hamiltonian formulation of surfaces with constant gaussian curvature dirac s method for constrained hamiltonian systems is used to describe surfaces of constant gaussian curvature a geometrical free energy for which these surfaces are equilibrium states is introduced and interpreted as an action an equilibrium surface can then be generated by the evolution of a closed space curve since the underlying action depends on second derivatives the velocity of the curve and its conjugate momentum must be included in the set of phase space variables furthermore the action is linear in the acceleration of the curve and possesses a local symmetry reparametrization invariance which implies primary constraints in the canonical formalism these constraints are incorporated into the hamiltonian through lagrange multiplier functions that are identified as the components of the acceleration of the curve the formulation leads to four first order partial differential equations one for each canonical variable with the appropriate choice of parametrization only one of these equations has to be solved to obtain the surface which is swept out by the evolving space curve to illustrate the formalism several evolutions of pseudospherical surfaces are discussed

algebraic approach to system identification a variety of identification procedures exists for estimating the parameters of an autoregressive moving average arma process from noise free excitation and noise contaminated response data in this paper an identification procedure is proposed for the more realistic situation in which both the excitation and response are contaminated by white noises the method is based upon the null space characterization of an associated data matrix some of the more important algebraic properties possessed by this data matrix are first established in the ideal noise free data case in particular it is found that an overordering of the arma model will not impair the identification of the underlying system in the more realistic noise contaminated data case an approximation of the data matrix s null space is affected by using an eigenvalue eigenvector decomposition by incorporating this null space approximation the deleterious effects of the noise are significantly reduced thereby giving rise to improved modeling performance this improvement is demonstrated by means of a standard example in which the proposed identification method is shown to produce a better modeling behavior than does the classical least squares method the corresponding iterative generalized least squares method and a commonly employed instrumental variable method

hamilton s equations for a fluid membrane consider a homogeneous fluid membrane described by the helfrich canham energy quadratic in the mean curvature of the membrane surface the shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in the mean curvature we introduce a hamiltonian formulation of this equation which dismantles it into a set of coupled first order equations this involves interpreting the helfrich canham energy as an action equilibrium surfaces are generated by the evolution of space curves two features complicate the implementation of a hamiltonian framework i the action involves second derivatives this requires treating the velocity as a phase space variable and the introduction of its conjugate momentum the canonical hamiltonian is constructed on this phase space ii the action possesses a local symmetry reparametrization invariance the two labels we use to parametrize points on the surface are themselves physically irrelevant this symmetry implies primary constraints one for each label that need to be implemented within the hamiltonian the two lagrange multipliers associated with these constraints are identified as the components of the acceleration tangential to the surface the conservation of the primary constraints implies two secondary constraints fixing the tangential components of the momentum conjugate to the position hamilton s equations are derived and the appropriate initial conditions on the phase space variables are identified finally it is shown how the shape equation can be reconstructed from these equations

identification of multivariable errors in variable models with dynamics this note considers the task of identifying a causal linear dynamic multivariable system excited by stationary zero mean noise of unknown spectrum and given measurements of the system inputs and outputs contaminated by independent additive noise also of unknown spectra although the solution is in general not unique finite dimensional parameterizations of the solution set are given even though the various spectra may not be rational

multiple criteria decision making with interval stochastic variables a method based on interval stochastic dominance abstract a novel method based on interval stochastic dominance to solve the stochastic multiple criteria decision making smcdm problem with interval stochastic variables is proposed by analyzing the uncertainty of interval stochastic variables we propose the method of determining cumulative distribution function of interval stochastic variables then three types of interval stochastic dominance isd rules are investigated the definition of interval stochastic dominance degree isdd is presented and some interesting properties of isd and isdd are proved with respect to the smcdm problem with interval stochastic variables to begin with interval cumulative distribution functions of alternative criterion values are determined then the isd relations matrix associated with pairwise comparison of alternatives on each criterion is obtained based on isd rules and the isdd matrix on each criterion is calculated further based on promethee method the net flows of each alternative are derived so as to obtain the ranking result consequently examples are presented to illustrate the effectiveness of the proposed method

time delay estimation using the cross bispectrum the cross bispectrum phase can be effectively used to estimate the time required for a nongaussian signal to propagate between a pair of spatially separated sensors in the presence of highly correlated gaussian noise the authors present a consistent estimator of the phase of the cross bispectrum derive the exact distribution of the phase of a complex gaussian sample bispectrum and show that in most cases the exact distribution can be approximated by a gaussian distribution using this gaussian approximation the authors derive the variance of the time delay estimate computed from the sample cross bispectrum of a signal in additive correlated noise these results allow the performance of time delay estimators based on the cross bispectrum phase to be quantified as a function of the sample size the skewness of the signal the signal to noise ratio snr and the noise correlation

third order cumulants based methods for continuous time errors in variables model identification in this paper the problem of identifying stochastic linear continuous time systems from noisy input output data is addressed the input of the system is assumed to have a skewed probability density function whereas the noises contaminating the data are assumed to be symmetrically distributed the third order cumulants of the input output data are then asymptotically insensitive to the noises that can be coloured and or mutually correlated using this noise cancellation property two computationally simple estimators are proposed the usefulness of the proposed algorithms is assessed through a numerical simulation

