scalar equations for synchronous boolean networks with biological applications one way of coping with the complexity of biological systems is to use the simplest possible models which are able to reproduce at least some nontrivial features of reality although two value boolean models have a long history in technology it is perhaps a little bit surprising that they can also represent important features of living organizms in this paper the scalar equation approach to boolean network models is further developed and then applied to two interesting biological models in particular a linear reduced scalar equation is derived from a more rudimentary nonlinear scalar equation this simpler but higher order two term equation gives immediate information about both cycle and transient structure of the network

unitary rotation of square pixellated images the unitary rotation of square pixellated images is based on the finite su 2 oscillator model which describes systems whose values for position momentum and energy are discrete and finite in a two dimensional position space this allows the construction of angular momentum states orthonormal and complete for which rotations are defined as multiplication by phases that carry the rotation angle the decomposition of a digital square images in terms of these angular momentum states determines a unitary hence invertible rotation of the image whose kernel can be computed as a four dimensional array of real numbers

a new method based on haar wavelet for the numerical solution of two dimensional nonlinear integral equations a new numerical method based on haar wavelet is proposed for two dimensional nonlinear fredholm volterra and volterra fredholm integral equations of first and second kind the proposed method is an extension of the haar wavelet method aziz and siraj ul islam 2013 siraj ul islam et al 2013 and siraj ul islam et al 2014 from one dimensional nonlinear integral equations fredholm and volterra to two dimensional nonlinear integral equations fredholm volterra and volterra fredholm the main characteristic of the method is that unlike several other methods it does not involve numerical integration which results in an improved accuracy of the method in order to show the effectiveness of the method it is applied to several benchmark problems the numerical results are compared with other methods existing in the recent literature

number and length of attractors in a critical kauffman model with connectivity one the kauffman model describes a system of randomly connected nodes with dynamics based on boolean update functions though it is a simple model it exhibits very complex behavior for critical parameter values at the boundary between a frozen and a disordered phase and is therefore used for studies of real network problems we prove here that the mean number and mean length of attractors in critical random boolean networks with connectivity one both increase faster than any power law with network size we derive these results by generating the networks through a growth process and by calculating lower bounds

brief paper controllability of boolean control networks with time delays in states this paper investigates the controllability of boolean networks with time invariant delays in states after a brief introduction on converting the logic dynamics to discrete time delay systems the controllability via two kinds of controls is studied one kind of control is generated by boolean control networks another kind of control is free boolean sequences in both cases necessary and sufficient conditions of the controllability of boolean control networks are proved finally examples are given to illustrate the efficiency of the obtained results

identification of boolean control networks in this paper the identification of boolean control networks is addressed first necessary and sufficient conditions are obtained for the identification of state equation from input state data then a necessary and sufficient condition for a controllable boolean network to be observable is presented based on these two results a necessary and sufficient condition for the identification from input output data is achieved to practically identify the model a numerical algorithm is proposed two particular cases i identification of systems with a known network graph ii identification of a higher order boolean network are also investigated finally the approximate identification for large size networks is explored

convolution based interpolation for fast high quality rotation of images this paper focuses on the design of fast algorithms for rotating images and preserving high quality the basis for the approach is a decomposition of a rotation into a sequence of one dimensional translations as the accuracy of these operations is critical we introduce a general theoretical framework that addresses their design and performance we also investigate the issue of optimality and present an improved least square formulation of the problem this approach leads to a separable three pass implementation of a rotation using one dimensional convolutions only we provide explicit filter formulas for several continuous signal models including spline and bandlimited representations finally we present rotation experiments and compare the currently standard techniques with the various versions of our algorithm our results indicate that the present algorithm in its higher order versions outperforms all standard high accuracy methods of which we are aware both in terms of speed and quality its computational complexity increases linearly with the order of accuracy the best quality results are obtained with the sine based algorithm which can be implemented using simple one dimensional ffts

the coiflet galerkin method for linear volterra integral equations this paper deals with the application of the wavelet galerkin method based on coiflets as a basis for solving linear volterra integral equations vies the main contribution of this work is that some new connection coefficients are introduced and a suitable algorithm is developed for their solution once they have been computed they can be stored and applied to any linear vie the convergence properties of the coiflet galerkin method are analyzed some test examples are presented to illustrate the performance of the method with respect to the error norms and cpu time

evolutionary computational intelligence in solving a class of nonlinear volterra fredholm integro differential equations in this paper a stochastic computational intelligence technique for solving a class of nonlinear volterra fredholm integro differential equations with mixed conditions is presented the strength of feed forward artificial neural networks is used to accurately model the integro equation comparisons with the exact solution and other numerical techniques are presented to show the efficiency of the proposed method theoretical and numerical results are presented analysis for the presented method is given

