error estimates for the discretization of the velocity tracking problem in this paper we are continuing our work casas and chrysafinos siam j numer anal 50 5 2281 2306 2012 concerning a priori error estimates for the velocity tracking of two dimensional evolutionary navier stokes flows the controls are of distributed type and subject to point wise control constraints the discretization scheme of the state and adjoint equations is based on a discontinuous time stepping scheme in time combined with conforming finite elements in space for the velocity and pressure provided that the time and space discretization parameters tau and h h respectively satisfy tau le ch 2 ch2 error estimates of order mathcal o h 2 o h2 and mathcal o h frac 3 2 frac 2 p o h32 2p with p 3 p 3 depending on the regularity of the target and the initial velocity are proved for the difference between the locally optimal controls and their discrete approximations when the controls are discretized by the variational discretization approach and by using piecewise linear functions in space respectively both results are based on new duality arguments for the evolutionary navier stokes equations

average path length in random networks analytic solution for the average path length in a large class of uncorrelated random networks with hidden variables is found we apply the approach to classical random graphs of erdos and renyi er evolving networks introduced by barabasi and albert as well as random networks with asymptotic scale free connectivity distributions characterized by an arbitrary scaling exponent alpha 2 our result for 2 infinity there is a saturation effect for the average path length

cluster synchrony in systems of coupled phase oscillators with higher order coupling we study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher order modes dominate the coupling between oscillators for the first time we develop a complete analytic description of the dynamics in the limit of a large number of oscillators and use it to quantify the degree of cluster synchrony cluster asymmetry and switching we use a variation of the recent dimensionality reduction technique of ott and antonsen chaos 18 037113 2008 and find an analytic description of the degree of cluster synchrony valid on a globally attracting manifold shaped by this manifold there is an infinite family of steady state distributions of oscillators resulting in a high degree of multistability in the cluster asymmetry we also show how through external forcing the degree of asymmetry can be controlled and suggest that systems displaying cluster synchrony can be used to encode and store data

a priori error estimates for space time finite element discretization of semilinear parabolic optimal control problems in this paper a priori error estimates for space time finite element discretizations of optimal control problems governed by semilinear parabolic pdes and subject to pointwise control constraints are derived we extend the approach from meidner and vexler siam control optim 47 3 1150 1177 2008 siam control optim 47 3 1301 1329 2008 where linear quadratic problems have been considered discretizing the state equation by usual conforming finite elements in space and a discontinuous galerkin method in time error estimates for controls discretized by piecewise constant functions in time and cellwise constant functions in space are derived in detail and we explain how error estimate for further discretization approaches e g cellwise linear discretization in space the postprocessing approach from meyer and rosch siam j control optim 43 970 985 2004 and the variationally discrete approach from hinze j comput optim appl 30 45 63 2005 can be obtained in addition we derive an estimate for a setting with finitely many time dependent controls

option pricing stochastic volatility singular dynamics and constrained path integrals abstract stochastic volatility models have been widely studied and used in the financial world the heston model heston 1993 7 is one of the best known models to deal with this issue these stochastic volatility models are characterized by the fact that they explicitly depend on a correlation parameter which relates the two brownian motions that drive the stochastic dynamics associated to the volatility and the underlying asset solutions to the heston model in the context of option pricing using a path integral approach are found in lemmens et al 2008 21 while in baaquie 2007 1997 12 13 propagators for different stochastic volatility models are constructed in all previous cases the propagator is not defined for extreme cases 1 it is therefore necessary to obtain a solution for these extreme cases and also to understand the origin of the divergence of the propagator in this paper we study in detail a general class of stochastic volatility models for extreme values 1 and show that in these two cases the associated classical dynamics corresponds to a system with second class constraints which must be dealt with using dirac s method for constrained systems dirac 1958 1967 22 23 in order to properly obtain the propagator in the form of a euclidean hamiltonian path integral henneaux and teitelboim 1992 25 after integrating over momenta one gets an euclidean lagrangian path integral without constraints which in the case of the heston model corresponds to a path integral of a repulsive radial harmonic oscillator in all the cases studied the price of the underlying asset is completely determined by one of the second class constraints in terms of volatility and plays no active role in the path integral

mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media abstract in this article we introduce a family of discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media the proposed schemes are based on mixed and discontinuous finite volume element methods in combination with the optimise then discretise approach for the approximation of the optimal control problem leading to nonsymmetric algebraic systems and employing minimum regularity requirements estimates for the error between a local reference solution of the infinite dimensional optimal control problem and its hybrid mixed discontinuous approximation measured in suitable norms are derived showing optimal orders of convergence

a 3d optimal control problem related to the urban heat islands abstract within the framework of numerical simulation and optimal control of partial differential equations in this work we deal with the mathematical modelling and control of the processes related to the urban heat island effect in particular we are interested in finding the optimal locations of green zones inside metropolitan areas in order to mitigate the consequences of this harmful phenomenon so we consider a three dimensional climate model and formulate a constrained optimal control problem that is extensively analyzed in the first part of the paper then we propose a complete numerical algorithm for its resolution interfacing the interior point algorithm ipopt with the freefem software package finally we present several numerical tests for a simple realistic case where the advantages of our approach are shown

a black scholes schrodinger option price bit versus qubit abstract the celebrated black scholes differential equation provides for the price of a financial derivative the uncertainty environment of such option price can be described by the classical bit a system with two possible states this paper argues for the introduction of a different uncertainty environment characterized by the so called qubit we obtain an information based option price and discuss the differences between this option price and the classical option price

entrainment of coupled oscillators on regular networks by pacemakers we study kuramoto oscillators driven by one pacemaker on d dimensional regular topologies with nearest neighbor interactions we derive the analytical expressions for the common frequency in the case of phase locked motion and for the critical frequency of the pacemaker placed at an arbitrary position in the lattice so that above the critical frequency no phase locked motion is possible we show that the mere change in topology from an open chain to a ring induces synchronization for a certain range of pacemaker frequencies and couplings while keeping the other parameters fixed moreover we demonstrate numerically that the critical frequency of the pacemaker decreases as a power of the linear size of the lattice with an exponent equal to the dimension of the system this leads in particular to the conclusion that for infinite dimensional topologies the critical frequency for having entrainment decreases exponentially with increasing size of the system or more generally with increasing depth of the network that is the average distance of the oscillators from the pacemaker

frequency synchronization in a random oscillator network we study the frequency synchronization of a randomly coupled oscillators by analyzing the continuum limit we obtain a sufficient condition for the mean field type synchronization we especially find that the critical coupling constant k becomes 0 in the random scale free network p k ensuremath propto k ensuremath ensuremath gamma if 2l ensuremath gamma ensuremath leqslant 3 numerical simulations in finite networks are consistent with this analysis