brief paper accuracy analysis of bias eliminating least squares estimates for errors in variables systems the bias eliminating least squares bels method is one of the consistent estimators for identifying dynamic errors in variables systems in this paper we investigate the accuracy properties of the bels estimates an explicit expression for the normalized asymptotic covariance matrix of the estimated parameters is derived and supported by some numerical examples

projects ordering with multicriteria analysis abstract this paper considers an actual case study where the best projects have to be chosen from a set a of n projects each projects p i of a is evaluated by k i experts according to a set of m criteria or points of view these evaluations lead to the distributive evaluation i e to the calculation of the distribution of the anticipated performance of each project with respect to each criterion that is the consequences of a project p i are evaluated by a vector of distributions f i f il f ij f im where f ij is the relative frequency distribution of the evaluations by the k i experts of p i with respect to the j th criterion after a description of the real evaluation and decision making processes used by the csssrmm in studying the development projects this document develops a multicriteria method of analysis based on the construction of an outranking relation leading to the ordering of the projects

balancing torques in membrane mediated interactions exact results and numerical illustrations torques on interfaces can be described by a divergence free tensor which is fully encoded in the geometry this tensor consists of two terms one originating in the couple of the stress the other capturing an intrinsic contribution due to curvature in analogy to the description of forces in terms of a stress tensor the torque on a particle can be expressed as a line integral along a contour surrounding the particle interactions between particles mediated by a fluid membrane are studied within this framework in particular torque balance places a strong constraint on the shape of the membrane symmetric two particle configurations admit simple analytical expressions which are valid in the fully nonlinear regime in particular the problem may be solved exactly in the case of two membrane bound parallel cylinders this apparently simple system provides some flavor of the remarkably subtle nonlinear behavior associated with membrane mediated interactions

counterexample to some shape equations for axisymmetrical vesicles three different shape equations for axisymmetric vesicles have been derived from the same spontaneous curvature model in literature the validity of the equations has been examined by means of a rigorous analytical solution for axisymmetric vesicles a counterexample is given to show the invalidity of two of the equations

laplace pressure as a surface stress in fluid vesicles consider a surface enclosing a fixed volume described by a free energy depending only on the local geometry for example the canham helfrich energy quadratic in the mean curvature describes a fluid membrane the stress at any point on the surface is determined completely by geometry in equilibrium its divergence is proportional to the laplace pressure normal to the surface maintaining the constraint on the volume it is shown that this source itself can be expressed as the divergence of a position dependent surface stress as a consequence the equilibrium can be described in terms of a conserved effective surface stress various non trivial geometrical consequences of this identification are explored in a cylindrical geometry the cross section can be viewed as a closed planar euler elastic curve with respect to an appropriate centre the effective stress itself vanishes this provides a remarkably simple relationship between the curvature and the position along the loop in two or higher dimensions it is shown that the only geometry consistent with the vanishing of the effective stress is spherical it is argued that the appropriate generalization of the loop result will involve null stresses

interface mediated interactions between particles a geometrical approach particles bound to an interface interact because they deform its shape the stresses that result are fully encoded in the geometry and described by a divergence free surface stress tensor this stress tensor can be used to express the force on a particle as a line integral along any conveniently chosen closed contour that surrounds the particle the resulting expression is exact i e free of any smallness assumptions and independent of the chosen surface parametrization additional surface degrees of freedom such as vector fields describing lipid tilt are readily included in this formalism as an illustration we derive the exact force for several important surface hamiltonians in various symmetric two particle configurations in terms of the midplane geometry its sign is evident in certain interesting limits specializing to the linear regime where the shape can be analytically determined these general expressions yield force distance relations several of which have originally been derived by using an energy based approach

identification of a class of nonlinear systems under stationary non gaussian excitation this paper provides new solutions to the nonlinear system identification problem when the input to the system is a stationary non gaussian process we propose the use of a model called the hammerstein series which leads to significant reductions in both the computational requirements and the mathematical tractability of the nonlinear system identification problem we show that unlike the volterra series one can obtain closed form expressions for the hammerstein series kernels and the quadratic coherence function in the non gaussian case estimation of the kernels and quadratic coherence function is discussed a comparison with a nonlinear system identification approach that uses the volterra series is provided an automotive engineering application illustrates the usefulness of the proposed method

how paper folds bending with local constraints a variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry this framework is applied to describe the patterns of a folded sheet of paper the unstretchability of paper implies a constraint on the surface metric bending is penalized by an energy quadratic in mean curvature the local lagrange multipliers enforcing the constraint are identified with a conserved tangential stress that couples to the extrinsic curvature of the sheet the framework is illustrated by examining the deformation of a flat sheet into a generalized cone

modeling uncertainty in multi criteria decision analysis abstract his paper provides a review of multiple criteria decision analysis mcda for cases where attribute evaluations are uncertain the main aim is to identify different tools which can be used to represent uncertain evaluations and to broadly survey the available decision models that can be used to support uncertain decision making the review includes models using probabilities or probability like quantities explicit risk measures such as quantiles and variances fuzzy numbers and scenarios the practical assessment of uncertain outcomes and preferences associated with these outcomes is also discussed

