backlund transformation and soliton interactions for the zakharov kuznetsov equation in plasmas abstract symbolically investigated in this paper is the zakharov kuznetsov equation which describes the propagation of the electrostatic excitations in a magnetized rotating and collisionless three component plasma bilinear form and backlund transformation for the zakharov kuznetsov equation are derived with the hirota method and symbolic computation n soliton solutions in terms of the wronskian determinant are constructed and the verification is finished through the direct substitution into bilinear equations propagation characteristics and interaction behaviors of the solitons are discussed through a graphical analysis during the propagation the one soliton width and amplitude are both unchanged and not related to the coefficients while the soliton interactions are elastic

face alignment by explicit shape regression we present a very efficient highly accurate explicit shape regression approach for face alignment unlike previous regression based approaches we directly learn a vectorial regression function to infer the whole facial shape a set of facial landmarks from the image and explicitly minimize the alignment errors over the training data the inherent shape constraint is naturally encoded into the regressor in a cascaded learning framework and applied from coarse to fine during the test without using a fixed parametric shape model as in most previous methods to make the regression more effective and efficient we design a two level boosted regression shape indexed features and a correlation based feature selection method this combination enables us to learn accurate models from large training data in a short time 20 min for 2 000 training images and run regression extremely fast in test 15 ms for a 87 landmarks shape experiments on challenging data show that our approach significantly outperforms the state of the art in terms of both accuracy and efficiency

new multiple soliton like solutions to the generalized 2 1 dimensional kp equation a new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations pdes in a unified way the main idea of this method is to take full advantage of the riccati equation which has more new solutions more new multiple soliton like solutions are obtained for the the generalized 2 1 dimensional kp equation

a functional regression approach to facial landmark tracking linear regression is a fundamental building block in many face detection and tracking algorithms typically used to predict shape displacements from image features through a linear mapping this paper presents a functional regression solution to the least squares problem which we coin continuous regression resulting in the first real time incremental face tracker contrary to prior work in functional regression in which b splines or fourier series were used we propose to approximate the input space by its first order taylor expansion yielding a closed form solution for the continuous domain of displacements we then extend the continuous least squares problem to correlated variables and demonstrate the generalisation of our approach we incorporate continuous regression into the cascaded regression framework and show its computational benefits for both training and testing we then present a fast approach for incremental learning within cascaded continuous regression coined iccr and show that its complexity allows real time face tracking being 20 times faster than the state of the art to the best of our knowledge this is the first incremental face tracker that is shown to operate in real time we show that iccr achieves state of the art performance on the 300 vw dataset the most recent large scale benchmark for face tracking

image denoising via sparse and redundant representations over learned dictionaries we address the image denoising problem where zero mean white and homogeneous gaussian additive noise is to be removed from a given image the approach taken is based on sparse and redundant representations over trained dictionaries using the k svd algorithm we obtain a dictionary that describes the image content effectively two training options are considered using the corrupted image itself or training on a corpus of high quality image database since the k svd is limited in handling small image patches we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image we show how such bayesian treatment leads to a simple and effective denoising algorithm this leads to a state of the art denoising performance equivalent and sometimes surpassing recently published leading alternative denoising methods

the hirota s direct method and the tanh coth method for multiple soliton solutions of the sawada kotera ito seventh order equation abstract in this work the sawada kotera ito seventh order equation is studied the tanh coth method is applied to obtain soliton solution of this equation the hirota s direct method combined with the simplified hereman s method are applied to determine the n soliton solutions for this equation the study highlights the significant features of the employed methods and its capability of handling completely integrable equations

exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method the authors present a systematic and formal approach toward finding solitary wave solutions of nonlinear evolution and wave equations from the real exponential solutions of the underlying linear equations the physical concept is one of the mixing of these elementary solutions through the nonlinearities in the system the emphasis is however on the mathematical aspects i e the formal procedure necessary to find single solitary wave solutions by means of examples it is shown how various cases of pulse type and kink type solutions are to be obtained by this method an exhaustive list of equations so treated is presented in tabular form together with the particular intermediate relations necessary for deriving their solutions the extension of the technique to construct n soliton solutions and indicate connections with other existing methods is outlined

g g expansion method for the fifth order forms of kdv sawada kotera equation in this work we establish the traveling wave solution with parameters of the kdv sawada kotera equation by using the g g expansion method this method is effectively employed when the parameters are taken as special values solitary periodic and rational solutions are obtained

