improvement and comparison of heuristics for solving the uncapacitated multisource weber problem the multisource weber problem is to locate simultaneouslym facilities in the euclidean plane to minimize the total transportation cost for satisfying the demand ofn fixed users each supplied from its closest facility many heuristics have been proposed for this problem as well as a few exact algorithms heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms we compare various heuristics i e alternative location allocation cooper 1964 projection bongartz et al 1994 tabu search brimberg and mladenovic 1996a p median plus weber hansen et al 1996 genetic search and several versions of variable neighbourhood search based on empirical tests that are reported it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that variable neighbourhood search gives consistently best results on average in moderate computing time

a tabu search approach to the constraint satisfaction problem as a general problem solver many combinatorial problems including a variety of combinatorial optimization problems can be naturally formulated as a constraint satisfaction problem csp we develop in this paper a tabu search based algorithm for the csp as a foundation for a general problem solver in addition to the basic components of tabu search we develop a number of elaborations such as an automatic control mechanism for the tabu tenure modification of the penalty function to handle objective functions and enlargement of the neighborhood by allowing swap operations computational results with our algorithm are reported for various problems selected from a wide range of applications i e graph coloring generalized assignment set covering timetabling and nurse scheduling our results appear to be competitive with those of existing algorithms specially developed for the respective problem domains

entangled three qubit states without concurrence and three tangle we provide a complete analysis of mixed three qubit states composed of a greenberger horne zeilinger state and a w state orthogonal to the former we present optimal decompositions and convex roofs for the three tangle further we provide an analytical method to decide whether or not an arbitrary rank 2 state of three qubits has vanishing three tangle these results highlight intriguing differences compared to the properties of two qubit mixed states and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states by studying the coffman kundu wootters inequality we find that while the amounts of inequivalent entanglement types strictly add up for pure states this monogamy can be lifted for mixed states by virtue of vanishing tangle measures

dynamic margins of stability during human walking in destabilizing environments understanding how humans maintain stability when walking particularly when exposed to perturbations is key to preventing falls here we quantified how imposing continuous pseudorandom anterior posterior ap and mediolateral ml oscillations affected the control of dynamic walking stability twelve subjects completed five 3 minute walking trials in the computer assisted rehabilitation environment caren system under each of 5 conditions no perturbation nop ap platform app or visual apv or ml platform mlp or visual mlv oscillations we computed ap and ml margins of stability mos for each trial mean mosml were consistently slightly larger during all perturbation conditions than during nop p 0 038 mean mosap for the app mlp and mlv oscillations were significantly smaller than during nop p 0 0005 variability of both mosap and mosml was significantly greater during the mlp and mlv oscillations than during nop p 0 0005 we also directly quantified how the mos on any given step affected the mos on the following step using first return plots there were significant changes in step to step mosml dynamics between experimental conditions p 0 0005 these changes suggested that subjects may have been trying to control foot placement and consequently stability during the perturbation conditions quantifying step to step changes in margins of dynamic stability may be more useful than mean mos in assessing how individuals control walking stability

a systematic two phase approach for the nurse rostering problem abstract nurse rostering is an np hard combinatorial problem which makes it extremely difficult to efficiently solve real life problems due to their size and complexity usually real problem instances have complicated work rules related to safety and quality of service issues in addition to rules about quality of life of the personnel for the aforementioned reasons computer supported scheduling and rescheduling for the particular problem is indispensable the specifications of the problem addressed were defined by the first international nurse rostering competition inrc2010 sponsored by the leading conference in the automated timetabling domain patat 2010 since the competition imposed quality and time constraint requirements the problem instances were partitioned into sub problems of manageable computational size and were then solved sequentially using integer mathematical programming a two phase strategy was implemented where in the first phase the workload for each nurse and for each day of the week was decided while in the second phase the specific daily shifts were assigned in addition local optimization techniques for searching across combinations of nurses partial schedules were also applied this sequence is repeated several times depending on the available computational time the results of our approach and the submitted software produced excellent solutions for both the known and the hidden problem instances which in respect gave our team the first position in all tracks of the inrc 2010 competition

optimal indecomposable witnesses without extremality or the spanning property one of the interesting problems of optimal indecomposable entanglement witnesses is whether there exists an optimal indecomposable entanglement witness which neither has the spanning property nor is associated with an extremal positive linear map here we answer this question in the negative by examining the extremality of the positive linear maps constructed by qi and hou 2011 j phys a math theor 44 215305

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

search with evolutionary ruin and stochastic rebuild a theoretic framework and a case study on exam timetabling this paper presents a state transition based formal framework for a new search method called evolutionary ruin and stochastic recreate which tries to learn and adapt to the changing environments during the search process it improves the performance of the original ruin and recreate principle by embedding an additional phase of evolutionary ruin to mimic the survival of the fittest mechanism within single solutions this method executes a cycle of solution decomposition evolutionary ruin stochastic recreate and solution acceptance until a certain stopping condition is met the solution decomposition phase first uses some problem specific knowledge to decompose a complete solution into its components and assigns a score to each component the evolutionary ruin phase then employs two evolutionary operators namely selection and mutation to destroy a certain fraction of the solution and the next stochastic recreate phase repairs the broken solution last the solution acceptance phase selects a specific strategy to determine the probability of accepting the newly generated solution hence optimisation is achieved by an iterative process of component evaluation solution disruption and stochastic constructive repair from the state transitions point of view this paper presents a probabilistic model and implements a markov chain analysis on some theoretical properties of the approach unlike the theoretical work on genetic algorithm and simulated annealing which are based on state transitions within the space of complete assignments our model is based on state transitions within the space of partial assignments the exam timetabling problems are used to test the performance in solving real world hard problems

quantifying entanglement resources we present an overview of the quantitative theory of single copy entanglement in finite dimensional quantum systems in particular we emphasize the point of view that different entanglement measures quantify different types of resources which leads to a natural interdependence of entanglement classification and quantification apart from the theoretical basis we outline various methods for obtaining quantitative results on arbitrary mixed states this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

