criteria for the assessment of random number generators abstract for any finite sequence of pseudo random numbers special simulation problems can be constructed such that this sequence yields useless results in order to study the quality of the result of a simulation the assessment of a pseudorandom number generator based on theoretical considerations is a great advantage several criteria for the assessment of random number generators are known the most important criteria are discussed

recurrence plots revisited abstract we show that recurrence plots rps give detailed characterizations of time series generated by dynamical systems driven by slowly varying external forces for deterministic systems we show that rps of the time series can be used to reconstruct the rp of the driving force if it varies sufficiently slowly if the driving force is one dimensional its functional form can then be inferred up to an invertible coordinate transformation the same results hold for stochastic systems if the rp of the time series is suitably averaged and transformed these results are used to investigate the nonlinear prediction of time series generated by dynamical systems driven by slowly varying external forces we also consider the problem of detecting a small change in the driving force and propose a surrogate data technique for assessing statistical significance numerically simulated time series and a time series of respiration rates recorded from a subject with sleep apnea are used as illustrative examples

one way hash function construction based on 2d coupled map lattices an algorithm for constructing one way hash function based on spatiotemporal chaos is proposed a two dimensional coupled map lattices 2d cml with parameters leading to the largest lyapunov exponent is employed the state of the 2d cml is dynamically determined by its previous state and the message bit at the corresponding positions the hash value is obtained by a linear transform on the final state of the 2d cml theoretical analysis and computer simulation indicate that our algorithm has good statistical properties strong collision resistance and high flexibility it is practical and reliable with high potential to be adopted as a strong hash function for providing data integrity

random walks exterior to a rectangle the author shows how to simulate random walks terminating on the periphery of a rectangle both in the continuum and on a square lattice the method is error free in principle except for a negligible bias arising from the rejection of very long walks the average machine time would be o 1 step in the modified procedure this method may be useful in exploring the distinction between the continuum and the lattice in diffusion limited aggregation

a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

on the shannon measure of entropy abstract this paper deals with the axiomatic characterization of shannon s entropy for generalized probability distributions a renyi 1961 also the author has extended shannon s entropy to subsets of n dimensional euclidean space n 1 2 3 finally he has introduced a functional equation which is a generalization of the one due to t w chaundy and j b mcleod 1963

a piecewise linear chaotic map and sequential quadratic programming based robust hybrid particle swarm optimization this paper presents a novel robust hybrid particle swarm optimization rhpso based on piecewise linear chaotic map pwlcm and sequential quadratic programming sqp the aim of the present research is to develop a new single objective optimization approach which requires no adjustment of its parameters for both unconstrained and constrained optimization problems this novel algorithm makes the best of ergodicity of pwlcm to help pso with the global search while employing the sqp to accelerate the local search five unconstrained benchmarks eighteen constrained benchmarks and three engineering optimization problems from the literature are solved by using the proposed hybrid approach the simulation results compared with other state of art methods demonstrate the effectiveness and robustness of the proposed rhpso for both unconstrained and constrained problems of different dimensions

local shannon entropy measure with statistical tests for image randomness in this paper we propose a new image randomness measure using shannon entropy over local image blocks the proposed local shannon entropy measure overcomes several weaknesses of the conventional global shannon entropy measure including unfair randomness comparisons between images of different sizes failure to discern image randomness before and after image shuffling and possible inaccurate scores for synthesized images statistical tests pertinent to this new measure are also derived this new measure is therefore both quantitative and qualitative the parameters in the local shannon entropy measure are further optimized for a better capture of local image randomness the estimated statistics and observed distribution from 50 000 experiments match the theoretical ones finally two examples are given applying the proposed measure to image randomness among shuffled images and encrypted images both examples show that the proposed method is more effective and more accurate than the global shannon entropy measure

design of image cipher using block based scrambling and image filtering an image cipher using block based scrambling and image filtering ic bsif is introduced it is the first time that image filtering is used to do encryption ic bsif uses the well known substitution permutation network and strictly follows the principles of confusion and diffusion the block based scrambling is to fast separate neighboring pixels to different rows and columns and thus can sufficiently weaken the strong correlation between adjacent pixels ic bsif can encrypt different kinds of images into noise like ones and security evaluations demonstrate that it can achieve better performance than some state of the art encryption schemes the operation of image filtering is widely used to deblur digital images however using inappropriate masks it can also blur images motivated by this concept this paper introduces an image cipher using block based scrambling and image filtering ic bsif to the best of our knowledge this is the first time that image filtering has been used for image encryption ic bsif uses the well known substitution permutation network and strictly follows the concepts of confusion and diffusion the block based scrambling is able to separate neighboring pixels to different rows and columns and thus can efficiently weaken the strong correlations between adjacent pixels using randomly generated masks by the secret key the image filtering can spread little change of plain images to the entire pixels of cipher images simulation results show that ic bsif can encrypt different kinds of images into noise like ones and security evaluations demonstrate that it can achieve better performance than several state of the art encryption schemes

