power law shot noise the behavior of power law shot noise for which the associated impulse response functions assume a decaying power law form is explored expressions are obtained for the moments moment generating functions amplitude probability density functions autocorrelation functions and power spectral densities for a variety of parameters of the process for certain parameters the power spectral density exhibits 1 f type behavior over a substantial range of frequencies so that the process serves as a source of 1 f sup alpha shot noise for alpha in the range 0

a modified interpolated cell mapping method abstract a modified interpolated cell mapping micm method is developed for global analysis of deterministic dynamical systems with smooth basin boundaries by improving the algorithm of the interpolated cell mapping icm and including the idea of sampling mappings of cells from the generalized cell mapping gcm micm gives a more complete and precise global analysis of systems that icm in addition based on analysis using micm a method using exact mappings is proposed to remedy the inaccuracy and incompleteness of global analysis due to interpolated mappings and the assumption of the sink cell for the three systems studied in this paper this method locates identical attractors and basins of attraction as the integration of a grid of points igp method with a 100 fold improvement in computational efficiency

a procedure to find discrete representations of the efficient set with specified coverage errors an important issue in multiple objective mathematical programming is finding discrete representations of the efficient set because discrete points can be directly studied by a decision maker a discrete representation can serve as the solution to the multiple objective problem at hand however the discrete representation must be of acceptable quality to ensure that a most preferred solution identified by a decision maker is of acceptable quality recently attributes for measuring the quality of discrete representations have been proposed although discrete representations can be obtained in many different ways and their quality evaluated afterwards the ultimate goal should be to find such representations so as to conform to specified quality standards we present a method that can find discrete representations of the efficient set according to a specified level of quality the procedure is based on mathematical programming tools and can be implemented relatively easily when the domain of interest is a polyhedron the nonconvexity of the efficient set is dealt with through a coordinated decomposition approach we conduct computational experiments and report results

application of the incremental harmonic balance method to cubic non linearity systems abstract in this paper the formulation of the incremental harmonic balance ihb method is derived for a general system of differential equations with cubic non linearity which governs a wide range of engineering problems such as large amplitude vibration of beams or plates an incremental arc length method combined with a cubic extrapolation technique is adopted to trace the response curve automatically the stability of its periodic solutions can also be evaluated from the ihb formulation by multi variable floquet theory hsu s method is adopted for computing the transition matrix at the end of one period two numerical examples are presented which demonstrate the effectiveness of the ihb method and hsu s method in treating the non linear vibration of a strongly non linear multiple degree of freedom system

the entire regularization path for the support vector machine the support vector machine svm is a widely used tool for classification many efficient implementations exist for fitting a two class svm model the user has to supply values for the tuning parameters the regularization cost parameter and the kernel parameters it seems a common practice is to use a default value for the cost parameter often leading to the least restrictive model in this paper we argue that the choice of the cost parameter can be critical we then derive an algorithm that can fit the entire path of svm solutions for every value of the cost parameter with essentially the same computational cost as fitting one svm model we illustrate our algorithm on some examples and use our representation to give further insight into the range of svm solutions

non linear dynamic analysis and control of chaos for a two degrees of freedom rigid body with vibrating support abstract the dynamic behaviors of a two degrees of freedom rigid body with vibrating support are studied in this paper both analytical and computational results are employed to obtain the characteristics of the system by using the lyapunov direct method the conditions of stability of the relative equilibrium position can be determined the incremental harmonic balance method ihb is used to find the stable and unstable periodic solutions for the strongly non linear system by applying various numerical results such as phase plane poincare map time history and power spectrum analysis a variety of periodic solutions and the phenomena of the chaotic motion is presented the effects of the changes of parameters in the system can be found in the bifurcation diagrams further the chaotic behavior is verified by using lyapunov exponents the modified interpolated cell mapping method micm is used to study the basins of attraction of periodic attractors and the fractal structure besides additions of a constant torque a periodic torque addition of dither signals delayed feedback control adaptive control and bang bang control are used to control the chaos phenomena effectively

