control design of uncertain quantum systems with fuzzy estimators an approach of control design using fuzzy estimators fes is proposed for quantum systems with uncertainties two types of quantum control problems are considered 1 control of a pure state quantum system in the presence of uncertainties and 2 control design of quantum systems with initial mixed states and uncertainties for the first type of tasks a partial feedback control scheme with an fe is presented to design controllers in this scheme an fe is trained to estimate the quantum state for feedback control of a quantum system and controlled projective measurement is used to assist in controlling the system for the second type of quantum control tasks a probabilistic fuzzy estimator pfe is trained to estimate the quantum state for control design of a quantum system with an initial mixed state and a corresponding control algorithm is proposed to design a control law that drives the system from the mixed state to a target pure state two examples of two spin 1 2 systems are also presented and analyzed to demonstrate the process of control design and potential applications of the proposed approach

quantum set intersection and its application to associative memory we describe a quantum algorithm for computing the intersection of two sets and its application to associative memory the algorithm is based on a modification of grover s quantum search algorithm grover 1996 we present algorithms for pattern retrieval pattern completion and pattern correction we show that the quantum associative memory can store an exponential number of memories and retrieve them in sub exponential time we prove that this model has advantages over known classical associative memories as well as previously proposed quantum models

fuzzy convex set based pattern classification for analysis of mammographic microcalcifications abstract there are many different criteria for the comparative analysis of pattern classifiers they include generalization ability computational complexity and understanding of the feature space in some applications such as the medical diagnostic systems it is crucial to use reliable tools whose behavior is always predictable so that the risk of misdiagnosis is minimized in such applications the use of the popular feedforward backpropagation bp neural network algorithm can be seen as questionable this is because it is not inherent for the backpropagation method to analyze the problem s feature space during training which can sometimes result in inadequate decision surfaces a novel convex set based neuro fuzzy algorithm for classification of difficult to diagnose instances of breast cancer is described in this paper with its structural approach to feature space the new method offers rational advantages over the backpropagation algorithm the classification performance computational and structural efficiencies are analyzed and compared with that of the bp network a 20 dimensional set of difficult to diagnose mammographic microcalcifications was used to evaluate the neuro fuzzy pattern classifier nfpc and the bp methods in order to evaluate the learning ability of both methods the relative size of training sets was varied from 40 to 90 the comparative results obtained using receiver operating characteristic roc analysis show that the ability of the convex set based method to infer knowledge was better than that of backpropagation in all of the tests performed making it more suitable for use in real diagnostic systems

cohomogeneity one manifolds with positive ricci curvature one of the central problems in riemannian geometry is to determine how large the classes of manifolds with positive nonnegative sectional ricci or scalar curvature are see gr for scalar curvature the situation is fairly well understood by comparison special surgery constructions as in sy wr and bundle constructions as in na have resulted in a large number of interesting manifolds with positive ricci curvature so far the only known obstructions to have positive ricci curvature come from obstructions to have positive scalar curvature see li and rs and from the classical bonnet myers theorem which implies that a closed manifold with positive ricci curvature must have finite fundamental group it is well known that among homogeneous manifolds g h this is also a sufficient condition see e g the proof of corollary 3 5 or br in this paper we prove that this is true as well when the manifold admits an action by a compact lie group g with orbits of codimension one

biomechanical influences on balance recovery by stepping abstract stepping represents a common means for balance recovery after a perturbation to upright posture yet little is known regarding the biomechanical factors which determine whether a step succeeds in preventing a fall in the present study we developed a simple pendulum spring model of balance recovery by stepping and used this to assess how step length and step contact time influence the effort leg contact force and feasibility of balance recovery by stepping we then compared model predictions of step characteristics which minimize leg contact force to experimentally observed values over a range of perturbation strengths at all perturbation levels experimentally observed step execution times were higher than optimal and step lengths were smaller than optimal however the predicted increase in leg contact force associated with these deviations was substantial only for large perturbations furthermore increases in the strength of the perturbation caused subjects to take larger quicker steps which reduced their predicted leg contact force we interpret these data to reflect young subjects desire to minimize recovery effort subject to neuromuscular constraints on step execution time and step length finally our model predicts that successful balance recovery by stepping is governed by a coupling between step length step execution time and leg strength so that the feasibility of balance recovery decreases unless declines in one capacity are offset by enhancements in the others this suggests that one s risk for falls may be affected more by small but diffuse neuromuscular impairments than by larger impairment in a single motor capacity

