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"Geometric shapes"
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Shapes and patterns in nature
A motivating introduction to using essential non-fiction reading skills, children will love to find out about zebras' stripes, arches in the sky and where to find spirals.
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Morphological correlates of bite force and diet in the skull and mandible of phyllostomid bats
1. Bite force is an important performance measure for vertebrate and is related to a variety of ecological challenges. Phyllostomid bats present highly diversified feeding habits associated with extensive cranial shape divergence. Biomechanical models predict that the cranial shape changes are linked to dietary variation through bite force. However, the relationship of cranial shape, diet and bite force had not been explicitly tested before. 2. Here we use a combination of geometric morphometric techniques and comparative methods to test for morphological correlates of bite force and diet in 14 phyllostomid bat species. Skull and mandible shape variation were assessed by vectors, derived from a two-block partial least squares analysis of geometric shape and size-independent bite forces. The relationship between bite force, skull shape and diet was assessed by phylogenetic generalized least square regressions. 3. Most variation in the bite force data examined here (approximately 74%) was explained by size variation alone, but the shape vectors for both skull and mandible explained a significant part of the residual variation in bite force (83% and 56%, respectively), as did the dietary differences (56%). Although the first principal component of diet variation is associated with a negative correlation between insectivory and frugivory, residual bite force and cranial shape are not associated with this diet contrast. Shape and residual bite force variation in the sample were strongly associated with the second diet component, depicting an increase in nectarivory. 4. Species with stronger bites (insectivorous and frugivorous) than expected for their sizes presented a shorter rostrum and mandible, higher skulls, and more developed muscle attachment areas. On the other hand, the characteristic cranial elongation of nectarivorous species (supporting the long tongue) is a trade-off with bite force. These morphological correlates of bite force are similar to those observed in carnivores and non-herbivorous marsupials, and can be related to morphological characters used in biomechanical models for bite force prediction. 5. Our results reinforce the effectiveness of statistically integrating geometric shape variables to bite force and diet information in the investigation of patterns of cranial shape change and trophic radiation in ecologically diverse vertebrate groups.
Journal Article
Marquardt inverse modeling of the residual gravity anomalies due to simple geometric structures: A case study of chromite deposit
In this paper, an inversion method based on the Marquardt’s algorithm is presented to invert the gravity anomaly of the simple geometric shapes. The inversion outputs are the depth and radius parameters. We investigate three different shapes, i.e. the sphere, infinite horizontal cylinder and semi-infinite vertical cylinder for modeling. The proposed method is used for analyzing the gravity anomalies from assumed models with different initial parameters in all cases as the synthetic data are without noise and also corrupted with noise to evaluate the ability of the procedure. We also employ this approach for modeling the gravity anomaly due to a chromite deposit mass, situated east of Sabzevar, Iran. The lowest error between the theoretical anomaly and computed anomaly from inverted parameters, determine the shape of the causative mass. The inversion using different initial models for the theoretical gravity and also for real gravity data yields approximately consistent solutions. According to the interpreted parameters, the best shape that can imagine for the gravity anomaly source is the vertical cylinder with a depth to top of 7.4 m and a radius of 11.7 m.
Journal Article
Engineering the shape and structure of materials by fractal cut
In this paper we discuss the transformation of a sheet of material into a wide range of desired shapes and patterns by introducing a set of simple cuts in a multilevel hierarchy with different motifs. Each choice of hierarchical cut motif and cut level allows the material to expand into a unique structure with a unique set of properties. We can reverse-engineer the desired expanded geometries to find the requisite cut pattern to produce it without changing the physical properties of the initial material. The concept was experimentally realized and applied to create an electrode that expands to >800% the original area with only very minor stretching of the underlying material. The generality of our approach greatly expands the design space for materials so that they can be tuned for diverse applications.
