efficient merged longest common subsequence algorithms for similar sequences abstract given a pair of merging sequences a b and a target sequence t the merged longest common subsequence mlcs problem is to find out the longest common subsequence lcs between sequences e a b and t where e a b is obtained from merging two subsequences of a and b in this paper we first propose an algorithm for solving the mlcs problem in o n r l 1 l m time and o n l m space where r and l denote the lengths of t and mlcs respectively and m and n denote the shorter and longer lengths of a and b respectively from the time complexity it is clear that our algorithm is very efficient when t and e a b are very similar with slight modification our algorithm can also solve another merged lcs problem variant the block merged lcs bmlcs problem in o n r l 1 l time and o n l space where denotes the larger number of blocks of a and b experimental results show that our algorithms are faster than other previously published mlcs and bmlcs algorithms for sequences with high similarities the source codes and datasets for experiments can be found on our web site http par cse nsysu edu tw mlcs 20

projections in free product c algebras ii let a varphi be the reduced free product of infinitely many c algebras a iota varphi iota with respect to faithful states assume that the a iota are not too small in a specific sense if varphi is a trace then the positive cone of k 0 a is determined entirely by k 0 varphi if furthermore the image of k 0 varphi is dense in mathbb r then a has real rank zero on the other hand if varphi is not a trace then a is simple and purely infinite

block edit models for approximate string matching in this paper we examine string block edit distance in which two strings a and b are compared by extracting collections of substrings and placing them into correspondence this model accounts for certain phenomena encountered in important real world applications including pen computing and molecular biology the basic problem admits a family of variations depending on whether the strings must be matched in their entireties and whether overlap is permitted we show that several variants are npcomplete and give polynomial time algorithms for solving the remainder

an accurate validation of a computational model of a human lumbosacral segment clinical studies have recently documented that there is sufficient evidence to suggest that abnormal motion may be an indicator of abnormal mechanics of the spine and therefore may be associated with some types of low back pain however designating a motion as abnormal requires knowledge of normal motions this work hence aims to develop an accurate computational model to simulate the bio mechanical response of the whole lumbosacral spinal unit l1 s1 under physiological loadings and constraint conditions in order to meet this objective computed tomography ct scanning protocols finite element fe analysis and accurate constitutive modelling have been integrated then the ranges of motion rom under flexion extension and lateral bending moment were measured and compared with experimental data finding an excellent agreement in particular the ability of the model to reproduce the relative rotation between each couple of vertebrae was proved finally the shear stresses for the most extreme load cases were reported in order to predict which are the most risky conditions and where the maximum damage would be located the results indicate that the greater values of the stresses were located at l4 s1 levels just in the interfaces between disc and vertebrae across the posterior and posterolateral zone this result can be clinically correlated with the existence of damage exactly where the stresses were maximal in the proposed finite element model

the effect of control strategies for an active back support exoskeleton on spine loading and kinematics during lifting with mechanical loading as the main risk factor for lbp exoskeletons exo are designed to reduce the load on the back by taking over part of the moment normally generated by back muscles the present study investigated the effect of an active exoskeleton controlled using three different control modes inclination emg hybrid on spinal compression forces during lifting with various techniques ten healthy male subjects lifted a 15 kg box with three lifting techniques free squat stoop each of which was performed four times once without exo and once each with the three different control modes using inverse dynamics we calculated l5 s1 joint moments subsequently we estimated spine forces using an emg assisted trunk model peak compression forces substantially decreased by 17 8 when wearing the exo compared to no exo however this reduction was partly by about one third attributable to a reduction of 25 in peak lifting speed when wearing the exo while subtle differences in back load patterns were seen between the three control modes no differences in peak compression forces were found in part this may be related to limitations in the torque generating capacity of the exo therefore with the current limitations of the motors it was impossible to determine which of the control modes was best despite these limitations the exo still reduced both peak and cumulative compression forces by about 18

hypersensitivity of trunk biomechanical model predictions to errors in image based kinematics when using fully displacement control techniques abstract recent advances in medical imaging techniques have allowed pure displacement control trunk models to estimate spinal loads with no need to calculate muscle forces sensitivity of these models to the errors in post imaging evaluation of displacements reported to be 0 4 0 9 and 0 2 0 3 mm in vertebral displacements has not yet been investigated a monte carlo analysis was therefore used to assess the sensitivity of results in both musculoskeletal ms and passive finite element fe spine models to errors in measured displacements six static activities in upright standing flexed and extended postures were initially simulated using a force control hybrid ms fe model computed vertebral displacements were subsequently used to drive two distinct fully displacement control ms and fe models effects of alterations in the reference vertebral displacements at 3 error levels with sd standard deviation 0 1 0 2 and 0 3 mm in input translations together with respectively 0 2 0 4 and 0 6 in input rotations were investigated on the model predictions results indicated that outputs of both models had substantial task dependent sensitivities to errors in the measured vertebral translations for instance l5 s1 intradiscal pressures idps were considerably affected sd values reaching 1 05 mpa and axial compression and shear forces even reversed directions as translation errors increased to 0 3 mm outputs were however generally much less sensitive to errors in measured vertebral rotations accounting for the accuracies in image based kinematics measurements therefore it is concluded that the current measured vertebral translation errors at and beyond 0 1 mm are too large to drive biomechanical models of the spine

the disappearance of causality at small scale in almost commutative manifolds this paper continues the investigations of noncommutative ordered spaces put forward by one of the authors these metaphoric spaces are defined dually by the so called isocones which generalize to the noncommutative setting the convex cones of order preserving functions in this paper we will consider the case of isocones inside almost commutative algebras of the form c m af with m a compact metrizable space we will give a family of isocones in such an algebra with the property that every possible isocone is contained in exactly one member of the family we conjecture that this family is in fact a complete classification a hypothesis related with the noncommutative stone weierstrass conjecture we also obtain that every isocone in c m af with af noncommutative induces an order relation on m with the property that every point in m lies in a neighbourhood of incomparable points thus if the causal order relation on spacetime is induced by an isocone in an almost commutative but not commutative alg