on the optimality of ideal filters for pyramid and wavelet signal approximation the reconstructed lowpass component in a quadrature mirror filter qmf bank provides a coarser resolution approximation of the input signal since the outputs of the two qmf branches are orthogonal the transformation that provides the maximum energy compaction in the lowpass channel is also the one that results in the minimum approximation error this property is used as a common strategy for the optimization of qmf banks orthogonal wavelet transforms and least squares pyramids a general solution is derived for the qmf bank that provides the optimal decomposition of an arbitrary wide sense stationary process this approach is extended to the continuous case to obtain the minimum error approximation of a signal at a given sampling rate in particular it is shown that the sine wavelet transform is optimal for the representation at all scales of signals with non increasing spectral density

a maximum principle for single input boolean control networks boolean networks have recently been attracting considerable interest as computational models for genetic and cellular networks we consider a mayer type optimal control problem for a single input boolean network and derive a necessary condition for a control to be optimal this provides an analog of pontryagin s maximum principle for single input boolean networks

comparison of interpolating methods for image resampling when resampling an image to a new set of coordinates for example when rotating an image there is often a noticeable loss in image quality to preserve image quality the interpolating function used for the resampling should be an ideal low pass filter to determine which limited extent convolving functions would provide the best interpolation five functions were compared a nearest neighbor b linear c cubic b spline d high resolution cubic spline with edge enhancement a 1 and e high resolution cubic spline a 0 5 the functions which extend over four picture elements c d e were shown to have a better frequency response than those which extend over one a or two b pixels the nearest neighbor function shifted the image up to one half a pixel linear and cubic b spline interpolation tended to smooth the image the best response was obtained with the high resolution cubic spline functions the location of the resampled points with respect to the initial coordinate system has a dramatic effect on the response of the sampled interpolating function the data are exactly reproduced when the points are aligned and the response has the most smoothing when the resampled points are equidistant from the original coordinate points thus at the expense of some increase in computing time image quality can be improved by resampled using the high resolution cubic spline function as compared to the nearest neighbor linear or cubic b spline functions

minimum time control of boolean networks boolean networks bns are discrete time dynamical systems with boolean state variables bns have recently been attracting considerable interest as computational models for biological systems and in particular gene regulating networks boolean control networks bcns are boolean networks with boolean inputs we consider the problem of steering a bcn from a given state to a desired state in minimal time using the algebraic state space representation assr of bcns we derive several necessary conditions stated in the form of maximum principles mps for a control to be time optimal in the assr every state and input vector is a canonical vector using this special structure yields an explicit state feedback formula for all time optimal controls to demonstrate the theoretical results we develop a bcn model for the genetic switch controlling the lambda phage development upon infection of a bacteria our results suggest that this biological switch is designed in a way that guarantees minimal time respon

rationalized haar functions method for solving fredholm and volterra integral equations this paper presents a computational technique for fredholm integral equation of the second kind and volterra integral equation of the second kind the method is based upon haar functions approximation properties of rationalized haar functions are first presented the operational matrix of integration together with product operational matrix and newton cotes nodes are utilized to reduce the computation of integral equations into some algebraic equations the method is computationally attractive and applications are demonstrated through illustrative examples

moms maximal order interpolation of minimal support we consider the problem of interpolating a signal using a linear combination of shifted versions of a compactly supported basis function spl phi z we first give the expression for the cases of spl phi that have minimal support for a given accuracy also known as approximation order this class of functions which we call maximal order minimal support functions moms is made of linear combinations of the b spline of the same order and of its derivatives we provide an explicit form of the moms that maximizes the approximation accuracy when the step size is small enough we compute the sampling gain obtained by using these optimal basis functions over the splines of the same order we show that it is already substantial for small orders and that it further increases with the approximation order l when l is large this sampling gain becomes linear more specifically its exact asymptotic expression is 2 spl pi e l since the optimal functions are continuous but not differentiable for even orders and even only piecewise continuous for odd orders our result implies that regularity has little to do with approximating performance these theoretical findings are corroborated by experimental evidence that involves compounded rotations of images

numerical solution of nonlinear volterra fredholm hammerstein integral equations via tau collocation method with convergence analysis in this paper we consider the nonlinear volterra fredholm hammerstein integral equations the approximate solution for the nonlinear volterra fredholm hammerstein integral equations is obtained by using the tau collocation method to do this the nonlinear volterra fredholm hammerstein integral equations is transformed into a system of nonlinear algebraic equations in matrix form thus by solving this system unknown coefficients are obtained the spectral rate of convergence for the proposed method is established in the l 2 norm the numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method the results show that the tau collocation method is of high accuracy more convenient and efficient for solving nonlinear volterra fredholm hammerstein integral equations

