universality of sequential spiking neural p systems based on minimum spike number spiking neural p systems sn p systems for short are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes each neuron can have several spiking rules and forgetting rules and neurons work in parallel in the sense that each neuron that can fire should fire at each computation step in this work we consider sn p systems working in the sequential way where the sequentiality is induced by the minimum number of spikes at each step one resp all of the neurons with the minimum number of spikes among the neurons that are active can fire will fire called min sequentiality resp min pseudo sequentiality we prove that sn p systems working in min sequentiality or min pseudo sequentiality are universal as both number generating and accepting devices where the computation results are encoded by the time elapsed between the first two spikes of the output neuron the results give positive answers to two open problems formulated in o h ibarra a paun a rodriguez paton sequential snp systems based on min max spike number theoretical computer science 410 30 32 2009 2982 2991

normal forms for spiking neural p systems the spiking neural p systems are a class of computing devices recently introduced as a bridge between spiking neural nets and membrane computing in this paper we prove a series of normal forms for spiking neural p systems concerning the regular expressions used in the firing rules the delay between firing and spiking the forgetting rules used and the outdegree of the graph of synapses in all cases surprising simplifications are found without losing the computational completeness sometimes at the price of slightly increasing other parameters which describe the complexity of these systems

efficient parallel boolean matrix based algorithms for computing composite rough set approximations in information systems there may exist multiple different types of attributes like categorical attributes numerical attributes set valued attributes interval valued attributes missing attributes etc such information systems are called as composite information systems to process such attributes with rough set theory composite rough set model and corresponding matrix methods were introduced in our previous study calculation of rough set approximations of a concept is the key step for rule acquisition and attribute reduction in rough set based methods to accelerate the computation process of rough set approximations this paper first presents the boolean matrix representation of the lower and upper approximations in the composite information system then designs a parallel method for computing approximations based on matrix and implements it on multi gpu the experiments on data sets from uci and user defined data sets show that the proposed method can accelerate the computation process efficiently the multi gpu implementation achieves up to a speedup of 334 9 over the cpu implementation

an exact penalty function for semi infinite programming this paper introduces a global approach to the semi infinite programming problem that is based upon a generalisation of the l1 exact penalty function the advantages are that the ensuing penalty function is exact and the penalties include all violations the merit function requires integrals for the penalties which provides a consistent model for the algorithm the discretization is a result of the approximate quadrature rather than an a priori aspect of the model

reducts and constructs in classic and dominance based rough sets approach abstract the idea of the reduct as defined in the classic rough sets approach crsa has proven to be inspiring enough to get into closely related theories including the dominance based rough sets approach drsa the procedure of reduction is generally similar to that of feature selection but narrower as it is the descriptive rather than the predictive aspect of data exploration that constitutes its principal goal crsa reducts are thus defined as minimal subsets of attributes that retain sufficiently high quality of object description developed within crsa the crsa reducts have given rise to the generalized notion of crsa constructs which have turned out to be superior to reducts in numerous practical experiments with real life data sets the generalization process is continued in this paper in which a definition of constructs in the context of drsa is introduced the definition fully analogous to that of crsa constructs differs only in that it is context based in drsa while context free in crsa consequently the presented drsa constructs are expected to have analogous properties to that of crsa constructs including superiority to drsa reducts in experiments with real life data sets

depth imaging with multiples depth imaging with multiples is a prestack depth migration method that uses multiples as the signal for more accurate boundary mapping and amplitude recovery the idea is partially related to model based multiple suppression techniques and reverse time depth migration conventional reverse time migration uses the two way wave equation for the backward wave propagation of recorded seismic traces and ray tracing or the eikonal equation for the forward traveltime computation the excitation time imaging principle consequently reverse time migration differs little from most other one way wave equation or ray tracing migration methods which expect only primary reflection events because it is almost impossible to attenuate multiples without degrading primaries there has been a compelling need to devise a tool to use multiples constructively in data processing rather than attempting to destroy them furthermore multiples and other nonreflecting wave types can enhance boundary imaging and amplitude recovery