the application of the auxiliary equation technique to a generalized mkdv equation with variable coefficients the auxiliary differential equation technique is employed to investigate a generalized mkdv equation with variable coefficients the jacobi elliptic function wave like solutions of the equation are expressed under several circumstances the degenerated soliton like and trigonometric function solutions are discussed in detail as the modulus of the jacobi elliptic wave like solutions tends to 1 and 0 respectively

towards a unified framework for pose expression and occlusion tolerant automatic facial alignment we propose a facial alignment algorithm that is able to jointly deal with the presence of facial pose variation partial occlusion of the face and varying illumination and expressions our approach proceeds from sparse to dense landmarking steps using a set of specific models trained to best account for the shape and texture variation manifested by facial landmarks and facial shapes across pose and various expressions we also propose the use of a novel ell 1 regularized least squares approach that we incorporate into our shape model which is an improvement over the shape model used by several prior active shape model asm based facial landmark localization algorithms our approach is compared against several state of the art methods on many challenging test datasets and exhibits a higher fitting accuracy on all of them

link between solitary waves and projective riccati equations many solitary wave solutions of nonlinear partial differential equations can be written as a polynomial in two elementary functions which satisfy a projective hence linearizable riccati system from that property the authors deduce a method for building these solutions by determining only a finite number of coefficients this method is much shorter and obtains more solutions than the one which consists of summing a perturbation series built from exponential solutions of the linearized equation they handle several examples for the henon heiles hamiltonian system they obtain several exact solutions one of them defines a new solitary wave solution for a coupled system of boussinesq and nonlinear schrodinger equations for a third order dispersive equation with two monomial nonlinearities they isolate all cases where the general solution is single valued

backlund transformations and abundant exact explicit solutions of the sharma tasso olver equation abstract by using an extension of the homogeneous balance method and maple the backlund transformations for the sharma tasso olver equation are derived the connections between the sharma tasso olver equation and some linear partial differential equations are found with the aid of the transformations given here and the computer program maple 12 abundant exact explicit special solutions to the sharma tasso olver equation are constructed in addition to all known solutions re deriving in a systematic way several entirely new and more general exact explicit solitary wave solutions can also be obtained these solutions include a the algebraic solitary wave solution of rational function b single soliton solutions c double soliton solutions d n soliton solutions e singular traveling solutions f the periodic wave solutions of trigonometric function type and g many non traveling solutions by using the airy s function and the backlund transformations obtained here the exact explicit solution of the initial value problem for the sto equation is presented the variety of the structure of the solutions for the sharma tasso olver equation is illustrated

existence and non existence of area minimizing hypersurfaces in manifolds of non negative ricci curvature we study minimal hypersurfaces in manifolds of non negative ricci curvature euclidean volume growth and quadratic curvature decay at infinity by comparison with capped spherical cones we identify a precise borderline for the ricci curvature decay above this value no complete area minimizing hypersurfaces exist below this value in contrast we construct examples

local exponential stabilization of fisher s equation using the backstepping technique abstract this paper deals with the boundary stabilization problem for the 1d fisher s partial differential equation pde defined on a bounded interval which is a nonlinear unstable distributed parameter system the stabilizing controller derived using the backstepping technique for linear parabolic pdes associated with fisher s pde can be extended to the nonlinear case in the work we can prove that the boundary controller based on the linear backstepping synthesis approach can make the closed loop nonlinear fisher s system exponentially stable with any desired decay rate locally in both l 2 0 1 and h 1 0 1 respectively the effectiveness of the control synthesis approach is illustrated by a numerical simulation

exact solutions of some nonlinear partial differential equations abstract we implemented a generalized tanh function method for approximating the solution of the combined korteweg de vries ckdv equation and sharma tasso olver equation by using this scheme we found some exact solutions of the ckdv equation and sharma tasso olver equation for the further investigation of the method some exact solutions of the boussinesq equation and the complexly coupled kdv equations have been obtained

stably embedded minimal hypersurfaces we use schoen s curvature estimates to prove that the subfocal tubular neighborhood of a nonplanar minimal hypersurface with bounded second fundamental form stably embedded in mathbb r n 1 n 5 whose radius decays sufficiently slowly cannot be embedded in particular such hypersurfaces admit no embedded tubular neighborhoods of constant radius whatever small the radius however assuming a further hypothesis on the embedding we prove that such hypersurfaces admit an embedded tube whose radius decays sufficiently fast