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

are recruitment patterns of the trunk musculature compatible with a synergy based on the maximization of endurance abstract to verify that maximization of endurance is important among the functional criteria determining trunk muscle activation patterns symmetric and asymmetric exertions were simulated using a detailed model consisting of 114 muscle slips crossing the lumbosacral junction and employing a cost function which maximizes endurance first the question whether meaningful comparisons can be made between activity predictions for individual muscle slips and surface emg data recorded from larger anatomical entities was addressed this was answered affirmatively since activation patterns predicted by a coarse and a middle version of the model in which activation was constrained to be equal within 14 or 32 groups of muscle slips were similar to those predicted with each muscle slip controlled independently median correlation coefficients between activity vectors predicted by the simplified models and the detailed model were 0 88 and 0 97 respectively the coarse model underestimated the endurance capacity by a median of 21 the middle model by only 0 7 second predicted activities within anatomical entities defined at this level of detail were compared to reference data derived from the literature lavender et al 1992 human factors 34 239 247 1992 journal of orthopaedic research 10 691 700 vink et al 1988 electromyography and clinical neurophysiology 28 517 525 the predicted activity patterns of the crector spinae external oblique and rectus abdominis muscles closely resembled the emg patterns r2 0 48 0 99 furthermore the observed distribution of activity between parts of the crector spinae muscle was adequately predicted

a discussion on embedding the black scholes option pricing model in a quantum physics setting abstract in this paper we consider the implications of embedding the black scholes option pricing model within a quantum physical setting the option price is considered to be a state function and a potential function is found which allows the option price to satisfy the schrodinger differential equation once this arbitrage free potential function is obtained we argue for the construction of a so called arbitrage potential function this functional is instrumental in determining the existence of a financial state function we show the existence of an arbitrage free price when the potential function converges to one the existence of arbitrage hinges on the non zero value of the planck constant this constant is then linked to a parameter which regulates the probability of occurence of strategy paths we call this parameter the belief parameter we argue that it is the belief parameter which may indeed proxy arbitrage the outcome of this paper shows that the black scholes model can be captured within a quantum physical setting and that the advantages of doing so may indeed provide for a first step to include arbitrage in a natural way in an otherwise arbitrage free model

onset of synchronization in large networks of coupled oscillators we study the transition from incoherence to coherence in large networks of coupled phase oscillators we present various approximations that describe the behavior of an appropriately defined order parameter past the transition and generalize recent results for the critical coupling strength we find that under appropriate conditions the coupling strength at which the transition occurs is determined by the largest eigenvalue of the adjacency matrix we show how with an additional assumption a mean field approximation recently proposed is recovered from our results we test our theory with numerical simulations and find that it describes the transition when our assumptions are satisfied we find that our theory describes the transition well in situations in which the mean field approximation fails we study the finite size effects caused by nodes with small degree and find that they cause the critical coupling strength to increase

hole structures in nonlocally coupled noisy phase oscillators we demonstrate that a system of nonlocally coupled noisy phase oscillators can collectively exhibit a hole structure which manifests itself in the spatial phase distribution of the oscillators the phase model is described by a nonlinear fokker planck equation which can be reduced to the complex ginzburg landau equation near the hopf bifurcation point of the uniform solution by numerical simulations we show that the hole structure clearly appears in the space dependent order parameter which corresponds to the nozaki bekki hole solution of the complex ginzburg landau equation

spectra of random graphs with given expected degrees in the study of the spectra of power law graphs there are basically two competing approaches one is to prove analogues of wigner s semicircle law whereas the other predicts that the eigenvalues follow a power law distribution although the semicircle law and the power law have nothing in common we will show that both approaches are essentially correct if one considers the appropriate matrices we will prove that under certain mild conditions the eigenvalues of the normalized laplacian of a random power law graph follow the semicircle law whereas the spectrum of the adjacency matrix of a power law graph obeys the power law our results are based on the analysis of random graphs with given expected degrees and their relations to several key invariants of interest are a number of new values for the exponent where phase transitions for eigenvalue distributions occur the spectrum distributions have direct implications to numerous graph algorithms such as for example randomized algorithms that involve rapidly mixing markov chains

the quantum dark side of the optimal control theory abstract in a recent article a generic optimal control problem was studied from a physicist s point of view contreras et al 2017 through this optic the pontryagin equations are equivalent to the hamilton equations of a classical constrained system by quantizing this constrained system using the right ordering of the operators the corresponding quantum dynamics given by the schrodinger equation is equivalent to that given by the hamilton jacobi bellman equation of bellman s theory the conclusion drawn there were based on certain analogies between the equations of motion of both theories in this paper a closer and more detailed examination of the quantization problem is carried out by considering three possible quantization procedures right quantization left quantization and feynman s path integral approach the bellman theory turns out to be the classical limit 0 of these three different quantum theories also the exact relation of the phase s x t of the wave function x t e i s x t of the quantum theory with bellman s cost function j x t is obtained in fact s x t satisfies a conjugate form of the hamilton jacobi bellman equation which implies that the cost functional j x t must necessarily satisfy the usual hamilton jacobi bellman equation thus the bellman theory effectively corresponds to a quantum view of the optimal control problem

