The measurement of the elastic properties of cells is widely used as an indicator for cellular changes during differentiation, upon drug treatment, or resulting from the interaction with the supporting matrix. Elasticity is routinely quantified by indenting the cell with a probe of an AFM while applying nano-Newton forces. Because the resulting deformations are in the micrometer range, the measurements will be affected by the finite thickness of the cell, viscous effects and even cell damage induced by the experiment itself. Here, we have analyzed the response of single 3T3 fibroblasts that were indented with a micrometer-sized bead attached to an AFM cantilever at forces from 30–600 pN, resulting in indentations ranging from 0.2 to 1.2 micrometer. To investigate the cellular response at lower forces up to 10 pN, we developed an optical trap to indent the cell in vertical direction, normal to the plane of the coverslip. Deformations of up to two hundred nanometers achieved at forces of up to 30 pN showed a reversible, thus truly elastic response that was independent on the rate of deformation. We found that at such small deformations, the elastic modulus of 100 Pa is largely determined by the presence of the actin cortex. At higher indentations, viscous effects led to an increase of the apparent elastic modulus. This viscous contribution that followed a weak power law, increased at larger cell indentations. Both AFM and optical trapping indentation experiments give consistent results for the cell elasticity. Optical trapping has the benefit of a lower force noise, which allows a more accurate determination of the absolute indentation. The combination of both techniques allows the investigation of single cells at small and large indentations and enables the separation of their viscous and elastic components. Understanding the mechanics of cells has become increasingly important, since many cellular processes have been found to be regulated by, or linked to changes in the mechanical properties of the cell. Determining parameters such as the stiffness and the viscosity of cells is useful to understand cellular processes that involve mechanical changes and have been related to different conditions of the cell. Previously it was shown that during differentiation of cells, but also during the cell cycle, morphological changes of cells are in part governed by cell mechanics Animal cells have a highly complicated architecture with a plasma membrane that is relatively inextensible and supported by a ≈100 nm thin cortical layer. This cortical network is composed of actin filaments, actin-binding proteins including myosin motors, and encloses a crowded liquid environment, the cytoplasm. The different components of the cell all contribute to the cell-mechanical response, but in a manner that depends on the measurement technique and timescale of the experiment. A variety of techniques have successfully been applied to measure the mechanics of single cells, including atomic force microscopy (AFM) AFM which employs a probe to indent the cell, is often the method of choice to quantitatively measure the cell’s stiffness. As compared to other techniques the contact between the AFM probe and the cell can be reasonably well defined when the cell is indented in an almost vertical direction, normal to the coverslip. By using the Hertzian contact model, this symmetrical geometry of the experiment allows the extraction of the elastic Young’s modulus k) does not depend linear on the frequency (f) but obeys a weak power law: αk(f)∼ f α lies in the range 0.1–0.35, and depends on the part of the cell that is probed α a useful parameter to mechanically identify different structures of the cell.All of the aforementioned techniques have been applied to measure the mechanical response of cells at different loading rates (rheology). Although the variation in reported values for the absolute cell stiffness is large, most studies agree that cells respond stiffer when probed at higher frequencies. More recently it was recognized that the majority of the rheology experiments show that the cell stiffness  and to distinguish cellular responses upon forces below 10 pN. Using this technique, we were able to minimally indent the cells in the vertical direction, which enables us to calculate the Young’s modulus at small indentations (≈0.2 µm). To compare the mechanical response at larger (≈1 µm) indentations, we indented the cells with a bead that was attached to an AFM cantilever while applying forces of a few hundred pN.We found that at low indentation (<0.2 µm) the cell showed an almost ideal elastic response, whereas at larger indentation the measured cell stiffness was dependent on the loading rate, following a weak power law. These results indicate that to extract mechanical properties such as the Young’s modulus and the response to dynamic perturbations, it is important to take the complex composition of the cell into account. Different cell mechanical properties can be accessed by changing the depth of indentation. A vertically operating optical trap together with AFM measurements provide the tools to measure surface-adhered cells at small and large indentations and enables the separation of viscous and elastic components of the cell.We first investigated the cellular response at different forces by performing indentation measurements with a 1.98 µm diameter bead that was attached to an AFM cantilever . Under tTo quantify the relative amount of energy that was lost due to hysteresis during the AFM experiments, we compared the energy that was required to indent the cells and the energy that was recovered during the retraction. Any loss of energy will be visible as a difference between the curves. To quantify for each experiment the difference between the indentation and retraction energy, we numerically calculated the integrals for all indentation and retraction curves. To be able to measure the cellular response at lower forces we developed an optical trap that operates vertical with respect to the coverslip. Single cells were indented in the vertical direction with a 0.76 µm diameter bead that was held by the optical trap. The force is obtained by measuring the vertical displacement of the bead out of the centre of the focused laser beam see . When thE for the cell by fitting this 7–30 pN part using the Hertz model , and measured a slope of 88.5±8.27 µN/m (n = 21). In order to calculate the Young’s modulus we need to know the contact area. To obtain an estimate, we calculated the contact radius between the bead and the cell during the initial indentation. When the bead is pushed into the cell, cR will increase with the indentation . In order to test to what extent the cell follows this ideal behaviour we performed stretching instead of indenting experiments on the cells at forces below 10 pN. We made use of the fact that in about 50% of all optical trapping experiments the bead got stuck to the cell and could therefore be used as a handle to stretch the cell . To derieriments , a valueA variety of techniques have been employed during the last decades to measure cell mechanical responses upon stress. The obtained results have led to a picture of the cell as a complex composite material with both elastic and viscous components −4 N/m compared to 0.08 N/m for the AFM). The clear advantage of the optical trapping experiments is that the force noise is much lower due to the absence of a large cantilever, which allows more accurate force spectroscopic experiments at lower forces. The noise levels of conventional AFM cantilevers are around 20 pN To study the cell mechanical responses at very small deformations we constructed a vertically operating optical trap that allowed the application of forces of less than 10 pN, which will minimally disturb the physiological condition of the cell. The main difference as compared to the AFM is that the cantilever is replaced by a focused laser beam to hold the bead. With the optical trap a much lower spring constant is achieved , the estimated Young’s modulus is approximately twice as high as compared to what we found in the indentation experiments. A recent report, where lung fibroblast were indented and stretched with a flat-ended AFM tip, showed also an anisotropic response but in the opposite direction Using the optical trap we obtained a Young’s modulus of 100 Pa for fibroblasts. Previous measurements of the Young’s modulus using AFM had reported values that were 10 to 100-times higher Previous work by Rotsch and Radmacher showed that the cell’s mechanical response is determined to a large extend by the underlying cytoskeleton, when indented by AFM in the range of a few micrometers α = 0.13–0.17, whereas measurements that deformed the whole cell at larger deformations gave α = 0.24–0.29 As soon the cell is deformed for more than a few hundred nanometres the cell response is increasingly determined by viscous effects. Larger deformations will be much more sensitive to the cell interior, the cytoplasm and cell nucleus and the remodelling of the actin cytoskeleton will start to play a role. This results in an increase of the apparent Young’s modulus and a hysteresis between the indentation and retraction curves, both of which depend on the rate of deformation. This is also evident from multiple rheology experiments on cells that have showed that the frequency dependent stiffness of the cells follows a weak power law. A recent review on this topic showed that the majority of these experiments that probed the outermost layer of the cells at small deformations yielded values for the exponent α = 1) but decreases at higher deformation rates. Within a single AFM indentation experiment one can simply differentiate between small and large deformations by analyzing different parts of the indentation curves. Thus, within a single set of measurements we found α = 0.17 for deformations of ≈0.3 µm, and α = 0.31 for larger deformations of ≈1 µm. Both values are consistent with values described in the literature for small and large deformations α at forces below 10 pN.Also in our measurements the apparent modulus followed a weak power law, which shows that the cell’s viscosity is not constant  3T3 mouse embryonic fibroblasts  were grown in Dulbecco’s modified Eagle’s medium (DMEM) supplemented with 10% fetal bovine serum, and Penicillin/streptomycin . At least 24 hours before the experiment, cells were removed from the culture flasks with 0.25% trypsin/EDTA  and seeded onto poly-L lysine coated coverslips. Before the experiment, a coverslip containing the cells was briefly washed with modified Krebs’-Ringer solution , that was mounted on a custom built inverted optical microscope using an oil immersion objective . A coverslip containing the cells was mounted in an open sample chamber. First a cell was selected using the optical microscope. The AFM tip was brought down to indent the cell, during which the motion of the z-piezo and the applied force were recorded . The celThis problem was successfully solved by using cantilevers with a 1.98 µm diameter bead glued to the end . Under these conditions where a low force is distributed over a large area, we expect the induced cell damage to be negligible and the effects of the underlying substrate on the measured cell response to be small. To be able to detect and to apply low forces, we used cantilevers with a low spring constant of 0.08 N/m. All cantilevers were individually calibrated by fitting the power spectrum to a simple harmonic oscillator The optical trap that was used to indent the cells at low force was built around a commercial upright microscope body  and set up for trapping and detection vertical to the coverslip . The 980A coverslip containing the cells was mounted in a closed sample chamber, consisting of a microscope slide, a 100 µm thick spacer and the coverslip. Before the sample chamber was closed, polystyrene beads of 0.76 µm diameter  were added to the buffer.Although the trapping laser is focused onto the bead and outside of the cell, most of the laser light will pass through the cell for the duration of the experiment . To miniThe trap stiffness and the detector response were calibrated by recording the power spectrum of the position signal of the trapped bead and applying the equipartition theorem E from our indentation experiments we used the Hertz model that describes the indentation of a large elastic body with a rigid spherical indenter:To calculate the Young’s modulus F to increase exponentially with the indentation zd. bR is the bead radius and v the Poisson’s ratio for which we choose 0.4 cR will increase with the indentation:Eq. 1 predicts the force To calculate the Young’s modulus from our stretching experiments we used a variation on Eq. 1 that describes the deformation of a large elastic body with a disc shaped contact area cR is the radius of the disc shaped contact area between the bead and the cell. As long as this radius is constant the relation between F and zd will be linear.


