Bibliography of computational models of rat spatial behavior

A bibliography of computational models of rat spatial behavior

Torsion and the second fundamental form for distributions

The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form itself is closely related to the shape map of the connection. The codimension one case generalises the traditional shape operator of Riemannian geometry

Alternative kinetic energy metrics for Lagrangian systems

We examine Lagrangian systems on R-n with standard kinetic energy terms for the possibility of additional, alternative Lagrangians with kinetic energy metrics different to the Euclidean one. Using the techniques of the inverse problem in the calculus of variations we find necessary and sufficient conditions for the existence of such Lagrangians. We illustrate the problem in two and three dimensions with quadratic and cubic potentials. As an aside we show that the well-known anomalous Lagrangians for the Coulomb problem can be removed by switching on a magnetic field, providing an appealing resolution of the ambiguous quantizations of the hydrogen atom

Introduction: The Third International Conference on Epigenetic Robotics

This paper summarizes the paper and poster contributions to the Third International Workshop on Epigenetic Robotics. The focus of this workshop is on the cross-disciplinary interaction of developmental psychology and robotics. Namely, the general goal in this area is to create robotic models of the psychological development of various behaviors. The term "epigenetic" is used in much the same sense as the term "developmental" and while we could call our topic "developmental robotics", developmental robotics can be seen as having a broader interdisciplinary emphasis. Our focus in this workshop is on the interaction of developmental psychology and robotics and we use the phrase "epigenetic robotics" to capture this focus

Humanoid Theory Grounding

In this paper we consider the importance of using a humanoid physical form for a certain proposed kind of robotics, that of theory grounding. Theory grounding involves grounding the theory skills and knowledge of an embodied artificially intelligent (AI) system by developing theory skills and knowledge from the bottom up. Theory grounding can potentially occur in a variety of domains, and the particular domain considered here is that of language. Language is taken to be another “problem space” in which a system can explore and discover solutions. We argue that because theory grounding necessitates robots experiencing domain information, certain behavioral-form aspects, such as abilities to socially smile, point, follow gaze, and generate manual gestures, are necessary for robots grounding a humanoid theory of language

A generalization of Szebehely's inverse problem of dynamics in dimension three

Extending a previous paper, we present a generalization in dimension 3 of the traditional Szebehely-type inverse problem. In that traditional setting, the data are curves determined as the intersection of two families of surfaces, and the problem is to find a potential V such that the Lagrangian L = T - V, where T is the standard Euclidean kinetic energy function, generates integral curves which include the given family of curves. Our more general way of posing the problem makes use of ideas of the inverse problem of the calculus of variations and essentially consists of allowing more general kinetic energy functions, with a metric which is still constant, but need not be the standard Euclidean one. In developing our generalization, we review and clarify different aspects of the existing literature on the problem and illustrate the relevance of the newly introduced additional freedom with many examples.Comment: 23 pages, to appear in Rep. Math. Phy

A generalization of Szebehely's inverse problem of dynamics

The so-called inverse problem of dynamics is about constructing a potential for a given family of curves. We observe that there is a more general way of posing the problem by making use of ideas of another inverse problem, namely the inverse problem of the calculus of variations. We critically review and clarify different aspects of the current state of the art of the problem (mainly restricted to the case of planar curves), and then develop our more general approach.Comment: 21 pages, to appear in Rep. Math. Phy

Shape maps for second order partial differential equations

We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a congruence volume whose collapse we study through an appropriate evolution equation, akin to Raychaudhuri's equation. We develop the necessary geometric framework on a suitable jet space in which the shape maps appear naturally associated with certain linear connections. Explicit computations are given, along with a nontrivial example

Time-dependent kinetic energy metrics for Lagrangians of electromagnetic type

We extend the results obtained in a previous paper about a class of Lagrangian systems which admit alternative kinetic energy metrics to second-order mechanical systems with explicit time-dependence. The main results are that a time-dependent alternative metric will have constant eigenvalues, and will give rise to a time-dependent coordinate transformation which partially decouples the system

The United States, The United Nations, and Micronesia: Questions of Procedure, Substance, and Faith

This study first considers the procedural requirements for proper termination and concludes that Security Council approval is required. Second, this writing identifies the major issues that should be considered if the proposed termination of the Trusteeship Agreement for Micronesia is subjected to Security Council review. Two basic concerns should be the propriety of the division of the Trust Territory into four separate entities and the legitimacy of the agreements between the new governments and the United States for continuing relations as either commonwealth or freely associated states. The history of and practice under the trusteeship system indicate that the particular arrangements for commonwealth and free association statuses do not fit neatly into recognized categories of self-governance. Nonetheless, as a general matter, the arrangements are within the broader realm of acceptable relations because they reflect the free choices of the Micronesian peoples