composite rough sets for dynamic data mining as a soft computing tool rough set theory has become a popular mathematical framework for pattern recognition data mining and knowledge discovery it can only deal with attributes of a specific type in the information system by using a specific binary relation however there may be attributes of multiple different types in information systems in real life applications such information systems are called as composite information systems in this paper a composite relation is proposed to process attributes of multiple different types simultaneously in composite information systems then an extended rough set model called as composite rough sets is presented we also redefine lower and upper approximations positive boundary and negative regions in composite rough sets through introducing the concepts of the relation matrix the decision matrix and the basic matrix we propose matrix based methods for computing the approximations positive boundary and negative regions in composite information systems which is crucial for feature selection and knowledge discovery moreover combined with the incremental learning technique a novel matrix based method for fast updating approximations is proposed in dynamic composite information systems extensive experiments on different data sets from uci and user defined data sets show that the proposed incremental method can process large data sets efficiently

double fold localized multiple matrixized learning machine in this paper we develop an effective multiple matrixized learning machine named double fold localized multiple matrixized learning machine dlmmlm the characteristic of the proposed dlmmlm is that it possesses double folds of local information from data the first fold lies in the whole representation space which consists of different matrix representations it is known that each pattern can be represented by different matrix representations the matrices have their respective representation information and can play different discriminant roles in the final classification therefore from the viewpoint of the whole representation space each matrix has its own local information the second fold is that in each matrix representation learning different patterns represented with the same matrix representation can carry different information therefore in the pattern space with the same matrix size local information of different patterns should be introduced into the classifier design on the whole the advantages of the proposed dlmmlm are i establishing a pattern depended function in the matrixized learning so as to realize different roles of patterns for the first time ii adopting the double fold local information in both the representation space and the pattern space iii proposing a new nonlinear classifier that is different from the state of the art kernelization one and iv getting a tighter empirical generalization risk bound in terms of the rademacher complexity and thus achieving a statistically superior classification performance than those classifiers without the introduction of the double fold local information

relational interpretations of neighborhood operators and rough set approximation operators this paper presents a framework for the formulation interpretation and comparison of neighborhood systems and rough set approximations using the more familiar notion of binary relations a special class of neighborhood systems called 1 neighborhood systems is introduced three extensions of pawlak approximation operators are analyzed properties of neighborhood and approximation operators are studied and their connections are examined

spiking neural p systems with polarizations spiking neural p sn p systems are a class of parallel computation models inspired by neurons where the firing condition of a neuron is described by a regular expression associated with spiking rules however it is np complete to decide whether the number of spikes is in the length set of the language associated with the regular expression in this paper in order to avoid using regular expressions two major and rather natural modifications in their form and functioning are proposed the spiking rules no longer check the number of spikes in a neuron but in exchange a polarization is associated with neurons and rules one of the three electrical charges 0 surprisingly enough the computing devices obtained are still computationally complete which are able to compute all turing computable sets of natural numbers on this basis the number of neurons in a universal sn p system with polarizations is estimated several research directions are mentioned at the end of this paper

migration with the full acoustic wave equation conventional finite difference migration has relied on one way wave equations which allow energy to propagate only downward although generally reliable such equations may not give accurate migration when the structures have strong lateral velocity variations or steep dips the present study examined an alternative approach based on the full acoustic wave equation the migration algorithm which developed from this equation was tested against synthetic data and against physical model data the results indicated that such a scheme gives accurate migration for complicated structures