controllability and observability of boolean control networks the controllability and observability of boolean control networks are investigated after a brief review on converting a logic dynamics to a discrete time linear dynamics with a transition matrix some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix based on the discrete time dynamics the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely then the problem of observability is also solved by giving necessary and sufficient conditions

observability of boolean networks a graph theoretic approach boolean networks bns are discrete time dynamical systems with boolean state variables and outputs bns are recently attracting considerable interest as computational models for genetic and cellular networks we consider the observability of bns that is the possibility of uniquely determining the initial state given a time sequence of outputs our main result is that determining whether a bn is observable is np hard this holds for both synchronous and asynchronous bns thus unless p np there does not exist an algorithm with polynomial time complexity that solves the observability problem we also give two simple algorithms with exponential complexity that solve this problem our results are based on combining the algebraic representation of bns derived by d cheng with a graph theoretic approach some of the theoretical results are applied to study the observability of a bn model of the mammalian cell cycle

observability reconstructibility and state observers of boolean control networks the aim of this paper is to introduce and characterize observability and reconstructibility properties for boolean networks and boolean control networks described according to the algebraic approach proposed by d cheng and co authors in the series of papers 3 6 7 and in the recent monography a complete characterization of these properties based both on the boolean matrices involved in the network description and on the corresponding digraphs is provided finally the problem of state observer design for reconstructible bns and bcns is addressed and two different solutions are proposed

brief paper controllability of boolean control networks via the perron frobenius theory boolean control networks bcns are recently attracting considerable interest as computational models for genetic and cellular networks addressing control theoretic problems in bcns may lead to a better understanding of the intrinsic control in biological systems as well as to developing suitable protocols for manipulating biological systems using exogenous inputs we introduce two definitions for controllability of a bcn and show that a necessary and sufficient condition for each form of controllability is that a certain nonnegative matrix is irreducible or primitive respectively our analysis is based on a result that may be of independent interest namely a simple algebraic formula for the number of different control sequences that steer a bcn between given initial and final states in a given number of time steps while avoiding a set of forbidden states

b spline signal processing ii efficiency design and applications for pt i see ibid vol 41 no 2 p 821 33 1993 a class of recursive filtering algorithms for the efficient implementation of b spline interpolation and approximation techniques is described in terms of simplicity of realization and reduction of computational complexity these algorithms compare favorably with conventional matrix approaches a filtering interpretation low pass filter followed by an exact polynomial spline interpolator of smoothing spline and least squares approximation methods is proposed these techniques are applied to the design of digital filters for cubic spline signal processing an efficient implementation of a smoothing spline edge detector is proposed it is also shown how to construct a cubic spline image pyramid that minimizes the loss of information in passage from one resolution level to the next in terms of common measures of fidelity this data structure appears to be superior to the gaussian laplacian pyramid

recursive regularization filters design properties and applications least squares approximation problems that are regularized with specified highpass stabilizing kernels are discussed for each problem there is a family of discrete regularization filters r filters which allow an efficient determination of the solutions these operators are stable symmetric lowpass filters with an adjustable scale factor two decomposition theorems for the z transform of such systems are presented one facilitates the determination of their impulse response while the other allows an efficient implementation through successive causal and anticausal recursive filtering a case of special interest is the design of r filters for the first and second order difference operators these results are extended for two dimensional signals and for illustration purposes are applied to the problem of edge detection this leads to a very efficient implementation 8 multiplies 10 adds per pixel of the optimal canny edge detector based on the use of a separable second order r filter

optimal control of logical control networks this paper considers the infinite horizon optimal control of logical control networks including boolean control networks as a special case using the framework of game theory the optimal control problem is formulated in the sight of the algebraic form of a logical control network its cycles can be calculated algebraically then the optimal control is revealed over a certain cycle when the games using memory 1 which means the players only consider previous steps action at each step are considered the higher order logical control network is introduced and its algebraic form is also presented which corresponds to a conventional logical control network i e 1 then it is proved that the optimization technique developed for conventional logical control networks is also applicable to this memory case