images in quantum entanglement a system for classifying and quantifying entanglement in spin 1 2 pure states is presented based on simple images from the image point of view an entangled state can be described as a linear superposition of separable object wavefunction o plus a portion of its own inverse image bell states can be defined in this way using the method of images the three spin 1 2 system is discussed in some detail this system can exhibit exclusive three particle 123 entanglement two particle entanglements 12 13 23 and or mixtures of all four all four image states are orthogonal both to each other and to the object wavefunction in general five entanglement parameters 12 13 23 123 and 123 are required to define the general entangled state in addition it is shown that there is considerable scope for encoding numbers at least from the classical point of view but using quantum mechanical principles methods are developed for their extraction it is shown that concurrence can be used to extract even partite but not odd partite information additional relationships are also presented which can be helpful in the decoding process however in general numerical methods are mandatory a simple roulette method for decoding is presented and discussed but it is shown that if the encoder chooses to use transcendental numbers for the angles defining the target function 1 1 etc the method rapidly turns into the devil s roulette requiring finer and finer angular steps

large neighborhood search for multi trip vehicle routing abstract we consider the multi trip vehicle routing problem in which each vehicle can perform several routes during the same working shift to serve a set of customers the problem arises when customers are close to each other or when their demands are large a common approach consists of solving this problem by combining vehicle routing heuristics with bin packing routines in order to assign routes to vehicles we compare this approach with a heuristic that makes use of specific operators designed to tackle the routing and the assignment aspects of the problem simultaneously two large neighborhood search heuristics are proposed to perform the comparison we provide insights into the configuration of the proposed algorithms by analyzing the behavior of several of their components in particular we question the impact of the roulette wheel mechanism we also observe that guiding the search with an objective function designed for the multi trip case is crucial even when exploring the solution space of the vehicle routing problem we provide several best known solutions for benchmark instances

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

the impact of a systematic reduction in shoe floor friction on heel contact walking kinematics a gait simulation approach falls initiated by slips and trips are a serious health hazard to older adults experimental studies have provided important descriptions of postural responses to slipping but it is difficult to determine why some slips result in falls from experiments alone computational modeling and simulation techniques can complement experimental approaches by identifying causes of failed recovery attempts the purpose of this study was to develop a method to determine the impact of a systematic reduction in the foot floor friction coefficient mu on the kinematics of walking shortly after heel contact approximately 200ms a walking model that included foot floor interactions was utilized to find the set of moments that best tracked the joint angles and measured ground reaction forces obtained from a non slipping dry trial a passive slip was simulated by driving the model with the joint moments from the dry simulation and by reducing mu slip simulations with values of mu greater than the subject specific peak required coefficient of friction rcof an experimental measure of slip resistant gait resulted in only minor deviations in gait kinematics from the dry condition in contrast slip simulations run in environments characterized by mu language en

variable neighborhood search principles and applications abstract systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization called variable neighborhood search vns we present a basic scheme for this purpose which can easily be implemented using any local search algorithm as a subroutine its effectiveness is illustrated by solving several classical combinatorial or global optimization problems moreover several extensions are proposed for solving large problem instances using vns within the successive approximation method yields a two level vns called variable neighborhood decomposition search vnds modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed vns svns heuristic finally we show how to stabilize column generation algorithms with help of vns and discuss various ways to use vns in graph theory i e to suggest disprove or give hints on how to prove conjectures an area where metaheuristics do not appear to have been applied before

dynamic stability and compensatory stepping responses during anterior gait slip perturbations in people with chronic hemiparetic stroke abstract to examine the control of dynamic stability and characteristics of the compensatory stepping responses to an unexpected anterior gait slip induced under the non involved limb in people with hemi paretic stroke pwhs and to examine any resulting adaptive changes in these on the second slip due to experience from prior slip exposure ten pwhs experienced overground slip s1 during walking on the laboratory walkway after 5 8 regular walking rw trials followed by a second consecutive slip trial s2 the slip outcome backward loss of balance blob and no loss of balance nlob and com state i e its com position and velocity stability were examined between the rw and s1 and s1 and s2 at touchdown td of non involved limb and at liftoff lo of the contralateral limb at td there was no difference in stability between rw and s1 however at lo subjects demonstrated a lower stability on s1 than rw resulting in a 100 backward loss of balance blob with compensatory stepping response recovery step rs 4 10 or aborted step as 6 10 on s2 although there was no change in stability at td there was a significant improvement in stability at lo with a 40 decrease in blob there was also a change in step strategy with a decrease in as response 60 to 35 p

the nurse rostering problem a critical appraisal of the problem structure this paper is concerned with the problem of nurse rostering within hospitals we analyse a class of four benchmark instances from the nurse rostering literature to provide insight into the nature of the problem by highlighting the structure of the problem we are able to reduce the relevant solution space a mixed integer linear programme is then able to find optimal solutions to all four instances of this class of benchmark problems each within half an hour our second contribution is to extend current mathematical approaches to nurse rostering to take better account of the practical considerations we provide a methodology for handling rostering constraints and preferences arising from the continuity from one scheduling period to the next

direct parameterization of postural stability during quiet upright stance effects of age and altered sensory conditions the purpose of this study was to determine the relationship between measures of local dynamic stability lds during upright stance and both descriptive measures of postural sway and a scaling index derived from detrended fluctuation analysis center of pressure cop time series were obtained from healthy participants 16 young and 16 older during upright quiet stance vision and somatosensation were altered by eye closure and standing on a compliant surface respectively a non linear time series analysis method was used to compute three lds parameters from the cop data a which was defined as the cop excursion range in state space and s and l which were defined as the divergence rates over short and long term timescales respectively lds parameters descriptive cop measures and had generally consistent sensitivities to age and or altered sensory conditions age x sensory condition interactions however had distinct effects on lds parameters compared to the other cop based measures older individuals exhibited faster divergence rates while having similar magnitudes of a compared to young individuals these results suggest that older individuals stiffen the musculoskeletal system via increased muscle activity perhaps as an age related postural adaptation in addition correlations between lds parameters and other cop measures were relatively small r2 0 29 hence lds parameters a s and l provide distinct information on postural control and stability supplementing other cop based measures

classification of mixed three qubit states we introduce a classification of mixed three qubit states in which we define the classes of separable biseparable w and greenberger horne zeilinger states these classes are successively embedded into each other we show that contrary to pure w type states the mixed w class is not of measure zero we construct witness operators that detect the class of a mixed state we discuss the conjecture that all entangled states with positive partial transpose pptes belong to the w class finally we present a new family of pptes edge states with maximal ranks