adjustments to zatsiorsky seluyanov s segment inertia parameters zatsiorsky et al in contemporary problems in biomechanics pp 272 291 crc press massachusetts 1990a obtained by means of a gamma ray scanning technique the relative body segment masses center of mass cm positions and radii of gyration for samples of college aged caucasian males and females although these data are the only available and comprehensive set of inertial parameters regarding young adult caucasians they have been rarely utilized for biomechanical analyses of subjects belonging to the same or a similar population the main reason is probably that zatsiorsky et al used bony landmarks as reference points for locating segment cms and defining segment lengths some of these landmarks were markedly distant from the joint centers currently used by most researchers as reference points the purpose of this study was to adjust the mean relative cm positions and radii of gyration reported by zatsiorsky et al in order to reference them to the joint centers or other commonly used landmarks rather than the original landmarks the adjustments were based on a number of carefully selected sources of anthropometric data

sensitivity of lumbar spine loading to anatomical parameters musculoskeletal simulations of lumbar spine loading rely on a geometrical representation of the anatomy however this data has an inherent inaccuracy this study evaluates the influence of defined geometrical parameters on lumbar spine loading utilising five parametrised musculoskeletal lumbar spine models for four different postures the influence of the dimensions of vertebral body disc posterior parts of the vertebrae as well as the curvature of the lumbar spine was studied additionally simulations with combinations of selected parameters were conducted changes in l4 l5 resultant joint force were used as outcome variable variations of the vertebral body height disc height transverse process width and the curvature of the lumbar spine were the most influential these parameters can be easily acquired from x rays and should be used to morph a musculoskeletal lumbar spine model for subject specific approaches with respect to bone geometry furthermore the model was very sensitive to uncommon configurations and therefore it is advised that stiffness properties of discs and ligaments should be individualised

response of trunk muscle coactivation to changes in spinal stability the goal of this effort was to assess the neuromuscular response to changes in spinal stability biomechanical models suggest that antagonistic co contraction may be related to stability constraints during lifting exertions a two dimensional biomechanical model of spinal equilibrium and stability was developed to predict trunk muscle co contraction as a function of lifting height and external load the model predicted antagonistic co contraction must increase with potential energy of the system even when the external moment was maintained at a constant value predicted trends were compared with measured electromyographic emg data recorded during static trunk extension exertions wherein subjects held weighted barbells at specific horizontal and vertical locations relative to the lumbo sacral spine junction the task was designed to assure the applied moment was identical during each height condition thereby changing potential energy without influencing moment measured emg activity in the trunk flexors increased with height of the external load as predicted by the model gender difference in spinal stability were also noted results empirically demonstrate that the neuromuscular system responds to changes in spinal stability and provide insight into the recruitment of trunk muscle activity

investigation of optimal follower load path generated by trunk muscle coordination it has been reported that the center of rotation of each vertebral body is located posterior to the vertebral body center moreover it has been suggested that an optimized follower load fl acts posterior to the vertebral body center however the optimal position of the fl with respect to typical biomechanical characteristics regarding spinal stabilization such as joint compressive force shear force joint moment and muscle stress has not been studied a variation in the center of rotation of each vertebra was formulated in a three dimensional finite element model of the lumbar spine with 117 pairs of trunk muscles then the optimal translation of the fl path connecting the centers of rotations was estimated by solving the optimization problem that was to simultaneously minimize the compressive forces the shear forces and the joint moments or to minimize the cubic muscle stresses an upright neutral standing position and a standing position with 200 n in both hands were considered the fl path moved posterior regardless of the optimization criteria and loading conditions the fl path moved 5 0 and 7 8 mm posterior in upright standing and 4 1 mm and 7 0 mm posterior in standing with 200 n in hands for each optimization scheme in addition it was presented that the optimal fl path may have advantages in comparison to the body center fl path the present techniques may be important in understanding the spine stabilization function of the trunk muscles

algorithms for approximate string matching the edit distance between strings a 1 a m and b 1 b n is the minimum cost s of a sequence of editing steps insertions deletions changes that convert one string into the other a well known tabulating method computes s as well as the corresponding editing sequence in time and in space o mn in space o min m n if the editing sequence is not required starting from this method we develop an improved algorithm that works in time and in space o s min m n another improvement with time o s min m n and space o s min s m n is given for the special case where all editing steps have the same cost independently of the characters involved if the editing sequence that gives cost s is not required our algorithms can be implemented in space o min s m n since s o max m n the new methods are always asymptotically as good as the original tabulating method as a by product algorithms are obtained that given a threshold value t test in time o t min m n and in space o min t m n whether s t finally different generalized edit distances are analyzed and conditions are given under which our algorithms can be used in conjunction with extended edit operation sets including for example transposition of adjacent characters

finding approximate palindromes in strings abstract we introduce a novel definition of approximate palindromes in strings and provide an algorithm to find all maximal approximate palindromes in a string with up to k errors our definition is based on the usual edit operations of approximate pattern matching and the algorithm we give for a string of size n on a fixed alphabet runs in o k 2 n time we also discuss two implementation related improvements to the algorithm and demonstrate their efficacy in practice by means of both experiments and an average case analysis

measurement of a spinal motion segment stiffness matrix the six degrees of freedom elastic behavior of spinal motion segments can be approximated by a stiffness matrix a method is described to measure this stiffness matrix directly with the motion segment held under physiological conditions of axial preload and in an isotonic fluid bath by measuring the forces and moments associated with each of the six orthogonal translations and rotations the stiffness matrix was obtained from the load displacement measurements by linear least squares assuming a symmetric matrix results from a pig lumbar spinal motion segment in an isotonic bath with and without a 500 n axial preload showed a large stiffening effect with axial preload