boolean dynamics of networks with scale free topology the dynamics of boolean networks with scale free topology are studied the existence of a phase transition from ordered to chaotic dynamics governed by the value of the scale free exponent of the network is shown analytically by analyzing the overlap between two distinct trajectories the phase diagram shows that the phase transition occurs for values of the scale free exponent in the open interval 2 2 5 since the boolean networks under study are directed graphs the scale free topology of the input connections and that of the output connections are studied separately ultimately these two topologies are shown to be equivalent a numerical study of the attractor structure of the configuration space reveals that this structure is similar in both networks with scale free topologies and networks with homogeneous random topologies however an important result of this work is that the fine tuning usually required to achieve stability in the dynamics of networks with homogeneous random topologies is no longer necessary when the network topology is scale free finally based on the results presented in this work it is hypothesized that the scale free topology favors the evolution and adaptation of network functioning from a biological perspective

bisimulations of boolean control networks a framework for analyzing bisimulation relations of boolean control networks bcns is set up in this paper bisimulation relations are natural objectives in control systems theory a bisimulation relation between a pair of control systems defines a relation on their state spaces or state sets explaining how a trajectory or transition of one system can be paired with a trajectory or transition of the other system and vice versa the paper first formalizes the notion of bi simulation in bcns and presents detailed results characterizing bi simulation relations for bcns then as an application of the notion of bisimulation it considers the propagation of the fundamental properties of macro controllability and stabilizability through a bisimulation relation it thereby suggests the possibility that certain control properties of a bcn can be inferred by analyzing a potentially simpler bcn the analysis developed in this paper is based on the semitensor product approach which gives algorithms that have e

addendum b spline interpolation in medical image processing analyzes b spline interpolation techniques of degree 2 4 and 5 with respect to all criteria that have been applied to evaluate various interpolation schemes in a recently published survey on image interpolation in medical imaging lehmann et al 1999 it is shown that high degree b spline interpolation has superior fourier properties smallest interpolation error and reasonable computing times therefore high degree b splines are preferable interpolators for numerous applications in medical image processing particularly if high precision is required if no aliasing occurs this result neither depends on the geometric transform applied for the tests nor the actual content of images

new closed formula for the univariate hermite interpolating polynomial of total degree and its application in medical image slice interpolation this work investigates the usefulness of univariate hermite interpolation of the total degree htd for a biomedical signal processing task slice interpolation in a variety of medical imaging modalities the htd is an algebraically demanding interpolation method that utilizes information of the values of the signal to be interpolated at distinct support positions as well as the values of its derivatives up to a maximum available order first a novel closed form solution for the univariate hermite interpolating polynomial is presented for the general case of arbitrarily spaced support points and its computational and algebraic complexity is compared to that of the classical expression of the hermite interpolating polynomial then an implementation is proposed for the case of equidistant support positions with computational complexity comparable to any convolution based interpolation method we assess the proposed implementation of htd interpolation with equidistant support points in the task of slice interpolation which is usually treated as a one dimensional problem we performed a large number of interpolation experiments for 220 magnetic resonance imaging mri datasets and 50 computer tomography ct datasets and compared the proposed htd implementation to several other well established interpolation techniques in our experiments we approximated the signal derivatives using finite differences however the proposed htd can accommodate any type of derivative calculation results show that the htd interpolation outperforms the other interpolation methods under comparison in terms of root mean square error rmse in every one of the interpolation experiments resulting in higher accuracy interpolated images finally the behavior of the htd with respect to its controlling parameters is explored and its computational complexity is determined

symbolic dynamics of boolean control networks we consider boolean control networks bcns and in particular boolean networks bns in the framework of symbolic dynamics sd we show that the set of state space trajectories of a bcn is a shift space of finite type sft this observation allows us to extend two important analysis tools from sd namely the artin mazur zeta function and the topological entropy to bns and bcns some of the theoretical results are illustrated using a bcn model of the core network regulating the mammalian cell cycle

a semi analytical approach to solve integro differential equations in this work we present a semi analytical method for solving integro differential equations under multi point or mixed boundary conditions the proposed method solves linear and nonlinear fredholmvolterra integro differential equations a convergence analysis of the proposed method is directly examined numerical examples are worked out to demonstrate the main results moreover proper graphs are provided to confirm the efficiency and the accuracy of the proposed scheme we show that with a few number of obtained approximating terms we achieve a high accuracy level of the obtained results however increasing the number of approximating terms yields a significant decrease of the error of the approximation the proposed method is very useful reliable and flexible for solving different kinds of integro differential equations

shifting interpolation kernel toward orthogonal projection orthogonal projection offers the optimal solution for many sampling reconstruction problems in terms of the least square error in the standard interpolation setting where the sampling is assumed to be ideal however the projection is impossible unless the interpolation kernel is related to the sinc function and the input is bandlimited in this paper we propose a notion of shifting kernel toward the orthogonal projection for a given interpolation kernel we formulate optimization problems whose solutions lead to shifted interpolations that while still being interpolatory are closest to the orthogonal projection in the sense of the minimax regret the quality of interpolation is evaluated in terms of the average approximation error over input shift for the standard linear interpolation we obtain several values of optimal shift dependent on a priori information on input signals for evaluation we apply the new shifted linear interpolations to a gaussian signal an ecg signal a speech signal a two dimensional signal and three natural images significant improvements are observed over the standard and the 0 21 shifted linear interpolation proposed early

