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Concept: Euclidean space


Leukocytes and other amoeboid cells change shape as they move, forming highly dynamic, actin-filled pseudopods. Although we understand much about the architecture and dynamics of thin lamellipodia made by slow-moving cells on flat surfaces, conventional light microscopy lacks the spatial and temporal resolution required to track complex pseudopods of cells moving in three dimensions. We therefore employed lattice light sheet microscopy to perform three-dimensional, time-lapse imaging of neutrophil-like HL-60 cells crawling through collagen matrices. To analyze three-dimensional pseudopods we: (i) developed fluorescent probe combinations that distinguish cortical actin from dynamic, pseudopod-forming actin networks, and (ii) adapted molecular visualization tools from structural biology to render and analyze complex cell surfaces. Surprisingly, three-dimensional pseudopods turn out to be composed of thin (<0.75 µm), flat sheets that sometimes interleave to form rosettes. Their laminar nature is not templated by an external surface, but likely reflects a linear arrangement of regulatory molecules. Although we find that Arp2/3-dependent pseudopods are dispensable for three-dimensional locomotion, their elimination dramatically decreases the frequency of cell turning, and pseudopod dynamics increase when cells change direction, highlighting the important role pseudopods play in pathfinding.

Concepts: DNA, Protein, Eukaryote, Dimension, Euclidean space, Analytic geometry, Amoeboid, Pseudopod


In contrast to most other sensory modalities, the basic perceptual dimensions of olfaction remain unclear. Here, we use non-negative matrix factorization (NMF) - a dimensionality reduction technique - to uncover structure in a panel of odor profiles, with each odor defined as a point in multi-dimensional descriptor space. The properties of NMF are favorable for the analysis of such lexical and perceptual data, and lead to a high-dimensional account of odor space. We further provide evidence that odor dimensions apply categorically. That is, odor space is not occupied homogenously, but rather in a discrete and intrinsically clustered manner. We discuss the potential implications of these results for the neural coding of odors, as well as for developing classifiers on larger datasets that may be useful for predicting perceptual qualities from chemical structures.

Concepts: Dimension, Euclidean space, Vector space, Space, Spacetime, Linear algebra, Real number, Point


Three-dimensional (3D) assemblies based on carbon nanomaterials still lag behind their individual one-dimensional building blocks in terms of mechanical and electrical properties. Here we demonstrate a simple strategy for the fabrication of an open porous 3D self-organized double-hierarchical carbon nanotube tube structure with properties advantageous to those existing so far. Even though no additional crosslinking exists between the individual nanotubes, a high reinforcement effect in compression and tensile characteristics is achieved by the formation of self-entangled carbon nanotube (CNT) networks in all three dimensions, employing the CNTs in their high tensile properties. Additionally, the tubular structure causes a self-enhancing effect in conductivity when employed in a 3D stretchable conductor, together with a high conductivity at low CNT concentrations. This strategy allows for an easy combination of different kinds of low-dimensional nanomaterials in a tube-shaped 3D structure, enabling the fabrication of multifunctional inorganic-carbon-polymer hybrid 3D materials.

Concepts: Dimension, Euclidean space, Carbon, Carbon nanotube, Graphite, Materials science, Tensile strength, Electrical conductivity


A new bioprinting method is reported for fabricating 3D tissue constructs replete with vasculature, multiple types of cells, and extracellular matrix. These intricate, heterogeneous structures are created by precisely co-printing multiple materials, known as bioinks, in three dimensions. These 3D micro-engineered environments open new -avenues for drug screening and fundamental studies of wound healing, angiogenesis, and stem-cell niches.

Concepts: Wound healing, Extracellular matrix, Healing, Angiogenesis, Dimension, Euclidean space, Abstract algebra, Method


We acquire the first experimental 3-D tomographic images with magnetic particle imaging (MPI) using projection reconstruction methodology, which is similar to algorithms employed in X-ray computed tomography. The primary advantage of projection reconstruction methods is an order of magnitude increase in signal-to-noise ratio (SNR) due to averaging. We first derive the point spread function, resolution, number of projections required, and the SNR gain in projection reconstruction MPI. We then design and construct the first scanner capable of gathering the necessary data for nonaliased projection reconstruction and experimentally verify our mathematical predictions. We demonstrate that filtered backprojection in MPI is experimentally feasible and illustrate the SNR and resolution improvements with projection reconstruction. Finally, we show that MPI is capable of producing three dimensional imaging volumes in both phantoms and postmortem mice.