the discriminant capabilities of stability measures trunk kinematics and step kinematics in classifying successful and failed compensatory stepping responses by young adults abstract this study evaluated the discriminant capability of stability measures trunk kinematics and step kinematics to classify successful and failed compensatory stepping responses in addition the shared variance between stability measures step kinematics and trunk kinematics is reported the stability measures included the anteroposterior distance d between the body center of mass and the stepping limb toe the margin of stability mos as well as time to boundary considering velocity ttb v velocity and acceleration ttb a and mos ttb mos kinematic measures included trunk flexion angle and angular velocity step length and the time after disturbance onset of recovery step completion fourteen young adults stood on a treadmill that delivered surface accelerations necessitating multiple forward compensatory steps thirteen subjects fell from an initial disturbance but recovered from a second identical disturbance trunk flexion velocity at completion of the first recovery step and trunk flexion angle at completion of the second step had the greatest overall classification of all measures 92 3 ttb v and ttb a at completion of both steps had the greatest classification accuracy of all stability measures 80 8 the length of the first recovery step r 0 70 and trunk flexion angle at completion of the second recovery step r 0 54 had the largest correlations with stability measures although ttb v and ttb a demonstrated somewhat smaller discriminant capabilities than trunk kinematics the small correlations between these stability measures and trunk kinematics r 0 52 suggest that they reflect two important yet different aspects of a compensatory stepping response

moving beyond quiet stance applicability of the inverted pendulum model to stooping and crouching postures background currently it is unknown whether the inverted pendulum model is applicable to stooping or crouching postures therefore the aim of this study was to determine the degree of applicability of the inverted pendulum model to these postures via examination of the relationship between the centre of mass com acceleration and centre of pressure cop com difference methods ten young adults held static standing stooping and crouching postures each for 20 s for both the anterior posterior ap and medio lateral ml directions the time varying com acceleration and the cop com were computed and the relationship between these two variables was determined using pearson s correlation coefficients additionally in both directions the average absolute com acceleration average absolute cop com signal and the inertial component i e i wh were compared across postures results pearson correlation coefficients revealed a significant negative relationship between the com acceleration and cop com signal for all comparisons regardless of the direction p 0 001 while no effect of posture was observed in the ap direction p 0 463 in the ml direction the correlation coefficients for stooping were different i e stronger than standing p 0 008 regardless of direction the average absolute com acceleration for both the stooping and crouching postures was greater than standing p 0 002 conclusion the high correlations indicate that the inverted pendulum model is applicable to stooping and crouching postures due to their importance in completing activities of daily living there is merit in determining what type of motor strategies are used to control such postures and whether these strategies change with age

on the use of multi neighbourhood structures within a tabu based memetic approach to university timetabling problems finding a good university timetabling system is not a simple task for a higher educational organisation as a result many approaches to generating sufficiently good solutions have been introduced this is mainly due to the high complexity within the search landscape moreover each educational organisation has its own rules and specifications in this paper a tabu based memetic algorithm that hybridises a genetic algorithm with a tabu search algorithm is proposed as an improved algorithm for university timetabling problems this algorithm is employed on a set of neighbourhood structures during the search process with the aim of gaining significant improvements in solution quality the sequence of neighbourhood structures has been considered to understand its effect on the search space random best and general sequences of neighbourhood structures have been evaluated in this work the concept of a tabu list is embedded to control the selection of neighbourhood structures that are not dependent on the problem domains during the optimisation process after the crossover and mutation operators are applied to the selected solutions from the population pool the algorithm will penalise neighbourhood structures that are unable to generate better solutions the proposed algorithm has been applied and evaluated against the latest methodologies in the literature with respect to standard benchmark problems we demonstrate that the proposed algorithm produces some of the best known results when tested on itc2007 competition datasets

iterated tabu search and variable neighborhood descent for packing unequal circles into a circular container this paper presents an iterated tabu search and variable neighborhood descent its vnd algorithm for packing unequal circles into a circular container pucc the algorithm adapts the tabu search procedure of iterated tabu search algorithms and proposes a tabu search and variable neighborhood descent ts vnd procedure we observe there are strong complementarities between the small circles and the large vacant places and propose the insert neighborhood to match up the small circles with the large vacant places although the insert neighborhood is inefficient and time consuming it is an important supplement to the classic swap neighborhood as it could arrange the small circles properly predicated on these features we employ the insert neighborhood only at chosen local minima of the swap neighborhood that shows promise for an improvement the traditional tabu search procedure is then transformed into a hybrid procedure composed of two alternative parts namely variable neighborhood descent and tabu search respectively besides this reformed procedure its vnd also incorporates other new features such as an adaptive evaluation function a novel method for accelerating the neighborhood exploration and the collision accidents criterion for evaluating how intensively the area near the current solution has been explored the computational results on three well established benchmark sets show that the proposed algorithm not only has a good discovery capability but also can provide good results within a reasonable time for a total of 84 benchmark instances the proposed algorithm improves the best known results on 23 instances matches 60 and only misses one

a greedy based neighborhood search approach to a nurse rostering problem a practical nurse rostering problem which arises at a ward of an italian hospital is considered the nurse rostering problem is a typical employee timetabling problem where each month it is required to generate the nursing staff shifts subject to various contractual and operational requirements these requirements may be in conflict especially for those months in which manpower is reduced due to seasonal holidays it is required to consider both holidays planning and parametric contractual constraints but no cyclic schedules and corresponding weekly patterns a local search approach is introduced which is based on a neighborhood operating on partial solutions completed by means of a greedy procedure so as to avoid the generation of infeasible solutions both a tabu search procedure and an iterated local search procedure are proposed the solutions computed by the proposed procedures compare well with respect to a straightforward lower bound and strongly outperform those manually generated in the hospital ward the proposed approach is now currently used on site

adaptive tabu search for course timetabling this paper presents an adaptive tabu search algorithm denoted by ats for solving a problem of curriculum based course timetabling the proposed algorithm follows a general framework composed of three phases initialization intensification and diversification the initialization phase constructs a feasible initial timetable using a fast greedy heuristic then an adaptively combined intensification and diversification phase is used to reduce the number of soft constraint violations while maintaining the satisfaction of hard constraints the proposed ats algorithm integrates several distinguished features such as an original double kempe chains neighborhood structure a penalty guided perturbation operator and an adaptive search mechanism computational results show the high effectiveness of the proposed ats algorithm compared with five reference algorithms as well as the current best known results this paper also shows an analysis to explain which are the essential ingredients of the ats algorithm

