a generalizable formulation of conditional logit with diagnostics abstract the conditional logit model is a multinomial logit model that permits the inclusion of choice specific attributes this article shows that the conditional logit model will maximize entropy given a set of attribute value preserving constraints a correspondence between the maximum entropy me and maximum likelihood ml estimates for logit probabilities is established some easily computable and useful diagnostics for logit analysis are provided and it is shown that an evaluation of the relative importance of attributes can be made using the me formulation the me formulation is also generalized to accommodate initial choice probabilities into the logit model an example is given key words choice models entropy kullback leibler discrimination information function relative importance

partially ordered permutation complexity of coupled time series abstract a new information theoretic complexity measure of coupling among multiple time series is proposed based on ordinal patterns we regard ordinal patterns extracted from time series as total orders and exploit their algebraic properties to introduce a multiplication among them the result of the multiplication is in general a partial order a kullback leibler divergence for the partial orders gives rise to a complexity measure of coupling in the sense that it vanishes in two extreme cases when time series are uncoupled and when they are identical the performance of the proposed complexity measure is tested on two model multivariate dynamical systems and its advantage over the existing complexity measures is discussed

information geometry on hierarchy of probability distributions an exponential family or mixture family of probability distributions has a natural hierarchical structure this paper gives an orthogonal decomposition of such a system based on information geometry a typical example is the decomposition of stochastic dependency among a number of random variables in general they have a complex structure of dependencies pairwise dependency is easily represented by correlation but it is more difficult to measure effects of pure triplewise or higher order interactions dependencies among these variables stochastic dependency is decomposed quantitatively into an orthogonal sum of pairwise triplewise and further higher order dependencies this gives a new invariant decomposition of joint entropy this problem is important for extracting intrinsic interactions in firing patterns of an ensemble of neurons and for estimating its functional connections the orthogonal decomposition is given in a wide class of hierarchical structures including both exponential and mixture families as an example we decompose the dependency in a higher order markov chain into a sum of those in various lower order markov chains

neural coding higher order temporal patterns in the neurostatistics of cell assemblies recent advances in the technology of multiunit recordings make it possible to test hebb s hypothesis that neurons do not function in isolation but are organized in assemblies this has created the need for statistical approaches to detecting the presence of spatiotemporal patterns of more than two neurons in neuron spike train data we mention three possible measures for the presence of higher order patterns of neural activation coef ficients of log linear models connected cumulants and redundancies and present arguments in favor of the coefficients of loglinear models we present test statistics for detecting the presence of higher order interactions in spike train data by parameterizing these interactions in terms of coefficients of log linear models we also present a bayesian approach for inferring the existence or absence of interactions and estimating their strength the two methods the frequentist and the bayesian one are shown to be consistent in the sense that interactions that are detected by either method also tend to be detected by the other a heuristic for the analysis of temporal patterns is also proposed finally a bayesian test is presented that establishes stochastic differences between recorded segments of data the methods are applied to experimental data and synthetic data drawn from our statistical models our experimental data are drawn from multiunit recordings in the prefrontal cortex of behaving monkeys the somatosensory cortex of anesthetized rats and multiunit recordings in the visual cortex of behaving monkeys

error estimates for the implicit mac scheme for the compressible navier stokes equations we prove existence of a solution to the implicit mac scheme for the compressible navier stokes equations we derive error estimates for this scheme on two and three dimensional cartesian grids error estimates are obtained by using the discrete version of the relative energy method introduced on the continuous level in feireisl et al j math fluid mech 14 4 717 730 2012 a systematic use of the theoretical continuous analysis of the equations in combination with the numerical tools is crucial for the result this error estimate does not uses stability hypotheses on the solution of the numerical scheme

multigrid solution of the two dimensional euler equations on unstructured triangular meshes a multigrid algorithm has been developed to accelerate the convergence of the euler equations to a steady state on unstructured triangular meshes the method operates on a sequence of coarse and fine unstructured meshes and assumes no relation exists between the various meshes a tree search algorithm is used to efficiently identify regions of overlap between coarse and fine grid cells the multigrid method is applied to two different discretizations of the euler equations and results about multi element airfoils are presented for both discretization schemes convergence is accelerated by an order of magnitude resulting in convergence rates comparable to those obtained with structured multigrid algorithms

extrapolation effects on coupled computational fluid dynamics computational structural dynamics simulations between them passing loads from the e ow code to the structural code and displacements back theother way forunsteady problems the sequencing is done within the pseudotime loop used for the e ow solver and removes sequencing errors the mesh movement for the aerodynamic solver is done using transe nite interpolation of displacements 7 we restrict ourselves in this note to the case of a wing modeled structurally by a plate this case is interesting as a building block to more complex structural descriptions transformation of data between the two grids is broken into two components in and out of the plane of the structural model the outplane treatment follows the considerations of ref 5 the in plane treatment turns out to have a much stronger ine uence on the test case considered next the two approaches used are the ine nite plate spline ips 8 and linear interpolation for ips a solution of the thin plate equation is forced to pass through the known structural points and is then evaluated at the projected aerodynamic points for the required displacements for linear interpolation each projected e uid point is associated with a triangle on the structural mesh and the deformation is calculated using a linear approximation within the triangle in both cases the relationship between displacements on the e uid and structural grids is linear and the principle of virtual work is then applied for transferring forces iii test cases