on the global controllability of nonlinear systems fountains recurrence and applications to hamiltonian systems in this paper a form of open local accessibility for nonlinear control systems is introduced called the continuous fountain condition subject to the conditions that i the states of a system are continuous fountains and ii one of various recurrence conditions holds it is established that the system state space is globally controllable it is shown that these controllability results imply the controllability of certain subsets of the state space of hamiltonian control systems called energy slices the relations between the notion of a fountain and i local accessibility and ii the full lie algebra rank condition for control affine systems are investigated finally the results in this paper are shown to have application to hierarchical hybrid control theory in that they give conditions for a finite analytic partition to satisfy the so called in block controllability property this is illustrated with a linear mass spring system example

globally valid adaptive controllers of mechanical systems the adaptive controller design of a large class of mechanical systems is addressed in this paper the configuration space for the attitude of a vehicle is modelled as so 3 namely the rotation matrix group to avoid singularity problems some studies adopt the representation of unit quaternions for modeling system dynamics and for the design of controllers however the complicated formulation of quatrains makes the application of this method limited to simple mechanical systems here the strategy is to carry out the modeling and analysis in terms of the global representations of jet bundles of so 3 while the unit quaternion is chosen to implement the controller for its least number of parameters four to represent so 3 globally based on the transformation between the rotation matrix and the quaternion the method explored in this paper gives rise to an adaptive controller in a clean and efficient way

a chaos based symmetric image encryption scheme using a bit level permutation in recent years a variety of chaos based digital image encryption algorithms have been suggested most of these algorithms implement permutations and diffusions at the pixel level by considering the pixel as the smallest atomic element of an image in fact a permutation at the bit level not only changes the position of the pixel but also alters its value here we propose an image cryptosystem employing the arnold cat map for bit level permutation and the logistic map for diffusion simulations have been carried out and analyzed in detail demonstrating the superior security and high efficiency of our cryptosystem

position space calculation of a two loop lattice diagram the authors evaluate the finite portion in the massless limit of a two loop graph built on a pair of polyakov lines in scalar phi 3 theory on an infinite hypercubical lattice in 3 1 dimensions the actual calculation involves only three dimensions they calculate in position space using propagators obtained by a method previously described by means of the laplace difference equation they are able to obtain the answer as a function of r0 the separation of the polyakov lines for all r0 in a large cube in a single procedure the cpu time vax 780 is about 6 ms per inequivalent value of r0 most of the time is taken by two two dimensional fast fourier transforms however the values calculated pertain to the infinite lattice in their main calculation 41 2 minutes 45760 inequivalent values they obtain 8 decimal accuracy over most of the domain this far surpasses the momentum space method in both speed and accuracy

keyed hash function based on a chaotic map secure hash functions play a fundamental role in cryptographic and web applications they are mainly used within digital signature schemes to verify the integrity and authenticity of information in this paper we propose a simple and efficient keyed hash function based on a single chaotic map theoretical and simulation results demonstrate that the suggested scheme satisfies all cryptographic requirements of secure keyed hash functions such as strong confusion and diffusion capability good collision resistance high sensitivity to message and secret key etc furthermore it is fast and can be easily implemented through software or hardware moreover the length of the hash value is flexible without any impact on the algorithm this function is shown to have better statistical performance than many existing hash functions thus the suggested hash function seems to be a good candidate as a secure keyed hash function for use in cryptographic applications

multicavity formations and complexity modulation in a hyperchaotic discrete system abstract this paper introduces a novel and unified approach for controlling the directions and number of cavities of a two dimensional sine icmic modulation map 2d simm two controllers are added to the system for arranging the cavity fluctuations and translating the cavities respectively both the controllers can effectively redesign the dynamics of reproducing cavities in different directions with grid representations the dynamics of the proposed controlled model are investigated with bifurcation lyapunov and fuzzyen algorithms under various cavity formations in different directions a relationship is established for the complexity of the phase space with the directional control and various arrangements of the sinusoidal cavities the proposed model is overall hyperchaotic with the high complexity in the whole parameter plane the proposed scheme is effective for a dynamical model to reproduce the self phase structure in various arrangements for the optimization and modulation of complexity

local equilibrium controllability of multibody systems controlled via shape change we study local equilibrium controllability of shape controlled multibody systems the multibody systems are defined on a trivial principal fiber bundle by a lagrangian that characterizes the base body motion and shape dynamics a potential dependent on an advected parameter e g uniform gravitational potential is considered this potential breaks base body symmetries but a symmetry subgroup is assumed to exist symmetric product formulas are derived and important properties are obtained for symmetric products of horizontal shape control vector fields and a potential vector field that is dependent on an advected parameter based on these properties sufficient conditions for local equilibrium controllability and local fiber equilibrium controllability are developed these results are applied to two classes of shape controlled multibody systems in a uniform gravitational field multibody attitude systems and neutrally buoyant multibody underwater vehicles

the characterization of a measure of information discrepancy abstract a function of degree of disagreement fdod function has been introduced in the study of information discrepancies among multiple information sources w fang mathematical social sciences 28 2 1994 85 111 j global optim 11 1997 387 408 it possesses some peculiar properties and can be applied in some areas in which the traditional measures of information discrepancy are not valid for example in the study of multiple dna sequence comparison in this paper based on the ideas concerned with shannon entropy and measures of difference we investigate its characterization the final results and even intermediate results show a close connection between the fdod function and shannon entropy

