optimization of type 2 fuzzy systems based on bio inspired methods a concise review a review of the optimization methods used in the design of type 2 fuzzy systems which are relatively novel models of imprecision has been considered in this work the fundamental focus of the work has been based on the basic reasons of the need for optimizing type 2 fuzzy systems for different areas of application recently bio inspired methods have emerged as powerful optimization algorithms for solving complex problems in the case of designing type 2 fuzzy systems for particular applications the use of bio inspired optimization methods have helped in the complex task of finding the appropriate parameter values and structure of the fuzzy systems in this review we consider the application of genetic algorithms particle swarm optimization and ant colony optimization as three different paradigms that help in the design of optimal type 2 fuzzy systems we also provide a comparison of the different optimization methods for the case of designing type 2 fuzzy systems

a recency effect in sound localization in a free field pointing task listeners localized trains of 4 32 spatially distributed gabor clicks narrowband impulses centered at 4 khz carrier frequency and repeating at an interval of 5ms multiple regression coefficients estimated the perceptual weight applied to each click in a train during location judgments temporal weighting functions obtained in this way exhibited two key features onset dominance as evidenced by high weight on the initial click and upweighting of late arriving sound as evidenced by weights that gradually increased over the duration of each click train across all tested click train durations and despite randomly varying the durations from trial to trial the greatest post onset weights were consistently found for clicks at or near the offset the results imply a special importance of late arriving sound rather than feedforward recovery from onset dominance and are broadly consistent with recency effects resulting from temporal integration

extension of a binaural cross correlation model by contralateral inhibition i simulation of lateralization for stationary signals running interaural cross correlation is a basic assumption to model the performance of the binaural auditory system although this concept is particularly suited to simulate psychoacoustic localization phenomena there exist some localization effects which cannot be explained by pure cross correlation in this paper a model of interaural cross correlation is extended by a contralateral inhibition mechanism and by monaural detectors in order to simulate a wide range of psychoacoustic lateralization data the extended model explains lateralization of pure tones with interaural time differences as well as with interaural level differences multiple images are predicted for tones with characteristic combinations of interaural signal parameters and for noise signals with different degrees of interaural cross correlation the model is also capable of simulating dynamic lateralization phenomena such as the law of the first wave front which is dealt with in a companion paper lindemann j acoust so

lateralization of complex binaural stimuli a weighted image model this article describes a new model that predicts the subjective lateral position of bandpass stimuli it is assumed as in other models that stimuli are bandpass filtered and rectified and that the rectified outputs of filters with matching center frequencies undergo interaural cross correlation the model specifies and utilizes the shape and location of assumed patterns of neural activity that describe the cross correlation function individual modes of this function receive greater weighting if they are straighter describing consistent interaural delay over frequency and or more central describing interaural delays of smaller magnitude this weighting of straightness and centrality is used by the model to predict the perceived laterality of several types of low frequency bandpass stimuli with interaural time delays and or phase shifts including bandpass noise amplitude modulated stimuli with time delayed envelopes and bandpass filtered clicks this model is compared to other theories that describe lateralization in terms of the relative contributions of information in the envelopes and fine structures of binaural stimuli

zariski theorems and diagrams for braid groups empirical properties of generating systems for complex reflection groups and their braid groups have been observed by orlik solomon and broue malle rouquier using shephard todd classification we give a general existence result for presentations of braid groups which partially explains and generalizes the known empirical properties our approach is invariant theoretic and does not use the classification the two ingredients are springer theory of regular elements and a zariski like theorem

fuzzy clustering analysis for optimizing fuzzy membership functions fuzzy model identification is an application of fuzzy inference system for identifying unknown functions for a given set of sampled data the most important thing for fuzzy identification task is to decide the parameters of membership functions mfs used in fuzzy systems a lot of efforts chung and lee 1994 jang 1993 sun and jang 1993 have been given to initialize the parameters of fuzzy membership functions however the problems of parameter identification were not solved formally assessments of these algorithms are discussed in the paper based on the fuzzy c means fcm bezdek 1987 clustering algorithm we propose a heuristic method to calibrate the fuzzy exponent iteratively a hybrid learning algorithm for refining the system parameters is then presented examples are demonstrated to show the effectiveness of the proposed method comparing with the equalized universe method eum and subtractive clustering method scm chiu 1994 the simulation results indicate the general applicability of our methods to a wide range of applications

