim of the present work. Our explicit formulae are new, to our knowledge, in spite of the numerous studies of this problem. The relationship between the quantum-group-invariant (of IRF type) and quantum-group-covariant (of vertex type) chiral operator-algebras is fully clarified, and connected with the transition to the shadow world for quantum-group symbols. The corresponding 3-j-symbol dressing is shown to reduce to the simpler transformation of Babelon and one of the author (J.-L. G.) in a suitable infinite limit defined by analytic continuation. The above two types of operators are found to coincide when applied to states with Liouville momenta going to $\infty$ in a suitable way. The introduction of quantum-group-covariant operators in the three dimensional picture gives a generalisation of the quantum-group version of discrete three-dimensional gravity that includes tetrahedra associated with 3-j symbols and universal R-matrix elements. Altogether the present work gives the concrete realization of Moore and Seiberg's scheme that describes the chiral operator-algebra of two-dimensional gravity and minimal models.Comment: 56 pages, 22 figures. Technical problem only, due to the use of an old version of uuencode that produces blank characters some times suppressed by the mailer. Same content

Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity

This review contains a summary of work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables -the Liouville exponentials and the Liouville field itself - and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev.Comment: 38 pages, LaTex file. Proceedings of the Vth International Conference on Mathematical Physics, Strings and Quantum gravity, Alushta, Ukraine 199

A Quasi-Hopf algebra interpretation of quantum 3-j and 6-j symbols and difference equations

We consider the universal solution of the Gervais-Neveu-Felder equation in the ${\cal U}_q(sl_2)$ case. We show that it has a quasi-Hopf algebra interpretation. We also recall its relation to quantum 3-j and 6-j symbols. Finally, we use this solution to build a q-deformation of the trigonometric Lam\'e equation.Comment: 9 pages, 4 figure

Training parents in the evaluation of the Individualized Education Plan (IEP) process.

Active parental involvement in the special education process has historically been emphasized. In addition, legal impetus (94-142, 766) has been provided for this active involvement. However, research has indicated that some educators tend to disregard, manipulate, and often intimidate parents during special education TEAM meetings, thus violating their due process rights. As a result, parental involvement in the Team process and development of the IEP document has continued to be lacking. The purpose of this study was to investigate parental attitudes toward the Team process and the IEP document and to implement a training program designed to assist parents in the development of the skills necessary to critically analyze their child\u27s IEP document\u27s effectiveness. The underlying theory behind the training program was, that given the appropriate training and information, parental skills to effectively participate in the Team meeting and development of the IEP document would increase. A group of 15 parents from the central Massachusetts area participated in this study. Their experiences within Special Education ranged from 3 months to 11 years. Severity of the handicapping conditions of their children ranged from speech/language services to full time special education. A pre/post test design was utilized to evaluate parental perception of the Team process and IEP evaluative skills. Based on the data gleaned from this research, the following has been concluded: (1) in spite of 17 years of mandated involvement in the Team process and development of the IEP document at the Team level, the parents; (a) view the child\u27s IEP as not being the product of the entire Team\u27s input, and (b) indicated that they did not participate in the development of the document. In regards to qualitative effectiveness of the IEP, it was determined that: (1) the student profile section; (a) did not contain all of the mandated information, and (b) was not concisely written. In addition, other information (teaching strategies, service delivery and plan duration) was not contained within. In spite of their passive roles, the parents generally expressed satisfaction with their child\u27s program and IEP document. The need for parent training and professional staff development was cited

Continuum limit of the Volterra model, separation of variables and non standard realizations of the Virasoro Poisson bracket

The classical Volterra model, equipped with the Faddeev-Takhtadjan Poisson bracket provides a lattice version of the Virasoro algebra. The Volterra model being integrable, we can express the dynamical variables in terms of the so called separated variables. Taking the continuum limit of these formulae, we obtain the Virasoro generators written as determinants of infinite matrices, the elements of which are constructed with a set of points lying on an infinite genus Riemann surface. The coordinates of these points are separated variables for an infinite set of Poisson commuting quantities including $L\_0$. The scaling limit of the eigenvector can also be calculated explicitly, so that the associated Schroedinger equation is in fact exactly solvable.Comment: Latex, 43 pages Synchronized with the to be published versio

Empirically Guided Case Conceptualization of Posttraumatic Stress Disorder with the Minnesota Multiphasic Personality Inventory-2 Restructured Form (MMPI-2-RF) in a Forensic Disability Evaluation

The following article discusses how the Restructured Form of the Minnesota Multiphasic Personality Inventory (MMPI -2-RF; Ben-Porath & Tellegen, 2008) can be used in case conceptualizations for Posttraumatic Stress Disorder (PTSD), particularly in compensation seeking settings. We review contemporary conceptualizations of PTSD, particularly emphasizing the role that affect and personality in regards to etiology of the disorder, as well as different manifestations of the disorder. We then review the case of an individual seeking compensation for trauma related disability performed by the third author. Particular emphasis is placed on examining how interpretation of the MMPI-2-RFprofile is guided by empirical findings

Trial 1 versus Trial 2 of the Test of Memory Malingering: Evaluating Accuracy Without a “Gold Standard”

This study examines the accuracy of the Test of Memory Malingering (TOMM), a frequently administered measure for evaluating effort during neurocognitive testing. In the last few years, several authors have suggested that the initial recognition trial of the TOMM (Trial 1) might be a more useful index for detecting feigned or exaggerated impairment than Trial 2, which is the source for inference recommended by the original instruction manual (Tombaugh, 1996). We used latent class modeling (LCM) implemented in a Bayesian framework to evaluate archival Trial 1 and Trial 2 data collected from 1198 adults who had undergone outpatient forensic evaluations. All subjects were tested with two other performance validity tests (the Word Memory Test and the Computerized Assessment of Response Bias), and for 70% of the subjects, data from the California Verbal Learning Test–Second Edition Forced Choice trial were also available. Our results suggest that not even a perfect score on Trial 1 or Trial 2 justifies saying that an evaluee is definitely responding genuinely, although such scores imply a lower-than-base-rate probability of feigning. If one uses a Trial 2 cut-off higher than the manual’s recommendation, Trial 2 does better than Trial 1 at identifying individuals who are almost certainly feigning while maintaining a negligible false positive rate. Using scores from both trials, one can identify a group of definitely feigning and very likely feigning subjects who comprise about two-thirds of all feigners; only 1 percent of the members of this group would not be feigning

On anomalies in classical dynamical systems

The definition of "classical anomaly" is introduced. It describes the situation in which a purely classical dynamical system which presents both a lagrangian and a hamiltonian formulation admits symmetries of the action for which the Noether conserved charges, endorsed with the Poisson bracket structure, close an algebra which is just the centrally extended version of the original symmetry algebra. The consistency conditions for this to occur are derived. Explicit examples are given based on simple two-dimensional models. Applications of the above scheme and lines of further investigations are suggested.Comment: arXiv version is already officia