Explicit differential characterization of the Newtonian free particle system in m > 1 dependent variables

In 1883, as an early result, Sophus Lie established an explicit necessary and sufficient condition for an analytic second order ordinary differential equation y_xx = F(x,y,y_x) to be equivalent, through a point transformation (x,y) --> (X(x,y), Y(x,y)), to the Newtonian free particle equation Y_XX = 0. This result, preliminary to the deep group-theoretic classification of second order analytic ordinary differential equations, was parachieved later in 1896 by Arthur Tresse, a French student of S. Lie. In the present paper, following closely the original strategy of proof of S. Lie, which we firstly expose and restitute in length, we generalize this explicit characterization to the case of several second order ordinary differential equations. Let K=R or C, or more generally any field of characteristic zero equipped with a valuation, so that K-analytic functions make sense. Let x in K, let m > 1, let y := (y^1, ..., y^m) in K^m and let y_xx^j = F^j(x,y,y_x^l), j = 1,...,m be a collection of m analytic second order ordinary differential equations, in general nonlinear. We provide an explicit necessary and sufficient condition in order that this system is equivalent, under a point transformation (x, y^1, ..., y^m) --> (X(x,y), Y^1(x,y),..., Y^m(x, y)), to the Newtonian free particle system Y_XX^1 = ... = Y_XX^m = 0. Strikingly, the (complicated) differential system that we obtain is of first order in the case m > 1, whereas it is of second order in S. Lie's original case m = 1.Comment: 76 pages, no figur

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

EEG Biofeedback as a Treatment for Substance Use Disorders: Review, Rating of Efficacy, and Recommendations for Further Research

Electroencephalographic (EEG) biofeedback has been employed in substance use disorder (SUD) over the last three decades. The SUD is a complex series of disorders with frequent comorbidities and EEG abnormalities of several types. EEG biofeedback has been employed in conjunction with other therapies and may be useful in enhancing certain outcomes of therapy. Based on published clinical studies and employing efficacy criteria adapted by the Association for Applied Psychophysiology and Biofeedback and the International Society for Neurofeedback and Research, alpha theta training—either alone for alcoholism or in combination with beta training for stimulant and mixed substance abuse and combined with residential treatment programs, is probably efficacious. Considerations of further research design taking these factors into account are discussed and descriptions of contemporary research are given

The Strengths and Difficulties Questionnaire in the Nordic countries

Background: The Strengths and Difficulties Questionnaire (SDQ) has been translated into the different Nordic languages between 1996 and 2003. During the past few years, SDQs have been completed for nearly 100,000 children and adolescents in population-based studies as well as in clinical samples. The largest studies have been performed in Norway and Denmark, and in these countries the diagnostic interview DAWBA has also been used in conjunction with the SDQ. Aims: In addition to a brief overview of past and ongoing SDQ work in Sweden, Finland, Norway, Denmark, and Iceland, we present scale means and standard deviations from selected community studies with comparable age groups, including parental reports for 7, 9 and 11 year-old children and self-reports of 13 and 15 year-olds. Conclusions: The descriptive statistics suggest that the distributions of SDQ scores are very similar across the Nordic countries. Further collaborative efforts in establishing norms and evaluating the validity of the SDQ as a screening instrument are encouraged

The strengths and difficulties questionnaire in the Nordic countries

To access publisher full text version of this article. Please click on the hyperlink in Additional Links fieldBACKGROUND: The Strengths and Difficulties Questionnaire (SDQ) has been translated into the different Nordic languages between 1996 and 2003. During the past few years, SDQs have been completed for nearly 100,000 children and adolescents in population-based studies as well as in clinical samples. The largest studies have been performed in Norway and Denmark, and in these countries the diagnostic interview DAWBA has also been used in conjunction with the SDQ. AIMS: In addition to a brief overview of past and ongoing SDQ work in Sweden, Finland, Norway, Denmark, and Iceland, we present scale means and standard deviations from selected community studies with comparable age groups, including parental reports for 7, 9 and 11 year-old children and self-reports of 13 and 15 year-olds. CONCLUSIONS: The descriptive statistics suggest that the distributions of SDQ scores are very similar across the Nordic countries. Further collaborative efforts in establishing norms and evaluating the validity of the SDQ as a screening instrument are encouraged

You and I, Robot

I address a number of issues related to building an autonomous social robot. I review different approaches to social cognition and ask how these different approaches may inform the design of social robots. I argue that regardless of which theoretical approach to social cognition one favors, instantiating that approach in a workable robot will involve designing that robot on enactive principles.Peer reviewe