multi asset black scholes model as a variable second class constrained dynamical system abstract in this paper we study the multi asset black scholes model from a structural point of view for this we interpret the multi asset black scholes equation as a multidimensional schrodinger one particle equation the analysis of the classical hamiltonian and lagrangian mechanics associated with this quantum model implies that in this system the canonical momentums cannot always be written in terms of the velocities this feature is a typical characteristic of the constrained system that appears in the high energy physics to study this model in the proper form one must apply dirac s method for constrained systems the results of the dirac s analysis indicate that in the correlation parameters space of the multi assets model there exists a surface called the kummer surface k where the determinant of the correlation matrix is null on which the constraint number can vary we study in detail the cases with n 2 and n 3 assets for these cases we calculate the propagator of the multi asset black scholes equation and show that inside the kummer k surface the propagator is well defined but outside k the propagator diverges and the option price is not well defined on k the propagator is obtained as a constrained path integral and their form depends on which region of the kummer surface the correlation parameters lie thus the multi asset black scholes model is an example of a variable constrained dynamical system and it is a new and beautiful property that had not been previously observed

a multilevel correction method for optimal controls of elliptic equations we propose in this paper a multilevel correction method to solve optimal control problems constrained by elliptic equations with the finite element method in this scheme solving an optimization problem on the finest finite element space is transformed into a series of solutions of linear boundary value problems by the multigrid method on multilevel meshes and a series of solutions of optimization problems on the coarsest finite element space our proposed scheme instead of solving a large scale optimization problem in the finest finite element space solves only a series of linear boundary value problems and the optimization problems in a very low dimensional finite element space and thus can improve the overall efficiency of the solution of optimal control problems governed by pdes

lumbar spinal muscle activation synergies predicted by multi criteria cost function the hypothesis that control of lumbar spinal muscle synergies is biomechanically optimized was studied by comparing emg data with an analytical model with a multi component cost function that could include 1 trunk displacements 2 intervertebral displacements 3 intervertebral forces 4 sum of cubed muscle stresses and 5 eigenvalues for the first two spinal buckling modes the model s independent variables were 180 muscle forces the 36 displacements of 6 vertebrae were calculated from muscle forces and the spinal stiffness calculated muscle activation was compared with emg data from 14 healthy human subjects who performed isometric voluntary ramped maximum efforts at angles of 0 degrees 45 degrees 90 degrees 135 degrees and 180 degrees to the right from the anterior direction muscle activation at each angle was quantified as the linear regression slope of the rms emg versus external force relationship normalized by the maximum observed emg there was good agreement between the analytical model and emg data for the dorsal muscles when the model included either minimization of intervertebral displacements or minimization of intervertebral forces in its cost function but the model did not predict a realistic level of abdominal muscles activation agreement with emg data was improved with the sum of the cubed muscle stresses added to the cost function addition of a cost function component to maximize the trunk stability produced higher levels of antagonistic muscle activation at low efforts than at greater efforts it was concluded that the muscle activation strategy efficiently limits intervertebral forces and displacements and that costs of higher muscle stresses are taken into account but stability does not appear to be maximized trunk muscles are apparently not controlled solely to optimize any one of the biomechanical costs considered here

optimal control of semilinear parabolic equations by bv functions optimal control problems for semilinear parabolic equations with control costs involving the total bounded variation seminorm are analyzed this choice of control cost favors optimal controls which are piecewise constant and it penalizes the number of jumps it is an appropriate choice if a simple structure of the optimal controls is desired which however is still sufficiently flexible so that good tracking properties can be maintained existence of optimal controls necessary and sufficient optimality conditions and sparsity properties of the derivatives are obtained convergence of a finite element approximation is analyzed and numerical examples illustrating structural properties of the optimal controls are provided

muscular synergism ii a minimum fatigue criterion for load sharing between synergistic muscles a new physiological criterion for muscular load sharing is developed the criterion is based on the assumption that the endurance time of muscular contractions is maximized hence muscular fatigue is minimized the optimization problem is cast in the form of a linearly constrained non linear minimax optimization the new method predicts that 1 there is synergistic muscle action 2 muscle force increases non linearly with external force load 3 relatively more force is allocated to muscles that have a large maximum force large muscles 4 relatively more force is allocated to muscles with a high percentage of slow twitch fibers muscles that are fatigue resistant 5 the load sharing does not depend on the moment arm of the muscles although the absolute force levels do depend on this variable the predicted load sharing between two cat muscles during standing and walking is in good agreement with direct force measurement data from the literature

resilience to damage of graphs with degree correlations the existence or nonexistence of a percolation threshold on power law correlated graphs is a fundamental question for which a general criterion is lacking in this work we investigate the problems of site and bond percolation on graphs with degree correlations and their connection with spreading phenomena we obtain some general expressions that allow the computation of the transition thresholds or their bounds using these results we study the effects of assortative and disassortative correlations on the resilience to damage of networks

effects of external trunk loads on lumbar spine stability abstract stability of the lumbar spine is an important factor in determining spinal response to sudden loading using two different methods this study evaluated how various trunk load magnitudes and directions affect lumbar spine stability the first method was a quick release procedure in which effective trunk stiffness and stability were calculated from trunk kinematic response to a resisted force release the second method combined trunk muscle emg data with a biomechanical model to calculate lumbar spine stability twelve subjects were tested in trunk flexion extension and lateral bending under nine permutations of vertical and horizontal trunk loading the vertical load values were set at 0 20 and 40 of the subject s body weight bw the horizontal loads were 0 10 and 20 of bw effective spine stability as obtained from quick release experimentation increased significantly p

the onset of synchronization in systems of globally coupled chaotic and periodic oscillators abstract a general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled heterogeneous continuous time dynamical systems the formalism allows for the simultaneous presence of ensemble members exhibiting chaotic and periodic behavior and in a special case yields the kuramoto model for globally coupled periodic oscillators described by a phase numerical experiments using different types of ensembles of lorenz equations with a distribution of parameters are presented

path integral approach to closed form option pricing formulas with applications to stochastic volatility and interest rate models we present a path integral method to derive closed form solutions for option prices in a stochastic volatility model the method is explained in detail for the pricing of a plain vanilla option the flexibility of our approach is demonstrated by extending the realm of closed form option price formulas to the case where both the volatility and interest rates are stochastic this flexibility is promising for the treatment of exotic options our analytical formulas are tested with numerical monte carlo simulations

