Symmetric Projection Research Articles

Characterization of a constrained paired‐view technique in iterative reconstruction for breast tomosynthesis

The order in which the projection views are employed in the reconstruction of tomosynthesis by iterative algorithms, such as simultaneous algebraic reconstruction technique and maximum likelihood, has a strong effect on the rate of convergence, accuracy, and the edge-blurring artifacts in the reconstructed image. The purpose of this investigation was to characterize and evaluate the effects of ordering schemes on image quality for breast tomosynthesis reconstruction and to explore a new constrained paired-view technique that could provide reduction of reconstruction artifacts. In this work, the authors compared several different ordering schemes and characterized the image quality and the formation of out-of-plane artifacts. Furthermore, a new normalization method is presented. It produces more accurate reconstructions with reduced artifacts comparing to the standard method of sequential ordering. In addition to visual assessment of image quality, several indices such as the signal-difference-to-noise ratio, the artifact-spread function, and the lesion detectability (d(')) were computed to quantitatively evaluate the effect of ordering scheme. The sets of breast tomosynthesis projection images were simulated for reconstruction; one set had uniform background (white noise only) and the other two contained both anatomic background and quantum noise. Clinical breast images were also studied for comparison. The authors have quantified the image quality in reconstructed slices for a range of tumor sizes. The authors' proposed method provides better performance for all of the metrics tested (contrast, d('), and the level of artifacts) both for the uniform phantom case and in the presence of anatomical structure. The paired projection normalization provides better performance in the image quality of the reconstructed slices, and results in a lower level of artifacts in the Z direction. This implies that even a relatively simple method like the "side-to-side" sequence, which pairs two symmetrical projections with equal angular distance from the central projection, would achieve better reconstructed image quality than the conventional "step-by-step" method, which uses sequential projections one after another.

Dynamic symmetrical pattern projection based laser triangulation sensor for precise surface position measurement of various material types

This paper describes a custom, material-type-independent laser-triangulation-based measurement system that utilizes a high-quality ultraviolet laser beam. Laser structuring applications demand material surface alignment regarding the laser focus position, where fabrication conditions are optimal. Robust alignment of various material types was solved by introducing dynamic symmetrical pattern projection, and a "double curve fitting" centroid detection algorithm with subsurface scattering compensation. Experimental results have shown that the measurement system proves robust to laser intensity variation, with measurement bias lower than 50 μm and standard deviation lower than ±6.3 μm for all materials. The developed probe has been integrated into a PCB prototyping system for material referencing purposes.

Symmetric parareal algorithms for Hamiltonian systems

The parareal in time algorithm allows for efficient parallel numerical simulations of time-dependent problems. It is based on a decomposition of the time interval into subintervals, and on a predictor-corrector strategy, where the propagations over each subinterval for the corrector stage are concurrently performed on the different processors that are available. In this article, we are concerned with the long time integration of Hamiltonian systems. Geometric, structure-preserving integrators are preferably employed for such systems because they show interesting numerical properties, in particular excellent preservation of the total energy of the system. Using a symmetrization procedure and/or a (possibly also symmetric) projection step, we introduce here several variants of the original plain parareal in time algorithm [L. Baffico, et al. Phys. Rev. E 66 (2002) 057701; G. Bal and Y. Maday, A parareal time discretization for nonlinear PDE’s with application to the pricing of an American put, in Recent developments in domain decomposition methods, Lect. Notes Comput. Sci. Eng. 23 (2002) 189–202; J.-L. Lions, Y. Maday and G. Turinici, C. R. Acad. Sci. Paris, Série I 332 (2001) 661–668.] that are better adapted to the Hamiltonian context. These variants are compatible with the geometric structure of the exact dynamics, and are easy to implement. Numerical tests on several model systems illustrate the remarkable properties of the proposed parareal integrators over long integration times. Some formal elements of understanding are also provided.

Unified universal quantum cloning machine and fidelities

We present a unified universal quantum cloning machine, which combines several different existing universal cloning machines together including the asymmetric case. In this unified framework, the identical pure states are projected equally into each copy initially constituted by input and one half of the maximally entangled states. We show explicitly that the output states of those universal cloning machines are the same. One importance of this unified cloning machine is that the cloning procession is always the symmetric projection which reduces dramatically the difficulties for implementation. Also it is found that this unified cloning machine can be directly modified to the general asymmetric case. Besides the global fidelity and the single-copy fidelity, we also present all possible arbitrary-copy fidelities.