cluster aggregation by shortest path travel the authors have studied a new growth process of cluster aggregation in this process particles are released randomly from a hypersphere enclosing the cluster and stick to those perimeter sites of the growing cluster which are closest at shortest distance to the releasing sites they find d 1 62 or 0 09 for d 2 and d 2 02 or 0 13 for d 3 for the fractal dimensions d of such aggregates in euclidean dimension d using hentschel s mean field theory for generalised cluster aggregations they argue that these aggregates should have the least fractal dimension because of maximum screening present in this model among all the aggregation models in which particles coming from outside form the aggregates the mean field values of d predicted by the theory are shown to be comparable with observation

image encryption using 2d logistic adjusted sine map with complex properties of ergodicity unpredictability and sensitivity to initial states chaotic systems are widely used in cryptography this paper proposes a two dimensional logistic adjusted sine map 2d lasm performance evaluations show that it has better ergodicity and unpredictability and a wider chaotic range than many existing chaotic maps using the proposed map this paper further designs a 2d lasm based image encryption scheme las ies the principle of diffusion and confusion are strictly fulfilled and a mechanism of adding random values to plain image is designed to enhance the security level of cipher image simulation results and security analysis show that las ies can efficiently encrypt different kinds of images into random like ones that have strong ability of resisting various security attacks

self similarity versus self affinity the sierpinski gasket revisited a hilbert curve is constructed on the sierpinski gasket it is shown that despite the fact that the sierpinski gasket is rigorously self similar the hilbert curve is merely self affine

2d sine logistic modulation map for image encryption because of the excellent properties of unpredictability ergodicity and sensitivity to their parameters and initial values chaotic maps are widely used in security applications in this paper we introduce a new two dimensional sine logistic modulation map 2d slmm which is derived from the logistic and sine maps compared with existing chaotic maps it has the wider chaotic range better ergodicity hyperchaotic property and relatively low implementation cost to investigate its applications we propose a chaotic magic transform cmt to efficiently change the image pixel positions combining 2d slmm with cmt we further introduce a new image encryption algorithm simulation results and security analysis demonstrate that the proposed algorithm is able to protect images with low time complexity and a high security level as well as to resist various attacks

randomizing nonlinear maps via symbolic dynamics abstract pseudo random number generators prng have attracted intense attention due to their obvious importance for many branches of science and technology a randomizing technique is a procedure designed to improve the prng randomness degree according the specific requirements it is obviously important to quantify its effectiveness in order to classify randomizing techniques based on a symbolic dynamics approach we advance a novel physically motivated representation based on the statistical properties of chaotic systems recourse is made to a plane that has as coordinates i the shannon entropy and ii a form of the statistical complexity measure each statistical quantifier incorporates a different probability distribution function generating thus a representation that i sheds insight into just how each randomizing technique operates and also ii quantifies its effectiveness using the logistic map and the three way bernoulli map as typical examples of chaotic dynamics it is shown that our methodology allows for choosing the more convenient randomizing technique in each instance comparison with measures of complexity based on diagonal lines on the recurrence plots n marwan m c romano m thiel j kurths phys rep 438 2007 237 support the main conclusions of this paper

a skew symmetric property of rigid body systems the configuration space for the attitude of a vehicle can be modeled as so 3 namely the rotation matrix group this work investigates the globally valid dynamics of natural lagrangian systems and gyroscopic systems with configuration space including so 3 the dynamics is derived by using the global representations of jet bundles of so 3 a skew symmetric property associated with the systems can be then established such property can be used in many applications such as the adaptive controller design

controllability of a class of underactuated mechanical systems with symmetry in this paper we develop results based on geometric mechanics to study the controllability of a class of controlled under actuated left invariant mechanical systems on lie groups we exploit the invariance of the controlled nonlinear dynamics to the group action symmetry to derive a set of reduced dynamics for the system we first present sufficient conditions for the controllability of the reduced dynamics we prove conditions boundedness of coadjoint orbits and existence of a radially unbounded lyapunov function under which the drift vector field of the reduced system is weakly positively poisson stable wpps the wpps nature of the drift vector field along with the lie algebra rank condition is used to show controllability of the reduced system we then extend these results to the unreduced dynamics considering separately the cases when the symmetry group is compact and noncompact in the noncompact case under further assumptions of equilibrium controllability sufficient conditions for controllability of the unreduced dynamics are derived jetpuck hovercraft and underwater vehicles are used as mechanical systems to motivate our work and illustrate our theoretical results

discrete fractional wavelet transform and its application to multiple encryption the fractional wavelet transform is a useful mathematical transformation that generalizes the most prominent tool in signal and image processing namely wavelet transform by rotation of signals in the time frequency plane the definition of discrete fractional wavelet transform is not reported yet in the literature therefore a definition of the discrete fractional wavelet transform is consolidated by discretizing continuous fractional wavelet transform in the proposed work possible applications of the transform are in transient signal processing image analysis image transmission biometrics image compression etc in this paper image transmission is chosen as the primary application and hence a novel encryption scheme is proposed for securing multiple images during communication and transmission over insecure channel the proposed multiple image encryption scheme is consolidated by fractional wavelet transform and chaotic maps first all the images are encrypted followed by their sharing the sharing process is done considering numerical techniques by making the sharing process a system of linear equations experimental results and security analysis demonstrate the efficiency and robustness of the proposed primary application

small time local controllability of spacecraft attitude using control moment gyros nonlinear controllability theory is utilized to investigate the small time local controllability stlc of the combined dynamics of a spacecraft with control moment gyros cmgs specifically speaking with three or more independent type cmgs the dynamics are stlc from and hence can be stabilized via time invariant piecewise continuous feedback laws to the equilibrium as long as the cmgs never reach certain definite singularities and semidefinite singularities at the equilibrium these results are then applied to a spacecraft carrying four pyramid type cmgs and further extended to a spacecraft using roof type cmgs in addition to the special case of two cmgs