a fuzzy outranking relation in multicriteria decision making abstract it frequently happens that a decision maker must establish a ranking within a finite set of alternatives with respect to multiple criteria the subjective evaluation of each alternative according to each criterion is expressed in the form of a distributive evaluation to capture the preferences of one alternative over another a concept of fuzzy outranking relation can be used this fuzzy outranking relation is characterized by a degree of credibility which is computed from two indices a confidence index and a doubt index each of these indices is calculated from the distributive evaluations over the various criteria in this paper such a fuzzy outranking relation fuzzy binary relation is constructed and an application is presented

rough set approach to multi attribute decision analysis abstract we review the methodology of the rough set analysis of multi attribute decision problems rough set theory proved to be a useful tool for analysis of a vague description of decision situations it answers two basic questions related to multi attribute decision problems one about explanation of a decision situation and another about prescription of some decisions basing on analysis of a decision situation we define four classes of multi attribute decision problems depending on the structure of their representation its interpretation and the kind of questions related then we characterize the rough set methodology for each particular class of decision problems we use simple practical examples to illustrate this presentation a review of related literature is made throughout the paper

generating true minima in constrained variational formulations via modified lagrange multipliers variational principles are important in the investigation of large classes of physical systems they can be used both as analytical methods as well as starting points for the formulation of powerful computational techniques such as dynamical optimization methods systems with charged objects in dielectric media and systems with magnetically active particles are important examples in these examples and other important cases the variational principles describing the system are required to obey a number of constraints these constraints are implemented within the variational formulation by means of lagrange multipliers such constrained variational formulations are in general not unique for the application of efficient simulation methods one must find specific formulations that satisfy a number of important conditions an often required condition is that the functional be positive definite in other words its extrema be actual minima in this article we present a general approach to attack the problem of finding among equivalent variational functionals those that generate true minima the method is based on the modification of the lagrange multiplier which allows us to generate large families of effective variational formulations associated with a single original constrained variational principle we demonstrate its application to different examples and in particular to the important cases of poisson and poisson boltzmann equations we show how to obtain variational formulations for these systems with extrema that are always minima

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

time delay estimation in unknown gaussian spatially correlated noise a novel class of methods that estimate the difference in arrival time between signals corrupted by spatially correlated gaussian noise sources of unknown cross correlation is presented the methods are based on the idea of comparing the similarities between the two sensor measurements in higher order spectrum domains bispectrum rather than in the cross correlation domain it is demonstrated that estimation techniques based on higher order cumulants suppress the effect of correlated gaussian noise sources and therefore exhibit improved performance over generalized cross correlation methods results are reported for different types of signals lengths of data records and signal to noise ratios

inverted catenoid as a fluid membrane with two points pulled together under inversion in any interior point a catenoid transforms into a deflated compact geometry which touches at two points its poles the catenoid is a minimal surface and as such is an equilibrium shape of a symmetric fluid membrane the conformal symmetry of the hamiltonian implies that inverted minimal surfaces are also equilibrium shapes however they will exhibit curvature singularities at their poles such singularities are the geometrical signature of the external forces required to pull the poles together these forces will set up stresses in the inverted shapes tuning the force corresponds geometrically to the translation of the point of inversion for any fixed surface area there will be a maximum force the associated shape is a symmetric discocyte lowering the external force will induce a transition from the discocyte to a cup shaped stomatocyte

conformally invariant bending energy for hypersurfaces the most general conformally invariant bending energy of a closed four dimensional surface polynomial in the extrinsic curvature and its derivatives is constructed this invariance manifests itself as a set of constraints on the corresponding stress tensor if the topology is fixed there are three independent polynomial invariants two of these are the straightforward quartic analogues of the quadratic willmore energy for a two dimensional surface one is intrinsic the weyl invariant the other extrinsic the third invariant involves a sum of a quadratic in gradients of the extrinsic curvature which is not itself invariant and a quartic in the curvature the four dimensional energy quadratic in extrinsic curvature plays a central role in this construction

environmental bias and elastic curves on surfaces the behavior of an elastic curve bound to a surface will reflect the geometry of its environment this may occur in an obvious way the curve may deform freely along directions tangent to the surface but not along the surface normal however even if the energy itself is symmetric in the curve s geodesic and normal curvatures which control these modes very distinct roles are played by the two if the elastic curve binds preferentially on one side or is itself assembled on the surface not only would one expect the bending moduli associated with the two modes to differ binding along specific directions reflected in spontaneous values of these curvatures may be favored the shape equations describing the equilibrium states of a surface curve described by an elastic energy accommodating environmental factors will be identified by adapting the method of lagrange multipliers to the darboux frame associated with the curve the forces transmitted to the surface along the surface normal will be determined features associated with a number of different energies both of physical relevance and of mathematical interest are described the conservation laws associated with trajectories on surface geometries exhibiting continuous symmetries are also examined

identification of linear systems using input output cumulants a new identification method is proposed for estimating the parameters of a discrete time linear dynamic system excited by non gaussian inputs using kth order k 2 cumulants of input and output signals contaminated by additive possibly coloured gaussian noise the parameter estimates obtained by this method are proved to be consistent under weak conditions this method has an on line algorithm for computing the parameter estimates just like the least squares method a simulation example is included to demonstrate the effectiveness of this method