the role of phases in detecting three qubit entanglement we propose separability criteria for three qubit states in terms of diagonal and anti diagonal entries to detect entanglement with positive partial transposes we report that the phases that is the angular parts of anti diagonal entries play a crucial role in determining whether a given three qubit state is separable or entangled and they must obey even an identity for separability in some cases these criteria are strong enough to detect ppt positive partial transpose entanglement with nonzero volume in several cases when all the entries are zero except for diagonal and anti diagonal entries we characterize separability using phases these include the cases when anti diagonal entries of such states share a common magnitude and when ranks are less than or equal to six we also compute the lengths of rank six cases and find three qubit separable states with lengths 8 whose maximum ranks of partial transposes are 7

adaptive neighborhood search for nurse rostering abstract this paper presents an adaptive neighborhood search method ans for solving the nurse rostering problem proposed for the first international nurse rostering competition inrc 2010 ans uses jointly two distinct neighborhood moves and adaptively switches among three intensification and diversification search strategies according to the search history computational results assessed on the three sets of 60 competition instances show that ans improves the best known results for 12 instances while matching the best bounds for 39 other instances an analysis of some key elements of ans sheds light on the understanding of the behavior of the proposed algorithm

a hybrid model of integer programming and variable neighbourhood search for highly constrained nurse rostering problems abstract this paper presents a hybrid multi objective model that combines integer programming ip and variable neighbourhood search vns to deal with highly constrained nurse rostering problems in modern hospital environments an ip is first used to solve the subproblem which includes the full set of hard constraints and a subset of soft constrains a basic vns then follows as a postprocessing procedure to further improve the ip s resulting solutions the satisfaction of the excluded constraints from the preceding ip model is the major focus of the vns very promising results are reported compared with a commercial genetic algorithm and a hybrid vns approach on real instances arising in a dutch hospital the comparison results demonstrate that our hybrid approach combines the advantages of both the ip and the vns to beat other approaches in solving this type of problems we also believe that the proposed methodology can be applied to other resource allocation problems with a large number of constraints

a complete set of local invariants for a family of multipartite mixed states we study the equivalence of quantum states under local unitary transformations by using the singular value decomposition a complete set of invariants under local unitary transformations is presented for several classes of tripartite mixed states in composite systems two density matrices in the same class are equivalent under local unitary transformations if and only if all these invariants have equal values for these density matrices

the classification of multipartite quantum correlation in multipartite entanglement theory the partial separability properties have an elegant yet complicated structure which becomes simpler in the case when multipartite correlations are considered in this work we elaborate this by giving necessary and sufficient conditions for the existence and uniqueness of the class of a given class label by the use of which we work out the structure of the classification for some important particular cases namely for the finest classification for the classification based on k partitionability and k producibility and for the classification based on the atoms of the correlation properties

a note on solving large p median problems abstract in a previous paper we presented a tree search algorithm for the p median problem the problem of locating p facilities medians on a network which was based upon la grangean relaxation and subgradient optimisation that algorithm solved optimally problems with an arbitrary number of medians and having up to 200 vertices in this note we show that it is possible to enhance that algorithm to solve optimally problems having up to 900 vertices using the cray 1s computer

center of pressure control for balance maintenance during lateral waist pull perturbations in older adults when balance is disturbed location of the center of pressure cop contributes to a person s ability to recover from a perturbation this study investigated cop control prior to first step lift off fslo during lateral perturbations in older non fallers and fallers 38 non fallers and 16 fallers received lateral waist pulls at 5 different intensities crossover stepping responses at the intensity level where the largest number of subjects responded with crossover steps were analyzed whole body center of mass com and cop positions in the medio lateral ml direction with respect to the base of support bos and cop velocity were calculated an inverted pendulum model was used to define the bos stability boundary at fslo which was also adjusted using the cop position at fslo functional boundary no significant differences were found in the cop velocities between fallers and non fallers p 093 however the cop positions for fallers were located significantly more medial at fslo p 01 resulting in a significantly reduced functional boundary although the stability margins measures of stability based on the bos were significantly larger than zero for fallers p 004 they were not significantly different from zero for the functional boundary i e reaching the functional stability limit fallers had reduced functional limits of stability in the ml direction which would predispose them to more precarious stability conditions than non fallers this could be a cause for taking more steps than non fallers for balance recovery as we observed the functional boundary estimation may be a more sensitive marker of balance instability than the bos boundary

a subproblem centric model and approach to the nurse scheduling problem the number of hospitals in japan exceeds 10 000 and every month nurses are scheduled to shifts in about 30 000 units in total there is serious demand for automating this scheduling task in this paper we introduce a mathematical programming formulation of the nurse scheduling problem in japan and develop a meta heuristic approach to solve the problem this scheduling problem is a hard combinatorial problem due to tight constraints involving such factors as the skill level of a team the need to balance workload among nurses and the consideration of nurses preferences even though the number of the nurses to be scheduled is not large at between 20 and 40 the performance of our approach is demonstrated by the successful solution of data taken from actual scheduling problems the proposed model and approach can be adapted for the majority of hospitals in japan as well as for some hospitals in other countries and is likely applicable to many other scheduling problems in the fields of business and logistics

quantifying dynamic and postural balance difficulty during gait perturbations using stabilizing destabilizing forces intensity of balance exercises used to reduce fall risk is often poorly quantified the study aimed to test whether balance difficulty can be rated during gait perturbations against balance difficulty during gait without perturbation using the stabilizing destabilizing forces these forces represent the difficulty to maintain balance as the theoretical forces necessary to cancel body velocity and to set the body into an unstable posture respectively ten healthy subjects walked on a split belt treadmill that also generated perturbations kinetic and kinematic data were collected during gait at comfortable and fast speeds without perturbation and in five trials at comfortable speed with perturbations perturbations consisted of increasing or decreasing the speed of one belt to three different levels in each direction in a random order during the stance phase of 12 random steps per trial the difficulty of maintaining balance was measured during the perturbation and the three following recovery steps compared to comfortable speed higher stabilizing and lower destabilizing forces indicated higher balance difficulty during the perturbation step for faster belt perturbations and recovery steps for slower belt perturbations this was also associated with the center of mass shifted forward and moving faster and with the center of pressure closer to the forward limit of the base of support difficulty increased proportionally with the intensity of perturbation and was significantly higher for the more intense perturbations than at fast speed thus the stabilizing destabilizing forces seem adequate to evaluate balance difficulty during gait perturbations and could be used to determine the optimal difficulty for balance rehabilitation

