on characterization of elementary trapping sets of variable regular ldpc codes in this paper we study the graphical structure of elementary trapping sets etss of variable regular low density parity check ldpc codes etss are known to be the main cause of error floor in ldpc coding schemes for the set of ldpc codes with a given variable node degree dl and girth g we identify all the nonisomorphic structures of an arbitrary class of a b etss where a is the number of variable nodes and b is the number of odd degree check nodes in the induced subgraph of the ets this paper leads to a simple characterization of dominant classes of etss those with relatively small values of a and b based on short cycles in the tanner graph of the code for such classes of etss we prove that any set s in the class is a layered superset lss of a short cycle where the term layered is used to indicate that there is a nested sequence of etss that starts from the cycle and grows one variable node at a time to generate s this characterization corresponds to a simple search algorithm that starts from the short cycles of the graph and finds all the etss with lss property in a guaranteed fashion specific results on the structure of etss are presented for d l 3 4 5 6 g 6 8 and a b 10 in this paper the results of this paper can be used for the error floor analysis and for the design of ldpc codes with low error floors

nicholson s blowflies revisited a fuzzy modeling approach we apply fuzzy modeling to derive a mathematical model for a biological phenomenon the regulation of population size in the australian sheep blowfly lucilia cuprina this behavior was described by several ethologists and fuzzy modeling allows us to transform their verbal descriptions into a well defined mathematical model the behavior of the resulting mathematical model as studied using both simulations and rigorous analysis is congruent with the behavior actually observed in nature we believe that the fuzzy modeling approach demonstrated here may supply a suitable framework for biomimicry that is the design of artificial systems based on mimicking natural behavior

on the dynamics of the error floor behavior in regular ldpc codes it is shown that dominant trapping sets of regular low density parity check ldpc codes so called absorption sets undergo a two phased dynamic behavior in the iterative message passing decoding algorithm using a linear dynamic model for the iteration behavior of these sets it is shown that they undergo an initial geometric growth phase which stabilizes in a final bit flipping behavior where the algorithm reaches a fixed point this analysis is shown to lead to very accurate numerical calculations of the error floor bit error rates down to error rates that are inaccessible by simulation the topology of the dominant absorption sets of an example code the ieee 802 3an 2048 1723 regular ldpc code are identified and tabulated using topological relationships in combination with search algorithms

error rate estimation of low density parity check codes decoded by quantized soft decision iterative algorithms this paper describes a combinatorial approach to estimate the error rate performance of low density parity check ldpc codes decoded by quantized soft decision iterative decoding algorithms the method is based on efficient enumeration of input vectors with small distances to a reference vector whose elements are selected to be the most reliable values from the input alphabet several techniques including modified cycle enumeration and the efficient derivation of problematic inputs for finer quantizers from those of coarser ones are employed to reduce the complexity of the enumeration the error rate estimate is derived by testing the input vectors of small distances followed by estimating the contribution of larger distance vectors we demonstrate by a number of examples that the proposed method provides accurate estimates of error rate with computational complexity much lower than that of monte carlo simulations especially at the error floor region

error floor approximation for ldpc codes in the awgn channel this paper addresses the prediction of error floors of low density parity check codes transmitted over the additive white gaussian noise channel using a linear state space model to estimate the behavior of the sum product algorithm spa decoder in the vicinity of trapping sets tss we study the performance of the spa decoder in the log likelihood ratio llr domain as a function of the llr saturation level when applied to several widely studied codes the model accurately predicts a significant decrease in the error floor as the saturation level is allowed to increase for nonsaturating decoders however we find that the state space model breaks down after a small number of iterations due to the strong correlation of llr messages we then revisit richardson s importance sampling methodology for estimating error floors due to tss when those floors are too low for monte carlo simulation we propose modifications that account for the behavior of a nonsaturating decoder and present the resulting error floor estimates for the margulis code these estimates are much lower significantly steeper and more sensitive to iteration count than those previously reported