modelling the dynamic margins of stability for use in evaluations of balance following a support surface perturbation the dynamic margin of stability provides a method that captures the center of mass com state position velocity in relation to the base of support bos however the model upon which this concept was derived does not consider how the inertial characteristics of forced support surface perturbations would influence balance control within the current article the inverted pendulum model was restructured to account for fixed piecewise accelerations of the bos from this logic two variations of the adjusted margin of stability each maintaining a similar definition of extrapolated com are proposed one ignoring horizontal ground contact and inertial forces applied to the bos the other incorporating these forces unique within the proposed models is the time variant bos boundaries that depend on the perturbation applied verification of the solution for each model is provided along with a comparison of obtained values to previous methods of defining com position velocity stability metrics using a computational model and optimal control for the simpler model variation ignoring forces we also assessed how com position and perturbation parameter selection over underestimate the predicted maximal permissible velocity the results of these analyses suggest that factors which increase the acceleration impulse decrease the difference between the two models the opposite was observed for factors increasing displacements between the com and bos boundary lastly use of the proposed adjusted margin of stability within an experimental data set highlights the ability of our model to predict instability stepping strategies negative margin of stability relative to the use of the extrapolated com alone

center of mass velocity position predictions for balance control the purposes of this analysis were to predict the feasible movements during which balance can be maintained based on environmental contact force anatomical foot geometry and physiological muscle strength constraints and to identify the role of each constraint in limiting movement an inverted pendulum model with a foot segment was used with an optimization algorithm to determine the set of feasible center of mass cm velocity position combinations for movement termination the upper boundary of the resulting feasible region ran from a velocity of 1 1 s 1 normalized to body height at 2 4 foot lengths behind the heel to 0 45 s 1 over the heel to zero over the toe and the lower boundary from a velocity of 0 9 s 1 at 2 7 foot lengths behind the heel to zero over the heel forward falls would be initiated if states exceeded the upper boundary and backward falls would be initiated if the states fell below the lower boundary under normal conditions the constraint on the size of the base of support bos determined the upper and lower boundaries of the feasible region however friction and strength did limit the feasible region when friction levels were less than 0 82 when dorsiflexion was reduced more than 51 or when plantar flexion strength was reduced more than 35 these findings expand the long held concept that balance is based on cm position limits i e the horizontal cm position has to be confined within the bos to guarantee stable standing to a concept based on cm velocity position limits

normalization of joint moments during gait a comparison of two techniques joint moments are commonly used to characterize gait factors like height and weight influence these moments this study determined which of two commonly used normalization methods body mass or body weight times height most reduced the effects of height and weight on peak hip knee and ankle external moments during walking the effectiveness of each normalization method in reducing gender differences was then tested gait data from 158 normal subjects were analyzed using unnormalized values body mass normalized values and body weight times height normalized values without normalization height or weight accounted for 7 82 of the variance in all 10 peak components of the moments with normalization height and weight accounted for at most 6 of the variance with the exception of the hip adduction moment normalized by body weight times height and the ankle dorsiflexion moment normalized by body mass for the hip adduction moment normalized by body weight times height height still accounted for 13 of the variance p 0 001 and for the ankle dorsiflexion moment normalized by body mass 22 of the variance p 0 001 after normalization significant differences between males and females remained for only two out of 10 moments with the body weight times height method compared to six out of 10 moments with the body mass method when compared to the unnormalized data both normalization methods were highly effective in reducing height and weight differences even for the two cases where one normalization method was less effective than the other hip adduction body weight times height ankle dorsiflexion body mass the normalization process reduced the variance ascribed to height or weight by 48 and 63 respectively as compared to the unnormalized data

inhomogeneous isoparametric hypersurfaces in complex hyperbolic spaces we construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces

ancient solutions to mean curvature flow for isoparametric submanifolds mean curvature flow for isoparametric submanifolds in euclidean spaces and spheres was studied in liu and terng duke math j 147 1 157 179 2009 in this paper we will show that all these solutions are ancient solutions and study their limits as time goes to negative infinity we also discuss rigidity of ancient mean curvature flows for hypersurfaces in spheres and its relation to the chern s conjecture on the norm of the second fundamental forms of minimal hypersurfaces in spheres

quantum neural networks qnns inherently fuzzy feedforward neural networks this paper introduces quantum neural networks qnns a class of feedforward neural networks ffnns inherently capable of estimating the structure of a feature space in the form of fuzzy sets the hidden units of these networks develop quantized representations of the sample information provided by the training data set in various graded levels of certainty unlike other approaches attempting to merge fuzzy logic and neural networks qnns can be used in pattern classification problems without any restricting assumptions such as the availability of a priori knowledge or desired membership profile convexity of classes a limited number of classes etc experimental results presented here show that qnns are capable of recognizing structures in data a property that conventional ffnns with sigmoidal hidden units lack

quantum computational networks the theory of quantum computational networks is the quantum generalization of the theory of logic circuits used in classical computing machines quantum gates are the generalization of classical logic gates a single type of gate the universal quantum gate together with quantum unit wires is adequate for constructing networks with any possible quantum computational property

hamiltonian stability of the gauss images of homogeneous isoparametric hypersurfaces i the image of the gauss map of any oriented isopara metric hypersurface of the unit standard sphere s n 1 1 is a mini mal lagrangian submanifold in the complex hyperquadric qn c in this paper we determine the hamiltonian stability of all com pact minimal lagrangian submanifolds embedded in complex hy perquadrics which are obtained as the images of the gauss map of homogeneous isoparametric hypersurfaces in the unit spheres

effects of age and step length on joint kinetics during stepping task following a balance perturbation a stepping response is commonly used to regain support and the distance of the recovery step can vary to date no other studies have examined joint kinetics in young and old adults during increasing step distances when participants are required to bring their rear foot forward therefore the purpose of this study was to examine age related differences in joint kinetics with increasing step distance twenty young and 20 old adults completed the study participants completed a step starting from double support at an initial distance equal to the individual s average step length the distance was increased by 10 body height until an unsuccessful attempt a one way repeated measures anova was used to determine the effects of age on joint kinetics during the maximum step distance a two way repeated measures mixed model anova was used to determine the effects of age step distance and their interaction on joint kinetics during the first three step distances for all participants young adults completed a significantly longer step than old adults during the maximum step in general kinetic measures were greater in the young than in the old as step distance increased all but one kinetic measure increased for both young and old adults this study has shown the ability to discriminate between young and old adults and could potentially be used in the future to distinguish between fallers and non fallers

on the classification of isoparametric hypersurfaces with four distinct curvatures in spheres in this paper we give a new proof for the classification result in 3 we show that isoparametric hypersurfaces with four distinct principal curvatures in spheres are of clifford type provided that the multiplicities m 1 m 2 of the principal curvatures satisfy m 2 2m 1 1 this inequality is satisfied for all but five possible pairs m 1 m 2 with m 1 m 2 our proof implies that for m 1 m 2 1 1 the clifford system may be chosen in such a way that the associated quadratic forms vanish on the higher dimensional of the two focal manifolds for the remaining five possible pairs m 1 m 2 with m 1 m 2 see 13 1 and 15 this stronger form of our result is incorrect for the three pairs 3 4 6 9 and 7 8 there are examples of clifford type such that the associated quadratic forms necessarily vanish on the lower dimensional of the two focal manifolds and for the two pairs 2 2 and 4 5 there exist homogeneous examples that are not of clifford type cf 5 4 3 4 4

