a new algorithm for testing diagnosability of fuzzy discrete event systems failure diagnosis and detection of fuzzy discrete event systems play a significant role in the study of complex systems in this paper we investigate the diagnosability of fuzzy discrete event systems by proposing a new algorithm based on the concept of undistinguishable strings moreover a necessary and sufficient condition for fuzzy diagnosability is obtained in terms of certain properties of the diagnoser which is constructed with respect to the minimal observable event the computing process to check the diagnosability of fuzzy dess and some examples serving to illuminate the applications are developed and described

fault detection and isolation based on fuzzy automata fuzzy automata are proposed for fault diagnosis the output of the monitored system is partitioned into linear segments which in turn are assigned to pattern classes templates with the use of membership functions a sequence of templates is generated and becomes input to fuzzy automata which have transitions that correspond to the templates of the properly functioning system if the automata reach their final states i e the input sequence is accepted by the automata with a membership degree that exceeds a certain threshold then normal operation is deduced otherwise a failure is diagnosed fault diagnosis of a dc motor and detection of abnormalities in the ecg signal are used as case studies

lapped transforms for efficient transform subband coding two lapped transforms for subband transform coding of signals are introduced a version of the lapped orthogonal transform lot which can be efficiently computed for any transform length and the modulated lapped transform mlt which is based on a modulated quadrature mirror qmf bank the mlt can also be efficiently computed by means of a type iv discrete sine transform dst iv the lot and the mlt are both asymptotically optimal lapped transforms for coding an ar 1 signal with a high intersample correlation coefficient the coding gains of the lot and mlt of length m are higher than that of the discrete cosine transform dct of the same length they are actually close to the coding gains obtained with a dct of length 2m an mlt based adaptive transform coder act for speech signals is simulated the code is essentially free from frame rate noise and has a better spectral resolution that dct based atc systems

failure detection framework for stochastic discrete event systems with guaranteed error bounds this paper studies the online fault detection for stochastic discrete event systems dess under partial observability of events prior works have only studied the verification of the stochastic diagnosability s diagnosability property to the best of our knowledge this is a first paper that investigates the online detection schemes and also introduces the notions of their missed detections mds and false alarms fas due to the probabilistic nature of the problem mds and fas are possible even for s diagnosable systems and we establish that s diagnosability is a necessary and sufficient condition for achieving any desired levels of md and fa rates we also provide a detection scheme that can achieve the specified md and fa rates based on comparing a suitable detection statistic that we define with a suitable detection threshold that we algorithmically compute we also algorithmically compute the corresponding detection delay bound the detection scheme also works for non s diagnosable systems with the difference that in this case there exists a lower bound for achievable md rate that increases as the fa rate requirement is made more stringent by decreasing it

research problems from the aveiro workshop on graph spectra abstract this is a collection of open problems presented at the aveiro workshop on graph spectra held at the university of aveiro portugal from april 10 12 2006

theory of two dimensional multirate filter banks results are presented on 2 d fir two dimensional finite impulse response filter banks for multirate applications the theory is valid for all sampling lattices conditions for alias free and perfect signal reconstruction are derived synthesis structures for paraunitary and nonparaunitary polynomial matrices are derived which yield perfect reconstruction filter banks the degrees of freedom are given for these systems linear phase conditions are posed on the polyphase form of filter banks which is used to derive a design structure for the restricted but important case of linear phase filter banks

a polynomial algorithm for testing diagnosability of discrete event systems failure diagnosis in large and complex systems is a critical task in the realm of discrete event systems sampath et al 1995 proposed a language based failure diagnosis approach they introduced the diagnosability for discrete event systems and gave a method for testing the diagnosability by first constructing a diagnoser for the system the complexity of this method of testing diagnosability is exponential in the number of states of the system and doubly exponential in the number of failure types we give an algorithm for testing diagnosability that does not construct a diagnoser for the system and its complexity is of fourth order in the number of states of the system and linear in the number of the failure types

fast computation of von neumann entropy for large scale graphs via quadratic approximations abstract the von neumann graph entropy vnge can be used as a measure of graph complexity which can be the measure of information divergence and distance between graphs however computing vnge is extensively demanding for a large scale graph we propose novel quadratic approximations for fast computing vnge various inequalities for error between the quadratic approximations and the exact vnge are found our methods reduce the cubic complexity of vnge to linear complexity computational simulations on random graph models and various real network datasets demonstrate superior performance

