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Concept: Analytic geometry


The human face is a complex trait under strong genetic control, as evidenced by the striking visual similarity between twins. Nevertheless, heritability estimates of facial traits have often been surprisingly low or difficult to replicate. Furthermore, the construction of facial phenotypes that correspond to naturally perceived facial features remains largely a mystery. We present here a large-scale heritability study of face geometry that aims to address these issues. High-resolution, three-dimensional facial models have been acquired on a cohort of 952 twins recruited from the TwinsUK registry, and processed through a novel landmarking workflow, GESSA (Geodesic Ensemble Surface Sampling Algorithm). The algorithm places thousands of landmarks throughout the facial surface and automatically establishes point-wise correspondence across faces. These landmarks enabled us to intuitively characterize facial geometry at a fine level of detail through curvature measurements, yielding accurate heritability maps of the human face (

Concepts: Face perception, Analytic geometry, Morphology, General relativity, Differential geometry, Evolution, Genetics, Heredity


BACKGROUND: Shape of the dental root canal is highly patient specific. Automated identification methods of themedial line of dental root canals and the reproduction of their 3D shape can be beneficial forplanning endodontic interventions as severely curved root canals or multi-rooted teeth may posetreatment challenges. Accurate shape information of the root canals may also be used bymanufacturers of endodontic instruments in order to make more efficient clinical tools. METHOD: Novel image processing procedures dedicated to the automated detection of the medial axis of theroot canal from dental micro-CT and cone-beam CT records are developed. For micro-CT, the 3Dmodel of the root canal is built up from several hundred parallel cross sections, using imageenhancement, histogram based fuzzy c-means clustering, center point detection in the segmentedslice, three dimensional inner surface reconstruction, and potential field driven curve skeletonextraction in three dimensions. Cone-beam CT records are processed with image enhancement filtersand fuzzy chain based regional segmentation, followed by the reconstruction of the root canalsurface and detecting its skeleton via a mesh contraction algorithm. RESULTS: The proposed medial line identification and root canal detection algorithms are validated on clinicaldata sets. 25 micro-CT and 36 cone-beam-CT records are used in the validation procedure. Theoverall success rate of the automatic dental root canal identification was about 92% in bothprocedures. The algorithms proved to be accurate enough for endodontic therapy planning. CONCLUSIONS: Accurate medial line identification and shape detection algorithms of dental root canal have beendeveloped. Different procedures are defined for micro-CT and cone-beam CT records. Theautomated execution of the subsequent processing steps allows easy application of the algorithms inthe dental care. The output data of the image processing procedures is suitable for mathematicalmodeling of the central line. The proposed methods can help automate the preparation and design ofseveral kinds of endodontic interventions.

Concepts: Canal, Analytic geometry, Canal+, Curve, Dimension, Endodontics, Endodontic therapy, Root canal


This study explores how contact angle hysteresis and titling angle relate with stickiness on superhydrophobic surfaces. The result indicates that contact angle hysteresis could not be mentioned as a proper factor to evaluate the surface stickiness. By analyzing the system pinning force of droplet placed on a titled surface, we concluded that both solid fraction and surface geometric factor are the critical factors determining the surface stickiness.

Concepts: Division, Fraction, Analytic geometry, Surface, Contact angle, Hysteresis, Differential geometry, Angle


This paper presents a vehicle autonomous localization method in local area of coal mine tunnel based on vision sensors and ultrasonic sensors. Barcode tags are deployed in pairs on both sides of the tunnel walls at certain intervals as artificial landmarks. The barcode coding is designed based on UPC-A code. The global coordinates of the upper left inner corner point of the feature frame of each barcode tag deployed in the tunnel are uniquely represented by the barcode. Two on-board vision sensors are used to recognize each pair of barcode tags on both sides of the tunnel walls. The distance between the upper left inner corner point of the feature frame of each barcode tag and the vehicle center point can be determined by using a visual distance projection model. The on-board ultrasonic sensors are used to measure the distance from the vehicle center point to the left side of the tunnel walls. Once the spatial geometric relationship between the barcode tags and the vehicle center point is established, the 3D coordinates of the vehicle center point in the tunnel’s global coordinate system can be calculated. Experiments on a straight corridor and an underground tunnel have shown that the proposed vehicle autonomous localization method is not only able to quickly recognize the barcode tags affixed to the tunnel walls, but also has relatively small average localization errors in the vehicle center point’s plane and vertical coordinates to meet autonomous unmanned vehicle positioning requirements in local area of coal mine tunnel.