Generalized Nonlinear Complementary Attitude Filter

A = matrices a = true value ~ A = Â T A ; left multiply error â = estimated value a = measured value ~ a = error between estimated and true values hai = time-averaged expectation value A;B , fA;Bg = commutator or anticommutator of A and B A = equilibrium point AI = CAC ; matrix in inertial frame Ps A , Pa A = symmetric or antisymmetric projection of A x = vectors x = matrix equivalent form of cross product xI = Cx; vector in inertial frame

Differential geometry with a projection: application to double field theory

In recent development of double field theory, as for the description of the massless sector of closed strings, the spacetime dimension is formally doubled, i.e. from D to D+D, and the T-duality is realized manifestly as a global O(D,D) rotation. In this paper, we conceive a differential geometry characterized by a O(D,D) symmetric projection, as the underlying mathematical structure of double field theory. We introduce a differential operator compatible with the projection, which, contracted with the projection, can be covariantized and may replace the ordinary derivatives in the generalized Lie derivative that generates the gauge symmetry of double field theory. We construct various gauge covariant tensors which include a scalar and a tensor carrying two O(D,D) vector indices.

Distribution and Development of Brown Adipocytes in the Murine and Human Adipose Organ

Murine white and brown adipocytes are found together in dissectible visceral and subcutaneous fat depots supplied by specific vessels and nerves, forming a multi-depot organ with plastic properties. Many of the anatomo-physiological features of murine fat depots apply to humans.

On a residual local projection method for the Darcy equation

A new symmetric local projection method built on residual bases (RELP) makes linear equal-order finite element pairs stable for the Darcy problem. The derivation is performed inside a Petrov–Galerkin enriching space approach (PGEM) which indicates parameter-free terms to be added to the Galerkin method without compromising consistency. Velocity and pressure spaces are augmented using solutions of residual dependent local Darcy problems obtained after a static condensation procedure. We prove the method achieves error optimality and indicates a way to recover a locally mass conservative velocity field. Numerical experiments validate theory. To cite this article: L.P. Franca et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).

Reconstruction of the P2X2 Receptor Reveals a Vase-Shaped Structure with Lateral Tunnels above the Membrane

In response to the intercellular messenger ATP, P2X receptors transfer various sensory information, including pain. Here we have reconstructed the structure of the P2X(2) receptor at 15 A resolution from more than 90,000 particle images, taken with a cryo-electron microscope equipped with a helium-cooled stage. This three-dimensional depiction, presumably in a closed state, revealed an elongated vase-shaped structure 202 A in height and 160 A in major diameter. The extracellular and transmembrane domains present a two-layered structure, in which a sparse outer layer surrounds a pore-forming inner density. The decreased diameter of a putative ion-conducting pathway at the middle of the membrane was considered to be the narrowest part of the pore, which has been predicted from electrophysiological studies. The sparse, extended structure of the P2X(2) receptor indicates a loose assembly of subunits, which could be a basis for the activation-dependent pore dilation of P2X receptors.

A note on the statistical properties of nonparametric trend estimators by means of smoothing matrices

Smoothing matrices associated with linear filters for the estimation of time series’ unobserved components differ from those used in linear regression or generalised additive models due to asymmetry. In fact, while projection smoother matrices are in general symmetric, filtering matrices are not. It follows that many inferential properties developed for symmetric projection matrices no longer hold for time-series smoothing matrices. However, the latter have a well-defined algebraic structure that allows one to derive many properties useful for inference in smoothing problems. In this note, some properties of symmetric smoother matrices are extended to centrosymmetric smoothing matrices. A decomposition of smoothing matrices in submatrices associated with the symmetric and asymmetric components of a filter enables us to consider the different assumptions that characterise estimation in the interior and at the boundaries of a finite time series. Matrix-based measures are defined to approximate the bias and the variance of a trend estimator, both in the interior and at the boundaries. These measures do not depend on the data and provide useful information on the bias–variance trade-off that affects non-parametric estimators.

