Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Phylogeny of genes for secretion NTPases: Identification of the widespread tadA subfamily and development of a diagnostic key for gene classification

Macromolecular transport systems in bacteria currently are classified by function and sequence comparisons into five basic types. In this classification system, type II and type IV secretion systems both possess members of a superfamily of genes for putative NTP hydrolase (NTPase) proteins that are strikingly similar in structure, function, and sequence. These include VirB11, TrbB, TraG, GspE, PilB, PilT, and ComG1. The predicted protein product of tadA, a recently discovered gene required for tenacious adherence of Actinobacillus actinomycetemcomitans, also has significant sequence similarity to members of this superfamily and to several unclassified and uncharacterized gene products of both Archaea and Bacteria. To understand the relationship of tadA and tadA-like genes to those encoding the putative NTPases of type II/IV secretion, we used a phylogenetic approach to obtain a genealogy of 148 NTPase genes and reconstruct a scenario of gene superfamily evolution. In this phylogeny, clear distinctions can be made between type II and type IV families and their constituent subfamilies. In addition, the subgroup containing tadA constitutes a novel and extremely widespread subfamily of the family encompassing all putative NTPases of type IV secretion systems. We report diagnostic amino acid residue positions for each major monophyletic family and subfamily in the phylogenetic tree, and we propose an easy method for precisely classifying and naming putative NTPase genes based on phylogeny. This molecular key-based method can be applied to other gene superfamilies and represents a valuable tool for genome analysis.

Structure and function of declarative and nondeclarative memory systems

This article reviews recent studies of memory systems in humans and nonhuman primates. Three major conclusions from recent work are that (i) the capacity for nondeclarative (nonconscious) learning can now be studied in a broad array of tasks that assess classification learning, perceptuomotor skill learning, artificial grammar learning, and prototype abstraction; (ii) cortical areas adjacent to the hippocampal formation, including entorhinal, perirhinal, and parahippocampal cortices, are an essential part of the medial temporal lobe memory system that supports declarative (conscious) memory; and (iii) in humans, bilateral damage limited to the hippocampal formation is nevertheless sufficient to produce severe anterograde amnesia and temporally graded retrograde amnesia covering as much as 25 years.