For the design and characterization of ultrasonic particle manipulation devices the pressure field in the fluid cavity is of great interest. The schlieren method provides an optical tool for the visualization of such pressure fields. Due to its purely optical nature this experimental method has got some unique advantages compared to methods like particle tracking.A vertical schlieren setup and an investigation with the same of a mm-sized chamber used to agglomerate particles are presented here. The schlieren images show a two-dimensional representation of the whole pressure distribution recorded simultaneously with a good resolution in time. The gained description of the pressure field is shown to be in agreement with a numerical simulation. Thermal effects as well as streaming effects are shown.The results show the great potential of schlieren visualization to investigate ultrasonic particle manipulation devices. Visualized are pressure fields, acoustic streaming, temperature effects and effects caused by fluid volumes of different density. The schlieren method is a proven tool for the experimental characterization of optically transparent liquids and for the visualization of ultrasonic fields . This meAcoustic radiation forces  are exerf1 to pinhole diameter p the relation α∝p/f1 holds, where α is the beam deviation angle at the collimation lens L1 which should be as small as possible. For p there is a lower limit in the order of the Airy disc and Rayleigh criterion λ is the optical wavelength. The diffraction angle θ is given by sinθ = λ/Λ for the first intensity peak, where λ is the acoustic wavelength. The diffracted beam separation distance ε = θf2 is a measure for the sensitivity of the schlieren setup. For the work presented here the two field lenses  have a lens diameter of 50 mm where lens L1 is a planoconvex lens with a focal length of 250 mm and lens L2 is an achromatic lens doublet with a focal length of 400 mm which is also corrected for spherical aberration and coma. As light source a modified high power white LED with a 300 μm pinhole has been used. Since the acoustic devices are operated in quasi stationary mode relatively long camera exposure times can be used as compared to imaging of traveling waves. This eases the requirements for the light source and camera in terms of brightness. In the cut-off plane either a knife edge filter which allows to emphasize directional effects dependent on its rotational position or a dark field filter has been used. The camera objective is a Minolta 135 mm and the camera is a Lynx IPX-2M30-G resulting in a spatial resolution in the order of 20 μm /pixel. The focal plane of the objective is at the position of the acoustic device resulting in an image where the spacing of the interference fringes is equal to the ultrasonic wavelength multiplied by the lateral magnification of real images [The setup presented here is a conventional (Töpler) three lens schlieren system which has been mounted vertically as shown in Figure L. They are operated in the lower MHz frequency range. Assuming the optical axis to be parallel to the ultrasonic wave front and an optical wavelength λ of at least 700 nm the Klein-Cook parameter Q = 2 πλL/Λ2 ≪ 1 and thus Raman-Nath diffraction [L or length that the optical waves cross the acoustic waves, is sufficiently small for the effect of multiple diffraction to be neglected. The devices are excited with a 1 mm thick piezo electric element, Pz26, which is either directly glued to one of the chamber walls or first glued to an aluminium waveguide and then clamped to the device. The excitation signal is a frequency sweep of 1.5 MHz to 2.5 MHz modulated with a saw-tooth frequency of 0.05 Hz. This type of excitation allows to move particles or cells from one side of the chamber to another or back by reversing the frequency range. The devices are built up with three layers, a PMMA frame with 0.5 mm thick walls and a planar top and bottom cover which are either 250 μm PMMA foils or 0.5 mm glass slides. The glass is introduced to minimize disturbances in the optical path. A comparison of both cover materials did not show significant differences in the qualitative image of the acoustics.With a device that uses continuous frequency sweeping in combination with standing pressure fields, particles can be moved over larger distances using acoustic radiation forces . In macrfraction  is expecz-axis is along the optical axis of the schlieren setup. Figure y-axis significantly with a relatively small frequency change in the order of 1 kHz. This is an example that would be difficult to see with particle tracking as these changes are often too fast and or the amplitudes, and with it the primary acoustic radiation forces are too low. For many frequencies the simulation also shows low pressure amplitudes close to the two boundaries along y = 0 mm and y = 21 mm.Top views of the device are shown in Figure G is obtained with G = min) where B is the background image and F the front image. The front image is the schlieren image of interest. The resulting grain extract images have a pressure node where the local intensity field is the darkest, for both knife edge filter and dark field filter. Areas within the fluid chamber without a standing pressure wave present, or with one of low amplitude show no local variation in the schlieren image. Figure B is a schlieren image of the device without ultrasound and F a snap-shot image during sweeping at 2.105 MHz and 1.650 MHz obtained with the schlieren setup. For the image in b) a dark field filter has been used, revealing both the standing pressure field as well as changes in x- and y-direction. These changes appear to be in line with the numerical simulation, both in shape and response to small frequency changes. The schlieren image in c) is obtained with a knife edge filter in x-direction. The visualized nodal pressure planes show to be almost parallel with some disturbances around the four boundaries. The bright white stripe at the boundary along x = 0 mm close to the piezo element, as well as the other disturbances close to it are due to thermal gradients and convection caused by heat dissipation of the transducer. For prolonged experiments with high driving voltages and without cooling these thermal effects appear very clearly on the schlieren images.The schlieren images are shown as grain extract images. For images with a linear intensity range from 0 (black) to 1 (white) a grain extract image y = 0 mm and y = 21 mm) are in good agreement with the results from the numerical simulation as well as with the experiments with particles. They all indicate that close to these boundaries the pressure amplitudes are quite low. The schlieren images given here are from devices with 1 mm openings in two opposing corners  =  and  which will also have an effect on the pressure on the boundary. However experiments with closed cover slides as well as the numerical simulation which are both without these openings, indicate that the low pressure is only partly due to these openings. Some disturbances can also be caused by convection in the air, even though they should be small in a vertical setup where the airflow of rising air is parallel to the light path.The rather weakly developed schlieren image at the side boundaries (B used for the three shown grain extract images is an image right before the streaming burst starts. Like this any static part or low velocity change as e.g. the bubble will be suppressed, emphasizing high velocity changes like caused by fluid flow. The time passed between two images is 50 ms.Figure x = 16 mm to x = 18 mm at y = 4 mm in the reference frame given in Figure δx if started at x = 16.5 mm. For a starting point of particles closer to the transducer, that is with decreasing x, the distance δx increases. However the given uniformity of the pressure amplitude over time and periodicity over space of the pixel area shown here is not given for the whole fluid chamber within the same frequency range. Therefore a larger range spanning over 1 MHz is used.For the transport of particles the evolution in time of the pressure field is of interest. As an example a row of pixels from grain extract schlieren images over a time period of 4 s is shown in Figure xy-plane which can be visualized with the schlieren setup. The transient time for the change of these gradients is in the order of seconds. Structural vibrations in comparison have a significantly lower decay time, typically two or three orders of magnitude lower for the same frequency as these lower harmonics.With liquids of different density in the chamber even further phenomena can be visualized. One example is shown in Figure Schlieren visualization has proven to be a strong and simple tool to visualize standing pressure waves in ultrasonic micro manipulation devices. Both local and large scale pressure distributions can be imaged. Streaming effects as well as thermal effects can be studied at the same time as the pressure field. The method appears to be particularly suited to image changes over time while keeping the full resolution of the field. The quality of the imaging setup has the potential to be improved in order to record with higher sensitivity and homogeneity which can be achieved by introducing colour filters and light blocking filters of different shape  or with The authors declare that they have no competing interests.DM designed the ultrasonic device, performed the experiments and simulations and wrote the manuscript. ND proposed, built and tested an initial schlieren setup. DM refined the schlieren setup. JD contributed to the design of the study, revised the manuscript and is responsible for the research group. All authors read and approved the final manuscript.