the tanh coth method for solitons and kink solutions for nonlinear parabolic equations abstract the tanh coth method is used to derive solitons and kink solutions for some of the well known nonlinear parabolic partial differential equations the equations include the fisher equation newell whithead equation allen cahn equation fitzhugh nagumo equation fisher s equation and the burgers fisher equation the new tanh coth approach provides abundant solitons and kink solutions in addition to the existing ones the power of this manageable method is confirmed

exact solutions for the nonlinear schrodinger equation with variable coefficients using the generalized extended tanh function the sine cosine and the exp function methods abstract in this article we find the exact traveling wave solutions of the generalized nonlinear schrodinger gnls equation with variable coefficients using three methods via the generalized extended tanh function method the sine cosine method and the exp function method the main objective of this article is to compare the efficiency of these methods by delivering the exact traveling wave solutions of the proposed nonlinear equation

exact solutions for some nonlinear evolution equations which describe pseudo spherical surfaces for some nonlinear evolution equations which describe pseudo spherical surfaces two new exact solution classes are generated from known solutions either the seed solution is constant or a traveling wave exact traveling wave and solitary wave solutions for burgers equation and also for a fifth order evolution equation containing the fifth order korteweg de vries equation and also the sawada kotera equation are obtained by using an improved sine cosine method and the wu s elimination method we also apply backlund transformations to these solutions and generate new soliton solution classes

active appearance models revisited active appearance models aams and the closely related concepts of morphable models and active blobs are generative models of a certain visual phenomenon although linear in both shape and appearance overall aams are nonlinear parametric models in terms of the pixel intensities fitting an aam to an image consists of minimising the error between the input image and the closest model instances i e solving a nonlinear optimisation problem we propose an efficient fitting algorithm for aams based on the inverse compositional image alignment algorithm we show that the effects of appearance variation during fitting can be precomputed projected out using this algorithm and how it can be extended to include a global shape normalising warp typically a 2d similarity transformation we evaluate our algorithm to determine which of its novel aspects improve aam fitting performance

new exact solutions for the generalized variable coefficient gardner equation with forcing term abstract in this work we study the generalized variable coefficient gardner equation gvg with nonlinear terms of any order and forcing term abundant new exact solutions for the equation are obtained by using the general mapping deformation method with the aid of symbolic computation which include several kinds of types such as jacobi elliptic wave like solutions soliton like solutions trigonometric function solutions weierstrass elliptic function solution and rational type solution some of them are found for the first time which shows that the applied method is more powerful and will be used in further works to establish more entirely new exact solutions for other kinds of nonlinear partial differential equations arising in mathematical physics

active appearance models we describe a new method of matching statistical models of appearance to images a set of model parameters control modes of shape and gray level variation learned from a training set we construct an efficient iterative matching algorithm by learning the relationship between perturbations in the model parameters and the induced image errors

nonlinear preconditioning for diffuse interfaces a method of transforming problems with diffuse interfaces is presented which leads to equations that are easier to compute accurately information obtained by internal layer asymptotic analysis is utilized to motivate transformations of the dependent variables the new evolution equations which result from this change of variables can be solved numerically in a straightforward manner numerical experiments indicate that truncation errors can be significantly reduced in such problems allowing a coarser grid to be used applications to several well known models are presented

exact solutions of the combined kdv burgers equation with variable coefficients in this letter the exp function method is used to obtain generalized solitary solutions and periodic solutions of the general types of combined kdv burgers equation with variable coefficients it is shown that the exp function method via symbolic computation provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations with variable coefficients in mathematical physics

bayesian constrained local models revisited this paper presents a novel bayesian formulation for aligning faces in unseen images our approach revisits the constrained local models clm formulation where an ensemble of local feature detectors are constrained to lie within the subspace spanned by a point distribution model pdm fitting such a model to an image typically involves two main steps a local search using a detector obtaining response maps for each landmark likelihood term and a global optimization that finds the pdm parameters that jointly maximize all the detections at once the so called global optimization can be posed as a bayesian inference problem where the posterior distribution of the shape and pose parameters can be inferred in a maximum a posteriori map sense this work introduces an extended bayesian global optimization strategy that includes two novel additions 1 to perform second order updates of the pdm parameters accounting for their covariance and 2 to model the underlying dynamics of the shape variations encoded in the prior term by using recursive bayesian estimation extensive evaluations were performed against state of the art methods on several standard datasets imm bioid xm2vts lfw and fgnet talking face results show that the proposed approach significantly increases the fitting performance

