the effect of text based math task on dynamic stability control during stair descent abstract stair descent imposes a significant challenge for dynamic stability among young adults the effect of a concurrent text based math task on dynamic stability control remains unclear during stair descent when considering the influence of gait velocity twenty six participants performed three successful stair descent trials under texting or no texting conditions at their preferred speed synchronous kinematics and kinetics were collected by an eight camera vicon infrared motion capture system and two force platforms repeated measures analysis of covariance and wilcoxon signed rank test were used to analyze the differences between the two different task conditions with gait velocity as a covariate the outcomes indicated that under texting condition sagittal margin of stability increased at right foot landing step cadence double support percentage sagittal and frontal joint moment decreased and sagittal and frontal joint angles were also modified it is concluded that concurrent texting impaired sagittal and frontal stability control during stair descent despite slowing down the step cadence knee and ankle joint adjustment strategies were mainly adopted in response to stability control in the sagittal plane with the interference of texting whereas the hip joint adjustment strategy was adopted in the frontal plane in conclusion texting behaviors on mobile phones should be minimized during stair descent

ricci collineations of static spherically symmetric spacetimes the ricci collineations of static spherically symmetric spacetimes are classified and their relationship with isometries is discussed a general theorem about this relationship is stated and its extension to all spherically symmetric spacetimes is discussed

classification of curvature collineations of plane symmetric static spacetimes a complete classification of curvature collineations of static plane symmetric spacetimes is obtained and then a comparison between isometries and ricci collineations of the corresponding metrics is given

classification of spherically symmetric static space times by their curvature collineations a complete classification of all spherically symmetric static space times according to their curvature collineations is presented and compared with ricci collineations of corresponding space times

a new class of estimators for the reduced second moment measure of point processes a class of edge corrected estimators for the reduced second moment measure of a stationary isotropic point process is proposed all estimators in this class have the same unbiasedness properties as previously suggested edge corrected estimators one natural element in this class has superior asymptotic properties to existing estimators when the underlying process is poisson a simulation study shows that this superiority also holds for certain cluster processes

geodesic first integrals with explicit path parameter dependence in riemannian space times in a riemannian space vn general formulas are obtained for geodesic first integrals which are mth order polynomials in the tangent vector and which are assumed to depend explicitly on the path parameter s it is found that such first integrals must also be polynomials in s necessary and sufficient conditions are found for the existence of these first integrals the existence of many well known symmetries such as homothetic motions scale change affine collineations conformal motions projective collineations conformal collineations or special curvature collineations are shown to be sufficient for the existence of such first integrals with explicit path parameter dependence to illustrate the theory geodesic first integrals of this type have been calculated for four riemannian space times of general relativity

estimating the k function of a point process with an application to cosmology motivated by the study of an important data set for understanding the large scale structure of the universe this work considers the estimation of the reduced second moment function or k function of a stationary point process on r observed over a large number of segments of possibly varying lengths theory and simulation are used to compare the behavior of isotropic and rigid motion correction estimators and some modifications of these estimators these results generally support the use of modified versions of the rigid motion correction when applied to a catalog of astronomical objects known as absorbers the proposed methods confirm results from earlier analyses of the absorber catalog showing clear evidence of clustering up to 50 h 1 mpc and marginal evidence for clustering of matter on spatial scales beyond 100 h 1 mpc which is beyond the distance at which clustering of matter is now generally accepted to exist

kaplan meier estimators of distance distributions for spatial point processes when a spatial point process is observed through a bounded window edge effects hamper the estimation of characteristics such as the empty space function f the nearest neighbor distance distribution g and the reduced second order moment function k here we propose and study product limit type estimators of f g and k based on the analogy with censored survival data the distance from a fixed point to the nearest point of the process is right censored by its distance to the boundary of the window the resulting estimators have a ratio unbiasedness property that is standard in spatial statistics we show that the empty space function f of any stationary point process is absolutely continuous and so is the product limit estimator of f the estimators are strongly consistent when there are independent replications or when the sampling window becomes large we sketch a clt for independent replications within a fixed observation window and asymptotic theory for independent replications of sparse poisson processes in simulations the new estimators are generally more efficient than the border method estimator but for estimators of k somewhat less efficient than sophisticated edge corrections