superconvergence properties of optimal control problems an optimal control problem for a two dimensional 2 d elliptic equation is investigated with pointwise control constraints this paper is concerned with discretization of the control by piecewise constant functions the state and the adjoint state are discretized by linear finite elements approximations of the optimal solution of the continuous optimal control problem will be constructed by a projection of the discrete adjoint state it is proved that these approximations have convergence order h2

a priori error estimates for space time finite element discretization of parabolic optimal control problems part i problems without control constraints in this paper we develop a priori error analysis for galerkin finite element discretizations of optimal control problems governed by linear parabolic equations the space discretization of the state variable is done using usual conforming finite elements whereas the time discretization is based on discontinuous galerkin methods for different types of control discretizations we provide error estimates of optimal order with respect to both space and time discretization parameters the paper is divided into two parts in the first part we develop some stability and error estimates for space time discretization of the state equation and provide error estimates for optimal control problems without control constraints in the second part of the paper the techniques and results of the first part are used to develop a priori error analysis for optimal control problems with pointwise inequality constraints on the control variable

path integral approach to dynamics in a sparse random network we study the dynamics involved in a sparse random network model we extend the standard mean field approximation for the dynamics of a random network by employing the path integral approach the result indicates that the distribution of the variable is essentially identical to that obtained from globally coupled oscillators with random gaussian interaction we present the results of a numerical simulation of the kuramoto transition in a random network which is found to be consistent with this analysis

co activation alters the linear versus non linear impression of the emg torque relationship of trunk muscles the use of electromyographic signals in the modeling of muscle forces and joint loads requires an assumption of the relationship between emg and muscle force this relationship has been studied for the trunk musculature and been shown to be predominantly non linear with more emg producing less torque output at higher levels of activation however agonist antagonist muscle co activation is often substantial during trunk exertions yet has not been adequately accounted for in determining such relationships the purpose of this study was to revisit the emg moment relationship of the trunk recognizing the additional moment requirements necessitated due to antagonist muscle activity eight participants generated a series of isometric ramped trunk flexor and extensor moment contractions emg was recorded from 14 torso muscles and the externally resisted moment was calculated agonist muscle moments either flexor or extensor were estimated from an anatomically detailed biomechanical model of the spine and fit to the externally calculated moment alone the externally calculated moment combined with the antagonist muscle moment when antagonist activity was ignored the emg moment relationship was found to be non linear similar to previous work however when accounting for the additional muscle torque generated by the antagonist muscle groups the relationships became in three of the four conditions more linear therefore it was concluded that antagonist muscle co activation must be included when determining the emg moment relationship of trunk muscles and that previous impressions of non linear emg force relationships should be revisited

finite element approximations of impulsive optimal control problems for heat equations abstract in this paper we study the priori error analysis for semidiscrete galerkin finite element approximation of the impulsive optimal control problem governed by linear heat equation with control constraint we first derive pontryagin s maximum principle and construct the semidiscrete finite element approximation scheme for our impulsive optimal control problem then the error estimates for optimal control u the related state y and the adjoint state will be obtained finally an efficient algorithm for our numerical experiment is designed which verifies the theoretical results obtained in this paper

network connectivity during mergers and growth optimizing the addition of a module the principal eigenvalue of a network s adjacency matrix often determines dynamics on the network e g in synchronization and spreading processes and some of its structural properties e g robustness against failure or attack and is therefore a good indicator for how strongly a network is connected we study how is modified by the addition of a module or community which has broad applications ranging from those involving a single modification e g introduction of a drug into a biological process to those involving repeated additions e g power grid and transit development we describe how to optimally connect the module to the network to either maximize or minimize the shift in noting several applications of directing dynamics on networks

accelerated monte carlo for optimal estimation of time series by casting stochastic optimal estimation of time series in path integral form one can apply analytical and computational techniques of equilibrium statistical mechanics in particular one can use standard or accelerated monte carlo methods for smoothing filtering and or prediction here we demonstrate the applicability and efficiency of generalized nonlocal hybrid monte carlo and multigrid methods applied to optimal estimation specifically smoothing we test these methods on a stochastic diffusion dynamics in a bistable potential this particular problem has been chosen to illustrate the speedup due to the nonlocal sampling technique and because there is an available optimal solution which can be used to validate the solution via the hybrid monte carlo strategy in addition to showing that the nonlocal hybrid monte carlo is statistically accurate we demonstrate a significant speedup compared with other strategies thus making it a practical alternative to smoothing filtering and data assimilation on problems with state vectors of fairly large dimensions as well as a large total number of time steps

identification of dynamic myoelectric signal to force models during isometric lumbar muscle contractions a 14 muscle myoelectric signal mes driven muscle force prediction model of the l3 l4 cross section is developed which includes a dynamic mes force relationship and allows for cocontraction model parameters are estimated from mes and moments data recorded during rapid exertions in trunk flexion extension lateral bending and axial twist nine young healthy males participated in the experimental testing the model used in the parameter estimation is of the output error type consistent and physically feasible parameter estimates were obtained by normalizing the rms mes to maximum exertion levels and using nonlinear constrained optimization to minimize a cost function consisting of the trace of the output error covariance matrix model performance was evaluated by comparing measured and mes predicted moments over a series of slow and rapid exertions moment prediction errors were on the order of 25 30 and 40 during attempted trunk flexion extensions lateral bends and axial twists respectively the model and parameter estimation methods developed provide a means to estimate lumbar muscle and spine loads as well as to empirically investigate the use and effects of cocontraction during physical task performances

a priori error estimates for finite element discretizations of parabolic optimization problems with pointwise state constraints in time in this paper we consider an optimal control problem which is governed by a linear parabolic equation and is subject to state constraints pointwise in time optimal order error estimates are developed for a space time finite element discretization of this problem numerical examples confirm the theoretical results as a by product of our analysis we derive a new regularity result for the optimal control

