An important problem in reproductive medicine is deciding when people who have failed to become pregnant without medical assistance should begin investigation and treatment. This study describes a computational approach to determining what can be deduced about a couple's future chances of pregnancy from the number of menstrual cycles over which they have been trying to conceive. The starting point is that a couple's fertility is inherently uncertain. This uncertainty is modelled as a probability distribution for the chance of conceiving in each menstrual cycle. We have developed a general numerical computational method, which uses Bayes' theorem to generate a posterior distribution for a couple's chance of conceiving in each cycle, conditional on the number of previous cycles of attempted conception. When various metrics of a couple's expected chances of pregnancy were computed as a function of the number of cycles over which they had been trying to conceive, we found good fits to observed data on time to pregnancy for different populations. The commonly-used standard of 12 cycles of non-conception as an indicator of subfertility was found to be reasonably robust, though a larger or smaller number of cycles may be more appropriate depending on the population from which a couple is drawn and the precise subfertility metric which is most relevant, for example the probability of conception in the next cycle or the next 12 cycles. We have also applied our computational method to model the impact of female reproductive ageing. Results indicate that, for women over the age of 35, it may be appropriate to start investigation and treatment more quickly than for younger women. Ignoring reproductive decline during the period of attempted conception added up to two cycles to the computed number of cycles before reaching a metric of subfertility. Among infertile couples, a longer period of time without conception is associated with a lower probability of conception in the following six or twelve months There are two reasons why couples who are trying to conceive experience differing outcomes with respect to when - and if - conception occurs. The first is pure randomness. Even if all such couples were identical in every relevant respect, becoming pregnant is an inherently stochastic process. It can be compared to repeatedly casting a die until a six is achieved: success may occur the first time, or the second, and so on; but over any finite number of attempts it may not be achieved at all.The second reason why outcomes differ is that couples are not identical: they vary in characteristics which have a bearing on the probability of achieving a pregnancy in a new cycle. In simple terms, some couples can be said to be more fertile than others tend to be those of lower fertility, but there will nevertheless be some higher fertility couples among their number. As the number of cycles increases, the population of couples who have not yet achieved a conception will become increasing biased towards the lower end of the fertility spectrum, which is the main reason why the probability of conception declines after a number of cycles of non-conception Overall variation in outcomes results from a combination of both randomness and variation among couples in their underlying fertility et al.perfect information about a couple's fertility. In other words, there is some component of a couple's fertility that cannot be directly measured from variables such as age, physical characteristics, previous medical history, fertility history and currently available medical tests. This conclusion is consistent with the large proportion of patients whose failure to conceive is not explained by routine investigations; the UK Human Fertilisation and Embryology Authority reported that “Nearly a quarter of patients [in 2008] had unexplained infertility” Empirical models to predict a couple's chance of conceiving spontaneously are discussed by Hunault A number of authors have described analytical methods for calculating conception probabilities over time for a couple whose probability of conception each cycle is drawn from a probability distribution e.g. . In thisDemographers use the term “fecundability” e.g.  to referintrinsic conception rate, defined as their probability of achieving a pregnancy in the next cycle, if they have not yet achieved a pregnancy. It corresponds to the monthly fecundity rate in The first is the measure that would apply if one had perfect information about a couple, i.e. if there were no uncertainty in their fertility. We refer to this as the couple's The second is a measure of a couple's probability of conception in the next cycle, according to the  information available. This is the expected value of the intrinsic conception rate, reflecting uncertainty, and for this study will be simply referred to as the probability of conception.In statistical terminology, the intrinsic conception rate represents the latent true value of the parameter, whereas what we refer to as the probability of conception is an estimate of this parameter under uncertainty.In this study, we define conception as achievement of a clinical pregnancy. Not all clinical pregnancies lead to a live birth. Thus, the probability of a pregnancy leading to a live birth is on average about 10% lower than the probability of a clinical pregnancy per se. As a live birth is ultimately the desired outcome, it may appear that live birth would be the relevant end-point. There are two reasons why, for this study, it is preferable to use clinical pregnancy as the end-point. The first is consistency with the way pregnancy rates have been measured in previous studies e.g. . The secth cycle will be smaller than it was on their first cycle attempting to conceive indicator that this couple's intrinsic conception rate is low. In other words, the period of non-conception has yielded information about their intrinsic conception rate. The effect of the couple's intrinsic conception rate declining due to ageing over the time period in question (in this case about one year) is likely to be smaller. Conversely, in a couple where the woman is approaching her menopause, an additional year of age may make a much greater contribution to the declining intrinsic conception rate. It is of interest to have some idea of how much difference ignoring reproductive ageing during the time period of attempted conception makes to results. We have explored this by implementing a model of reproductive ageing, described in the section on reproductive ageing and applied in example 5 of this study. The implications for patient management decisions of reproductive ageing during the period of attempted conception are also discussed.In the basic analysis, which we apply to four specific examples, it is assumed that the intrinsic conception rate for a given couple remains constant over the period of time being modelled. In practice there will be some decline in the intrinsic conception rate for a couple due to the effects of ageing. Is it reasonable to ignore this decline for modelling purposes? A rationale for so doing is that, where the female partner is not older than her mid 30 s For the basic analysis, the assumption of a constant intrinsic conception rate also requires that a couple's successive cycles are statistically independent with respect to the probability of conception. This does not assume that all cycles are equally good. Suppose, for example, that a woman ovulates successfully in 50% of her cycles, and that whether or not she ovulates on a given cycle is independent of previous cycles; and that, given the quality of her partner's sperm, she has a 1/3 probability of conceiving in cycles when she ovulates, and a zero chance in cycles when she does not ovulate. Then her chance of becoming pregnant in each new cycle is ½×1/3 = 1/6: this is the intrinsic conception rate for her and her partner.y. We assume that 0≤y<1, i.e. it is possible for a couple to be completely sterile but it is not possible for a couple to be so fertile that they are certain to achieve a pregnancy on the first cycle that they try. Let P be the cumulative probability of conception for that couple, i.e. the probability that the couple will conceive within n cycles. This is the cumulative distribution function for a geometric random variable, given byy = 0.2. Then the chance of the couple conceiving within two cycles (i.e. n = 2) is, from 2 = 0.36. Therefore the couple will have a 36% chance of conceiving within two cycles.Suppose a couple has an intrinsic conception rate y and n it is possible to calculate P using P within a given number of cycles depends on the number of cycles n and the intrinsic conception rate y.For any y which will give a certain probability P of achieving a pregnancy within n cycles  = 0.5. So a couple with an intrinsic conception rate of 5.61%, would have a 50% chance of achieving a pregnancy within 12 cycles. A couple with an intrinsic conception rate higher than 5.61% would have a >50% chance of conceiving within 12 cycles, and one with an intrinsic conception rate <5.61% would have a <50% chance of conceiving within 12 cycles.It is possible to invert indicator of a couple's intrinsic conception rate, but it is a noisy indicator. Numerical examples of cumulative conception probabilities are also given in probability distribution for the intrinsic conception rate. One interpretation of the distribution applies where the couple are drawn at random from a specific population, and no additional information relevant to the couple's fertility is available. The probability distribution of the intrinsic conception rate then corresponds to the distribution of intrinsic conception rates within that population. This interpretation is appropriate for understanding the distribution of time-to-conception in a cohort of couples which is considered as a single population hypothetical population of couples which share the same observed, objective characteristics but vary in certain hidden variables and therefore vary in their intrinsic conception rates.As discussed above, a couple's true fertility is unknown. This is the case both when a couple starts trying to conceive, and when a couple seeks medical help because of a presumed fertility problem. We model this uncertainty by assuming a For descriptive simplicity, we will treat the examples of distributions considered below as referring to populations.prior distribution. We can regard the couple as being drawn from a prior population. After one or more cycles of attempted conception, the information that a couple has failed to conceive can be used to update the prior distribution, leading to a new distribution which we describe as a posterior distribution.We describe the probability distribution for a couple's intrinsic conception rate at the start of their attempt to achieve