comparison of base of support size during gait initiation using force plate and motion capture system a bland and altman analysis this study aimed to estimate the error made by investigators when force plate data are used to approximate base of support size during gait initiation step length and step width obtained with a method based on motion capture system kinematics method considered the gold standard and with a method based on the centre of pressure traces obtained from a force plate force plate method were purposely compared using descriptive statistics and the bland and altman ba method participants n 19 performed series of gait initiation in spontaneous and maximal velocity conditions svc and mvc respectively ba analysis showed that 1 step length and width biases corresponding to the difference between the two methods were very small 2 1 in both velocity conditions and 2 the 95 limits of agreement of the ba plots ranged between 10 and 15 in absolute value repeated measures anova showed that step length was significantly larger in mvc than in svc with no velocity x method interaction there was no significant effect of the method on both step parameters the present results suggest that the force plate method is sufficiently accurate to compare step parameters across conditions however researchers should be aware that non negligible errors might occur when considering individual data

affine collineations in space time the existence of affine collineations in space time is discussed and the types of space time admitting proper affine collineations is displayed the close connection between such space times and their holonomy structure and local decomposability is established affine collineations with fixed points are also considered as is the problem of extending local affine collineations to the whole of space time

covariantly constant tensors and holonomy structure in general relativity this paper attempts to give a comprehensive discussion of space times that admit vector fields or second order symmetric or skew symmetric tensor fields which are covariantly constant or recurrent the relationship between such space times m and their holonomy group is given

analysis of low pass filtered shoeprints and pedobarograph images abstract the shape and extent of the general wear apparent on a shoe sole contains information about the foot function and gait of the wearer a method of analysing this information and comparing it to the foot ground pressure pattern is given shoeprint and pedobarograph pbg images are transformed into the fourier domain passed through a butterworth filter and then transformed back to the spatial domain from the filtered images a series of four connected contours are extracted showing the shape and extent of the general wear patterns in shoeprint images and the pressure patterns in dynamic pbg images an appropriate contour is selected from each image the contours are normalized for position and size and then compared pairwise for shape the method of comparing contours is illustrated with contours from pbg images taken from three subjects these are compared with each other to indicate the degree of inter and intrasubject variation

estimating the large scale structure of the universe using quasi stellar object carbon iv absorbers galaxies have long been known to form large clusters and cosmologists are interested in characterizing this clustering as a way of studying the large scale structure of the universe this work is motivated by a data catalog consisting of information on lines of sight from earth to distant quasi stellar objects qso s and the carbon iv absorbers that lie on them the absorbers are believed to be gas clouds near galaxies too far away to be easily observed thus the absorber catalog provides a unique and interesting way to examine the large scale structure of the universe on large scales previous studies have mainly used pairs of absorbers on the same lines of sight to obtain estimates describing the clustering of absorbers it is clear that absorbers on different lines of sight contain information about the degree of clustering we develop an adaptation of the rigid motion corrected estimator of the reduced second moment function for the absorber catalog taking into account the across line of sight info

special conformal killing vector space times and symmetry inheritance viscous heat conducting fluid and anisotropic fluid space times admitting a special conformal killing vector sckv are studied and some general theorems concerning the inheritance of the symmetry associated with the sckv are proved in particular for viscous fluid space times it is shown that i if the sckv maps fluid flow lines into fluid flow lines then all physical components of the energy momentum tensor inherit the sckv symmetry or ii if the lie derivative along a sckv of the shear viscosity term ab is zero then again we have symmetry inheritance all space times admitting a sckv and satisfying the dominant energy condition are found apart from the vacuum pp wave solutions which are the only vacuum solutions that can admit a sckv the energy momentum tensor associated with these space times is shown to admit at least one null eigenvector and can represent either a viscous fluid with heat conduction or an anisotropic fluid no perfect fluid space times can admit a sckv these sckv space t

affine collineations in robertson walker space time in a recent paper m l bedran and b lesche j math phys 27 2360 1986 an attempt was made to find an affine collineation in robertson walker space time however only a homothetic affine collineation was found in the case of a linear scale factor r t t it is pointed out that another homothetic affine collineation exists when r t tb and a proper nonhomothetic affine collineation in the einstein static space times has been found