2d sudoku associated bijections for image scrambling sudoku refers to a two dimensional 2d number placement puzzle with simple constraints that there are no repeated digits in each row each column or each block motivated by this sudoku configuration we introduce a number of sudoku associated matrix element representations besides the conventional representation using matrix row column pair specifically they are representations via sudoku matrix row digit pair digit row pair column digit pair digit column pair block digit pair and digit block pair this means we can secretly represent matrix elements via a sudoku matrix and furthermore develop new sudoku associated 2d parametric bijections to demonstrate the effectiveness and randomness of bijections we introduce a simple but effective sudoku associated image scrambler only using 2d sudoku associated bijections for image scrambling without bandwidth expansion simulations and comparisons demonstrate that the proposed method outperforms several state of the art methods

cross entropy measure of uncertain variables ross entropy is a measure of the difference between two distribution functions in order to deal with the divergence of uncertain variables via uncertainty distributions this paper aims at introducing the concept of cross entropy for uncertain variables based on uncertain theory as well as investigating some mathematical properties of this concept several practical examples are also provided to calculate uncertain cross entropy furthermore the minimum cross entropy principle is proposed in this paper finally a study of generalized cross entropy for uncertain variables is carried out

the structure of two dimensional witten sander aggregates a relatively large number 102 103 of reasonably large about 105 particles or sites two dimensional witten sander aggregates are simulated using new algorithms this enables the reduction of statistical errors by an order of magnitude and provides an opportunity to determine some new quantities describing in more detail the structure of witten sander clusters a quantitate description of the distortion of large lattice based witten sander clusters into a diamond like shape is provided the orientational correlation in the bond directions for off lattice witten sander clusters is also measured this quantity has a power law dependence on distance with an exponent of about 0 37

negentropy as a function of cumulants suppose f is a density that is close to that of a standard normal for the first time exact expressions are given for the negentropy the differential entropy and related quantities such as fr x r 1 x dx for r 2 3 in terms of cumulants several advantages of our expressions over known ones are pointed out

a randomness test for block ciphers this paper describes a randomness test which can be used to measure the cryptographic strength of a block cipher or its underlying cryptographic primitive s cryptographic strength in the context of this paper is related to the ability of the round function to produce a random output which in turn is defined as the distance between a theoretical calculation and an experimental measure the measurements are based on the diffusion characteristic of the cipher potentially the test for randomness proposed in this paper could be used as a distinguisher based on diffusion

is it really possible to grow isotropic on lattice diffusion limited aggregates in a recent paper bogoyavlenskiy v a 2002 j phys a math gen 35 2533 an algorithm aiming to generate isotropic clusters of the on lattice diffusion limited aggregation dla model was proposed the procedure consists of aggregation probabilities proportional to the squared number of occupied sites k2 in the present work we analysed this algorithm using the noise reduced version of the dla model and large scale simulations in the noiseless limit instead of isotropic patterns a 45 30 rotation in the anisotropy directions of the clusters grown on square triangular lattices was observed a generalized algorithm in which the aggregation probability is proportional to k was proposed the exponent has a nonuniversal critical value c for which the patterns generated in the noiseless limit exhibit the original axial anisotropy for c the values c 1 395 0 005 and c 0 82 0 01 were found for square and triangular lattices respectively moreover large scale simulations show that there is a nontrivial relation between the noise reduction and anisotropy direction the case 2 bogoyavlenskiy s rule is an example where the patterns exhibit the axial anisotropy for small and the diagonal one for large noise reduction

laplacian growth with separately controlled noise and anisotropy conformal mapping models are used to study the competition of noise and anisotropy in laplacian growth for this purpose a family of models is introduced with the noise level and directional anisotropy controlled independently fractalization is observed in both anisotropic growth and growth with varying noise the fractal dimension is determined from the cluster size scaling with cluster area for isotropic growth d 1 7 at both high and low noise for anisotropic growth with reduced noise the dimension can be as low as d 1 5 and apparently is not universal also we study the fluctuations of particle areas and observe in agreement with previous studies that exceptionally large particles may appear during growth leading to pathologically irregular clusters this difficulty is circumvented by using an acceptance window for particle areas

diffusion limited aggregation improved algorithms have been developed for both off lattice and hypercubic lattice diffusion limited aggregation dla in dimensionalities d 3 8 and for two dimensional off lattice dla in two dimensional off lattice dla a fractal dimensionality d of about 1 71 was obtained for clusters containing up to 10 6 particles this is significantly larger than the value of d 2 1 d 1 5 3 for d 2 predicted by mean field theories for d 2 the off lattice simulations give results that are consistent with the mean field theories for d 3 and d 4 the effects of lattice anisotropy can easily be seen for clusters containing 3 x 10 6 and 10 6 sites respectively and the effective fractal dimensionalities are slightly smaller for the lattice model clusters than for the off lattice clusters results are also presented for two three and four dimensional lattice model clusters with noise reduction