a pregnancy (i.e. after zero cycles), as the As Bayes' theorem provides the formula for generating a posterior probability distribution from a prior distribution and an event which carries relevant information. In this case, the relevant event is that conception has not occurred.f(y) be the prior distribution for a couple's intrinsic conception rate. We begin by calculating the probability s(n) that a couple drawn at random from the prior population will fail to conceive within n cycles. This constitutes a ‘survival function’, where ‘survival’ in this case means not conceiving within a given number of cycles. If the intrinsic conception rate y for this couple were known, the survival function would, by definition, be given by 1−P. From (1), this is (1−y)n. However, the value of y is unknown, so the survival function is derived by taking an appropriate weighted mean over all values of y in the distribution. The problem closely resembles that of survival under an uncertain hazard rate f(y) have not conceived after n cycles, we obtain:s(0) = 1 for any f(y).Let nf(y) be the distribution of the intrinsic conception rate conditional on n cycles of non-conception. Applying Bayes' theorem for a continuous distribution Let We have applied these methods to four examples of prior distributions for the intrinsic conception rate. For examples 1 to 3, as in Leridon Example 1: 5% of couples are assumed to be sterile, therefore having an intrinsic conception rate of zero. The remaining 95% are assumed to have intrinsic conception rates drawn from a beta distribution with parameters α = 2.3 and β = 3.7 (see the supporting information: text S1). The distribution is illustrated in Example 2: 5% of couples are assumed to have a zero probability of conceiving spontaneously. The remaining 95% again are assumed to have intrinsic conception rates described by a beta distribution, but for this example the parameters are α = 1.8 and β = 4.2. Example 2 deliberately describes a less fertile population than that in example 1: whilst 5% of the population are sterile in both examples, for the upper 95% of the distribution all percentiles of the prior distribution of the intrinsic conception rate are lower for population 2 than for population 1; we have verified this numerically from the probability density functions. The distribution is illustrated in Example 3: 1% of couples are assumed to have an intrinsic conception rate of zero. The remaining 99% of the population are assumed to have intrinsic conception rates described by a beta distribution, with α = 11 and β = 22. .Example 4. 5% of couples are assumed to have an intrinsic conception rate of zero; 85% have intrinsic conception rates drawn from a beta distribution with α = 11 and β = 22 (as used in example 3); and 10% have intrinsic conception rates drawn from a beta distribution with α = 4 and β = 76. This example can be conceptualised as a mixture of distinct fertile and subfertile populations; it has two separate peaks in the distribution of the intrinsic conception rate of the non-sterile population .s(n), where s(n) is given in For examples 1, 2, 3, and 4, The results for example 1, shown in It is interesting that, although the number of cycles taken to reach a particular threshold varies with the different examples, the results do not differ greatly. In particular, for each example it is approximately a year before the chance of conceiving in the next cycle falls below 10%.As couples grow older, their fertility declines. In particular, increasing female age is associated with a decreasing intrinsic conception rate. Female age, therefore, may be expected to have a bearing on how many cycles of attempted natural conception need to elapse before medical investigation and treatment is appropriate. A particular fertility metric could be applied, such as the chance of conceiving in the next cycle falling to below 10%, or the chance of conceiving in the next 12 cycles falling below 50%. When a specific metric is reached, medical intervention may be appropriate. How does the number of non-conception cycles required to reach the threshold metric depend upon the couple's female age? To investigate this question, we considered a population fertility model which explicitly includes the effects of declining fertility with female age. The model uses data presented by Leridon Example 5: For this example, it is assumed that couples vary in the female age at which they become sterile. As female age increases, the proportion of couples who are sterile increases. We use the sterility data given in Leridon We have incorporated this model of declining fertility into the computational analysis. Details of the technical methods used are given in the supporting information (text S1).We have run the computational analysis of time to pregnancy for example 5, for female ages of 25, 30, 35 and 40. For the data used in the model, sterility was defined as an inability to conceive and become pregnant  We now consider an important technical question: what effect does reproductive ageing during the time that a couple is trying to conceive have on the calculated number of cycles of attempted conception before various metrics of subfertility are reached? For example 5, we have investigated this by running a modified version of the program, in which there is no reproductive ageing during the period of attempted conception. In using this model of reproductive ageing, it should be recognised that exactly how fertility declines for an individual couple is not known. To model a population requires assumptions about (a) the changing fertility profile over time for an individual couple, and (b) the variation among couples in the parameters describing this profile. Leridon's model However, we believe that the general pattern of the results for example 5 is likely to hold for any reasonable assumptions about reproductive ageing in a human population.Couples vary in their fertility. A model of conception has been used to shed light on the following question: what can be deduced about a couple's fertility from the duration of their attempt to conceive? When a couple starts trying for a baby, there will be some uncertainty in their intrinsic conception rate, i.e. their probability of conception per cycle. In our modelling framework, this uncertainty is described by a prior probability distribution for the intrinsic conception rate; this distribution will depend on the population from which the couple is drawn. We have developed a numerical computational method for analysing attempted conception, for any chosen prior distribution of the intrinsic conception rate, over any specified number of cycles. For couples who do not conceive over these cycles, the program calculates a posterior distribution of the intrinsic conception rate, together with various fertility metrics, potentially relevant to clinical decision-making.For the basic analysis, it is assumed that each couple's intrinsic conception rate can, for modelling purposes, be treated as constant over the period of time being considered. Results have been computed for four examples of prior distributions of the intrinsic conception rate. For each example it has been assumed that a small proportion of couples are sterile, and the remainder vary continuously in their intrinsic conception rate. Examples 1 to 3 produce conception patterns over time which are consistent with those given in When a clinician is faced with a couple, how will he or she know to which population the couple belongs? The answer is probabilistic: if the couple belong to one of several populations, but it is not known which, then they can be treated as a random draw from a composite population, given by the appropriately weighted mixture of the component populations. Example 4 was devised to illustrate such a composite population.probabilistic measures of subfertility. In For clinical decision-making, the important question is: how many cycles of non-conception should be taken as an indicator that a couple needs investigation and treatment? As this analysis has shown, it is necessary to consider For these examples we did not use a formal mathematical optimisation process to fit distributions to data. Bongaarts Female age is of particular importance to a couple's conception prospects These results for female ageing raise the question of whether reproductive ageing during the time period of attempted conception should be incorporated more generally into computational modelling of time to pregnancy in different populations. It should be noted first that the computations required to incorporate reproductive decline after each cycle of non-conception in example 5 required orders of magnitude more computational time than examples 1 to 4. A more fundamental difficulty is that the model of ageing used in example 5 is based on a specific population model Further empirical and theoretical work on reproductive ageing would be useful. This may draw on IVF studies A number of variables other than age are also associated with conception probability, such as previous fertility history of each member of the couple The modelling approach, as applied to all five examples, assumes that successive cycles of attempted conception are independent. That is, it is assumed that there is no correlation in successive cycles between temporary random factors that may affect the couple's probability of conceiving. Because of this assumption, the approach described here cannot in its present formulation properly represent a situation in which one member of a couple has a disorder which causes temporary subfertility and may last for several months, but has a non-trivial probability of spontaneously dissipating so that fertility is restored, such as, for example, low-weight-related anovulation. This could be captured by incorporating into the model a dynamic process representing how a couple's fertility status evolves over time, e.g. as a Markov process Simulation can be a useful tool for evaluating outcomes of models of biological processes, including attempted conception over time The methods described in this study may be helpful for the further development of decision support systems in fertility assessment, with potential benefits to patients and clinicians, and to health service funders who must allocate resources through decisions that affect large numbers of patients. We are happy to make the software developed for this study available to readers who wish to explore other examples of prior distributions and to develop these methods further.Finally we note that, whilst this study has considered the application of uncertainty in intrinsic conception rates to non-medically assisted conception, the finding that the outcomes of repeat IVF cycles for the same patients are positively correlated Text S1(PDF)Click here for additional data file.


