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Concept: Circle


The ability to intercept uncooperative targets is key to many diverse flight behaviors, from courtship to predation. Previous research has looked for simple geometric rules describing the attack trajectories of animals, but the underlying feedback laws have remained obscure. Here, we use GPS loggers and onboard video cameras to study peregrine falcons, Falco peregrinus, attacking stationary targets, maneuvering targets, and live prey. We show that the terminal attack trajectories of peregrines are not described by any simple geometric rule as previously claimed, and instead use system identification techniques to fit a phenomenological model of the dynamical system generating the observed trajectories. We find that these trajectories are best-and exceedingly well-modeled by the proportional navigation (PN) guidance law used by most guided missiles. Under this guidance law, turning is commanded at a rate proportional to the angular rate of the line-of-sight between the attacker and its target, with a constant of proportionality (i.e., feedback gain) called the navigation constant (N). Whereas most guided missiles use navigation constants falling on the interval 3 ≤ N ≤ 5, peregrine attack trajectories are best fitted by lower navigation constants (median N < 3). This lower feedback gain is appropriate at the lower flight speed of a biological system, given its presumably higher error and longer delay. This same guidance law could find use in small visually guided drones designed to remove other drones from protected airspace.

Concepts: Circle, Attack, Falconry, Falcon, Rocket, Mathematical constant, Peregrine Falcon, Falconidae


OBJECTIVE Although 70% of football players in the United States are youth players (6-14 years old), most research on head impacts in football has focused on high school, collegiate, or professional populations. The objective of this study was to identify the specific activities associated with high-magnitude (acceleration > 40g) head impacts in youth football practices. METHODS A total of 34 players (mean age 9.9 ± 0.6 years) on 2 youth teams were equipped with helmet-mounted accelerometer arrays that recorded head accelerations associated with impacts in practices and games. Videos of practices and games were used to verify all head impacts and identify specific drills associated with each head impact. RESULTS A total of 6813 impacts were recorded, of which 408 had accelerations exceeding 40g (6.0%). For each type of practice drill, impact rates were computed that accounted for the length of time that teams spent on each drill. The tackling drill King of the Circle had the highest impact rate (95% CI 25.6-68.3 impacts/hr). Impact rates for tackling drills (those conducted without a blocker [95% CI 14.7-21.9 impacts/hr] and those with a blocker [95% CI 10.5-23.1 impacts/hr]) did not differ from game impact rates (95% CI 14.2-21.6 impacts/hr). Tackling drills were observed to have a greater proportion (between 40% and 50%) of impacts exceeding 60g than games (25%). The teams in this study participated in tackling or blocking drills for only 22% of their overall practice times, but these drills were responsible for 86% of all practice impacts exceeding 40g. CONCLUSIONS In youth football, high-magnitude impacts occur more often in practices than games, and some practice drills are associated with higher impact rates and accelerations than others. To mitigate high-magnitude head impact exposure in youth football, practices should be modified to decrease the time spent in drills with high impact rates, potentially eliminating a drill such as King of the Circle altogether.

Concepts: United States, Shock, Drill, Circle, Acceleration, Impact factor, American football, Specific force


Introduction: In this study the angiogenetic effect of sintered 45S5 Bioglass® was quantitatively assessed for the first time in the arteriovenous loop model. Materials and Methods: An arteriovenous loop was created by interposition of a venous graft from the contralateral side between the femoral artery and vein in the medial thigh of 8 rats. The loop was placed in a teflon isolation chamber and was embedded in a sintered 45S5 Bioglass® granula matrix filled with fibrin gel. Specimens were investigated three weeks postoperatively by means of micro-computed tomography, histological and morphometrical techniques. Results: All animals tolerated the operations well. At 3 weeks both, micro-computed tomography and histology demonstrated a dense network of newly formed vessels originating from the AV loop. All constructs were filled with cell-rich, highly vascularised connective tissue around the vascular axis. Analysis of vessel diameter revealed constant small vessel diameters indicating immature new vessel sprouts. Conclusion: This study shows for the first time axial vascularization of a sintered 45S5 Bioglass® granula matrix. After three weeks the newly generated vascular network already interfused most parts of the scaffolds and showed signs of immaturity. The intrinsic type of vascularisation allows transplantation of the entire construct using the AV loop pedicle.