impact of material and morphological parameters on the mechanical response of the lumbar spine a finite element sensitivity study finite element models are frequently used to study lumbar spinal biomechanics deterministic models are used to reflect a certain configuration including the means of geometrical and material properties while probabilistic models account for the inherent variability in the population because model parameters are generally uncertain their predictive power is frequently questioned in the present study we determined the sensitivities of spinal forces and motions to material parameters of intervertebral discs vertebrae and ligaments and to lumbar morphology we performed 1200 model simulations using a generic model of the human lumbar spine loaded under pure moments coefficients of determination and of variation were determined for all parameter and response combinations material properties of the vertebrae displayed the least impact on results whereas those of the discs and morphology impacted most the most affected results were the axial compression forces in the vertebral body and in several ligaments during flexion and the facet joint forces during extension intervertebral rotations were considerably affected only when several parameters were varied simultaneously results can be used to decide which model parameters require careful consideration in deterministic models and which parameters might be omitted in probabilistic studies findings allow quantitative estimation of a model s precision

incremental string comparison the problem of comparing two sequences a and b to determine their longest common subsequence lcs or the edit distance between them has been much studied in this paper we consider the following incremental version of these problems given an appropriate encoding of a comparison between a and b can one incrementally compute the answer for a and bb and the answer for a and bb with equal efficiency where b is an additional symbol our main result is a theorem exposing a surprising relationship between the dynamic programming solutions for two such adjacent problems given a threshold k on the number of differences to be permitted in an alignment the theorem leads directly to an o k algorithm for incrementally computing a new solution from an old one as contrasts the o k2 time required to compute a solution from scratch we further show with a series of applications that this algorithm is indeed more powerful than its nonincremental counterpart we show this by solving the applications with greater asymptotic efficiency than heretofore possible for example we obtain o nk algorithms for the longest prefix approximate match problem the approximate overlap problem and cyclic string comparison

maximal common subsequences and minimal common supersequences the problems of finding a longest common subsequence and a shortest common supersequence of a set of strings are well known they can be solved in polynomial time for two strings in fact the problems are dual in this case or for any fixed number of strings by dynamic programming but both problems are np hard in general for an arbitrary numberkof strings here we study the related problems of finding a shortest maximal common subsequence and a longest minimal common supersequence we describe dynamic programming algorithms for the case of two strings for which case the problems are no longer dual which can be extended to any fixed number of strings we also show that both problems are np hard in general forkstrings although the latter problem unlike shortest common supersequence is solvable in polynomial time for strings of length 2 finally we prove a strong negative approximability result for the shortest maximal common subsequence problem

g central subalgebras and extensions of kms states abstract let a g be a g central c dynamical system and b be a separable seminuclear g invariant c subalgebra of b then b g b is g central if b r is any one parameter c dynamical system is a kms state of b and a is a c algebra containing b then has a state extenstion satisfying i b a ab for all a in a and all analytic b in b if and only if there is a contraction q a b such that q b

string alignment with substitution insertion deletion squashing and expansion operations abstract let x and y be any two strings of finite length the problem of transforming x to y using the edit operations of substitution deletion and insertion has been extensively studied in the literature the problem can be solved in quadratic time if the edit operations are extended to include the operation of transposition of adjacent characters and is np complete if the characters can be edited repeatedly in this paper we consider the problem of transforming x to y when the set of edit operations is extended to include the squashing and expansion operations whereas in the squashing operation two or more contiguous characters of x can be transformed into a single character of y in the expansion operation a single character in x may be expanded into two or more contiguous characters of y these operations are typically found in the recognition of cursive script a quadratic time solution to the problem has been presented this solution is optimal for the infinite alphabet case the strategy to compute the sequence of edit operations is also presented

approximate string matching using factor automata given a text t over alphabet and a complete index for t constructed using the finite automaton called the factor automaton or dawg accepting all the substrings factors of text t an answer to the query whether a pattern p occurs in text t with k differences is discussed to be done by an algorithm having the time complexity independent on the length of text t the algorithm searches for the final state of the finite automaton accepting the intersection of languages fac t the set of all factors of t and lk p the set of all strings having at most k differences with respect to pattern p

on a simple unital projectionless c algebra we construct a unital separable c algebra z as an analog of the hyperfinite type ii 1 factor besides being nuclear simple projectionless and infinite dimensional z has a unique tracial state and is kk equivalent to inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i the algebra of complex numbers it is shown that unital endomorphisms on z are approximately inner and that z is isomorphic to the infinite tensor product of its replicas it is also shown that a z a for certain interesting classes of unital simple nuclear c algebras a of real rank zero

a non optimized follower load path may cause considerable intervertebral rotations abstract osseoligamentous spinal specimens buckle under even a small vertical compressive force to allow higher axial forces a compressive follower load fl was suggested previously that approximates the curvature of the spine without inducing intervertebral rotation in both the frontal and the sagittal planes in in vitro experiments and finite element analyses the location of the fl path is subjected to estimation by the investigator such non optimized fls may induce bending and so far it is still unknown how this affects the results of the study and their comparability a symmetrical finite element model of the lumbar spine was employed to simulate upright standing while applying a follower load in analogy to in vitro experiments the path of this fl was estimated seven times by different members of our institute s spine group additionally an optimized fl path was determined and additional moments of 7 5 nm were applied to simulate flexion and extension application of the optimized 500 n compressive fl causes only a marginal alteration of the curvature cardan angle l1 s1 in sagittal plane a preceding optimization of the location of the fl path would increase the comparability of different studies

effects of inter individual lumbar spine geometry variation on load sharing geometrically personalized finite element study there is a large at times contradictory body of research relating spinal curvature to low back pain lbp mechanical load is considered as important factor in lbp etiology geometry of the spinal structures and sagittal curvature of the lumbar spine govern its mechanical behavior thus understanding how inter individual geometry particularly sagittal curvature variation affects the spinal load sharing becomes of high importance in lbp assessment this study calculated and compared kinematics and load sharing in three ligamentous lumbosacral spines one hypo lordotic hypo l with low lordosis one normal lordotic norm l with normal lordosis and one hyper lordotic hyper l with high lordosis in flexed and extended postures using 3d nonlinear finite element fe modeling these postures were simulated by applying follower load fl combined with flexion or extension moment the hypo l spine demonstrated stiffer behavior in flexion but more flexible response to extension compared to the norm l spine the excessive lordosis stiffened response of the hyper l spine to extension but did not affect its resistance to flexion compared to the norm l spine despite the different resisting actions of the posterior ligaments to flexion moment the increase of disc compression was similar in all the spines leading to similar load sharing however resistance of the facet joints to extension was more important in the norm and hyper l spines which reduced the disc compression the spinal curvature strongly influenced the magnitude and location of load on the spinal components and also altered the kinematics and load sharing particularly in extension consideration of the subject specific geometry and sagittal curvature should be an integral part of mechanical analysis of the lumbar spine