an asymptotic preserving all speed scheme for the euler and navier stokes equations we present an asymptotic preserving all speed scheme for the simulation of compressible flows valid at all mach numbers ranging from very small to order unity the scheme is based on a semi implicit discretization which treats the acoustic part implicitly and the convective and diffusive parts explicitly this discretization which is the key to the asymptotic preserving property provides a consistent approximation of both the hyperbolic compressible regime and the elliptic incompressible regime the divergence free condition on the velocity in the incompressible regime is respected and an the pressure is computed via an elliptic equation resulting from a suitable combination of the momentum and energy equations the implicit treatment of the acoustic part allows the time step to be independent of the mach number the scheme is conservative and applies to steady or unsteady flows and to general equations of state one and two dimensional numerical results provide a validation of the asymptotic preserving all speed properties

deforming mesh for computational aeroelasticity using a nonlinear elastic boundary element method a nonlinear elastic boundary element method nbem approach is developed as an innovative deforming mesh generator for computational aeroelastic simulation the computational fluid dynamics cfd mesh is assumed to be embedded in an infinite nonlinear elastic medium of a hardening material leading to the formulation of a pseudononlinear elastostatic problem whereas the cfd surface mesh is treated as a boundary element model and the cfd flowfield grid as domain sample points the nbem approach solves navier s equations using a particular solution scheme that removes the requirement of the domain integral in the conventional nbem formulation the nbem approach has a unified feature that is applicable to all mesh systems including unstructured multiblock structured and overset grids an optimization strategy is employed to determine the optimum hardening material properties by minimizing the mesh distortion in the viscous region where grid orthogonality must be preserved three test cases are performed to demonstrate the robustness and effectiveness of the nbem approach for deforming mesh generation

a superlinearly convergent finite volume method for the incompressible navier stokes equations on staggered unstructured grids a method for linear reconstruction of staggered vector fields with special treatment of the divergence is presented an upwind biased finite volume scheme for solving the unsteady incompressible navier stokes equations on staggered unstructured triangular grids that uses this reconstruction is described the scheme is applied to three benchmark problems and is found to be superlinearly convergent in space

irreducible multiparty correlations in quantum states without maximal rank the correlations of an n partite quantum state are classified into a series of irreducible k party ones 2 ensuremath le k ensuremath le n with the irreducible k party correlation being the correlation in the states of k parties but nonexistent in the states of k ensuremath 1 parties a measure of the degree of irreducible k party correlation is defined based on the principle of maximal entropy adopting a continuity approach we overcome the difficulties in calculating the degrees of irreducible multiparty correlations for the multipartite states without maximal rank in particular we obtain the degrees of irreducible multiparty correlations in the n qubit stabilizer states and the n qubit generalized greenberger horne zeilinger states which reveals the distribution of multiparty correlations

convergence of the mac scheme for the compressible stokes equations we prove in this paper the convergence of the marker and cell mac scheme for the discretization of the steady state compressible stokes equations on two or three dimensional cartesian grids the existence of a solution to the scheme is proven followed by estimates on approximate solutions which yield the convergence of the approximate solutions up to a subsequence and in an appropriate sense we then prove that the limit of the approximate solutions satisfies the mass and momentum balance equations as well as the equation of state which is the main difficulty of this study

interfacing of fluid and structural models via innovative structural boundary element method an innovative structural boundary element method bem solver is developed for interfacing the computational fluid dynamics cfd and computational structural dynamics csd grids formulated as a solid mechanics problem with a minimum strain energy requirement the bem solver generates a truly three dimensional universal spline matrix the universal spline matrix is a vector operator that includes the coupling of displacements and forces along all axes based on a similar formulation an exterior bem solver is also developed to account for the flowfield grid deformation thus the bem solver allows a unified treatment of the displacement and force transformation for cfd csd interfacing as well as the computation of the flowfield grid deformation the solution procedure is fully automated and no additional model generation is required therefore is ideally suitable for computational aeroelasticity and multidisciplinary optimization applications

high quality mesh deformation using quaternions for orthogonality preservation many mesh deformation techniques developed in the past have been widely used but for large deformations the mesh properties can be severely altered in particular the mesh lines orthogonality near the boundaries can be lost in this paper a method initially proposed by samareh application of quaternions for mesh deformation nasa tm 2002 211646 april 2002 is developed to overcome this limitation and to provide a high quality mesh orthogonality preservation technique each node displacement is composed of a translation vector and a quaternion which takes into account local mesh rotations algebraic unitary quaternion properties lie group algebra are used to obtain a robust interpolation method two quaternion interpolation methods are compared respectively the spherical linear interpolation and the lie algebra linear interpolation furthermore thanks to a new process transformation division the method becomes independent of the rotation center used the accuracy and generality of the met

linearized euler predictions of unsteady aerodynamic loads in cascades a linearized euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and vibratory blade motion is presented using the linearized euler technique one decomposes the flow into a mean or steady flow plus an unsteady harmonically varying small disturbance flow linear variable coefficient equations describe the small disturbance behavior of the flow and are solved using a pseudotime time marching lax wendroff scheme for the blade motion problem a harmonically deforming computational grid that conforms to the motion of vibrating blades eliminates large error producing mean flow gradient terms that would otherwise appear in the unsteady flow tangency boundary condition