Concepts: Medical imaging, Radiography, Tomographic reconstruction, Dimension, Euclidean space, Tomography, Virtopsy, Signal-to-noise ratio


The topological study of the electronic charge density is useful to obtain information about the kinds of bonds (ionic or covalent) and the atom charges on a molecule or crystal. For this study, it is necessary to calculate, at every space point, the electronic density and its electronic density derivatives values up to second order. In this work, a grid-based method for these calculations is described. The library, implemented for three dimensions, is based on a multidimensional Lagrange interpolation in a regular grid; by differentiating the resulting polynomial, the gradient vector, the Hessian matrix and the Laplacian formulas were obtained for every space point. More complex functions such as the Newton-Raphson method (to find the critical points, where the gradient is null) and the Cash-Karp Runge-Kutta method (used to make the gradient paths) were programmed. As in some crystals, the unit cell has angles different from 90°, the described library includes linear transformations to correct the gradient and Hessian when the grid is distorted (inclined). Functions were also developed to handle grid containing files (grd from DMol® program, CUBE from Gaussian® program and CHGCAR from VASP® program). Each one of these files contains the data for a molecular or crystal electronic property (such as charge density, spin density, electrostatic potential, and others) in a three-dimensional (3D) grid. The library can be adapted to make the topological study in any regular 3D grid by modifying the code of these functions. © 2012 Wiley Periodicals, Inc.

Concepts: Electric charge, Mathematics, Fundamental physics concepts, Atom, Chemical bond, Dimension, Euclidean space, Numerical analysis


BACKGROUND: Multiple variations of the musculocutaneous trapezius flap have been described, each of which use a single composite musculocutaneous unit in their designs. The limitation of such designs is the ability to use the components in a 3-dimensional manner, with only 1 vector existing in the geometry of the musculocutaneous unit. METHODS: A review of the literature was undertaken with regard to designs of the musculocutaneous trapezius flap, and we present a new technique for flap design. With identification of individual perforators to each of the muscle and fasciocutaneous portions of the trapezius flap, the 2 components can act in a chimeric fashion, able to fill both a deep and complex 3-dimensional space while covering the wound with robust skin. RESULTS: A range of flap designs have been described, including transverse, oblique, and vertical skin paddles accompanying the trapezius muscle. We describe a technique with which a propeller-style skin paddle based on a cutaneous perforator can be raised in any orientation with respect to the underlying muscle. In a presented case, separation of the muscular and fasciocutaneous components of the trapezius flap was able to obliterate dead space around exposed cervicothoracic spinal metalwork and obtain robust wound closure in a patient with previous radiotherapy. CONCLUSIONS: This concomitant use of a muscle and fasciocutaneous perforator flap based on a single perforator, a so-called chimeric perforator flap, is a useful modification to trapezius musculocutaneous flap design.

Concepts: Dimension, Euclidean space, Vector space, Graphic design, Analytic geometry, Dorsal scapular artery, Manner of articulation, Trapezius muscle


The center of resistance is considered the most important reference point for tooth movement. It is often stated that forces through this point will result in tooth translation. The purpose of this article is to report the results of numeric experiments testing the hypothesis that centers of resistance do not exist in space as 3-dimensional points, primarily because of the geometric asymmetry of the periodontal ligament. As an alternative theory, we propose that, for an arbitrary tooth, translation references can be determined by 2-dimensional projection intersections of 3-dimensional axes of resistance.

Concepts: Physics, Dimension, Euclidean space, Empiricism, Experiment, Hypothesis, Theory, Reference


This study examined whether gender moderated the association between age cohort and the cognitive, reflective, and compassionate dimensions of wisdom, using an Iranian sample of 439 adults from three age cohorts: young (18-34), middle-aged (35-54), and older (55 and above). Results indicated that the interaction effect between gender and age cohort was significant for three-dimensional wisdom and all three wisdom dimensions. Compared with younger women and older men, older women tended to have less education and to score lower on the cognitive wisdom dimension, but they had similar average scores as older men on the compassionate wisdom dimension. Overall, the association between age and wisdom was only positive for men, due mainly to the positive relation between age and the reflective and compassionate wisdom dimensions for men after adjusting for education. The results are interpreted with reference to generation gaps, socialization of men versus women, and life experiences and opportunities.

Concepts: Cohort study, Gender, Dimension, Euclidean space, Gender role, Real number, Virtue, Transgender


A grand challenge in material science is to understand the correlation between intrinsic properties and defect dynamics. Radiation tolerant materials are in great demand for safe operation and advancement of nuclear and aerospace systems. Unlike traditional approaches that rely on microstructural and nanoscale features to mitigate radiation damage, this study demonstrates enhancement of radiation tolerance with the suppression of void formation by two orders magnitude at elevated temperatures in equiatomic single-phase concentrated solid solution alloys, and more importantly, reveals its controlling mechanism through a detailed analysis of the depth distribution of defect clusters and an atomistic computer simulation. The enhanced swelling resistance is attributed to the tailored interstitial defect cluster motion in the alloys from a long-range one-dimensional mode to a short-range three-dimensional mode, which leads to enhanced point defect recombination. The results suggest design criteria for next generation radiation tolerant structural alloys.

Concepts: Dimension, Euclidean space, Solid, Materials science, Alloy, Solid solution, Intensive and extensive properties, Toleration