rough approximation of a fuzzy concept on a hybrid attribute information system and its uncertainty measure abstract one important and valuable topic in rough set theory is the concept of approximation over various generalized information systems although rough set models and approaches over hybrid attribute sets have been studied by many researchers recently the studies focus on the rough approximation of a crisp concept over a hybrid attribute information system this paper considers the rough approximation of a fuzzy concept over a hybrid attribute information system we define a hybrid indiscernibility relation by compounding the fuzzy indiscernibility similarity relation over numerical attributes with the equivalence relation over symbolic attributes then we present the lower and upper approximations of a fuzzy set based on the hybrid indiscernibility relation i e the fuzzy rough set over a hybrid attribute information system also some interesting properties of the hybrid fuzzy rough approximation operators are presented in detail and the relationship between the fuzzy rough set and the existing rough set model over a hybrid attribute information system is established meanwhile based on the definition of the cut set of a fuzzy set of the universe of discourse the representations of the lower and upper approximations of a fuzzy set are given with respect to hybrid attribute approximation space furthermore the concept of the cut set of the hybrid indiscernibility relation of the hybrid attribute approximation space is defined then the characterizations of the hybrid fuzzy rough approximation operators are established as well two different types of characterization theorems of the hybrid fuzzy rough approximation operators are presented based on the cut set of the hybrid indiscernibility relation over the hybrid attribute information system at the same time we study the uncertainty measure of the fuzzy rough set over a hybrid attribute information system by using knowledge granulation the main contribution of this paper is twofold one is to extend the existing rough set approach over hybrid attribute information systems to a fuzzy environment another is to present a new way to define the rough approximation of a fuzzy concept as well the uncertainty measure over hybrid attribute information systems

a fuzzy rough set approach for incremental feature selection on hybrid information systems in real applications there may exist many kinds of data e g boolean categorical real valued and set valued data and missing data in an information system which is called as a hybrid information system his a new hybrid distance hd in his is developed based on the value difference metric and a novel fuzzy rough set is constructed by combining the hd distance and the gaussian kernel considering the information systems often vary with time the updating mechanisms for attribute reduction feature selection are analyzed with the variation of the attribute set fuzzy rough set approaches for incremental feature selection on his are presented then two corresponding incremental algorithms are proposed respectively finally extensive experiments on eight datasets from uci and an artificial dataset show that the incremental approaches significantly outperform non incremental approaches with feature selection in the computational time

spiking neural p systems with rules on synapses spiking neural p systems sn p systems for short are a class of membrane systems inspired from the way the neurons process information and communicate by means of spikes in this paper we introduce and investigate a new class of sn p systems with spiking rules placed on synapses the computational completeness is first proved then two small universal sn p systems with rules on synapses for computing functions are constructed specifically when using standard spiking rules we obtain a universal system with 39 neurons while when using extended spiking rules on synapses a universal sn p system with 30 neurons is constructed

neighborhood rough set based heterogeneous feature subset selection feature subset selection is viewed as an important preprocessing step for pattern recognition machine learning and data mining most of researches are focused on dealing with homogeneous feature selection namely numerical or categorical features in this paper we introduce a neighborhood rough set model to deal with the problem of heterogeneous feature subset selection as the classical rough set model can just be used to evaluate categorical features we generalize this model with neighborhood relations and introduce a neighborhood rough set model the proposed model will degrade to the classical one if we specify the size of neighborhood zero the neighborhood model is used to reduce numerical and categorical features by assigning different thresholds for different kinds of attributes in this model the sizes of the neighborhood lower and upper approximations of decisions reflect the discriminating capability of feature subsets the size of lower approximation is computed as the dependency between decision and condition attributes we use the neighborhood dependency to evaluate the significance of a subset of heterogeneous features and construct forward feature subset selection algorithms the proposed algorithms are compared with some classical techniques experimental results show that the neighborhood model based method is more flexible to deal with heterogeneous data

inversion versus migration a new perspective to an old discussion seismic imaging techniques can be subdivided into inversion and migration the object functions for inversion and migration are respectively the medium contrast parameters and reflectivity in this paper the relationship between inversion and migration is approached by analyzing the underlying representations the forward models it appears that the two way representation which underlies inversion as well as the one way representation which underlies migration can both be expressed in terms of a volume integral over the appropriate object function in their linearized form these representations account for primaries only in this case the one way representation in terms of reflectivity is the most accurate of the two which implies that proper migration is more accurate than linearized inversion internal multiples can be taken into account by the nonlinear representations as an alternative however the generalized primary representation is introduced in its explicit form this one way