the effect of three dimensional geometrical changes during adolescent growth on the biomechanics of a spinal motion segment abstract during adolescent growth vertebrae and intervertebral discs undergo various geometrical changes although such changes in geometry are well known their effects on spinal stiffness remains poorly understood however this understanding is essential in the treatment of spinal abnormalities during growth such as scoliosis a finite element model of an l3 l4 motion segment was developed validated and applied to study the quantitative effects of changing geometry during adolescent growth on spinal stiffness in flexion extension lateral bending and axial rotation height width and depth of the vertebrae and intervertebral disc were varied as were the width of the transverse processes the length of the spinous process the size of the nucleus facet joint areas and ligament size these variations were based on average growth data for girls as reported in literature overall adolescent growth increases the stiffness with 36 lateral bending and extension to 44 flexion two thirds of this increase occurs between 10 and 14 years of age and the last third between 14 years of age and maturity although the height is the largest geometrical change during adolescent growth its effect on the biomechanics is small the depth increase of the disc and vertebrae significantly affects the stiffness in all directions while the width increase mainly affects the lateral bending stiffness hence when analysing the biomechanics of the growing adolescent spine for instance in scoliosis research the inclusion of depth and width changes in addition to the usually implemented height change is essential

a hilbert bundle characterization of hilbert c modules the category of hilbert c modules over a given c algebra is shown to be equivalent to a certain simply described category of hilbert bundles i e continuous fields of hilbert spaces over the space of pure states of the c algebra with the zero functional adjoined

are there characteristic motion patterns in the lumbar spine during flexion abstract flexion is the main motion of the lumbar spine while in vitro tests with pure moments suggest larger intra segmental rotations for the more caudal segments in vivo results show diverging motion distributions the present study analysed the motion distribution in vivo of 320 asymptomatic subjects the change of the back curvature between standing and upper body flexion was determined using a non invasive measurement device linear bilinear trilinear quadratic and cubic regression models were fitted to the segmental motion distribution over the lengths of the lordosis to categorise characteristic motion patterns simplicity and approximation quality were used to assign the motion distributions to the regression models seventy seven percent of the motion distributions could be explained by a bilinear model a further 12 and 11 could be represented by a trilinear and linear model respectively less than 1 of the distributions could not satisfactorily be represented by the models all of the bilinear models displayed maximum flexion in approximately the middle of lordosis all linear models showed a decreasing rotation from caudal to cranial most of the trilinear models displayed a distribution similar to the bilinear age sex body height and weight did not significantly affect these distributions this in vivo study identified characteristic motion patterns in the lumbar spine during flexion the quantitative results provide a clear description of the healthy condition and may serve to identify spinal motion abnormalities

pattern recognition of strings with substitutions insertions deletions and generalized transpositions abstract we study the problem of recognizing a string y which is the noisy version of some unknown string x chosen from a finite dictionary h the traditional case which has been extensively studied in the literature is the one in which y contains substitution insertion and deletion sid errors although some work has been done to extend the traditional set of edit operations to include the straightforward transposition of adjacent eharacters see j assoc comput mach 22 177 183 1975 the problem is unsolved when the transposed characters are themselves subsequently substituted as is typical in cursive and typewritten script in molecular biology and in noisy chain coded boundaries in this paper we present the first reported solution to the analytic problem of editing one string x to another y using these four edit operations a scheme for obtaining the optimal edit operations has also been given both these solutions are optimal for the infinite alphabet case using these algorithms we present a syntactic pattern recognition scheme which corrects noisy text containing all these types of errors the paper includes experimental results involving sub dictionaries of the most common english words which demonstrate the superiority of our system over existing methods

geometry strongly influences the response of numerical models of the lumbar spine a probabilistic finite element analysis typical fe models of the human lumbar spine consider a single fixed geometry such models cannot account for potential effects of the natural variability of the spine s geometry in this study we performed a probabilistic uncertainty and sensitivity analysis of a fully parameterized geometrically simplified model of the l3 l4 segment we examined the impact of the uncertainty in all 40 geometry parameters estimated lower and upper bounds for the required sample size and determined the most important geometry parameters the natural variability of the spine s geometry indeed strongly affects intradiscal pressure range of motion and facet joint contact forces deriving generalized statements from fixed geometry models as well as transferring those results to different cases thus can easily lead to wrong conclusions and should only be performed with extreme caution we recommend a sample size of 100 to obtain reasonable accurate point estimates and a sufficient overview of the remaining uncertainties yet only few parameters especially those determining the disc geometry disc height end plate width and depth and the facets position intra articular space pedicle length facet angles proved to be truly important accurate measurement and modeling of those structures should therefore be prioritized

