Canonical Orientation Research Articles

On the Rational Homotopy Type of Configuration Spaces

In this article we prove that the rational homotopy type of the configuration space of n distinct points on a smooth projective variety X over C is determined by the rational cohomology ring of X together with its canonical orientation class. This strengthens a previous result of Fulton and MacPherson [FM] (see previous issue in this volume). A few words are due on the history of differential graded algebras. By a DGA we shall mean a graded-commutative differential graded algebra. Fulton and MacPherson [FM] gave a model F(n) for the space F(X, n) by resolving the singularities of the inclusion F(X, n) C Xn and using a result of Morgan [M] on the rational homotopy type of smooth quasiprojective varieties over C. Surprisingly the DGA F(n) depended not only on H*X and its orientation class, but also on the Chern classes of X. Fulton suggested that one should be able to find another explicit model of F(X, n) independent of Chern classes. The DGA used here, E(n), was found independently by the author and by Totaro [T]. Totaro's idea was to study the Leray spectral sequence of the inclusion F(X, n) C Xn. By a weight-filtration argument he showed that the only nontrivial differential in this spectral sequence is d2m. The E2 term with the differential d2m is isomorphic to E(n). Thus, by a result of Deligne [D2], H*E(n) ' H*F(X, n) as rings. Finally the relations (1)-(3) of Theorem 1.2 are much older than any of the results mentioned above. They were discovered by F. Cohen [C] (see also [CLMa]) in the study of configuration spaces of IR'. What happens could be described by saying that H*F(X, n) for a smooth projective variety X is related to H*F(lR2m, n) in the simplest possible way.

Does orientation-independent object recognition precede orientation-dependent recognition? Evidence from a cuing paradigm.

Object recognition may entail an incremental normalization process before access to canonical orientation representations, but is this process guided by prior access to object-centered representations? In Experiment 1, the authors showed observers figure-ground stimuli known to reflect access to, and output from, stored shape representations. The stimuli appeared in each of 6 different orientations, preceded by cues providing either (a) no information, (b) upright shape information only, (c) upright shape information plus orientation information (separately), or (d) shape information in the same orientation as the upcoming figure-ground test stimulus. Contrary to predictions by a postaccess account, the cues failed to eliminate orientation dependency in shape recognition. The results favor a preaccess account of the normalization process within the context of canonical orientation representations.

Canonical Orderings of Hexagons That: (1) Nearly Meet the Intent of Patterson's Nomenclature Rules and (2) Orient a Molecule for Purposes of Assigning a IUPAC Name

Abstract A nomenclature technique developed earlier by the author is expanded to produce an ordering of hexagons that nearly meets the original intent of Patterson's nomenclature rules in organic chemistry for a system of polycyclic aromatic hydrocarbons formed using only benzene modules. The result desired is a simple systematic method which orients a figure formed by the fusion of regular hexagonal rings so that, first, there is a maximum number of rings on a horizontal line and, second, that as many of the remaining rings as possible are above and to the right of this horizontal reference line. In the process of trying to formulate such a system, problems that are inherent in interpreting the intent of Patterson's rules and in pragmatically implementing these rules are examined. Furthermore, a minor modification of the technique produces a canonical orientation of a long molecule which can then be used to formulate the I.U.P.A.C. name for this molecule.

Mental rotation and orientation-dependence in shape recognition

How do we recognize objects despite differences in their retinal projections when they are seen at different orientations? Marr and Nishihara (1978) proposed that shapes are represented in memory as structural descriptions in object-centered coordinate systems, so that an object is represented identically regardless of its orientation. An alternative hypothesis is that an object is represented in memory in a single representation corresponding to a canonical orientation, and a mental rotation operation transforms an input shape into that orientation before input and memory are compared. A third possibility is that shapes are stored in a set of representations, each corresponding to a different orientation. In four experiments, subjects studied several objects each at a single orientation, and were given extensive practice at naming them quickly, or at classifying them as normal or mirror-reversed, at several orientations. At first, response times increased with departure from the study orientation, with a slope similar to those obtained in classic mental rotation experiments. This suggests that subjects made both judgments by mentally transforming the orientation of the input shape to the one they had initially studied. With practice, subjects recognized the objects almost equally quickly at all the familiar orientations. At that point they were probed with the same objects appearing at novel orientations. Response times for these probes increased with increasing disparity from the previously trained orientations. This indicates that subjects had stored representations of the shapes at each of the practice orientations and recognized shapes at the new orientations by rotating them to one of the stored orientations. The results are consistent with a hybrid of the second (mental transformation) and third (multiple view) hypotheses of shape recognition: input shapes are transformed to a stored view, either the one at the nearest orientation or one at a canonical orientation. Interestingly, when mirrorimages of trained shapes were presented for naming, subjects took the same time at all orientations. This suggests that mental transformations of orientation can take the shortest path of rotation that will align an input shape and its memorized counterpart, in this case a rotation in depth about an axis in the picture plane.