a chebyshev spectral collocation method for solving burgers type equations in this paper we elaborated a spectral collocation method based on differentiated chebyshev polynomials to obtain numerical solutions for some different kinds of nonlinear partial differential equations the problem is reduced to a system of ordinary differential equations that are solved by runge kutta method of order four numerical results for the nonlinear evolution equations such as 1d burgers kdv burgers coupled burgers 2d burgers and system of 2d burgers equations are obtained the numerical results are found to be in good agreement with the exact solutions numerical computations for a wide range of values of reynolds number show that the present method offers better accuracy in comparison with other previous methods moreover the method can be applied to a wide class of nonlinear partial differential equations

new solitary wave and periodic wave solutions to the 2 1 dimensional nizhnik novikov veselov system in this work the 2 1 dimensional nizhnik novikov veselov nnv system is studied the tanh method the extended tanh method and the cosh sinh method are used to investigate this system by means of these methods new solitary wave and periodic wave solutions are determined

multiple periodic soliton solutions to kadomtsev petviashvili equation abstract based on the extended homoclinic test technique we introduce two new ansatz functions to construct multiple periodic soliton solutions of kadomtsev petviashvili kp equation by the hirota s bilinear method some entirely new periodic soliton solutions are obtained the obtained results show that there exist multiple periodic solitary waves in the different directions for the kp equation which differ from complexiton the employed approach is powerful and can be also applied to solve other nonlinear differential equations

series solution of nonlinear coupled reaction diffusion equations a nonlinear set of two coupled reaction diffusion equations is investigated analytically to obtain travelling wave solutions first the series method of hereman et al 1990 involving powers of decaying exponentials is used to determine the width and the velocity of those waves further to get a suitable analytical expression for them another power series is introduced for which now a tanh function acts as a new variable as a result recursion relations can be set up keeping only the lowest order terms neglecting coefficients of higher order the author finds solutions which correspond with earlier numerical calculations

solutions of the cahn hilliard equation in this paper we found some exact solutions of the cahn hilliard equation and the system of the equations by considering a modified extended tanh function method a numerical solution to a cahn hilliard equation is obtained using a homotopy perturbation method hpm combined with the adomian decomposition method adm the comparisons are given in the tables

greedy function approximation a gradient boosting machine function estimation approximation is viewed from the perspective of numerical optimization in function space rather than parameter space a connection is made between stagewise additive expansions and steepest descent minimization a general gradient descent boosting paradigm is developed for additive expansions based on any fitting criterion specific algorithms are presented for least squares least absolute deviation and huber m loss functions for regression and multiclass logistic likelihood for classification special enhancements are derived for the particular case where the individual additive components are regression trees and tools for interpreting such treeboost models are presented gradient boosting of regression trees produces competitive highly robust interpretable procedures for both regression and classification especially appropriate for mining less than clean data connections between this approach and the boosting methods of freund and shapire and friedman hastie and tibshirani are discussed

algebro geometric solutions for the complex sharma tasso olver hierarchy this paper is dedicated to provide theta function representation of algebro geometric solutions and related crucial quantities for the complex sharma tasso olver csto hierarchy our main tools include the polynomial recursive formalism to derive the csto hierarchy the hyper elliptic curve with finite number of genus the baker akhiezer functions the meromorphic function the dubrovin type equations for auxiliary divisors and the associated trace formulas by use of these tools the explicit representations of the baker ahhiezer functions the meromorphic function and the algebro geometric solutions are obtained for the entire csto hierarchy

numerical solutions of the generalized kuramoto sivashinsky equation by chebyshev spectral collocation methods chebyshev spectral collocation methods known as el gendi method s e el gendi chebyshev solution of differential integral and integro differential equations comput j 12 1969 282 287 b mihaila i mihaila numerical approximation using chebyshev polynomial expansions el gendi s method revisited j phys a 35 2002 731 746 are extended to deal with the generalized kuramoto sivashinsky equation the problem is reduced to a system of ordinary differential equations that are solved by combinations of backward differential formula and appropriate explicit schemes implicit explicit bdf methods g akrivis y s smyrlis implicit explicit bdf methods for the kuramoto sivashinsky equation appl numer math 51 2004 151 169 good numerical results have been obtained and compared with the exact solutions

nonlinear periodic solutions for isothermal magnetostatic atmospheres the equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically for equilibria with one ignorable spatial coordinate the equations reduce to a single nonlinear elliptic equation for the magnetic potential known as the grad shafranov equation specifying the arbitrary function in the latter equation yields a nonlinear elliptic equation analytical nonlinear periodic solutions of this elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field e g a model for the solar atmosphere we obtained several classes of exact solutions of five nonlinear evolution equations liouville sinh poisson double sinh poisson sine poisson and double sine poisson using the generalized tanh method moreover the backlund transformations are used to generate further new classes of solutions the final results may be used to investigate some models in solar physics