statistical mechanics of the us supreme court we build simple models for the distribution of voting patterns in a group using the supreme court of the united states as an example the maximum entropy model consistent with the observed pairwise correlations among justices votes an ising spin glass agrees quantitatively with the data while all correlations perhaps surprisingly are positive the effective pairwise interactions in the spin glass model have both signs recovering the intuition that ideologically opposite justices negatively influence each another despite the competing interactions a strong tendency toward unanimity emerges from the model organizing the voting patterns in a relatively simple energy landscape besides unanimity other energy minima in this landscape or maxima in probability correspond to prototypical voting states such as the ideological split or a tightly correlated conservative core the model correctly predicts the correlation of justices with the majority and gives us a measure of their influence on the majority decision these results suggest that simple models grounded in statistical physics can capture essential features of collective decision making quantitatively even in a complex political context

application of the godunov method and its second order extension to cascade flow modeling the godunov method and a new second order accurate extension of the method are used for the solution of two dimensional euler equations both numerical schemes are described in detail their performances in the subsonic transonic and supersonic flow regimes are first tested on the problem of flow in a channel with a circular arc bump the niethods are then applied to calculate the transonic flow through a supercritical com pressor cascade designed by j sanzo for this case the solution with the second order extension of the godunov method gives verygood agreement with the design distribution of parameters given by sanzo

torsional springs for two dimensional dynamic unstructured fluid meshes abstract dynamic fluid grids are commonly used for the solution of flow problems with moving boundaries they are often represented by a network of fictitious lineal springs that can become unreliable when the fluid mesh undergoes large displacements and or deformations in this paper we propose to control the arbitrary motion of two dimensional dynamic unstructured fluid grids with additional torsional springs we show that such springs can be designed to prohibit the interpenetration of neighboring triangles and therefore to provide the method of spring analogy with the robustness needed for enlarging its range of applications we illustrate our new dynamic mesh motion algorithm with several examples that highlight its advantages in terms of robustness quality and performance

pairwise network information and nonlinear correlations reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines the fundamental first step is to establish whether or to what extent the interactions between the units can be considered pairwise and thus can be modeled as an interaction network with simple links corresponding to pairwise interactions in principle this can be determined by comparing the maximum entropy given the bivariate probability distributions to the true joint entropy in many practical cases this is not an option since the bivariate distributions needed may not be reliably estimated or the optimization is too computationally expensive here we present an approach that allows one to use mutual informations as a proxy for the bivariate probability distributions this has the advantage of being less computationally expensive and easier to estimate we achieve this by introducing a novel entropy maximization scheme that is based on conditioning on entropies and mutual informations this renders our approach typically superior to other methods based on linear approximations the advantages of the proposed method are documented using oscillator networks and a resting state human brain network as generic relevant examples

ghz extraction yield for multipartite stabilizer states let psi be an arbitrary stabilizer state distributed between three remote parties such that each party holds several qubits let s be a stabilizer group of psi we show that psi can be converted by local unitaries into a collection of singlets ghz states and local one qubit states the numbers of singlets and ghzs are determined by dimensions of certain subgroups of s for an arbitrary number of parties m we find a formula for the maximal number of m partite ghz states that can be extracted from psi by local unitaries a connection with earlier introduced measures of multipartite correlations is made an example of an undecomposable four party stabilizer state with more than one qubit per party is given these results are derived from a general theoretical framework that allows one to study interconversion of multipartite stabilizer states by local clifford group operators as a simple application we study three party entanglement in two dimensional lattice models that can be exactly solved by the stabilizer formalism

efficient mesh motion using radial basis functions with data reduction algorithms mesh motion using radial basis functions has been demonstrated previously by the authors to produce high quality meshes suitable for use within unsteady and aeroelastic cfd codes in the aeroelastic case the structural mesh may be used as the set of control points governing the deformation which is efficient since the structural mesh is usually small however as a stand alone mesh motion tool where the surface mesh points control the motion radial basis functions may be restricted by the size of the surface mesh as an update of a single volume point depends on all surface points in this paper a method is presented that allows an arbitrary deformation to be represented to within a desired tolerance by using a significantly reduced set of surface points intelligently identified in a fashion that minimises the error in the interpolated surface this method may be used on much larger cases and is successfully demonstrated here for a 10 6 cell mesh where the initial solve phase cost reduces by a factor of eight with the new scheme and the mesh update by a factor of 55 it has also been shown that the number of surface points required to represent the surface is only geometry dependent i e grid size independent and so this reduction factor actually increases for larger meshes

defect correction based velocity reconstruction for physically consistent simulations of non newtonian flows on unstructured grids abstract a new algorithm to recover centroidal velocities from face normal data on two dimensional unstructured staggered meshes is presented the proposed approach uses iterative defect correction in conjunction with a lower order accurate gauss reconstruction to obtain second order accurate centroidal velocities we derive the conditions that guarantee the second order accuracy of the velocity reconstruction and demonstrate its efficacy on arbitrary polygonal mesh topologies the necessity of the proposed algorithm for non newtonian flow simulations is elucidated through numerical simulations of channel flow driven cavity and backward facing step problems with power law and carreau fluids numerical investigations show that second order accuracy of the reconstructed velocity field is critical to obtaining physically consistent solutions of vorticity dominated flows on non orthogonal meshes it is demonstrated that the spurious solutions are not linked to discrete conservation and arise solely due to the lower order accuracy of velocity reconstruction the importance of the proposed algorithm for hemodynamic simulations is highlighted through studies of laminar flow in an idealized stenosed artery using different blood models