constructing short length irregular ldpc codes with low error floor trapping sets tss are known to cause error floors in regular and irregular low density parity check ldpc codes by avoiding major error contributing tss during the code construction process codes with low error floors can effectively be built in it has been shown that tss labeled as w u are considered as being equivalent under the automorphism of the graph and are therefore contributing equally to the error floor however tss with the same label w u are not identical in general particularly for the case of irregular ldpc codes in this paper we introduce a parameter e that can identify the number of distinguishable cycles in the connected subgraph induced by an elementary trapping set further we propose a code construction algorithm namely the progressive edge growth approximate minimum cycle set extrinsic message degree peg acse method that aims to avoid small elementary trapping sets etss particularly detrimental etss we also develop theorems evaluating the minimum possible etss formed by peg construction algorithms in general we compare the characteristics of the codes built using the proposed method and those built using peg only or peg approximate minimum cycle extrinsic message degree peg ace methods results from simulations show that the codes constructed using the proposed peg acse method produce lower error rates particularly at the high signal to noise snr region compared with codes constructed using other peg based algorithms

the fourier collocation method for the cahn hilliard equation abstract in this paper a fourier collocation method for numerically solving cahn hilliard equations with periodic boundary conditions is developed we establish their semidiscrete and fully discrete schemes that inherit the energy dissipation property and mass conservation property from the associated continuous problem we prove existence and uniqueness of the numerical solution and derive the optimal error bounds we perform some numerical experiments which confirm our results

counting short cycles in bipartite graphs a fast technique algorithm and a hardness result in this paper we propose a new technique based on the so called breadth first search algorithm to count the short cycles of a bipartite graph for a general bipartite graph with v nodes and girth g our technique has a time complexity of mathcal o v 2 delta to count g cycles and g 2 cycles and a time complexity of mathcal o v 2 delta 2 to count g 4 cycles where delta is the maximum node degree in the graph moreover for bi regular bipartite graphs the latter complexity is further reduced to mathcal o v 2 delta compared to the fastest known algorithm which has a complexity mathcal o g v 2 delta 2 the proposed method always has a lower complexity for counting g cycles and g 2 cycles it also has a lower complexity for counting g 4 cycles in bi regular graphs and in scenarios where g is increased with the size of the graph related to the problem of counting short cycles we also demonstrate using a long standing conjecture that there is no algorithm with time complexity less than mathcal o left v 2 frac 2 1 i right that can determine whether a given sparse bipartite graph has a cycle of length 4i an important application of the results presented here is to count the short cycles of tanner graphs of low density parity check ldpc codes

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

hybrid fuzzy control of robotics systems this paper presents a new approach towards optimal design of a hybrid fuzzy controller for robotics systems the salient feature of the proposed approach is that it combines the fuzzy gain scheduling method and a fuzzy proportional integral derivative pid controller to solve the nonlinear control problem the resultant fuzzy rule base of the proposed controller can be decomposed into two layers in the upper layer the gain scheduling method is incorporated with a takagi sugeno ts fuzzy logic controller to linearize the robotics system for a given reference trajectory in the lower layer a fuzzy pid controller is derived for all the locally linearized systems by replacing the conventional pi controller by a linear fuzzy logic controller which has different gains for different linearization conditions within the guaranteed stability region the controller gains can be optimally tuned by genetic algorithms simulation studies on a pole balancing robot and a multilink robot manipulator demonstrate the effectiveness and robustness of the proposed approach

finite length analysis of low density parity check codes on the binary erasure channel in this paper we are concerned with the finite length analysis of low density parity check ldpc codes when used over the binary erasure channel bec the main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of ldpc codes when decoded iteratively we also give expressions for upper bounds on the average bit and block erasure probability for regular ldpc ensembles and the standard random ensemble under maximum likelihood ml decoding finally we present what we consider to be the most important open problems in this area

fuzzy unidirectional force control of constrained robotic manipulators the end effector of a robotic arm is required to keep a contact on the contour of the constraint surface in tasks such as deburring and grinding being different from contacts resulted from general mechanical pairs such a contact is unidirectional or equivalently the contact force can only act along the outward normal of the constraint surface at the contact point how to achieve this specification was not addressed explicitly in many position force control schemes developed so far instead it was assumed in the development of controllers in this paper the unidirectionality of the contact force is explicitly included in modeling and control of constrained robot system a fuzzy tuning mechanism is developed to generate the impedance model resulted from the continuous contact made by the end effector of the robotic manipulator on the constraint surface while it is in motion a controller is then developed based on the fuzzy rule bases and the nonlinear feedback technique the simulation is carried out to verify the effectiveness of the approach