interpolation artifacts in multimodality image registration based on maximization of mutual information mutual information mi is an increasingly popular match metric for multimodality image registration however its value is affected by interpolation which may limit registration accuracy the purpose of this study was to characterize the artifacts from eight interpolators and to investigate efficient strategies to overcome these artifacts the interpolators were 1 nearest neighbor 2 linear 3 cubic catmull rom 4 hamming windowed sinc 5 partial volume 6 nn with jittered sampling jit 7 nn with histogram blurring blur and 8 nn with jit and blur the impact of interpolation on mi was evaluated in two dimensions over different translational and rotational misregistration interpolation caused spurious fluctuations in mi whenever the voxel grids had coinciding periodicities and were nearly aligned the artifacts did not lessen by using intensity interpolators with wider support e g cubic catmull rom hamming windowed sinc pv could lead to either arch artifacts or inverted arch artifacts depending on the relative voxel sizes several strategies reduced artifacts and improved registration robustness jit blur avoiding an extreme number of intensity bins and resampling the images in a rotated orientation with different relative voxel sizes e g spl pi 3 these findings also apply to related methods including normalized mi joint entropy and hill s third moment

bessel polynomial solutions of high order linear volterra integro differential equations abstract in this study a practical matrix method which is based on collocation points is presented to find approximate solutions of high order linear volterra integro differential equations vides under the mixed conditions in terms of bessel polynomials numerical examples are included to demonstrate the validity and applicability of the technique and comparisons are made with the existing results the results show the efficiency and accuracy of the present work all of the numerical computations have been performed on the computer using a program written in matlab v7 6 0 r2008a

fast b spline transforms for continuous image representation and interpolation efficient algorithms for the continuous representation of a discrete signal in terms of b splines direct b spline transform and for interpolative signal reconstruction indirect b spline transform with an expansion factor m are described expressions for the z transforms of the sampled b spline functions are determined and a convolution property of these kernels is established it is shown that both the direct and indirect spline transforms involve linear operators that are space invariant and are implemented efficiently by linear filtering fast computational algorithms based on the recursive implementations of these filters are proposed a b spline interpolator can also be characterized in terms of its transfer function and its global impulse response cardinal spline of order n the case of the cubic spline is treated in greater detail the present approach is compared with previous methods that are reexamined from a critical point of view it is concluded that b spline interpolation correctly applied does not result in a loss of image resolution and that this type of interpolation can be performed in a very efficient manner

enlargement or reduction of digital images with minimum loss of information the purpose of this paper is to derive optimal spline algorithms for the enlargement or reduction of digital images by arbitrary noninteger scaling factors in our formulation the original and rescaled signals are each represented by an interpolating polynomial spline of degree n with step size one and spl delta respectively the change of scale is achieved by determining the spline with step size spl delta that provides the closest approximation of the original signal in the l sub 2 norm we show that this approximation can be computed in three steps i a digital prefilter that provides the b spline coefficients of the input signal ii a resampling using an expansion formula with a modified sampling kernel that depends explicitly on spl delta and iii a digital postfilter that maps the result back into the signal domain we provide explicit formulas for n 0 1 and 3 and propose solutions for the efficient implementation of these algorithms we consider image processing examples and show that the present method compares favorably with standard interpolation techniques finally we discuss some properties of this approach and its connection with the classical technique of bandlimiting a signal which provides the asymptotic limit of our algorithm as the order of the spline tends to infinity

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations haar wavelet operational matrix has been widely applied in system analysis system identification optimal control and numerical solution of integral and differential equations in the present paper we derive the haar wavelet operational matrix of the fractional order integration and use it to solve the fractional order differential equations including the bagley torvik ricatti and composite fractional oscillation equations the results obtained are in good agreement with the existing ones in open literatures and it is shown that the technique introduced here is robust and easy to apply