euler solution using cartesian grid with a gridless least squares boundary treatment an approach that uses gridless or meshless methods to address the problem of boundary implementation associated with the use of cartesian grid is discussed this method applies the gridless concept only at the interface whereas a standard structured grid method is used everywhere else the cartesian grid is used to specify and distribute the computational points on the boundary surface but not to define the geometrical properties euler fluxes for the neighbors of cut cells are computed using the gridless method involving a local least squares curve fit of a cloud of grid points the boundary conditions implemented on the surface points are automatically satisfied in the process of evaluating the surface values in a similar least squares fashion the present method does not require the use of halo points subsonic transonic and supersonic flows are computed for the naca 0012 and rae 2822 airfoils and the results compare well with solutions obtained by a standard euler solver on body fitted grids the method is also used to calculate the flow over a three element airfoil configuration and the result is compared with the exact solution for this configuration obtained by conformal mapping

time efficient aeroelastic simulations based on radial basis functions aeroelasticity studies the interaction between aerodynamic forces and structural responses and is one of the fundamental problems to be considered in the design of modern aircraft the fluid structure interpolation fsi and mesh deformation are two key issues in the cfd csd coupling approach the partitioned approach which is the mainstream numerical strategy in aeroelastic simulations in this paper a time efficient coupling scheme is developed based on the radial basis function interpolations during the fsi process the positive definite system of linear equations is constructed with the introduction of pseudo structural forces the acting forces on the structural nodes can be calculated more efficiently via the solution of the linear system avoiding the costly computations of the aerodynamic structural coupling matrix the multi layer sequential mesh motion algorithm msm is proposed to improve the efficiency of the volume mesh deformations which is adequate for large scale time dependent applications with frequent mesh updates two dimensional mesh motion cases show that the msm algorithm can reduce the computing cost significantly compared to the standard rbf based method the computations of the agard 445 6 wing flutter and the static deflections of the three dimensional high aspect ratio aircraft demonstrate that the developed coupling scheme is applicable to both dynamic and static aeroelastic problems

parallel efficient mesh motion using radial basis functions with application to multi bladed rotors radial basis functions are used to provide a solution to the problem of mesh motion for unsteady aerodynamic simulation the method is independent of connectivity and produces high quality meshes but is expensive for large meshes in its full form hence the efficiency of the technique has been greatly improved here by reducing the number of surface points used to define deformations of the surface and the minor error in position that this implies at other surface points is corrected with a simple decaying perturbation thus splitting the method into a primary basis function method and a secondary local correction method this means that the exact surface is retained but the mesh motion is significantly faster while splitting the motion into two stages allows both the methods to work on appropriate problems given their relative strengths an example deformation for a 5 x10 6 cell helicopter rotor mesh with an exaggerated cyclic pitch motion shows excellent mesh quality thus validating a scheme that is also simple robust and readily parallelized

a causal perspective on the analysis of signal and noise correlations and their role in population coding the role of correlations between neuronal responses is crucial to understanding the neural code a framework used to study this role comprises a breakdown of the mutual information between stimuli and responses into terms that aim to account for different coding modalities and the distinction between different notions of independence here we complete the list of types of independence and distinguish activity independence related to total correlations conditional independence related to noise correlations signal independence related to signal correlations coding independence related to information transmission and information independence related to redundancy for each type we identify the probabilistic criterion that defines it indicate the information theoretic measure used as statistic to test for it and provide a graphical criterion to recognize the causal configurations of stimuli and responses that lead to its existence using this causal analysis we first provide sufficiency conditions relating these types second we differentiate the use of the measures as statistics to test for the existence of independence from their use for quantification we indicate that signal and noise correlation cannot be quantified separately third we explicitly define alternative system configurations used to construct the measures in which noise correlations or noise and signal correlations are eliminated accordingly we examine which measures are meaningful only as a comparison across configurations and which ones provide a characterization of the actually observed responses without resorting to other configurations fourth we compare the commonly used nonparametric approach to eliminate noise correlations with a functional model based approach showing that the former approach does not remove those effects of noise correlations captured by the tuning properties of the individual neurons and implies nonlocal causal structure manipulations these results improve the interpretation of the measures on the framework and help in understanding how to apply it to analyze the role of correlations