new solitons and kinks solutions to the sharma tasso olver equation abstract in this work the sharma tasso olver sto equation is investigated the tanh method the extended tanh method and other ansatze involving hyperbolic and exponential functions are efficiently used for analytic study of this equation new solitons and kinks solutions are formally derived the proposed schemes are reliable and manageable

on nonlinear population waves we discuss a model system of partial differential equations for description of the spatio temporal dynamics of interacting populations we are interested in the waves caused by migration of the populations we assume that the migration is a diffusion process influenced by the changing values of the birth rates and coefficients of interaction among the populations for the particular case of one population and one spatial dimension the general model is reduced to analytically tractable pde with polynomial nonlinearity up to 4th order we investigate this particular case and obtain two kinds of solutions i approximate solution for small value of the ratio between the coefficient of diffusion and the wave velocity and ii exact solutions which describe nonlinear kink and solitary waves in an appropriate phase space the kinks correspond to a connection between two states represented by a saddle point and a stable node finally we derive conditions for the asymptotic stability of the obtained solutions

travelling wave solutions of some classes of nonlinear evolution equations in 1 1 and 2 1 dimensions 1 the tanh method is proposed to find travelling wave solutions in 1 1 and 2 1 dimensional wave equations it can be extended to solve a whole family of modified korteweg de vries type of equations higher dimensional wave equations and nonlinear evolution equations

new travelling wave solutions to some nonlinear equations via a combined method abstract based on the sine gordon and the sinh gordon equations transformations are introduced in a variable separated ode method to construct entirely new doubly periodic jacobian elliptic function solutions of some nonlinear differential equations which are powerful and simple distinct sets of exact doubly periodic solutions that possess distinct physical structures are obtained for the mkdv sine gordon the mkdv sinh gordon equations and born infeld equation when the module m 1 or 0 the corresponding solitary wave solutions are also found this approach can be also applied to solve other nonlinear differential equations

learning kernel extended dictionary for face recognition a sparse representation classifier src and a kernel discriminant analysis kda are two successful methods for face recognition an src is good at dealing with occlusion while a kda does well in suppressing intraclass variations in this paper we propose kernel extended dictionary ked for face recognition which provides an efficient way for combining kda and src we first learn several kernel principal components of occlusion variations as an occlusion model which can represent the possible occlusion variations efficiently then the occlusion model is projected by kda to get the ked which can be computed via the same kernel trick as new testing samples finally we use structured src for classification which is fast as only a small number of atoms are appended to the basic dictionary and the feature dimension is low we also extend ked to multikernel space to fuse different types of features at kernel level experiments are done on several large scale data sets demonstrating that not only does ked get impressive results for nonoccluded samples but it also handles the occlusion well without overfitting even with a single gallery sample per subject

multi variable regression methods using modified chebyshev polynomials of class 2 abstract so far many regression works have been implemented by using linear regression methods although more accurate predictions results could be obtained polynomial regression is not used as much as compared to linear regression in real applications due to occurrence of coefficient explosion to overcome this problem two regression algorithms using chebyshev polynomials of class 2 based on cascade regression and feature selection are proposed in this paper in the experimental part three separate experiments including function interpolation and real case regression were conducted on three datasets to test the proposed algorithms as shown by the experimental results the proposed algorithms performed better than other regression methods in terms of both accuracy and processing time

backlund transformations and exact solutions for some nonlinear evolution equations in solar magnetostatic models the backlund transformations for some nonlinear evolution equations the liouville the sine and sinh poisson equations are constructed through the akns system in unified manner the obtained backlund transformations are used to generate new classes of solutions the latter is employed to obtain an infinite sequence of solutions moreover we generate an infinite sequence of additional solutions by employing the permutability theorem and give a general expression for the nth order solution it turns out that this general expression can be employed to obtain solutions for the sine and sinh poisson equations the final results are used to investigate some models in solar plasma physics conclusions and comments are given

the tanh method for traveling wave solutions of nonlinear equations in this work we employ the tanh method for traveling wave solutions of nonlinear equations the study is extended to equations that do not have tanh polynomial solutions the efficiency of the method is demonstrated by applying it for a variety of selected equations

exact solutions for some coupled nonlinear equations ii for pt i see ibid vol 23 p 3923 1990 the authors use the method previously presented to obtain the exact solutions for some coupled nonlinear equations