gaussian approximation for the wireless multi access interference distribution the problem of gaussian approximation for the wireless multi access interference distribution in large spatial wireless networks is addressed first a principled methodology is presented to establish rates of convergence of the multi access interference distribution to a gaussian distribution for general bounded and power law decaying path loss functions the model is general enough to also include various random wireless channel dynamics such as fading and shadowing arising from multi path propagation and obstacles existing in the communication environment it is shown that the wireless multi access interference distribution converges to the gaussian distribution with the same mean and variance at a rate 1 where 0 is a parameter controlling the intensity of the planar possibly non stationary poisson point process generating node locations an explicit expression for the scaling coefficient is obtained as a function of fading statistics and the path loss function second an extensive numerical and simulation study is performed to illustrate the accuracy of the derived gaussian approximation bounds a good statistical fit between the interference distribution and its gaussian approximation is observed for moderate to high values of

the multiobjective discrete optimization problem a weighted min max two stage optimization approach and a bicriteria algorithm we study the multiple objective discrete optimization modo problem and propose two stage optimization problems as subproblems to be solved to obtain efficient solutions the mathematical structure of the first level subproblem has similarities to both tchebycheff type of approaches and a generalization of the lexicographic max ordering problem that are applicable to multiple objective optimization we present some results that enable us to develop an algorithm to solve the bicriteria discrete optimization problem for the entire efficient set we also propose a modification of the algorithm that generates a sample of efficient solutions that satisfies a prespecified quality guarantee we apply the algorithm to solve the bicriteria knapsack problem our computational results on this particular problem demonstrate that our algorithm performs significantly better than an equivalent tchebycheff counterpart moreover the computational behavior of the sampling version is quite promising

chaos control of new mathieu van der pol systems with new mathieu duffing systems as functional system by gyc partial region stability theory abstract in this paper a new strategy by using gyc partial region stability theory is proposed to achieve chaos control using the gyc partial region stability theory the new lyapunov function used is a simple linear homogeneous function of error states and the lower order controllers are much more simple and introduce less simulation error numerical simulations are given for new mathieu van der pol system and new mathieu duffing system to show the effectiveness of this strategy

knowledge based proximal support vector machines we propose a proximal version of the knowledge based support vector machine formulation termed as knowledge based proximal support vector machines kbpsvms in the sequel for binary data classification the kbpsvm classifier incorporates prior knowledge in the form of multiple polyhedral sets and determines two parallel planes that are kept as distant from each other as possible the proposed algorithm is simple and fast as no quadratic programming solver needs to be employed effectively only the solution of a structured system of linear equations is needed

adaptive control in nonlinear dynamics abstract we extend an adaptive control algorithm recently suggested by huberman and lumer to multi parameter and higher dimensional nonlinear systems this control mechanism is remarkably effective in returning a system to its original dynamics after a sudden perturbation in the system parameters changes the dynamical behaviour we find that in all cases the recovery time is linearly proportional to the inverse of control stiffness for small stiffness in higher dimensions there is an additional optimization problem since increasing stiffness beyond a certain value can retard recovery the control of fixed point dynamics in systems capable of a wide variety of dynamical behaviour is demonstrated we further suggest methods by which periodic motion such as limit cycles can be adaptively controlled and demonstrate the robustness of the procedure in the presence of additive background noise

horseshoes in the driven damped pendulum abstract folding and horseshoes are found in two dimensional maps computed from simulations of the driven damped pendulum a simple model illustrates how horseshoes produce fractal boundaries of the basins of attraction for separate steady state solutions fractal basin boundaries result in noise amplification through extrinsic intermittency and in long transients when the dimension of the boundary approaches that of the phase space folding of the phase space beyond a crisis in which chaotic attractors collide with the boundary that separates their basins of attraction produces complex intermittent dynamical behavior both noise and crisis induced intermittency can produce power spectra s 1 with 1 over several decades in frequency