nonblocking check in fuzzy discrete event systems based on observation equivalence in this paper we deal with the synthesis about nonblocking check in fuzzy discrete event systems fdess by using abstraction and observation equivalence of fuzzy finite automaton ffa in fdess such a check imposes a great computational challenge because of the complexity incurred by the composition of plants and the supervisors with respect to ideas in modeling control system we present procedure based on ffa abstractions which removes internal transitions of irrelevant transitions allowing the nonblocking check to be performed on relatively small automata

diagnosability of stochastic discrete event systems we investigate diagnosability of stochastic discrete event systems we define the notions of a and aa diagnosability for stochastic automata these notions are weaker than the corresponding notion of diagnosability for logical automata introduced by sampath et al through the construction of a stochastic diagnoser we determine offline conditions necessary and sufficient to guarantee a diagnosability and sufficient to guarantee aa diagnosability we also show how the stochastic diagnoser can be used for on line diagnosis of failure events we illustrate the results through two examples from hvac systems

diagnosability of fuzzy discrete event systems a fuzzy approach in order to more effectively cope with the real world problems of vagueness fuzzy discrete event systems fdess were proposed by lin and ying recently then we and cao and ying investigated the supervisory control of fdess independently in this paper we are concerned with another important issue of fdess the failure diagnosis more specifically 1 we propose a ldquofuzzy diagnosabilityrdquo approach by introducing a fuzzy diagnosability function to characterize the diagnosability degree which takes values in the interval 0 1 rather than 0 1 2 based on the observability of events we formalize the construction of the diagnosers that are used to perform fuzzy diagnosis 3 a number of basic properties of the diagnosers are investigated in particular we present a necessary and sufficient condition for failure diagnosis of fdess our results generalize the important consequences of the diagnosability for crisp discrete event systems dess introduced by sampath et al the newly proposed approach allows us to deal with the problem of diagnosability for both crisp dess and fdess 4 in addition a method for checking the fuzzy diagnosability for fdess is proposed also some examples are provided to illustrate the application of the diagnosability of fdess

two dimensional perfect reconstruction fir filter banks with triangular supports we present a theory and design of two dimensional 2 d perfect reconstruction pr filter banks fbs prfbs in which the supports of the analysis and synthesis filters consist of two triangulars the two triangular fb can be realized by designing an appropriate 2 d complex prototype whose passband support is a triangle that is a half of a parallelepiped shaped passband support defined by the sampling matrix then a complex prototype filter is modulated by the dft and each analysis filter is derived by taking the real part of the modulated output we show that the two triangular fb satisfies the condition of permissibility a necessary and sufficient condition for 2 d prfbs is derived moreover we present a design method of the 2 d prfb that minimizes the cost function consisting of the frequency constraint and pr condition finally a design example is presented to confirm the validity of the proposed method

spectral distances of graphs abstract let 1 g 2 g n g be the adjacency spectrum of a graph g on n vertices the spectral distance g 1 g 2 between n vertex graphs g 1 and g 2 is defined by g 1 g 2 i 1 n i g 1 i g 2 here we provide some initial results regarding this quantity first we give some general results concerning the spectral distances between arbitrary graphs and compute these distances in some particular cases certain relation with the theory of graph energy is identified the spectral distances bounded by a given constant are also considered next we introduce the cospectrality measure and the spectral diameter and obtain specific results indicating their relevance for the theory of cospectral graphs finally we give and discuss some computational results and conclude the paper by a list of conjectures

distance between the normalized laplacian spectra of two graphs abstract let g v e be a simple graph of order n the normalized laplacian eigenvalues of graph g are denoted by 1 g 2 g n 1 g n g 0 also let g and g be two nonisomorphic graphs on n vertices define the distance between the normalized laplacian spectra of g and g as n g g i 1 n i g i g p p 1 define the cospectrality of g by c s n g min n g g g not isomorphic to g let c s n n max c s n g g a graph on n vertices in this paper we give an upper bound on c s n g in terms of the graph parameters moreover we obtain an exact value of c s n n an upper bound on the distance between the normalized laplacian spectra of two graphs has been presented in terms of randic energy as an application we determine the class of graphs which are lying closer to the complete bipartite graph than to the complete graph regarding the distance of normalized laplacian spectra