on minimum period of nonlinear feedback shift registers in grain like structure grain is one of three hardware oriented finalists of the estream project a nonlinear feedback shift register nfsr in grain like structure is a cascade connection of a linear feedback shift register lfsr into an nfsr in which the characteristic polynomial of the lfsr is primitive and the feedback function of the nfsr is nonsingular in 2011 hu and gong pointed out that the period of the sequence generated by an nfsr in grain like structure is a multiple of the period of the sequence generated by its lfsr if the initial state of the lfsr is nonzero meanwhile they proposed an open problem for fixed feedback functions of an nfsr and an lfsr determine whether the sequences generated by the nfsr in grain like structure can achieve the minimum period i e the period of the lfsr when the initial state of the lfsr is nonzero and if they can achieve provide at least one pair of the initial states of the nfsr and lfsr clearly from a security point of view it is not preferable if the sequences generated by an nfsr in grain like structure achieve the minimum period this paper converts the open problem into a problem of solving an integer equation with respect to two unknown integers that uniquely correspond to the initial states of the nfsr and lfsr by viewing the nfsr as a boolean control network based on the integer equation this paper shows that for any given initial state of an n stage nfsr and any given nonzero initial state of an m stage lfsr the probability that the sequence generated by the nfsr in grain like structure achieves the minimum period 2 m 1 is at most 2 n this implies that the probability of the cascade connection used in grain achieving the minimum period is very small

a new formula for bivariate hermite interpolation on variable step grids and its application to image interpolation in this paper we present a novel formula of the bivariate hermite interpolating bhi polynomial in the case of support points arranged on a grid with variable step this expression is applicable when interpolation of a bivariate function is required given its value and the values of its partial derivatives of arbitrarily high order at the support points the proposed formula is a generalization of an existing formula for the bivariate hermite polynomial it is also algebraically much simpler thus can be computed more efficiently in order to apply hermite interpolation to image interpolation we simplify the proposed bhi to handle support points on a regular unit step grid the values of image partial derivatives are arithmetically approximated using compact finite differences the proposed method is being assessed in a number of image interpolation experiments that include a synthetic image for which the values of the partial derivatives are computed analytically as well as a collection of images from different medical modalities the proposed bhi with up to second order image partial derivatives outperforms the convolution based interpolation methods as well as generalized interpolation methods with the same number of support points that was compared with in the majority of image interpolation experiments the computational load of the proposed bhi is calculated and its behaviour with respect to its controlling parameters is investigated

an objective comparison of 3 d image interpolation methods to aid in the display manipulation and analysis of biomedical image data they usually need to be converted to data of isotropic discretization through the process of interpolation traditional techniques consist of direct interpolation of the grey values when user interaction is called for in image segmentation as a consequence of these interpolation methods the user needs to segment a much greater typically 4 10 spl times amount of data to mitigate this problem a method called shape based interpolation of binary data was developed resides significantly reducing user time this method has been shown to provide more accurate results than grey level interpolation the authors proposed an approach for the interpolation of grey data of arbitrary dimensionality that generalized the shape based method from binary to grey data this method has characteristics similar to those of the binary shape based method in particular the authors showed preliminary evidence that it produced more accurate results than conventional grey level interpolation methods in this paper concentrating on the three dimensional 3 d interpolation problem the authors compare statistically the accuracy of 8 different methods nearest neighbor linear grey level grey level cubic spline grey level modified cubic spline goshtasby et al 1992 and 3 methods from the grey level shape based class a population of patient magnetic resonance and computed tomography images corresponding to different parts of the human anatomy coming from different 3 d imaging applications are utilized for comparison each slice in these data sets is estimated by each interpolation method and compared to the original slice at the same location using 3 measures mean squared difference number of sites of disagreement and largest difference the methods are statistically compared pairwise based on these measures the shape based methods statistically significantly outperformed all other methods in all measures in all applications considered here with a statistical relevance ranging from 10 to 32 mean 15 for mean squared difference

hybrid function method for solving fredholm and volterra integral equations of the second kind numerical solutions of fredholm and volterra integral equations of the second kind via hybrid functions are proposed in this paper based upon some useful properties of hybrid functions integration of the cross product a special product matrix and a related coefficient matrix with optimal order are applied to solve these integral equations the main characteristic of this technique is to convert an integral equation into an algebraic hence the solution procedures are either reduced or simplified accordingly the advantages of hybrid functions are that the values of n and m are adjustable as well as being able to yield more accurate numerical solutions than the piecewise constant orthogonal function for the solutions of integral equations we propose that the available optimal values of n and m can minimize the relative errors of the numerical solutions the high accuracy and the wide applicability of the hybrid function approach will be demonstrated with numerical examples the hybrid function method is superior to other piecewise constant orthogonal functions w f blyth r l may p widyaningsih volterra integral equations solved in fredholm form using walsh functions anziam j 45 e 2004 c269 c282 m h reihani z abadi rationalized haar functions method for solving fredholm and volterra integral equations j comp appl math 200 2007 12 20 for these problems