the survival curve under monotone density constraints with applications to two dimensional line segment processes summary several situations involving survival data are examined in which the nonparametric maximum likelihood estimator is not the kaplan meier estimator cases covered are inclusion of initial observations in field studies estimation of the length distribution from convex window sampling of line segment processes in two dimensions and estimation of a survival curve with monotone density the first two cases are nonstandard because survival and censoring are not independent and thus form simple tractable variable sum models williams lagakos 1977

an example of affine collineation in the robertson walker metric an affine collineation for the robertson walker metric is found it implies a condition on the metric that is compatible with einstein s equations for a perfect fluid satisfying the hawking ellis energy conditions it is shown how the geodesics of the metric are obtained from the constant of motion associated to the affine collineation

smoothing techniques and estimation methods for nonstationary boolean models with applications to coverage processes kernel smoothing methods are applied to nonparametric estimation for nonstationary boolean models in many applications only exposed tangent points of the models are observable rather than full realisations several methods are developed for estimating the distribution of the underlying boolean model from observation of the exposed tangent points in particular estimation methods for coverage processes are studied in detail and applied to neurobiological data

ricci collineation vectors in fluid space times the properties of fluid space times that admit a ricci collineation vector rcv parallel to the fluid unit four velocity vector ua are briefly reviewed these properties are expressed in terms of the kinematic quantities of the timelike congruence generated by ua the cubic equation derived by oliver and davis ann inst henri poincare 30 339 1979 for the equation of state p p of a perfect fluid space time that admits an rcv which does not degenerate to a killing vector is solved for physically realistic fluids necessary and sufficient conditions for a fluid space time to admit a spacelike rcv parallel to a unit vector na orthogonal to ua are derived in terms of the expansion shear and rotation of the spacelike congruence generated by na perfect fluid space times are studied in detail and analogues of the results for timelike rcvs parallel to ua are obtained properties of imperfect fluid space times for which the energy flux vector qa vanishes and na is a spacelike eigenvector of the aniso

influence of gait speed on the control of mediolateral dynamic stability during gait initiation this study investigated the influence of gait speed on the control of mediolateral dynamic stability during gait initiation thirteen healthy young adults initiated gait at three self selected speeds slow normal and fast the results indicated that the duration of anticipatory postural adjustments apa decreased from slow to fast i e the time allocated to propel the centre of mass com towards the stance leg side was shortened likely as an attempt at compensation the peak of the anticipatory centre of pressure cop shift increased however cop compensation was not fully efficient since the results indicated that the mediolateral com shift towards the stance leg side at swing foot off decreased with gait speed consequently the com shift towards the swing leg side at swing heel contact increased from slow to fast indicating that the mediolateral com fall during step execution increased as gait speed rose however this increased com fall was compensated by greater step width so that the margin of stability the distance between the base of support boundary and the mediolateral component of the extrapolated centre of mass at heel contact remained unchanged across the speed conditions furthermore a positive correlation between the mediolateral extrapolated com position at heel contact and step width was found indicating that the greater the mediolateral com fall the greater the step width globally these results suggest that mediolateral apa and step width are modulated with gait speed so as to maintain equivalent mediolateral dynamical stability at the time of swing heel contact

incorporation of space time symmetries in einstein s field equations in the search for exact solutions to einstein s field equations the main simplification tool is the introduction of space time symmetries motivated by this fact we develop a method to write the field equations for general matter in a form that fully incorporates the character of the symmetry the method is being expressed in a covariant formalism using the framework of a double congruence the basic notion on which it is based is that of the geometrization of a general symmetry as a special application of our general method we consider the case of a space like conformal killing vector field on the space time manifold regarding special types of matter fields new perspectives in general relativity are discussed

ricci and contracted ricci collineations of the robertson walker space time ricci collineations and contracted ricci collineations of the robertson walker metric associated with a vector field of the form 0 t r 1 t r 0 0 are presented