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

deciding word neighborhood with universal neighborhood automata given some form of distance between words a fundamental operation is to decide whether the distance between two given words w and v is within a given bound in earlier work we introduced the concept of a universal levenshtein automaton for a given distance bound n this deterministic automaton takes as input a sequence g of bitvectors computed from w and v the sequence g is accepted iff the levenshtein distance between w and v does not exceed n the automaton is called universal since the same automaton can be used for arbitrary input words w and v regardless of the underlying input alphabet here we extend this picture after introducing a large abstract family of generalized word distances we exactly characterize those members where word neighborhood can be decided using universal neighborhood automata similar to universal levenshtein automata our theoretical results establish several bridges to the theory of synchronized finite state transducers and dynamic programming for small neighborhood bounds universal neighborhood automata can be held in main memory this leads to very efficient algorithms for the above decision problem evaluation results show that these algorithms are much faster than those based on dynamic programming

sensitivity of predicted muscle forces to parameters of the optimization based human leg model revealed by analytical and numerical analyses there are different opinions in the literature on whether the cost functions the sum of muscle stresses squared and the sum of muscle stresses cubed can reasonably predict muscle forces in humans one potential reason for the discrepancy in the results could be that different authors use different sets of model parameters which could substantially affect forces predicted by optimization based models in this study the sensitivity of the optimal solution obtained by minimizing the above cost functions for a planar three degrees of freedom dof model of the leg with nine muscles was investigated analytically for the quadratic function and numerically for the cubic function analytical results revealed that generally the non zero optimal force of each muscle depends in a very complex non linear way on moments at all three joints and moment arms and physiological cross sectional areas pcsas of all muscles deviations of the model parameters moment arms and pcsas from their nominal values within a physiologically feasible range affected not only the magnitude of the forces predicted by both criteria but also the number of non zero forces in the optimal solution and the combination of muscles with non zero predicted forces muscle force magnitudes calculated by both criteria were similar they could change several times as model parameters changed whereas patterns of muscle forces were typically not as sensitive it is concluded that different opinions in the literature about the behavior of optimization based models can be potentially explained by differences in employed model parameters

complete inverted files for efficient text retrieval and analysis given a finite set of texts s w 1 w k over some fixed finite alphabet s a complete inverted file for s is an abstract data type that provides the functions find w which returns the longest prefix of w that occurs as a subword of a word in s freq w which returns the number of times w occurs in s and locations w which returns the set of positions where w occurs in s a data structure that implements a complete inverted file for s that occupies linear space and can be built in linear time using the uniform cost ram model is given using this data structure the time for each of the above query functions is optimal to accomplish this techniques from the theory of finite automata and the work on suffix trees are used to build a deterministic finite automaton that recognizes the set of all subwords of the set s this automaton is then annotated with additional information and compacted to facilitate the desired query functions the result is a data structure that is smaller and more flexible than the suffix tree

role of disc area and trabecular bone density on lumbar spinal column fracture risk curves under vertical impact abstract while studies have been conducted using human cadaver lumbar spines to understand injury biomechanics in terms of stability energy to fracture and physiological responses under pure moment follower loads data are sparse for inferior to superior impacts injuries occur under this mode from underbody blasts objectives determine role of age disc area and trabecular bone density on tolerances risk curves under vertical loading from a controlled group of specimens t12 s1 columns were obtained pretest x rays and cts taken load cells attached to both ends impacts applied at s1 end using custom vertical accelerator device and posttest x ray ct and dissections done bmd of l2 l4 vertebrae were obtained from qct survival analysis based human injury probability curves hipcs were derived using proximal and distal forces age area and bmd were covariates forces were considered uncensored representing the load carrying capacity the akaike information criterion was used to determine optimal distributions the mean forces 95 confidence intervals and normalized confidence interval size ncis were computed the lognormal distribution was the optimal function for both forces age area and bmd were not significant p 0 05 covariates for distal forces while only bmd was significant for proximal forces the ncis was the lowest for force bmd covariate hipc the hipcs for both genders at 35 and 45 years were based on population bmds these hipcs serve as human tolerance criteria for automotive military and other applications in this controlled group of samples bmd is a better predictor covariate that characterizes lumbar column injury under inferior to superior impacts

transition probabilities of normal states determine the jordan structure of a quantum system let x1d516 m1 x1d516 m2 be a bijection not assumed affine nor continuous between the sets of normal states of two quantum systems modelled on the self adjoint parts of von neumann algebras m1 and m2 respectively this paper concerns with the situation when preserves or partially preserves one of the following three notions of transition probability on the normal state spaces the transition probability pu introduced by uhlmann rep math phys 9 273 279 1976 the transition probability pr introduced by raggio lett math phys 6 233 236 1982 and an asymmetric transition probability p0 as introduced in this article it is shown that the two systems are isomorphic i e m1 and m2 are jordan isomorphic if preserves all pairs with zero uhlmann respectively raggio or asymmetric transition probability in the sense that for any normal states and we have p 0 if and only if p 0 where p stands for pu respectively pr or p0 furthermore as an extension of wi

document listing on repetitive collections with guaranteed performance abstract we consider document listing on string collections that is finding in which strings a given pattern appears in particular we focus on repetitive collections a collection of size n over alphabet 1 is composed of d copies of a string of size n and s edits are applied on ranges of copies we introduce the first document listing index with size o n s precisely o n lg s lg 2 n lg d bits and with useful worst case time guarantees given a pattern of length m the index reports the ndoc 0 strings where it appears in time o m lg 1 n ndoc for any constant 0 and tells in time o m lg n if ndoc 0 our technique is to augment a range data structure that is commonly used on grammar based indexes so that instead of retrieving all the pattern occurrences it computes useful summaries on them we show that the idea has independent interest we introduce the first grammar based index that on a text t 1 n with a grammar of size r uses o r lg n bits and counts the number of occurrences of a pattern p 1 m in time o m 2 m lg 2 r for any constant 0 we also give the first index using o z lg n z lg n bits where t is parsed by lempel ziv into z phrases counting occurrences in time o m lg 2 n

the generator problem for z stable c algebras the generator problem was posed by kadison in 1967 and it remains open until today we provide a solution for the class of c algebras absorbing the jiang su algebra z tensorially more precisely we show that every unital separable z stable c algebra a is singly generated which means that there exists an element x a that is not contained in any proper sub c algebra of a to give applications of our result we observe that z can be embedded into the reduced group c algebra of a discrete group that contains a non cyclic free subgroup it follows that certain tensor products with reduced group c algebras are singly generated in particular c r f c r f is singly generated