response time is more important than walking speed for the ability of older adults to avoid a fall after a trip abstract we previously reported that the probability of an older adult recovering from a forward trip and using a lowering strategy increases with decreased walking velocity and faster response time to determine the within subject interaction of these variables we asked three questions 1 is the body orientation at the time that the recovery foot is lowered to the ground tilt angle critical for successful recovery 2 can a simple inverted pendulum model using subject specific walking velocity and response time as input variables predict this body orientation and thus success of recovery 3 is slower walking velocity or faster response time more effective in preventing a fall after a trip tilt angle was a perfect predictor of a successful recovery step indicating that the recovery foot placement must occur before the tilt angle exceeds a critical value of between 23 and 26 from vertical the inverted pendulum model predicted the tilt angle from walking velocity and response time with an error of 0 4 2 2 and a correlation coefficient of 0 93 the model predicted that faster response time was more important than slower walking velocity for successful recovery in a typical individual who is at risk for falling we predicted that a reduction of response time to a normal value allows a 77 increase in safe walking velocity the mathematical model produced patient specific recommendations for fall prevention and suggested the importance of directing therapeutic interventions toward improving the response time of older adults

incorporating fuzzy membership functions into the perceptron algorithm the perceptron algorithm one of the class of gradient descent techniques has been widely used in pattern recognition to determine linear decision boundaries while this algorithm is guaranteed to converge to a separating hyperplane if the data are linearly separable it exhibits erratic behavior if the data are not linearly separable fuzzy set theory is introduced into the perceptron algorithm to produce a fuzzy algorithm which ameliorates the convergence problem in the nonseparable case it is shown that the fuzzy perceptron like its crisp counterpart converges in the separable case a method of generating membership functions is developed and experimental results comparing the crisp to the fuzzy perceptron are presented

quantum mechanical hamiltonian models of turing machines quantum mechanical hamiltonian models which represent an aribtrary but finite number of steps of any turing machine computation are constructed here on a finite lattice of spin 1 2 systems different regions of the lattice correspond to different components of the turing machine plus recording system successive states of any machine computation are represented in the model by spin configuration states both time independent and time dependent hamiltonian models are constructed here the time independent models do not dissipate energy or degrade the system state as they evolve they operate close to the quantum limit in that the total system energy uncertainty computation speed is close to the limit given by the time energy uncertainty relation however the model evolution is time global and the hamiltonian is more complex the time dependent models do not degrade the system state also they are time local and the hamiltonian is less complex

a closed loop stepper motor waist pull system for inducing protective stepping in humans past approaches for inducing protective stepping to preserve standing balance in humans have either lacked the flexibility of control over the initial conditions of falling or involved considerable mass which limits mobility of the system this report describes the design and function of a stepper motor closed loop waist pull system for evoking protective stepping responses bench testing with applied load motion profile combinations indicated performance degradation for force levels greater than 204 n which was well within the levels encountered in human experiments an optical encoder feedback design allowed a positional accuracy of 0 00225 mm per step a regression analysis of specified versus recorded velocities resulted in an acceptable fit r2 0 99 the mean rise time was 63 0 18 0 sd ms and was consistent up to the load limits of the device in human experiments repeated perturbations were consistently realized applied motion profiles were generally comparable at the pelvic level for subjects of different geometry weight and inertia despite a tendency for slight positional lag the method allows flexible and accurate control of the initial conditions of a perturbation induced fall to elicit steps the system dimensions and moveability allow it to be implemented into clinical environments

dupin hypersurfaces with three principal curvatures using the method of moving frames we prove that any locally irreducible dupin hypersurface in sn with three distinct principal curvatures is equivalent by lie sphere transformation to an isoparametric hypersurface in sn

isoparametric hypersurfaces in complex hyperbolic spaces we review some results of an ongoing research on isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in the complex hyperbolic space in order to motivate this topic we recall first the main steps of its long history

parallelization of a fuzzy control algorithm using quantum computation quantum computation is proposed for the parallelization of a fuzzy logic control flc algorithm quantum computation speeds up the fuzzy inference since serial operations between matrices of large dimensionality are now replaced by a one step quantum addition or a quantum subtraction the unitarity properties of the algorithm prove that the flc stands for a simulator of a quantum computing machine

neurofuzzy networks with nonlinear quantum learning nonlinear quantum processing allows the solution of an optimization problem by the exhaustive search on all its possible solutions hence it can replace advantageously the algorithms for learning from a training set in order to pursue this possibility in the case of neurofuzzy networks we propose in this paper to tailor their architectures to the requirements of quantum processing in particular superposition is introduced to pursue parallelism and entanglement to associate the network performance with each solution present in the superposition two aspects of the proposed method are considered in detail the binary structure of membership functions and fuzzy reasoning and the use of a particular nonlinear quantum algorithm for extracting the optimal neurofuzzy network by exhaustive search