fuzzy lyapunov based approach to the design of fuzzy controllers in this paper we extend the classical lyapunov synthesis method to the domain of computing with words this new approach is used to design fuzzy controllers assuming minimal knowledge about the plant to be controlled the proposed method enables us to systematically derive the fuzzy rules that constitute the rule base of the controller we demonstrate the approach by designing mamdani type and takagi sugeno kang type fuzzy controllers for two well known plants

regular and irregular progressive edge growth tanner graphs we propose a general method for constructing tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge by edge manner called progressive edge growth peg algorithm lower bounds on the girth of peg tanner graphs and on the minimum distance of the resulting low density parity check ldpc codes are derived in terms of parameters of the graphs simple variations of the peg algorithm can also be applied to generate linear time encodeable ldpc codes regular and irregular ldpc codes using peg tanner graphs and allowing symbol nodes to take values over gf q q 2 are investigated simulation results show that the peg algorithm is a powerful algorithm to generate good short block length ldpc codes

error rate estimation of low density parity check codes on binary symmetric channels using cycle enumeration the performance of low density parity check ldpc codes decoded by hard decision iterative decoding algorithms can be accurately estimated if the weight j and the number ej of the smallest error patterns that cannot be corrected by the decoder are known to obtain j and ej one would need to perform the direct enumeration of error patterns with weight i les j the complexity of enumeration increases exponentially with j essentially as nj where n is the code block length this limits the application of direct enumeration to codes with small n and j in this letter we approximate j and ej by enumerating and testing the error patterns that are subsets of short cycles in the code s tanner graph this reduces the computational complexity by several orders of magnitude compared to direct enumeration making it possible to estimate the error rates for almost any practical ldpc code to obtain the error rate estimates we propose an algorithm that progressively improves the estimates as larger cycles are enumerated through a number of examples we demonstrate that the proposed method can accurately estimate both the bit error rate ber and the frame error rate fer of regular and irregular ldpc codes decoded by a variety of hard decision iterative decoding algorithms

a class of stable spectral methods for the cahn hilliard equation in this work the initial boundary value problem of two dimensional cahn hilliard equation is considered a class of fully discrete dissipative fourier spectral schemes are proposed moreover semi implicit prediction correction schemes are presented the numerical simulations are performed to demonstrate the effectiveness of the proposed schemes

on implementation of min sum algorithm and its modifications for decoding low density parity check ldpc codes the effects of clipping and quantization on the performance of the min sum algorithm for the decoding of low density parity check ldpc codes at short and intermediate block lengths are studied it is shown that in many cases only four quantization bits suffice to obtain close to ideal performance over a wide range of signal to noise ratios moreover we propose modifications to the min sum algorithm that improve the performance by a few tenths of a decibel with just a small increase in decoding complexity a quantized version of these modified algorithms is also studied it is shown that when optimized modified quantized min sum algorithms perform very close to and in some cases even slightly outperform the ideal belief propagation algorithm at observed error rates

estimation of bit and frame error rates of finite length low density parity check codes on binary symmetric channels a method for estimating the performance of low density parity check ldpc codes decoded by hard decision iterative decoding algorithms on binary symmetric channels bscs is proposed based on the enumeration of the smallest weight error patterns that cannot be all corrected by the decoder this method estimates both the frame error rate fer and the bit error rate ber of a given ldpc code with very good precision for all crossover probabilities of practical interest through a number of examples we show that the proposed method can be effectively applied to both regular and irregular ldpc codes and to a variety of hard decision iterative decoding algorithms compared with the conventional monte carlo simulation the proposed method has a much smaller computational complexity particularly for lower error rates