criterion for slocc equivalence of multipartite quantum states we study the stochastic local operation and classical communication slocc equivalence for arbitrary dimensional multipartite quantum states for multipartite pure states we present a necessary and sufficient criterion in terms of their coefficient matrices this condition can be used to classify some slocc equivalent quantum states with coefficient matrices having the same rank for multipartite mixed state we provide a necessary and sufficient condition by means of the realignment of matrix some detailed examples are given to identify the slocc equivalence of multipartite quantum states

multi partite separable states with unique decompositions and construction of three qubit entanglement with positive partial transpose we investigate conditions on a finite set of multi partite product vectors for which separable states with corresponding product states have unique decompositions and show that this is true in most cases if the number of product vectors is sufficiently small in the three qubit case generic five dimensional spaces give rise to faces of the convex set consisting of all separable states which are affinely isomorphic to the five dimensional simplex with six vertices we construct as a byproduct three qubit entangled positive partial transpose edge states of rank 4 with explicit formulas this covers those entanglements which cannot be constructed from an unextendible product basis

stepping boundary of external force controlled perturbations of varying durations comparison of experimental data and model simulations abstract this study investigated the stepping boundary the force that can be resisted without stepping for force controlled perturbations of different durations twenty two healthy young adults 19 37 years old were instructed to try not to step in response to 86 different force time combinations of forward waist pulls the forces at which 50 of subjects stepped f50 were identified for each tested perturbation durations results showed that f50 decreased hyperbolically when the perturbation s duration increased and converged toward a constant value about 10 bw for longer perturbations over 1500 ms the effect of perturbation duration was critical for the shortest perturbations less than 1 s in parallel a simple function was proposed to estimate this stepping boundary considering the dynamics of a linear inverted pendulum foot model and simple balance recovery reactions we could express the maximum pulling force that can be withstood without stepping as a simple function of the perturbation duration when used with values of the main model parameters determined experimentally this function replicated adequately the experimental results this study demonstrates for the first time that perturbation duration has a major influence on the outcomes of compliant perturbations such as force controlled pulls the stepping boundary corresponds to a constant perturbation force duration product and is largely explained by only two parameters the reaction time and the displacement of the center of pressure within the functional base of support future work should investigate pathological populations and additional parameters characterizing the perturbation time profile such as the time derivative of the perturbation

an interior point algorithm for minimum sum of squares clustering an exact algorithm is proposed for minimum sum of squares nonhierarchical clustering i e for partitioning a given set of points from a euclidean m space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong this problem is expressed as a constrained hyperbolic program in 0 1 variables the resolution method combines an interior point algorithm i e a weighted analytic center column generation method with branch and bound the auxiliary problem of determining the entering column i e the oracle is an unconstrained hyperbolic program in 0 1 variables with a quadratic numerator and linear denominator it is solved through a sequence of unconstrained quadratic programs in 0 1 variables to accelerate resolution variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region proved minimum sum of squares partitions are determined for the first time for several fairly large data sets from the literature including fisher s 150 iris

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

limits of recovery against slip induced falls while walking abstract slip induced falls in gait often have devastating consequences the purposes of this study were 1 to select the determinants that can best discriminate the outcomes recoveries or falls of an unannounced slip induced in gait and to find their corresponding threshold i e the limits of recovery which can clearly separate these two outcomes and 2 to verify these results in a subset of repeated slip trials based on the data collected from 69 young subjects during a slip induced in gait nine different ways of combining the center of mass com stability the hip height and its vertical velocity were investigated with the aid of logistic regression the results revealed that the com stability s and limb support represented by the quotient of hip vertical velocity to hip height s hip recorded at the instant immediately prior to the recovery step touchdown were sufficiently sensitive to account for all 100 variance in falls and specific enough to account for nearly all 98 3 variability in recoveries this boundary s hip 0 22 s 0 25 which quantifies the risk of falls in the stability limb support quotient s s hip domain was fully verified using second slip and third slip trials n 76 with classification of falls at 100 and recoveries at 98 6 the severity of an actual fall is likely to be greater further below the boundary while the likelihood of a fall diminishes above it finally the slope of the boundary also indicates the tradeoff between the stability and limb support whereby high stability can compensate for the insufficiency in limb support or vice versa

heuristic concentration two stage solution construction abstract by utilizing information from multiple runs of an interchange heuristic we construct a new solution that is generally better than the best local optimum previously found this new two stage approach to combinatorial optimization is demonstrated in the context of the p median problem two layers of optimization are superimposed the first layer is a conventional heuristic the second is a heuristic or exact procedure which draws on the concentrated solution set generated by the initial heuristic the intention is to provide an alternative heuristic procedure which when dealing with large problems has a higher probability of producing optimal solutions than existing methods the procedure is fairly general and appears to be applicable to combinatorial problems in a number of contexts

an improved column generation algorithm for minimum sum of squares clustering given a set of entities associated with points in euclidean space minimum sum of squares clustering mssc consists in partitioning this set into clusters such that the sum of squared distances from each point to the centroid of its cluster is minimized a column generation algorithm for mssc was given by du merle et al in siam journal scientific computing 21 1485 1505 the bottleneck of that algorithm is the resolution of the auxiliary problem of finding a column with negative reduced cost we propose a new way to solve this auxiliary problem based on geometric arguments this greatly improves the efficiency of the whole algorithm and leads to exact solution of instances with over 2 300 entities i e more than 10 times as much as previously done

an efficient tabu search procedure for the p median problem abstract in this paper we present a new solution heuristic for the p median problem the algorithm is based on tabu search principles and uses short term and long term memory as well as strategic oscillation and random tabu list sizes our proposed procedure is compared with two other move heuristics a well known interchange heuristic and a recent hybrid heuristic in computational tests on networks ranging in size up to 500 nodes the new heuristic is found to be superior with respect to the quality of solutions produced

new insertion and postoptimization procedures for the traveling salesman problem this paper describes a new insertion procedure and a new postoptimization routine for the traveling salesman problem the combination of the two methods results in an efficient algorithm genius which outperforms known alternative heuristics in terms of solution quality and computing time