A unified theory of the meaning of some spatial relational terms

This paper presents a unified account of the meaning of the spatial relational terms right, left, in front of, behind, above and below. It claims that each term has three types of meanings, basic, deictic and intrinsic, and that the definitions of each type of meaning are identical in form for all six terms. Restrictions on the use of the terms, which are different for above and below than for the rest, are explained by a general constraint on all uses of spatial relational terms, the framework vertical constraint. This constraint depends on the existence of a fourth type of meaning for above and below, one defined by the framework in which the related objects are located. It is argued that a theory centred on the framework vertical constraint is preferable to one centred on the principle of canonical orientation (Levelt, 1984).

Face recognition: A general or specific right hemisphere capacity?

Face-recognition ability has been claimed to be qualitatively different from other pattern-recognition abilities. One argument for this claim is the finding of a significant right hemisphere advantage for the recognition of upright but not inverted faces. However, this argument is justified only if this orientation-sensitive pattern is unique to faces. In the present study, comparable patterns of orientation-sensitive involvement of the right hemisphere are found for the recognition of faces and houses. This finding is interpreted as evidence for a right hemisphere schema formation capacity that is applied not only to upright faces but also to other familiar classes of stimuli in their canonical upright orientation. It is suggested that any greater right hemisphere involvement in the recognition of upright faces is due to our greater expertise at recognizing faces than other stimulus types. We also find evidence that only a subset of right-handed adults show orientation-sensitive right hemisphere involvement in the recognition of faces and houses: in particular, those dextrals with a characteristic hemispheric arousal asymmetry in favor of the right hemisphere. In contrast, dextrals with a characteristic arousal asymmetry in favor of the left hemisphere do not show significant visual field asymmetries for faces or houses in either upright or inverted orientations.

Distinguishing clockwise from counterclockwise: Does it require mental rotation?

In three experiments, subjects were timed as they judged whether stimuli, presented in different angular orientations, represented clockwise or counterclockwise directions. In each experiment, there was also a control condition in which the subjects were required to make mirror image judgments relative to some canonical orientation. Analysis of reaction times suggested that, in the control tasks, the subjects generally rotated the stimuli mentally to the canonical orientation before making their decision. Mental rotation was invoked less frequently in the case of the experimental tasks, suggesting at least limited access to an orientation-free code representing the difference between clockwise and counterclockwise. This was most evident in Experiment 1, where the stimuli represented 1-h jumps of a hand on a clock face. It was less so in Experiment 2, where direction of motion was indicated in a static display. In Experiment 3, only a few subjects proved able to use an orientation-free, clockwise versus counterclockwise rubric in order to discriminate normal from backward letters.

Cloning of Alu-containing cDNAs from human fibroblasts and identification of small Alu + poly(A) + RNAs in a variety of human normal and tumor cells

Two clones have been selected from a human fibroblast cDNA bank. By DNA sequencing the clones were shown to contain Alu elements located near the ends of the cDNA inserts. DNA of the clones was used for Northern blot hybridization analysis of a number of poly(A)-containing RNAs from normal human tissues (brain, stomach, uterus, spleen, fibroblasts) and tumors (neurinoma, glioma, neuroblastoma, liposarcoma, adrenal cortex adenocarcinoma). All RNA samples reveal a heterodisperse distribution of Alu transcripts with discrete bands in the region of 7-12 S RNA. The majority of these small poly(A) + Alu + RNAs contain Alu sequences only in one (canonical) orientation with functional signals including the split promoter for RNA polymerase III.

Conflict between canonicality and array‐specificity in young children's drawings

Previous research on young children's drawings has typically studied children's representation of individual objects quite separately from their representation of the spatial relationships between objects in a scene. This paper reports two experiments which explored the relationship between these two aspects of graphic representation. In particular it looks at the problem posed to children in depicting an array of familiar objects with canonical (or stereotyped) orientations which conflict with the way children typically represent within‐array spatial relationships. Four‐seven‐year‐old children were presented with two‐object arrays with one object placed behind the other and in which the orientation of each object was also varied. There were three main findings. First, children's concern to draw a familiar object in its canonical orientation tended to override their concern for depicting between‐object spatial relationships. Second, different array presentations resulted in significant differences in the number of children who drew their own view of the array. Lastly, both these findings were subject to a paradoxical U‐shaped developmental age trend.