outranking under uncertainty using scenarios abstract this paper considers the use of scenarios to treat uncertain attribute evaluations in the outranking methods the scenario based approach allows the decision maker to think deterministically about the problem by attaching causal links to a small number of potential outcomes instead of using probability distributions the scenario approach can be expressed as a simplified version of the comprehensive but practically complex distributive outranking method of d avignon and vincke using a scenario approach has distinct practical advantages but also presents the inherent danger that meaningful information is ignored the extent of this danger is assessed using a simulation experiment where it is found to be of a magnitude that is non trivial but still potentially acceptable for certain decision contexts

stochastic system identification with noisy input output measurements using polyspectra two new classes of parametric frequency domain approaches are proposed for estimation of the parameters of scalar linear errors in variables models i e linear systems where measurements of both input and output of the system are noise contaminated the first approach consists of linear estimators where using the bispectrum or the integrated polyspectrum of the input and the cross bispectrum or the integrated cross polyspectrum the system transfer function is first estimated at a number of frequencies exceeding one half the number of unknown parameters the estimated transfer function is then used to estimate the unknown parameters using an overdetermined linear system of equations in the second class of approaches quadratic transfer function matching criteria are optimized by using the results of the linear estimators as initial guesses both classes of the parameter estimators are shown to be consistent in any measurement noise that has symmetric probability density function when the bispectral approaches are used the proposed parameter estimators are shown to be consistent in gaussian measurement noise when trispectral approaches are used

membrane geometry with auxiliary variables and quadratic constraints consider a surface described by a hamiltonian which depends only on the metric and extrinsic curvature induced on the surface the metric and the curvature along with the basis vectors which connect them to the embedding functions defining the surface are introduced as auxiliary variables by adding appropriate constraints all of them quadratic the response of the hamiltonian to a deformation in each of the variables is determined and the relationship between the multipliers implementing the constraints and the conserved stress tensor of the theory established for the purpose of illustration a fluid membrane described by a hamiltonian quadratic in curvature is considered

identification of closed loop linear systems via cyclic spectral analysis given noisy input output time domain data the problem of closed loop system identification given noisy time domain input output measurements is considered it is assumed that the various disturbances affecting the system are zero mean stationary whereas the closed loop system operates under an external cyclostationary input which is not measured noisy measurements of the direct input and output of the plant are assumed to be available the closed loop system must be stable but it is allowed to be unstable in open loop no knowledge about the linear feedback mechanism is assumed two identification algorithms are investigated using cyclic spectral analysis of noisy input output data for both approaches the open loop transfer function is first estimated using the cyclic spectrum and cyclic cross spectrum of the input output data these transfer function estimates are then used as data for the proposed algorithms both classes of parameter estimators are shown to be weakly consistent in any stationary noise both at input as well as output asymptotic performance analysis of the proposed parameter estimators is also provided computer simulation examples are presented in support of the proposed approaches

fluid membrane tethers minimal surfaces and elastic boundary layers thin cylindrical tethers are common lipid bilayer membrane structures arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the golgi apparatus we study the shape and formation of a tether in terms of the classical soap film problem which is applied to the case of a membrane disk under tension subject to a point force a tether forms from the elastic boundary layer near the point of application of the force for sufficiently large displacement analytic results for various aspects of the membrane shape are given

lipid membranes with an edge consider an open lipid membrane with a free exposed edge the energy describing this membrane is quadratic in the extrinsic curvature that describing the edge is proportional to its length we determine the boundary conditions satisfied by the equilibria of the membrane on this edge the derivation is free of any assumptions on the symmetry of the membrane geometry with respect to the axially symmetric case there is an additional boundary condition that is identically satisfied in that limit by considering the balance of the forces operating at the edge a physical interpretation for the boundary conditions is provided the effect of the addition of a gaussian rigidity term for the membrane is also considered

insdecm an interactive procedure for stochastic multicriteria decision problems abstract a new interactive technique for a discrete stochastic multiattribute decision making problem is proposed in this paper it is assumed that performance probability distribution for each action on each attribute is known two concepts are combined in the procedure stochastic dominance and interactive approach the first one is employed for generating efficient actions and constructing rankings of actions with respect to attributes the second concept is used when the communication between the dm and the model is conducted it is assumed that decision maker s restrictions are defined by specifying minimal or maximal values of scalar criteria measuring either expected outcome or variability of outcomes as such restrictions are in general not consistent with stochastic dominance rules we suggest verifying this consistency and asking the decision maker to redefine inconsistent restrictions

moving frames applied to shell elasticity exterior calculus and moving frames are used to describe the curved elasticity of shells the kinematics follow from the lie derivative on forms whereas the dynamics follow from stress forms

spinor representation of surfaces and complex stresses on membranes and interfaces variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface this is a far reaching generalization of the weierstrass enneper representation for minimal surfaces introduced by mathematicians in the 1990s permitting the relaxation of the vanishing mean curvature constraint in this representation the surface geometry is described by a spinor field satisfying a two dimensional dirac equation coupled through a potential associated with the mean curvature as an application the mesoscopic model for a fluid membrane as a surface described by the canham helfrich energy quadratic in the mean curvature is examined an explicit construction is provided of the conserved complex valued stress tensor characterizing this surface