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

accelerated tabu search for no wait flowshop scheduling problem with maximum lateness criterion abstract for the no wait flowshop scheduling problem with maximum lateness criterion properties are developed to speed up three kinds of basic operations generating candidate solutions i e the insertion of a new job into a partial sequence and the insertion and exchange neighborhood moves the properties reduce the time to evaluate a candidate from o nm to o 1 and simplify the implementation of the heuristics based on the basic operations by evaluating candidates before their generation the properties also reduce from o n 3 m to o n 2 the time complexity of well known neh heuristic and the complete evaluation of the insertion and exchange neighborhoods tabu search ts is applied to the considered problem since ts tries to find the best neighbor of the current solution in each iteration and therefore can much benefit from the speedups three different ways to use insertion and exchange neighborhoods are compared in ts computational experiments show that the speedups are more helpful as job number increases and all proposed ts algorithms are more effective and robust than the existing algorithms although two and single neighborhood ts algorithms are not significantly different two neighborhood ts algorithms are more preferable

entanglement measure for general pure multipartite quantum states we propose an explicit formula for a measure of entanglement of pure multipartite quantum states we discuss the mathematical structure of the measure and give a brief explanation of its physical motivation we apply the measure on some pure tripartite qubit states and demonstrate that in general the entanglement can depend on what actions are performed on the various subsystems and specifically if the parties in possession of the subsystems cooperate or not we also give some simple but illustrative examples of the entanglement of four qubit and m qubit states

large multiple neighborhood search for the clustered vehicle routing problem abstract the clustered vehicle routing problem is a variant of the classical capacitated vehicle routing problem in which customers are partitioned into clusters and it is assumed that each cluster must have been served completely before the next cluster is served this decomposes the problem into three subproblems i e the assignment of clusters to routes the routing inside each cluster and the sequencing of the clusters in the routes the second task requires the solution of several hamiltonian path problems one for each possibility to route through the cluster we pre compute the hamiltonian paths for every pair of customers of each cluster we present a large multiple neighborhood search which makes use of multiple cluster destroy and repair operators and a variable neighborhood descent vnd for post optimization the vnd is based on classical neighborhoods such as relocate 2 opt and swap all working on the cluster level and a generalization of the balas simonetti neighborhood modifying simultaneously the intra cluster routings and the sequence of clusters in a route computational results with our new approach compare favorably to existing approaches from the literature

separability criterion for three qubit states with a four dimensional norm we give a separability criterion for three qubit states in terms of diagonal and anti diagonal entries this gives us a complete characterization of separability when all the entries are zero except for diagonal and anti diagonals the criterion is expressed in terms of a norm arising from anti diagonal entries we compute this norm in several cases so that we get criteria with which we can decide the separability by routine computations

generalization of treadmill perturbation to overground slip during gait effect of different perturbation distances on slip recovery treadmill perturbation training tm training may improve a person s fall resistance whereby adjusting slip distance can be a simple way to manipulate training intensity the purpose of this study was to determine the effects of different slip distances in tm training 12 cm vs 18 cm on its generalization to the recovery from a novel free slip during overground walking generalization here means the ability to apply learned skill from tm training to slip recovery during overground walking thirty six young adults in the tm 12 or the tm 18 group underwent either a 12 cm or an 18 cm slip during the treadmill walking for seven times or in the control group were not exposed to any perturbation their responses were also contrasted with previously reported results from overground perturbation training og training in which participants received either a 12 cm or an 18 cm slip during level walking with the same number of repetitions everyone was then exposed to the same generalization test during a novel free slip in overground walking their proactive and reactive control of stability was measured and compared tm training displayed a significant training effect in comparison to the control group p 0 05 these results underscore the further needs to investigate the potential of the treadmill as a convenient instrument that can effectively deliver perturbation training

concurrence classes for general pure multipartite states we propose concurrence classes for general pure multipartite states based on an orthogonal complement of a positive operator valued measure on quantum phase in particular we construct wm class ghzm and ghzm 1 class concurrences for general pure m partite states we give explicit expressions for w3 and ghz3 class concurrences for general pure three partite states and for w4 ghz4 and ghz3 class concurrences for general pure four partite states

heuristic concentration and tabu search a head to head comparison earlier this year two papers applying the metaheuristics tabu search ts and heuristic concentration hc to the p median problem were published in consecutive volumes of this journal here we apply the method of hc to some of the data sets which were used for computational experience in the paper on ts for these examples which we regard as being of a particularly challenging character hc discovers the superior solution superior to ts in about 95 of the cases and where the optimal solution is known the optimal solution in about 80 of the cases no general conclusion on the relative times for the two approaches can be drawn

quantum entanglement and geometry of determinantal varieties quantum entanglement was first recognized as a feature of quantum mechanics in the famous paper of einstein podolsky and rosen recently it has been realized that quantum entanglement is a key ingredient in quantum computation quantum communication and quantum cryptography in this paper we introduce algebraic sets which are determinantal varieties in the complex projective spaces or the products of complex projective spaces for the mixed states on bipartite or multipartite quantum systems as their invariants under local unitary transformations these invariants are naturally arised from the physical consideration of measuring mixed states by separable pure states our construction has applications in the following important topics in quantum information theory 1 separability criterion it is proved that the algebraic sets must be a union of the linear subspaces if the mixed states are separable 2 simulation of hamiltonians it is proved that the simulation of semipositive hamiltonians of the same rank implies the projective isomorphisms of the corresponding algebraic sets 3 construction of bound entangled mixed states examples of the entangled mixed states which are invariant under partial transpositions thus ppt bound entanglement are constructed systematically from our new separability criterion

stability analysis via the concept of lyapunov exponents a case study in optimal controlled biped standing balancing control is important for biped standing in spite of large efforts it is very difficult to design balancing control strategies satisfying three requirements simultaneously maintaining postural stability improving energy efficiency and satisfying the constraints between the biped feet and the ground in this article a proportional derivative pd controller is proposed for a standing biped which is simplified as a two link inverted pendulum with one additional rigid foot link the genetic algorithm ga is used to search for the control gain meeting all three requirements the stability analysis of such a deterministic biped control system is carried out using the concept of lyapunov exponents les based on which the system stability where the disturbance comes from the initial states and the structural stability where the disturbance comes from the pd gains are examined quantitively in terms of stability region this article contributes to the biped balancing control more significan

three qubit entanglement witnesses with the full spanning properties we construct three qubit entanglement witnesses with the full spanning property by which we mean that all the partial transposes have the spanning properties these witnesses determine faces for separable states whose interior lies in the interior of positive partial transposes ppt states and so they detect sets of ppt entangled states with nonempty interiors these witnesses also detect fully bi separable states as well as all kinds of bi separable pure product states our construction depends on the observation that multi partite entanglement witnesses correspond to positive multi linear maps