Analysis of variance, coefficient of determination and F-test for local polynomial regression

This paper provides ANOVA inference for nonparametric local polynomial regression (LPR) in analogy with ANOVA tools for the classical linear regression model. A surprisingly simple and exact local ANOVA decomposition is established, and a local R-squared quantity is defined to measure the proportion of local variation explained by fitting LPR. A global ANOVA decomposition is obtained by integrating local counterparts, and a global R-squared and a symmetric projection matrix are defined. We show that the proposed projection matrix is asymptotically idempotent and asymptotically orthogonal to its complement, naturally leading to an F-test for testing for no effect. A by-product result is that the asymptotic bias of the projected response based on local linear regression is of quartic order of the bandwidth. Numerical results illustrate the behaviors of the proposed R-squared and F-test. The ANOVA methodology is also extended to varying coefficient models.

Critical period plasticity of axonal arbors of layer 2/3 pyramidal neurons in rat somatosensory cortex: layer-specific reduction of projections into deprived cortical columns.

We examined the effect of whisker trimming during early postnatal development on the morphology of axonal arbors in rat somatosensory cortex. Axonal arbors from populations of layer 2/3 pyramidal neurons in the D2 column were labeled by lentivirus-mediated expression of green fluorescent protein. Axonal projection patterns were compared between untrimmed control animals and animals with all whiskers in A-, B-, and C-rows trimmed (D- and E-rows left intact) from postnatal days 7 to 15 (termed from here on DE-pairing). Control animals had approximately symmetrical horizontal projections toward C- and E-row columns in both supra- and infragranular layers. Following DE-pairing, the density of axons in supragranular layers projecting from the labeled neurons in the D2 column was higher in E- than in C-row columns. This asymmetry resulted primarily from a reduction in projection density toward the deprived C-row columns. In contrast, no change was observed in infragranular layers. The results indicate that DE-pairing during early postnatal development results in reduced axonal projection from nondeprived into deprived columns and that cortical neurons are capable of structural rearrangements at subsets of their axonal arbors.

Experimental measurement of multidimensional entanglement via equivalent symmetric projection

We construct a linear optics measurement process to determine the entanglement measure, named I concurrence, of a set of 4x4-dimensional two-photon entangled pure states produced in the optical parametric down conversion process. In our experiment, an equivalent symmetric projection for the twofold copy of a single subsystem [presented by L. Aolita and F. Mintert, Phys. Rev. Lett. 97, 050501 (2006)] can be realized by observing the one-side two-photon coincidence without any triggering detection on the other subsystem. Here, for the first time, we realize the measurement for entanglement contained in biphoton pure states by taking advantage of the indistinguishability and the bunching effect of photons. Our method can determine the I concurrence of generic high-dimensional bipartite pure states produced in the parametric down conversion process.

The Structure of the Prokaryotic Cyclic Nucleotide-Modulated Potassium Channel MloK1 at 16 Å Resolution

The gating ring of cyclic nucleotide-modulated channels is proposed to be either a two-fold symmetric dimer of dimers or a four-fold symmetric tetramer based on high-resolution structure data of soluble cyclic nucleotide-binding domains and functional data on intact channels. We addressed this controversy by obtaining structural data on an intact, full-length, cyclic nucleotide-modulated potassium channel, MloK1, from Mesorhizobium loti, which also features a putative voltage-sensor. We present here the 3D single-particle structure by transmission electron microscopy and the projection map of membrane-reconstituted 2D crystals of MloK1 in the presence of cAMP. Our data show a four-fold symmetric arrangement of the CNBDs, separated by discrete gaps. A homology model for full-length MloK1 suggests a vertical orientation for the CNBDs. The 2D crystal packing in the membrane-embedded state is compatible with the S1-S4 domains in the vertical "up" state.

Realizing any central projection with a mirror pair

We show that, for any rotationally symmetric projection with a single virtual viewpoint, it is possible to design a two-mirror rotationally symmetric system that realizes the projection exactly. These mirror pairs are derived from two coupled differential equations. We give examples in which the projections from the sphere at infinity are stereographic, perspective, and equiresolution.