uncertainty and rank order in the analytic hierarchy process abstract the analytic hierarchy process uses paired comparisons to derive a scale of relative importance for alternatives we investigate the effect of uncertainty in judgment on the stability of the rank order of alternatives the uncertainty experienced by decision makers in making comparisons is measured by associating with each judgment an interval of numerical values the approach leads to estimating the probability that an alternative or project exchanges rank with other projects these probabilities are then used to calculate the probability that project would change rank at all we combine the priority of importance of each project with the probability that it does not change rank to obtain the final ranking

hamilton s equations for a fluid membrane axial symmetry consider a homogeneous fluid membrane or vesicle described by the helfrich canham energy quadratic in the mean curvature when the membrane is axially symmetric this energy can be viewed as an action describing the motion of a particle the contours of equilibrium geometries are identified with particle trajectories a novel hamiltonian formulation of the problem is presented which exhibits the following two features i the second derivatives appearing in the action through the mean curvature are accommodated in a natural phase space and ii the intrinsic freedom associated with the choice of evolution parameter along the contour is preserved as a result the phase space involves momenta conjugate not only to the particle position but also to its velocity and there are constraints on the phase space variables this formulation provides the groundwork for a field theoretical generalization to arbitrary configurations with the particle replaced by a loop in space

a method for stochastic multiple attribute decision making based on concepts of ideal and anti ideal points this paper proposes a novel method for solving the stochastic multiple attribute decision making smadm problem where consequences of alternatives with respect to attributes are represented by random variables with cumulative distribution functions first the concepts of ideal and anti ideal cumulative distribution functions are introduced and the related theoretical analysis is given next according to the concept of classical topsis the ideal and anti ideal points of the smadm problem are determined which are in the form of cumulative distribution function vectors then the closeness coefficient of each alternative is obtained by calculating the distances to the ideal and anti ideal points simultaneously based on the obtained closeness coefficients a ranking of alternatives is determined finally two numerical examples are given to illustrate the use of the proposed method

on the uniqueness of prediction error models for systems with noisy input output data abstract this paper addresses the uniqueness problem of the prediction error pe identification for a class of linear systems with noisy input and output data necessary and sufficient conditions are derived for the corresponding pe loss function to have asymptotically a unique global minimum the results indicate that a pe algorithm may give very bad parameter estimates for systems not satisfying these conditions such a possibility is illustrated by a numerical example while the pe method is used as a vehicle for illustration the derived conditions for global uniqueness or identifiability apply to any consistent estimation method based on second order data

an outranking method under uncertainty abstract the uncertainty of consequences and the imprecision of data often imply in multicriteria decision problems the use of probability distributions to characterize the evaluation of each action with respect to eacg criterion to keep as much information as possible the analysis should treat directly these probability distributions instead of reducing them to single values such as mean or median in this context the paper proposes a multicriteria procedure which transforms these distributive evaluations of actions according to decisionmaker s preferences in order to progress to a ranking of these actions the procedure consists for each couple of actions to construct a distributive preference degree with respect to each criterion and a distributive outranking degree over all criteria these distributive outranking degrees are then explored in order to rank the actions totally or partially

a method for stochastic multiple criteria decision making based on dominance degrees this paper proposes a method for solving the stochastic multiple criteria decision making smcdm problem where consequences of alternatives with respect to criteria are represented by random variables with probability distributions firstly definitions and related analysis of dominance degree of one probability distribution over another are given then by calculating the dominance degrees the dominance degree matrix of alternative pairwise comparisons with respect to each criterion is built further using promethee ii method an overall dominance degree matrix of alternative pairwise comparisons is constructed and a net flow of each alternative is calculated based on the obtained net flows a ranking of alternatives is determined finally numerical examples for the three cases are given to illustrate the use of the proposed method

brief paper accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors in variables and output error identification for identifying errors in variables models the time domain maximum likelihood tml method and the sample maximum likelihood sml method are two approaches both methods give optimal estimation accuracy but under different assumptions in the tml method an important assumption is that the noise free input signal is modelled as a stationary process with rational spectrum for sml the noise free input needs to be periodic it is interesting to know which of these assumptions contain more information to boost the estimation performance in this paper the estimation accuracy of the two methods is analyzed statistically for both errors in variables eiv and output error models oem numerical comparisons between these two estimates are also done under different signal to noise ratios snrs the results suggest that tml and sml have similar estimation accuracy at moderate or high snr for eiv for oem identification these two methods have the same accuracy at any snr

identification of multivariable stochastic linear systems via polyspectral analysis given noisy input output time domain data the paper considers the problem of identification of unknown parameters of multivariable linear errors invariables models attention is focused on frequency domain approaches where the integrated polyspectrum bispectrum or trispectrum of the input and the integrated cross polyspectrum respectively of the given time domain input output data are exploited two new classes of parametric frequency domain approaches are proposed and analyzed an integrated polyspectrum based persistence of excitation condition on system input is defined both classes of the parameter estimators are shown to be strongly consistent in any measurement noise sequences with vanishing bispectra when integrated bispectrum based approaches are used the proposed parameter estimators are shown to be strongly consistent in gaussian measurement noise when integrated trispectrum based approaches are used the input to the system need not be a linear process but must have nonvanishing bispectrum or trispectrum