fuzzy control of a benchmark problem a computing with words approach the rotational translational proof mass actuator rtac system is a well known benchmark for nonlinear control for which a number of controllers were designed in this paper we apply fuzzy lyapunov synthesis which is a computing with words version of classical lyapunov synthesis to design fuzzy controllers for the rtac system this allows us to systematically design state feedback and output feedback controllers using only a linguistic description of the rtac system the designed fuzzy controllers yield a globally asymptotically stable closed loop system we demonstrate their advantages in comparison with a previously designed linear controller for the rtac system

the legendre collocation method for the cahn hilliard equation in this paper a legendre collocation method for numerically solving cahn hilliard equations with neumann boundary conditions is developed we establish their semi discrete and fully discrete schemes that inherit the energy dissipation property and mass conservation property from the associated continuous problem we prove existence and uniqueness of the numerical solution and derive the optimal error bounds we perform some numerical experiments which confirm our results

how does the dendrocoleum lacteum orient to light a fuzzy modeling approach we apply fuzzy modeling to derive a mathematical model for a biological phenomena the orientation to light of the planarian dendrocoleum lacteum this behavior was described by several ethologists and fuzzy modeling allows us to transform their verbal descriptions into a mathematical model the behavior of the resulting mathematical model as studied using both simulations and rigorous analysis is congruent with the behavior actually observed in nature this seems to indicate that the verbal explanations suggested by the ethologists are indeed correct we believe that the fuzzy modeling approach demonstrated here may supply a suitable framework for biomimicry that is the design of artificial systems based on mimicking a natural behavior observed in nature

chebyshev collocation method for the constant mobility cahn hilliard equation in a square domain abstract chebyshev collocation method was developed for constant mobility cahn hilliard equation the accuracy of the method was indirectly checked with the aid of two separate calculations of temporal derivative of total free energy we found that the derivatives of total free energy by two different ways of calculation coincided exactly when the number of grid points in the transitional layer within mixing region was 16 or more when the coefficient of gradient energy 2 was chosen correspondingly in the given domain we also investigated the application of kosloff and tal ezer mapping for the chebyshev collocation grid points in space and showed the possibility of the use of much larger timestep size than that of the chebyshev collocation method without mapping

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

robust fuzzy logic control of mechanical systems an approach for the design of fuzzy control laws for tracking control of a large class of mechanical systems is proposed the approach employs the framework of lyapunov s stability theory to formulate a class of control laws that guarantee convergence of the tracking errors to within specification limits in presence of bounded parameter uncertainties and input disturbances the proposed control laws possess a large number of parameters and functional relationships to be chosen by the designer according to a methodology developed in the paper the large number of design degrees of freedom makes the approach suitable for fuzzy logic implementation a number of fuzzy implementations of the proposed control methodology are provided all implementations guarantee tracking error convergence to within prespecified performance limits an extensive simulation study using a model of a two degree of freedom robot manipulator was conducted fuzzy and non fuzzy implementations of the proposed methodology were compared to control laws designed using other design methods simulation study results indicate a superiority of the proposed control methodology compared to other approaches the study also demonstrates better performance of the fuzzy control implementation compared to its non fuzzy counterpart

efficient algorithm for finding dominant trapping sets of ldpc codes this paper presents an efficient algorithm for finding the dominant trapping sets of a low density parity check ldpc code the algorithm can be used to estimate the error floor of ldpc codes or as a tool to design ldpc codes with low error floors for regular codes the algorithm is initiated with a set of short cycles as the input for irregular codes in addition to short cycles variable nodes with low degree and cycles with low approximate cycle extrinsic message degree ace are also used as the initial inputs the initial inputs are then expanded recursively to dominant trapping sets of increasing size at the core of the algorithm lies the analysis of the graphical structure of dominant trapping sets and the relationship of such structures to short cycles low degree variable nodes and cycles with low ace the algorithm is universal in the sense that it can be used for an arbitrary graph and that it can be tailored to find a variety of graphical objects such as absorbing sets and zyablov pinsker trapping sets known to dominate the performance of ldpc codes in the error floor region over different channels and for different iterative decoding algorithms simulation results on several ldpc codes demonstrate the accuracy and efficiency of the proposed algorithm in particular the algorithm is significantly faster than the existing search algorithms for dominant trapping sets