conservation properties of unstructured staggered mesh schemes classic cartesian staggered mesh schemes have a number of attractive properties they do not display spurious pressure modes and they have been shown to locally conserve mass momentum kinetic energy and circulation to machine precision recently a number of generalizations of the staggered mesh approach have been proposed for unstructured triangular or tetrahedral meshes these unstructured staggered mesh methods have been created to retain the attractive pressure aspects and mass conservation properties of the classic cartesian mesh method this work addresses the momentum kinetic energy and circulation conservation properties of unstructured staggered mesh methods it is shown that with certain choices of the velocity interpolation unstructured staggered mesh discretizations of the divergence form of the navier stokes equations can conserve kinetic energy and momentum both locally and globally in addition it is shown that unstructured staggered mesh discretizations of the rotational form of the navier stokes equations can conserve kinetic energy and circulation both locally and globally the analysis includes viscous terms and a generalization of the concept of conservation in the presence of viscosity to include a negative definite dissipation term in the kinetic energy equation these novel conserving unstructured staggered mesh schemes have not been previously analyzed it is shown that they are first order accurate on nonuniform two dimensional unstructured meshes and second order accurate on uniform unstructured meshes numerical confirmation of the conservation properties and the order of accuracy of these unstructured staggered mesh methods is presented

adaptive radial basis function mesh deformation using data reduction radial basis function rbf mesh deformation is one of the most robust mesh deformation methods available using the greedy data reduction method in combination with an explicit boundary correction results in an efficient method as shown in literature however to ensure the method remains robust two issues are addressed 1 how to ensure that the set of control points remains an accurate representation of the geometry in time and 2 how to use automate the explicit boundary correction while ensuring a high mesh quality in this paper we propose an adaptive rbf mesh deformation method which ensures the set of control points always represents the geometry displacement up to a certain user specified criteria by keeping track of the boundary error throughout the simulation and re selecting when needed opposed to the unit displacement and prescribed displacement selection methods the adaptive method is more robust user independent and efficient for the cases considered secondly the analysis of a single high aspect ratio cell is used to formulate an equation for the correction radius needed depending on the characteristics of the correction function used maximum aspect ratio minimum first cell height and boundary error based on the analysis two new radial basis correction functions are derived and proposed this proposed automated procedure is verified while varying the correction function reynolds number and thus first cell height and aspect ratio and boundary error finally the parallel efficiency is studied for the two adaptive methods unit displacement and prescribed displacement for both the cpu as well as the memory formulation with a 2d oscillating and translating airfoil with oscillating flap a 3d flexible locally deforming tube and deforming wind turbine blade generally the memory formulation requires less work due to the large amount of work required for evaluating rbf s but the parallel efficiency reduces due to the limited bandwidth available between cpu and memory in terms of parallel efficiency scaling the different studied methods perform similarly with the greedy algorithm being the bottleneck in terms of absolute computational work the adaptive methods are better for the cases studied due to their more efficient selection of the control points by automating most of the rbf mesh deformation a robust efficient and almost user independent mesh deformation method is presented

eigenmode analysis of unsteady flows about airfoils we present a reduced order modelling technique for analyzing the unsteady subsonic aerodynamic flow about isolated airfoils to start we model the flow using the time linearized full potential equation the linearized potential equation is discretized on a computational mesh composed of quadrilateral elements using a variational finite element technique the resulting discretized equations are linear in the unknown potential but quadratic in the reduced frequency of vibration we compute the dominant low frequency eigenfrequencies and mode shapes of the unsteady fluid motion using a nonsymmetric lanczos algorithm and then we use these eigenmodes to construct a low degree of freedom reduced order model of the unsteady flow field a static correction technique is used to account for the high frequency eigenmodes not retained in the model we show that the unsteady flow can be modelled accurately using a relatively small number of eigenmodes

improved radial basis function fluid structure coupling via efficient localized implementation previous work by the authors has developed a universal interpolation scheme using radial basis functions rbfs which results in a unified formulation for robust fluid structure interpolation and high quality mesh motion the method has several significant advantages primarily all volume mesh structural mesh and flow solver type dependence is removed entirely as all operations are performed on totally arbitrary point clouds of any form hence all connectivity requirements are removed from both the coupling and mesh motion problems furthermore only matrix vector multiplications are required during unsteady simulation because dependence relations are computed once prior to any simulation and then remain constant this property means that the method is both perfectly parallel and totally independent from the flow solver however the full method is expensive since the dependence matrix between two sets of points is n points1 n points2 the fluid structure coupling behaviour can also be influenced by parameters used in the interpolation to alleviate these difficulties a more efficient form of the rbf fluid structure coupling is presented which also greatly reduces the interpolation parameter influence a pointwise form of the partition of unity approach is developed that localizes the interpolation with results presented for static aeroelastic simulations of the brite euram multi disciplinary optimization wing using a very fine mesh containing 58000 surface points it is shown that a 58 reduction in data size is achieved and equally importantly the interpolation has a much smaller influence on final aeroelastic results

network information and connected correlations entropy and information provide natural measures of correlation among elements in a network we construct here the information theoretic analog of connected correlation functions irreducible n point correlation is measured by a decrease in entropy for the joint distribution of n variables relative to the maximum entropy allowed by all the observed n 1 variable distributions we calculate the connected information terms for several examples and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source

statistical mechanics of letters in words we consider words as a network of interacting letters and approximate the probability distribution of states taken on by this network despite the intuition that the rules of english spelling are highly combinatorial and arbitrary we find that maximum entropy models consistent with pairwise correlations among letters provide a surprisingly good approximation to the full statistics of words capturing ensuremath sim 92 mathrm of the multi information in four letter words and even discovering words that were not represented in the data these maximum entropy models incorporate letter interactions through a set of pairwise potentials and thus define an energy landscape on the space of possible words guided by the large letter redundancy we seek a lower dimensional encoding of the letter distribution and show that distinctions between local minima in the landscape account for ensuremath sim 68 mathrm of the four letter entropy we suggest that these states provide an effective vocabulary which is matched to the frequency of word use and much smaller than the full lexicon

