Primitive Axes Research Articles

Structure of primitive axial algebras

A “fusion law” is a collection of multiplication rules among eigenspaces of an idempotent. This terminology is relatively new and is closely related to primitive axial algebras, introduced recently by Hall, Rehren and Shpectorov. Axial algebras are closely related to 3-transposition groups and vertex operator algebras.In earlier work we studied primitive axial algebras, not necessarily commutative, and showed that they all have Jordan type. In this paper, we show that all finitely generated primitive axial algebras are direct sums of specifically described flexible finite-dimensional noncommutative algebras, and commutative axial algebras generated by primitive axes of the same type. In particular, all primitive axial algebras are flexible. They also have Frobenius forms. We give a precise description of all the primitive axes of axial algebras generated by two primitive axes.

Primitive axial algebras are of Jordan type

The notion of axial algebra is closely related to 3-transposition groups, the Monster group and vertex operator algebras. In this work we continue our previous works and compete the proof that all algebras generated by a set of primitive axes not necessarily of the same type (see the definition in the body of the paper), are primitive axial algebras of Jordan type.

Ambiguity-Aware Multi-Object Pose Optimization for Visually-Assisted Robot Manipulation

6D object pose estimation aims to infer the relative pose between the object and the camera using a single image or multiple images. Most works have focused on predicting the object pose without associated uncertainty under occlusion and structural ambiguity (symmetricity). However, these works demand prior information about shape attributes, and this condition is hardly satisfied in reality; even asymmetric objects may be symmetric under the viewpoint change. In addition, acquiring and fusing diverse sensor data is challenging when extending them to robotics applications. Tackling these limitations, we present an ambiguity-aware 6D object pose estimation network, PrimA6D++, as a generic uncertainty prediction method. The major challenges in pose estimation, such as occlusion and symmetry, can be handled in a generic manner based on the measured ambiguity of the prediction. Specifically, we devise a network to reconstruct the three rotation axis primitive images of a target object and predict the underlying uncertainty along each primitive axis. Leveraging the estimated uncertainty, we then optimize multi-object poses using visual measurements and camera poses by treating it as an object SLAM problem. The proposed method shows a significant performance improvement in T-LESS and YCB-Video datasets. We further demonstrate real-time scene recognition capability for visually-assisted robot manipulation.

Many-particle based evaluations for maximum current output from bimodal electron emitter arrays

Evaluations of the current output from emitter arrays have been carried out based on time-dependent kinetic simulations that include many-body Coulombic contributions from the electron swarm, geometric field enhancements with shielding based on a line charge model, and dynamic screening due to the evolution of the swarm in the position and velocity space. Numerical evaluations are applied to different multi-emitter array arrangements having a hexagonal lattice, with a focus on bimodal distributions. Our results show the expected role of field screening with reductions in emitter separation and positional dependence within the array based on connectivity. Different patterns were examined within a hexagonal lattice structure. For a bimodal distribution, output current optimization is shown for alternating arrangements with three or more successive emitters of the same length along primitive axes predicted to have an advantage.

On primitive 3-generated axial algebras of Jordan type

Axial algebras of Jordan type η are commutative algebras generated by idempotents whose adjoint operators have the minimal polynomial dividing (x−1)x(x−η), where η∉{0,1} is fixed, with restrictive multiplication rules. These properties generalize the Peirce decompositions for idempotents in Jordan algebras, where 12 is replaced with η. In particular, Jordan algebras generated by idempotents are axial algebras of Jordan type 12. If η≠12 then it is known that axial algebras of Jordan type η are factors of the so-called Matsuo algebras corresponding to 3-transposition groups.We call the generating idempotents axes and say that an axis is primitive if its adjoint operator has 1-dimensional 1-eigenspace. It is known that a subalgebra generated by two primitive axes has dimension at most three. The 3-generated case has been opened so far. We prove that every axial algebra of Jordan type generated by three primitive axes has dimension at most nine. If the dimension is nine and η=12 then we either show how to find a proper ideal in this algebra or prove that the algebra is isomorphic to certain Jordan matrix algebras.