Concepts: Blood, Blood vessel, Histology, Artery, Vein, Circle, Femoral artery, Deep vein


Venn diagrams with three curves are used extensively in various medical and scientific disciplines to visualize relationships between data sets and facilitate data analysis. The area of the regions formed by the overlapping curves is often directly proportional to the cardinality of the depicted set relation or any other related quantitative data. Drawing these diagrams manually is difficult and current automatic drawing methods do not always produce appropriate diagrams. Most methods depict the data sets as circles, as they perceptually pop out as complete distinct objects due to their smoothness and regularity. However, circles cannot draw accurate diagrams for most 3-set data and so the generated diagrams often have misleading region areas. Other methods use polygons to draw accurate diagrams. However, polygons are non-smooth and non-symmetric, so the curves are not easily distinguishable and the diagrams are difficult to comprehend. Ellipses are more flexible than circles and are similarly smooth, but none of the current automatic drawing methods use ellipses. We present eulerAPE as the first method and software that uses ellipses for automatically drawing accurate area-proportional Venn diagrams for 3-set data. We describe the drawing method adopted by eulerAPE and we discuss our evaluation of the effectiveness of eulerAPE and ellipses for drawing random 3-set data. We compare eulerAPE and various other methods that are currently available and we discuss differences between their generated diagrams in terms of accuracy and ease of understanding for real world data.

Concepts: Scientific method, Sample size, Function, Circle, Venn diagram, Illustration, Ellipse, Technical drawing


In this first of three articles we show construction of the articular part of the elytron, the root. The root bears a conspicuous field of campaniform sensilla. This field was studied using light and scanning electron microscopes. Diversity of shape of the field among beetles, types of orientation of elongated sensilla within the field, individual variability of their number among conspecifics are demonstrated. Elongated sensilla point to the junction of the elytron with the second axillary plate. Presumably, they monitor twist movement in this junction which is possible if the elytron is open. The goal of the whole project is to reveal the effect of both structure and function of the hind wings and elytra on morphology of this mechanosensory field. Our data on allometric relationships between the animal size and quantitative characteristics of the field in normally flying beetles provide an important background for further functional analysis of this sensory organ. We selected 14 series of several species belonging to the same taxon but differing in size from big to small. It is revealed that the area of the sensory field is directly proportional to the elytral area, whereas the number of sensilla is proportional to the square root of the elytral area. Despite the great range in the elytral area (1500 times) in series of selected species the area of an external pit or cap of a single sensillum varies only 25-fold. The density of sensilla per unit area of the sensory field increases with a decrease of the elytral area.

Concepts: Function, Visual system, Vector space, Beetle, Circle, Scanning electron microscope, Complex number, Elytron


BACKGROUND The circle of Willis is a major collateral pathway important in ischemic conditions. The aim of our study was to assess the structural characteristics of the circle of Willis within the Turkish adult population, along with variations and arteries involved in the measurement of diameters and lengths on cranial computed tomography angiography (CTA). MATERIAL AND METHODS One hundred adult patients who underwent CTA images were evaluated retrospectively. RESULTS Results of the study revealed 82% adult, 17% fetal, and 1% transitional configurations. A complete polygonal structure was observed in 28% of cases. Variations of the circle of Willis were more common in the posterior portion. Hypoplasia was found to be the most common variation and was observed as a maximum in the posterior communicating artery (AComP). CONCLUSIONS The patency and size of arteries in the circle of Willis are important in occlusive cerebrovascular diseases and cerebrovascular surgery. Although CTA is an easily accessible non-invasive clinical method for demonstrating the vascular structure, CTA should be evaluated taking into account image resolution quality and difficulties in the identification of small vessels.