a physiologically based criterion of muscle force prediction in locomotion abstract the inversely nonlinear relationship of muscle contraction force and the possible contraction duration i e endurance is utilized in a method to mathematically predict individual muscle forces the method uses a nonlinear optimization scheme to solve the redundant distribution problem at the joints of interest the method is demonstrated at the elbow during isometric contraction and in the lower extremity during locomotion during gait the observed muscle activity pattern in the lower extremity as determined by emg shows substantial agreement with that activity pattern predicted when endurance is used as the optimization criterion the importance of selecting muscle prediction criteria based on sound physiological bases rather than on an arbitrary or mathematically convenient basis is emphasized

constraining spine stability levels in an optimization model leads to the prediction of trunk muscle cocontraction and improved spine compression force estimates a major limitation of optimization models of the spine has been the inability to accurately predict trunk muscle co activity antagonist muscle activity is thought to be necessary to maintain adequate levels of spine stability but in turn creates increased loading on the spine it is thus hypothesized that the cns attempts to optimize the relationship between spine loading and spine stability in determining muscular activation patterns this study presents an optimization model of the spine in which stability was constrained to target levels predicted from regression equations of independent loading variables objective functions were set to either minimize the sum of the cubed muscle forces or minimize the sum of the squared intervertebral forces at the l4 l5 disc level results demonstrate that the inclusion of stability constraints in optimization simulations produced realistic predictions of antagonist muscle activity and predictions of spine compression levels that agree more closely with emg based estimates compared to simulations in which stability was unconstrained it was concluded that spinal stability is a vital consideration for the cns when dictating trunk muscle recruitment patterns

strong effects of network architecture in the entrainment of coupled oscillator systems random networks of coupled phase oscillators representing an approximation for systems of coupled limit cycle oscillators are considered entrainment of such networks by periodic external forcing applied to a subset of their elements is numerically and analytically investigated for a large class of interaction functions we find that the entrainment window with a tongue shape becomes exponentially narrow for networks with higher hierarchical organization however the entrainment is significantly facilitated if the networks are directionally biased i e closer to the feedforward networks furthermore we show that the networks with high entrainment ability can be constructed by evolutionary optimization processes the neural network structure of the master clock of the circadian rhythm in mammals is discussed from the viewpoint of our results

a priori error estimates for space time finite element discretization of parabolic optimal control problems in this article we summarize recent results on a priori error estimates for space time finite element discretizations of linear quadratic parabolic optimal control problems we consider the following three cases problems without inequality constraints problems with pointwise control constraints and problems with state constraints pointwise in time for all cases error estimates with respect to the temporal and to the spatial discretization parameters are derived the results are illustrated by numerical examples

on the implications of interpreting the stability index a spine example quantifying the stability of the spinal column offers a perspective on the effectiveness of the motor control strategy to ensure a stable spine and minimize the risk of injury from experiencing an unstable event there are essentially three energy based methods of calculating a stability index for the lumbar spine all three methods involve mathematical manipulation of an 18 x 18 hessian matrix the purpose of this paper was to consider the mathematical implications for the three methods of determining a single stability index and examine the effects of biological factors such as muscle activation in each of these methods the first approach computes the hessian s determinant and is thought to represent a more global or average perspective on stability a second approach computes the smallest eigenvalue of the hessian matrix to determine the weakest link of the spine the final method determines an average critical stiffness difference for the spine and is intended to effectively determines how far a human spine is from instability and allows comparison between tasks this study shows that the same interpretation of stability is achieved via all three computational approaches they agree as to whether the spine is stable or not however they appear to differ in their sensitivity to the effect of muscle activation patterns

the relationship between trunk muscle electromyography and lifting moments in the sagittal and frontal planes in this study we explore the relationship between moments in the frontal and sagittal planes generated by a lifting task vs the electromyographic emg activity of right and left trunk muscle groups in particular we postulate that the functional dependence between erector spinae muscle activity and the applied lifting moments about the spine is as follows 1 the sum of left and right erector spinae processed emg depends on the sagittal plane moment and 2 the difference of left and right erector spinae processed emg depends on the frontal plane moment a simple out of sagittal plane physical model treating the lumbar spine as a two degree of freedom pivot point is discussed to justify these hypotheses to validate this model we collected surface emg and lifting moment data for ten males performing a grid of frontal and sagittal plane lifting tasks a digital rms to dc algorithm was developed for processing raw emg for these tests we measured emg for the left and right erector spinae and for the left and right external oblique muscles the processed emg signals of the left and right erector spinae muscles are summed and differenced for comparison to the measured sagittal and frontal plane moments a linear correlation r2 of 0 96 was obtained for the sum of erector spinae emg vs the sagittal plane moment a corresponding value of r2 0 95 was obtained for the difference vs the frontal plane moment no correlations r2 0 004 was found for 1 the sagittal plane moment and the difference of the left and right erector spinae emg and 2 the frontal plane moment and the sum of the left and right erector spinae emg

path integral control and state dependent feedback in this paper we address the problem of computing state dependent feedback controls for path integral control problems to this end we generalize the path integral control formula and utilize this to construct parametrized state dependent feedback controllers in addition we show a relation between control and importance sampling better control in terms of control cost yields more efficient importance sampling in terms of effective sample size the optimal control provides a zero variance estimate

synchronization of coupled oscillators on small world networks abstract we investigate the synchronous dynamics of kuramoto oscillators and van der pol oscillators on watts strogatz type small world networks the order parameters to characterize macroscopic synchronization are calculated by numerical integration we focus on the difference between frequency synchronization and phase synchronization in both oscillator systems the critical coupling strength of the phase order is larger than that of the frequency order for the small world networks the critical coupling strength for the phase and frequency synchronization diverges as the network structure approaches the regular one for the kuramoto oscillators the behavior can be described by a power law function and the exponents are obtained for the two synchronizations the separation of the critical point between the phase and frequency synchronizations is found only for small world networks in the theoretical models studied