The notochord: structure and functions.

The notochord is an embryonic midline structure common to all members of the phylum Chordata, providing both mechanical and signaling cues to the developing embryo. In vertebrates, the notochord arises from the dorsal organizer and it is critical for proper vertebrate development. This evolutionary conserved structure located at the developing midline defines the primitive axis of embryos and represents the structural element essential for locomotion. Besides its primary structural function, the notochord is also a source of developmental signals that patterns surrounding tissues. Among the signals secreted by the notochord, Hedgehog proteins play key roles during embryogenesis. The Hedgehog signaling pathway is a central regulator of embryonic development, controlling the patterning and proliferation of a wide variety of organs. In this review, we summarize the current knowledge on notochord structure and functions, with a particular emphasis on the key developmental events that take place in vertebrates. Moreover, we discuss some genetic studies highlighting the phenotypic consequences of impaired notochord development, which enabled to understand the molecular basis of different human congenital defects and diseases.

Research on Mechanical Property of Top Drive Casing Running Tool’s Slips

Top drive casing running tool, because of its convenience, speed and safety, has been widely received by the research enterprises of petroleum mechanism and instrument. Now, there have been developed several kinds of casing running tools which have gradually been used by the drilling corporation at home and abroad. The slips system’s parameters, such as the axial thrust, slips length, teeth form, teeth interval, etc., directly affect the performance and safety of casing running tools. Those have no reports about correlative theoretical investigation results. Here, we found the mechanical analysis model between slip and casing and gain the minimum primitive axis thrust of slips. Then the minimum teeth interval of the slips is deduced by contact mechanics. And then the slips available working length is worked out through the shell theory and empirical formulas. Finally, based on finite element method, we obtain tooth form angles’ recommendable range by studying the tooth form. This study supplies theoretical basis to structural design of slips system of the top drive casing running tool.

The effect of in-plane mass anisotropy on the properties of high temperaturesuperconductors in states of mixed symmetry

Experiments have suggested that the high-Tc cuprate YBCO shows marked anisotropy in penetration depth and coherence lengthmeasurements. In order to take into account the presence of this anisotropy inthe system and its corresponding effect on the various properties of the high-Tc superconducting materials, we have developed an anisotropic two-orderparameter Ginzburg–Landau (GL) theory involving a mixed symmetrystate of the order parameter components. For this we have generalized atwo-order parameter GL theory, recently developed for the isotropic high-Tc superconductors involving a mixed symmetry state of the order parameter components(Karmakar and Dey 2008 J. Phys. Condens. Matter 20 255218), in which the effect ofthe presence of in-plane anisotropy has been taken into account by an effectivemass approximation, with the anisotropy being characterized by the parameterγ = mx/my. The work goes beyond the limitations of the earlier studies in this field as it enables us tocarry out a detailed study of the various properties of the system over the entire range ofapplied magnetic field and wide range of temperature for arbitrary values of the GL parameterκy and vortex lattice symmetry. The model successfully explains not only the observed obliquevortex lattice structure in the presence of in-plane anisotropy but also the experimentallyobserved angle between the primitive axes of the vortex lattice. The generation oftwo-fold symmetry of the vortices in the presence of in-plane anisotropy, for avery low applied magnetic field can also be analyzed by our model. We havealso compared our theoretical results with various other experiments on high-Tc cuprate YBCO.