Electron difference density maps through cross-sections of three differently oriented Cu–CNT  composites (top) and the electrostatic difference potential along the transport direction (bottom). The quantum transport properties of a Cu–CNT composite are studied using a non-equilibrium Green's function approach combined with the self-consistent-charge density-functional tight-binding method. The results show that the electrical conductance of the composite depends strongly on CNT density and alignment but more weakly on chirality. Alignment with the applied bias is preferred and the conductance of the composite increases as its mass density increases. It is expected that better control over the structural morphology of the CNTs will result in improvements to the conductivity. Computational analysis of the underlying transport properties and microstructure of the composites will guide this process.The growing demand for electrical energy, changing weather conditions, rising prices and the need for power in extreme environments all limit the use of conventional conductors in electrical wires and interconnects. Furthermore, power losses cause serious performance issues in these conductors. Novel composite materials containing carbon nanostructures can potentially improve a number of properties of conventional conductors but one important area would be to allow them to transmit current more efficiently and at lower cost. They would also reduce the weight required for a designated transmission line. Carbon nanotubes (CNTs) are obvious candidates for this purpose because of their remarkable physical properties, 17 Electron transport across the interface between the CNT and the metal surface is clearly important but the CNT is not embedded within the metal and therefore other transmission pathways cannot occur. More recently, Feng et al.18 studied the electrical performance of a Cu–CNT matrix using a simple electrical model and concluded that the ratio of aligned CNTs and their dimensions affect the current density distribution. To gain further insight at the microscopic level large-scale quantum transport calculations are necessary. In this work, the electronic structure and transport properties of Cu–CNT composites are investigated using a density-functional based approximation method combined with the non-equilibrium Green's function (NEGF) scheme. The effect of CNT density, chirality and alignment to the bias potential is studied. Due to the presence of quantum confinement, each parameter is likely to influence the electrical properties. For the first time a model is constructed in which the CNT is fully embedded within a 3D copper matrix. The results show that the conductance is highest when the long axis of the CNT is parallel to the applied bias. Furthermore the conductance decreases with CNT number density and increases with overall mass density of the composite as expected.First principles calculations on the interaction between copper and CNTs have so far focused on the end or side contact between a nanotube and two copper electrodes.θ = 0°, 45°, 90° where θ is the angle of inclination of the nanotube axis with respect to the transport direction  and a semiconducting CNT  with almost same length (∼11 Å) and very similar diameter (∼8 Å) are considered. This enables a direct comparison of the results for these two cases without the complication of the size dependence. The volume of the Cu cavity containing the CNT is chosen such that the distance between the Cu and CNT surfaces agrees with recent density functional theory (DFT) results16 for optimal separation between the materials, i.e. about 1.9–2.4 Å. For the θ = 0° and 90° orientations, the CNT connects with Cu{100} surfaces at the end contacts whereas for the θ = 45° orientation the surfaces are {110}. To further support this choice of orientations and surface contacts, separate DFT calculations were performed on a  CNT in contact with three low-index Cu surfaces .20 The structures are optimized applying 3D periodic boundary conditions and total energies are converged to within 10–5 eV. The Brillouin zone of the whole structure is sampled using (1 × 1 × 100) k points. The Poisson equation is solved using a Fast Fourier Transform (FFT) solver. The coherent transport calculations are performed using the DFTB method in conjunction with the NEGF technique.21 The calculations involve the self-consistent charge correction (SCC),22 which takes into account the electron density redistribution due to interatomic interactions. The NEGF + DFTB method is an accurate and efficient method for calculating transport properties and has been applied successfully to various nanostructured systems.25 The DFTB parameters for carbon and copper have been validated and reported earlier.26 The steady-state electrical current through the device under non-equilibrium conditions, i.e. for a finite bias voltage (VBias) is calculated using the Landauer formula:27where f is the Fermi–Dirac distribution function,  represent the chemical potentials of the left and right electrodes and T is the energy and voltage-resolved transmission function. Electron transport is assumed to be ballistic since the electron mean free path in copper (∼40 nm) is much greater than the supercell dimensions. The calculations of the current are performed at 300 K. For reference the bulk atomic and electronic structures of copper and graphene calculated with the DFTB method have been compared with DFT calculations and experimental data and the agreement is good  method13 cm–2 CNTs. Also shown is the characteristic of pure Cu. Note that inelastic scattering effects, e.g. electron–phonon coupling, have been ignored in the transport model. However, this approximation does not change the general trends and conclusions obtained here, as the relative change in the conductance is not affected. It is seen that the presence of a CNT within the Cu matrix reduces the conductance (slope of the IV curve) by ∼30% in all cases compared to the intrinsic conductance of the copper. Noticeably the current through the composites is suppressed with increasing θ. These results are consistent with previous reports that show that the end rather than the side of the CNT is the more favourable electron injection path.15 The effect of chirality on the conductance, at least for this CNT density, is very small and therefore the rest of the paper will focus on results for composites containing metallic  CNTs.15 It can be seen that the presence of the interface causes energy level re-alignment and the formation of a potential barrier, which can quench the electron transport. This evident from the two sharp peaks in the electrostatic difference potential which appear at c = ∼6 Å and ∼17 Å for the composite where the CNT is aligned along the bias direction. For the composite with oblique CNT alignment (θ = 45°), the two end effects overlap because of the shortness of the nanotube and only one peak is observed which decays smoothly along the transport direction.In order to understand how the surface interactions between Cu and the CNT affect the transport properties, the electron difference density and electrostatic difference potential for the three  CNT orientations are computed see . The eleθ = 0°. Due to the strong metallic character of the Cu, the electronic structure close to the Fermi level is mostly governed by Cu d orbitals, while C atoms have no significant impact on the total DOS. Because of the dominance by Cu, the orientation of the CNT does not have a significant effect on the total density of states. Further DFT results, shown in Fig. S2  CNT  composite with the most favourable orientation, = 0° see . The resI/dV) of the Cu–CNT  composite with θ = 0° is calculated as a function of CNT number density per unit area and mass density of the composite  is smaller than the expected value of 8.9 g cm–3 due to the ∼2.4% larger DFTB-predicted lattice constant compared to experiment (see Table S2, ESIFinally, the specific differential conductance (dsite see . The higUsing the non-equilibrium Green's function approach, the transport properties of a Cu–CNT composite are determined as a function of CNT density, chirality and alignment to the bias potential. A model is used in which the CNT is fully embedded within the Cu matrix. The electrical conductance is found to be highest when the axial direction of the CNT is along the transport direction. Compared to pure Cu the reduced conductance is attributed to localized charge exchange between the CNT and the metal surface that raises the potential barrier at the interface. The chirality of the CNT does not appear have a major effect on the conductance at least for the CNTs and densities considered here. The results could play an important role in guiding the design and fabrication of Cu–CNT composites for optimal performance. Understanding and controlling the interface between the Cu and CNT in the bulk composite is critical for maximising the electrical performance of this promising new generation of materials.


We use visual information to guide our grasping movements. When grasping an object with a precision grip, the two digits need to reach two different positions more or less simultaneously, but the eyes can only be directed to one position at a time. Several studies that have examined eye movements in grasping have found that people tend to direct their gaze near where their index finger will contact the object. Here we aimed at better understanding why people do so by asking participants to lift an object off a horizontal surface. They were to grasp the object with a precision grip while movements of their hand, eye and head were recorded. We confirmed that people tend to look closer to positions that a digit needs to reach more accurately. Moreover, we show that where they look as they reach for the object depends on where they were looking before, presumably because they try to minimize the time during which the eyes are moving so fast that no new visual information is acquired. Most importantly, we confirmed that people have a bias to direct gaze towards the index finger’s contact point rather than towards that of the thumb. In our study, this cannot be explained by the index finger contacting the object before the thumb. Instead, it appears to be because the index finger moves to a position that is hidden behind the object that is grasped, probably making this the place at which one is most likely to encounter unexpected problems that would benefit from visual guidance. However, this cannot explain the bias that was found in previous studies, where neither contact point was hidden, so it cannot be the only explanation for the bias. Visual information guides most of our everyday actions. Human gaze behaviour has been examined in many such actions, such as making tea and sandwiches ,2, driviWhen grasping an object, people need to first select suitable contact points on the object and then bring their digits to these points –16. WhenThe index finger generally moves along a more curved trajectory towards its contact point –25. To eAltogether, most studies find that people direct their eyes close to the positions at which their index finger will contact the object, but none of them has managed to explain this behaviour. In most studies that recorded eye movements during grasping, participants grasped a thin target object that was attached to a frontal screen, mostly by placing their finger at the top and the thumb at the bottom of the object –19. In sIn a series of seven experimental sessions, we asked participants to grasp either a block or a sphere. The object was placed on a table in front of them. The participant’s head was not constrained . TheWe performed seven experiments, each in a separate session. Since the experiments were all very similar to each other, and the changes that we made were guided by the results of the preceding experiment, we describe the general methods here, and the precise conditions when introducing each of the experiments.In total, fourteen healthy participants took part in the experiments. Seven or eight participants took part in each experimental session, so not all participants took part in all sessions. We numbered the participants from P1 for the youngest (26 years old) to P14 for the oldest (32 years old), with P1, P10, P13 and P14 being male, and the other 10 female. The participants were unaware of the purpose of the study and gave their signed informed consent prior to the experiment. All were right-handed by self-report and had normal vision. This study was part of a program that has been approved by the ethical committee of the Department of Human Movement Sciences of the VU University Amsterdam.starting LED (a red light emitting diode indicating the starting position of the participant’s gaze). The starting LED was at the far edge of the table  three additional light-emitting diodes (LEDs) were used, each aligned with an infrared marker along the participant’s line of sight  with an Optotrak 3020 motion tracking system . Three infrared markers were attached to an individually fitted dental-impression bite-board that the participant held in his or her mouth, but that did not restrain his or her movements. The positions of these three markers were used to determine the position and orientation of the participant’s head. Single infrared markers were attached to the nails of the thumb and index finger of the participant’s right hand. An additional single infrared marker was attached either to the far-left of the target block’s upper surface see also  or to thThe experiment was performed in a normally illuminated room. The participant stood in front of a wooden table  unless any of the markers was moving (standard deviation in position of more than 1 mm during the preceding 100 ms), in which case a sound was heard and the alignment had to be repeated. The two crosses only looked aligned when the eye was situated along the tube’s main axis, so each measurement constrained the Cartesian position of the eye to a line, whose location is known relative to the bite-board.The crosses were aligned 25 times, while ensuring that the orientation of the tube varied with respect to the participant’s head, so that the lines would fan out from the eye in many directions. The point relative to the bite-board for which the sum of the squared distances to the 25 lines was the smallest was considered to be the centre of the eye . Knowing this point with respect to the position of three markers on the bite-board, we could tell where the participant’s eye was, as long as he or she held the bite-board in his or her mouth (and the markers were visible). This calibration was performed separately for each eye. It took approximately 5 minutes per eye.The second step in the calibration was to relate the raw output of the eye-tracker to orientations of the eye in the head. This was done at the beginning of each experimental session. The raw eye tracker values correspond with the position of the pupil as seen by the camera. The eye-tracker was attached to the participant’s head and the bite-board was placed in their mouth. Four LEDs, each accompanied by an infrared marker, were placed at strategic positions in the workspace . InitialBased on the gaze-directions of both eyes, we could in principle determine a 3D gaze-position in space. However, as the depth-component (based on vergence) is very imprecise, and the positions of the finger and thumb when grasping the objects were more or less at the same distance from the participant, we decided to present 2D gaze-directions, obtained by averaging the data of the two eyes. We used the direction of the line connecting the two eyes as the horizontal direction . This is the most natural coordinate system for reporting eye movements. In order to relate the gaze-patterns to the grasping behaviour, we use the same angular coordinate system to represent digit trajectories. It is important to realize that since participants were free to move their heads, fixed positions in space, such as the starting LED and the initial position of the hand, varied slightly in position in this representation.Participants stood in front of the wooden table. The table’s height was aligned with the participant’s hip. The eye-tracker’s cameras were positioned so that they did not occlude any parts of the workspace. After calibrating the eye movements, the experimenter removed all the LEDs except the starting LED, and attached single infrared markers to the nails of the participant’s right thumb and index finger, taking care that the wires did not interfere with the participant’s arm movements.Each trial started with the participant bringing his or her hand to the initial hand position for that experimental session and fixating the illuminated starting LED. Meanwhile, the experimenter placed the object at the appropriate position (thus the object was not occluded from the participant). The experimenter then pressed a computer key, which started the recording and switched off the LED to indicate that the participant could start moving. During the trial, the participant could look wherever he or she wanted. The task was to reach and grasp the target object with a precision grip (between thumb and index finger), lift it, put it back down near its original position, and move the hand back to its initial position. The participant then fixated the starting LED in anticipation of the next trial.No instructions were given as to where participant should look  or how to grasp the object (other than that it was to be done with a precision grip). Participants always lifted the object within a few seconds. Each of our conditions (that will be described in the introductory sections for each experiment) was presented 22 times, and there were either two or three conditions in each experimental session, so each session consisted of 44 or 66 trials, that were presented in a pseudo-random order.italics. We determined the velocity of the hand by numerical differentiation of the average of the positions of the markers attached to the thumb and index finger. A velocity threshold of 10 cm/sec determined the onset of the hand movement. Grip aperture was defined as the three-dimensional distance between the markers on the two digits.A number of measures were only determined in order to obtain other measures, such as when the grasping movement started and when each of the digits made contact with the object. The measures that we will analyse are printed in The moment of contact was determined for each digit separately using the Multiple Sources of Information method . The momContact asynchrony was the time difference between the two digits’ moments of contact, with positive values indicating that the index finger contacted the object earlier than the thumb.The digit that contacted the object first was the one on which we based the moment of contact when analysing gaze. Final grip size was the length of that line, and is expressed as a visual angle. Looking at plots of the digits’ trajectories (available in the results sections) confirmed that final grip orientation provides reliable information about the surfaces by which the objects were grasped, despite being based on the positions of the markers and not on the actual positions of the fingertips that made contact with the object. Final grip size provides a measure for relating magnitudes of shifts in gaze to the angular size of the object. This measure slightly overestimates the distance between the contact points because it too is based on the positions of the markers rather than the fingertips.Grip orientation was used to determine by which surfaces the block was grasped and the angular grip size was determined to be able to report its approximate magnitude for comparison with the gaze data. The final grip orientation was defined as the angle of the projection on the horizontal plane of a line connecting the two markers on the digits at the moment of the grasp. The first step in the analysis of the eye movements was to convert the raw data from the eye-tracker to gaze trajectories expressed in visual angles on the basis of the calibration. We used the measured positions of the markers on the bite-board to determine the Cartesian positions of the eyes and to identify the horizontal direction. To determine the direction of gaze, we had to combine data from the eye-tracker with Cartesian positions that were sampled at a lower frequency. We did so by selecting the eye-tracker value that was the closest in time for each sample of the Cartesian positions of the eyes, resulting in two 100 Hz gaze trajectories (one for each eye) that were then averaged. We next converted the positions of all relevant landmarks (including the positions of the digits) to the same coordinate system. We could hereby express distances between gaze and any relevant landmarks as gaze angles. We corrected for drifts of the Eyelink system by assuming that the gaze is at the starting LED when fixating the latter at the onset of each trial .initial gaze bias when considering the first fixation and as the critical gaze bias when considering the critical fixation. In both cases, positive values indicate that fixation is closer to the index finger.In order to separate fixations from saccades, gaze angular velocity was calculated by numerical differentiation of the gaze trajectory. The onset of a saccade was the first sample on which the gaze velocity exceeded a threshold of 35°/sec. The onset of a fixation was the first sample on which the velocity dropped back below 35°/sec. We were mainly interested in the critical fixation, which is the gaze when the first digit made contact with the object, or just before the saccade if a saccade was being made at the moment of contact. We also determined the first fixation, which was where participants fixated after their first saccade away from the starting LED. We determined the visual angle between each of these two fixation points and each of the two contact points. The difference between the two visual angles for each fixation point was taken as a measure of the extent to which gaze was closer to the index finger than to the thumb. We refer to this difference as the maximal distance between any two fixations  from the first fixation until the critical fixation. Note that we determine the maximal distance between any two fixations, not the maximal distance between consecutive fixations, so this does not require a single saccade to have been made between these positions. We determined this maximal distance for each trial, and report the median value across trials. We report the median rather than the mean because the distances are not normally distributed: they can only be positive and they are sometimes exceptionally large because participants occasionally shift their gaze back to the starting LED, presumably in anticipation of the next trial, before touching the object. If the median maximal distance between any two fixations is much smaller than the final grip size, participants cannot have regularly shifted their gaze between the contact points.To examine the extent to which gaze changed during the reach-to-grasp movement, and thus whether participants regularly shifted their gaze between the contact points, we determined the Except for discarding trials because we were uncertain about the moments of contact, we also discarded trials if gaze was missing for more than half the duration of the reach-to-grasp movement (e.g. due to equipment failure), if gaze data was missing during the last 200 ms before the grasp (e.g. due to blinks), or if the participant did not fixate the starting LED at the beginning of the trial. We determined the initial and the critical gaze biases, the contact asynchrony, the final grip size and the maximal distance between fixations for each trial. We then determined the average  across the repetitions for each condition performed by each participant. The influence of the different conditions on the critical gaze bias and contact asynchrony was evaluated with one-way repeated measures ANOVAs. The consistency of gaze biases (deviation from zero) was evaluated with one-sample t-tests. To evaluate the possible relationship between contact asynchrony and critical gaze bias, we determined the correlation between the participants’ average contact asynchrony and their average critical gaze bias for each experimental session.middle, clockwise and anti-clockwise, respectively). We used several orientations (three conditions) because previous studies [In our first experiment, we attempted to replicate the finding that people fixate near their index finger when grasping an object, but using a more natural configuration than has been studied until now. Participants were asked to reach and grasp a block that was placed in front of them. The initial hand position was at the right edge of the platform as seen by the participant (approximately 20 cm from the object). The block could have one of three different orientations  took part in this experiment. Of the 528 trials , 66 had to be discarded, mainly because markers on the digits were occluded and because of uncertainty about the contact moments, resulting in 462 trials for further analysis .7 = 10.5, p < 0.001; 7 = 5.1, p < 0.001; 2,14 = 0.4, p = 0.7; 2,14 = 1.3, p = 0.3). There was no significant correlation between contact asynchrony and critical gaze bias . Participants did not systematically look back and forth between their contact points during the reaching movements. The median maximal distance between any fixations that took place during individual reach-to-grasp movements was 3.6 ± 2.5°. The average final grip size was 10.8 ± 1.2°.The participants showed a large initial gaze bias: 6.7 ± 1.8° . As a result, participants had to shift their gaze upwards to fixate the target object, instead of downwards as in the first experiment.Seven participants  took part in this experiment. Of the 462 trials , 40 had to be discarded, mainly because markers on the digits were occluded and because of uncertainty about the contact times, resulting in 422 trials for further analysis.6 = 0.8, p = 0.4; 6 = 2.1, p = 0.07; 2,12 = 0.8, p = 0.9; 2,12 = 3.6, p = 0.06), which was 18 ± 5 ms. No significant correlation was found between contact asynchrony and the critical gaze bias . The median maximal distance between fixations during a trial was 3.2 ± 1.1°. The average final grip size was 8.9 ± 0.8°.Starting with one’s gaze closer to the thumb’s anticipated contact point removed the initial gaze bias that we found in the first experiment. The bias was now 0.8 ± 3.1°  than when gaze started at the far edge of the table . This is probably the result of a tendency of saccades to undershoot the aiming location (that might have been the same for both experiments). Saccadic undershoot could help obtain visual information sooner, because the larger the amplitude of the saccade, the longer the eye will be moving so fast that no useful new information can be obtained . HoweverComparing experiments 1 and 2 we see that placing the starting LED between the participant and the object, rather than behind the object, reduced the initial gaze bias from 6.7° to 0.8°, and the critical gaze bias from 5.1° to 2.8°. Thus, reducing the saccade amplitude and duration to quickly obtain visual information about the target probably contributes to the biases. However, even with the starting LED between the participant and the object, most participants’ gaze was biased towards the index finger’s contact point, so reducing the saccade amplitude and duration is clearly not the main reason for people to look closer to the index finger’s contact point.middle position, a position at the far edge of the support (relative to the participant), and a position at the close edge of the support. We asked participants to grasp the sphere without it falling off the support. All other details were as in experiment 1.The index finger generally made contact with the object earlier than the thumb , in order to reduce the chance of tapping the object towards oneself, off the support, with one’s index finger.We expected the index finger to touch the object slightly earlier than the thumb, as before, when the object was in the Eight participants  took part in this experiment. Of the 528 trials , 41 had to be discarded, mainly because markers on the digits were occluded and because of equipment failure, resulting in 487 trials for further analysis.2,14 = 0.2, p = 0.7; average asynchrony: 11 ± 19 ms). The initial gaze bias was 5.8 ± 3.1°  is not a critical factor for the gaze bias.near edge of an additional support surface failed to make people contact the object with their thumb before they made contact with their index finger. This can be explained in hindsight by the difference between the timing of contact by the two digits being so small that the other digit was always close enough to the sphere to ensure that it would not roll off the edge. Thus, we could not completely rule out the possibility that differences in the average contact asynchrony are responsible for the bias in eye movements, but the fact that we failed to influence the contact asynchrony suggests that the contact asynchrony is unlikely to arise from evaluating the risks involved in first making contact with each of the digits.In experiment 3, placing a sphere on the near or a far initial position of the hand, each about 20 cm from the block at the same height as the top of the platform . We oriented the block in a way that ensured that the index finger had to curve around the block when starting near, whereas the thumb had to curve around the block when starting far. We examined whether people are more likely to look at their thumb’s contact point when starting their grasping movements from the far position. Again, all other details were identical to those of experiment 1, except that we only used one orientation of the block .Another possible origin for the biases in fixations is that the index finger generally curves around the object to reach its contact point. This curvature may make reaching this contact point harder, and therefore people may need more visual information about this area. This did not seem to be the reason for the gaze bias when grasping thin objects that were attached to a frontal plane , but in Eight participants  took part in this experiment. Of the 352 trials , 28 had to be discarded, mainly because markers on the digits were occluded and because of equipment failure, resulting in 324 trials for further analysis.far position (blue trajectories), and close to where her index finger made contact with the object when starting from the near position (red trajectories), as we proposed that might happen. However, this was not a general tendency.7 = 19, p < 0.001; 7 = 12, p < 0.001; 1,7 = 0.5, p = 0.5; 1,7 = 0.05, p = 0.7) which was 12 ± 11 ms. No significant correlation was found between contact asynchrony and the critical gaze bias . The median maximal distance between fixations was 1.4 ± 0.8°. The average final grip size was 9.9 ± 1.1°.The initial gaze bias was 7.3 ± 1.5° (tIn this experiment we tested whether the gaze bias depends on the curvature of the digit’s movement towards its contact point. One participant (P11) did tend to look near where her thumb made contact with the object when starting the movement from the far position, as we had anticipated, but otherwise neither the initial nor the critical gaze bias was influenced by the initial hand position. This shows that the bias towards the index finger’s contact point is not actually a bias towards the contact point of the digit that curves around the object’s surface.A manipulation that will more obviously influence the actual grasp than does placing a sphere at the edge of a surface (experiment 3) or choosing initial hand positions that force one of the digits to curve around the target object (experiment 4), is to attach a protrusion near the contact point on one of the surfaces. Changing the object’s shape, so that more accuracy is required by one digit than by the other, has been shown to give rise to small shifts in gaze . In thisEight participants  took part in this experiment. Of the 352 trials , 36 had to be discarded, mainly because markers on the digits were occluded, resulting in 316 trials for further analysis.7 = 11.3, p < 0.001; 7 = 8.3, p < 0.001; 1,7 = 17.03, p < 0.005; 1,7 = 1.9, p = 0.6; average: 12 ± 16 ms). No significant correlation was found between contact asynchrony and the critical gaze bias . The median maximal distance between fixations was 2.1 ± 1.2°. The average final grip size was 9.4 ± 1.2°.The initial gaze bias was 6.3 ± 1.7°  between their thumb and little finger. If actual constraints are critical, we would expect participants to look even closer to their little finger’s contact point than they do for the index finger, because it is less common to grasp objects in this manner, so doing so is likely to require more visual control. If the eyes are simply directed to the index finger’s contact point out of habit, it is not clear what they will do if the index finger is not involved in the grasp. For this experiment, looking closer to the little finger’s contact point and making contact first with the little finger are considered to be positive biases. All further details in this experiment were identical to those in experiment 1.Seven participants  took part in this experiment. Of the 462 trials , 77 had to be discarded, mainly because of equipment failure and because of uncertainty about the contact times, resulting in 385 trials for further analysis.6 = 1.5, p = 0.1; 6 = 1.2, p = 0.2; 2,12 = 1.9, p = 0.2; 2,12 = 3.8, p = 0.6; average: 11 ± 18 ms). No significant correlation was found between contact asynchrony and the critical gaze bias . The median maximal distance between fixations was 1.9 ± 0.9°. The average final grip size was 10.9 ± 1.1°.The participants’ initial gaze bias was not significantly different from zero: 3.9 ± 4.0° . Note that although the variability between the participants’ biases is larger in this experiment than in the former ones, the distance between fixations during a trial and the variability across trials for individual participants were not larger, so participants were consistently doing different things, not just shifting their gaze around to learn where they can best look during this unusual way of grasping.middle, clockwise and anti-clockwise, respectively). They started with their hands close to their body, as in the near condition of experiment 4. For stability, they held their hands together with the digits interleaved [In the previous experiment we found that some people looked near the contact point of their little finger, but the tendency was less consistent than when using the index finger. To further examine whether people fixate near their index finger’s contact point out of habit, we asked participants to reach and grasp a block between the index fingers of both their hands. The block could have one of three different orientations  took part in this experiment. Of the 462 trials , 56 had to be discarded, mainly because of missing markers, resulting in 406 trials for further analysis.6 = 0.3, p = 0.7; 6 = 0.6, p = 0.5; 2,12 = 11.7, p = 0.002; 2,12 = 