progress in dla research abstract the diffusion limited aggregation dla model has become an important paradigm for non equilibrium pattern formation and provides a basis for understanding a broad range of natural processes progress in the simulation and quantitative characterization of dla clusters is described despite advances in this direction and extensive theoretical studies the dla process and the scaling structure of dla clusters are still not well understood clusters generated by the dla model have a fractal geometry but it is not certain whether the asymptotic structure is self similar or must be described by a more complex scaling model lattice anisotropy has a strong influence on the asymptotic shape of dla clusters and the asymptotic stucture of dla clusters with anisotropy and noise reduction is relatively well understood

a novel lossless color image encryption scheme using 2d dwt and 6d hyperchaotic system this paper proposes a new lossless encryption algorithm for color images based on a six dimensional 6d hyperchaotic system and the two dimensional 2d discrete wavelet transform dwt different from the current image encryption methods our image encryption scheme is constructed using the 2d dwt and 6d hyperchaotic system in both the frequency domain and the spatial domain where the key streams depend on not only the hyperchaotic system but the plain image in the presented algorithm the plain image is firstly divided into four image sub bands by means of the 2d dwt secondly the sub bands are permutated by a key stream and then the size of them is decreased by a constant factor thirdly the 2d inverse dwt is employed to reconstruct an intermediate image by the four encrypted image sub bands finally to further enhance the security the pixel values of the intermediate image are modified by using another key stream experimental results and security analysis demonstrate that the proposed algorithm has a high security fast speed and can resist various attacks

on small controllability and controllability of a class of nonlinear systems in this paper small controllability and controllability of a class of nonlinear systems are studied both the discrete time case and continuous time case are considered by proposing an implicit function approach sufficient conditions for the systems respectively to be small controllable and controllable are obtained examples are also provided to illustrate the results of the paper

controllability of poisson systems sufficient conditions for the controllability of affine nonlinear control systems on poisson manifolds are given the important special case when the poisson manifold is the reduced space of a symplectic manifold by a free lie group action is studied the controllability of the reduced system is linked to that of the given affine nonlinear system several examples illustrating the theory are also presented

invasion percolation in an external field dielectric breakdown in random media the authors propose a model to describe electric discharge in inhomogeneous insulators by introducing an external laplacian field in the invasion percolation model the patterns generated have a fractal structure with a tunable fractal dimension

noise reduced diffusion limited deposition to investigate the role of fluctuations in diffusion limited growth the authors apply the noise reduction algorithm to the problem of two dimensional deposition on a substrate consisting of a straight line the authors consider the scaling of the height and the width of trees growing on the square lattice for the sizes studied they find two length scales characterised by different exponents depending on the noise reduction parameter m using these exponents the effective fractal dimension deff of trees is calculated and for m 1 they obtain deff approximately 1 57 the density profile in the direction of growth and the scaling properties of the lateral correlation function are also determined

control systems which generate decomposable lie algebras let x y be real analytic vector fields on an n manifold m ad x y x y denote the lie product inductively ad k 1 x y x ad k x y and 1 ad v x y v 0 the attainable set at time t denoted download full size image t for the control system 1 x x x u t y x x 0 p u t 1 is contained in the integral manifold through p of the lie algebra l 1 generated by 1 l 1 is said to be decomposable at p if essentially when dim l 1 p n the solution of 1 can be written as exp tx exp f 1 t u v 1 exp f n t u v n p with v 1 v n l 1 this is true for example at any p if l 1 is nilpotent the f i t u are shown to satisfy a system on n of the form 2 x i u t g i t x 1 x i 1 x i 0 0 i 1 n where if l 1 is nilpotent each g i is a polynomial in x 1 x i 1 in this case reachability properties of 2 for controls being countably additive measures impluses reduce to the study of algebraic equations homogeneity allows these to be considered on projective space n giving local results by bezout s theorem similar results hold for controls in the unit ball of krener s results on approximating systems of the form 1 by systems which generate nilpotent lie algebras can then be used to remove the condition that l 1 be nilpotent the method applies to show that if m denotes the set of all products of k elements of 1 with k m and dim span m 1 p dim span m for all odd m then exp tx p int download full size image t for all t 0

null controllable region of delta operator systems subject to actuator saturation abstractin this paper we give exact description of null controllable regions for delta operator systems subject to actuator saturation the null controllable region is in terms of a set of extremal trajectories of anti stable subsystems for the delta operator system with real eigenvalues or complex eigenvalues the description is simplified to an explicit formula which is used to characterise the boundary of a null controllable region the relations of null controllable regions are shown separately for continuous time systems discrete time systems and delta operator systems two numerical examples are given to illustrate the effectiveness of the proposed techniques on null controllable regions