On the Moduli Space of Anti-Self-Dual Yang–Mills Connections on Kähler Surfaces

The purpose of this paper is to give a complete proof of the result announced in [7]. In fact in this paper we discuss the dimension of moduli space consisting of anti-self-dual solutions of Yang-Mills equation in the case where the base space is Kahler and we obtain the dimension formula which is similar to the case of moduli space of self-dual solutions over a self-dual base space, given by Atiyah, Hitchin and Singer [2]. Further we get on a compact Kahler surface a suggestive observation that the moduli space of anti-self-dual Yang-Mills connections may have a close relation to moduli space of holomorphic vector bundles. Yang-Mills connections, namely, solutions to Yang-Mills equation have originated from field theory in physics ([12]). Yang-Mills equation is considered as a generalization of Maxwell equation from a viewpoint of non-abelian gauge group. Mathematically, Yang-Mills connections are formulated by the aid of notions of connections on a principal fibre bundle. Let P be a principal bundle over a compact oriented Riemannian 4-manifold M with a compact semi-simple Lie group G. Let E be an associated complex vector bundle. A functional ^M is defined over the space CE,G consisting of all G-connections on E by ^5^(7)=(1/2) H^!! for the curvature form R^ of 7. The Euler-Lagrangian equation of the functional is written by d(^)—0. A G-connection which gives a solution to this equation is called a Yang-Mills Gconnection. From Bianchi's identity an (anti-)self-dual G-connection which satisfies that *R^=±R^ is a special Yang-Mills G-connection. If we denote by J>E,G the set of all (anti-)self-dual G-connections, then the space M%tGt which is a quotient space of J.E, G, modulo the group of gauge transformations SP represents moduli space of essentially distinct (anti-)self-dual G-connections. Now suppose that M is a Kahler surface. Then M admits the canonical orientation induced from the complex structure of M. With respect to the space of infinitesimal deformations of anti-self-dual G-connections, that is, the tangent

EPR study of oriented photoexcited triplets of zinc porphyrin in a discotic liquid crystal: Evidence for axial symmetry in the condensed phase

An EPR study of the photoexcited triplet of ZnTPP in the dicostic mesophase of p-n-hexa-hexyloxytriphenylene is reported. The results indicate that (i) the observed spectra are temperature independent (between ∼100–140 K) and typical of axially symmetric guest molecules, with zero field splitting values ‖D‖=0.0308 cm−1, and ‖E‖=0, (ii) the line intensity of the out-of-plane canonical orientation of the guest molecules exhibits anisotropic patterns with respect to the sample orientation in the external field. These results are best interpreted by the columnar structure of the host mesogen which forms rodlike structures whose directors are distributed about a plane perpendicular to the applied external magnetic field with a normal distribution and standard deviation of ∼3–8°. The ZnTPP guest molecules are located outside the columns and orient such that the porphyrin planes are parallel to the columns axes. It is also concluded that, in the temperature range studied, the porphyrin molecules are distributed in this liquid crystal as noninteracting monomers retaining their axial symmetry.

Infant search tasks reveal early concepts of containment and canonical usage of objects

It is difficult to gain unambiguous evidence on the use of concepts by infants. Many results can be accounted for in terms of action-based strategies. The evidence reported here fulfils the minimal criteria for the operation of working concepts in infants. Search tasks are used with a filled interval which forces memory-search, and the object is hidden in containers which fulfil their customary job or violate it. Infants treat an upright cup as a more reliable location marker than an inverted one. A series of experiments probes the phenomenon. The results indicate that the infants have a working concept of containment which can be triggered by the provision of containers in their canonical orientation. Even “object permanence tasks” lead infants to access their knowledge of the relationships into which things typically enter in the world outside the laboratory.