maximally decimated perfect reconstruction fir filter banks with pairwise mirror image analysis and synthesis frequency responses structures are presented for the perfect reconstruction quadrature mirror filter bank that are based on lossless building blocks these structures ensure that the frequency responses of the analysis and synthesis filters have pairwise symmetry with respect to pi 2 and require fewer parameters than recently reported structures also based on lossless building blocks the design time for the proposed structures is correspondingly much less than for the earlier methods which did not incorporate such symmetry

distance between spectra of graphs richard brualdi proposed in stevanivic 2007 10 the following problem problem awgs 4 let gngn and gn be two nonisomorphic graphs on n vertices with spectra 1 2 nand 1 2 n respectively define the distance between the spectra of gngn and gn as gn gn i 1n i i 2 or use i 1n i i define the cospectrality of gngn by cs gn min gn gn gn not isomorphic to gn let csn max cs gn gn a graph on n vertices problem a investigate cs gn cs gn for special classes of graphs problem b find a good upper bound on csncsn in this paper we completely answer problem b by proving that csn 2csn 2 for all n 2n 2 whenever csncsn is computed with respect to any lplp norm with 1 p 1 p and csn 1csn 1 with respect to the l l norm the cospectrality cs km n cs km n of the complete bipartite graph km nkm n for all positive integers m and n with m n m 1 2m 1 is computed as a consequence of the latter result it is proved that in general there is no constant upper bound on e e e e where e and e e denote the number of edges of the graphs g and g g respectively such that cs g g g cs g g g in contrast we show that for such graphs g and g g we have e e 1 in particular e e 3e e e 3e

decentralized diagnosis of stochastic discrete event systems we investigate the decentralized diagnosis of stochastic discrete event systems sdess by using multiple local stochastic diagnosers each possessing its own sensors to deal with different information we formalize the notions of decentralized diagnosis for sdess by defining the concept of codiagnosability for stochastic automata in which any communication among the local stochastic diagnosers or to any coordinators is not involved these notions are weaker than the corresponding notions of decentralized diagnosis of classical dess a stochastic system being codiagnosable means that a fault can be detected by at least one local stochastic diagnoser within a finite delay we construct a codiagnoser from a given stochastic system with a finite number of projections whose each diagnosis component uses the complete model of the system we also deal with a number of basic properties of the codiagnoser in particular a necessary and sufficient condition of the codiagnosability for sdess is presented which generalizes the corresponding results of centralized diagnosis for sdess also we give a computing method in detail to check the codiagnosability of sdess as an application of our results some examples are described

theory and design of m channel maximally decimated quadrature mirror filters with arbitrary m having the perfect reconstruction property based on the concept of losslessness in digital filter structures this paper derives a general class of maximally decimated m channel quadrature mirror filter banks that lead to perfect reconstruction the perfect reconstruction property guarantees that the reconstructed signal hat x n is a delayed version of the input signal x n i e hat x n x n n 0 it is shown that such a property can be satisfied if the alias component matrix ac matrix for short is unitary on the unit circle of the z plane the number of channels m is arbitrary and when m is two the results reduce to certain recently reported 2 channel perfect reconstruction qmf structures a procedure based on recently reported fir cascaded lattice structures is presented for optimal design of such fir m channel filter banks design examples are included

two dimensional 2 times oversampled dft modulated filter banks and critically sampled modified dft modulated filter banks this paper investigates two dimensional 2d 2 oversampled dft modulated filter banks and 2d critically sampled modified dft mdft modulated filter banks as well as their design the structure and perfect reconstruction pr condition of 2d 2 oversampled dft modulated filter banks are presented in terms of the polyphase decompositions of prototype filters pfs in the double prototype case the part solutions of the pr condition are parameterized by imposing the 2d two channel lifting structure on each pair of the polyphase components of analysis and synthesis pfs based on the parametric structure the analysis and synthesis pfs are separately designed by constrained quadratic programs the obtained filter banks are of structurally pr moreover 2d critically sampled mdft modulated filter banks are proposed it is proved that 2d critically sampled pr mdft modulated filter banks can be rebuilt from 2d 2 oversampled pr dft modulated filter banks when the decimation matrices satisfy a permissible condition and the analysis and synthesis pfs are identical and symmetric with respect to the origin a numerical algorithm is given to design 2d critically sampled pr mdft modulated filter banks and the obtained filter banks are of numerically pr