rough approximation of a preference relation by dominance relations an original methodology for using rough sets to preference modeling in multi criteria decision problems is presented this methodology operates on a pairwise comparison table pct including pairs of actions described by graded preference relations on particular criteria and by a comprehensive preference relation it builds up a rough approximation of a preference relation by graded dominance relations decision rules derived from the rough approximation of a preference relation can be used to obtain a recommendation in multi criteria choice and ranking problems the methodology is illustrated by an example of multi criteria programming of water supply systems

on closed loop system identification using polyspectral analysis given noisy input output time domain data parametric models of linear systems operating in closed loop can be consistently identified from time domain noisy input output measurements using cumulant spectra without requiring parametric modeling of noise two algorithms are proposed and their asymptotic performance is analyzed

time delay estimation using phase data the estimation of time delays between two received signals using phase measurements is discussed and the accuracy of such estimates is detailed for the ideal case of statistically independent noise and no scattering at the receiver locations it is shown that phase data regression lines yield time delay estimates with the same accuracy as other optimal time delay estimation procedures for less ideal situations the potential advantages of time delay estimation using phase data are discussed and illustrated it is shown that regression analysis of phase estimates at properly selected frequencies can sometimes be employed to reduce bias errors in time delay estimates due to correlated receiver noise it is also shown that the estimation errors due to scattering at the receiver location can often be assessed in nonparametric terms to provide time delay estimates with a realistic error bound

a geometric theory on the elasticity of bio membranes the purpose of this paper is to study the shapes and stabilities of bio membranes within the framework of exterior differential forms after a brief review of the current status of theoretical and experimental studies on the shapes of bio membranes a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers the shape equation and boundary conditions of open lipid bilayers and two component membranes the shape equation and in plane strain equations of cell membranes with cross linking structures and the stabilities of closed lipid bilayers and cell membranes the key point of this scheme is to deal with the variational problems on surfaces embedded in three dimensional euclidean space by using exterior differential forms

a method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations this paper proposes a method for solving stochastic multiple criteria decision making mcdm problems where evaluations of alternatives on considered criteria are random variables with known probability density functions or probability mass functions probabilities on all possible results of pairwise comparisons of alternatives are first calculated using probability theory then all possible results of pairwise comparisons are classified into superior indifferent and inferior ones using a predefined identification rule consequently the probabilities on all possible results of pairwise comparisons are partitioned into superior indifferent and inferior probabilities furthermore based on the derived probabilities an algorithm is developed to rank the alternatives finally a numerical example is used to illustrate the feasibility and validity of the proposed method

statistical mechanics approach to some problems in conformal geometry a weak law of large numbers is established for a sequence of systems of n classical point particles with logarithmic pair potential in rn or sn n n which are distributed according to the configurational microcanonical measure e h or rather some regularization thereof where h is the configurational hamiltonian and e the configurational energy when n with non extensive energy scaling e n2e the particle positions become i i d according to a self consistent boltzmann distribution respectively a superposition of such distributions the self consistency condition in n dimensions is some nonlinear elliptic pde of order n pseudo pde if n is odd with an exponential nonlinearity when n 2 this pde is known in statistical mechanics as poisson boltzmann equation with applications to point vortices 2d coulomb and magnetized plasmas and gravitational systems it is then also known in conformal differential geometry where it is the central equation in nirenberg s problem of prescribed gaussian curvature for constant gauss curvature it becomes liouville s equation which also appears in two dimensional so called quantum liouville gravity the pde for n 4 is paneitz equation and while it is not known in statistical mechanics it originated from a study of the conformal invariance of maxwell s electromagnetism and has made its appearance in some recent model of four dimensional quantum gravity in differential geometry the paneitz equation and its higher order n generalizations have applications in the conformal geometry of n manifolds but no physical applications yet for general n interestingly though all the paneitz equations have an interpretation in terms of statistical mechanics

closed loop linear model validation and order estimation using polyspectral analysis suppose that we perform closed loop linear system identification using polyspectral analysis given noisy time domain input output measurements in this setup it is assumed that various disturbances affecting the system are zero mean stationary gaussian whereas the closed loop system operates under an external possibly noisy non gaussian input the closed loop system must be stable but it is allowed to be unstable in the open loop various techniques have been proposed for system identification using polyspectral analysis having obtained a model how do we know if the fitted model is good this paper is devoted to the problem of statistical model validation using polyspectral analysis we propose simple statistical tests based on the estimated polyspectrum integrated bispectrum and or integrated trispectrum of an output error signal or the estimated cross polyspectrum between the external reference and the output error signal model order estimation is performed by repeatedly using the model validation procedure computer simulation examples are presented in support of the proposed approaches