controllability of spacecraft systems in a central gravitational field the configuration space for rigid spacecraft systems in a central gravitational field can be modeled by so 3 spl times ir sup 3 where the special orthogonal group so 3 represents the attitude dynamics and ir sup 3 is for the orbital motion the attitude dynamics of the spacecraft system is affected by the orbital elements through the well known gravity gradient torque on the other hand the effects of attitude orbit coupling can also possibly be used to alter orbital motions by controlling the attitude this controllability property is the primary issue of this paper the control systems for spacecraft with either reaction wheels or gas jets being used as attitude controllers are proven in this study to be controllable rigorously establishing these results necessitates starting with the formal definitions of controllability and poisson stability it is then shown that if the drift vector field of the system is weakly positively poisson stable and the lie algebra rank condition is satisfied controllability can be concluded the hamiltonian structure of the spacecraft model provides a natural route of verifying the property of weakly positive poisson stability accordingly the controllability is obtained after confirming the lie algebra rank condition developing a methodology in deriving lie brackets in the tangent space of t so 3 spl times ir sup 3 i e the second tangent bundle is thus deemed necessary a general formula is offered for the computation of lie brackets of second tangent vector fields in tt so 3 sup m spl times ir sup n in light of its importance in the fields of mechanics robotics optimal control and nonlinear control among others with these tools the controllability results can be proved the analysis in this paper gives some insight into the attitude orbit coupling effects and may potentially lead towards new techniques in designing controllers for large spacecraft systems

circular inter intra pixels bit level permutation and chaos based image encryption the new image encryption architecture presented in this paper employs a novel circular inter intra pixels bit level permutation strategy this strategy aims to reduce redundancies implied by the fridrich s structure the newly proposed scheme was subject to extensive security analyses including statistical and differential analysis and information entropy calculation these highlight a desirable security level provided by the insurance of the coveted confusion and diffusion factors

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

a general efficient method for chaotic signal estimation this article presents a general computationally efficient method for chaotic signal estimation based on the connection between the symbolic sequence and the initial condition of a chaotic system the performance of the method in white gaussian noise is evaluated the new method is asymptotically unbiased and attains the cramer rao lower bound at high signal to noise ratios

image encryption to protect image contents most existing encryption algorithms are designed to transform an original image into a texture like or noise like image which is however an obvious visual sign indicating the presence of an encrypted image and thus results in a significantly large number of attacks to address this problem this paper proposes a new image encryption concept to transform an original image into a visually meaningful encrypted one as an example of the implementation of this concept we introduce an image encryption system simulation results and security analysis demonstrate excellent encryption performance of the proposed concept and system

random walks for on lattice dla simulations two efficient ways to accelerate on lattice dla simulations without introducing any bias are presented the first requires one dimensional tables but little arithmetic the second needs no tables but necessitates the evaluation of a few elementary functions

geological entropy and solute transport in heterogeneous porous media we propose a novel approach to link solute transport behavior to the physical heterogeneity of the aquifer which we fully characterize with two measurable parameters the variance of the log k values math formula and a new indicator hr that integrates multiple properties of the k field into a global measure of spatial disorder or geological entropy from the results of a detailed numerical experiment considering solute transport in k fields representing realistic distributions of hydrofacies in alluvial aquifers we identify empirical relationship between the two parameters and the first three central moments of the distributions of arrival times of solute particles at a selected control plane the analysis of experimental data indicates that the mean and the variance of the solutes arrival times tend to increase with spatial disorder i e hr increasing while highly skewed distributions are observed in more orderly structures i e hr decreasing or at higher math formula we found that simple closed form empirical expressions of the bivariate dependency of skewness on hr and math formula can be used to predict the emergence of non fickian transport in k fields considering a range of structures and heterogeneity levels some of which based on documented real aquifers the accuracy of these predictions and in general the results from this study indicate that a description of the global variability and structure of the k field in terms of variance and geological entropy offers a valid and broadly applicable approach for the interpretation and prediction of transport in heterogeneous porous media

fractal dimension from the back scattering cross section the feasibility of recovering the fractal dimension of self similar fractals from the back scattering measurements is demonstrated for this purpose the well known sierpinski gasket is modelled as an ensemble of lossless dielectric beads and the scattered field computations are carried out using the coupled dipole approximation procedure

image cryptographic algorithm based on the haar wavelet transform lossless encryption methods are more applicable than lossy encryption methods when marginal distortion is not tolerable in this research the authors propose a novel lossless symmetric key encryption decryption technique in the proposed algorithm the image is transformed into the frequency domain using the haar wavelet transform then the image sub bands are encrypted in a such way that guarantees a secure reliable and an unbreakable form the encryption involves scattering the distinguishable frequency data in the image using a reversible weighting factor amongst the rest of the frequencies the algorithm is designed to shuffle and reverse the sign of each frequency in the transformed image before the image frequencies are transformed back to the pixel domain the results show a total deviation in pixel values between the original and encrypted image the decryption algorithm reverses the encryption process and restores the image to its original form the proposed algorithm is evaluated using standard security and statistical methods results show that the proposed work is resistant to most known attacks and more secure than other algorithms in the cryptography domain

filtered noise can mimic low dimensional chaotic attractors this contribution presents four results first calculations indicate that when examined by the grassberger procaccia algorithm alone filtered noise can mimic low dimensional chaotic attractors given the ubiquity of signal filtering in experimental investigations this is potentially important second a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor third it is shown that a criterion derived by eckmann and ruelle physica d 56 185 1992 to estimate the minimum number of data points required in a grassberger procaccia calculation can be used to provide a further check on these dimension estimates fourth it is shown that surrogate data techniques recently published by theiler and his colleagues in nonlinear modeling and forecasting edited by m casdagli and s eubanks addison wesley reading ma 1992 can successfully distinguish between linearly correlated noise and nonlinear structure these results and most particularly the first indicate that grassberger procaccia results must be interpreted with far greater circumspection than has previously been the case and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data when filtered signals are examined by this algorithm alone a finite noninteger value of mathit d 2 is consistent with low dimensional chaotic behavior but it is certainly not a definitive diagnostic of chaos