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

classification and characterization of rationally elliptic manifolds in low dimensions we give a characterization of closed simply connected rationally elliptic 6 manifolds in terms of their rational cohomology rings and a partial classification of their real cohomology rings we classify rational real and complex homotopy types of closed simply connected rationally elliptic 7 manifolds we give partial results in dimensions 8 and 9

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

factors influencing the quick onset of stepping following postural perturbation abstract it has been shown that the stepping to recover balance following a forward fall occurs at a constant time on average 293 ms do et al journal of biomechanics 15 1982 933 939 in this study we tested the hypothesis according to which programming to make fast movement could trigger the movement earlier than when programming self pace movement the same experimental paradigm of forward fall was used see do et al 1982 to induce stepping different extents of stepping were manipulated by instructions subjects were instructed to step to recover their balance naturally control condition to make shorter steps than in the control condition longer steps faster steps lastly a fast step was also induced by the biomechanical constraint on the initial posture i e by inclining the subject forward at his maximum capacity data were collected from 12 subjects the variables analyzed were the onset latency of step execution and other classical parameters time of heel contact duration of the swing phase step length center of mass progression velocity and step velocity the results showed that the onset of stepping was unchanged in the longer and faster step conditions relative to the control condition mean control value 280 ms in contrast the onset of stepping was significantly earlier in the short step condition and when the initial inclination was greater 250 and 252 ms respectively the swing phase duration in these two conditions averaged 140 and 185 ms was significantly shorter than in the other conditions whereas step length was obviously expected to be shorter in the shorter step condition and longer in the longer step condition than in the other conditions step length was similar between the other conditions we conclude that neither step length or step velocity programming could induce an earlier onset latency of stepping step programming in relation to these specific instructions seemed to concern the extent of step execution and not the time of triggering of the stepping we suggest that the control of short swing phase duration resulted in an earlier onset latency of stepping to recover the balance this control depends on the combination of biomechanical constraints and cognitive processes including subject s interpretation of the instructions and evaluation of the risk of fall

minimal step length necessary for recovery of forward balance loss with a single step although the boundary conditions necessary to trigger a step in reaction to a forward balance loss have been predicted in previous research the relationship between minimal step length needed for balance recovery with this single step and the center of mass com motion state i e its position and velocity remains unknown the purpose of this paper was to present a theoretical framework within which the minimal step length needed for balance recovery can be estimated we therefore developed a simplified four segment sagittal model of human body stepping for balance recovery the work energy principle of the newtonian mechanics was employed in the simulation to determine the amount of excess mechanical energy that can be absorbed as a function of step length and the corresponding eccentric joint work that can be generated in a single step we found that an increase in initial forward velocity and a greater forward shift of the com require a corresponding increase in the minimal step length needed for balance recovery furthermore the minimal step length is also a function of the muscle strength at the ankle the lower the muscle strength the greater the minimal step length required our theoretical framework reduces the complexity associated with previous studies relying on forward dynamics and iterative optimization processes this method may also be applied to study aspects of balance control such as the prevention of balance loss in the posterior or mediolateral direction

isoparametric hypersurfaces with four principal curvatures let m be an isoparametric hypersurface in the sphere s n with four distinct principal curvatures munzner showed that the four principal curvatures can have at most two distinct multiplicities m1 m 2 and stolz showed that the pair m1 m 2 must either be 2 2 4 5 or be equal to the multiplicities of an isoparametric hypersurface of fkm type constructed by ferus karcher and munzner from orthogonal representations of clifford algebras in this paper we prove that if the multiplicities satisfy m2 2m1 1 then the isoparametric hypersurface m must be of fkm type together with known results of takagi for the case m1 1 and ozeki and takeuchi for m1 2 this handles all possible pairs of multiplicities except for four cases for which the classification problem remains open

