Functions of Multivector Variables

As is well known, the common elementary functions defined over the real numbers can be generalized to act not only over the complex number field but also over the skew (non-commuting) field of the quaternions. In this paper, we detail a number of elementary functions extended to act over the skew field of Clifford multivectors, in both two and three dimensions. Complex numbers, quaternions and Cartesian vectors can be described by the various components within a Clifford multivector and from our results we are able to demonstrate new inter-relationships between these algebraic systems. One key relationship that we discover is that a complex number raised to a vector power produces a quaternion thus combining these systems within a single equation. We also find a single formula that produces the square root, amplitude and inverse of a multivector over one, two and three dimensions. Finally, comparing the functions over different dimension we observe that C?(?³) provides a particularly versatile algebraic framework.     

Misshapen decreases integrin levels to promote epithelial motility and planar polarity in Drosophila

Complex organ shapes arise from the coordinate actions of individual cells. The Drosophila egg chamber is an organ-like structure that lengthens along its anterior–posterior axis as it grows. This morphogenesis depends on an unusual form of planar polarity in the organ’s outer epithelial layer, the follicle cells. Interestingly, this epithelium also undergoes a directed migration that causes the egg chamber to rotate around its anterior–posterior axis. However, the functional relationship between planar polarity and migration in this tissue is unknown. We have previously reported that mutations in the Misshapen kinase disrupt follicle cell planar polarity. Here we show that Misshapen’s primary role in this system is to promote individual cell motility. Misshapen decreases integrin levels at the basal surface, which may facilitate detachment of each cell’s trailing edge. These data provide mechanistic insight into Misshapen’s conserved role in cell migration and suggest that follicle cell planar polarity may be an emergent property of individual cell migratory behaviors within the epithelium.     

Nonequilibrium Brownian Motion beyond the Effective Temperature

The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein’s relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of thermal equilibrium resulting in at least two main scenarios. With well separated timescales, as in aging glassy systems, equilibrium Fluctuation-Dissipation Theorem applies at each scale with its own “effective” temperature. With mixed timescales, as for example in active or granular fluids or in turbulence, temperature is no more well-defined, the dynamical nature of fluctuations fully emerges and a Generalized Fluctuation-Dissipation Theorem (GFDT) applies. Here, we study experimentally the mixed timescale regime by studying fluctuations and linear response in the Brownian motion of a rotating intruder immersed in a vibro-fluidized granular medium. Increasing the packing fraction, the system is moved from a dilute single-timescale regime toward a denser multiple-timescale stage. Einstein’s relation holds in the former and is violated in the latter. The violation cannot be explained in terms of effective temperatures, while the GFDT is able to impute it to the emergence of a strong coupling between the intruder and the surrounding fluid. Direct experimental measurements confirm the development of spatial correlations in the system when the density is increased.     

Your Space or Mine? Mapping Self in Time

While humans are capable of mentally transcending the here and now, this faculty for mental time travel (MTT) is dependent upon an underlying cognitive representation of time. To this end, linguistic, cognitive and behavioral evidence has revealed that people understand abstract temporal constructs by mapping them to concrete spatial domains (e.g. past = backward, future = forward). However, very little research has investigated factors that may determine the topographical characteristics of these spatiotemporal maps. Guided by the imperative role of episodic content for retrospective and prospective thought (i.e., MTT), here we explored the possibility that the spatialization of time is influenced by the amount of episodic detail a temporal unit contains. In two experiments, participants mapped temporal events along mediolateral (Experiment 1) and anterioposterior (Experiment 2) spatial planes. Importantly, the temporal units varied in self-relevance as they pertained to temporally proximal or distal events in the participant’s own life, the life of a best friend or the life of an unfamiliar other. Converging evidence from both experiments revealed that the amount of space used to represent time varied as a function of target (self, best friend or unfamiliar other) and temporal distance. Specifically, self-time was represented as occupying more space than time pertaining to other targets, but only for temporally proximal events. These results demonstrate the malleability of space-time mapping and suggest that there is a self-specific conceptualization of time that may influence MTT as well as other temporally relevant cognitive phenomena.     

People’s desire to be in nature and how they experience it are partially heritable

Nature experiences have been linked to mental and physical health. Despite the importance of understanding what determines individual variation in nature experience, the role of genes has been overlooked. Here, using a twin design (TwinsUK, number of individuals = 2,306), we investigate the genetic and environmental contributions to a person’s nature orientation, opportunity (living in less urbanized areas), and different dimensions of nature experience (frequency and duration of public nature space visits and frequency and duration of garden visits). We estimate moderate heritability of nature orientation (46%) and nature experiences (48% for frequency of public nature space visits, 34% for frequency of garden visits, and 38% for duration of garden visits) and show their genetic components partially overlap. We also find that the environmental influences on nature experiences are moderated by the level of urbanization of the home district. Our study demonstrates genetic contributions to individuals’ nature experiences, opening a new dimension for the study of human–nature interactions.

Nature experiences have been linked to mental and physical health. This twin study reveals genetic influences on an individual’s orientation towards nature and nature experiences, opening a new dimension to understanding human-nature interactions.     

The Avian Head Induces Cues for Sound Localization in Elevation

Accurate sound source localization in three-dimensional space is essential for an animal’s orientation and survival. While the horizontal position can be determined by interaural time and intensity differences, localization in elevation was thought to require external structures that modify sound before it reaches the tympanum. Here we show that in birds even without external structures like pinnae or feather ruffs, the simple shape of their head induces sound modifications that depend on the elevation of the source. Based on a model of localization errors, we show that these cues are sufficient to locate sounds in the vertical plane. These results suggest that the head of all birds induces acoustic cues for sound localization in the vertical plane, even in the absence of external ears.     

Re-Examination of Globally Flat Space-Time

In the following, we offer a novel approach to modeling the observed effects currently attributed to the theoretical concepts of “dark energy,” “dark matter,” and “dark flow.” Instead of assuming the existence of these theoretical concepts, we take an alternative route and choose to redefine what we consider to be inertial motion as well as what constitutes an inertial frame of reference in flat space-time. We adopt none of the features of our current cosmological models except for the requirement that special and general relativity be local approximations within our revised definition of inertial systems. Implicit in our ideas is the assumption that at “large enough” scales one can treat objects within these inertial systems as point-particles having an insignificant effect on the curvature of space-time. We then proceed under the assumption that time and space are fundamentally intertwined such that time- and spatial-translational invariance are not inherent symmetries of flat space-time (i.e., observable clock rates depend upon both relative velocity and spatial position within these inertial systems) and take the geodesics of this theory in the radial Rindler chart as the proper characterization of inertial motion. With this commitment, we are able to model solely with inertial motion the observed effects expected to be the result of “dark energy,” “dark matter,” and “dark flow.” In addition, we examine the potential observable implications of our theory in a gravitational system located within a confined region of an inertial reference frame, subsequently interpreting the Pioneer anomaly as support for our redefinition of inertial motion. As well, we extend our analysis into quantum mechanics by quantizing for a real scalar field and find a possible explanation for the asymmetry between matter and antimatter within the framework of these redefined inertial systems.     

Does Subjective Rating Reflect Behavioural Coding? Personality in 2 Month-Old Dog Puppies: An Open-Field Test and Adjective-Based Questionnaire

A number of studies have recently investigated personality traits in non-human species, with the dog gaining popularity as a subject species for research in this area. Recent research has shown the consistency of personality traits across both context and time for adult dogs, both when using questionnaire based methods of investigation and behavioural analyses of the dogs’ behaviour. However, only a few studies have assessed the correspondence between these two methods, with results varying considerably across studies. Furthermore, most studies have focused on adult dogs, despite the fact that an understanding of personality traits in young puppies may be important for research focusing on the genetic basis of personality traits. In the current study, we sought to evaluate the correspondence between a questionnaire based method and the in depth analyses of the behaviour of 2-month old puppies in an open-field test in which a number of both social and non-social stimuli were presented to the subjects. We further evaluated consistency of traits over time by re-testing a subset of puppies. The correspondence between methods was high and test- retest consistency (for the main trait) was also good using both evaluation methods. Results showed clear factors referring to the two main personality traits ‘extroversion,’ (i.e. the enthusiastic, exuberant approach to the stimuli) and ‘neuroticism,’ (i.e. the more cautious and fearful approach to the stimuli), potentially similar to the shyness-boldness dimension found in previous studies. Furthermore, both methods identified an ‘amicability’ dimension, expressing the positive interactions the pups directed at the humans stranger, and a ‘reservedness’ dimension which identified pups who largely chose not to interact with the stimuli, and were defined as quiet and not nosey in the questionnaire.     

Kinematics of Visually-Guided Eye Movements

One of the hallmarks of an eye movement that follows Listing’s law is the half-angle rule that says that the angular velocity of the eye tilts by half the angle of eccentricity of the line of sight relative to primary eye position. Since all visually-guided eye movements in the regime of far viewing follow Listing’s law (with the head still and upright), the question about its origin is of considerable importance. Here, we provide theoretical and experimental evidence that Listing’s law results from a unique motor strategy that allows minimizing ocular torsion while smoothly tracking objects of interest along any path in visual space. The strategy consists in compounding conventional ocular rotations in meridian planes, that is in horizontal, vertical and oblique directions (which are all torsion-free) with small linear displacements of the eye in the frontal plane. Such compound rotation-displacements of the eye can explain the kinematic paradox that the fixation point may rotate in one plane while the eye rotates in other planes. Its unique signature is the half-angle law in the position domain, which means that the rotation plane of the eye tilts by half-the angle of gaze eccentricity. We show that this law does not readily generalize to the velocity domain of visually-guided eye movements because the angular eye velocity is the sum of two terms, one associated with rotations in meridian planes and one associated with displacements of the eye in the frontal plane. While the first term does not depend on eye position the second term does depend on eye position. We show that compounded rotation - displacements perfectly predict the average smooth kinematics of the eye during steady- state pursuit in both the position and velocity domain.     

A Flexible Calibration Method Using the Planar Target with a Square Pattern for Line Structured Light Vision System

A flexible calibration approach for line structured light vision system is proposed in this paper. Firstly a camera model is established by transforming the points from the 2D image plane to the world coordinate frame, and the intrinsic parameters of camera can be obtained accurately. Then a novel calibration method for structured light projector is presented by moving a planar target with a square pattern randomly, and the method mainly involves three steps: first, a simple linear model is proposed, by which the plane equation of the target at any orientations can be determined based on the square’s geometry information; second, the pixel coordinates of the light stripe center on the target images are extracted as the control points; finally, the points are projected into the camera coordinate frame with the help of the intrinsic parameters and the plane equations of the target, and the structured light plane can be determined by fitting these three-dimensional points. The experimental data show that the method has good repeatability and accuracy.     

Parrondo’s Games Based on Complex Networks and the Paradoxical Effect

Parrondo’s games were first constructed using a simple tossing scenario, which demonstrates the following paradoxical situation: in sequences of games, a winning expectation may be obtained by playing the games in a random order, although each game (game A or game B) in the sequence may result in losing when played individually. The available Parrondo’s games based on the spatial niche (the neighboring environment) are applied in the regular networks. The neighbors of each node are the same in the regular graphs, whereas they are different in the complex networks. Here, Parrondo’s model based on complex networks is proposed, and a structure of game B applied in arbitrary topologies is constructed. The results confirm that Parrondo’s paradox occurs. Moreover, the size of the region of the parameter space that elicits Parrondo’s paradox depends on the heterogeneity of the degree distributions of the networks. The higher heterogeneity yields a larger region of the parameter space where the strong paradox occurs. In addition, we use scale-free networks to show that the network size has no significant influence on the region of the parameter space where the strong or weak Parrondo’s paradox occurs. The region of the parameter space where the strong Parrondo’s paradox occurs reduces slightly when the average degree of the network increases.     

Ecological Niche Transferability Using Invasive Species as a Case Study

Species distribution modeling is widely applied to predict invasive species distributions and species range shifts under climate change. Accurate predictions depend upon meeting the assumption that ecological niches are conserved, i.e., spatially or temporally transferable. Here we present a multi-taxon comparative analysis of niche conservatism using biological invasion events well documented in natural history museum collections. Our goal is to assess spatial transferability of the climatic niche of a range of noxious terrestrial invasive species using two complementary approaches. First we compare species’ native versus invasive ranges in environmental space using two distinct methods, Principal Components Analysis and Mahalanobis distance. Second we compare species’ native versus invaded ranges in geographic space as estimated using the species distribution modeling technique Maxent and the comparative index Hellinger’s I. We find that species exhibit a range of responses, from almost complete transferability, in which the invaded niches completely overlap with the native niches, to a complete dissociation between native and invaded ranges. Intermediate responses included expansion of dimension attributable to either temperature or precipitation derived variables, as well as niche expansion in multiple dimensions. We conclude that the ecological niche in the native range is generally a poor predictor of invaded range and, by analogy, the ecological niche may be a poor predictor of range shifts under climate change. We suggest that assessing dimensions of niche transferability prior to standard species distribution modeling may improve the understanding of species’ dynamics in the invaded range.     

Interplay between Yersinia pestis and its flea vector in lipoate metabolism

To thrive, vector-borne pathogens must survive in the vector’s gut. How these pathogens successfully exploit this environment in time and space has not been extensively characterized. Using Yersinia pestis (the plague bacillus) and its flea vector, we developed a bioluminescence-based approach and employed it to investigate the mechanisms of pathogenesis at an unprecedented level of detail. Remarkably, lipoylation of metabolic enzymes, via the biosynthesis and salvage of lipoate, increases the Y. pestis transmission rate by fleas. Interestingly, the salvage pathway’s lipoate/octanoate ligase LplA enhances the first step in lipoate biosynthesis during foregut colonization but not during midgut colonization. Lastly, Y. pestis primarily uses lipoate provided by digestive proteolysis (presumably as lipoyl peptides) rather than free lipoate in blood, which is quickly depleted by the vector. Thus, spatial and temporal factors dictate the bacterium’s lipoylation strategies during an infection, and replenishment of lipoate by digestive proteolysis in the vector might constitute an Achilles’ heel that is exploited by pathogens.Subject terms: Bacterial pathogenesis, Metabolism     

Preference for Orientations Commonly Viewed for One’s Own Hand in the Anterior Intraparietal Cortex

Brain regions in the intraparietal and the premotor cortices selectively process visual and multisensory events near the hands (peri-hand space). Visual information from the hand itself modulates this processing potentially because it is used to estimate the location of one’s own body and the surrounding space. In humans specific occipitotemporal areas process visual information of specific body parts such as hands. Here we used an fMRI block-design to investigate if anterior intraparietal and ventral premotor ‘peri-hand areas’ exhibit selective responses to viewing images of hands and viewing specific hand orientations. Furthermore, we investigated if the occipitotemporal ‘hand area’ is sensitive to viewed hand orientation. Our findings demonstrate increased BOLD responses in the left anterior intraparietal area when participants viewed hands and feet as compared to faces and objects. Anterior intraparietal and also occipitotemporal areas in the left hemisphere exhibited response preferences for viewing right hands with orientations commonly viewed for one’s own hand as compared to uncommon own hand orientations. Our results indicate that both anterior intraparietal and occipitotemporal areas encode visual limb-specific shape and orientation information.     