Concepts: Blood vessel, Medical imaging, Posterior communicating artery, Cardiovascular system, Circle, Circle of Willis, Posterior cerebral artery


Studies have shown the effectiveness of cervical disk replacement. However, clinical outcomes, particularly by radiographic assessment during the 36-month follow-up visit, have not been reported for cervical disk replacement with Mobi-C (LDR, Austin, Texas) disk prostheses. A retrospective study was conducted at 10 centers across China and included 65 patients who underwent single-level Mobi-C disk prosthesis replacement from October 2009 to July 2010. Clinical and radiographic data were collected before replacement, 7 days postoperatively, and 1, 3, 6, 12, 24, and 36 months postoperatively. Clinical and neurologic outcomes were assessed by the Japanese Orthopaedic Association (JOA) score, visual analog scale (VAS), Neck Disability Index (NDI), and Odom’s criteria. Static and dynamic radiographs were measured to determine intervertebral height and range of motion (ROM) of the cervical spine, the functional spinal unit, the treated segment, and adjacent segments. JOA, VAS, and NDI scores showed statistically significant improvement 36 months after replacement (P<.05). The ROM of the cervical spine, functional spinal unit, treated segment, and adjacent segments did not show a significant difference before and after replacement (P>.05). The intervertebral height of the treated segment increased significantly, and the intervertebral height of adjacent segments showed no statistical significance between time points and at follow-up. Clinical outcomes indicated that Mobi-C artificial cervical disk replacement is reliable. Radiographic data showed that it plays a role in reconstruction or maintenance of intervertebral height and ROM of the cervical spine, functional spinal unit, treated segment, and adjacent segments after Mobi-C cervical disk replacement.

Concepts: Statistics, Statistical significance, Vertebral column, Ronald Fisher, Statistical hypothesis testing, Circle, Artificial organ, Cervical vertebrae


The ability to wirelessly power electrical devices is becoming of greater urgency as a component of energy conservation and sustainability efforts. Due to health and safety concerns, most wireless power transfer (WPT) schemes utilize very low frequency, quasi-static, magnetic fields; power transfer occurs via magneto-inductive (MI) coupling between conducting loops serving as transmitter and receiver. At the “long range” regime - referring to distances larger than the diameter of the largest loop - WPT efficiency in free space falls off as (1/d)(6); power loss quickly approaches 100% and limits practical implementations of WPT to relatively tight distances between power source and device. A “superlens”, however, can concentrate the magnetic near fields of a source. Here, we demonstrate the impact of a magnetic metamaterial (MM) superlens on long-range near-field WPT, quantitatively confirming in simulation and measurement at 13-16 MHz the conditions under which the superlens can enhance power transfer efficiency compared to the lens-less free-space system.

Concepts: Electromagnetism, Energy, Circle, Sustainability, Radio, Wireless, Transmitter power output, Wireless energy transfer


Applying uniform electric field (EF) in vitro in the physiological range has been achieved in rectangular shaped microchannels. However, in a circular-shaped device, it is difficult to create uniform EF from two electric potentials due to different electrical resistances originated from the length difference between the diameter of the circle and the length of any parallel chord of the bottom circular chamber where cells are cultured. To address this challenge, we develop a three-dimensional (3D) computer-aided designed (CAD) polymeric insert to create uniform EF in circular shaped multi-well culture plates. A uniform EF with a coefficient of variation (CV) of 1.2% in the 6-well plate can be generated with an effective stimulation area percentage of 69.5%. In particular, NIH/3T3 mouse embryonic fibroblast cells are used to validate the performance of the 3D designed Poly(methyl methacrylate) (PMMA) inserts in a circular-shaped 6-well plate. The CAD based inserts can be easily scaled up (i.e., 100 mm dishes) to further increase effective stimulation area percentages, and also be implemented in commercially available cultureware for a wide variety of EF-related research such as EF-cell interaction and tissue regeneration studies.

Concepts: DNA, Electric potential, Extracellular matrix, Fibroblast, Cellular differentiation, Circle, Electrical resistance, Insert


The cerebrum of large mammals is convoluted, whereas that of small mammals is smooth. Mota and Herculano-Houzel (Reports, 3 July 2015, p. 74) inspired a model on an old theory that proposed a fractal geometry. I show that their model reduces to the product of gray-matter proportion times the folding index. This proportional relation describes the available data even better than the fractal model.

Concepts: Mathematics, Function, Database, Cerebral cortex, Mammal, Topology, Set theory, Circle