It has been suggested that dogs display a secure base effect similar to that found in human children . In children, this effect influences their daily lives and importantly also their performance in cognitive testing. Here, we investigate the importance of the secure base effect for dogs in a problem-solving task.Using a manipulative task, we tested dogs in three conditions, in which we varied the owner's presence and behavior (Our study is the first to provide evidence for an owner-specific secure base effect in dogs that extends from attachment tests to other areas of dogs' lives and also manifests itself in cognitive testing – thereby confirming the remarkable similarity between the secure base effect in dogs and in human children. These results also have important implications for behavioral testing in dogs, because the presence or absence of the owner during a test situation might substantially influence dogs' motivation and therefore the outcome of the test. Based on ethological principles, Bowlby Domestic dogs have been closely associated with humans for about 15,000 years The aim of our study was to investigate the importance of the secure base effect for dogs in a behavioral test situation. In children the secure base effect is mostly investigated by comparing their motivation to play in the caregiver's presence and absence http://kutyaetologia.elte.hu) at the Department of Ethology of the Eötvös Loránd University in Budapest, Hungary. Prior to the experiments reported in this manuscript, the owners were informed about the details of the procedures of each experiment and were given the possibility to withdraw from participation. No special permission for use of dogs in non-invasive studies is required in Hungary. The relevant committee that allows conducting research without special permissions regarding animals is the University Institutional Animal Care and Use Committee . Since the owners were only required to interact with their dogs in their usual manner during the experiments and their behavior was not coded or analyzed, no approval for human experimentation was obtained. The participants in the video clips that are part of the supporting information have given written informed consent, as outlined in the PLOS consent form, to publication of themselves.Owners gave their written consent for participating in behavioral studies with their dogs when entering the database of volunteer participants of the Family Dog Research Program . Therefore, 20 dogs  completed the experiment. The sample consisted of 14 purebred dogs from three different FCI  breed groups  and 6 mixed-breed dogs.Dogs first had to pass a pre-test to ensure that they were motivated to manipulate an apparatus to get food and that they were willing to consume food even in the absence of the owner. Dogs that passed the pre-test by taking food in the absence of the owner progressed to the test phase. In the test phase, we used three different test conditions, in which we varied the presence of the owner and the owner's behavior:Condition “Absent owner” (cAO): The owner is not present in the experimental room during the trial.Condition “Silent owner” (cSO): The owner is present in the experimental room during the trial, but remains silent.Condition “Encouraging owner” (cEO): The owner is present in the experimental room during the trial and is encouraging the dog verbally.We used a within-subject design so that each dog received one trial in each of the three test conditions. The sequence of the conditions was counterbalanced across dogs.© Dog Pyramid , Hunter© Snack Bottle , Hunter© Snack Cactus , and Hunter© Rolling Snack  under which the food reward was placed. As apparatuses for the test we used four types of commercial interactive dog toys, which could be filled with food rewards: Nina Ottossonack aRS, . The latThe experiments were carried out between February and June 2010 in a quiet experimental room (3 m×5 m) at the department. The room was equipped with two doors: door 1 could be used to enter the experimental room from the hallway, door 2 led to an adjacent room. A chair for the owner was placed on the left side of door 1. The experimenter was positioned on the right side of door 1 during the pre-test and test trials. Tape markings on the floor indicated a circular area (r = 1 m) around the owner's chair and the experimenter's position, respectively. A clock on the opposite wall was used by the experimenter to time the trials. A line on the floor marked the dog's release point. The apparatus was placed 2.5 m away from this line. The room was equipped with four cameras linked to monitoring and recording equipment in the adjacent room .All dogs participating in this experiment had previously been tested in a modified version of the ASST aimed at characterizing their relationship with their owners. This test consisted of several episodes in which either the owner, an unfamiliar human or both were present in the room with the dog. The test also comprised two separation episodes, which allowed us to assign a score of separation-related behavior (SRB) to every dog  and/or the baiting of the apparatus  in the hallway outside the experimental room. The experimenter then entered the room through door 1 and placed the food reward or the apparatus on the designated position see . After tPre-test phase – The pre-test phase consisted of four trials that were administered in a fixed order:Trial 1: Owner present, food reward on the floorTrial 2: Owner present, food reward under the towelTrial 3: Owner absent, food reward on the floorTrial 4: Owner absent, food reward under the towelIn the first two trials of the pre-test phase the owner sat down on the chair and put on opaque sunglasses. The food had either been placed in the location of the apparatus directly on the floor  or under the towel . Trial 1 ended when the dog had consumed all five pieces of food or after a maximum of one minute. Since it was not possible for the experimenter to assess whether the dog had retrieved all pieces of food from underneath the towel, trial 2 ended after exactly one minute. In trial 3 and trial 4 the owner – after first entering the experimental room though door 1 – left the room through door 2 and remained in the adjacent room during the trial. The rest of the procedure was the same as in trial 1 and trial 2, respectively. In the adjacent room the owner could observe the events in the experimental room via monitoring equipment. The owner therefore knew when the trial was over and he or she had to leave this room and exit the experimental room through door 1 again.Two dogs were not motivated to consume any piece of food from the floor in the absence of the owner  and could therefore not proceed to the test phase. Two further dogs failed to retrieve any piece of food from under the towel in the absence of the owner . However, these dogs were motivated to retrieve the food and actively manipulated the towel during this trial. Therefore we decided to include them in the test phase.Test phase – In the test phase, we administered three trials, each of which lasted 5 min.In a trial of the condition “Absent owner” (cAO) the owner left the room in the same way as in the trials 3 and 4 of the pre-test phase see . In a trAll experimental sessions were videotaped for later behavioral coding with Solomon Coder beta (©2006–2011 András Péter). All statistical analyses were carried out with SPSS Statistics 17.0.0 (©2008 SPSS Inc.).Since we were interested in the dogs' motivation to manipulate and not in potential individual differences in their ability to retrieve the food, we coded their duration of manipulation in the test trials and did not analyze their success. “Manipulating” was recorded continuously whenever the dog was interacting with the apparatus with its muzzle or paw. Additionally, “staying close to the owner” and “staying close to the experimenter” was recorded continuously whenever the dog was with at least one paw and the head within the area marked by the circle around each respective person. A second coder blind to the aim of the experiment and to the experimental conditions coded 20% of the videos of the test trials and Cronbach's alpha was calculated as a measure of inter-observer reliability. Cronbach's alpha was greater than α = 0.9 for all behavioral variables.st, 2nd, 3rd), “type of apparatus” , and “condition”  on the variable “duration of manipulation”. To investigate whether the duration that dogs spent manipulating the apparatus when the owner was absent (cAO) was correlated with the degree of SRB scored during the ASST, we used Spearman's rank correlation. To control for individual variation in general manipulation durations, we calculated a “relative duration of manipulation in cAO” by dividing the absolute duration of manipulation in cAO by the dog's average duration of manipulation across all three trials and correlated this score with the dog's SRB score.A linear mixed model (LMM) with main effects and two-way interactions was used to investigate the effect of the factors “sequence of conditions”  where we investigated the effects of the same factors as above on the variable “duration spent in the proximity of the owner” in those conditions where the owner was present in the room  and on the variable “duration spent in the proximity of the experimenter” in all three conditions.Analyses of the residuals confirmed normal distribution for all variables in the three LMMs. Post-hoc comparisons of estimated marginal means (EM means) were carried out with LSD confidence interval adjustment.2,36 = 12.478, P≤0.001, We found that the condition in which the dogs were tested had a highly significant effect on how long the dogs manipulated the apparatus  and a significant interaction term between condition and sequence . In the other two conditions there was no effect of sequence  than by one person . Therefore, in Prior to the experiment, the owners were informed about the details of the procedures of this experiment and gave their written consent to participate with their dogs. The study was discussed and approved by the institutional ethics committee (Ethik- und Tierschutzkommission) of the Veterinary University Vienna in accordance with GSP guidelines and national legislation . Since the owners were only required to interact with their dogs in their usual manner during the experiments and their behavior was not coded or analyzed, no approval for human experimentation was obtained. The participants in the video clips that are part of the supporting information have given written informed consent, as outlined in the PLOS consent form, to publication of themselves.Thirty dogs were recruited from a database of volunteer participants of the Clever Dog Lab Society in Vienna, Austria, using the same criteria as in Dogs first had to pass the same pre-test as in Condition “Absent owner” (cAO): The owner is not present in the experimental room during the trial.Condition “Silent owner” (cSO): The owner is present in the experimental room during the trial, but remains silent.Condition “Encouraging owner” (cEO): The owner is present in the experimental room during the trial and is encouraging the dog verbally.Condition “Replaced owner” (cRO): An unfamiliar human of the same gender as the owner is present in the experimental room during the trial and remains silent.We used a within-subject design so that each dog received one trial in each of the four test conditions. The sequence of the conditions was counterbalanced across dogs.The same apparatuses as in The experiments were carried out between August 2012 and March 2013 in a quiet experimental room (3 m×6 m) at the Clever Dog Lab. The set-up was the same as in Pre-test phase – The procedure of the pre-test trials was the same as in Test phase – The three test conditions “Absent owner” (cAO), “Silent owner” (cSO), and “Encouraging owner” (cEO) were the same as in All experimental sessions were videotaped, coded with Solomon Coder beta (©2006–2011 András Péter), and analyzed with SPSS Statistics 17.0.0 (©2008 SPSS Inc.).The same three behaviors as in st, 2nd, 3rd, 4th), “type of apparatus” , and “condition”  on the variable “duration of manipulation”. Additionally we calculated a separate LMM  where we investigated the effects of the same factors as above on the variable “duration spent in the proximity of the experimenter”. Analyses of the residuals confirmed normal distribution for all variables in the LMMs. Post-hoc comparisons of estimated marginal means (EM means) were carried out with LSD confidence interval adjustment.A linear mixed model (LMM) with main effects and two-way interactions was used to investigate the effect of the factors “sequence of conditions” (1We compared the duration spent close to the silent owner (cSO) to the duration spent close to the unfamiliar human (cRO) with a Wilcoxon signed-rank test.3,67 = 7.700, P≤0.001, As in 3,67 = 5.509, P = 0.002). They manipulated the Hunter© Rolling Snack longer than all the other apparatuses . Neither the sequence nor any of the interactions had an effect on how long the dogs continued to manipulate the apparatus . As in The dogs did not spend the same amount of time close to the experimenter in the different conditions  carried out prior to (PDF)Click here for additional data file.Movie S1Condition “Absent owner”. This video clip shows the beginning of a test trial in the condition “Absent owner” with the apparatus Hunter© Rolling Snack. Neither the owner nor the unfamiliar person is present. The experimenter releases the dog and then takes her position. The duration of the full trial is 5 minutes.(MP4)Click here for additional data file.Movie S2Condition “Silent owner”. This video clip shows the beginning of a test trial in the condition “Silent owner” with the apparatus Hunter© Snack Bottle. The owner (sitting on the chair) is present, wears opaque sunglasses and remains silent. The experimenter releases the dog and then takes her position. The duration of the full trial is 5 minutes.(MP4)Click here for additional data file.Movie S3Condition “Encouraging owner”. This video clip shows the beginning of a test trial in the condition “Encouraging owner” with the apparatus Nina Ottosson© Dog Pyramid. The owner (sitting on the chair) is present, wears normal sunglasses and is allowed to encourage the dog. The experimenter releases the dog and then takes her position. The duration of the full trial is 5 minutes.(MP4)Click here for additional data file.Movie S4Condition “Replaced owner”. This video clip shows the beginning of a test trial in the condition “Replaced owner” with the apparatus Hunter© Snack Cactus. The unfamiliar person (sitting on the chair) is present, wears opaque sunglasses and remains silent. The experimenter releases the dog and then takes her position. The duration of the full trial is 5 minutes.(MP4)Click here for additional data file.