Similar but Different: Dynamic Social Network Analysis Highlights Fundamental Differences between the Fission-Fusion Societies of Two Equid Species,the Onager and Grevy’s Zebra

Understanding why animal societies take on the form that they do has benefited from insights gained by applying social network analysis to patterns of individual associations. Such analyses typically aggregate data over long time periods even though most selective forces that shape sociality have strong temporal elements. By explicitly incorporating the temporal signal in social interaction data we re-examine the network dynamics of the social systems of the evolutionarily closely-related Grevy’s zebras and wild asses that show broadly similar social organizations. By identifying dynamic communities, previously hidden differences emerge: Grevy’s zebras show more modularity than wild asses and in wild asses most communities consist of solitary individuals; and in Grevy’s zebras, lactating females show a greater propensity to switch communities than non-lactating females and males. Both patterns were missed by static network analyses and in general, adding a temporal dimension provides insights into differences associated with the size and persistence of communities as well as the frequency and synchrony of their formation. Dynamic network analysis provides insights into the functional significance of these social differences and highlights the way dynamic community analysis can be applied to other species.     

Visualization of Chondrocyte Intercalation and Directional Proliferation via Zebrabow Clonal Cell Analysis in the Embryonic Meckel’s Cartilage

Development of the vertebrate craniofacial structures requires precise coordination of cell migration, proliferation, adhesion and differentiation. Patterning of the Meckel''s cartilage, a first pharyngeal arch derivative, involves the migration of cranial neural crest (CNC) cells and the progressive partitioning, proliferation and organization of differentiated chondrocytes. Several studies have described CNC migration during lower jaw morphogenesis, but the details of how the chondrocytes achieve organization in the growth and extension of Meckel’s cartilage remains unclear. The sox10 restricted and chemically induced Cre recombinase-mediated recombination generates permutations of distinct fluorescent proteins (RFP, YFP and CFP), thereby creating a multi-spectral labeling of progenitor cells and their progeny, reflecting distinct clonal populations. Using confocal time-lapse photography, it is possible to observe the chondrocytes behavior during the development of the zebrafish Meckel’s cartilage.Multispectral cell labeling enables scientists to demonstrate extension of the Meckel’s chondrocytes. During extension phase of the Meckel’s cartilage, which prefigures the mandible, chondrocytes intercalate to effect extension as they stack in an organized single-cell layered row. Failure of this organized intercalating process to mediate cell extension provides the cellular mechanistic explanation for hypoplastic mandible that we observe in mandibular malformations.     

Computational Effective Fault Detection by Means of Signature Functions

The paper presents a computationally effective method for fault detection. A system’s responses are measured under healthy and ill conditions. These signals are used to calculate so-called signature functions that create a signal space. The current system’s response is projected into this space. The signal location in this space easily allows to determine the fault. No classifier such as a neural network, hidden Markov models, etc. is required. The advantage of this proposed method is its efficiency, as computing projections amount to calculating dot products. Therefore, this method is suitable for real-time embedded systems due to its simplicity and undemanding processing capabilities which permit the use of low-cost hardware and allow rapid implementation. The approach performs well for systems that can be considered linear and stationary. The communication presents an application, whereby an industrial process of moulding is supervised. The machine is composed of forms (dies) whose alignment must be precisely set and maintained during the work. Typically, the process is stopped periodically to manually control the alignment. The applied algorithm allows on-line monitoring of the device by analysing the acceleration signal from a sensor mounted on a die. This enables to detect failures at an early stage thus prolonging the machine’s life.     