higher order spectrum factorization in one and two dimensions with applications in signal modeling and nonminimum phase system identification the problem of modeling a given higher order spectrum as that of the output of a linear time invariant lti system driven by a higher order white random signal is discussed this can be posed as a higher order spectrum factorization problem a theorem is provided to discuss the existence of such a factorization a fast algorithm for efficient implementation of the higher order spectrum factorization if it exists is then proposed the results are extended to two dimensions straightforwardly the relationship of the higher order spectrum factorization problem to the well known power spectrum factorization is also discussed as applications the problems of identification of nonminimum phase lti systems given the higher order statistics of both input and output processes and phase reconstruction are presented experimental results are provided for the one dimensional case

linear dynamic errors in variables models some structure theory abstract this paper gives a survey of some recent results on problems of identifiability or more general of the relation between the observations and certain system characteristics for linear dynamic errors in variables models for a large part of the paper the noise components are assumed to be mutually uncorrelated after the general problem statement a rather complete analysis of the single input single output case is given also the case of three variables and the case where the number of inputs is equal to the number of outputs are discussed in detail finally the use of higher order cummulant spectra for identifiability is investigated

identification of multivariable stochastic linear systems via spectral analysis given time domain data estimation of the parametric multiple input multiple output mimo infinite impulse response transfer function given time domain input output io data is considered we first propose a frequency domain solution to the least squares equation error multivariable system identification problem using the power spectrum and the cross spectrum of the io data to estimate the io parametric transfer function the proposed approach is shown to yield a unimodal performance surface and consistent identification in colored noise and the sufficient order case we then investigate an iterative pseudo maximum likelihood approach and analyze its consistency under sufficient order modeling finally a computer simulation example is provided to illustrate the two approaches

identification of linear systems with noisy input using input output cumulants abstract an identification method is presented for estimating the parameters of a discrete time linear dynamic system excited by non gaussian input signals using the fourth order cumulants of the input and output signals both of which are contaminated by additive gaussian noise two types of estimators of the fourth order cumulants of the input and output signals are proposed for this method the first is conventional the second which is new allows us only to have a recursive algorithm for computing the parameter estimators the parameter estimators obtained by this algorithm are shown to be strongly consistent under certain weak conditions simulation examples are included to demonstrate the effectiveness of the proposed method

axially symmetric membranes with polar tethers axially symmetric equilibrium configurations of the conformally invariant willmore energy are shown to satisfy an equation that is two orders lower in derivatives of the embedding functions than the equilibrium shape equation not one as would be expected on the basis of axial symmetry modulo a translation along the axis this equation involves a single free parameter c if c 0 a geometry with spherical topology will possess curvature singularities at its poles the physical origin of the singularity is identified by examining the noether charge associated with the translational invariance of the energy it is consistent with an external axial force acting at the poles a one parameter family of exact solutions displaying a discocyte to stomatocyte transition is described

paper identification of scalar errors in variables models with dynamics the paper considers the task of identifying a causal linear dynamic system excited by stationary gaussian zero mean noise of unknown spectrum and given measurements of the system input and output contaminated by independent additive stationary noise signals of unknown spectra while the solution is normally not unique finite dimensional parameterizations of the solution set are given in some cases involving just one parameter even though the various spectra may not be rational

on time delay estimation with unknown spatially correlated gaussian noise using fourth order cumulants and cross cumulants the problem of estimating the difference in arrival times of a linear non gaussian signal at two spatially separated sensors is considered the signal is assumed to be corrupted by spatially correlated gaussian noises of unknown cross correlation a parameter estimation approach is adopted and the fourth order cumulant statistics of the noisy measurements are exploited to obtain the time delay estimate specific and mild sufficient conditions are given for time delay identifiability via a persistence of excitation condition illustrative monte carlo simulation examples are also presented

rough approximation of a preference relation by a multi attribute dominance for deterministic stochastic and fuzzy decision problems abstract the case of mixed data in which attributes have a different nature is not well known in current literature although it is essential from a practical point of view this situation is particularly frequent in risk management modelling which incorporates various degrees of precision of the variables measured and can also be noted in a planning context for project evaluation problems taking into account information of a mixed qualitative and quantitative type for a set of alternatives evaluated by a set of attributes three kinds of evaluations are considered in this paper deterministic stochastic or fuzzy with relation to each attribute the mixed data multi attribute dominance for a reduced number of attributes mmd r is proposed to model the preferences in this kind of problem the approach is based on the dominance based rough set approach proposed by greco matarazzo and slowinski

identification of linear systems via spectral analysis given time domain data consistency reduced order approximation and performance analysis estimation of a parametric input output i o infinite impulse response transfer function given time domain i o data is considered some of the desirable properties of any approach to this problem are unimodality of the performance surface consistent identification in the sufficient order case and stability of the fitted model under undermodeling we first consider a frequency domain solution to the least squares equation error identification problem using the power spectrum and the cross spectrum of the i o data to estimate the i o parametric transfer function the proposed approach is shown to yield a unimodal performance surface consistent identification in colored noise and sufficient order case and stable fitted models under undermodeling for arbitrary stationary inputs so long as they are persistently exciting of sufficiently high order asymptotic performance analysis is carried out for both sufficient order and reduced order cases these asymptotic results are then used to derive statistics on the corresponding estimated transfer function we also investigate an iterative pseudomaximum likelihood approach and analyze its performance under sufficient order modeling finally computer simulation examples are provided to illustrate the two approaches