nonconsistent mesh movement and sensitivity calculation on adjoint aerodynamic optimization this paper presents an investigation of the influence of a nonconsistent approach in terms of mesh movement and mesh sensitivity calculation in a discrete adjoint based optimization some mesh movement methods are more robust or of higher quality whereas others can be more efficient for calculating mesh sensitivity it is found that a nonconsistent approach gives comparable results when compared to a consistent approach therefore an appropriate combination of nonconsistent approaches can be achieved for efficient adjoint optimization this paper investigates and compares various consistent and nonconsistent combinations by using linear elasticity delaunay graph mapping and radial basis function mesh movement methods an investigation is presented using a lift constrained drag minimization to assess which step of the chain introduces a deviation if any and to which degree this affects the final result

mesh deformation using the biharmonic operator the use of the biharmonic operator for deforming a mesh in an arbitrary lagrangian eulerian simulation is investigated the biharmonic operator has the advantage that two conditions can be specified on each boundary of the mesh this allows both the position and the normal mesh spacing along a boundary to be controlled which is important for two fluid interfaces and periodic boundaries at these boundaries we can simultaneously fix the position of the boundary and ensure that the normal mesh spacing is continuous across the boundary in addition results for deforming surfaces show that greater surface deformation can be tolerated when using biharmonic equations compared to approaches using second order partial differential equations a final advantage is that with the biharmonic operator the integrity of a grid in a moving boundary layer can be preserved as the boundary moves the main disadvantage of the approach is its increased computational expense

coupling dynamic mesh technique and heuristic algorithms in 3 d tapered wing design in this study onera m6 wing has been optimized by two parameters the wing section and the taper ratio by combining the recent mostly preferable popular approaches i e parallel computing and evolutionary techniques for the 3 d models developed during the optimization stages the mesh required has been generated by using dynamic mesh technique the code developed for this is robust and faster than the codes that produce mesh only by classical techniques an euler flow solver acer3d is used to obtain the flow parameters for each member from the results it is observed that the optimization process is working as expected during the optimization process the lift coefficient and the thickness ratio are tried to be maintained close to the design values determined at the beginning the taper ratio becomes smaller and converges to a certain value while the code tries to minimize the drag force additionally this study can be used as a reference for 2 d or 3 d aerodynamic body optimization by using heuristic type algorithms since all details are outlined referenced and interpreted with their advantages and disadvantages copyright 2007 john wiley sons ltd

efficient mesh motion using radial basis functions with volume grid points reduction algorithm abstract as one of the most robust mesh deformation technique available the radial basis function rbf mesh deformation has been accepted widely however for volume mesh deformation driven by surface motion the rbf system may become impractical for large meshes due to the large number of both surface control points and volume points surface points selection procedure based on the greedy algorithm results in an efficient implementation of the rbf based mesh deformation procedure the greedy algorithm could reduce the number of surface points involved in the rbf interpolation while acquire an acceptable accuracy as shown in literature to improve the efficiency of the rbf method furthermore an issue that how to reduce the number of the volume points needed to be moved is addressed in this paper we propose an algorithm for volume points reduction based on a wall distance based restricting function which is added to the formulation of the rbf based interpolation this restricting function is firstly introduced by the current article to support large deformation a multi level subspace interpolation is essentially needed although this technique was used to improve the efficiency of the surface points selection procedure in the existed literature the key point of this technique is setting the error of previous interpolation step as the object of current step and restricting interpolation region gradually because the tolerance of the error is decreased hierarchically the number of the surface points is increased but the number of the volume points needed to be moved is reduced gradually therefore the cpu cost of updating the mesh motion could be reduced eventually since it scales with the product of these two numbers the computational requirement of the proposed procedure is reduced evidently compared with the standard procedure as proved by some examples

fast dynamic grid deformation based on delaunay graph mapping a simple and efficient dynamic grid deformation technique is proposed for computing unsteady flow problems with geometrical deformation relative body movement or shape changes due to aerodynamic optimisation and fluid structure interaction a delaunay graph of the solution domain is first generated which can be moved easily during the geometric dynamic deformation even for very large distortion a one to one mapping between the delaunay graph and the computational grid is maintained during the movement therefore the new computational grid after the dynamic movement can be generated efficiently through the mapping while maintaining the primary qualities of the grid while most dynamic grid deformation techniques are iterative based on the spring analogy the present method is non iterative and much more efficient on the other hand in comparison with dynamic grid techniques based on transfinite interpolation for structured grids it offers both geometric and cell topology flexibility which is crucial for many unsteady flow problems involving geometric deformation and relative motions the method is demonstrated through some typical unsteady flow test cases including a pitching aerofoil in a fixed domain boundary relative movement between multi element aerofoils due to flap deployment for high lift a deformable sphere in a fixed cube and a three dimensional flexible wing with large deformation