Robots with Display Screens: A Robot with a More Humanlike Face Display Is Perceived To Have More Mind and a Better Personality

It is important for robot designers to know how to make robots that interact effectively with humans. One key dimension is robot appearance and in particular how humanlike the robot should be. Uncanny Valley theory suggests that robots look uncanny when their appearance approaches, but is not absolutely, human. An underlying mechanism may be that appearance affects users’ perceptions of the robot’s personality and mind. This study aimed to investigate how robot facial appearance affected perceptions of the robot’s mind, personality and eeriness. A repeated measures experiment was conducted. 30 participants (14 females and 16 males, mean age 22.5 years) interacted with a Peoplebot healthcare robot under three conditions in a randomized order: the robot had either a humanlike face, silver face, or no-face on its display screen. Each time, the robot assisted the participant to take his/her blood pressure. Participants rated the robot’s mind, personality, and eeriness in each condition. The robot with the humanlike face display was most preferred, rated as having most mind, being most humanlike, alive, sociable and amiable. The robot with the silver face display was least preferred, rated most eerie, moderate in mind, humanlikeness and amiability. The robot with the no-face display was rated least sociable and amiable. There was no difference in blood pressure readings between the robots with different face displays. Higher ratings of eeriness were related to impressions of the robot with the humanlike face display being less amiable, less sociable and less trustworthy. These results suggest that the more humanlike a healthcare robot’s face display is, the more people attribute mind and positive personality characteristics to it. Eeriness was related to negative impressions of the robot’s personality. Designers should be aware that the face on a robot’s display screen can affect both the perceived mind and personality of the robot.     

Mating tactics determine patterns of condition dependence in a dimorphic horned beetle

The persistence of genetic variability in performance traits such as strength is surprising given the directional selection that such traits experience, which should cause the fixation of the best genetic variants. One possible explanation is ‘genic capture’ which is usually considered as a candidate mechanism for the maintenance of high genetic variability in sexual signalling traits. This states that if a trait is ‘condition dependent’, with expression being strongly influenced by the bearer''s overall viability, then genetic variability can be maintained via mutation-selection balance. Using a species of dimorphic beetle with males that gain matings either by fighting or by ‘sneaking’, we tested the prediction of strong condition dependence for strength, walking speed and testes mass. Strength was strongly condition dependent only in those beetles that fight for access to females. Walking speed, with less of an obvious selective advantage, showed no condition dependence, and testes mass was more condition dependent in sneaks, which engage in higher levels of sperm competition. Within a species, therefore, condition dependent expression varies between morphs, and corresponds to the specific selection pressures experienced by that morph. These results support genic capture as a general explanation for the maintenance of genetic variability in traits under directional selection.     

Development of Eye Position Dependency of Slow Phase Velocity during Caloric Stimulation

The nystagmus in patients with vestibular disorders often has an eye position dependency, called Alexander’s law, where the slow phase velocity is higher with gaze in the fast phase direction compared with gaze in the slow phase direction. Alexander’s law has been hypothesized to arise either due to adaptive changes in the velocity-to-position neural integrator, or as a consequence of processing of the vestibular-ocular reflex. We tested whether Alexander’s law arises only as a consequence of non-physiologic vestibular stimulation. We measured the time course of the development of Alexander’s law in healthy humans with nystagmus caused by three types of caloric vestibular stimulation: cold (unilateral inhibition), warm (unilateral excitation), and simultaneous bilateral bithermal (one side cold, the other warm) stimulation, mimicking the normal push-pull pattern of vestibular stimulation. Alexander’s law, measured as a negative slope of the velocity versus position curve, was observed in all conditions. A reversed pattern of eye position dependency (positive slope) was found <10% of the time. The slope often changed with nystagmus velocity (cross-correlation of nystagmus speed and slope was significant in 50% of cases), and the average lag of the slope with the speed was not significantly different from zero. Our results do not support the hypothesis that Alexander’s law can only be observed with non-physiologic vestibular stimulation. Further, the rapid development of Alexander’s law, while possible for an adaptive mechanism, is nonetheless quite fast compared to most other ocular motor adaptations. These results suggest that Alexander’s law may not be a consequence of a true adaptive mechanism.