Journal Article
A Generalized K Statistic for Estimating Phylogenetic Signal from Shape and Other High-Dimensional Multivariate Data
Phylogenetic signal is the tendency for closely related species to display similar trait values due to their common ancestry. Several methods have been developed for quantifying phylogenetic signal in univariate traits and for sets of traits treated simultaneously, and the statistical properties of these approaches have been extensively studied. However, methods for assessing phylogenetic signal in high-dimensional multivariate traits like shape are less well developed, and their statistical performance is not well characterized. In this article, I describe a generalization of the statistic of Blomberg et al. that is useful for quantifying and evaluating phylogenetic signal in highly dimensional multivariate data. The method (Kmult) is found from the equivalency between statistical methods based on covariance matrices and those based on distance matrices. Using computer simulations based on Brownian motion, I demonstrate that the expected value of Kmult remains at 1.0 as trait variation among species is increased or decreased, and as the number of trait dimensions is increased. By contrast, estimates of phylogenetic signal found with a squared-change parsimony procedure for multivariate data change with increasing trait variation among species and with increasing numbers of trait dimensions, confounding biological interpretations. I also evaluate the statistical performance of hypothesis testing procedures based on and find that the method displays appropriate Type I error and high statistical power for detecting phylogenetic signal in highdimensional data. Statistical properties of Kmult were consistent for simulations using bifurcating and random phylogenies, for simulations using different numbers of species, for simulations that varied the number of trait dimensions, and for different underlying models of trait covariance structure. Overall these findings demonstrate that provides a useful means of evaluating phylogenetic signal in high-dimensional multivariate traits. Finally, I illustrate the utility of the new approach by evaluating the strength of phylogenetic signal for head shape in a lineage of Plethodon salamanders.
Journal Article
Impediments to Kindergarten Children Identifying Geometric Shapes
Research shows that children aged 3 to 6 years do not fully grasp the concept of geometric shapes. This paper aims to examine children's intuitive knowledge of triangles and squares. We analysed the effects of distractors on identification and the neglected properties of (non)examples. The purpose of the study was to establish the developmental path in the identification of shapes. It was operationalized by determining types of interfering distractors in shape recognition and properties neglected. The data obtained from individual interviews were processed by the method of statistical and descriptive qualitative analysis. A classification was made of distractors and properties of non-examples affecting identification.
Journal Article
Fisher information and entanglement of non-Gaussian spin states
Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian statistics. Here, we report on the creation and characterization of non-Gaussian many-body entangled states. We develop a general method to extract the Fisher information, which reveals that the quantum dynamics of a classically unstable system creates quantum states that are not spin squeezed but nevertheless entangled. The extracted Fisher information quantifies metrologically useful entanglement, which we confirm by Bayesian phase estimation with sub–shot-noise sensitivity. These methods are scalable to large particle numbers and applicable directly to other quantum systems.
Journal Article
Temperature-memory polymer actuators
Reading out the temperature-memory of polymers, which is their ability to remember the temperature where they were deformed recently, is thus far unavoidably linked to erasing this memory effect. Here temperature-memory polymer actuators (TMPAs) based on cross-linked copolymer networks exhibiting a broad melting temperature range (Δ T ₘ) are presented, which are capable of a long-term temperature-memory enabling more than 250 cyclic thermally controlled actuations with almost constant performance. The characteristic actuation temperatures T ₐcₜs of TMPAs can be adjusted by a purely physical process, guiding a directed crystallization in a temperature range of up to 40 °C by variation of the parameter T ₛₑₚ in a nearly linear correlation. The temperature T ₛₑₚ divides Δ T ₘ into an upper T ₘ range (T > T ₛₑₚ) forming a reshapeable actuation geometry that determines the skeleton and a lower T ₘ range (T < T ₛₑₚ) that enables the temperature-controlled bidirectional actuation by crystallization-induced elongation and melting-induced contraction. The macroscopic bidirectional shape changes in TMPAs could be correlated with changes in the nanostructure of the crystallizable domains as a result of in situ X-ray investigations. Potential applications of TMPAs include heat engines with adjustable rotation rate and active building facades with self-regulating sun protectors.
Journal Article
Simulation as an engine of physical scene understanding
In a glance, we can perceive whether a stack of dishes will topple, a branch will support a child’s weight, a grocery bag is poorly packed and liable to tear or crush its contents, or a tool is firmly attached to a table or free to be lifted. Such rapid physical inferences are central to how people interact with the world and with each other, yet their computational underpinnings are poorly understood. We propose a model based on an “intuitive physics engine,” a cognitive mechanism similar to computer engines that simulate rich physics in video games and graphics, but that uses approximate, probabilistic simulations to make robust and fast inferences in complex natural scenes where crucial information is unobserved. This single model fits data from five distinct psychophysical tasks, captures several illusions and biases, and explains core aspects of human mental models and common-sense reasoning that are instrumental to how humans understand their everyday world.
Journal Article