predicting dynamic postural instability using center of mass time to contact information our purpose was to determine whether spatiotemporal measures of center of mass motion relative to the base of support boundary could predict stepping strategies after upper body postural perturbations in humans we expected that inclusion of center of mass acceleration in such time to contact ttc calculations would give better predictions and more advanced warning of perturbation severity ttc measures were compared with traditional postural variables which do not consider support boundaries and with an inverted pendulum model of dynamic stability developed by hof et al 2005 the condition for dynamic stability journal of biomechanics 38 1 8 a pendulum was used to deliver sequentially increasing perturbations to 10 young adults who were strapped to a wooden backboard that constrained motion to sagittal plane rotation about the ankle joint subjects were instructed to resist the perturbations stepping only if necessary to prevent a fall peak center of mass and center of pressure velocity and acceleration demonstrated linear increases with postural challenge in contrast boundary relevant minimum ttc values decreased nonlinearly with postural challenge enabling prediction of stepping responses using quadratic equations when ttc calculations incorporated center of mass acceleration the quadratic fits were better and gave more accurate predictions of the ttc values that would trigger stepping responses in addition ttc minima occurred earlier with acceleration inclusion giving more advanced warning of perturbation severity our results were in agreement with ttc predictions based on hof s model and suggest that ttc may function as a control parameter influencing the postural control system s decision to transition from a stationary base of support to a stepping strategy

geodesic deviation and first integrals of motion generalized killing tensors gkt and generalized conformal killing tensors gckt are defined as the class of totally symmetric tensor fields that generate solutions of a suitable inhomogeneous equation of geodesic deviation along arbitrary and null geodesics respectively a geometric interpretation of these fields as generators of jacobi fields along arbitrary and null geodesics is also given it is shown that well known fields such as killing tensors conformal killing tensors and geodesic collineations belong to the above classes finally first integrals of geodesic motion concomitant with the existence of gkt s and gckt s are determined

asymptotically optimal estimation for the reduced second moment measure of point processes summary a modification of the rigid motion correction estimator for the reduced second moment measure of a stationary isotropic point process is shown to possess an asymptotic optimality property as the observation region grows furthermore a modification of the translation correction estimator for stationary anisotropic point processes has a similar defined as k t a e number of other points within t of x point at x where t 0 xe rd for a stationary poisson process in two dimensions k t xt so deviations of k t from irt2 are one way of describing deviations from the poisson model to estimate k t based on observing n in some bounded region a c rd we need to account for the fact that for points within t of the boundary of a we do not get to observe the number of other points within t of them ripley 1988 ch 3 and stein 1991 describe various estimators that correct for this edge effect while the estimator suggested by stein 1991 appears to work fairly well its motivation is somewhat ad hoc this paper describes how to construct an estimator motivated more clearly by the goal of attempting to minimize the mean squared error of the estimator when n is poisson subject to an unbiasedness constraint furthermore among a large class of estimators the estimator developed here is proven to come very close to minimizing the mean squared error when a is large and n is poisson the estimator is obtained by applying the haijek projection lemma hajek 1968 lemma 4 1 to the rigid motion correction due to miles 1974 and ohser stoyan 1981 the same approach also works for stationary but possibly anisotropic processes in which case the recommended estimator is obtained by applying the hajek projection lemma to the translation correction due to ohser stoyan 1981

collineations of a symmetric 2 covariant tensor ricci collineations the infinitesimal transformations that leave invariant a two covariant symmetric tensor are studied the interest of these symmetry transformations lays in the fact that this class of tensors includes the energy momentum and ricci tensors we find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional lie algebra but in some cases exhibiting a higher degree of degeneracy this class is infinite dimensional and may fail to be a lie algebra as an application we study the ricci collineations of a type b warped spacetime

when and how does steady state gait movement induced from upright posture begin abstract the aim of this research was to study when and how the stationary process of gait begins when walking starts from upright posture the subject initially stood up on a large force plate then walked three conditions of speed slow normal fast were examined five subjects participated in the experiment a total of 105 trials were performed the results show that at the end of the first step the progression velocity of the center of gravity is not significantly different from the mean progression velocity of gait during the second step of gait and that the time necessary to reach steady state gait from initial posture phase is constant furthermore the frequency of the first step when compared to published values of the steady state gait frequency is not significantly different from these frequencies it can be concluded that the aim of the gait initiation process is to place the subject in steady state gait within the first step in an invariant time which is dependent only on the body segment parameters of each subject