multiresolution direction filterbanks theory design and applications this paper presents new developments of directional filterbanks dfbs the motivation for the paper is the existence of multiresolution and multidirection orthogonal transform for two dimensional 2 d discrete signals based on the frequency supports of the ideal transform a new uniformly maximally decimated dfb with six highpass directional subbands and two lowpass subands is introduced the uniform dfb udfb can be implemented by a binary tree structure of two channel filterbanks the filterbank employed in the tree is shown to be alias free decimation and permissible the udfb is then extended to a nonuniform case nudfb which is still maximally decimated by combining the two lowpass subbands the nudfb yields nonuniform frequency division which composes of one lowpass filter with a decimation factor of one fourth and six highpass directional filters with a decimation factor of one eighth the new dfbs offer alternative image decompositions which overcome the limited directional selectivity of the separable wavelets and the limited multiresolution of the conventional dfb the lowpass subband of the nudfb can be used to obtain a multiresolution representation by simply reiterating the same nudfb decomposition on the other hand the directional subbands can also be further refined by simply applying a two channel conventional dfb at each highpass component a simple design method yielding near orthogonal uniform and nonuniform multidimensional filterbanks is presented finally the performances of the newly proposed nudfb are compared with other conventional transforms in nonlinear approximation image denoising and texture classification to demonstrate its potential

cospectrality of graphs richard brualdi proposed in stevanivic 2007 6 the following problem problem awgs 4 let gngn and gn be two nonisomorphic graphs on n vertices with spectra 1 2 nand 1 2 n respectively define the distance between the spectra of gngn and gn as gn gn i 1n i i 2 or use i 1n i i define the cospectrality of gngn by cs gn min gn gn gn not isomorphic to gn let csn max cs gn gn a graph on n vertices problem a investigate cs gn cs gn for special classes of graphs problem b find a good upper bound on csncsn in this paper we study problem a and determine the cospectrality of certain graphs by the euclidian distance let knkn denote the complete graph on n vertices nk1nk1 denote the null graph on n vertices and k2 n 2 k1k2 n 2 k1 denote the disjoint union of the k2k2 with n 2n 2 isolated vertices where n 2n 2 in this paper we find cs kn cs kn cs nk1 cs nk1 cs k2 n 2 k1 cs k2 n 2 k1 n 2n 2 and cs kn n cs kn n

cosine modulated fir filter banks satisfying perfect reconstruction the authors obtain a necessary and sufficient condition on the 2m m number of channels polyphase components of a linear phase prototype filter of length n 2 mm where m an arbitrary positive integer such that the polyphase component matrix of the modulated filter is lossless the losslessness of the polyphase component matrix in turn is sufficient to ensure that the analysis synthesis system satisfies perfect reconstruction pr using this result a novel design procedure is presented based on the two channel lossless lattice this enables the design of a large class of fir finite impulse response pr filter banks and includes the n 2m case it is shown that this approach requires fewer parameters to be optimized than in the pseudo qmf quadrature mirror filter designs and in the lossless lattice based pr qmf designs for equal length filters in the three designs this advantage becomes significant when designing long filters for large m the design procedure and its other advantages are described in detail design examples and comparisons are included

six classes of trees with largest normalized algebraic connectivity abstract the normalized algebraic connectivity of a graph g denoted by 2 g is the second smallest eigenvalue of its normalized laplacian matrix in this paper we firstly determine all trees with 2 g 1 6 3 then we classify such trees into six classes c 1 c 6 and prove that 2 t i 2 t j for 1 i j 6 where t i c i and t j c j at the same time the values of the normalized algebraic connectivity for the six classes of trees are provided respectively these results are similar to those on the algebraic connectivity which were obtained by yuan et al 2008 8