l1 regularization path algorithm for generalized linear models summary we introduce a path following algorithm for l1 regularized generalized linear models the l1 regularization procedure is useful especially because it in effect selects variables according to the amount of penalization on the l1 norm of the coefficients in a manner that is less greedy than forward selection backward deletion the generalized linear model path algorithm efficiently computes solutions along the entire regularization path by using the predictor corrector method of convex optimization selecting the step length of the regularization parameter is critical in controlling the overall accuracy of the paths we suggest intuitive and flexible strategies for choosing appropriate values we demonstrate the implementation with several simulated and real data sets

regular and chaotic dynamic analysis and control of chaos of an elliptical pendulum on a vibrating basement the dynamic behavior of an elliptical pendulum subjected to external disturbance is studied in this paper the lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of the system by applying numerical results phase diagrams power spectrum period t maps and lyapunov exponents are presented to observe periodic and chaotic motions the effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams for global analysis the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping micm method finally several methods the delayed feedback control the addition of constant torque the addition of periodic force adaptive control algorithm and bang bang control are used to control chaos effectively

periodic forced vibration of unsymmetrical piecewise linear systems by incremental harmonic balance method abstract a single degree of freedom non linear system subjected to periodic excitation is considered the non linearity is in the restoring force and is represented by unsymmetrical piecewise linear stiffness the steady state response are analysed by an extended incremental harmonic balance ihb method all possible subharmonic harmonic and superharmonic resonances and bifurcations are sought the results reveal some interesting details of responses of unsymmetrical piecewise linear systems comparisons with available published findings are also made

exploring the trade off between generalization and empirical errors in a one norm svm abstract we propose a one norm support vector machine svm formulation as an alternative to the well known formulation that uses parameter c in order to balance the two inherent objective functions of the problem our formulation is motivated by the constraint approach that is used in bicriteria optimization and we propose expressing the objective of minimizing total empirical error as a constraint with a parametric right hand side using dual variables we show equivalence of this formulation to the one with the trade off parameter we propose an algorithm that enumerates the entire efficient frontier by systematically changing the right hand side parameter we discuss the results of a detailed computational analysis that portrays the structure of the efficient frontier as well as the computational burden associated with finding it our results indicate that the computational effort for obtaining the efficient frontier grows linearly in problem size and the benefit in terms of classifier performance is almost always substantial when compared to a single run of the corresponding svm in addition both the run time and accuracy compare favorably to other methods that search part or all of the regularization path of svm

performance analysis of hypothesis testing for sparse pairwise interaction point processes the sufficient statistic for performing the likelihood ratio test for pairwise interaction point processes is well known however the evaluation of its performance is a very difficult problem it is shown that the distribution of the sufficient statistic can be approximated by the distribution of a poisson driven shot noise random variable which can be readily computed

pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control a new kind of generalized synchronization of two chaotic systems with uncertain parameters is proposed based on a pragmatical asymptotical stability theorem and an assumption of equal probability for ergodic initial conditions an adaptive control law is derived so that it can be proved strictly that the common null solution of error dynamics and of parameter dynamics is actually asymptotically stable i e these two identical systems are in generalized synchronization and the estimated parameters approach the uncertain values it is called pragmatical generalized synchronization finally two numerical examples are studied for two quantum cnn oscillator chaotic systems to show the effectiveness of the proposed generalized synchronization strategy with a double duffing chaotic system as a goal system

boosting as a regularized path to a maximum margin classifier in this paper we study boosting methods from a new perspective we build on recent work by efron et al to show that boosting approximately and in some cases exactly minimizes its loss criterion with an l1 constraint on the coefficient vector this helps understand the success of boosting with early stopping as regularized fitting of the loss criterion for the two most commonly used criteria exponential and binomial log likelihood we further show that as the constraint is relaxed or equivalently as the boosting iterations proceed the solution converges in the separable case to an l1 optimal separating hyper plane we prove that this l1 optimal separating hyper plane has the property of maximizing the minimal l1 margin of the training data as defined in the boosting literature an interesting fundamental similarity between boosting and kernel support vector machines emerges as both can be described as methods for regularized optimization in high dimensional predictor space using a computational trick to make the calculation practical and converging to margin maximizing solutions while this statement describes svms exactly it applies to boosting only approximately