eigenanalysis of unsteady flow about airfoils cascades and wings a general technique for constructing reduced order models of unsteady aerodynamic flows about two dimensional isolated airfoils cascades of airfoils and three dimensional wings is developed the starting point is a the domain computational model of the unsteady small disturbance flow for illustration purposes we apply the technique to an unsteady incompressible vortex lattice model the eigenmodes of the system which may be thought of as aerodynamic states are computed and subsequently used to construct computationally efficient reduced order models of the unsteady flowfield only a handful of the most dominant eigenmodes are retained in the reduced order model the effect of the remaining eigenmodes is included approximately using a static correction technique an important advantage of the present method is that once the eigenmode information has been computed reduced order models can be constructed for any number of arbitrary modes of airfold motion very inexpensively numerical examples are presented that demonstrate the accuracy and computational efficiency of the present method finally we show how the reduced order model may be incorporated into an aeroelastic flutter model

finite element euler computations in three dimensions an explicit finite element solution procedure for the three dimensional euler equations is presented the solution domain is automatically meshed using a tetrahedral mesh generator which is an extension of our previous two dimensional work several examples are included to illustrate the performance of the generator and solver an adaptive mesh regeneration procedure is used for the first time in three dimensions

ensemble inhibition and excitation in the human cortex an ising model analysis with uncertainties the pairwise maximum entropy model also known as the ising model has been widely used to analyze the collective activity of neurons however controversy persists in the literature about seemingly inconsistent findings whose significance is unclear due to lack of reliable error estimates we therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive markov chain monte carlo after the convergence of the main optimization algorithm we apply our method to the activity patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake sleep cycle our analysis shows that the ising model captures neuronal collective behavior much better than the independent model during wakefulness light sleep and deep sleep when both excitatory e and inhibitory i neurons are modeled ignoring the inhibitory effects of i neurons dramatically overestimates synchrony among e neurons furthermore information theoretic measures reveal that the ising model explains about 80 95 of the correlations depending on sleep state and neuron type thermodynamic measures show signatures of criticality although we take this with a grain of salt as it may be merely a reflection of long range neural correlations

a superlinearly convergent mach uniform finite volume method for the euler equations on staggered unstructured grids a mach uniform finite volume scheme for solving the unsteady euler equations on staggered unstructured triangular grids that uses linear reconstruction is described the scheme is applied to three benchmark problems and is found to be considerably more accurate than a similar scheme based on piecewise constant reconstruction

finite volume solution of the two dimensional euler equations on a regular triangular mesh the two dimensional euler equations have been solved on a triangular grid by a multigrid scheme using the finite volume approach by careful construction of the dissipative terms the scheme is designed to be secondorder accurate in space provided the grid is smooth except in the vicinity of shocks where it behaves as firstorder accurate in its present form the accuracy and convergence rate of the triangle code are comparable to that of the quadrilateral mesh code of jameson

unified fluid structure interpolation and mesh motion using radial basis functions a multivariate interpolation scheme using radial basis functions is presented which results in a completely unified formulation for the fluid structure interpolation and mesh motion problems the method has several significant advantages primarily all volume mesh structural mesh and flow solver type dependence is removed and all operations are performed on totally arbitrary point clouds of any form hence all connectivity and user input requirements are removed from the computational fluid dynamics computational structural dynamics cfd csd coupling problem as only point clouds are required to determine the coupling also it may equally well be applied to structured and unstructured grids or structural and aerodynamic grids that intersect again because no connectivity information is required furthermore no expensive computations are required during an unsteady simulation just matrix vector multiplications since the required dependence relations are computed only once prior to any simulation and then remain constant this property means that the method is both perfectly parallel since only the data relevant to each structured block or unstructured partition are required to move those points and totally independent from the flow solver hence a completely generic black box tool can be developed which is ideal for use in an optimization approach aeroelastic behaviour of the brite euram mdo wing is analysed in terms of both static deflection and dynamic responses and it is demonstrated that responses are strongly dependent on the exact cfd csd interpolation used mesh quality is also examined during the motion resulting from a large surface deformation global grid quality is shown to be preserved well with local grid orthogonality also being maintained well particularly at and near the moving surface where the original orthogonality is retained copyright 2007 john wiley sons ltd

aeroelastic design optimization for laminar and turbulent flows abstract the design of flexible structures undergoing aeroelastic deformations is a challenging task in particular if the prediction of the fluid loads and the evaluation of the aerodynamic performance criteria require accounting for laminar and turbulent effects this paper presents a general optimization methodology for fluid structure interaction problems based on turbulent flow models the structure is modeled via a geometrically nonlinear finite element method the flow field is computed by solving a finite volume approximation of the navier stokes equations on moving grids augmented by turbulence models the global design sensitivity equations are presented and solution methods for computing the numerically consistent and approximated design sensitivities are introduced the accuracy of the sensitivity analysis methods are studied by numerical examples for three dimensional problems the potential of the overall optimization methodology is illustrated by the shape and thickness optimization of a realistic wing the numerical examples suggest that the derivatives of the turbulence variables can be neglected in the sensitivity analysis without noticeable errors comparing the optimization results for euler and navier stokes flow models shows the importance of accounting for viscous laminar and turbulent effects for fine tuning the design and obtaining reliable optimization results