Antiferroelastic structural transitions in PrAlO3 by means of neutron diffraction

AbstractStructural phase transitions of the perovskite‐type PrAlO3 have been studied by using neutron diffraction. The results show that, on cooling, the structures are successively transformed from R$ \bar 3 $c (Phase II) to Imma (Phase III), Imma (Phase IV), I4/mcm (Phase V) by the 215‐K, 153‐K, and 122‐K transitions. The tilting schemes in Phase III, IV and V are mainly characterized by (ψa = ψc, ψb = 0), (ψa ≠ ψc, ψb = 0), and (ψc, ψa = ψb = 0), respectively, where ψa, ψb and ψc are rotational angles around a‐, b‐, and c‐primitive axes of the AlO6 octahedron. The refreezes of the condensed Rand R optical soft modes occurring at about 215 K and 122 K are interpreted by correlation with the cooperative Jahn–Teller distortion (JTD) of the Pr3+–4f orbitals in the PrO12 polyhedra. The phase IV is characterized as an intermediate state, in which the ψa tilts are continuously reduced by the JTD and disappear just above the 122‐K transition. The easy mobility of the domain walls suggests the PrAlO3 crystal to be of antiferroelastic nature, an unusual property that results from the cooperative displacements of O ions induced by the correlation between the antiphase tilts along primitive axes of the AlO6 octahedra and the JTD around Pr+3 ions in PrO12 polyhedra. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Structural phase transition and structural properties in oxygenated La2CuO4+y; y ∼0.02

The crystal structure of the oxygenated La2CuO4+y; y ∼0.02 has been studied by X-ray diffraction. It is found that the structural phase transition from tetragonal to orthorhombic symmetry occurring at about 450 K (Tc) is of second order and shows diffuse scattering above Tc. The diffuse scattering is related to static and/or dynamic short-range order of cooperative tilts of rigid-like elongated CuO6 octahedra, which make two-dimensional networks stacked along the [001] axis. The structures at room temperature and 210K are determined using a 4-circle X-ray diffractometer and have the orthorhombic space group 10D2h-Pccn. The structure is mainly characterized by anisotropic cooperative tilts of the CuO4 octahedra around the [100]p and [010]p primitive axes in two-dimensional octahedron-networks, where suffix “p” means pseudo K2NiF4-type structure. The anisotropy of the tilting-angles results from pushing by excess oxygen atoms to apical oxygen atoms of the CuO6 octahedra. It is also found by refinement of the structure that the excess oxygen atoms are randomly sited at the atomic coordinates (1/4,1/4,0.244) and/or (1/4, 1/4,0.279).

Model of crystal lattice strained along the preferential direction by anisotropic stress for GaAs heteroepitaxial films grown on vicinal Si(001) and Si(110) substrates by molecular-beam epitaxy

I estimated anisotropy of stress and strain for GaAs heteroepitaxial films grown on vicinal Si(001) and Si(110) substrates by molecular-beam epitaxy from measurements of in-plane substrate curvatures and components of lattice parameters by a Bond method using x-ray diffraction. It is shown that the GaAs heteroepitaxial film is anisotropically strained through different relaxation processes of stress due to anisotropic dislocations along the [110] and [11̄0] directions. The crystal lattice of the GaAs heteroepitaxial film on Si substrate is qualitatively represented considering the crystal structure elastically strained with the [110]-, [11̄0]-, and [001]-primitive axes as a primitive basis in the orthogonal rhombic system.