can stability really predict an impending slip related fall among older adults the primary purpose of this study was to systematically evaluate and compare the predictive power of falls for a battery of stability indices obtained during normal walking among community dwelling older adults one hundred and eighty seven community dwelling older adults participated in the study after walking regularly for 20 strides on a walkway participants were subjected to an unannounced slip during gait under the protection of a safety harness full body kinematics and kinetics were monitored during walking using a motion capture system synchronized with force plates stability variables including feasible stability region measurement margin of stability the maximum floquet multiplier the lyapunov exponents short and long term and the variability of gait parameters including the step length step width and step time were calculated for each subject sensitivity of predicting slip outcome fall vs recovery was examined for each stability variable using logistic regression results showed that the feasible stability region measurement predicted fall incidence among these subjects with the highest sensitivity 68 4 except for the step width with an sensitivity of 60 2 no other stability variables could differentiate fallers from those who did not fall for the sample included in this study the findings from the present study could provide guidance to identify individuals at increased risk of falling using the feasible stability region measurement or variability of the step width

a hybrid integer programming and variable neighbourhood search algorithm to solve nurse rostering problems abstract the nurse rostering problem nrp is defined as assigning a number of nurses to different shifts during a specified planning period considering some regulations and preferences this is often very difficult to solve in practice particularly by applying a sole approach in this paper we propose a novel hybrid algorithm combining the strengths of integer programming ip and variable neighbourhood search vns algorithms to design a hybrid method for solving the nrp after generating the initial solution using a greedy heuristic the solution is further improved by employing a variable neighbourhood descent algorithm then ip deeply embedded in the vns algorithm is employed within a ruin and recreate framework to assist the search process finally ip is called again to further refine the solution during the remaining time we utilise the strength of ip not only to diversify the search process but also to intensify the search efforts to identify the quality of the current solution we use a new generic scoring scheme to mark the low penalty parts of the solution based on the computational tests with 24 instances recently introduced in the literature we obtain better results with our proposed algorithm where the hybrid algorithm outperforms two state of the art algorithms and gurobi in most of the instances furthermore we introduce 11 randomly generated instances to further evaluate the efficiency of the hybrid algorithm and we make these computationally challenging instances publicly available to other researchers for benchmarking purposes

product vectors in the ranges of multi partite states with positive partial transposes and permanents of matrices in this paper we consider a system of homogeneous algebraic equations in complex variables and their conjugates which arise naturally from the range criterion for separability of ppt states we examine systematically these equations to get sufficient conditions for the existence of nontrivial solutions this gives us possible upper bounds of ranks of ppt entangled edge states and their partial transposes we will focus on the multi partite cases which are much more delicate than the bi partite cases we use the notion of permanents of matrices as well as techniques from algebraic geometry through the discussion

a biomechanical analysis of muscle strength as a limiting factor in standing posture we developed a method for studying muscular coordination and strength in multijoint movements and have applied it to standing posture the method is based on a musculoskeletal model of the human lower extremity in the sagittal plane and a technique to visualize geometrically how constraints internal and external to the body affect movement we developed an algorithm to calculate the set of all feasible accelerations i e the feasible acceleration set or fas that muscles can induce for the ankle knee and hip joints in the sagittal plane this set is a polyhedron in three dimensions using the volume of the fas as an indicator of overall mobility we found that strengthening muscles on the posterior side as opposed to the anterior of the body would cause greater increases in mobility employing the experimental observations of others we also found that acceleration constraints greatly reduce the range of feasible accelerations we then defined a set of four basic acceleration vectors which when used in various combinations can produce the repertoire of postural movements we used linear programming to find the maximum magnitudes of these vectors and the sensitivity of these magnitudes to muscle strength thereby delineating those muscles which if strengthened would cause the greatest increase in the body s ability to generate the basic acceleration vectors for our particular model those muscle groups were found to be hamstrings tibialis anterior rectus femoris and gastrocnemius these muscle groups would be of great importance in cases involving severely reduced muscle strength this methodology may therefore be useful for purposes such as design of functional electrical stimulation controllers or exercises for persons at risk for falling

everything you always wanted to know about locc but were afraid to ask in this paper we study the subset of generalized quantum measurements on finite dimensional systems known as local operations and classical communication locc while locc emerges as the natural class of operations in many important quantum information tasks its mathematical structure is complex and difficult to characterize here we provide a precise description of locc and related operational classes in terms of quantum instruments our formalism captures both finite round protocols as well as those that utilize an unbounded number of communication rounds while the set of locc is not topologically closed we show that finite round locc constitutes a compact subset of quantum operations additionally we show the existence of an open ball around the completely depolarizing map that consists entirely of locc implementable maps finally we demonstrate a two qubit map whose action can be approached arbitrarily close using locc but nevertheless cannot be implemented perfectly

a vns heuristic for escaping local extrema entrapment in normalized cut clustering normalized cut is one of the most popular graph clustering criteria the main approaches proposed for its resolution are spectral clustering methods and a multilevel approach of dhillon et al tpami 29 1944 1957 2007 called graclus their aim is to obtain good solutions in a small amount of time for large instances metaheuristics are general frameworks for stochastic searches often employed in global optimization to improve the solutions obtained by other heuristics variable neighborhood search vns is a metaheuristic which exploits systematically the idea of neighborhood change during the search in this paper we propose a vns heuristic for normalized cut segmentation computational experiments show that in most cases this vns heuristic improves significantly and in moderate time the solutions obtained by the current state of the art algorithms i e graclus and a spectral method proposed by yu and shi iccv 2003

separability problem for multipartite states of rank at most 4 one of the most important problems in quantum information is the separability problem which asks whether a given quantum state is separable we investigate multipartite states of rank at most 4 which are ppt i e all their partial transposes are positive semidefinite we show that any ppt state of rank 2 or 3 is separable and has length at most 4 for separable states of rank 4 we show that they have length at most 6 it is six only for some qubit qutrit or multiqubit states it turns out that any ppt entangled state of rank 4 is necessarily supported on a 3 3 or a 2 2 2 subsystem we obtain a very simple criterion for the separability problem of the ppt states of rank at most 4 such a state is entangled if and only if its range contains no product vectors this criterion can be easily applied since a four dimensional subspace in the 3 3 or 2 2 2 system contains a product vector if and only if its plucker coordinates satisfy a homogeneous polynomial equation the chow form of the corresponding segre variety we have computed an explicit determinantal expression for the chow form in the former case while such an expression was already known in the latter case

a hybrid heuristic algorithm for the open pit mining operational planning problem this paper deals with the open pit mining operational planning problem with dynamic truck allocation the objective is to optimize mineral extraction in the mines by minimizing the number of mining trucks used to meet production goals and quality requirements according to the literature this problem is np hard so a heuristic strategy is justified we present a hybrid algorithm that combines characteristics of two metaheuristics greedy randomized adaptive search procedures and general variable neighborhood search the proposed algorithm was tested using a set of real data problems and the results were validated by running the cplex optimizer with the same data this solver used a mixed integer programming model also developed in this work the computational experiments show that the proposed algorithm is very competitive finding near optimal solutions with a gap of less than 1 in most instances demanding short computing times

predicted threshold against backward balance loss in gait the purpose of this study was to determine the minimum forward center of mass com velocity required to prevent backward loss of balance in gait as function of the initial com position we hypothesized that these threshold values would be different from those previously published for standing because of the postural differences between gait and standing to investigate this issue we constructed a seven link nine degree of freedom biomechanical model and employed dynamic optimization to estimate these threshold values under two initial postural conditions 1 the posture at the beginning of swing phase i e at toe off and 2 symmetric bipedal standing in particular for a range of possible com positions posterior to the base of support bos simulated annealing was used to search for the minimum velocity that could carry the com into the bos and avoid backward loss of balance we found that the stability boundary against backward balance loss in walking had a similar overall trend as that previously published for standing in general the minimal com velocity necessary to prevent a backward loss of balance in walking was greater than that in symmetric bipedal standing and the difference could approach 30 or more when the com started 0 5 and 1 0 foot lengths behind the bos these discrepancies suggest that simpler biomechanical models while being more efficient and easier to employ may not always be adequate for exploring stability limits of humans

single and multiple step balance recovery responses can be different at first step lift off following lateral waist pull perturbations in older adults abstract an inability to recover lateral balance with a single step is predictive of future falls in older adults this study investigated if balance stability at first step lift off fslo would be different between multiple and single stepping responses to lateral perturbations 54 healthy older adults received left and right waist pulls at 5 different intensities levels 1 5 crossover stepping responses at and above intensity level 3 that induced both single and multiple steps were analyzed whole body center of mass com and center of pressure cop positions in the medio lateral direction with respect to the base of support were calculated an inverted pendulum model was used to define the lateral stability boundary which was also adjusted using the cop position at fslo functional boundary no significant differences were detected in the cop positions between the responses at fslo p 0 075 indicating no difference in the functional boundaries between the responses significantly smaller stability margins were observed at first step landing for multiple steps at all levels p 0 024 while stability margins were also significantly smaller at fslo for level 3 and 4 p 0 048 these findings indicate that although reduced stability at first foot contact would be associated with taking additional steps stepping responses could also be attributable to the com motion state as early as first step lift off preceding foot contact perturbation based training interventions aimed at improving the reactive control of stability would reduce initial balance instability at first step lift off and possibly the consequent need for multiple steps in response to balance perturbations

on the convex cones arising from classifications of partial entanglement in the three qubit system in order to classify partial entanglement of multi partite states it is natural to consider the convex hulls intersections and differences of basic convex cones obtained from partially separable states with respect to partitions of systems in this paper we consider convex cones consisting of x shaped three qubit states arising in this way the class of x shaped states includes important classes like greenberger horne zeilinger diagonal states we find all the extreme rays of those convex cones to exhibit corresponding partially separable states we also give characterizations for those cones which give rise to necessary criteria in terms of diagonal and anti diagonal entries for general three qubit states

a note on the optimality of decomposable entanglement witnesses and completely entangled subspaces entanglement witnesses ews constitute one of the most important entanglement detectors in quantum systems nevertheless their complete characterization in particular with respect to the notion of optimality is still missing even in the decomposable case here we show that for any qubit qunit decomposable ew dew w the three statements are equivalent i the set of product vectors obeying e f w e f 0 spans the corresponding hilbert space ii w is optimal and iii w q with q denoting a positive operator supported on a completely entangled subspace ces and standing for the partial transposition while implications i ii and ii iii are known here we prove that iii implies i this is a consequence of a more general fact saying that product vectors orthogonal to any ces in span after partial conjugation the whole space on the other hand already in the case of the hilbert space there exist dews for which iii does not imply i consequently either i does not imply ii or ii does not imply iii and the above transparent characterization obeyed by qubit qunit dews does not hold in general

concurrence classes for an arbitrary multi qubit state based on a positive operator valued measure in this paper we propose concurrence classes for an arbitrary multi qubit state based on orthogonal complement of a positive operator valued measure or povm for short on quantum phase in particular we construct concurrence for an arbitrary two qubit state and concurrence classes for the three and four qubit states finally we construct wm and ghzm class concurrences for multi qubit states the unique structure of our povm enables us to distinguish different concurrence classes for multi qubit states

construction of multi qubit optimal genuine entanglement witnesses we interpret multi partite genuine entanglement witnesses as simultaneous positivity of various maps arising from them we apply this result to multi qubit x shaped hermitian matrices and characterize the conditions for them to be genuine entanglement witnesses in terms of entries furthermore we find all optimal entries among them they turn out to have spanning properties and so they detect a non zero volume set of multi qubit genuine entanglement we also characterize decomposability for x shaped entanglement witnesses

predicted threshold against backward balance loss following a slip in gait the purpose of this study was to use a 7 link moment actuated human model to predict at liftoff of the trailing foot in gait the threshold of the center of mass com velocity relative to the base of support bos required to prevent backward balance loss during single stance recovery from a slip five dynamic optimization problems were solved to find the minimum com velocities that would allow the simulation to terminate with the com above the bos when the com started 0 25 0 5 0 75 1 0 and 1 25 foot lengths behind the heel of the stance foot i e behind the bos the initial joint angles of the model were based on averaged data from experimental trials foot ground contact was modeled using 16 visco elastic springs distributed under the stance foot slipping was modeled by setting the sliding coefficient of friction of these springs to 0 02 the forward velocity of the com necessary to avoid a backward balance loss is nearly two times larger under slip conditions under non slip conditions the predicted threshold for backward balance loss following a slip agreed well with experimental data collected from 99 young adults in response to 927 slips during walking in all trials in which a subject s com had a velocity below the predicted threshold the subject s recovery foot landed posterior to the slipping foot as predicted finally combining experimental data with optimization we verified that the 7 link model could more accurately predict gait stability than a 2 link model