mobius curvature laguerre curvature and dupin hypersurface abstract in this paper we show that a dupin hypersurface with constant mobius curvatures is mobius equivalent to either an isoparametric hypersurface in the sphere or a cone over an isoparametric hypersurface in a sphere we also show that a dupin hypersurface with constant laguerre curvatures is laguerre equivalent to a flat laguerre isoparametric hypersurface these results solve the major issues related to the conjectures of cecil et al on the classification of dupin hypersurfaces

multiplicities of dupin hypersurfaces all known examples of isoparametric hypersurfaces of spheres are of the following two types 1 the homogeneous examples which are principal orbits of isotropy representations of symmetric spaces of rank 2 2 the clifford examples of ferus karcher munzner which are constructed from modules over clifford algebras our main result which extends work of munzner thorbergsson and grove halperin is that any isoparametric hypersurface has the same number of principal curvatures and the same multiplicities as some hypersurface of type 1 or 2 more generally this holds for any dupin hypersurface the proof is homotopy theoretic the main tools are the hopf invariant and the ehp sequence

possibility and necessity pattern classification using neural networks abstract we propose two learning algorithms of neural networks for two group discriminant problems from the view point of possibility and necessity one algorithm corresponds to the possibility analysis and the other to the necessity analysis the proposed algorithms are similar to the back propagation algorithm and the difference stems from a formulation of a cost function to be minimized in each algorithm each cost function of the proposed algorithms is the weighted sum of squared errors that is the sum of squared errors with different penalties when we discuss the possibility of group 1 the penalty for the squared errors relating to the patterns in group 1 is greater than that of group 2 this means that in the possibility analysis of group 1 we attach greater importance to the patterns in group 1 than to those in group 2 on the other hand when we discuss the necessity of group 1 the penalty for the squared errors relating to the patterns in group 2 is greater than that of group 1

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

the threshold trip duration for which recovery is no longer possible is associated with strength and reaction time abstract the recovery of young adults from trips of increasing severity was studied our null hypothesis was that lower extremity strength and reaction time step time step distance and step velocity measured in a volitional stepping task would not explain a significant portion of the variance in the magnitude of the threshold trip duration for which recovery is no longer possible ten males and 11 females average age 26 8 and 28 4 years old respectively were subjected to trips of increasing duration until recovery was no longer possible with a single step the average threshold trip duration for which subjects were no longer able to recover with a single step was 681 169 m s the threshold trip duration significantly increased as lower extremity strength increased and volitional reaction time decreased multiple stepwise linear regression r 2 0 52 p 0 001 the other volitional step parameters and the subject characteristics were not significantly associated with the magnitude of the threshold trip duration these results suggest that some trip related falls may be due to slower reaction times and or reduced lower extremity strengths

quantum learning for neural associative memories abstract quantum information processing in neural structures results in an exponential increase of patterns storage capacity and can explain the extensive memorization and inferencing capabilities of humans an example can be found in neural associative memories if the synaptic weights are taken to be fuzzy variables in that case the weights update is carried out with the use of a fuzzy learning algorithm which satisfies basic postulates of quantum mechanics the resulting weight matrix can be decomposed into a superposition of associative memories thus the fundamental memory patterns attractors can be mapped into different vector spaces which are related to each other via unitary rotations quantum learning increases the storage capacity of associative memories by a factor of 2 n where n is the number of neurons

quantum associative memory abstract this paper combines quantum computation with classical neural network theory to produce a quantum computational learning algorithm quantum computation qc uses microscopic quantum level effects to perform computational tasks and has produced results that in some cases are exponentially faster than their classical counterparts the unique characteristics of quantum theory may also be used to create a quantum associative memory quam with a capacity exponential in the number of neurons this paper combines two quantum computational algorithms to produce such a quantum associative memory the result is an exponential increase in the capacity of the memory when compared to traditional associative memories such as the hopfield network the paper covers necessary high level quantum mechanical and quantum computational ideas and introduces a quam theoretical analysis proves the utility of the memory and it is noted that a small version should be physically realizable in the near future