Structure from motion with wide circular field of view cameras

This paper presents a method for fully automatic and robust estimation of two-view geometry, autocalibration, and 3D metric reconstruction from point correspondences in images taken by cameras with wide circular field of view. We focus on cameras which have more than 180 degrees field of view and for which the standard perspective camera model is not sufficient, e.g., the cameras equipped with circular fish-eye lenses Nikon FC-E8 (183 degrees), Sigma 8mm-f4-EX (180 degrees), or with curved conical mirrors. We assume a circular field of view and axially symmetric image projection to autocalibrate the cameras. Many wide field of view cameras can still be modeled by the central projection followed by a nonlinear image mapping. Examples are the above-mentioned fish-eye lenses and properly assembled catadioptric cameras with conical mirrors. We show that epipolar geometry of these cameras can be estimated from a small number of correspondences by solving a polynomial eigenvalue problem. This allows the use of efficient RANSAC robust estimation to find the image projection model, the epipolar geometry, and the selection of true point correspondences from tentative correspondences contaminated by mismatches. Real catadioptric cameras are often slightly noncentral. We show that the proposed autocalibration with approximate central models is usually good enough to get correct point correspondences which can be used with accurate noncentral models in a bundle adjustment to obtain accurate 3D scene reconstruction. Noncentral camera models are dealt with and results are shown for catadioptric cameras with parabolic and spherical mirrors.

Three-dimensional profilometry by symmetrical fringes projection technique

A precise interferometric method for three-dimensional surface measurements in a wide dynamic range is presented. The method is based on symmetrical two-spacing projection phase-stepping interferometry. Two approaches are proposed—one with double symmetrical illumination and the other with double symmetrical observation—which reduce influence of shadowing at investigation of complex surfaces and allow absolute coordinates estimation. The theoretical background, experimental check as well as accuracy and sensitivity assessment of the method are discussed. The proposed technique is especially useful for remote, non-destructive in-situ measurements of real objects—for example historical objects and monuments.

Quantitative Aspects of Corticocortical Connections: A Tracer Study in the Mouse

This study provides neuroanatomical data relevant to models and simulations of the propagation of activity over the cortex. We administered small injections of the anterograde tracer biotinylated dextran amine to various regions of the mouse cortex (1 per animal). Two-dimensional reconstructions of the cortical surface were made, showing the distribution, size, and density of the terminal fields. Within the injected hemisphere, the largest part of the terminal field always surrounded the injection site and extended over neighboring areas. On average, axons from injection sites of <or=0.1 mm2 (containing several thousand neurons) diverged onto a region about 180 times larger than the injection site. The density of stained fibers in distant terminal fields could reach about 25 m/mm3. More than half of the total terminal field from an individual injection site consisted of weak projections with densities of 3 or 4 m/mm3. The number of main axons entering an individual distant terminal field ranged between 14 and about 890. By indirect arguments we estimate that the density of stained fibers close to the injection site is 3-6 times that in the most densely labeled distant terminal fields. In addition to symmetric projections to the opposite hemisphere, nonhomotopic callosal projections were found.

Reversible methods of Runge-Kutta type for Index-2 DAEs

A new interpretation of Runge-Kutta methods for differential algebraic equations (DAEs) of index 2 is presented, where a step of the method is described in terms of a smooth map (smooth also with respect to the stepsize). This leads to a better understanding of the convergence behavior of Runge-Kutta methods that are not stiffly accurate. In particular, our new framework allows for the unified study of two order-improving techniques for symmetric Runge-Kutta methods (namely post-projection and symmetric projection) specially suited for solving reversible index-2 DAEs.

Odor maps of aldehydes and esters revealed by functional MRI in the glomerular layer of the mouse olfactory bulb.

Odorant identity is believed to be encoded in the olfactory bulb (OB) by glomerular activity patterns. It has not yet been possible to visualize and compare entire patterns for different odorants in the same animal because of technical limitations. For this purpose we used high-resolution functional MRI at 7 T, combined with glomerular-layer flat maps, to reveal responses to aliphatic homologues in the mouse OB. These odorants elicited reproducible patterns in the OB, with the medial and lateral regions containing the most intense signals. Unexpectedly, in view of the symmetrical projections of olfactory receptor neurons to medial and lateral glomeruli, the activity patterns in these regions were asymmetrical. The highly activated medial and lateral areas were shared by homologous members, generating a conserved "family signature" for a homologous series. The moderately active areas, including the dorsal region that has been extensively studied by optical imaging, were more sensitive to the length of the carbon chain, producing more subtle features of individual members and different changing trends among homologues. The global mapping with functional MRI not only extended previous studies but also revealed additional rules for representation of homologues in the OB. Insights into possible relations between the functional patterns, molecular projections, and odor perception may now be obtained based on the global from the olfactory epithelium to the OB glomerular activity patterns.