matrix factorisations arising from well generated complex reflection groups abstract we discuss an interesting duality known to occur for certain complex reflection groups namely the duality groups our main construction yields a concrete representation theoretic realisation of this duality this allows us to naturally identify invariant vector fields with vector fields on the orbit space for the action of a duality group as another application we construct matrix factorisations of the highest degree basic invariant which give free resolutions of the module of kahler differentials of the coinvariant algebra a associated to such a reflection group from this one can explicitly calculate the dimension of each graded piece of a c and of der c a a adding a new formula to the numerology of reflection groups this applies for instance when a is the cohomology of any complete flag manifold and hence has geometric consequences

data driven fuzzy modeling for takagi sugeno kang fuzzy system this paper presents a systematic approach to design first order tagaki sugeno kang tsk fuzzy systems this approach attempts to obtain the fuzzy rules without any assumption about the structure of the data the structure identification and parameter optimization steps in this approach are carried out automatically and are capable of finding the optimal number of the rules with an acceptable accuracy starting with an initial structure the system first tries to improve the structure and then as soon as an improved structure is found it fine tunes its rules parameters then it goes back to improve the structure again to find a better structure and re fine tune the rules parameters this loop continues until a satisfactory solution tsk model is found the proposed approach has successfully been applied to well known benchmark datasets and real world problems the obtained results are compared with those obtained with other methods from the literature experimental studies demonstrate that the predicted properties have a good agreement with the measured data by using the elicited fuzzy model with a small number of rules finally as a case study the proposed approach is applied to the desulfurization process of a real steel industry comparing the proposed approach with some other fuzzy systems and neural networks it is shown that the developed tsk fuzzy system exhibits better results with higher accuracy and smaller size of architecture

homological stability for topological chiral homology of completions abstract by proving that several new complexes of embedded disks are highly connected we obtain several new homological stability results our main result is homological stability for topological chiral homology on an open manifold with coefficients in certain partial framed e n algebras using this we prove a special case of a conjecture of vakil and wood on homological stability for complements of closures of particular strata in the symmetric powers of an open manifold and we prove that the bounded symmetric powers of closed manifolds satisfy homological stability rationally

hz algebra spectra are differential graded algebras we show that the homotopy theory of differential graded algebras coincides with the homotopy theory of h algebra spectra namely we construct quillen equivalences between the quillen model categories of unbounded differential graded algebras and h algebra spectra we also construct quillen equivalences between the differential graded modules and module spectra over these algebras we use these equivalences in turn to produce algebraic models for rational stable model categories we show that basically any rational stable model category is quillen equivalent to modules over a differential graded algebra with many objects

interaural level differences and the level meter model the interaural level difference ild plays a significant role in sound localization however the definition of ild for noise is open to some interpretation because it is not obvious how to deal with the inevitable level fluctuations in this article the ild is interpreted as an energylike time integrated measure of stimulus level independent of other stimulus details particularly interaural correlation this concept is called the level meter model the model was tested by measuring human ild thresholds for noise stimuli that were interaurally correlated or anticorrelated or uncorrelated an additional test not involving lateralization measured the threshold for level discrimination based on loudness according to the level meter model all four thresholds should be the same the experimental results showed that the predictions of the level meter model held good to within about half a db although thresholds for level discrimination were systematically higher than ilds among the ilds themselves thresholds were slightly higher for uncorrelated noise the latter result could be explained by replacing the level meter model with a loudness meter model incorporating temporal integration the same model accounted for the bandwidth dependence of the threshold