efficient numerical realization of discontinuous galerkin methods for temporal discretization of parabolic problems we present an efficient and easy to implement approach to solving the semidiscrete equation systems resulting from time discretization of nonlinear parabolic problems with discontinuous galerkin methods of order r it is based on applying newton s method and decoupling the newton update equation which consists of a coupled system of r 1 elliptic problems in order to avoid complex coefficients which arise inevitably in the equations obtained by a direct decoupling we decouple not the exact newton update equation but a suitable approximation the resulting solution scheme is shown to possess fast linear convergence and consists of several steps with same structure as implicit euler steps we construct concrete realizations for order one to three and give numerical evidence that the required computing time is reduced significantly compared to assembling and solving the complete coupled system by newton s method

alterations in trunk bending stiffness following changes in stability and equilibrium demands of a load holding task abstract the contribution of the trunk neuromuscular system tns to spine stability has been shown in earlier studies by characterizing changes in antagonistic activity of trunk muscles following alterations in stability demands of a task whether and or how much such changes in the response of tns to alteration in stability demand of the task alter spinal stiffness remains unclear to address this research gap a repeated measure study was conducted on twenty gender balanced asymptomatic individuals to evaluate changes in trunk bending stiffness throughout the lumbar spine s range of flexion following alterations in both stability and equilibrium demands of a load holding task trunk bending stiffness was determined using trunk stiffness tests in upright posture on a rigid metal frame under different equilibrium and stability demands on the lower back increasing the stability demand by increasing the height of lifted load 30 cm only increased trunk bending stiffness 39 over the lower range of lumbar flexion and under the low equilibrium demand condition similarly increasing the equilibrium demand of the task by increasing the weight of lifted load by 3 5 kg only increased trunk bending stiffness 55 over the low range of lumbar flexion and under the low stability demand condition our results suggest a non linear relationship between changes in stability and equilibrium demands of a task and the contribution of tns to trunk bending stiffness specifically alterations in tns response to changes in stability and equilibrium demand of a given task will increase stiffness of the trunk only if the background stiffness is low

subject specific regression equations to estimate lower spinal loads during symmetric and asymmetric static lifting abstract workplace safety assessment personalized treatment design and back pain prevention programs require accurate subject specific estimation of spinal loads since no noninvasive method can directly estimate spinal loads easy to use regression equations that are constructed based on the results of complex musculoskeletal models appear as viable alternatives thus we aim to develop subject specific regression equations of l4 l5 and l5 s1 shear and compression forces during various symmetric asymmetric tasks using a nonlinear personalized finite element musculoskeletal trunk model kinematics and electromyography emg activities of 19 young healthy subjects were collected during 64 different symmetric asymmetric tasks to investigate the reliability and accuracy of the musculoskeletal model and regression equations we compared estimated trunk muscle activities and l4 l5 intradiscal pressures idps respectively with our own electromyography data emgs and reported in vivo pressure measurements although in general six independent rotation components three trunk t11 rotations and three pelvic s1 rotations are required to determine kinematics along the spine only two surrogate variables trunk flexion and its asymmetric angles satisfactorily predicted all six rotation components r2 0 94 regression equations developed based on subject specific inputs predicted spinal loads in satisfactory agreement with idp measurements r2 0 85 predicted muscle activities in the personalized musculoskeletal models were in moderate to weak agreements with our measured emgs in 19 participants based on dominance analysis trunk flexion and its asymmetry angle hand load weight hand load lever arm and body weight were the most important variables while the effects of body height and sex on spinal loads remained small

analysis of relative influence of nodes in directed networks many complex networks are described by directed links in such networks a link represents for example the control of one node over the other node or unidirectional information flows some centrality measures are used to determine the relative importance of nodes specifically in directed networks we analyze such a centrality measure called the influence the influence represents the importance of nodes in various dynamics such as synchronization evolutionary dynamics random walk and social dynamics we analytically calculate the influence in various networks including directed multipartite networks and a directed version of the watts strogatz small world network the global properties of networks such as hierarchy and position of shortcuts rather than local properties of the nodes such as the degree are shown to be the chief determinants of the influence of nodes in many cases the developed method is also applicable to the calculation of the pagerank we also numerically show that in a coupled oscillator system the threshold for entrainment by a pacemaker is low when the pacemaker is placed on influential nodes for a type of random network the analytically derived threshold is approximately equal to the inverse of the influence we numerically show that this relationship also holds true in a random scale free network and a neural network

effects of emg processing on biomechanical models of muscle joint systems sensitivity of trunk muscle moments spinal forces and stability biomechanical models are in use to estimate parameters such as contact forces and stability at various joints in one class of these models surface electromyography emg is used to address the problem of mechanical indeterminacy such that individual muscle activation patterns are accounted for unfortunately because of the stochastical properties of emg signals emg based estimates of muscle force suffer from substantial estimation errors recent studies have shown that improvements in muscle force estimation can be achieved through adequate emg processing specifically whitening and high pass hp filtering of the signals the aim of this paper is to determine the effect of such processing on outcomes of a biomechanical model of the lumbosacral joint and surrounding musculature goodness of fit of estimated muscle moments to net moments and also estimated joint stability significantly increased with increasing cut off frequencies in hp filtering whereas no effect on joint contact forces was found whitening resulted in moment estimations comparable to those obtained from optimal hp filtering with cut off frequencies over 250 hz moreover compared to hp filtering whitening led to a further increase in estimated joint stability based on theoretical models and on our experimental results we hypothesize that the processing leads to an increase in pick up area this then would explain the improvements from a better balance between deep and superficial motor unit contributions to the signal

pontryagin s principle for state constrained boundary control problems of semilinear parabolic equations this paper deals with state constrained optimal control problems governed by semilinear parabolic equations we establish a minimum principle of pontryagin s type to deal with the state constraints we introduce a penalty problem by using ekeland s principle the key tool for the proof is the use of a special kind of spike perturbations distributed in the domain where the controls are defined conditions for normality of optimality conditions are given

the many proofs and applications of perron s theorem this paper chronicles the wide dispersal of perron s 1907 result on positive matrices into many fields of science the many proofs given during the last 93 years are categorized and critiqued including perron s original two proofs and a more natural proof is presented this simple to understand result of perron provides a unequaled vehicle for taking students on a tour of many applied areas with some depth