6.3, p = 0.01): it was 3 ± 10 ms for the middle orientation, 18 ± 12 ms for the clockwise orientation, and -10 ± 15 ms for the anti-clockwise object orientation. This means that the digit that made first contact with the object was the one that did not need to curve around the object’s corner to reach its contact point as in [Participants neither showed a significant initial gaze bias  in some conditions.In this study, we aimed at better understanding why people generally look near their index finger’s contact point when grasping an object. We found that fixations depended on where our participants were looking before they started the grasping movement, on the presence of protrusions, and on the orientation of the object when grasping with the index fingers of both hands. Fixations did not depend on the other factors that we examined, including the position at which the grasping movement itself started.In our first experiment, we asked participants to grasp a block that was placed on a table in front of them in various orientations. The hand was initially to the right of the object. In this way we tried to minimize the differences in the constraints imposed on the two digits, while maintaining a natural grasping movement. In accordance with previous studies –20; but , so theyThe tendency that we found in experiment 1 to fixate near the contact point of the index finger was not just due to the starting position of the gaze being closer to that contact point. In experiment 2, we moved the starting position of the gaze to the side of the thumb’s anticipated contact point. Although the initial and critical gaze biases were reduced in experiment 2, they did not change sign. The critical fixations of all but one participant (P11) were still clearly closer to the index finger’s contact point than to the thumb’s contact point. In experiment 2, the bias to look near the index finger’s contact point appeared to be less strong for first than for later fixations . SinWe also confirmed (experiment 4) that the tendency of the index finger to move along a more curved trajectory is not responsible for critical fixations being near the index finger’s contact point , despiteIt is somewhat surprising that the subtle differences in object orientation in experiment 7 influence gaze as much as does placing protrusions at the centre of the grasping surfaces in experiment 5. Perhaps the possibility of something obstructing one’s movements to a position that one cannot see (protrusion near the index finger’s contact point in experiment 5) attracts gaze more than does the presence of an object at a position that one can see (protrusion near the thumb’s contact point). This could explain why only one participant (P11) fixated nearer to her thumb’s contact point when the protrusion was on the thumb’s side in experiment 5, whereas the other participants fixated closer to their index finger’s anticipated contact point . It is also consistent with gaze sometimes being directed towards occluded parts of objects in previous studies . This miAnother idea that has been proposed to explain systematic fixations towards the index finger’s contact point is that the index finger generally contacts the object earlier than the thumb . Althoug2.5 Data analysis; [On average, the index finger contacted the object about 15 ms earlier than the thumb in our first five experiments, which is much less than the difference reported in some earlier studies . There nalysis; . It is tAnother possible reason for the systematic bias to fixate near the index finger’s contact point is that doing so may usually be the optimal thing to do when grasping objects in daily tasks. If the bias were directly related to where the index finger is heading, we would not have expected participants to fixate near their little finger’s contact point in experiment 6. That people’s first and critical fixations were generally near their little finger’s contact point, although some participants did fixate near their thumb’s contact point, suggests that the bias to fixate the index finger’s contact point in the previous experiments does not just arise out of habit. However, the larger variability in the fixation positions across participants in experiment 6 could arise from participants fixating the surface of the object near where their index finger will be at the moment of the grasp. The position of the index finger was not recorded in experiment 6, so we cannot completely exclude this possibility. We find it unlikely, though, because we do not have any reason to expect participants to fixate a region of the object near a digit that does not actually make contact with the object.Additional evidence against looking at the index finger’s contact point out of habit is provided by experiment 7. The participants’ first and critical fixations were neither systematically closer to the left nor closer to the right index finger’s contact point, suggesting that fixations neither depend on how often a digit is used nor on how much control it requires. Instead, participants in experiment 7 fixated nearer the surface that was oriented away from themselves. Their fingers first made contact with the surface that was oriented towards themselves. Thus, their critical fixations were not closer to the digit that contacted the object first. It therefore appears to be the position that is on the far, occluded side of the object, rather than the index finger’s contact point, that attracts gaze. We propose that there is a tendency to look closer to the surface that one does not see because the precise contact is less predictable at that surface; it is more likely that one will encounter unexpected collisions with occluded objects behind the object that one is grasping, or that one will encounter unexpected dents or protrusions of the surface of the object itself.One might have expected our participants to shift their gaze sequentially between both anticipated contact points and direct their gaze to the most important position at the critical moment. Our participants did not do this: the overall average maximal shift in gaze within a single trial  was 2.6 ± 0.6°, which is only a small fraction of the average final grip size  and is clearly smaller than the average critical fixation bias (about 5°).Although the selection of contact points is critical when planning and executing a grasping movement, we here found that looking directly at both these points does not seem to be particularly important. Most importantly, we show that the strong bias to fixate near the index finger’s contact point, even in head-free grasping, cannot be fully explained by any of the factors that have been proposed and that we examined. What we do show is that where one is looking before one starts the grasping movement, what the required accuracy is at the contact area, and whether the digit’s contact point is visible or not, all bias where one fixates.


Anonymisation of spatially referenced data has received increasing attention in recent years. Whereas the research focus has been on the anonymisation of point locations, the disclosure risk arising from the publishing of inter-point distances and corresponding anonymisation methods have not been studied systematically.We propose a new anonymisation method for the release of geographical distances between records of a microdata file—for example patients in a medical database. We discuss a data release scheme in which microdata without coordinates and an additional distance matrix between the corresponding rows of the microdata set are released. In contrast to most other approaches this method preserves small distances better than larger distances. The distances are modified by a variant of Lipschitz embedding.The effects of the embedding parameters on the risk of data disclosure are evaluated by linkage experiments using simulated data. The results indicate small disclosure risks for appropriate embedding parameters.The proposed method is useful if published distance information might be misused for the re-identification of records. The method can be used for publishing scientific-use-files and as an additional tool for record-linkage studies.The online version of this article (doi:10.1186/s12942-015-0031-7) contains supplementary material, which is available to authorized users. The amount of microdata gathered by governmental, research, and other institutions has increased considerably within the last decades. Due to laws such as the American Freedom of Information Act and the principles of good scientific practice, more and more of these datasets are available for secondary analyses. In many research fields such as medicine or social research, microdata files contain information about individuals. But the units of observation in a microdata file might also be hospitals and other health care providers, schools or households. Today, many data sets available for secondary analyses already contain location information for the units of observation. Given such data, techniques from spatial statistics can be used to approach research problems such as disease clustering and their causes .In principle, the anonymity of research data on individuals and organisations should be guaranteed. Therefore, the release of microdata is strongly regulated in most countries. In general, it is required that the re-identification risk of anonymised records should be very small. Of course, the technical details to comply with national legal requirements vary between countries and may be open to interpretation, as for example in the case of the American HIPAA rules .statistical disclosure control. There, a distinction between attribute and identity disclosure is made [The re-identification problem of anonymised records is discussed in the technical literature on  is made . As in tlocation is often one of the critical pieces of information for a successful re-identification attack ack , our attack can still be performed or even improved. Although the release of distance matrices instead of coordinates makes re-identification attacks more difficult, releasing the exact distance matrix Anonymisation of spatial data has been addressed in many research contexts . CompreFollowing , the metDue to its simplicity, aggregation is the most popular method for releasing administrative or health data containing spatial references. Using areal aggregation, a sufficient level of confidentiality can often be achieved. For example, the US HIPAA rules 45 CFR 164.514 demand aggregation of ZIP codes. However, the protective effect of aggregation is coupled with a massive loss of precision in the calculation of distances, especially for entities in close proximity. Therefore, the problem of choosing suitable aggregation units has received a lot of attention , 11.11k-anonymity in this case) is satisfied. The authors show that their approach outperforms aggregation concerning cluster detection under the privacy requirement of k-anonymity. Moreover, they show that their approach suffers from a minimal loss in cluster detection performance compared with random perturbation but yields a considerably higher degree of privacy protection.A special case of random perturbation is proposed in . In thatAnother innovative strategy for the anonymisation of spatial point data is due to Wieland et al.  who deveHowever, this approach also intends to preserve the spatial distribution of the sampling units, whereas our focus is on releasing spatial information only through the distance matrix (in addition to microdata without coordinates).d which depends on the acuteness of the grid. If the distance is greater than 2d no distance can be computed.In the literature, the preservation of distances has been mentioned only in passing. A notable exception is the