brief paper bisimilarity control of partially observed nondeterministic discrete event systems and a test algorithm in this paper the bisimilarity control of discrete event systems dess under partial observations is investigated where the plant and the specification are allowed to be nondeterministic a notation of simulation based controllability and a synchronization scheme for the supervised system are formalized based on the simulation relation between the specification and the plant it is shown that the existence of bisimilarity supervisors is characterized by the notions of the simulation based controllability and the language observability which extends the traditional results of supervisory control from language equivalence to bisimulation equivalence in addition a polynomial algorithm to test the simulation based controllability is developed by constructing a computing tree this algorithm together with the test of language observability can be used to check the existence of bisimilarity supervisors

global and local consistencies in distributed fault diagnosis for discrete event systems in this paper we present a unified framework for distributed diagnosis we first introduce the concepts of global and local consistency in terms of supremal global and local supports then present two distributed diagnosis problems based on them after that we provide algorithms to achieve supremal global and local supports respectively and discuss in detail the advantages and disadvantages of each finally we present an industrial example to demonstrate our distributed diagnosis approach

comparing large scale graphs based on quantum probability theory abstract in this paper a new measurement to compare two large scale graphs based on the theory of quantum probability is proposed an explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established our proposed distance between two graphs is defined as the distance between the corresponding moment matrices of their spectral distributions it is shown that the spectral distributions of their adjacency matrices in a vector state includes information not only about their eigenvalues but also about the corresponding eigenvectors moreover we prove that the proposed distance is graph invariant and sub structure invariant examples with various graphs are given and distances between graphs with few vertices are checked computational results for real large scale graphs show that its accuracy is better than any existing methods and time cost is extensively cheap

analysis and control of fuzzy discrete event systems using bisimulation equivalence in order to more effectively cope with the real world problems of vagueness impreciseness and subjectivity fuzzy discrete event systems fdess were proposed recently in this paper we deal with the analysis and control of fuzzy discrete event systems by using bisimulation equivalence in practice we design a supervisor such that the controlled system is bisimilar to the specification also a model theorem showing that a supervisor exists over a certain finite fuzzy state space is obtained furthermore the notion of fuzzy state controllability is introduced as part of a necessary and sufficient condition for the existence of a supervisor

fault diagnosis in discrete event systems framework and model reduction a state based approach for online passive fault diagnosis in systems modeled as finite state automata is presented in this framework the system and the diagnoser the fault detection system do not have to be initialized at the same time furthermore no information about the state or even the condition failure status of the system before the initiation of diagnosis is required the design of the fault detection system in the worst case has exponential complexity a model reduction scheme with polynomial time complexity is introduced to reduce the computational complexity of the design diagnosability of failures is studied and necessary and sufficient conditions for failure diagnosability are derived

a class of multiresolution directional filter banks in this paper we introduced a class of directional filter banks dfbs having the previously proposed uniform dfb udfb as a special case except for the udfb each dfb in this class can be used to decompose an image yielding up to 12 directions while maintaining perfect reconstruction and maximal decimation a multiresolution representation can be obtained by repeating the same decomposition at the lowpass band the permissible property of the filter banks in cases of being implemented by a tree structure and by direct implementation is discussed the result shows that only one dfb in the class called the uniform quincunx dfb uqdfb satisfies the permissible property when being implemented directly without using the tree structure the nonuniform quincunx dfb nuqdfb is then constructed from the uqdfb by merging its two lowpass subbands an alternative structure for constructing the nuqdfb is presented the new structure while yielding the same frequency partitioning allows the dfb to be realized with complexity comparable to that of the separable wavelet filter bank the connection between the discrete filter bank and the continuous directional wavelet is also established numerical experiments on directional feature extractions image denoising and nonlinear approximation are presented at the end of the paper to demonstrate the potential of the nuqdfb

multidimensional multirate filters and filter banks derived from one dimensional filters a method by which every multidimensional m d filter with an arbitrary parallelepiped shaped passband support can be designed and implemented efficiently is presented it is shown that all such filters can be designed starting from an appropriate one dimensional prototype filter and performing a simple transformation with d denoting the number of dimensions the complexity of design and implementation of the m d filter are reduced from o n sup d to o n using the polyphase technique an implementation with complexity of only 2n is obtained in the two dimensional even though the filters designed are in general nonseparable they have separable polyphase components one special application of this method is in m d multirate signal processing where filters with parallelepiped shaped passbands are used in decimation interpolation and filter banks some generalizations and other applications of this approach including m d uniform discrete fourier transform dft quadrature mirror filter banks that achieve perfect reconstruction are studied several design example are given