a multiscale guide to brownian motion we revise the levy s construction of brownian motion as a simple though rigorous approach to operate with various gaussian processes a brownian path is explicitly constructed as a linear combination of wavelet based geometrical features at multiple length scales with random weights such a wavelet representation gives a closed formula mapping of the unit interval onto the functional space of brownian paths this formula elucidates many classical results about brownian motion e g non differentiability of its path providing intuitive feeling for non mathematicians the illustrative character of the wavelet representation along with the simple structure of the underlying probability space is different from the usual presentation of most classical textbooks similar concepts are discussed for brownian bridge fractional brownian motion ornstein uhlenbeck process gaussian free field and fractional gaussian fields wavelet representations and dyadic decompositions form the basis of many highly efficient numerical methods to simulate gaussian processes and fields including brownian motion and other diffusive processes in confining domains

personalized information encryption using ecg signals with chaotic functions the development of efficient data encryption to ensure high security of information transmission has long been a popular research subject because electrocardiogram ecg signals vary from person to person and can be used as a new tool for biometric recognition this study introduces an individual feature of ecg with chaotic henon and logistic maps for personalized cryptography this study also develops an encryption algorithm based on the chaos theory to generate initial keys for chaotic logistic and henon maps the proposed personalized encryption system uses a convenient handheld device to collect ecg signals from the user high quality randomness in ecg signals results in a widely expanded key space making it an ideal key generator for personalized data encryption the experiments reported in this study demonstrate the use of this approach in encrypting texts and images and applied of the proposed approach to secure communications

generating connected textured fractal patterns using markov random fields an algorithm that yields textured and connected binary fractals is presented the texture is imposed by modelling the fractal as a markov random field mrf at every resolution level the model size and the parameters specify the texture the generation starts at a coarser level and continues at finer levels connectivity which is a global property is maintained by restricting the flow of the sample generating markov chain within a limited subset of all possible outcomes of the markov random field the texture is controlled by the parameters of the mrf model being used sample patterns are shown

topological properties of diffusion limited aggregation and cluster cluster aggregation the detailed topological or connectivity properties of the clusters formed in diffusion limited aggregation dla and cluster cluster aggregation cca are considered for spatial dimensions d 2 3 and 4 specifically for both aggregation phenomena the authors calculate the fractal dimension dmin nu 1 defined by l approximately rd min where l is the shortest path between two points separated by a pythagorean distance r for cca they find that dmin increases monotonically with d presumably tending toward a limiting value dmin 2 at the upper critical dimensionality dc as found previously for lattice animals and percolation for dla on the other hand they find that dmin 1 within the accuracy of the calculations for d 2 3 and 4 suggesting the absence of an upper critical dimension they also discuss some of the subtle features encountered in calculating dmin for dla

fast evaluation of lattice green functions numerical methods for obtaining lattice green functions are presented the whole array to arbitrary distance on an infinite lattice can be generated in approximately 50 mu s cpu vax per site the accuracy is close to machine error for small mass the coefficients of the power series expansion can be generated similarly results are given in two and three dimensions

a symmetric image encryption algorithm based on mixed linear nonlinear coupled map lattice abstract we propose a new image encryption algorithm based on the spatiotemporal chaos of the mixed linear nonlinear coupled map lattices this spatiotemporal chaotic system has more outstanding cryptography features in dynamics than the logistic map or the system of coupled map lattices does in the proposed image encryption we employ the strategy of bit level pixel permutation which enables the lower bit planes and higher bit planes of pixels permute mutually without any extra storage space simulations have been carried out and the results demonstrate the superior security and high efficiency of the proposed algorithm

flux to a trap the flux of particles to a single trap is investigated for two systems 1 particles in 3d space which jump a fixed step lengthl the rayleigh flight and are adsorbed by a spherical surface and 2 particles on a lattice jumping to nearest neighbor sites with a single adsorbing site initially the particles are uniformly distributed outside the traps when the jump length goes to zero both processes go over to regular diffusion and the first case yields the diffusive flux to a sphere as solved by smoluchowski for nonzero step length the flux for large times is given by a modified form of smoluchowski s result with the effective radius replaced byr cl wherec 0 29795219 andcl is the milne extrapolation length for this problem for the second problem a similar expression for the flux is found with the effective trap radius a function of the lattice sc bcc fcc being considered

multiscaling analysis of large scale off lattice dla abstract an improved algorithm has been used to simulate off lattice diffusion limited aggregation dla in two dimensions this enables us to grow clusters of up to 6 106 particles which are the largest such clusters made up to now the density profile in two dimensions is analyzed for the scaling form multiscaling g r r r d d x c x with x r r where r is the radius of gyration and r is the distance from the cluster origin in contrast with previous studies the dimension d x shows no symmetric tendency to drop at values of x but only fluctuates around the global fractal dimension d 1 712 0 003