sliding mode control in dynamic systems the concept of sliding modes in abstract dynamic systems described by a semigroup of state space transformations is introduced the sliding mode design procedure is used for designing finite observers sliding mode control for systems with delays and differential difference systems which is illustrated by sliding mode control of longitudinal oscillations

further results on the beaulieu series a frequent problem in digital communications is the computation of the probability density function pdf and cumulative distribution function cdf given the characteristic function chf of a random variable rv this problem arises in signal detection equalizer performance equal gain diversity combining intersymbol interference and elsewhere often it is impossible to analytically invert the chf to get the pdf and cdf in closed form beaulieu 1990 1991 has derived an infinite series for the cdf of a sum of rvs that has been widely used we rederive his series using the gil pelaez 1951 inversion formula and the poisson sum formula this derivation has several advantages including both the bridging of the well known sampling theorem with beaulieu s series and yielding a simple expression for calculating the truncation error term it is also shown that the pdf and cdf can be computed directly using a discrete fourier transform

solitons as invariant tori in the perturbed nonlinear schro dinger equation abstract stabilities of a bound state of nonlinear schrodinger solitons are studied in the presence of some hamiltonian perturbations by means of numerical and perturbational methods behaviours of perturbed solitons are explained by perturbed hamiltonians and finite dimensional properties of solitons are found to be preserved for small hamiltonian perturbations

algorithms for controlling chaotic motion application for the bvp oscillator the bvp oscillator is a biologically and physically important dynamical system exhibiting chaotic motion phaselocking phenomenon and so on in this paper we investigate the controlling of chaos in this system both when periodic and constant currents are present we use the various control algorithms and investigate their effectiveness in particular we study the controlling by the following mechanisms i adaptive control algorithm ii weak periodic perturbations iii ott grebogi yorke method iv weak feedback control and v addition of noise also we show the suppression of chaos by numerical models

non linear dynamics and chaos control of a physical pendulum with vibrating and rotating support the dynamic behavior of a physical pendulum system of which the support is subjected to both rotation and vertical vibration are studied in this paper both analytical and computational results are employed to obtain the characteristics of the system by using lyapunov s direct method the conditions of stability of the relative equilibrium position can be determined melnikov s method is applied to identify the existence of chaotic motion the incremental harmonic balance method is used to find the stable and unstable periodic solutions for the strong non linear system by applying various numerical results such as phase portrait pioncare map time history and power spectrum analysis a variety of the periodic solutions and the phenomena of the chaotic motion can be presented the effects of the changes of parameters in the system could be found in the bifurcation and parametric diagrams further chaotic motion can be verified by using lyapunov exponent and lyapunov dimension the global analysis of basin boundary and fractal structure are observed by the modified interpolated cell mapping method besides non feedback control delayed feedback control adaptive control and variable structure control are used to control the chaos effectively

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

computation of shot noise probability distributions and densities the computation of the cumulative distribution cdf the complementary cdf ccdf and the density of certain shot noise random variables is discussed after subtracting off a few terms that can be computed in closed form what remains can be approximated by a general method for approximating samples of a cdf or ccdf by summing a fourier series whose coefficients are modulated samples of their characteristic function to approximate the density a spline is fit to the cdf samples and then differentiated when the density has corners it is important that the spline have coincident knots at these locations for shot noise densities these locations are easily identified

analysis of avalanche diode receivers by saddlepoint integration the error probability in a binary fiber optical communication system whose receiver utilizes an avalanche diode detector is calculated by applying the method of numerical saddlepoint integration to laplace inversion integrals for the probabilities of errors of the first and second kinds it is shown how to choose the contours of integration for efficient numerical quadrature the effects of shot noise intersymbol interference and additive gaussian noise are taken into account and the decision level on the receiver output is set to minimize the average probability of error examples show how the method can be used in receiver design to select system parameters such as the output pulsewidth and the sampling time in order to minimize the probability of error