synchronization transition in scale free networks clusters of synchrony we study the synchronization transition in scale free networks that display power law asymptotic behaviors in their degree distributions the critical coupling strength and the order parameter critical exponent derived by the mean field approach depend on the degree exponent ensuremath lambda which implies a close connection between structural organization and the emergence of dynamical order in complex systems we also derive the finite size scaling behavior of the order parameter finding that the giant cluster of synchronized nodes is formed in different ways between scale free networks with 2l ensuremath lambda l3 and those with ensuremath lambda g3

strategies used to stabilize the elbow joint challenged by inverted pendulum loading abstract the stiffness of activated muscles may stabilize a loaded joint by preventing perturbations from causing large displacements and injuring the joint here the elbow muscle recruitment patterns were compared with the forearm loaded vertically a potentially unstable inverted pendulum configuration and with horizontal loading eighteen healthy subjects were studied with the forearm vertical and supinated and the elbow flexed approximately 90 in the first experiment emg electrodes recorded activity of biceps triceps and brachioradialis muscles for joint torques produced a by voluntarily exerting a horizontal force isometrically b by voluntarily flexing and extending the elbow while the forearm was loaded vertically with 135 n the relationship between the emg and the torque generated was quantified by the linear regression slope and zero torque intercept in a second experiment a vertical load increasing linearly with time up to 300 n was applied in experiment 1 the emg torque relationships for biceps and triceps had an intercept about 10 of maximum voluntary effort greater with the vertical compared to the horizontal force the inverse was found for brachioradialis but the emg torque slopes for both agonist and antagonistic muscles were not different in experiment 2 there were 29 trials with minimal elbow displacement and all the three muscles activated on the order of 11 of maximum activation to stabilize the elbow 19 trials had small elbow extension and 14 trials small flexion requiring altered muscle forces for equilibrium 7 trials ended in large unstable displacement or early termination of the test an analysis indicate that the observed levels of muscle activation would only provide stability if the muscles short range stiffness was at the high end of the published range hence the elbow was marginally stable the stability analysis also indicated that the small elbow extension increased stability and flexion decreased stability

guaranteed satisfaction of inequality state constraints in pde constrained optimization abstract optimal control problems with inequality path constraints ipcs are present in several engineering problems described by partial differential equations pde we propose an algorithm to solve pde constrained dynamic optimization problems with guaranteed satisfaction of ipcs the algorithm is based on a solution of a sequence of approximated dynamic optimization problems following the strategy of fu et al automatica 2015 for the approximation the path constraint is imposed only on a set of discrete points and is thus relaxed at the same time it is restricted by an adaptive back off and by the error bound of the pde solution the approximation is iteratively improved at iterations without violation the restriction is reduced at iterations with violation the point of maximal violation is added to the discrete set under mild assumptions we prove finite termination of the algorithm we test the algorithm on an optimal grade change of a tubular reactor

emergence of synchronization in complex networks of interacting dynamical systems abstract we study the emergence of coherence in large complex networks of interacting heterogeneous dynamical systems we show that for a large class of dynamical systems and network topologies there is a critical coupling strength at which the systems undergo a transition from incoherent to coherent behavior we find that the critical coupling strength at which this transition takes place is k c z 1 where z depends only on the uncoupled dynamics of the individual systems on each node while is the largest eigenvalue of the network adjacency matrix thus we achieve a separation of the problem into two parts one depending solely on the node dynamics and one depending solely on network topology

perturbation analysis of complete synchronization in networks of phase oscillators the behavior of weakly coupled self sustained oscillators can often be well described by phase equations here we use the paradigm of kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections to the frequency of the fully synchronized state for nonidentical oscillators the topology of the underlying coupling network is reflected in the eigenvalues and eigenvectors of the network laplacian which influence the synchronization frequency in a particular way they characterize the importance of nodes in a network and the relations between them expected values for the synchronization frequency are obtained for oscillators with quenched random frequencies on a class of scale free random networks and for a erdos renyi random network we briefly discuss an application of the perturbation theory in the second order to network structural analysis

a priori error estimates for elliptic optimal control problems with a bilinear state equation in this paper a priori error analysis for the finite element discretization of an optimal control problem governed by an elliptic state equation is considered the control variable enters the state equation as a coefficient and is subject to pointwise inequality constraints we derive a priori error estimates for the discretization error in the control variable and confirm our theoretical results by numerical examples

synchronization in oscillator networks with delayed coupling a stability criterion we derive a stability criterion for the synchronous state in networks of identical phase oscillators with delayed coupling the criterion applies to any network whether regular or random low dimensional or high dimensional directed or undirected in which each oscillator receives delayed signals from k others where k is uniform for all oscillators

slow switching in a population of delayed pulse coupled oscillators we show that peculiar collective dynamics called slow switching arises in a population of leaky integrate and fire oscillators with delayed all to all pulse couplings by considering the stability of cluster states and symmetry possessed by our model we argue that saddle connections between a pair of the two cluster states are formed under general conditions slow switching appears as a result of the system s approach to the saddle connections it is also argued that such saddle connections are easy to arise near the bifurcation point where the state of perfect synchrony loses stability we develop an asymptotic theory to reduce the model into a simpler form with which an analytical study of the cluster states becomes possible

an efficient nfem for optimal control problems governed by a bilinear state equation abstract in this paper a nonconforming finite element method nfem is proposed for the constrained optimal control problems ocps governed by a bilinear state equation the state and adjoint state are approximated by the nonconforming e q 1 r o t element and the control is approximated by the orthogonal projection through the state and adjoint state some superclose and superconvergence properties are obtained by full use of the distinguish characters of this e q 1 r o t element such as the interpolation operator equals the ritz projection and the consistency error is one order higher than its interpolation error in the broken energy norm finally some numerical results are provided to verify the theoretical analysis