paper by Kerschbaum  which foOur method does not use a regular grid but makes use of reference sets whose elements are randomly sampled points. Moreover, even small distances are preserved only approximately by our method rather than exactly which contributes to the resilience of our method against attacks.D containing the pairwise geographic distances between the units of observation. Using this kind of information is sufficient for statistical analyses of many research problems. For example, methods for the detection of spatial clusters of infectious diseases are important in epidemiology. In this context, the article [If the intended analysis requires the computation of distances, the necessary information is given by the distance matrix  article  introducIn general, the new method described in this article is intended for statistical analyses of inter-record distance matrices in combination with additional attributes. Such data are widely available in infectious disease modeling, environmental epidemiology and socio-geographics. We discuss a data release scheme in which the microdata without coordinates and an additional distance matrix between the rows of the microdata set are released. We assume that the one-to-one correspondence between the rows of the microdata set and the rows/columns of the distance matrix is known. Examples of applicable methods are agglomerative clustering algorithms  D to be released in addition to corresponding microdata. After the description of the technique in the “We introduce a new technique for generating an anonymised version Alice is willing to release microdata including geocodes that permit useful distance approximations between the observational units. Thus the published data should be available to any researcher  who wants to perform analyses based on this data. Hence, the data must be sufficiently anonymised by Alice such that re-identification of the observational units by a malicious adversary Eve is only a remote risk.We assume the following situation: A data holder T free from any spatial reference of the original database T a geographic point datum We assume that Alice has already created a sufficiently anonymised version T. The exact distances between the entities in T are stored in an i-th and the j-th record in T. The output of our method consists of an D more suitable for being released in addition to T.Let dimension parameter) and size parameter). The effect of these parameters on the accuracy and the provided anonymity will be studied below. The algorithm consists of the following steps:d and k.Choose the embedding parameters d random reference sets k, i.e. Create p is mapped to d is the distance between r. This step is illustrated in Fig. In this intermediate step each point location mentclass2pt{minimp and q is computed as the f(p) and f(q) in The approximate distance The output is the pair Our algorithm depends on two embedding parameters: An exemplary implementation of the above algorithm in the programming language R  is proviRemark The embedding into Lipschitz embedding [mbedding . Lipschimbedding ) or to pmbedding . Note thIn the field of data privacy, the use of Lipschitz embedding has been suggested for privacy-preserving string comparisons . FurtherIn general, accuracy of distance computations is linked with the provided degree of anonymity and vice versa. More accurate released distances will give more information to the adversary. Therefore, the attacker will study the amount of error in distance calculations caused by the embedding technique.d and k, we state a fundamental property of Lipschitz embeddings.Before considering the effect of the embedding parameters We havefor all p, q, so that the approximate distancenever exceeds the original distanced.(Contractivity of Lipschitz embedding) For a proof of Proposition d and k. Hence, it is important for the adversary Eve to study the effect of d and k on the accuracy of the transformed distances.The statement of Proposition d is obvious: As d increases, the maximum in  due to Proposition d increases.The approximation of distances is likely to become better if The dependence of the accuracy of transformed distances on the dimension parameter ximum in  is takenmentclass2pt{minimk. We denote a point for which the minimum over all anchor point. For p and all reference sets p and q does not guarantee that their distance is accurately approximated (the approximate distance can even be 0 in this case), it is easy to see that it makes accurate approximation more likely. For p and q are far away from each other. Under this condition, original distances will be underestimated.Let us now consider the dependence on the parameter mentclass2pt{minim2.k lead to a less accurate approximations of distances.Larger values of 3.In general, shorter distances will be better preserved than longer distances.This reasoning results in two additional conjectures:d decrease the deviation of approximated distances; therefore the approximations are closer to the original distances. The same effect can be observed as k decreases. The third conjecture  is also obvious in the plots.These effects will be demonstrated by an example of three pairs of British cities with different spatial distances: Liverpool–Manchester  the proportion of correct nearest neighbour classifications is large. Only for the smallest dimension considered  data mining tasks such as this cannot be computed at all.Standard methods for the evaluation of privacy of distance matrices seem to be unavailable.linkage attack which is widely discussed in the literature on statistical disclosure control [identification file) with the published microdata file (termed the target file), the attacker tries to match the records of both files. In this context, common attributes in both files  are referred to as quasi-identifiers [indirect identifiers [The graph theoretic linkage attack described here is related to a general attack mode termed  control . Linkagentifiers  or indirntifiers .The power of linkage attacks using quasi-identifiers has been demonstrated repeatedly . The mok-anonymity [k-anonymity if each record cannot be distinguished from at least k-anonymous if in case that an entity from the identification file can be linked with a given record from the target file, then it can be linked with at least To prevent linkage attacks, many of the well-known anonymisation techniques for microdata modify the original data. For instance, the R package sdcMicro  providesnonymity . A microV hereafter) contains correct matches (true positives) as well as incorrect ones . When an entity i from the identification file can be matched with more than one observation unit t of the target file, different potential matches are equally likely.Generally, the set of all potential matches between target and identification file  where t is a unit of observation from the target file and i a known entity from the identification file such that t and i coincide concerning the released attributes. Therefore, the pair  corresponds to a potential match.However, when additional information about the distances between the units of observation in the target file is released and the attacker can calculate the distances between the entities in the identification file, the compatibility of matches in compatible. This decision can only be made based on the knowledge of the released distance between Given two such pairs The precise definition of compatibility is critically dependent on the way the distances between the observation units have been modified by the data holder before releasing the data. Below we will give a specific definition for our case of interest, where the distances are modified by the variant of Lipschitz embedding introduced in the “V in terms of their compatibility can be modelled by means of a simple undirected graph V of this graph is just the set of all potential matches as above. The edge set E is defined as follows: two matches are tied by an edge  if and only if they are classified as compatible. From now on, we refer to this graph as the compatibility graph.3The result of checking all potential matches of C of vertices in V of maximum size such that any two vertices from C are adjacent. In the field of algorithmic graph theory, this problem is referred to as the maximum clique problem [C and drop other potential matches.Having constructed the compatibility graph, the attacker will try to find a set  problem . The advE. If only d and k to estimate the distribution tolerance interval by taking the smallest V of the compatibility graphs contains 7976 (resp. 15517) nodes of which only 40 (resp. 50) correspond to true matches. For this reason, performing a classical linkage attack in both scenarios is not promising and the target files would certainly be regarded as sufficiently anonymised if no additional distance information had been released.A visualisation of the target and the identification files for the two scenarios considered are given in Figs. k and d.The linkage attack was repeated using the data sets described above for different values of In a first experiment, we set the parameters In a second experiment, we used parameter values which should yield higher levels of protection than the set of parameter in the first experiment. Therefore, we considered http://www.sicmm.org/~konc/maxclique/. The number of iterations was set to 20.000.000; the maximal clique found until this iteration was used as result.Data preparation and analysis were done with the statistical programming language R . As indiprecision :For theDue to the contractivity of the Lipschitz embedding, small distances will be preserved better than large distances. Therefore, statistical models using local features will give accurate results despite the (intended) distortion of the distance matrix. For example, agglomerative cluster analysis will give very similar results. In general, treating the transformed distance matrix as censored data might give additional options for analysis. For a comprehensive review of suitable statistical approaches for the analysis of censored data, see .Of course, descriptive statistics based on the modified distance matrix alone will be biased. However, with the exception of quantiles, publishing additional descriptive statistics of the unmodified distance matrix seems not to increase the re-identification risk for the graph based attack since this information is not used in the attack. Since no other attack on distance matrices is known at the moment, there is no way to assess the risk for unknown attack methods.d and k by simulations. However, similar considerations are necessary for all other geo-masking methods.For one of our example data sets, we have shown that the only currently known attack on distance matrices fails if the embedding parameters are chosen carefully. For this data set consisting of simulated German population data, choosing We consider the levels of privacy protection reported here as conservative estimates, since real world attacks will suffer from practical obstacles such as measurement and data processing errors in distances. Furthermore, the amount of overlap between target and identification file will often be lower, resulting in lower precision and recall of an attack. Finally, for large files, the graph theoretical linkage attack becomes computationally expensive since the attack requires exponential resources with increasing size of the compatibility graph.However, the privacy analysis presented here is based only on the graph theoretic linkage attack. To our knowledge, no other attacks on distance matrices have been published. Therefore, for a detailed evaluation of disclosure risks for publishing distance matrices further research on attacks is needed.


Risk is a ubiquitous feature of the environment for all organisms. Very few things in life are achieved with absolute certainty. Therefore, it is essential that organisms process risky information efficiently to promote adaptive behaviour and enhance survival. Here we outline a clear definition of economic risk derived from economic theory and focus on two experiments in which we have shown subpopulations of single neurons in the orbitofrontal cortex of rhesus macaques that code either economic risk per se or an error-related risk signal, namely a risk prediction error. These biological risk signals are essential for processing and updating risky information in the environment to contribute to efficient decision making and adaptive behaviour. Knight defined risk as a quantity with known outcome values and known outcome probabilities and ambiguity as a quantity with known outcome values and unknown probabilities. Essentially Knight defined ‘risk’ as a measurable quantity of uncertainty that is distinct from immeasurable uncertainty (ambiguity). Although this is an accepted definition of ‘risk’ in the field of economics, your friends will undoubtedly provide you with several other definitions of ‘risk’ as they understand it.The variation in people’s definitions of risk is not simply due to naivety of the economic definition; the Oxford English Dictionary defines risk as ‘the possibility of loss, injury, or other adverse or unwelcome circumstance’. This dictionary definition invokes perhaps the most prevalent and common conception of risk outside of economic theory as a probabilistic sense of loss. This is not the case with the economic definition, as the possible outcomes in economic risk can be exclusively positive (or negative). Therefore, Knight’s contribution to the economic theory of risk was to define risk as a measurable quantity that captures the dispersion of probabilistic outcomes whether they are positive, negative or both.p = 0.5 to p = 1 and the certainty that an outcome will not occur increases from p = 0.5 to p = 0  or the coefficient of variation . Note that economic risk is distinct from reward probability, which has a non-monotonic relationship with risk: risk is maximal when probability is equal to 0.5 since the certainty that an outcome will occur increases from to p = 0 . As suchto p = 0 . For exaNote that in this example outcome probability = 0.5 due to the fact that there are two possible outcomes from a coin toss. The two-outcome approach has been utilised in the majority of neuroscientific investigations of risk processing, which comprise the focus of this article. This approach facilitates the most straightforward and simple method of orthogonalization of the independent variables of interest in such studies, namely reward probability, value and risk. Nonetheless, early work investigating the performance of patients with focal brain lesions using multiple outcomes highlighted the role of the ventromedial prefrontal cortex in risk processing , a findiA key area of interest for economists, psychologists and behavioural ecologists is whether organisms are sensitive to economic risk and the effect of economic risk on decision making and adaptive behaviour. Also, neuroscientists have begun addressing whether particular areas of the brain are responsible for processing economic risk, a putative necessity for informing decision-making mechanisms and adaptive behaviour.1.1Damage to the ventromedial prefrontal cortex (VMPFC) in humans has been shown to affect decision making under conditions of uncertainty in gambling tasks involving probabilistic judgements  and econMonkeys were trained to associate different visual cues with three binary symmetric equiprobable reward distributions that differed in economic risk . This deThus, this approach allowed us to behaviourally assess the monkeys’ risk preference and neuronal responses independent of a confounding reward maximisation strategy on behaviour or an expected value signal in neurons. In addition, we trained the monkeys on two sets of risky cues that varied in visual properties in order to control for potential neuronal responses coding the visual properties of the cues. The cues were presented on either the left or right side of a computer monitor requiring the monkeys’ to make eye movements to the corresponding side in order to receive reward to test whether neuronal responses were related to the action required to receive reward. Also, riskless cues that varied only in reward magnitude were used to explicitly test for any sensitivity of neurons to changes in value.When the monkeys were given a choice between the risky cues and a safe cue of the same expected value they preferred the risky options with a monotonic increase in preference with higher risk. This preference was independent of the visual properties of the cues; the monkeys preferred the higher risk options irrespective of whether the risk information was explicitly displayed on the cues or not . The experienced risk is the risk indicated by the visual cue on any given trial. Therefore, there is a predicted level of risk at the beginning of a trial when the monkeys are required to fixate on a neutral stimulus (a red dot in the centre of the computer monitor). This predicted risk is calculated as the standard deviation of the six possible rewards available at the end of the trial  = 5.31, p = 0.03; average SRC for neurons with negative slope = −0.26 versus −0.01 for risk, F = 48.36, p < 0.001; one way ANOVA). In addition, the amount of variance explained, measured as the coefficient of partial determination, was not correlated between risk prediction error and risk . Taken together these data show that the population of OFC neurons coding risk prediction error are largely separate from the OFC neurons coding risk per se.We identified and characterised OFC neurons that code the absolute value of risk prediction errors with either an increase or decrease in firing rate B and C. Therefore, single OFC neurons code either economic risk per se, as measured by reward variance or standard deviation, or deviations in experienced risk from predicted risk, namely a risk prediction error. These two separate pieces of information pertaining to rewarding outcomes under conditions of risk and uncertainty are likely to be vital for tracking risky information in the environment and comprise part of the neuronal architecture necessary for efficient decision making and adaptive behaviour in risky situations.2p = 0.5) compared to decisions with more or less certainty. An economic risk signal has also been identified in midbrain dopamine neurons  is a central tenet of the mean–variance approach. Under the normative assumptions of expected utility and prospect theory, a non-linear value function is capable of capturing risk attitude independent of a requirement on risk per se. For example, the curvature of a utility function captures the risk attitude of an organism as either risk averse  or risk seeking . The same rationale may be applied to descriptive, process-based explanations of risk sensitivity that take into account behavioural observations, learning theory and cognitive processes : risk seAlthough our data do not preclude the existence of neuronal mechanisms that comply with the assumptions of other economic models of decision making under risk and uncertainty, they do support the existence of a neuronal architecture involving the OFC that is explicitly sensitive to risk and expected value in accordance with the mean–variance approach.5Economic risk signals have been identified in single neurons and in distributed brain regions. The OFC risk signal is unique because it is independent of sensory and motor information therefore representing a high level abstraction of economic risk information. This high level abstraction of reward-related information processing in the OFC is not unprecedented. Economic values measured as subjective preferences for different reward types are also represented by a high level abstract coding mechanism in the OFC . MoreoveCharacterisation of the risk signal at the single neuron level in the OFC has advanced the knowledge provided by human studies that indicated a possible function for the OFC in processing risky information . In part6The risk signal observed in single OFC neurons to date is largely derived from objective measures of risk, which serve as an independent variable in the analysis of neuronal activity. Interestingly, the risk-related activity of neurons in the anterodorsal septal region is not exclusively objective as these neurons only code risk information pertaining to rewarding outcomes and not aversive outcomes . Moreove


Wireless sensor network plays an important role in intelligent navigation. It incorporates a group of sensors to overcome the limitation of single detection system. Dempster–Shafer evidence theory can combine the sensor data of the wireless sensor network by data fusion, which contributes to the improvement of accuracy and reliability of the detection system. However, due to different sources of sensors, there may be conflict among the sensor data under uncertain environment. Thus, this paper proposes a new method combining Deng entropy and evidence distance to address the issue. First, Deng entropy is adopted to measure the uncertain information. Then, evidence distance is applied to measure the conflict degree. The new method can cope with conflict effectually and improve the accuracy and reliability of the detection system. An example is illustrated to show the efficiency of the new method and the result is compared with that of the existing methods. Wireless Sensor Networks(WSN) play an important role in intelligent navigation. It can not only detect and process vehicle’s running information, such as the internal running states and external surroundings, dynamics and current position, but also transmit information via wireless, which improves the safety and the comfort of vehicles  Dempster  can be uHowever, different sensors’ reports may conflict highly with others due to different sources. When faced with such conflicting information, it may arrive at a counter-intuitive conclusion by using Dempster’s combination rule. How to effectually handle conflict is inevitable in data fusion of WSN , is first proposed by Dempster  and thenn mutually exclusive and collectively exhaustive events about some problem domain, Let nt Jones , also knm is also called the belief function or the Basic Probability Assignment(BPA), A  and the plausibility function Pl(A) represent the upper limit function and the lower limit function of hypothesis A respectively  is expressed below:And the Similarity Measure Matrix  of each evidence can be obtained.Step 2: Calculate the information volume of evidencesAccording to Eq. (Iv(i) to measure the uncertain information. It is defined as following: Step 3: Normalize the weights of evidencesFor each evidence, the weight k evidences, the normalization process is given in Eq. Step 1: Cg to Eq. , the Denn in Eq. . 19\docuThe specific flowchart of the new method is shown in Fig. A, B, C in a target recognition system. The frame of discernment is denoted by In this section, a numerical example from reference Zhang et al.  is illusmentclass2pt{minimAs for the BPAs given above, it is obvious that the detection of Table Sup(i) of each evidence.First, adopt Eqs. –13) to  to 13) tIv(i) of each evidence.Next, apply Eq.  to obtaiThen, obtain the weight of each evidence after normalization.Finally, modify the BPAs by weights and combine the weighted averaging evidence 4 times. The final results are listed in Table A. It’s clear that the proposed method has the highest belief degree of A whatever the number of evidences is.Figure Even though there are four of five evidences supporting the hypothesis B on account of the influence of When there are only two evidences, Yager’s method assigns most belief degree to the universal set A, the belief degree to object A assigned by the proposed method reaches up to 0.8274 while that of Zhang’s method is only 0.5681. It’s clear that the proposed method is not only efficient but also reliable even though there are only three evidences.When it comes to three evidences, the first four methods can not make decisions. The reason is that the belief degree they assigned to hypothesis Under the situation of five evidences, the proposed method improves the accuracy of identification to 0.9886. Therefore the proposed method can deal with conflict and make decision effectually.Evidence distance reflects the relationships of different evidences. Deng entropy represents the inner properties of evidences. The proposed method takes into account of not only evidences’ relationships but also the nature of evidences so that it is efficient in dealing with conflict.In this paper, a new weighted averaging combination method on basis of evidence distance and Deng entropy is brought up to manage conflict in sensor data fusion. The proposed method has three advantages. First, it adopts Deng entropy to measure the information volume and applies evidence distance in measuring conflict degree. The new method takes into consideration of not only evidences’ relationships but also evidences’ inner properties which is more reasonable. Besides, the proposed method preserves the desirable properties of the weighted averaging method. What’s more, the new method requires less information and is much more simple to make decision compared with other methods. Generally speaking, it is an efficient method to deal with conflict in sensor data fusion and helps a lot with proper identification in WSN.