full wave equation depth extrapolation for migration most of the traditional approaches to migration by downward extrapolation suffer from inaccuracies caused by using one waypropagation bothintheconstructionofsuchpropagatorsinavariablebackgroundandthesuppressionofpropagatingwavesgeneratedby e g steepreflectors wepresenta new mathematical formulation and an algorithm for downward extrapolation that suppress only the evanescent waves weshowthatevanescentwavemodesareassociatedwiththe positive eigenvalues of the spatial operator and introduce spectralprojectorstoremovethesemodes leavingallpropagating modes corresponding to nonpositive eigenvalues intact this approach suppresses evanescent modes in an arbitrarylaterallyvaryingbackground ifthebackgroundvelocityisonlydepthdependent thenthespectralprojectormaybe applied by using the fast fourier transform and a filter in the fourier domain in computing spectral projectors we use an iterationthatavoidstheexplicitconstructionoftheeigensystem moreover weusearepresentationofmatricesleadingto fast matrix matrix multiplication and as a result a fast algorithmnecessaryforpracticalimplementationofspectralprojectors the overall structure of the migration algorithm is similar to survey sinking with an important distinction of using a new method for downward continuation using a blurredversionofthetruevelocityasabackground steepreflectorscanbeimagedina2dsliceoftheseg eagemodel

incremental updating of rough approximations in interval valued information systems under attribute generalization interval valued information system ivis is a generalized model of single valued information system in which the attribute values of objects are all interval values instead of single values the attribute set in ivis is not static but rather dynamically changing over time with the collection of new information which results in the continuous updating of rough approximations for rough set based data analysis in this paper on the basis of the similarity based rough set model in ivis we develop incremental approaches for updating rough approximations in ivis under attribute generalization which refers to the dynamic changing of attributes firstly increment relationships between the original rough approximations and the updated ones when adding or deleting an attribute set are analyzed respectively and the incremental mechanisms for updating rough approximations in ivis are introduced which carry out the computation using the previous results from the original data set along with new results then the corresponding incremental algorithms are designed based on the proposed mechanisms finally comparative experiments on data sets from uci as well as artificial data sets are conducted respectively experimental results show that the proposed incremental algorithms can effectively reduce the running time for the computation of rough approximations in comparison with the static algorithm

machine learning models epistemic set valued data and generalized loss functions we study those problems where the goal is to find optimal models with respect to some specific criterion in regression and supervised classification problems alternatives to the usual expected loss minimization criterion are proposed and a general framework where this criterion can be seen as a particular instance of a general family of criteria is provided in the new setting each model is formally identified with a random variable that associates a loss value to each individual in the population based on this identification different stochastic orderings between random variables lead to different criteria to compare pairs of models our general setting encompasses the classical criterion based on the minimization of the expected loss but also other criteria where a numerical loss function is not available and therefore the computation of its expectation does not make sense the presentation of the new framework is divided into two stages first we consider the new framework under standard situations about the sample information where both the collection of attributes and the response variables are observed with precision then we assume that just incomplete information about them expressed in terms of set valued data sets is provided we cast some comparison criteria from the recent literature on learning methods from low quality data as particular instances of our general approach

sequential snp systems based on min max spike number we consider the properties of spiking neural p snp systems that work in a sequential manner these snp systems are a class of computing devices recently introduced as a bridge between spiking neural nets and membrane computing the general sequentiality of these systems was considered previously now we focus on the sequentiality induced by the spike number at each step the neuron with the maximum or minimum number of spikes among the neurons that are active can spike will fire this strategy corresponds to a global view of the whole network that makes the system sequential we study the properties of this type of a restriction i e considering the case of sequentiality induced by the function maximum defined on numbers of spikes as well as the case of the sequentiality induced by the function minimum similarly defined on numbers of spikes several universality results are obtained for the cases of maximum and minimum induced sequentiality

optimized chebyshev fourier migration a wide angle dual domain method for media with strong velocity contrasts a wide angle propagator is essential when imaging complex media with strong lateral velocity contrasts in one way waveequation migration we have developed a dual domain one way propagator using truncated chebyshev polynomials and a globally optimized scheme our method increases the accuracy of the expanded square root operator by adding two high order terms to the traditional split step fourier propagator first we approximate the square root operator using taylor expansion around the reference background velocity then we apply the first kindchebyshevpolynomialstoeconomizetheresultsofthe taylor expansion finally we optimize the constant coefficients using the globally optimized scheme which are fixed and feasible for arbitrary velocity models theoretical analysis and numericalexperimentshavedemonstratedthatthemethodhasvery highaccuracyandexceedstheunoptimizedfourierfinite difference propagator for the entire range of practical velocity contrasts the accurate propagation angle of the method is always about 60 under the relative error of 1 for complex media with weak moderate and even strong lateral velocity contrasts the method allows us to handle wide angle propagations and strong lateral velocity contrast simultaneously by using fourier transform alone only four 2d fourier transforms are required for each step of 3d wavefield extrapolation and the computing cost is similar to that of the fourier finite difference method compared with the finite difference method our method has no twowaysplittingerrori e azimuthal anisotropyerrorfor3dcases and almost no numerical dispersion for coarse grids in addition it has strong potential to be accelerated when an enhanced fast fouriertransformalgorithmemerges

set valued ordered information systems set valued ordered information systems can be classified into two categories disjunctive and conjunctive systems through introducing two new dominance relations to set valued information systems we first introduce the conjunctive disjunctive set valued ordered information systems and develop an approach to queuing problems for objects in presence of multiple attributes and criteria then we present a dominance based rough set approach for these two types of set valued ordered information systems which is mainly based on substitution of the indiscernibility relation by a dominance relation through the lower upper approximation of a decision some certain possible decision rules from a so called set valued ordered decision table can be extracted finally we present attribute reduction also called criteria reduction in ordered information systems approaches to these two types of ordered information systems and ordered decision tables which can be used to simplify a set valued ordered information system and find decision rules directly from a set valued ordered decision table these criteria reduction approaches can eliminate those criteria that are not essential from the viewpoint of the ordering of objects or decision rules

an axiomatic characterization of a fuzzy generalization of rough sets in rough set theory the lower and upper approximation operators defined by a fixed binary relation satisfy many interesting properties several authors have proposed various fuzzy generalizations of rough approximations in this paper we introduce the definitions for generalized fuzzy lower and upper approximation operators determined by a residual implication then we find the assumptions which permit a given fuzzy set theoretic operator to represent a upper or lower approximation derived from a special fuzzy relation different classes of fuzzy rough set algebras are obtained from different types of fuzzy relations and different sets of axioms of fuzzy set theoretic operator guarantee the existence of different types of fuzzy relations which produce the same operator finally we study the composition of two approximation spaces it is proved that the approximation operators in the composition space are just the composition of the approximation operators in the two fuzzy approximation spaces

dynamic maintenance of approximations in set valued ordered decision systems under the attribute generalization set valued information systems are important type of data tables and generalized models of single valued information systems approximations are the focal point of approaches to knowledge discovery based on rough set theory which can be used to extract and represent the hidden knowledge in the form of decision rules attribute generalization refers to dynamic change of the attribute set in an information system with respect to the requirements of real life applications in this paper we focus on maintaining approximations dynamically in set valued ordered decision systems under the attribute generalization firstly a matrix based approach for computing approximations of upward and downward unions of decision classes is constructed by introducing the dominant and dominated matrices with respect to the dominance relation then incremental approaches for updating approximations are proposed which involves several modifications to relevant matrices without having to retrain from the start on all accumulated training data finally comparative experiments on data sets from uci as well as synthetic data sets show the proposed incremental updating methods are efficient and effective for dynamic attribute generalization

set valued information systems set valued information systems are generalized models of single valued information systems incomplete information systems can be viewed as disjunctively interpreted set valued information systems since some objects in set valued information systems may have more than one value for an attribute so we define tolerance relation and use the maximal tolerance classes to classify the universe of discourse in order to derive optimal decision rules from set valued decision information systems we propose the concept of relative reduct of maximal tolerance classes and define a kind of discernibility function to compute the relative reduct by boolean reasoning techniques finally we define three kinds of relative reducts for set valued information systems and used them to evaluate the significance of attributes

an optimal image watermarking approach based on a multi objective genetic algorithm in accordance with the multi objective nature of image watermarking an optimal image watermarking approach using a multi objective genetic algorithm is presented in this paper both watermarking parameters and embedding positions are often important factors affecting the performance of watermarking systems the proposed multi objective watermarking method can automatically optimize system parameters and a variable length mechanism is specially designed to search the most suitable positions for embedding watermarks the method can also remove the difficult issue of determining optimal watermarking parameters from previous watermarking algorithms the proposed multi objective watermarking method directly deals with the problem of optimizing watermarking under non dominated meaning thus it can effectively avoid the difficulty of determining the optimally weighted factor in existing single objective watermarking schemes in addition a pareto optimal set generated by multi objective optimization can provide flexibility in selecting the most suitable watermarking parameters according to practical requirements

time free spiking neural p systems different biological processes take different times to be completed which can also be influenced by many environmental factors in this work a realistic definition of nonsynchronized spiking neural p systems sn p systems for short is considered during the work of an sn p system the execution times of spiking rules cannot be known exactly i e they are arbitrary in order to establish robust systems against the environmental factors a special class of sn p systems called time free sn p systems is introduced which always produce the same computation result independent of the execution times of the rules the universality of time free sn p systems is investigated it is proved that these p systems with extended rules several spikes can be produced by a rule are equivalent to register machines however if the number of spikes present in the system is bounded then the power of time free sn p systems falls and in this case a characterization of semilinear sets of natural numbers is obtained

new full wave phase shift approach to solve the helmholtz acoustic wave equation for modeling we have developed a method of solving the helmholtz equation based on a new way to generalize the one way wave equation impose correct boundary conditions and eliminate exponentially growing evanescent waves the full two way nature of the helmholtz equation is included but the equation is converted into a pseudo one way form in the framework of a generalized phase shift structure consisting of two coupled first order partial differential equations for wave propagation with depth a new algorithm based on the particular structure of the coupling between p z and 2p z2 is introduced to treat this problem by an explicit approach more precisely in a depth marching strategy the wave operator is decomposed into the sum of two matrices the first one is a propagator in a reference velocity medium whereas the second one is a perturbation term which takes into account the vertical and lateral variation of the velocity the initial conditions are generated by solving the lippmann schwinger integral e

solving air traffic conflict problems via local continuous optimization this paper first introduces an original trajectory model using b splines and a new semi infinite programming formulation of the separation constraint involved in air traffic conflict problems a new continuous optimization formulation of the tactical conflict resolution problem is then proposed it involves very few optimization variables in that one needs only one optimization variable to determine each aircraft trajectory encouraging numerical experiments show that this approach is viable on realistic test problems not only does one not need to rely on the traditional discretized combinatorial optimization approaches to this problem but moreover local continuous optimization methods which require relatively fewer iterations and thereby fewer costly function evaluations are shown to improve the performance of the overall global optimization of this non convex problem

hybrid attribute reduction based on a novel fuzzy rough model and information granulation feature subset selection has become an important challenge in areas of pattern recognition machine learning and data mining as different semantics are hidden in numerical and categorical features there are two strategies for selecting hybrid attributes discretizing numerical variables or numericalize categorical features in this paper we introduce a simple and efficient hybrid attribute reduction algorithm based on a generalized fuzzy rough model a theoretic framework of fuzzy rough model based on fuzzy relations is presented which underlies a foundation for algorithm construction we derive several attribute significance measures based on the proposed fuzzy rough model and construct a forward greedy algorithm for hybrid attribute reduction the experiments show that the technique of variable precision fuzzy inclusion in computing decision positive region can get the optimal classification performance number of the selected features is the least but accuracy is the best

weighted fuzzy spiking neural p systems spiking neural p systems sn p systems are a new class of computing models inspired by the neurophysiological behavior of biological spiking neurons in order to make sn p systems capable of representing and processing fuzzy and uncertain knowledge we propose a new class of spiking neural p systems in this paper called weighted fuzzy spiking neural p systems wfsn p systems new elements including fuzzy truth value certain factor weighted fuzzy logic output weight threshold new firing rule and two types of neurons are added to the original definition of sn p systems this allows wfsn p systems to adequately characterize the features of weighted fuzzy production rules in a fuzzy rule based system furthermore a weighted fuzzy backward reasoning algorithm based on wfsn p systems is developed which can accomplish dynamic fuzzy reasoning of a rule based system more flexibly and intelligently in addition we compare the proposed wfsn p systems with other knowledge representation methods such as fuzzy production rule conceptual graph and petri nets to demonstrate the features and advantages of the proposed techniques

how to solve a semi infinite optimization problem abstract after an introduction to main ideas of semi infinite optimization this article surveys recent developments in theory and numerical methods for standard and generalized semi infinite optimization problems particular attention is paid to connections with mathematical programs with complementarity constraints lower level wolfe duality semi smooth approaches as well as branch and bound techniques in adaptive convexification procedures a section on recent genericity results includes a discussion of the symmetry effect in generalized semi infinite optimization

on some classes of sequential spiking neural p systems spiking neural p systems sn p systems are a class of distributed parallel computing devices inspired by the way neurons communicate by means of spikes neurons work in parallel in the sense that each neuron that can fire should fire but the work in each neuron is sequential in the sense that at most one rule can be applied at each computation step in this work with biological inspiration we consider sn p systems with the restriction that at each step one of the neurons i e sequential mode or all neurons i e pseudo sequential mode with the maximum or minimum number of spikes among the neurons that are active can spike will fire if an active neuron has more than one enabled rule it nondeterministically chooses one of the enabled rules to be applied and the chosen rule is applied in an exhaustive manner a kind of local parallelism the rule is used as many times as possible this strategy makes the system sequential or pseudo sequential from the global view of the whole network and locally parallel at the level of neurons we obtain four types of sn p systems maximum minimum spike number induced sequential pseudo sequential sn p systems with exhaustive use of rules we prove that sn p systems of these four types are all turing universal as number generating computation devices these results illustrate that the restriction of sequentiality may have little effect on the computation power of sn p systems

rough set approach to incomplete information systems abstract in the paper we present rough set approach to reasoning in incomplete information systems we propose reduction of knowledge that eliminates only that information which is not essential from the point of view of classification or decision making in our approach we make only one assumption about unknown values the real value of a missing attribute is one from the attribute domain however we do not assume which one we show how to find decision rules directly from such an incomplete decision table which are as little non deterministic as possible and have minimal number of conditions

robust fuzzy rough classifiers fuzzy rough sets generalized from pawlak s rough sets were introduced for dealing with continuous or fuzzy data this model has been widely discussed and applied these years it is shown that the model of fuzzy rough sets is sensitive to noisy samples especially sensitive to mislabeled samples as data are usually contaminated with noise in practice a robust model is desirable we introduce a new model of fuzzy rough set model called soft fuzzy rough sets and design a robust classification algorithm based on the model experimental results show the effectiveness of the proposed algorithm

stable depth extrapolation of seismic wavefields by a neumann series several migration methods fail to work when applied to complex geological structures with strong lateral heterogeneity the generalized migration in the frequency wavenumber f k domain based on a convolution with a slowness inverse of velocity dependent operator is capable of downward continuation of wavefield in media with strong vertical and lateral variations of velocity unfortunately this method as presented in the literature is potentially unstable we propose a new stable extrapolator based on the solution of the integral fredholm equation which describes a one way wave equation in the form of a neumann series the resulting algorithm of depth migration is implemented in both the frequency wavenumber f k and frequency space f x domains and takes into account arbitrary lateral gradients of velocity using a low frequency filter in x f domain that is the sum of the power series the computation time of depth migration by a neumann series is slightly longer than for split step fourier

three way decisions with probabilistic rough sets the rough set theory approximates a concept by three regions namely the positive boundary and negative regions rules constructed from the three regions are associated with different actions and decisions which immediately leads to the notion of three way decision rules a positive rule makes a decision of acceptance a negative rule makes a decision of rejection and a boundary rule makes a decision of abstaining this paper provides an analysis of three way decision rules in the classical rough set model and the decision theoretic rough set model the results enrich the rough set theory by ideas from bayesian decision theory and hypothesis testing in statistics the connections established between the levels of tolerance for errors and costs of incorrect decisions make the rough set theory practical in applications

approximate distribution reducts in inconsistent interval valued ordered decision tables abstract many methods based on the rough set theory to deal with information systems have been proposed in recent decades in practice some information systems are based on dominance relations and may be inconsistent because of various factors moreover taking the imprecise evaluations and assignments in the description of objects into account single valued information systems have been generalized to interval valued information systems in this paper by introducing a dominance relation to interval valued ordered information systems we establish a dominance based rough set approach which is mainly based on substitution of the indiscernibility relation by the dominance relation to extract the minimal decision rules approximate distribution reducts are proposed in inconsistent interval valued ordered decision tables this paper presents a theoretical method based on the discernibility matrix to enumerate all reducts and a practical approach on the basis of significance to find one reduct and two equivalent definitions of approximate distribution reducts are also introduced in addition numerical examples are employed to examine the validity of the approaches proposed in this paper

tissue like p systems with evolutional symport antiport rules tissue p systems with symport antiport rules are a class of distributed parallel computing models inspired by the cell intercommunication in tissues where objects are never modified in the process of communication just changing their place within the system in this work a variant of tissue p systems called tissue p systems with evolutional symport antiport rules is introduced where objects are moved from one region to another region and may be evolved during this process the computational power of such p systems is studied specifically it is proved that such p systems with one cell and using evolutional symport rules of length at most 3 or using evolutional antiport rules of length at most 4 are turing universal only the family of all finite sets of positive integers can be generated by such p systems if standard symport antiport rules are used moreover cell division rules are considered in tissue p systems with evolutional symport antiport rules and a limit on the efficiency of such p systems is provided with evolutional communication rules of length at most 2 the computational efficiency of this kind of models is shown when using evolutional communication rules of length at most 4

positive approximation an accelerator for attribute reduction in rough set theory feature selection is a challenging problem in areas such as pattern recognition machine learning and data mining considering a consistency measure introduced in rough set theory the problem of feature selection also called attribute reduction aims to retain the discriminatory power of original features many heuristic attribute reduction algorithms have been proposed however quite often these methods are computationally time consuming to overcome this shortcoming we introduce a theoretic framework based on rough set theory called positive approximation which can be used to accelerate a heuristic process of attribute reduction based on the proposed accelerator a general attribute reduction algorithm is designed through the use of the accelerator several representative heuristic attribute reduction algorithms in rough set theory have been enhanced note that each of the modified algorithms can choose the same attribute reduct as its original version and hence possesses the same classification accuracy experiments show that these modified algorithms outperform their original counterparts it is worth noting that the performance of the modified algorithms becomes more visible when dealing with larger data sets

design of logic gates using spiking neural p systems with homogeneous neurons and astrocytes like control in biological nervous systems the operation of interacting neurons depends largely on the regulation from astrocytes inspired by this biological phenomenon spiking neural p systems i e sn p systems with astrocyte like control were proposed and were proven to have turing completeness as computing models in this work the application of such systems for creating logical operators is investigated specifically it is obtained in a constructive way that sn p systems with astrocyte like control can synthesize the operations of boolean logic gates i e and or not nor xor and nand gates the resulting systems are simple and homogeneous which means only one type of neuron with a unique spiking rule is used with these neural like logic gates more complex boolean circuits with cascade connections can be constructed as such they can be used to implement finite computing devices such as the finite transducers these results demonstrate a novel method of constructing logic circuits that work in a neural like manner as well as shed some lights on potential directions of designing neural circuits theoretically