the condition for dynamic stability the well known condition for standing stability in static situations is that the vertical projection of the centre of mass com should be within the base of support bos on the basis of a simple inverted pendulum model an extension of this rule is proposed for dynamical situations the position of the vertical projection of the com plus its velocity times a factor rootl g should be within the bos l being leg length and g the acceleration of gravity it is proposed to name this vector quantity extrapolated centre of mass position xcom the definition suggests as a measure of stability the margin of stability b the minimum distance from xcom to the boundaries of the bos an alternative measure is the temporal stability margin tau the time in which the boundary of the bos would be reached without intervention some experimental data of subjects standing on one or two feet flatfoot and tiptoe are presented to give an idea of the usual ranges of these margins of stability example data on walking are also presented c 2004 elsevier ltd all rights reserved

symmetries of space time and geodesic symmetries it is shown how to construct symmetries of the geodesic equation starting from space time symmetries the constants of motion associated with space time symmetries are recovered and a few new ones are found using non noetherian conservation theorems explicit examples are presented

comparing the performances of diggle s tests of spatial randomness for small samples with and without edge effect correction application to ecological data summary diggle s tests of spatial randomness based on empirical distributions of interpoint distances can be performed with and without edge effect correction we present here numerical results illustrating that tests without the edge effect correction proposed by diggle 1979 biometrics35 87 101 have a higher power for small sample sizes than those with correction ignoring the correction enables detection of departure from spatial randomness with smaller samples down to 10 points vs 30 points for the tests with correction these results are confirmed by an example with ecological data consisting of maps of two species of trees in a west african savanna tree numbers per species per map were often less than 20 for one of the species for which maps strongly suggest an aggregated pattern tests without edge effect correction enabled rejection of the null hypothesis on three plots out of five vs on only one for the tests with correction

affine collineations in riemannian spaces sufficient conditions on the christoffel symbols and metric tensors to insure the existence of affine collineations in riemann spaces are obtained a proof of the group property of affine collineations is given several examples of physically relevant riemannian spaces admitting affine collineations are presented and the constants of motion are constructed

determination of the step duration of gait initiation using a mechanical energy analysis the analysis of gait initiation the transient state between standing and walking is an important diagnostic tool in the study of pathologic gait and the evaluation of prosthetic devices therefore it is important to know the step duration of gait initiation however there is little agreement in the literature regarding this step duration since each author has based their conclusion on a different biomechanical parameter in this study gait initiation in seven normal subjects was studied using a mechanical energy analysis the number of steps necessary to reach steady state was determined based on the fact that in steady state gait the net mechanical work of the body over one stride is zero winter et al j biomechanics 9 253 257 1976 the variance of the work for a stride during steady state walking was calculated for 100 steady state trials from a separate database of normal subjects the stride work was normalized to the subject s body weight bw and leg length ll and 95 confidence limits were defined from this data at 1 68 bw ll epsilon 1 28 bw ll total body energy during gait initiation was then computed for the seven test subjects the energy analysis of gait initiation showed that steady state was attained by the end of three full steps therefore a researcher studying gait initiation must allow his her subject to take three full steps when recording data to ensure that the full event is included

a systematic approach to self similarity in newtonian space time after an introductory mathematical review of the general concept of self similarity with respect to a given rescaling algebra attention is focused on the case of newtonian systems in galilean space time whose self similarity transformations will form subgroups of the maximal self similarity group of the galilean space time structure itself as a prerequisite for a systematic general investigation of self similarity in such newtonian systems it is shown how an appropriately adapted similarity transporting coordinate system can be constructed explicitly for an arbitrary generator of the 12 parameter galilean self similarity group a concrete application is provided by the case of the keplerian disk which is kinematically self similar under the action of a three parameter subgroup it is shown in the explicit example of a eulerian fluid system how the generic self similarity problem can be formulated as an effective stationarity problem

geometrization of a general collineation geometrization of a general collineation means to express the collineation as necessary and sufficient conditions on the kinematic quantities shear vorticity expansion of the congruence of the vector field generating the collineation it is shown that the generic form of a collineation is l gab 2 gab hab where hab is a traceless symmetric tensor a general theorem concerning the geometrization of the generic collineation is presented and its applications are discussed