Gamma Band Activity (GBA) is increasingly studied for its relation with attention, change detection, maintenance of working memory and the processing of sensory stimuli. Activity around the gamma range has also been linked with early visual processing, although the relationship between this activity and the low frequency visual evoked potential (VEP) remains unclear. This study examined the ability of blind and semi-blind source separation techniques to extract sources specifically related to the VEP and GBA in order to shed light on the relationship between them. Blind  and semi-Blind  methods were applied to dense array EEG data recorded during checkerboard stimulation. FSS was performed with both temporal and spectral constraints to identify specifically the generators of the main peak of the VEP (P100) and of the GBA. Source localisation and time-frequency analyses were then used to investigate the properties and co-dependencies between VEP/P100 and GBA. Analysis of the VEP extracted using the different methods demonstrated very similar morphology and localisation of the generators. Single trial time frequency analysis showed higher GBA when a larger amplitude VEP/P100 occurred. Further examination indicated that the evoked (phase-locked) component of the GBA was more related to the P100, whilst the induced component correlated with the VEP as a whole. The results suggest that the VEP and GBA may be generated by the same neuronal populations, and implicate this relationship as a potential mediator of the correlation between the VEP and the Blood Oxygenation Level Dependent (BOLD) effect measured with fMRI. ► ICA and FSS are able to extract sources specifically related to the VEP/P100 and GBA. ► Localisation and frequency analyses show co-dependencies between VEP/P100 and GBA. ► Trial by trial induced GBA covaries with VEP amplitude. ► VEP and GBA may be generated by the same neuronal populations. ► VEP and GBA relationship may underlie the relationship between VEP and BOLD. Recording electric or magnetic fields from the scalp using electro- or magneto-encephalography (EEG/MEG) is one of the primary ways in which human brain activity can be characterised. However, the signals measured at the scalp are a mixture of the contributions from multiple generators or sources, added to background activity and system noise, meaning that it is often difficult to identify and study the dynamic activity of generators of interest at the level of the electrode/sensor space. Although the most common method of overcoming this limitation is time-domain averaging with or without source localisation , source Blind Source Separation (BSS) algorithms make some assumptions about the statistical properties of the sources contributing to the measured signal, but within the constraints of those assumptions are able to unmix or decompose the scalp signal into a number of underlying sources. The most common source separation technique in terms of EEG and MEG is Independent Component Analysis ICA, , which cThe advantages of source separation techniques are most evident when dealing with trial-by-trial variations of electrophysiological signals , or withThese questions have a wider significance when considering the combination of EEG with functional magnetic resonance imaging (fMRI). Although a number of lines of evidence from animal and human studies suggest that the tightest coupling between EEG and BOLD occurs in the gamma band  and semi-Blind (FSS) source separation methods were applied to dense-array EEG data recorded during checkerboard stimulation. FSS was performed with both temporal  and specFour subjects  were paid for their participation. Written informed consent was obtained and the protocol was approved by the Research Ethics Board of the University of Birmingham.A full field, high (100%) contrast, low spatial frequency (~ 0.5 cycles per degree) checkerboard stimulus was presented with a reversal rate of 2 Hz (i.e. the checkerboard was presented for 500 ms before reversing). This spatial frequency was chosen to be similar to the standards for generating VEPs used clinically  prior to the off line analysis. Some trials were discarded by visual inspection in each subject due to the movement artefacts, the majority of these trials were discarded at the beginning and the end of each runs. After this procedure we had 446, 548, 567 and 490 trials respectively for subjects 1, 2, 3 and 4. For the further analysis we used a consistent number of trials across the subjects using 400 trials for each subject. The analysis strategy aimed at extracting signals generated only in response to the stimulus.Two methods of source separation were used: blind ICA fastICA,  and semix(t) =  is the m-dimensional vector of the observed signal recorded by m electrodes; A is an m × n (withn ≤ m) unknown full-rank mixing matrix; s(t) = T is the n-dimensional unknown vector of the sources. The model is approached by processing electrode signals by an ICA demixing system described in the form:IC(t) = T is the n-dimensional vector of the estimated ICs and W is the separation matrix, i.e., the estimate of the inverse of the unknown mixing matrix A, up to permutation and scaling:ICA  is a genWe used the FastICA algorithm proposed by Hyvärinen .k ICs-subset such that the corresponding explained variance was at least 95% (In the case of a large number of channels (128 in this case) a direct extraction of all the ICs would have been extremely time consuming and component selection extremely challenging. We pursued a dimensionality reduction by applying an optimized procedure to select a east 95% . In our east 95% .Ak is the estimated mixing vector  triggered by rest (from − 5 to 0 s) and task (from 0 to + 5 s) was used to identify ICs of interest. Specifically, ICs were identified which had an increased power in the gamma band. In three subjects only one IC was identified , whilst three ICs were selected for subject 3 . After the identification of ICs, the data at the scalp electrodes were obtained by retroprojecting the selected ICs:X represents the observed EEG data, S are the underlying unknown sources and A is the source-sensor coupling matrix to be estimated. Additional information to a standard ICA model is used to bias the decomposition algorithm towards solutions that satisfy physiological assumptions. In other words, the aim of FSS is to enhance the separation of relevant signals by exploiting some a priori knowledge without renouncing the advantages of using only information contained in the original signal waveforms. A modified (with respect to standard ICA) contrast function is defined:J is the statistical index normally used in ICA, whilst RFS accounts for the prior information used to extract a single source. According to the weighting parameter λ it is possible to adjust the relative weight of these two aspects. In this study, λ was chosen to be equal to 1000 in all cases, as detailed in λ was chosen to both minimise computational time and maximise RFS. Moreover, since prior information about the sources may also be described by a non-differentiable function, the new contrast function F is optimised by means of simulated annealing ; tk is the time point with the maximum electric potential around 100 ms after the stimulus onset on the maximal original EEG channel; Δ1tk(Δ2tk) is the time point corresponding to a signal amplitude of 50% of the maximal value before (after) tk. The baseline was computed in the time interval from − 100 to 0 ms. The precise value of each latency tk was chosen for each subject, corresponding to the maximum electric potential in the time interval of interest (80–120 ms), see also A of Eq. P100.The functional constraint To investigate the GBA, the following ad-hoc functional constraint R was used:A of Eq. FSγ .This constraint computes the difference in the Power Spectrum Density (PSD) between Stimulus  and No-Stimulus  periods in the γ frequency band (30–90 Hz). This difference is then normalised with respect to the GBA in the No-Stimulus period . The souTo evaluate the quality of the data following ICA and FSS, four criteria were used: the VEP, Source Localisation, Discrepancy and Time Frequency Dynamics applied on both averaged trials and single trial levels. In order to facilitate comparison, the analysed data were taken from a single electrode selected for each subject based on the maximum of the voltage field Eq. . The selP100 and FSγ, scalp topographies were obtained by retroprojection of the identified sources using Eq. After identification of the ICs with increased gamma activity during the task with respect to the rest period, extraction of FShttp://www.sccn.ucsd.edu/eeglab  model, with a forward model consisting of four concentric conductive spheres (routine DIPFIT2  of EEGLAu/eeglab ). EEGLABu/eeglab . In ordeTo determine whether the data after source selection contained any residual signal of interest, the discrepancy was defined as the difference between the original EEG data and the data obtained from Eq. R is defined as in Eqs. tk refers to the latency of each extracted FS or ICs  was calculated as the ratio between the mean R computed on the discrepancy matrix and the mean R across the EEG electrodes: ICs see . The indOne problem when looking at time frequency plots of stimulus induced changes is that such maps contain both the evoked and induced responses. In order to specifically examine the induced changes we took the average evoked response over all trials and regressed this out of each individual trial. This gives an estimate of the purely induced component of the response, within the limitations of the standard model of evoked potential generation which assumes that the EP and background activity are additive. Although still a matter of