rough approximation of a preference relation by a multi attribute stochastic dominance for determinist and stochastic evaluation problems abstract let a be a set of actions evaluated by a set of attributes two kinds of evaluations will be considered in this paper determinist or stochastic in relation to each attribute the multi attribute stochastic dominance msd r for a reduced number of attributes will be suggested to model the preferences in this kind of problem the case of mixed data where we have the attributes of different natures is not well known in the literature although it is essential from a practical point of view to apply the msd r the subset r of attributes from which approximation of the global preference is valid should be known the theory of rough sets gives us an answer on this issue allowing us to determine a minimal subset of attributes that enables the same classification of objects as the whole set of attributes in our approach these objects are pairs of actions in order to represent preferential information we shall use a pairwise comparison table this table is built for subset b a described by stochastic dominance sd relations for particular attributes and a total order for the decision attribute given by the decision maker dm using a rough set approach to the analysis of the subset of preference relations a set of decision rules is obtained and these are applied to a set a b of potential actions the rough set approach of looking for the reduction of the set of attributes gives us the possibility of operating with msd r

stresses in lipid membranes the stresses in a closed lipid membrane described by the helfrich hamiltonian quadratic in th ee xtrinsic curvature are identified using noether s theorem three equations describe the conservation of the stress tensor the norma lp rojection is identified as the shape equation describing equilibrium configurations the tangential projections are consistency conditions on the stresses which capture the fluid character of such membranes the corresponding torque tensor is also identified the use of the stress tensor as a basis for perturbation theory is discussed the conservation laws are cast in terms of the forces and torques on closed curves as an application the first integral of the shape equation for axially symmetric configurations is derived by examining the forces which are balanced along the circles of constant latitude

second variation of the helfrich canham hamiltonian and reparametrization invariance a covariant approach towards a theory of deformations is developed to examine both the first and second variation of the helfrich canham hamiltonian quadratic in extrinsic curvature which describes fluid vesicles at mesoscopic scales deformations are decomposed into tangential and normal components at first order tangential deformations may always be identified with a reparametrization at second order they differ the relationship between tangential deformations and reparametrizations as well as the coupling between tangential and normal deformations is examined at this order for both the metric and the extrinsic curvature tensors expressions for the expansion to second order in deformations of geometrical invariants constructed with these tensors are obtained in particular the expansion of the hamiltonian to this order about an equilibrium is considered our approach applies as well to any geometrical model for membranes

a computationally efficient and interference tolerant nonparametric algorithm for lti system identification based on higher order cyclostationarity a new nonparametric algorithm for the identification of linear time invariant systems is proposed the method is based on the cyclic correlations of the input and output signals with a nonlinear transformation of the input signal consequently although it exploits the higher order cyclostationarity properties of the input and output signals its computational complexity is comparable with that of methods based on second order statistics the proposed estimator of the system transfer function is inherently immune to the presence of noise and interference on both input and output signal measurements and turns out to be asymptotically unbiased and consistent moreover bias and variance of the estimate exhibit a rate of convergence to zero equal to that of estimates based on second order statistics finally simulation results show that the proposed algorithm significantly outperforms in terms of both bias and variance of the estimates several nonparametric identification algorithms previously presented in the literature

new results on the canham helfrich membrane model via the generalized weierstrass representation the canham helfrich membrane model is discussed by making use of the generalized weierstrass representation formulae for arbitrary surfaces immersed into the three dimensional euclidean space particular solutions of the shape equation are considered and correlators describing thermal fluctuations in the one loop approximation are computed

stochastic system identification with noisy input using cumulant statistics addresses the problem of estimating the parameters of stochastic linear systems when the measurements of the system input as well as the system output are noise contaminated it is assumed that the input is non gaussian and the noises are gaussian the square root of the magnitude of the fourth cumulant of a generalized error signal is proposed as a performance criterion for parameter estimation an optimization algorithm is presented strong consistency of the proposed parameter estimators is proved under certain sufficient conditions both single input single output and multiple input multiple output cases are investigated finally simulation results are presented to illustrate the proposed approach

lipid membranes with free edges lipid membrane with freely exposed edge is regarded as smooth surface with curved boundary exterior differential forms are introduced to describe the surface and the boundary curve the total free energy is defined as the sum of helfrich s free energy and the surface and line tension energy the equilibrium equation and boundary conditions of the membrane are derived by taking the variation of the total free energy these equations can also be applied to the membrane with several freely exposed edges analytical and numerical solutions to these equations are obtained under the axisymmetric condition the numerical results can be used to explain recent experimental results obtained by saitoh et al proc natl acad sci 95 1026 1998

spherical vesicles distorted by a grafted latex bead an exact solution we present an exact solution to the problem of the global shape description of a spherical vesicle distorted by a grafted latex bead this solution is derived by treating the nonlinearity in bending elasticity through the topological bogomol nyi decomposition technique and elastic compatibility we recover the hat model approximation in the limit of a small latex bead and find that the region antipodal to the grafted latex bead flattens we also derive the appropriate shape equation using the variational principle and relevant constraints