conformal vector fields in general relativity a general discussion of conformal vector fields in space times is given amongst the topics considered are the maximum dimension of the conformal algebra for space times that are not conformally flat the nature of conformal isotropies and a new approach to the theorem of bilyalov and defrise carter concerning the reduction of the conformal algebra to a killing or homothetic algebra some deficiencies in the original statements of this theorem are discussed with reference to a general class of counterexamples and corrected the proof offered is geometrical in nature and has the advantage of displaying some of the more general features and properties of conformal vector fields and the ways in which they can differ from killing vector fields

the central limit theorem and the law of iterated logarithm for empirical processes under local conditions a clt and a lil are proved under weak l2 gaussian bracketing conditions weaker than the usual ones these results have wide applicability and in particular provide an improvement of the jain marcus central limit theorem for c s valued random variables

collineations of the ricci tensor ricci collineations for the ricci tensor which is constructed from a general spherically symmetric and static metric are classified for all possibilities of rab r such that rab 0 for a b it turns out that the only collineations admitted by this tensor can be ten six or four and there does not appear any case in between

a biomechanical study of balance recovery during the fall forward abstract the study deals with the biomechanics of balance recovery of human subjects in a falling forward situation eight subjects took part in the experiment the subject held in the initial leaning forward position was released without his knowledge the instruction was to recover the induced disequilibrium by walking the biomechanical analysis shows two phases in the balance recovery the first phase preparation phase is characterized by three events at fixed timing whatever the initial inclination i dynamic reaction time showing no significant inter individual variation mean value 90 8 ms ii braking of the forward fall between 184 ms and 237 2 ms depending on the subject iii beginning of the swing phase i e toe off instant between 235 9 ms and 328 3 ms depending on the subject the second phase gait execution phase is characterized by the duration of the swing phase the duration of the stance phase the stride length and execution speed the durations diminish whereas the stride length and the execution speed increase with respect to the initial inclination for the same execution speed the stride length is shorter than in normal walking it has been concluded that balance recovery following an induced fall forward begins with an invariable preparation process which is followed by an adaptable recovery one

first integrals of holonomic systems without noether symmetries a theorem is proved that determines the first integrals of the form i kab t q qaqb ka t q qa k t q of autonomous holonomic systems using only the collineations of the kinetic metric that is defined by the kinetic energy or the lagrangian of the system it is shown how these first integrals can be associated via the inverse noether theorem with a gauged weak noether symmetry which admits the given first integral as a noether integral it is shown also that the associated noether symmetry is possible to satisfy the conditions for a hojman or a form invariance symmetry therefore the so called non noetherian first integrals are gauged weak noether integrals the application of the theorem requires a certain algorithm due to the complexity of the special conditions involved we demonstrate this algorithm by a number of solved examples we choose examples from published works in order to show that our approach produces new first integrals not found before with the standard methods

bayesian semiparametric intensity estimation for inhomogeneous spatial point processes summary in this work we propose a fully bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process the basic idea is to first convert intensity estimation into a poisson regression setting via binning data points on a regular grid and then model the log intensity semiparametrically using an adaptive version of gaussian markov random fields to smooth the corresponding counts the inference is carried by an efficient markov chain monte carlo simulation algorithm compared to existing methods for intensity estimation for example parametric modeling and kernel smoothing the proposed estimator not only provides inference regarding the dependence of the intensity function on possible covariates but also uses information from the data to adaptively determine the amount of smoothing at the local level the effectiveness of using our method is demonstrated through simulation studies and an application to a rainforest dataset

spacelike conformal killing vectors and spacelike congruences necessary and sufficient conditions are derived for space time to admit a spacelike conformal motion with symmetry vector parallel to a unit spacelike vector field na these conditions are expressed in terms of the shear and expansion of the spacelike congruence generated by na and in terms of the four velocity of the observer employed at any given point of the congruence it is shown that either the expansion or the rotation of this spacelike congruence must vanish if dna dp 0 where p denotes arc length measured along the integral curves of na and also that there exist no proper spacelike homothetic motions with constant expansion propagation equations for the projection tensor and the rotation tensor are derived and it is proved that every isometric spacelike congruence is rigid fluid space times are studied in detail a relation is established between spacelike conformal motions and material curves in the fluid if a fluid space time admits a spacelike conformal killing vector parallel to na and

proper affine collineations in robertson walker space times it is shown that the only robertson walker space times admitting a proper affine collineation are static hence proving the uniqueness of the collineation found recently by maartens j math phys 28 2051 1987