THE PHOTOEXCITED TRIPLET STATE OF TETRAPHENYL CHLORIN, MAGNESIUM TETRAPHENYL PORPHYRIN AND WHOLE CELLS OF CHLAMYDOMONAS REINHARDI. A LIGHT MODULATION‐EPR STUDY

Abstract— The photoexcited triplet states of frozen solutions of tetraphenyl chlorin (TPC), magnesium tetraphenyl porphyrin (MgTPP) and whole cells of Chlamydomonas reinhardi have been studied by light modulation‐EPR spectroscopy. The porphyrins were chosen to be studied as model compounds for chlorophyll molecules, From EPR spectra the zero field splitting parameters (ZFS) were calculated. For TPC, |D| = 0.0364 ± 0.0002 cm‐1, |E| = 0.0063 ± 0.0002 cm‐1. For MgTPP, |D| = 0.0310 ± 0.0002 cm‐1. For chloroplasts, |D| = 0.0280 ± 0.0004 cm‐1, |E| = 0.0032 ± 0.0004 cm‐1. In all compounds studied, except MgTPP, electron spin polarization (ESP) was observed. From the analysis of the kinetic curves at each canonical orientation we evaluated the spin lattice relaxation rate W, the depopulation rate constants kp, and the ratio between the population rate constants, Ap, at zero magnetic field. For TPC in ethanol‐toluene (5:1) kx= (0.70 ± 0.10) × 103 s‐1, ky= (0.40 ± 0.07) × 103 s‐1, kx= (0.24 ± 0.05) × 103 s‐1; Ax:Ay:Az⋍ 1.0:0.6:0.4; W= (2.60 ± 0.40) × 103 s‐1. For MgTPP, only the total decay rate constant, kT, was calculated: (1.5 ± 0.2) × 10 s‐1 in n‐octane and (4.8 ± 0.8) × 10 s‐1 in ethanol. The results for TPC and MgTPP are compared to those reported previously for chlorophyll. It is concluded that the dynamics of the photoexcited triplet state in chlorophylls are mainly governed by the chlorin macrocycle. From the EPR spectrum and ZFS parameters of chloroplasts, we propose that both chlorophyll a and chlorophyll b are the main constituents of the EPR spectrum. From the analysis of the kinetic curves we obtain separately the kinetic parameters for chlorophylls a and b, kax= (1.30 ± 0.20) × 103 s‐1, kay;= (0.85 ± 0.15) × 103 s‐1kax= (0.32 ± 0.05) × 103 s‐1; Aax:Aay:Aaz⋍ 1.0:0.7:0.2; Wa= (1.20 ± 0.20) × 103 s‐1; kbx= (0.56 ± 0.09) × 103 s‐1, kby= (0.30 ± 0.04) × 103 s‐1, kbz= (0.06 ± 0.01) × 103 s‐1; Abx:Aby:Abx⋍ 1.0:0.6:0.1; Wb= (5.00 ± 0.80) × 103 s‐1. These results are very close to those found separately for chlorophyll a and chlorophyll b oligomers in vitro.

Method of ``Magnetophotoselection'' of the Lowest Excited Triplet State of Aromatic Molecules

The unique intensity distribution as a function of the angles between the principal magnetic axes and the applied magnetic field of the Δm=±1 ESR transitions of a collection of randomly oriented photoexcited triplet-state molecules has been used as a magnetoselection device, to observe only the molecules whose principal magnetic axes are parallel to the magnetic field. The latter is possible because the shape of the derivative of the Δm=±1 ESR absorption curve gives special prominence to those resonant fields corresponding to transitions of molecules possessing a canonical orientation. Changes in the relative intensities of the derivative ESR lines of the magnetophotoselected collection of molecules were observed as a function of the angle between the external field and the polarization direction of the exciting monochromatic light. The results obtained for glasses of naphthalene-d8 and quinoxaline were analyzed in terms of the known ESR spectra and polarization of the electronic absorption bands; the conclusions agree very well with theoretical predictions. The known directions of polarization of the electronic absorption bands of phenanthrene-d10 were then used to assign the Δm=±1 ESR spectrum of phenanthrene-d10 in EPA glass at 77°K. The assignment is found to agree with the first-order spectrum calculated using the published D and E values determined from single crystal studies. A simple procedure based on the magnetoselection method, and making use of the symmetry properties of π,π* and n,π* states, is then outlined by which assignments can be made for randomly oriented aromatic hydrocarbon or N-heterocyclic molecules, of the Δm=±1 ESR lines corresponding to those molecules which have their molecular plane either perpendicular or parallel to the magnetic field. The polarization of the electronic transitions used to excite these molecules to their triplet states need not be predetermined. A discussion is given of the advantages of using the method of magnetophotoselection instead of the normal photoselection method (where optical luminescence is used for analysis) to such problems as the assignment of optical electronic transitions and the mutual orientation of donor and acceptor in triplet—triplet transfer processes.