reformulated radial basis neural networks trained by gradient descent this paper presents an axiomatic approach for constructing radial basis function rbf neural networks this approach results in a broad variety of admissible rbf models including those employing gaussian rbfs the form of the rbfs is determined by a generator function new rbf models can be developed according to the proposed approach by selecting generator functions other than exponential ones which lead to gaussian rbfs this paper also proposes a supervised learning algorithm based on gradient descent for training reformulated rbf neural networks constructed using the proposed approach a sensitivity analysis of the proposed algorithm relates the properties of rbfs with the convergence of gradient descent learning experiments involving a variety of reformulated rbf networks generated by linear and exponential generator functions indicate that gradient descent learning is simple easily implementable and produces rbf networks that perform considerably better than conventional rbf models trained by existing algorithms

differentiable classification of 4 manifolds with singular riemannian foliations in this paper we first prove that any closed simply connected 4 manifold that admits a decomposition into two disk bundles of rank greater than 1 is diffeomorphic to one of the standard elliptic 4 manifolds mathbb s 4 mathbb cp 2 mathbb s 2 times mathbb s 2 or mathbb cp 2 pm mathbb cp 2 as an application we prove that any closed simply connected 4 manifold admitting a nontrivial singular riemannian foliation is diffeomorphic to a connected sum of copies of standard mathbb s 4 pm mathbb cp 2 and mathbb s 2 times mathbb s 2 a classification of singular riemannian foliations of codimension 1 on all closed simply connected 4 manifolds is obtained as a byproduct in particular there are exactly 3 non homogeneous singular riemannian foliations of codimension 1 complementing the list of cohomogeneity one 4 manifolds

isoparametric foliations diffeomorphism groups and exotic smooth structures abstract in this paper we are concerned with interactions between isoparametric theory and differential topology two foliations are called equivalent if there exists a diffeomorphism between the foliated manifolds mapping leaves to leaves using differential topology we obtain several results towards the classification problem of isoparametric foliations up to equivalence in particular we show that each homotopy n sphere has the same isoparametric foliations as the standard sphere s n has except for n 4 reducing the classification problem on homotopy spheres to that on the standard sphere moreover we prove the uniqueness up to equivalence of isoparametric foliations with two points as the focal submanifolds on each sphere s n except for n 5 besides we show that the uniqueness holds on s 5 if and only if 0 diff s 4 z 2 i e pseudo isotopy implies isotopy for diffeomorphisms on s 4 at last some ideas behind the proofs enable us to discover new exotic smooth structures on certain manifolds

rapid solution of problems by quantum computation a class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method the quantum computation solves the problem with certainty in exponentially less time than any classical deterministic computation

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

topology of dupin hypersurfaces with six distinct principal curvatures let m be a dupin hypersurface in the unit sphere s n 1 with six distinct principal curvatures we will prove in the present paper that m is either diffeomorphic to su 2 times su 2 q 8 or homeomorphic to a tube around an embedded 5 dimensional complex fermat hypersurface x 5 2 in s 13 where q 8 subset su 2 sp 1 denotes the subgroup pm 1 pm i pm j pm k and x 5 2 z 0 z 1 cdots z 6 in cp 6 vert z 0 2 z 1 2 cdots z 6 2 0 moreover in the former case all of the focal manifolds are diffeomorphic to s 3 times rp 2 in the latter case one of the focal manifolds is homeomorphic to x 5 2

instructions limiting the number of steps do not affect the kinetics of the threshold of balance recovery in younger adults to our knowledge no one has explored the effect of modifications in balance recovery instructions on the kinetics of the threshold of balance recovery in particular the effect of instructions limiting the number of steps on joint torques at the maximum lean angle has not been quantified we determined the joint torques at the ankle knee and hip of 28 younger adults recovering balance at their maximum lean angle using i only a single step ii no more than two steps and iii no limit on the number of steps results showed that instructions limiting the number of steps did not affect peak normalized joint torques by more than 0 0083 or 10 n m except for knee and hip flexion torques from first to second heel strike for the first step leg as well as from second toe off to heel strike for the second step leg however these large differences in peak normalized joint torques after the first step were simply caused by the additional steps used when participants could take more than one step compared to when participants were limited to only a single step between the three limits on the number of steps the kinetics of both legs were nearly identical up to the end of the first step and the additional steps did not help to increase the maximum lean angle therefore we have demonstrated that instructions limiting or not limiting the number of steps appear to be equally valid to study falls in younger adults