wavelets and dilation equations a brief introduction wavelets are new families of basis functions that yield the representation f x sum b jk w 2 j x k their construction begins with the solution phi x to a dilation equation with coefficients c k then w comes from phi and the basis comes by translation and dilation of w it is shown in part 1 how conditions on the c k lead to approximation properties and orthogonality properties of the wavelets part 2 describes the recursive algorithms also based on the c k that decompose and reconstruct f the object of wavelets is to localize as far as possible in both time and frequency with efficient algorithms

polynomial spline signal approximations filter design and asymptotic equivalence with shannon s sampling theorem the least squares polynomial spline approximation of a signal g t in l sub 2 r is obtained by projecting g t on s sup n r the space of polynomial splines of order n it is shown that this process can be linked to the classical problem of cardinal spline interpolation by first convolving g t with a b spline of order n more specifically the coefficients of the b spline interpolation of order 2n 1 of the sampled filtered sequence are identical to the coefficients of the least squares approximation of g t of order n it is shown that this approximation can be obtained from a succession of three basic operations prefiltering sampling and postfiltering which confirms the parallel with the classical sampling reconstruction procedure for bandlimited signals the frequency responses of these filters are determined for three equivalent spline representations using alternative sets of shift invariant basis functions of s sup n r the standard expansion in terms of b spline coefficients a representation in terms of sampled signal values and a representation using orthogonal basis functions

on boolean control networks with maximal topological entropy boolean control networks bcns are discrete time dynamical systems with boolean state variables and inputs that are interconnected via boolean functions bcns are recently attracting considerable interest as computational models for genetic and cellular networks with exogenous inputs the topological entropy of a bcn with m inputs is a nonnegative real number in the interval 0 m log 2 roughly speaking a larger topological entropy means that asymptotically the control is more powerful we derive a necessary and sufficient condition for a bcn to have the maximal possible topological entropy our condition is stated in the framework of cheng s algebraic state space representation of bcns this means that verifying this condition incurs an exponential time complexity we also show that the problem of determining whether a bcn with n state variables and m n inputs has a maximum topological entropy is np hard suggesting that this problem cannot be solved in general using a polynomial time algorithm

multivariate hermite interpolation by algebraic polynomials a survey abstract this is a survey of that theory of multivariate lagrange and hermite interpolation by algebraic polynomials which has been developed in the past 20 years its purpose is not to be encyclopedic but to present the basic concepts and techniques which have been developed in that period of time and to illustrate them with examples it takes classical hermite interpolation as a starting point but then successively broadens the assumptions so that finally interpolation of arbitrary functionals and the theory of singularities from algebraic geometry is discussed

survey interpolation methods in medical image processing image interpolation techniques often are required in medical imaging for image generation e g discrete back projection for inverse radon transform and processing such as compression or resampling since the ideal interpolation function spatially is unlimited several interpolation kernels of finite size have been introduced this paper compares 1 truncated and windowed sine 2 nearest neighbor 3 linear 4 quadratic 5 cubic b spline 6 cubic g lagrange and 7 gaussian interpolation and approximation techniques with kernel sizes from 1 spl times 1 up to 8 spl times 8 the comparison is done by 1 spatial and fourier analyses 2 computational complexity as well as runtime evaluations and 3 qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing for local and fourier analyses a standardized notation is introduced and fundamental properties of interpolators are derived successful methods should be direct current dc constant and interpolators rather than dc inconstant or approximators each method s parameters are tuned with respect to those properties this results in three novel kernels which are introduced in this paper and proven to be within the best choices for medical image interpolation the 6 spl times 6 blackman harris windowed sinc interpolator and the c2 continuous cubic kernels with n 6 and n 8 supporting points for quantitative error evaluations a set of 50 direct digital x rays was used they have been selected arbitrarily from clinical routine in general large kernel sizes were found to be superior to small interpolation masks except for truncated sine interpolators all kernels with n 6 or larger sizes perform significantly better than n 2 or n 3 point methods p spl lt 0 005 however the differences within the group of large sized kernels were not significant summarizing the results the cubic 6 spl times 6 interpolator with continuous second derivatives as defined in 24 can be recommended for most common interpolation tasks it appears to be the fastest six point kernel to implement computationally it provides eminent local and fourier properties is easy to implement and has only small errors the same characteristics apply to b spline interpolation but the 6 spl times 6 cubic avoids the intrinsic border effects produced by the b spline technique however the goal of this study was not to determine an overall best method but to present a comprehensive catalogue of methods in a uniform terminology to define general properties and requirements of local techniques and to enable the reader to select that method which is optimal for his specific application in medical imaging

a remark on scalar equations for synchronous boolean networks with biological applications by c farrow j heidel j maloney and j rogers the problem of finding all cycles in the exponentially growing state space of synchronous boolean networks was studied in the paper by c farrow j heidel j maloney and j r scalar equations for synchronous boolean networks with biological applications ieee trans neural networks vol 15 no 2 pp 348 354 mar 2004 no efficient algorithm was given to solve the problem we show that even the determination of the number of fixed points cycles of length 1 for monotone boolean networks and the determination of the existence of fixed points for general boolean networks are both strong np complete

new algorithms for the numerical solution of nonlinear fredholm and volterra integral equations using haar wavelets two new algorithms based on haar wavelets are proposed the first algorithm is proposed for the numerical solution of nonlinear fredholm integral equations of the second kind and the second for the numerical solution of nonlinear volterra integral equations of the second kind these methods are designed to exploit the special characteristics of haar wavelets in both one and two dimensions formulae for calculating haar coefficients without solving the system of equations have been derived these formulae are then used in the proposed numerical methods in contrast to other numerical methods the advantage of our method is that it does not involve any intermediate numerical technique for evaluation of the integral present in integral equations the methods are validated on test problems and numerical results are compared with those from existing methods in the literature

function perturbations on singular boolean networks abstract this paper is devoted to studying function perturbations on the transition matrix and topological structure of a singular boolean network sbn via the semi tensor product of matrices first the algebraic form of an sbn is given and we discuss how the transition matrix of the sbn changes under function perturbations then the local uniqueness of solutions to the sbn is studied under which the impacts of function perturbations on the topological structure are investigated finally examples are given to show the effectiveness of the obtained results

a new algorithm for the solution of nonlinear two dimensional volterra integro differential equations of high order abstract in this manuscript a new numerical approach is developed for approximating the solution of the one dimensional and two dimensional volterra integro differential equations 2d vides of high order new operational matrices of integration based on shifted jacobi polynomials are presented and used in combination with the collocation method to convert the 2d vide into a system of algebraic equations in addition the convergence analysis of the suggested approach is investigated the efficiency of the algorithm is demonstrated by means of several examples and the results are compared with those given using other numerical schemes

disturbance decoupling of boolean control networks disturbance decoupling problem ddp of boolean control networks is considered using semi tensor product of matrices and the matrix expression of logical functions a working procedure is proposed to solve the problem this procedure consists of two key design steps first how to convert a system into an output friendly coordinate frame an algorithm is provided to calculate the output friendly subspaces secondly it was shown how to find proper controllers to solve the problem if it is solvable a state variable separation form is introduced to guide the design of controllers based on the design technique necessary and sufficient conditions are obtained for the solvability of ddp

interpolation revisited medical images application based on the theory of approximation this paper presents a unified analysis of interpolation and resampling techniques an important issue is the choice of adequate basis functions the authors show that contrary to the common belief those that perform best are not interpolating by opposition to traditional interpolation the authors call their use generalized interpolation they involve a prefiltering step when correctly applied the authors explain why the approximation order inherent in any basis function is important to limit interpolation artifacts the decomposition theorem states that any basis function endowed with approximation order ran be expressed as the convolution of a b spline of the same order with another function that has none this motivates the use of splines and spline based functions as a tunable way to keep artifacts in check without any significant cost penalty the authors discuss implementation and performance issues and they provide experimental evidence to support their claims

accurate image rotation using hermite expansions in this paper we propose an approach for the accurate rotation of a digital image using hermite expansions this exploits the fact that if a 2 d continuous bandlimited hermite expansion is rotated the resulting function can be expressed as a hermite expansion with the same bandlimit furthermore the hermite coefficients of the initial 2 d expansion and the rotated expansion are mapped through an invertible linear relationship two efficient methods to compute the mapping between hermite coefficients during rotation are proposed we also propose a method for connecting the hermite expansion and a discrete image using this method we can obtain the hermite expansion from a discrete image and vice versa combining these techniques we propose new methods for the rotation of discrete images we assess the accuracy of our methods and compare them with an existing fft based method implementing three shears we find that the method proposed here consistently has better accuracy than the fft based method

interpolation artifacts in sub pixel image registration we consider the problem of registering aligning two images to sub pixel accuracy by optimization of objective functions constructed from the images intensity values we show that some widely used interpolation methods can introduce multiple local optima in the energy of the interpolated image which if not counter balanced by other terms can cause local optima in registration objective functions including the sum of squared differences cross correlation and mutual information we discuss different solutions to address the problem based on high degree b spline interpolation low pass filtering the images and stochastic integration numerical examples using synthetic and real signals and images are shown