a monolithic approach to fluid structure interaction using space time finite elements abstract the paper presents a simultaneous solution procedure for fluid structure interaction problems the structural motion is described by geometrically nonlinear elastodynamics the fluid is modeled by the incompressible navier stokes equations the space time finite element method is applied to both continua leading to an almost uniform discretization in which velocity variables are used for fluid and structure in order to enforce momentum conservation and geometric continuity at the interface a weighted residual formulation of coupling conditions is introduced the discretized model equations for fluid structure and coupling conditions are formulated in a single equation system the nonlinear system and the fluid mesh movement are solved in a single iteration loop two dimensional examples of membrane flutter and vortex excited plate vibrations demonstrate the efficiency of the methodology

adjoint based airfoil optimization with adaptive isogeometric discontinuous galerkin method abstract in this work an adjoint based airfoil shape optimization algorithm is developed based on the adaptive isogeometric discontinuous galerkin method for compressible euler equations to investigate the significance of each design variable of airfoil b spline parameterization we first parameterize the airfoil by b spline curve approximation with some control points viewed as design variables and build the b spline representation of the flow field with the curve to apply the goal oriented h adaptive isogeometric dg method for flow solution then we compute and employ the discrete adjoint solutions for both multi target error estimation in adaptive mesh refinement with the isogeometric nature not only all the geometrical cells but also the numerical basis functions can be analytically expressed by the design variables indicating that the numerical solutions and objective could be differentiable with respect to those variables consequently the gradient is totally computed in an accurate approach and the sensitivity analysis is thus improved by reducing the spatial discretization error and introducing the analytical expression of derivative to reveal the key parameters for optimization in an intuitive and efficient manner although the sqp optimization algorithm is adopted in the paper the given accurate gradient can be applied to any gradient based optimization algorithm the proposed algorithm is demonstrated on rae2822 airfoil with inviscid transonic flow where the shape is optimized to minimize the drag coefficient at a constrained lift and airfoil area the numerical results show that the drag is much more sensitive to the design variables near the tailing edge at the beginning but sensitivity is reduced when optimal

unsteady euler algorithm with unstructured dynamic mesh for complex aircraft aerodynamic analysis an euler solution algorithm is presented for unsteady aerodynamic analysis of complex aircr aft configurations the flow solver involves a multistage runge kutta time stepping scheme that uses a finite volume spatial discretization on an unstructured grid made up of tetrahedra a significant contribution of the research is the development and implementation of a moving mesh algorithm that is employed for problems involving static or dynamic deformation of the aircraft the mesh algorithm is a general procedure that can treat realistic motions and deformations of complex aircraft configurations steady and unsteady results are presented for a supersonic fighter configuration to demonstrate applications of the euler solver and dynamic mesh algorithm the unsteady flow results were obtained for the aircraft oscillating harmonically in a complete vehicle bending mode effects of angle of attack and reduced frequency on instantaneous pressures and force responses were investigated the paper presents descriptions of the euler solver and dynamic mesh algorithm along with results that assess the capability

efficient method to eliminate mesh sensitivity in adjoint based optimization a method based on the delaunay graph mapping mesh movement is proposed to eliminate mesh sensitivity which is required in the discrete adjoint optimization framework the method makes use of a one to one explicit algebraic mapping between the volume and surface mesh nodes for which the relative volume coefficients based on the delaunay graph are computed only once this procedure also results in a straightforward computation of the mesh sensitivity without the need to invert the large sparse matrix generally associated with implicit mesh movements such as the spring analogy torsional spring and linear elastic analogy the advantage of the method comes from the fact that the solution of the second linear mesh adjoint system of equations is no longer required the method has been verified for the two dimensional rae 5243 airfoil and for the three dimensional onera m6 wing for two cases 1 sensitivities of the objective function with respect to each surface mesh point as a design variable compared with

market structure explained by pairwise interactions financial markets are a typical example of complex systems where interactions between constituents lead to many remarkable features here we give empirical evidence by making as few assumptions as possible that the market microstructure capturing almost all of the available information in the data of stock markets does not involve higher order than pairwise interactions we give an economic interpretation of this pairwise model we show that it accurately recovers the empirical correlation coefficients thus the collective behaviors are quantitatively described by models that capture the observed pairwise correlations but no higher order interactions furthermore we show that an order disorder transition occurs as predicted by the pairwise model last we make the link with the graph theoretic description of stock markets recovering the non random and scale free topology shrinking length during crashes and meaningful clustering features as expected

functional structure of cortical neuronal networks grown in vitro we apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown in vitro we infer connectivity between two neurons via the measurement of the mutual information between their spike trains in addition we measure higher point multi information between any two spike trains conditional on the activity of a third cell as a means to identify and distinguish classes of functional connectivity among three neurons the use of a conditional three cell measure removes some interpretational shortcomings of the pairwise mutual information and sheds light on the functional connectivity arrangements of any three cells we analyze the resultant connectivity graphs in light of other complex networks and demonstrate that despite their ex vivo development the connectivity maps derived from cultured neural assemblies are similar to other biological networks and display nontrivial structure in clustering coefficient network diameter and assortative mixing specifically we show that these networks are weakly disassortative small world graphs which differ significantly in their structure from randomized graphs with the same degree we expect our analysis to be useful in identifying the computational motifs of a wide variety of complex networks derived from time series data