quantum theory the church turing principle and the universal quantum computer it is argued that underlying the church turing hypothesis there is an implicit physical assertion here this assertion is presented explicitly as a physical principle every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means classical physics and the universal turing machine because the former is continuous and the latter discrete do not obey the principle at least in the strong form above a class of model computing machines that is the quantum generalization of the class of turing machines is described and it is shown that quantum theory and the universal quantum computer are compatible with the principle computing machines resembling the universal quantum computer could in principle be built and would have many remarkable properties not reproducible by any turing machine these do not include the computation of non recursive functions but they do include quantum parallelism a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it the intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than everett s some of the numerous connections between the quantum theory of computation and the rest of physics are explored quantum complexity theory allows a physically more reasonable definition of the complexity or knowledge in a physical system than does classical complexity theory

influence of lateral destabilization on compensatory stepping responses previous studies of compensatory stepping in response to postural perturbation have focussed on forward or backward stepping however the ability to step in other directions is of equal functional importance since the perturbations encountered in daily life may often include a lateral component the primary objective of this study was to determine how lateral destabilization affects the compensatory stepping response in terms of 1 swing leg selection 2 preparatory unloading of the swing leg and 3 spatial and temporal characteristics of the swing trajectory a novel multi directional moving platform was used to apply transient perturbations in eight horizontal directions in 10 healthy young adults perturbation magnitude was varied unpredictably over a wide range and subjects were instructed to try not to step so as to discourage preplanned volitional foot movement the predominant strategy seen in 96 of stepping responses to lateral destabilization was to swing the leg that was unloaded by the perturbation this strategy allowed a much more rapid foot lift but required a longer and more complex swing trajectory compared to responses where the perturbation loaded leg was swung when compared to forward and backward steps the addition of a lateral component to the perturbation led to a 20 90 ms reduction in time to foot off a 20 7 cm increase in step length and a 70 110 ms increase in swing duration on average the results clearly demonstrate that compensatory stepping responses to non sagittal perturbations are strongly influenced by biomechanical constraints and affordances that do not affect the forward and backward stepping behaviour that has been studied traditionally these findings underscore the need to assess postural responses in multiple directions in order to understand more fully how balance is maintained in the exigencies of everyday life

infinite families of harmonic self maps of spheres abstract for each of the spheres s n n 5 we construct a new infinite family of harmonic self maps and prove that their members have brouwer degree 1 or 3 these self maps are obtained by solving a singular boundary value problem as an application we show that for each of the special orthogonal groups so 4 so 5 so 6 and so 7 there exist two infinite families of harmonic self maps

rational l s category and its applications let s be a 1 connected cw complex of finite type and put cat0 s lusternik schnirelmann category of the localization sq this invariant is char acterized in terms of the minimal model of s it is shown that if is the fibre inclusion of a fibration it is also shown that if dim h s q oo then either dim it s q oo or the groups nk s q grow exponentially with k introduction in this paper topological space means a pointed path connected normal space s1 such that the inclusion of the basepoint is a cofibration and the rational singular homology is finite dimensional in each degree all vector spaces and algebras have q as ground field homology and cohomology of spaces is singular with rational coefficients we shall be dealing with category of spaces cat s in the sense of lusternik and schnirelmann 18 a recent survey is given in 15 but our definition differs by one from that of 15 so that for us spheres have category one not two our purpose is to provide a computationally useful characterization of the rational category cat0 5 of space 5 and to apply this in a variety of situations the definition of cat0 5 is sketched below and given precisely in 4 it satisfies cat0 s cauls when 5 is 1 connected cat0 5 coincides with the category of the localization sq which has been studied by toomer in 26 and 27 and lemaire and sigrist in 17 the characterization problem was posed by berstein 26 most of the applications depend on the following fundamental mapping theorem which we derive as a consequence of our characterization