debate, with evidence for an alternative model whereby evoked responses are the result of phase resetting of ongoing activity , this evThe data subjected to the time frequency analysis were taken from the same electrodes as used to investigate the VEP . Time-frERP image plots were used to visualise the trial-by-trial variability on the different power bands. Instead of simply summing all the data trials, trials are first sorted based in order of a relevant data or external variable, and then plotted as a colour-coded two dimensional image. Essentially, 2-D ERP images generalise 1-D ERP averaging  comparison between the VEP/P100 and the different frequency bands was performed for the different methods .From the ICA decomposition of each subject, components displaying significant post stimulus GBA were selected and retro-projected to the scalp space (from 1 to 3 components). FSS results in only one source for each constraint, avoiding the need for component selection.Firstly, the VEP  and ‘method’  = 484.8, p < 0.001), indicating the improved GBA in the The upper half of Maintaining the same ST ordering model used above, the lower half of To emphasize these effects, This study examined the ability of blind and semi-blind source separation techniques to extract sources specifically related to the Visual Evoked Potential (VEP/P100) and Gamma Band Activity (GBA) elicited by a reversing checkerboard. The relationship between the low frequency VEP and the high frequency (~ 30–90 Hz) GBA, both of which can be generated by simple visual stimuli such as checkerboards and gratings, remains unclear. GBA is receiving an increasing amount of attention because of its purported links with many different brain processes , a domaiGBA has a very low signal-to-noise ratio (SNR), meaning that methods to improve its detectability and allow a more accurate characterisation of its properties are desirable. Three methods were examined in this study: Independent Component Analysis (ICA) and Functional Source Separation (FSS) with temporal and spectral constraints. ICA is a blind source separation technique that extracts sources based purely on statistical grounds, whilst FSS can be seen as an extension to ICA which incorporates some additional information to bias the decomposition algorithm towards solutions that satisfy physiological assumptions. In this study, a temporal constraint maximised the activity around the P100 of the VEP, and a spectral constraint maximised the difference in the GBA between the rest and the task periods. The purpose of applying these different analysis methods was threefold. Firstly, to determine which technique was able to provide the best characterisation of the GBA. Secondly, to provide a degree of validation to the comparison of the GBA and the VEP. Each of the techniques extracts a different part of the raw signal which is dependent on the assumptions underlying the decomposition. In particular, the ICA and the nstrated  and, espIn order to characterise the GBA in more detail, and specifically to determine whether it was phase locked to stimulus presentation (i.e. evoked or induced), the event-related spectral perturbation (ERSP) was calculated in two ways . FirstlyA concern when using source separation techniques is whether in selecting a few ICs or only one FS some of the signal of interest has been lost. This was addressed in These analyses point to a robust relationship between the VEP and the GBA on average. To investigate this further, and to examine other frequency bands to determine whether the VEP is solely related to the gamma band, the relationship was examined on a single trial basis. Trials were ordered based on properties of the VEP , and the frequency content examined. If there is a link between the VEP and the frequency content of the EEG, there should be a difference between the frequency content of the highest and lowest quartiles of the ordered data. Although it is very difficult to guarantee that all of the evoked component has been removed by the regression process, and as stated previously it explicitly assumes the standard model of evoked potential generation which is a matter of considerable debate , severalThis result may also have implications within the context of EEG-fMRI recordings, and in particular regarding a previous observation that the area of the VEP was correlated with the area of the BOLD response, but that the amplitudes were not related . Given tIn this study, the improvement in data quality provided by ICA and FSS facilitated a more detailed investigation of the spatiotemporal properties of the pattern-reversal EEG response than is generally possible. GBA was not clearly seen in the Raw data  as well The following are the supplementary materials related to this article.


Morone americana), moose  and red deer (Cervus elaphus) to demonstrate our approach. We show that the probability of detecting partial migration due to transient coexistence depends upon a minimum number of tracked or marked individuals for a given number of populations. Our approach provides a starting point in searching for explanations to the observed frequencies, by contrasting the observed pattern with both the predicted transient and the uniform random pattern. Aggregating such information on observed patterns (proportions of migrants and residents) may eventually lead to the development of a quantitative theory for the equilibrium (ESS) populations as well.Partial migration, whereby a proportion of the population migrates, is common across the animal kingdom. Much of the focus in the literature has been on trying to explain the underlying mechanisms for the coexistence of migrants and residents. In addition, there has been an increasing number of reports on the prevalence and frequency of partially migratory populations. One possible explanation for the occurrence of partial migration, which has received no attention in the literature, is that of ‘transient coexistence’ during the invasion phase of a superior behaviour. In this study we develop a theoretical basis for explaining partial migration as a transient coexistence and derive a method to predict the frequency of residents and migrants in partially migrating populations. This method is useful to predict the frequencies of migrants and residents in a small set of populations as a complementing hypothesis to ‘an Evolutionary Stable Strategy (ESS)’. We use the logistic growth equation to derive a formula for predicting the frequencies of residents and migrants. We also use simulations and empirical data from white perch ( Animal migration is a widely known phenomenon where individuals move between seasonal ranges on an annual basis A number of explanations have been suggested for the causes of partial migration and its maintenance in nature Besides the above-mentioned mechanisms, there is an additional and complementing explanation for the coexistence, is a ‘transient’ phenomenon. This has received little attention probably because it is assumed to be extremely infrequent. When a new behaviour (e.g. resident or migratory) enters a population, it will increase in frequency as long as it is superior to the existing behaviour. When the the frequency increase in a population as long as the fitness of individuals expressing one behaviour is higher than the fitness of individuals showing the other behaviour, one will eventually replace the existing one. Thus, there will be a time period when both behaviours can be observed and this type of transient coexistence could be mis-interpreted as partial migration at equilibrium if the transient phase is very long. This logic can also be followed in the way, that partial migration could be an early stage in the evolution of migration The existing explanations focus on the mechanisms behind the existence of two behaviours maintained at an equilibrium We demonstrate how an assumption of transient coexistence of partial migration can be used to derive a probability density function and the associated cumulative distribution function to predict the expected frequency of migrants and residents in naturally occurring populations. We also apply this approach to empirical data on one aquatic and two terrestrial species.We use the logistic growth equation to derive an expected frequency distribution of the two behaviours. We restrict the analyses to cases where there is density dependence in the shared habitat (breeding or non-breeding). We further assume that the population growth rate follows the classical logistic growth curve, and that the total population is at or close to its carrying capacity. The analytic derivation of the frequency distribution is simplified by the fact that the logistic function is symmetric in its S-shape. We show that small to moderate deviations from this assumption will lead to negligible changes in the predicted frequency distribution.Fmin to 1−Fmin, where Fmin is the minimum frequency at which we can observe the least common behaviour (either migratory or resident). The frequency (F) of the least common behaviour will be Min ≥Fmin. It does not matter if the least common behaviour (resident or migratory) is superior or not, which simplifies the observation process. We start the derivation with the classic logistic growth function:r describes the intrinsic rate of natural increase, K is the carrying capacity, and N0 is the (invaders') initial population density, to accommodate the invasion of the alternate behaviour in a population initially consisting of either residents or migrants. Even if the population growth is density dependent, the selection for a superior behaviour is considered density independent s, which is the difference between the r-values for each of the behaviours. Therefore, to avoid confusion in terminology