regularity properties in the classification program for separable amenable c algebras we report on recent progress in the program to classify separable amenable c algebras our emphasis is on the newly apparent role of regularity properties such as finite decomposition rank strict comparison of positive elements and z stability and on the importance of the cuntz semigroup we include a brief history of the program s successes since 1989 a more detailed look at the villadsen type algebras which have so dramatically changed the landscape and a collection of announcements on the structure and properties of the cuntz semigroup

effects of eight different ligament property datasets on biomechanics of a lumbar l4 l5 finite element model ligaments assist trunk muscles in balancing external moments and providing spinal stability in absence of the personalized material properties for ligaments finite element fe models use dispersed data from the literature this study aims to investigate the relative effects of eight different ligament property datasets on fe model responses eight l4 l5 models distinct only in ligament properties were constructed and loaded under moment 15nm alone or combined with a compressive follower load fl range of motions rom of the disc alone model matched well in vitro data ligament properties significantly affected only sagittal roms 3 0 7 1 in flexion and 3 8 5 8 in extension at 10nm sequential removal of ligaments shifted sagittal roms in and out of the corresponding in vitro ranges when moment was combined with fl center of rotation matched in vivo data for all models 3 8 0 9mm and 4 3 1 8mm posterior to the disc center in flexion and extension respectively under 15nm sagittal moments ligament strains were often smaller or within the in vitro range in flexion whereas some posterior ligament forces approached their failure forces in some models ligament forces varied substantially within the models and affected the moment sharing and internal forces on the disc and facet joints intradiscal pressure idp had the greatest variation between models in extension none of the datasets yielded results in agreement with all reported measurements results emphasized the important role of ligaments especially under larger moments and the need for their accurate representation in search for valid spinal models

the jiang su algebra revisited we give a number of new characterizations of the jiang su algebra z both intrinsic and extrinsic in terms of c algebraic dynamical topological and k theoretic conditions along the way we study divisibility properties of c algebras we give a precise characterization of those unital c algebras of stable rank one that admit a unital embedding of the dimensiondrop c algebra zn n 1 and we prove a cancellation theorem for the cuntz semigroup of c algebras of stable rank one

a database of lumbar spinal mechanical behavior for validation of spinal analytical models data from two experimental studies with eight specimens each of spinal motion segments and or intervertebral discs are presented in a form that can be used for comparison with finite element model predictions the data include the effect of compressive preload 0 250 and 500n with quasistatic cyclic loading 0 0115hz and the effect of loading frequency 1 0 1 0 01 and 0 001hz with a physiological compressive preload mean 642n specimens were tested with displacements in each of six degrees of freedom three translations and three rotations about defined anatomical axes the three forces and three moments in the corresponding axis system were recorded during each test linearized stiffness matrices were calculated that could be used in multi segmental biomechanical models of the spine and these matrices were analyzed to determine whether off diagonal terms and symmetry assumptions should be included these databases of lumbar spinal mechanical behavior under physiological conditions quantify behaviors that should be present in finite element model simulations the addition of more specimens to identify sources of variability associated with physical dimensions degeneration and other variables would be beneficial supplementary data provide the recorded data and matlab codes for reading files linearized stiffness matrices derived from the tests at different preloads revealed few significant unexpected off diagonal terms and little evidence of significant matrix asymmetry

extending alignments with k mismatches and l gaps recently the problem of extending an alignment with k mismatches and a single gap for pairwise sequence alignment was introduced flouri et al 2011 the authors considered the problem of extending an alignment under the hamming distance model by also allowing the insertion of a single gap and presented a q email protected time algorithm to solve it where m is the length of the shortest sequence to be extended and b is the maximum allowed length of the single gap very recently it was shown flouri et al 2012 that this problem is strongly and directly motivated by the next generation re sequencing application aligning tens of millions of short dna sequences against a reference genome in this article we consider an extension of this problem extending an alignment with k mismatches and two gaps and present a q email protected time algorithm to solve it this extension is proved to be fundamental in the next generation re sequencing application alachiotis et al 2012 in addition we present a generalisation of our solution to solve the problem of extending an alignment with k mismatches and gaps in time q email protected the presented solutions work provided that all gaps in the alignment must occur in one of the two sequences

extensions of factorial states of c algebras let a be a c algebra b be a c subalgebra of a and be a factorial state of b sometimes may be extended to a factorial state of a by a tensor product method of sakai c algebras and w algebras springer verlag berlin heidelberg new york 1971 sometimes there is a weak expectation of a into b and then factorial extensions may be found by a method of sakai and tsui yokohama math j 29 1981 157 160 these two methods are shown to have the same effect and the factorial extensions produced by them are analysed 1985

frontier search the critical resource that limits the application of best first search is memory we present a new class of best first search algorithms that reduce the space complexity the key idea is to store only the open list of generated nodes but not the closed list of expanded nodes the solution path can be recovered by a divide and conquer technique either as a bidirectional or unidirectional search for many problems frontier search dramatically reduces the memory required by best first search we apply frontier search to breadth first search of sliding tile puzzles and the 4 peg towers of hanoi problem dijkstra s algorithm on a grid with random edge costs and the a algorithm on the fifteen puzzle the four peg towers of hanoi problem and optimal sequence alignment in computational biology

characterization of the l4 l5 s1 motion segment using the stepwise reduction method the two aims of this study were to generate data for a more accurate calibration of finite element models including the l5 s1 segment and to find mechanical differences between the l4 l5 and l5 s1 segments then the range of motion rom and facet forces for the l4 s1 segment were measured using the stepwise reduction method this consists of sequentially testing and reducing each segment in nine stages by cutting the ligaments facet capsules and removing the nucleus five l4 s1 human segments median 65 years range 53 84 years sd 11 0 years were loaded under a maximum pure moment of 8nm the rom was measured using stereo photogrammetry via tracking of three markers and the facet contact forces cf were measured using a tekscan system the rom for the l4 l5 segment and all stages showed good agreement with published data the major differences in rom between the l4 l5 and l5 s1 segments were found for lateral bending and all stages for which the l4 l5 rom was about 1 5 3 times higher than that of the l5 s1 segment consistent with l5 s1 facet cf about 1 3 to 4 times higher than those measured for the l4 l5 segment for the other movements and few stages the l4 l5 rom was significantly lower that of the l5 s1 segment rom and cf provide important baseline data for more accurate calibration of fe models and to understand the role that their structures play in lower lumbar spine mechanics

complements to various stone weierstrass theorems for c algebras and a theorem of shultz j glimm s stone weierstrass theorem states that ifa is ac algebra p a is the set of pure states ofa andb is ac subalgebra which separates overline p a cup left 0 right thenb a we show that ifb is ac subalgebra ofa andx an element ofa such that any two elements of overline p a cup left 0 right which agree onb agree also onx thenx b similar complements are given to other stone weierstrass theorems a theorem of f shultz states that ifx a the enveloping von neumann algebra ofa and ifx x x andxx are uniformly continuous onp a 0 then there is an element ofa which agrees withx onp a we show that the hypotheses onx x andxx can be dropped

mean field approximations to the longest common subsequence problem the longest common subsequence lcs problem is a fundamental problem of sequence comparison a natural approximation to this problem is a model in which every pair of letters of two sequences are matched independently of the other pairs with probability 1 s s representing the size of the alphabet this model is analogous to a mean field version of the lcs problem which can be solved with a cavity approach j boutet de monvel eur phys j b 7 293 1999 we refine here this approximation by incorporating in a systematic way correlations among the matches in the cavity calculation we obtain a series of closer and closer approximations to the lcs problem which we quantify in the large s limit both with a perturbative approach and by monte carlo simulations we find that as it happens in the expansion around mean field for other disordered systems the corrections to our approximations depend upon long ranged correlation effects that render the large s expansion nonperturbative

comparison of eight published static finite element models of the intact lumbar spine predictive power of models improves when combined together finite element fe model studies have made important contributions to our understanding of functional biomechanics of the lumbar spine however if a model is used to answer clinical and biomechanical questions over a certain population their inherently large inter subject variability has to be considered current fe model studies however generally account only for a single distinct spinal geometry with one set of material properties this raises questions concerning their predictive power their range of results and on their agreement with in vitro and in vivo values eight well established fe models of the lumbar spine l1 5 of different research centres around the globe were subjected to pure and combined loading modes and compared to in vitro and in vivo measurements for intervertebral rotations disc pressures and facet joint forces under pure moment loading the predicted l1 5 rotations of almost all models fell within the reported in vitro ranges and their median values differed on average by only 2 for flexion extension 1 for lateral bending and 5 for axial rotation predicted median facet joint forces and disc pressures were also in good agreement with published median in vitro values however the ranges of predictions were larger and exceeded those reported in vitro especially for the facet joint forces for all combined loading modes except for flexion predicted median segmental intervertebral rotations and disc pressures were in good agreement with measured in vivo values in light of high inter subject variability the generalization of results of a single model to a population remains a concern this study demonstrated that the pooled median of individual model results similar to a probabilistic approach can be used as an improved predictive tool in order to estimate the response of the lumbar spine

special factors and the combinatorics of suffix and factor automata the suffix automaton resp factor automaton of a finite word w is the minimal deterministic automaton recognizing the set of suffixes resp factors of w we study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w we derive formulae for the number of states of these automata we also characterize the languages l s a and l f a of words having respectively suffix automaton and factor automaton with the minimal possible number of states

nuclear dimension and mathcal z stability of pure c algebras in this article i study a number of topological and algebraic dimension type properties of simple c algebras and their interplay in particular a simple c algebra is defined to be tracially m bar m pure if it has strong tracial m comparison and is tracially bar m almost divisible these notions are related to each other and to nuclear dimension

continuous fields of c algebras over finite dimensional spaces abstract let x be a finite dimensional compact metrizable space we study a technique which employs semiprojectivity as a tool to produce approximations of c x algebras by c x subalgebras with controlled complexity the following applications are given all unital separable continuous fields of c algebras over x with fibers isomorphic to a fixed cuntz algebra o n n 2 3 are locally trivial they are trivial if n 2 or n for n 3 finite such a field is trivial if and only if n 1 1 a 0 in k 0 a where a is the c algebra of continuous sections of the field we give a complete list of the kirchberg algebras d satisfying the uct and having finitely generated k theory groups for which every unital separable continuous field over x with fibers isomorphic to d is automatically locally trivial or trivial in a more general context we show that a separable unital continuous field over x with fibers isomorphic to a kk semiprojective kirchberg c algebra is trivial if and only if it satisfies a k theoretical fell type condition

classification of inductive limits of 1 dimensional nccw complexes abstract a classification result is obtained for the c algebras that are stably isomorphic to inductive limits of 1 dimensional noncommutative cw complexes with trivial k 1 group the classifying functor cu is defined in terms of the cuntz semigroup of the unitization of the algebra for the simple c algebras covered by the classification cu reduces to the ordered k 0 group the cone of traces and the pairing between them as an application of the classification it is shown that the crossed products by a quasi free action o 2 r are all isomorphic for a dense set of positive irrational numbers

applications of approximate string matching to 2d shape recognition abstract a new method for the recognition of arbitrary two dimensional 2d shapes is described it is based on string edit distance computation the recognition method is invariant under translation rotation scaling and partial occlusion a set of experiments are described demonstrating the robustness and reliability of the proposed approach

biomechanical properties of human lumbar spine ligaments biomechanical properties of the six major lumbar spine ligaments were determined from 38 fresh human cadaveric subjects for direct incorporation into mathematical and finite element models anterior and posterior longitudinal ligaments joint capsules ligamentum flavum interspinous and supraspinous ligaments were evaluated using the results from in situ isolation tests individual force deflection responses from 132 samples were transformed with a normalization procedure into mean force deflection properties to describe the nonlinear characteristics ligament responses based on the mechanical characteristics as well as anatomical considerations were grouped into t12 l2 l2 l4 and l4 s1 levels maintaining individuality and nonlinearity a total of 18 data curves are presented geometrical measurements of original length and cross sectional area for these six major ligaments were determined using cryomicrotomy techniques derived parameters including failure stress and strain were computed using the strength and geometry information these properties for the lumbar spinal ligaments which are based on identical definitions used in mechanical testing and geometrical assay will permit more realistic and consistent inputs for analytical models