error estimates for discontinuous galerkin time stepping schemes for robin boundary control problems constrained to parabolic pdes we consider fully discrete finite element approximations of a robin optimal boundary control problem constrained by linear parabolic pdes with rough initial data conforming finite element methods for spatial discretization combined with discontinuous time stepping galerkin schemes are being used for the space time discretization error estimates are proved under weak regularity hypotheses for the state adjoint and control variables computational examples validating our expected rates of convergence are also provided

collective synchronization of pulse coupled oscillators and excitable units abstract a phase model is proposed and studied for a population of integrate and fire type oscillators and excitable units with pulsatile coupling the units are subject to external noise and their mutual connection is all to all an evolution equation is derived for the phase distribution in a closed form its steady state analysis in the limit of weak noise shows the possibility of collective bistability the evolution equation is simplified drastically when the coupling as well as noise is sufficiently weak this reduction of equation enables analytical calculation of various quantities among others the stability of the steady distribution is analyzed explicity and the onset of collective oscillations is described in terms of the hopf bifurcation it is also shown that the present model is improved in some respects by introducing absolute refractoriness

stochastic volatility models at ρ 1 as second class constrained hamiltonian systems abstract the stochastic volatility models used in the financial world are characterized in the continuous time case by a set of two coupled stochastic differential equations for the underlying asset price s and volatility in addition the correlations of the two brownian movements that drive the stochastic dynamics are measured by the correlation parameter 1 1 this stochastic system is equivalent to the fokker planck equation for the transition probability density of the random variables s and solutions for the transition probability density of the heston stochastic volatility model heston 1993 were explored in dragulescu and yakovenko 2002 where the fundamental quantities such as the transition density itself depend on in such a manner that these are divergent for the extreme limit 1 the same divergent behavior appears in hagan et al 2002 where the probability density of the sabr model was analyzed in an option pricing context the propagator of the bi dimensional black scholes equation was obtained in lemmens et al 2008 in terms of the path integrals and in this case the propagator diverges again for the extreme values 1 this paper shows that these similar divergent behaviors are due to a universal property of the stochastic volatility models in the continuum all of them are second class constrained systems for the most extreme correlated limit 1 in this way the stochastic dynamics of the 1 cases are different of the 1 1 case and it cannot be obtained as a continuous limit from the 1 regimen this conclusion is achieved by considering the fokker planck equation or the bi dimensional black scholes equation as a euclidean quantum schrodinger equation then the analysis of the underlying classical mechanics of the quantum model implies that stochastic volatility models at 1 correspond to a constrained system to study the dynamics in an appropriate form dirac s method for constrained systems dirac 1958 1967 must be employed and dirac s analysis reveals that the constraints are second class in order to obtain the transition probability density or the option price correctly one must evaluate the propagator as a constrained hamiltonian path integral henneaux and teitelboim 1992 in a similar way to the high energy gauge theory models in fact for all stochastic volatility models after integrating over momentum variables one obtains an effective euclidean lagrangian path integral over the volatility alone the role of the second class constraints is determining the underlying asset price s completely in terms of volatility so it plays no role in the path integral in order to examine the effect of the constraints on the dynamics for both extreme limits the probability density function is evaluated by using semi classical arguments in an analogous manner to that developed in hagan et al 2002 for the sabr model

a discontinuous galerkin time stepping scheme for the velocity tracking problem the velocity tracking problem for the evolutionary navier stokes equations in two dimensions is studied the controls are of distributed type and are submitted to bound constraints first and second order necessary and sufficient conditions are proved a fully discrete scheme based on the discontinuous in time galerkin approach combined with conforming finite element subspaces in space is proposed and analyzed provided that the time and space discretization parameters tau and h respectively satisfy tau leq ch 2 then l 2 error estimates of order o h are proved for the difference between the locally optimal controls and their discrete approximations

dynamic optimization and its relation to classical and quantum constrained systems abstract we study the structure of a simple dynamic optimization problem consisting of one state and one control variable from a physicist s point of view by using an analogy to a physical model we study this system in the classical and quantum frameworks classically the dynamic optimization problem is equivalent to a classical mechanics constrained system so we must use the dirac method to analyze it in a correct way we find that there are two second class constraints in the model one fix the momenta associated with the control variables and the other is a reminder of the optimal control law the dynamic evolution of this constrained system is given by the dirac s bracket of the canonical variables with the hamiltonian this dynamic results to be identical to the unconstrained one given by the pontryagin equations which are the correct classical equations of motion for our physical optimization problem in the same pontryagin scheme by imposing a closed loop strategy the optimality condition for the action gives a consistency relation which is associated to the hamilton jacobi bellman equation of the dynamic programming method a similar result is achieved by quantizing the classical model by setting the wave function x t e i s x t in the quantum schrodinger equation a non linear partial equation is obtained for the s function for the right hand side quantization this is the hamilton jacobi bellman equation when s x t is identified with the optimal value function thus the hamilton jacobi bellman equation in bellman s maximum principle can be interpreted as the quantum approach of the optimization problem

human ankle joint stiffness over the full range of muscle activation levels abstract system identification techniques have been used to track changes in dynamic stiffness of the human ankle joint over a wide range of muscle contraction levels subjects lay supine on an experimental table with their left foot encased in a rigid low inertia cast which was fixed to an electro hydraulic actuator operating as a position servo subjects generated tonic plantarflexor or dorsiflexor torques of different magnitudes ranging from rest to maximum voluntary contractions mvc during repeated presentations of a stochastic ankle angular position perturbation compliance impulse response functions irf were determined from every 2 5 s perturbation sequence the gain g natural freqency n and damping parameters of the second order model providing the best fit to each irf were determined and used to compute the corresponding inertial i viscous b and elastic k stiffness parameters the behaviour of these parameters with mean torque was found to follow two simple rules first the elastic parameter k increased in proportion to mean ankle torque as it was varied from rest to mvc these changes were considerable involving increases of more than an order of magnitude second the damping parameter remained almost invariant over the entire range of contractions despite the dramatic changes in k

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

generalized percolation in random directed networks we develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges that is edges pointing in both directions simultaneously these two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena equations for the percolation threshold and the sizes of the giant components are derived in the most general case we also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions