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.

Origins and antiquity of X-linked triallelic color vision systems in New World monkeys

It is known that the squirrel monkey, marmoset, and other related New World (NW) monkeys possess three high-frequency alleles at the single X-linked photopigment locus, and that the spectral sensitivity peaks of these alleles are within those delimited by the human red and green pigment genes. The three alleles in the squirrel monkey and marmoset have been sequenced previously. In this study, the three alleles were found and sequenced in the saki monkey, capuchin, and tamarin. Although the capuchin and tamarin belong to the same family as the squirrel monkey and marmoset, the saki monkey belongs to a different family and is one of the species that is most divergent from the squirrel monkey and marmoset, suggesting the presence of the triallelic system in many NW monkeys. The nucleotide sequences of these alleles from the five species studied indicate that gene conversion occurs frequently and has partially or completely homogenized intronic and exonic regions of the alleles in each species, making it appear that a triallelic system arose independently in each of the five species studied. Nevertheless, a detailed analysis suggests that the triallelic system arose only once in the NW monkey lineage, from a middle wavelength (green) opsin gene, and that the amino acid differences at functionally critical sites among alleles have been maintained by natural selection in NW monkeys for >20 million years. Moreover, the two X-linked opsin genes of howler monkeys (a NW monkey genus) were evidently derived from the incorporation of a middle (green) and a long wavelength (red) allele into one chromosome; these two genes together with the (autosomal) blue opsin gene would immediately enable even a male monkey to have trichromatic vision.

Pitch perception: A dynamical-systems perspective

Two and a half millennia ago Pythagoras initiated the scientific study of the pitch of sounds; yet our understanding of the mechanisms of pitch perception remains incomplete. Physical models of pitch perception try to explain from elementary principles why certain physical characteristics of the stimulus lead to particular pitch sensations. There are two broad categories of pitch-perception models: place or spectral models consider that pitch is mainly related to the Fourier spectrum of the stimulus, whereas for periodicity or temporal models its characteristics in the time domain are more important. Current models from either class are usually computationally intensive, implementing a series of steps more or less supported by auditory physiology. However, the brain has to analyze and react in real time to an enormous amount of information from the ear and other senses. How is all this information efficiently represented and processed in the nervous system? A proposal of nonlinear and complex systems research is that dynamical attractors may form the basis of neural information processing. Because the auditory system is a complex and highly nonlinear dynamical system, it is natural to suppose that dynamical attractors may carry perceptual and functional meaning. Here we show that this idea, scarcely developed in current pitch models, can be successfully applied to pitch perception.

T-cell alpha beta + and gamma delta + deficient mice display abnormal but distinct phenotypes toward a natural, widespread infection of the intestinal epithelium.

Vertebrate immune systems contain T cells bearing either alpha beta or gamma delta T-cell antigen receptors (TCRs). alpha beta T cells perform all well-characterized T-cell effector functions, while the biological functions of gamma delta + cells remain unclear. Of particular interest is the role of gamma delta + cells during epithelial infections, since gamma delta + cells are commonly abundant within epithelia. Eimeria spp. are intracellular protozoa that infect epithelia of most vertebrates, causing coccidiosis. This study shows that in response to Eimeria vermiformis, mice lacking alpha beta T cells display defects in protective immunity, while mice lacking gamma delta + cells display exaggerated intestinal damage, apparently due to a failure to regulate the consequences of the alpha beta T cell response. An immuno-downregulatory role during infection, and during autoimmune disease, may be a general one for gamma delta + cells.

The role of DT-diaphorase in the maintenance of the reduced antioxidant form of coenzyme Q in membrane systems.

The experiments reported here were designed to test the hypothesis that the two-electron quinone reductase DT-diaphorase [NAD(P)H:(quinone-acceptor) oxidoreductase, EC 1.6.99.2] functions to maintain membrane-bound coenzyme Q (CoQ) in its reduced antioxidant state, thereby providing protection from free radical damage. DT-diaphorase was isolated and purified from rat liver cytosol, and its ability to reduce several CoQ homologs incorporated into large unilamellar vesicles was demonstrated. Addition of NADH and DT-diaphorase to either large unilamellar or multilamellar vesicles containing homologs of CoQ, including CoQ9 and CoQ10, resulted in the essentially complete reduction of the CoQ. The ability of DT-diaphorase to maintain the reduced state of CoQ and protect membrane components from free radical damage as lipid peroxidation was tested by incorporating either reduced CoQ9 or CoQ10 and the lipophylic azoinitiator 2,2'-azobis(2,4-dimethylvaleronitrile) into multilamellar vesicles in the presence of NADH and DT-diaphorase. The presence of DT-diaphorase prevented the oxidation of reduced CoQ and inhibited lipid peroxidation. The interaction between DT-diaphorase and CoQ was also demonstrated in an isolated rat liver hepatocyte system. Incubation with adriamycin resulted in mitochondrial membrane damage as measured by membrane potential and the release of hydrogen peroxide. Incorporation of CoQ10 provided protection from adriamycin-induced mitochondrial membrane damage. The incorporation of dicoumarol, a potent inhibitor of DT-diaphorase, interfered with the protection provided by CoQ. The results of these experiments provide support for the hypothesis that DT-diaphorase functions as an antioxidant in both artificial membrane and natural membrane systems by acting as a two-electron CoQ reductase that forms and maintains the antioxidant form of CoQ. The suggestion is offered that DT-diaphorase was selected during evolution to perform this role and that its conversion of xenobiotics and other synthetic molecules is secondary and coincidental.

Models of natural language understanding.

This paper surveys some of the fundamental problems in natural language (NL) understanding (syntax, semantics, pragmatics, and discourse) and the current approaches to solving them. Some recent developments in NL processing include increased emphasis on corpus-based rather than example- or intuition-based work, attempts to measure the coverage and effectiveness of NL systems, dealing with discourse and dialogue phenomena, and attempts to use both analytic and stochastic knowledge. Critical areas for the future include grammars that are appropriate to processing large amounts of real language; automatic (or at least semi-automatic) methods for deriving models of syntax, semantics, and pragmatics; self-adapting systems; and integration with speech processing. Of particular importance are techniques that can be tuned to such requirements as full versus partial understanding and spoken language versus text. Portability (the ease with which one can configure an NL system for a particular application) is one of the largest barriers to application of this technology.

Integration of speech with natural language understanding.

The integration of speech recognition with natural language understanding raises issues of how to adapt natural language processing to the characteristics of spoken language; how to cope with errorful recognition output, including the use of natural language information to reduce recognition errors; and how to use information from the speech signal, beyond just the sequence of words, as an aid to understanding. This paper reviews current research addressing these questions in the Spoken Language Program sponsored by the Advanced Research Projects Agency (ARPA). I begin by reviewing some of the ways that spontaneous spoken language differs from standard written language and discuss methods of coping with the difficulties of spontaneous speech. I then look at how systems cope with errors in speech recognition and at attempts to use natural language information to reduce recognition errors. Finally, I discuss how prosodic information in the speech signal might be used to improve understanding.

New trends in natural language processing: statistical natural language processing.

The field of natural language processing (NLP) has seen a dramatic shift in both research direction and methodology in the past several years. In the past, most work in computational linguistics tended to focus on purely symbolic methods. Recently, more and more work is shifting toward hybrid methods that combine new empirical corpus-based methods, including the use of probabilistic and information-theoretic techniques, with traditional symbolic methods. This work is made possible by the recent availability of linguistic databases that add rich linguistic annotation to corpora of natural language text. Already, these methods have led to a dramatic improvement in the performance of a variety of NLP systems with similar improvement likely in the coming years. This paper focuses on these trends, surveying in particular three areas of recent progress: part-of-speech tagging, stochastic parsing, and lexical semantics.