Concepts: Frame of reference, Coordinate systems, Barcode, Polar coordinate system, Geometry, Geographic coordinate system, Analytic geometry, Coordinate system


Primates recognize complex objects such as faces with remarkable speed and reliability. Here, we reveal the brain’s code for facial identity. Experiments in macaques demonstrate an extraordinarily simple transformation between faces and responses of cells in face patches. By formatting faces as points in a high-dimensional linear space, we discovered that each face cell’s firing rate is proportional to the projection of an incoming face stimulus onto a single axis in this space, allowing a face cell ensemble to encode the location of any face in the space. Using this code, we could precisely decode faces from neural population responses and predict neural firing rates to faces. Furthermore, this code disavows the long-standing assumption that face cells encode specific facial identities, confirmed by engineering faces with drastically different appearance that elicited identical responses in single face cells. Our work suggests that other objects could be encoded by analogous metric coordinate systems. PAPERCLIP.

Concepts: Analytic geometry, Dimension, Brain, Face, Primate, Organism, Geometry, DNA


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


The proliferation of computer-aided design and additive manufacturing enables on-demand fabrication of complex, three-dimensional structures. However, combining the versatility of cell-laden hydrogels within the 3D printing process remains a challenge. Herein, we describe a facile and versatile method that integrates polymer networks (including hydrogels) with 3D-printed mechanical supports to fabricate multicomponent (bio)materials. The approach exploits surface tension to coat fenestrated surfaces with suspended liquid films that can be transformed into solid films. The operating parameters for the process are determined using a physical model, and complex geometric structures are successfully fabricated. We engineer, by tailoring the window geometry, scaffolds with anisotropic mechanical properties that compress longitudinally (~30% strain) without damaging the hydrogel coating. Finally, the process is amenable to high cell density encapsulation and co-culture. Viability (>95%) was maintained 28 days after encapsulation. This general approach can generate biocompatible, macroscale devices with structural integrity and anisotropic mechanical properties.

Concepts: Water, Geometry, Rapid manufacturing, Computer-aided engineering, System, Differential geometry, Liquid, Analytic geometry


For adhering to three-dimensional (3D) surfaces or objects, current adhesion systems are limited by a fundamental trade-off between 3D surface conformability and high adhesion strength. This limitation arises from the need for a soft, mechanically compliant interface, which enables conformability to nonflat and irregularly shaped surfaces but significantly reduces the interfacial fracture strength. In this work, we overcome this trade-off with an adhesion-based soft-gripping system that exhibits enhanced fracture strength without sacrificing conformability to nonplanar 3D surfaces. Composed of a gecko-inspired elastomeric microfibrillar adhesive membrane supported by a pressure-controlled deformable gripper body, the proposed soft-gripping system controls the bonding strength by changing its internal pressure and exploiting the mechanics of interfacial equal load sharing. The soft adhesion system can use up to ∼26% of the maximum adhesion of the fibrillar membrane, which is 14× higher than the adhering membrane without load sharing. Our proposed load-sharing method suggests a paradigm for soft adhesion-based gripping and transfer-printing systems that achieves area scaling similar to that of a natural gecko footpad.

Concepts: Pressure, Fracture, Analytic geometry, Surface, Adhesion, Materials science, Adhesive, Object-oriented programming


This paper presents localized and temporal control of release kinetics over 3-dimensional (3D) hybrid wound devices to improve wound-healing process. Imaging study is performed to extract wound bed geometry in 3D. Non-Uniform Rational B-Splines (NURBS) based surface lofting is applied to generate functionally graded regions. Diffusion-based release kinetics model is developed to predict time-based release of loaded modifiers for functionally graded regions. Multi-chamber single nozzle solid freeform dispensing system is used to fabricate wound devices with controlled dispensing concentration. Spatiotemporal control of biological modifiers thus enables a way to achieve target delivery to improve wound healing.

Concepts: Computer graphics, Analytic geometry, Scientific method, Control, 3D computer graphics, Interpolation, 2002 albums, Wound healing


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