we replace r with s. Next we divide both the left and the right hand side of K to make the equation dimensionless. Dividing both the numerator and the denominator on the right hand side by K, and replacing N0/K with minF, leaves us with an equation for t. (see Eq. 2).s, is likely to be much smaller than the intrinsic growth rate, we expect the transient times from F(t) = Fmin to F(t) = 1−Fmin to exceed the generation time by several orders of magnitude, which can be seen in t, was solved from F(t) = 1−Fmin. Thus, partial migration may exist as a transient coexistence for long periods of time  for different populations will eventually give enough data to produce a histogram of the expected frequencies of the least common behaviour. In order to make F(t) comparable between populations we need to remove the dependence on s, since we do not necessarily expect s to be the same in different populations. Moreover, it would be difficult to estimate the magnitude of s. To cancel out s, we create a new variable that fulfills the properties of a cumulative distribution function (CDF). The CDF accumulates the probabilities from zero (at F = Fmin) to 1 (at F = 1/2). The upper limit at F = 1/2 condition is fulfilled because the least common behaviour can by definition never exceed half the population. To derive the CDF we replace F(t) by F(X) and solve for X to have X(F). Then we let X(1/2) = 1, which give us CDF(F) = X(F)/X(1/2).Often, our interest lies in determining if a species is partially migratory Fmin≤F≤1/2, and the mathematical function for the final CDF is independent of s The p becomes :4)EitheEitheFmiK's, the initial increase of the invader will be slower than the final disappearance of the original behaviour. The classic logistic function will therefore give biased results when K's are very different; however, is this bias negligible for reasonable differences in K-values? To estimate the magnitude of bias in our predictions, we tested three ratios of c = KInvader/KOriginal, in the differential equations describing population growth  exceeded 1- FMin, and the result for each run was extracted at a single random time that fulfilled the criterion; FMin ≤PInvader≤1−FMin. Frequency distributions of F were compiled for each of the three c-values, for comparison with the frequency distribution predicted using the classic logistic equation  of the “least common behaviour” can be used to compare the fit to each of the two distributions, the transient versus the uniform random distribution. In the absence of an existing explicit framework, we use the uniform random distribution as an alternative, i.e. as a null hypothesis, to represent the distribution of frequencies of the two behaviours from different populations. This comparison can be made by calculating the log-likelihood (LL) for the data based on each of the distributions probability density functions (PDFs). The distribution resulting in the largest LL has a better fit to the data since both distributions have exactly the same parameters, Fmin and 0.5. The log-likelihoods are calculated as:iF is the frequency of the least common behaviour in population i, and PDFdist is the probability density function for distribution dist. The PDF for a uniform distribution in this case will be 1/(1/2−Fmin) for Fmin≤F≤1/2 and 0 elsewhere. It appears that when applying uniform random data in a Monte-Carlo simulation to compare the LL from the two distributions, reliable tests can be made with as few observations as 4, given that Fmin is very low, ca. 0.0001. The reason why few samples are required to separate between the two PDFs at a low detection limit is that the PDF for the transient hypothesis is much steeper at low than at high F-values. With higher Fmin-limits more samples will be required for reliable separation of the distributions  exceeds the log-likelihood of the uniform distribution (LLU) and α<0.05. When the reverse is true the uniform random distribution might still not be the most appropriate distribution. It rather means that the uniform random distribution describes the data better than the transient distribution. A standard distribution test like a Kolmogorov-Smirnov test can be used to test if the data was drawn from a uniform distribution (H0) or not (HA). If H0 is rejected then there may be aggregations of frequencies at some F-values, but so far there is no existing theory to explain the existence of aggregations at some intermediate F-values.The transient PDF describes the data better than the uniform distribution when the log-likelihood of the data based on the transient distribution , n = 6 (Fmin was 0.026 and the estimate for transient PDF function was 5.25 in contrast to 5.23 for the uniform random distribution ∼U(0.026–0.5), n = 7 (Fmin = 0.06) the estimates were 4.14 and 4.93 for transient PDF and uniform random distribution ∼U(0.06–0.5) respectively , n = 6 . For moo), n = 7 . Finallyectively . The traConsidering “transient coexistence” as an additional complementing hypothesis for the existence of partial migration allowed us to analytically derive a frequency distribution for the two behaviours, residency and migrants, among populations. This does not mean that the aim of this study was to explain that all partially migrating populations are in a transient state. The idea is rather to provide a framework in which the observed patterns of partial migration can be assessed, for example as another null hypothesis. We also show how the expected frequency distribution can be used to assess the transient versus a null hypothesis consisting of a uniform random distribution that will represent the equilibrium conditions in real populations until a quantitative theory is derived for these conditions.Fmin and 0.5.In terms of log likelihood values, moose data was found to support the transient hypothesis whereas red deer and white perch did not. From a frequentist's perspective, none of the populations fulfilled the requirements for statistical inference due to either too low number of populations studied for each species, or alternatively that too few individuals were tagged or analyzed in each population. For the white perch analysis 17 populations would have been needed to allow a reliable comparison at α = 0.05. In contrast, staying with six populations would have required that 784 individuals from each population had been analyzed in the first place. For moose 26 populations would have been needed, or that 38 individuals had been tagged in each population. For the red deer the corresponding numbers should have been 60 populations, but increasing the number of tagged red deer would not have made a difference as long as the frequencies had remained the same. At least some of these numbers are not unrealistic, such as tagging 38 moose per population. Nevertheless, there are other methods such as repeated censuses that could be used to estimate the proportion of migrants and residents as these methods generate more observations than tagging studies. The main reason for having the proportions based on more observations is that it reduces the detection limit, which in turn reduces the number of populations needed for statistical inference. Otherwise, model selection approaches such as AIC/BIC could also be employed The existing explanation for the observed patterns of partial migration pattern in moose is that partial migration is an adaptation to the latitudinal variation in the climate s (the rate of spread) in the derivation, we assumed that the carrying capacity does not change when the superior behaviour invades. According to the simulations of an invasion of a superior behaviour, the predictions should still be applicable for empirical data when the carrying capacities for the two behaviours differ. Minor bias might be expected if the KInvader/KOriginal-ratios are very high, c≥5, but such magnitudes should be rare in nature. There are at least two reasons for this: first, it is unlikely that a recent invader can increase the carrying capacity significantly in the shared habitat. Secondly, if the ratio is large, then the invasion time will be relatively short and partial migration might not be observed.There are method related aspects in the study that require explanation and justification. In order to cancel out The PDF and CDF that we derived were based on the assumption that all included populations were in a transient state. Therefore, a mixture of transient and equilibrium populations will create an intermediate fit. It is hence more likely, that a transient state may be observed within the same species, from only a few sub-populations, since the mutants are likely to spread to other populations in time.Fmin is set for all populations in the study. If Fmin is set very low then the occurrence of partial migration needs to be detectable in any population at that level. In studies where individuals are tagged, the Fmin equals 1/the number tagged, as long as the number of tagged individuals are the same in each population. A solution for the case, when the number of tagged individuals is not equal across populations, could be to use the harmonic mean of the 1/n ratios, as we did in the three presented examples. Alternatively, if the smallest 1/n ratio is less than the harmonic mean, then it should be used instead, since empirical ratios below Fmin will produce erroneous results.For the method to predict the frequency of migrants and residents, it is important that a common Another contribution of our framework is that it might provide information on how common or uncommon “mutant invasions” are in natural populations Luis-Miguel Chevin and three anonymous reviewers provided valuable comments, which greatly improved the manuscript. Göran Spong and Andrew Allen gave valuable advice on writing.


Radiation risk of thyroid cancer incidence among survivors of the atomic bombings of Hiroshima and Nagasaki and preliminary estimates of thyroid dose due to the Fukushima accident were used for the prediction of baseline and radiation-related thyroid cancer risks. We estimate a prevalence of thyroid cancer of 0.027 %  for the first screening campaign in the Fukushima Prefecture. Compared with the incidence rate in Japan in 2007, the ultrasonography survey is predicted to increase baseline thyroid cancer incidence by a factor of 7.4 . Under the condition of continued screening, thyroid cancer during the first fifty years after the accident is predicted to be detected for about 2 % of the screened population. The prediction of radiation-related thyroid cancer in the most exposed fraction (a few ten thousand persons) of the screened population of the Fukushima Prefecture has a large uncertainty with the best estimates of the average risk of 0.1–0.3 %, depending on average dose.Thyroid cancer is one of the major health concerns after the accident in the Fukushima Dai-ichi nuclear power station (NPS). Currently, ultrasonography surveys are being performed for persons residing in the Fukushima Prefecture at the time of the accident with an age of up to 18 years. Here, the expected thyroid cancer prevalence in the Fukushima Prefecture is assessed based on an ultrasonography survey of Ukrainians, who were exposed at an age of up to 18 years to The online version of this article (doi:10.1007/s00411-013-0508-3) contains supplementary material, which is available to authorized users. Thanks to prompt actions of Japanese authorities, radiation exposures of the population were generally low. However, average thyroid doses of young children in some settlements were reported to be of the order of or even exceeding 100 mSv WHO . These dThere is concern about thyroid cancer induced by the accident at the Fukushima Dai-ichi NPS. The concern is caused by the massive increase in thyroid cancer among those who were highly exposed during childhood due to the Chernobyl accident  %.The UkrAm cohort consists of 13,127 Ukrainians who were up to 18 years old on 26 April 1986, the date of the Chernobyl accident  and larger than 10 mm (UkrAm cohort) under otherwise the same conditions is the maximum of fsp, because also some nodules in the size range from 5 to 10 mm were selected in the UkrAm for further investigation and turned out to be cancer  cases per 105 person-years per Gy, and the ERRUA to 1.91  Gy−1. These numbers indicate a best estimate of the baseline incidence rate in the UkrAm cohort during the second to fourth screening of 11.6 cases per 105 person-years. The incidence rate in Ukraine with the same sex–age structure as in the UkrAm cohort during the second to fourth screening, λUkraine,U2–4, is 3.3 cases per 105 person-years  has been assumed to be uniformly distributed from 0.7 to 1.0.The impact of the second to fourth screenings on the incidence rate in the UkrAm cohort can be calculated as the ratio of the baseline incidence rate in the cohort , having different values before and after 1970:Recently, thyroid cancer risk in the cohort of survivors of the atomic bombings of Hiroshima and Nagasaki has been analysed by Furukawa et al.  in the fThese two time periods were chosen to differentiate the early period with many autopsies from the later period with fewer autopsies  is assumed to be the same in both populations , FL(a–e) that takes into account that radiation-induced cases are not expected before 3 years after the exposure  is the excess relative risk per unit dose for LSS cohort members not participating in the AHS, where s is an indicator for sex.The standard approach of transferring risk estimates for thyroid cancer in the LSS to other populations is assuming a multiplicative interaction of radiation and other risk factors, i.e. the excess relative risk per unit dose  with thyroid dose, D, and taking into account cancer-free survival, S, in Japan in 2007  , and for the period afterwards of 1.23 .ERR in the LSS decreases with age at exposure and age attained see Fig. . EAR dec4 person-years at an attained age of 10 years to 6 cases per 104 person-years at an attained age 50 years.In the mixed transfer model, the risk rate attributable to radiation exposure increases for young ages at exposure after the minimal latency period of 3 years for a few years steeply with time since exposure .With the exception of young attained age, the multiplicative transfer, Eq. , gives rMost of the long-term attributable risk accumulates over several decades, whereas the risk during the first years after exposure is small Table . The conFor the same thyroid dose, the attributable risk accumulating over several decades after exposure decreases with increasing age at exposure. However, the effect is relatively modest (about a factor of two for ages at exposure of 1 and 18 years).Under the condition of continued screening, baseline thyroid cancer risk during the first 50 years after exposure in the screened population of the Fukushima Prefecture is predicted to be 2.2  %  % .harvesting effect that might appear after 20 years after exposure: Early detection may lead to lower numbers of detected cases at later campaigns of a survey. However, we are not aware of studies that give evidence of a harvesting effect of ultrasonography for thyroid cancer incidence.Whereas our predictions for the first 20 years after exposure are supported by some studies of thyroid cancer after the Chernobyl accident, our longer-time predictions are more uncertain and may overestimate the risk. This is so because we have neglected a so-called For a period of 50 years after exposure at ages at exposure of up to 18 years, we predict that an average thyroid dose of 20 mSv would result in a relative contribution of about 6 % to the total thyroid cancer risk. This is in accordance with the results of WHO , because131I. Independent of these uncertainties, however, the order of magnitude of the predicted thyroid cancer prevalence and incidence rate may help to be prepared for a relatively large number of thyroid cancer cases that are to be expected. It is emphasized that most of the cases would not have become clinically relevant without the ultrasonography survey.Based on the results presented here, it is expected that the ultrasonography survey of residents of Fukushima Prefecture will increase thyroid cancer incidence compared with thyroid cancer incidence in 2007 in Japan drastically. The estimated increase has a large uncertainty with a best estimate of a factor of about 7. For an average thyroid dose of 20 mSv of the most exposed in the surveyed population, it is estimated that in the early period, about 10 % and in later periods about 5 % of the reported incidence will be attributable to radiation exposure. Thus, the fraction of thyroid cancer cases attributable to radiation exposure will be small, although there are regional differences due to varying doses. The present assessment includes large uncertainties caused by uncertainties in the thyroid cancer risk function for the LSS, the impact of the ultrasonography survey, and the transfer of the risk function to low-dose exposures to Supplementary material 1 (DOCX 319 kb)Below is the link to the electronic supplementary material.


This paper describes a novel design methodology using non-linear models for complex closed loop electro-mechanical sigma-delta modulators (EMΣΔM) that is based on genetic algorithms and statistical variation analysis. The proposed methodology is capable of quickly and efficiently designing high performance, high order, closed loop, near-optimal systems that are robust to sensor fabrication tolerances and electronic component variation. The use of full non-linear system models allows significant higher order non-ideal effects to be taken into account, improving accuracy and confidence in the results. To demonstrate the effectiveness of the approach, two design examples are presented including a 5th order low-pass EMΣΔM for a MEMS accelerometer, and a 6th order band-pass EMΣΔM for the sense mode of a MEMS gyroscope. Each example was designed using the system in less than one day, with very little manual intervention. The strength of the approach is verified by SNR performances of 109.2 dB and 92.4 dB for the low-pass and band-pass system respectively, coupled with excellent immunities to fabrication tolerances and parameter mismatch. In particular, MEMS inertial sensors employing a capacitive sensing element incorporated in sigma-delta modulator (ΣΔM) control systems with electrostatic feedback have gained popularity in the past due to their direct digital output signal, and avoidance of potential electro-static instability (due to the ‘pull-in’ effect). Earlier work used the micro-machined sensing element as the sole loop filter, and, since the sensing element is typically a second order mass-damper-spring low-pass filter, this resulted in a second order electro-mechanical ΣΔM (EMΣΔM) –3. It isLinearized analytical models for ΣΔMs are described in for example  and emplIn this work we present a novel design methodology for EMΣΔM based on genetic algorithms (GA) and Monte Carlo simulations, both using accurate non-linear models. Genetic algorithms are based on the mechanics of natural selection and genetics combining the fittest individuals in the population in order to search for the best solution . These ei.e., parameter) comes from the first parent and vice versa. An initial population function was written and used to randomly generate the first population with a uniform distribution within the specified constraints.In this work the genetic algorithm used is the gamultiobj function in Matlab which is variant on the Non-dominated Sorting Genetic Algorithm-II (NGSA-II) . NumerouAs part of the overall design methodology, the GA facilitates multi-objective optimisation for the design of low-pass or band-pass EMΣΔM with a wide range of orders and with any architecture. Since the result of the optimisation is a large number of equally optimal solutions the design procedure subsequently carries out a robustness analysis based on statistical simulations to ensure stability of the design in the presence of fabrication tolerances, which can be substantial for micromachined sensing elements. Although numerous methods exist for output variation estimation, e.g., , in thisThis paper is organised as follows: Section 2 describes the developed GA process in general; Section 3 gives an example for the design of a 5th order EMΣΔM MEMS accelerometer; Section 4 gives a second example of a band-pass EMΣΔM for a MEMS gyroscope; in Section 5 the design approach is discussed and in Section 6 conclusions are drawn.2.An EMΣΔM consists of the following building blocks: (i) the micromachined sensing element; (ii) the pick-off circuit that capacitively measures the displacement of the proof mass in response to an inertial force and converts it to a voltage; (iii) a phase compensator (which may not be required if the sensing element is overdamped); (iv) an electronic loop filter comprising several integrators and minor feedback or feedforward loops; (v) a clocked one bit quantizer; (vi) a feedback block that converts the feedback voltage into an electrostatic force acting on the proof mass and counterbalancing the inertial force. For our design methodology the user must first choose an architecture and the order, which can either be taken from the literature on EMΣΔM, an architecture for a purely electronic A/D ΣΔM, or a novel architecture developed by the user. The next step is to develop a Simulink model. The model can be as simple or as complex as deemed necessary by the user. Second order effects may be included. A few examples include: (i) the pick-off circuit can be modelled simply as a gain constant, or the nonlinear relationship between displacement and differential change in capacitance may be included; (ii) The micromachined sensing element may be simply modelled as a second order lumped parameter system with mass, damping and mechanical spring constant as the only parameters, or higher order modes e.g., from the dynamics of the sense fingers can be included ; (iii) TThe proposed methodology is represented by the flow-chart in R of, within the constraints, randomly chosen parameter sets; which is termed a population. Each parameter set is termed an individual. This initial population represents generation 1. The system then runs NR simulations  and records the performance objectives for each individual, for example SNR and proof mass displacement as previously discussed. Once the first generation has been simulated, the result is stored as a table where each row consists of the parameter set for one individual and its performance. As explained in the previous section, the GA sorts the results and then performs a number of functions including picking the very best individuals (elite preservation), generating a certain number of new random individuals (mutation) and cross fertilising good individuals to create new offspring. This last step actually involves taking different parameters from different good individuals and combining them to create a new individual (child). These three steps create generation 2, which again consists of NR individuals. The whole process continues until either a specified maximum number of generations has been reached or the user monitoring the evolution determines that sufficient convergence has been achieved. Although it would be possible to automate the convergence detection, for example by calculating bit string affinity, we have found in practice that the insight gained from making this an interactive decision is very valuable.The GA