string matching with weighted errors abstract in the approximate string matching problem differences are allowed between the pattern string p and each of its occurrences in the text string t and one is interested in finding all the occurrences of p in t with at most k differences we consider here weighted differences errors between p and t and develop fast sequential and parallel algorithms in particular we allow the following types of errors mismatch whose weight depends on the mismatching characters extra character with constant weight missing character with constant weight and transposition of two consecutive characters with constant weight a set of theoretical results allows to extend known algorithms to solve this problem with o kn sequential time and o k log m parallel time on a 4pram model with max n k 1 mp2 processors where k is the maximum sum of the error weights n is the length of t and m is the length of p

pure states as a dual object for c algebras we consider the set of pure states of ac algebra as a uniform space equipped with transition probabilities and orientation and show that the pure states with this structure determine thec algebra up to isomorphism

semiprojectivity with and without a group action abstract the equivariant version of semiprojectivity was recently introduced by the first named author we study properties of this notion in particular its relation to ordinary semiprojectivity of the crossed product and of the algebra itself we show that equivariant semiprojectivity is preserved when the action is restricted to a cocompact subgroup thus if a second countable compact group acts semiprojectively on a c algebra a then a must be semiprojective this fails for noncompact groups we construct a semiprojective action of z on a nonsemiprojective c algebra we also study equivariant projectivity and obtain analogous results however with fewer restrictions on the subgroup for example if a discrete group acts projectively on a c algebra a then a must be projective this is in contrast to the semiprojective case we show that the crossed product by a semiprojective action of a finite group on a unital c algebra is a semiprojective c algebra we give examples to show that this does not generalize to all compact groups

on factorial states of operator algebras results for the factorial state space of a c algebra a which are analogous to results of glimm ann of math 72 1960 216 244 73 1961 572 612 tomiyama and takesaki tohoku math j 2 13 1961 498 523 for the pure state space it is shown that a is prime if and only if the type i factorial states are dense in the state space it follows that every factorial state is a w limit of type i factorial states the factorial state space of a von neumann algebra is determined and it is shown that if a is unital and acts non degenerately on a hilbert space then the factorial state space of the generated von neumann algebra restricts precisely to the factorial state space of a it is shown that the set of factorial states is w compact if and only if a is unital liminal and has hausdorff primitive ideal space

computation of trunk equilibrium and stability in free flexion extension movements at different velocities velocity of movement has been suggested as a risk factor for low back disorders the effect of changes in velocity during unconstrained flexion extension movements on muscle activations spinal loads base reaction forces and system stability was computed in vivo measurements of kinematics and ground reaction forces were initially carried out on young asymptomatic subjects the collected kinematics of three subjects representing maximum mean and minimum lumbar rotations were subsequently used in the kinematics driven model to compute results during the entire movements at three different velocities estimated spinal loads and muscle forces were significantly larger in fastest pace as compared to slower ones indicating the effect of inertial forces spinal stability was improved in larger trunk flexion angles and fastest movement partial or full flexion relaxation of global extensor muscles occurred only in slower movements some local lumbar muscles especially in subjects with larger lumbar flexion and at slower paces also demonstrated flexion relaxation results confirmed the crucial role of movement velocity on spinal biomechanics predictions also demonstrated the important role on response of the magnitude of peak lumbar rotation and its temporal variation

moment rotation responses of the human lumbosacral spinal column abstract the objective of this study was to test the hypothesis that the human lumbosacral joint behaves differently from l1 l5 joints and provides primary moment rotation responses under pure moment flexion and extension and left and right lateral bending on a level by level basis in addition range of motion rom and stiffness data were extracted from the moment rotation responses ten t12 s1 column specimens with ages ranging from 27 to 68 years mean 50 6 13 2 were tested at a load level of 4 0 n m nonlinear flexion and extension and left and right lateral bending moment rotation responses at each spinal level are reported in the form of a logarithmic function the mean rom was the greatest at the l5 s1 level under flexion 7 37 3 69 and extension 4 62 2 56 and at the l3 l4 level under lateral bending 4 04 1 11 the mean rom was the least at the l1 l2 level under flexion 2 42 0 90 l2 l3 level under extension 1 58 0 63 and l1 l2 level under lateral bending 2 50 0 75 the present study proved the hypothesis that l5 s1 motions are significantly greater than l1 l5 motions under flexion and extension loadings but the hypothesis was found to be untrue under the lateral bending mode these experimental data are useful in the improved validation of fe models which will increase the confidence of stress analysis and other modeling applications

approximating edit distance within constant factor in truly sub quadratic time edit distance is a measure of similarity of two strings based on the minimum number of character insertions deletions and substitutions required to transform one string into the other the edit d

computation of trunk stability in forward perturbations effects of preload perturbation load initial flexion and abdominal preactivation spine stability demand influences active passive coordination of the trunk response especially during sudden perturbations the objective of this study was to look at the role of passive stationary active and reflexive subsystems on spinal stability spine stability was evaluated here during pre and post perturbation phases by computing the minimum i e critical muscle stiffness coefficient required to maintain stability the effects of pre perturbation conditions preloading initial posture and abdominal antagonistic coactivation as well as perturbation magnitude were studied results revealed that higher preload initially flexed trunk posture and abdominal pre activation enhanced pre perturbation stiffness and stability in contrast to the preload however larger sudden load initial flexion and abdominal preactivation significantly increased post perturbation stability margin as a result much lower critical muscle stiffness coefficient was required post perturbation compared to the pre perturbation phase the trunk stiffness and stability substantially increased post perturbation demanding thus a much lower critical muscle stiffness coefficient overall these findings highlight the crucial role of the ligamentous spine and muscles in both passive and active states in augmenting the trunk stiffness and hence stability during pre and post perturbation phases a role much evident in the presence of initial trunk flexion