a globally convergent angular velocity observer for rigid body motion the problem of obtaining the angular velocity of a rigid body from orientation and torque measurements only without noisy numerical differentiation is considered a novel angular velocity angular momentum observer for rigid body motion is presented using euler quaternions and a mechanical energy function approach it is shown that the observer estimates converge globally and that the convergence is eventually exponential it is hoped that a mechanical energy function approach to rigid body control can be combined with the observer presented to lead to a globally stable nonlinear observer based rigid body controller in which the observer and controller errors can be separated in much the same way as one can separate controller and observer poles in the output feedback controllers of linear system theory

controllability of nonlinear time varying systems applications to spacecraft attitude control using magnetic actuation nonlinear controllability theory is applied to the time varying attitude dynamics of a magnetically actuated spacecraft in a keplerian orbit in the geomagnetic field first sufficient conditions for accessibility strong accessibility and controllability of a general time varying system are presented these conditions involve application of lie algebraic rank conditions to the autonomous extended system obtained by augmenting the state of the original time varying system by the time variable and require the rank conditions to be checked only on the complement of a finite union of level sets of a finite number of smooth functions at each point of each level set it is sufficient to verify escape conditions involving lie derivatives of the functions defining the level sets along linear combinations over smooth functions of vector fields in the accessibility algebra these sufficient conditions are used to show that the attitude dynamics of a spacecraft actuated by three magnetic actuators and subjected to a general time varying magnetic field are strongly accessible if the magnetic field and its time derivative are linearly independent at every instant in addition if the magnetic field is periodic in time then the attitude dynamics of the spacecraft are controllable these results are used to show that the attitude dynamics of a spacecraft actuated by three magnetic actuators in a closed keplerian orbit in a nonrotating dipole approximation of the geomagnetic field are strongly accessible and controllable if the orbital plane does not coincide with the geomagnetic equatorial plane

an improved estimator of dimension and some comments on providing confidence intervals abstract an estimator of dimension is described that has many advantages over the conventional implementation of the grassberger procaccia method it can in some circumstances provide a confidence interval for the dimension estimate for high dimension sets greater than about 3 5 the dimension estimate has a bias which depends on the structure of the set if one has suitable knowledge of the structure of the set it is possible to make a bias adjustment some numerical calculations are presented which indicate the largest error in the dimension estimate that can be expected the problem of providing confidence intervals for dimension estimates in general is not solved completely but we do take a step away from a meaningless number

the attitude control problem a general framework for the analysis of the attitude tracking control problem for a rigid body is presented a large family of globally stable control laws is obtained by using the globally nonsingular unit quaternion representation in a lyapunov function candidate whose form is motivated by the consideration of the total energy of the rigid body the controllers share the common structure of a proportional derivative feedback plus some feedforward which can be zero the model independent case the coriolis torque compensation or an adaptive compensation these controller structures are compared in terms of the requirement on the a priori model information guaranteed transient performance and robustness the global stability of the luh walker paul robot end effector controller is also analyzed in this framework

algebraic break of image ciphers based on discretized chaotic map lattices in this paper we provide an algebraic cryptanalysis of a recently proposed chaotic image cipher we show that the secret parameters of the algorithm can be revealed using chosen plaintext attacks our attack uses the orbit properties of the permutation maps to deduce encryption values for a single round once a single round encryption is revealed the secret parameters are obtained using simple assignments

hierarchy of effective sizes of dla clusters the authors discuss the possibility of having an infinite hierarchy of length scales characterising the moments of the laplacian field outside dla clusters in the entire space this hierarchy constitutes a multifractality for dla which is different from the usual one associated with the near field of these clusters the radius of gyration and the hydrodynamic radius are both members of this new family of length scales they present numerical simulations on the usual dla model and on the fracture growth model i e elastic dla testing this hypothesis

compression unimpaired batch image encryption combining vector quantization and index compression as the network bandwidth has grown rapidly it has become common to share a large number of still images via the internet by means of batch transmission unfortunately most existing methods encrypt only a single image so there is room for improvement in our ability to send batches of images at one time a complete reconstruction of the methods is sometimes necessary especially when considering performance criteria this paper presents a novel batch image encryption algorithm that combines vector quantization vq and additional index compression process to benefit from their computational efficiency and low transmission bandwidth without affecting the original compression rate the experimental results show the performance of this new scheme in terms of compression rate and computational cost

true random number generator based on mouse movement and chaotic hash function a true random number generator trng makes use of a non deterministic source to produce randomness it is considered as more secure than a pseudorandom number generator as the degree of randomness is higher in this letter we propose a novel trng which generates random bits by moving the mouse casually it is convenient universal and low cost for the personal computer pc platform to eliminate the regular patterns of mouse movements caused by the habit of the same user we propose three trngs based on chaotic hash functions experiments are conducted to evaluate the speed diffusion and randomness performance of these trngs the results show that two of them possess satisfactory performance and can be implemented on common pc platform

a new method to estimate the kolmogorov entropy from recurrence plots its application to neuronal signals recurrence plots are a useful graphic tool for studying dynamical systems a new variable is proposed to quantify their deterministic structure it allows an easy computation of the k2 entropy since the distance between points needs to be calculated only once instead of every time for each new embedding dimension and it bypasses some of the limitations inherent to the classical grassberger and procaccia method it is valuable for biological data as illustrated here by tests with various dynamical models and its application to experimental signals recorded from neurons