is then initialized with a user specified number, NSimulation length is an important consideration during the GA process and introduces a trade-off between accuracy and total optimisation time. Often systems can appear initially stable, only to lose stability a short time later and therefore it is possible to unwittingly promote unstable systems forward in the evolutionary process if the simulation time is too short. However, long simulation times can result in excessively time-consuming optimisation periods, given the large number of simulations involved. This issue has been addressed in this work by typically running a small number of simulations initially to establish a ‘quick’ simulation period that represents a reasonable trade-off between the chance of missed instability and computation time. When the final solution is chosen at the end of the whole process, a more extensive simulation is performed with a ‘long’ simulation period to verify stability beyond doubt. Values for the ‘quick’ simulation periods will depend strongly on the type of architecture being designed but typically lie in the region of a few seconds, and the ‘long’ simulation period is typically 8 times longer than the ‘quick’ period. Both of these parameters are defined alongside all the goals, parameters and constraints in the system file.The next step in the methodology is to consider robustness, which is an important measure of how parameter variation will affect performance or stability and a key contribution of this work. It cannot be assumed that the individuals in the final population of the GA step are the most robust, since they have only been optimized for SNR and RMS displacement, not tolerance to variation. For example, an individual in one of the earlier populations may have only slightly lower performance than one in the final population but may be far more robust. For this reason, the robustness stage of the process must consider the full history of individuals, which we refer to as a census. Theoretically, Monte Carlo simulations could be performed on every individual in the census, however, with hundreds of simulations per individual required for the robustness analysis this would be too time consuming.i.e., the goals). After this filtering process, there may still exist a very large number of acceptable individuals, many of which may be close to each other in the design space. To run Monte Carlo simulations on two individuals which are themselves very similar would be inefficient. For this reason a thinning algorithm has been implemented which thins out the filtered set to give a smaller, more unique, and dispersed set of fit individuals. The thinning algorithm works by considering each individual in turn and adding an adjustable margin either side of the parameters for that solution. Any other individuals in the census whose parameters all lie within the margin of the individual under consideration are removed. After the census is traversed a smaller number of distinct design points are left. The algorithm repeats this whole process, whilst adjusting the separation margin, until the desired number of solutions remains. Monte Carlo simulations are then performed on each remaining individual using user specified standard deviation values for all electrical and mechanical parameters of the system model. The results from these statistical simulations are analysed to determine how many of the Monte Carlo simulations passed the goals for that individual, and from this a yield is calculated. After the robustness process is complete, the result is therefore a list of all feasible and optimal individuals and their simulated yields, and from this list the user can choose the final design solution.Therefore, before Monte Carlo robustness analysis is performed, the census needs to be filtered to discard all individuals that do not meet the objectives (3.3.1.To demonstrate the design procedure we present a 5th order low-pass ΣΔM for a MEMS accelerometer with a sensing element fabricated in SOI (Silicon on Insulator). The main specifications of the sensor are listed in In this example the ten parameters shown in i.e., the goal values) for the GA to optimize need to be defined; in this example these are the SNR (to be maximized) and the root mean square (RMS) value of the proof mass deflection (to be minimized). Here, we choose pass goal values of a SNR > 100 dB and the RMS proof mass deflection <40 nm. Finally, the GA needs to have values for the number of individuals in each generation, and the number of generations; we choose here 200 and 15, respectively. The choice of population size and number of generations is a trade-off between simulation time, and the degree of design space exploration and individual diversity that will be achieved during the GA evolution process. In practice we have found that a population size in the order of 20 times the number of design parameters represents a good trade-off. Progress of the evolution can be monitored in real time since the program streams text results to the Matlab command window. When the SNR performance changes very little from generation to generation, this is a good indicator that peak performance has been achieved. Therefore, a large number of generations are often specified and the GA process halted when it is visually clear that peak fitness has been reached. Following this method can significantly reduce overall simulation time.For the ΣΔM the oversampling ratio (OSR) needs to be specified. The OSR is related to the sensor bandwidth, BW and the sampling frequency fs by OSR = fs/(2 × BW). Here, we choose OSR = 64 resulting in a sampling frequency of 128 kHz. Furthermore, the criteria , it can be seen that some SNR values are negative in the first block; this indicates an unstable system, as the SNR is a good indicator for system stability . The las3.3.The next step in the design process is robustness analysis which starts with a thinning and filtering algorithm. All individuals of all generations are stored in a matrix with 200 × 15 rows . For the robustness analysis the same goal function values (a minimum SNR of 100 dB and a maximum RMS deflection of 40 nm) are chosen; if required these values can be modified at this point. The filtering algorithm simply discards the individuals that have a SNR < 100 dB or an RMS proof mass deflection >40 nm. The thinning algorithm now finds the most distinct individuals in the remaining design space, as explained in Section 2. The number of individuals to be considered for the robustness analysis is specified as a user defined parameter, and is set to 40 here. Another user defined parameter sets the number of Monte Carlo simulations that will be performed for each individual; in this example 100. For each design parameter the user specifies a standard deviation providing a measure of parameter variation. The robustness analysis typically varies more design parameters than those explored by GA; for example the parameters of the sensing elements  were considered as fixed for the GA, but for the robustness analysis were varied by 2%, 25% and 5%, respectively, whereas the electronic gain constants optimized by the GA were varied only by 2%. This reflects the considerable fabrication tolerances that a micromachined sensing element typically exhibits. A function in the program generates 100 Gaussian distributed parameter sets based on a particular individual’s parameters (as the means) and the user supplied standard deviations. For each individual therefore, 100 simulations are run and the SNR and RMS displacement performance recorded. A yield value is calculated representing the percentage of the simulations for each individual that exceed the specified goal values. The user can then review the yield and performance of the investigated individuals and choose one as the final design. Here, the final parameter set is shown in 4.A further example of the proposed design methodology is now presented for a continuous time, 6th order band-pass EMΣΔM for a vibratory rate MEMS gyroscope fabricated in SOI technology, as described in . ContinuThe Simulink model is shown in The genetic algorithm is then executed, which again creates and simulates an initial population of individuals, determining their fitness by combining their SNR and sense mode proof mass displacement. A combination of cross fertilisation, mutation, and elite preservation is used to create a new population and the evolution continues. After the specified number of generations, the algorithm halts, storing the entire multi generation census for the next step. Filtering and thinning is performed on the census results to ignore individuals which do not pass the specified goal values of 70 dB SNR and 20 nm RMS displacement, or are too close to one another. The individuals remaining after the thinning algorithm are feasible and distinct solutions, and are then used as the input to the Monte Carlo based robustness analysis of the next stage. A total of 200 Monte Carlo simulations are performed on each of these solutions using realistic standard deviations for all electrical and mechanical parameters, and from this a simulated yield is calculated and documented against the solution point. The designer then has the opportunity to choose a solution from this final list, trading off performance against yield for their particular application. In this case the parameters for the chosen design are shown in 5.The two examples presented illustrate the usefulness of the methodology for the design of arbitrarily complex EMΣΔM. To the best of the authors’ knowledge this is the first time such a design methodology has been presented based on non-linear models. The design methodology for the majority of EMΣΔM presented in the literature is not described, which is an indication that a manual process relying on trial and error was used. This requires a considerable experience in ΣΔM and MEMS sensor design and hence has a high initial knowledge threshold. Even after sufficient knowledge has been gained it can often take weeks to develop a satisfactory system design, with no real certainty that the system is robust or even optimal. The proposed approach greatly expedites the design process and gives much greater confidence that the results are both optimal and robust. In some literature sources a design methodology for EMΣΔM is described based on root locus techniques  or direcThe design methodology described here circumvents both drawbacks: it is based on a full non-linear system model and it yields a design solution that is very close to the optimum, as it takes into account both SNR and proof mass displacement as performance measures. Additional performance parameters, such as dynamic range and maximum input signal could be additionally included as optimization metrics as required. Another advantage is the designer’s total freedom in the initial choice of the control system architecture; whereas the EMΣΔM described in the literature to date all are adapted architectures of ΣΔM analogue to digital converters. Therefore, our methodology facilitates the exploration of novel architectures for EMΣΔM; one example is to have a two-channel ΣΔM for the sense mode of a gyroscope, one channel for the signal, the other for the quadrature error. Furthermore, the GA design parameter set could be extended such that different architectures, or loop orders could be available as part of the GA evolution, allowing extremely diverse design space exploration.versus yield trade-off in the final step. This final solution can then be implemented in hardware, using standard circuit techniques, and hence is not discussed here; the reader is referred to e.g., [The robustness analysis performed following the GA is a key contribution of the work, giving confidence in a design and ensuring manufacturability. Without this it is possible to design a system which may easily become unstable due to inevitable fabrication tolerances. As with any multi objective optimisation, there is no single optimal solution but instead a range of equally optimal solutions, which is why it is important for the designer to choose the final design solution based on a performance to e.g., ,7,9,10.Many design flows have been performed by the authors for a wide range of EMΣΔM architectures and they are confident to claim that the GA explores the design space well and finds an excellent design solution even for complex and non-linear design spaces with multiple objectives. A side benefit of the approach is the insight gained from its use by those who have little experience in the area. With typical design times of a single day for complex architectures, the approach offers an extremely efficient alternative to manual design procedures which often take weeks.6.The presented methodology allows the system level design of arbitrarily complex EMΣΔM with ease and in a short period of time. The design process relies on a GA that varies a set of system parameters and records the performance for each set. After a filtering and thinning step a robustness analysis is carried out to ensure system stability in the presence of fabrication tolerances, which can be considerable especially for micromachined sensors. The usefulness of the approach has been illustrated through two design examples including a 5th order low-pass EMΣΔM for a MEMS accelerometer, and a 6th order band-pass EMΣΔM for the sense mode of a MEMS gyroscope. In both cases the described methodology delivers near optimum system level design parameters. Compared with previously described design of EMΣΔM our methodology provides the users with greater confidence that the final design solution is near optimum and robust, ensuring stability in the presence of fabrication tolerances.