The role of reward pathways in the development of drug dependence

In commenting on the discovery of "opiate" receptors, Goldstein (1976) said: "It seemed unlikely, a priori, that such highly stereospecific receptors should have been developed by nature to interact with alkaloids from the opium poppy" (p. 1081). Endogenous opioid peptides and opioid receptor systems have now been identified in invertebrates that are unlikely to have had ancestors exposed to opium poppies (Kavaliers et al., 1983; Kream et al., 1980; Leung and Stefano, 1984; Stefano et al., 1980). Moreover, endogenous opioids play a role in stress-induced feeding in the slug (Kavaliers and Hirst, 1986) just as they play a role in stress-induced feeding in rodents (Lowy et al., 1980; Morley and Levine, 1980). If we are to understand the actions of opiates and other drugs of abuse we must understand them in terms of their abilities to interact with neural systems that evolved in the service of primitive biological functions, long before any serious incidence of addiction itself. The most primitive axes of the biological substrates of behavior are the axes of approach and withdrawal. Addictive drugs appear to be able to activate the mechanisms of approach, which is termed "positive reinforcement" and to inhibit the mechanisms of withdrawal, which is termed "negative reinforcement." Anatomically distinct sets of pathways have evolved to serve these two forms of reward. Activation of the medial forebrain bundle and associated structures serves positive reinforcement and induces forward locomotion. Approach and forward locomotion are the unconditioned responses to positive reinforcing stimuli such as food and sex partners, and approach to environmental objects and positive reinforcement is induced by electrical stimulation of this structure. The locomotor stimulating effects and the positive reinforcing effects of opiates and psychomotor stimulants result from their activation of this mechanism; stimulants activate the mechanism at the level of dopaminergic synapses of the nucleus accumbens, frontal cortex, and perhaps other forebrain structures, while opiates activate the system at two points: at the level of the dopaminergic synapse and at the level of the afferents to the dopaminergic cell bodies. Ethanol, nicotine, caffeine and phencyclidine stimulate both locomotor activity and dopamine turnover, but their sites of interaction with reward pathways have not yet been identified. Benzodiazepines and barbiturates stimulate locomotor activity without stimulating dopamine turnover; they may interact with reward pathways at a synapse efferent to the dopaminergic link in the pathways.(ABSTRACT TRUNCATED AT 400 WORDS)

Computerized group theory for lattice dynamical problems

The calculation of the normal modes of vibration of a crystal in general requires the diagonalization of the dynamical matrix for wave vector q, which has rank 3n, where n is the number of atoms per unit cell. The symmetry of the crystal can be used to block diagonalize the dynamical matrix using group representation theory. Here we describe a subroutine, named BLOCDI that computes the unitary matrix which group theoretically block diagonalizes the dynamical matrix for any crystal structure and wave vector. The input to the subroutine is first put into a form that is generally acceptable for all crystal structures. This is made possible by specifying the structure in terms of integer variables which relate to the primitive axes. The projection operator is used to generate and print out possible symmetry coordinates, labeled according to their irreducible representation and site symmetry. The set of coordinates to be used in the construction of the transformation matrix is then easily selected by inspection from the printed sets. In a second run the selected coordinates are computed and the nonzero values of the matrix and their indices are stored in singly dimensioned arrays. Possible reductions due to time reversal symmetry are not considered. There is essentially no restriction on the size of the unit cell. The actual transformation of the dynamical matrix (using the output of BLOCDI) becomes a time and storage problem long before the computation and indexing of the nonzero elements of the transformation matrix becomes a problem.

Explanation In Vitro of Transverse Pieces of Early Rat Embryos

The primitive axis of the rat embryo appears during the ninth day after insemination, on the inner concavity of the upper or anti-mesometrial portion of the blastodermic vesicle. Accordingly its sagittal section is U-shaped. In order to isolate definite portions of the axis, the embryonic end of the cylinder is first cut off from the rest by a transection in the region of the amnion; then the embryo is flattened by means of a slit in each lateral wall of the vesicle so isolated. Transverse cuts may now be made at any level of the axis. In the present series the whole posterior half was isolated as a single explant, the anterior half usually being divided into thirds transversely. The isolated fragments of the embryonic regions of the rat in stages just previous to and during the formation of the embryonic axis are capable of typical differentiation in vitro. The pieces were explanted on cover slip clots of rat plasma and rat embryo or placental extract. The plasma donor was injected with a few cc. of 10% dextrose immediately before the bleeding. The cultures were usually washed or transferred after 48 hours; fixed after 3 or 4 days, photographed in toto and later examined in serial sections. The designated levels of embryos in stage 14 (medullary plate) and stage 15 (head-fold) round up into little vesicular structures, and differentiate characteristic primitive organs. The anteriormost third of the anterior part of the axis always includes part of the yolk-sac which forms its typical epithelium, blood islands and vascular channels. One or two pulsating myocardial masses invariably develop; histologically these may show little differentiation. Mesenchyme frequently is found; less frequently medullary tube. The second third of the anterior axis usually forms yolk-sac, and always pulsating heart-masses.