a function space model approach to the rational evaluation subgroups let f u x be a map from a connected nilpotent space u to a connected rational space x the evaluation subgroup g u x f which is a generalization of the gottlieb group of x is investigated the key device for the study is an explicit sullivan model for the connected component containing f of the function space of maps from u to x which is derived from the general theory of such a model due to brown and szczarba trans am math soc 349 4931 4951 1997 in particular we show that non gottlieb elements are detected by analyzing a sullivan model for the map f and by looking at non triviality of higher order whitehead products in the homotopy group of x the gottlieb triviality of a fibration in the sense of lupton and smith the evaluation subgroup of a fibre inclusion 2006 is also discussed from the function space model point of view moreover we proceed to consideration of the evaluation subgroup of the fundamental group of a nilpotent space in consequence the first gottlieb group of the total space of each s1 bundle over the n dimensional torus is determined explicitly in the non rational case

mpeg vbr video traffic modeling and classification using fuzzy technique we present an approach for mpeg variable bit rate vbr video modeling and classification using fuzzy techniques we demonstrate that a type 2 fuzzy membership function i e a gaussian mf with uncertain variance is most appropriate to model the log value of i p b frame sizes in mpeg vbr video the fuzzy c means fcm method is used to obtain the mean and standard deviation std of t p b frame sizes when the frame category is unknown we propose to use type 2 fuzzy logic classifiers flcs to classify video traffic using compressed data five fuzzy classifiers and a bayesian classifier are designed for video traffic classification and the fuzzy classifiers are compared against the bayesian classifier simulation results show that a type 2 fuzzy classifier in which the input is modeled as a type 2 fuzzy set and antecedent membership functions are modeled as type 2 fuzzy sets performs the best of the five classifiers when the testing video product is not included in the training products and a steepest descent algorithm is used to tune its parameters

temporal weighting of interaural time and level differences in high rate click trains temporal weighting functions twfs quantifying sensitivity to interaural time differences itd and interaural level differences ild over the duration of brief stimuli were measured in 6 normal hearing subjects using trains of 16 gabor clicks centered at 4 khz presented dichotically at 4 rates inter click intervals ici of 10 5 2 5 and 1 25 ms random itd or ild were imposed independently on each click in the train in separate conditions the subject s task was to discriminate the lateral position of the click train left or right receiver operating characteristic roc analysis was then used to quantify the effectiveness or weight of each click according to individual click itd or ild although individual differences were evident onset cues appeared to dominate at high rates onset dominance was apparent for both itd and ild at 1 25 ms ici and for itd at 2 5 ms ici but for neither cue at 5 or 10 ms ici onset dominance was greater on average for itd than ild although twfs were qualitatively similar for the two cues no evidence was found for upweighting of late arriving ild stecker g c and hafter e r 2009 j acoust soc am 125 3914 3924

footprint of uncertainty for type 2 fuzzy sets in the paper a new and comprehensible definition is proposed for type 2 fuzzy sets t2 fss and the primary and secondary memberships function are defined respectively by using multi valued mapping a new definition and formula for the footprint of uncertainty fou is presented and based on the new definitions the relation between fou and the original definition of t2 fs is discussed finally the partition method of fou is provided to represent the primary membership grade the fou and the interval type 2 fuzzy sets it2 fs when the upper and lower membership functions umf lmf of fou are given

temporal effects in interaural and sequential level difference perception temporal effects in interaural level difference ild perception are not well understood while it is often assumed that ild sensitivity is independent of the temporal stimulus properties a reduction of ild sensitivity for stimuli with a high modulation rate has been reported known under the term binaural adaptation experiment 1 compared ild thresholds and sequential level difference sld thresholds using 300 ms bandpass filtered pulse trains centered at 4 khz with rates of 100 400 and 800 pulses per second pps in contrast to the sld thresholds ild thresholds were elevated at 800 pps consistent with literature data that had previously been attributed to binaural adaptation experiment 2 showed better ild sensitivity for pulse trains than for pure tones suggesting that amplitude modulation enhances ild sensitivity the present ild data and binaural adaptation data from the literature were predicted by a model combining well established auditory periphery front ends with an interaural comparison stage the model also accounted for other published ild data including target ild thresholds in diotic forward and backward fringes and ild thresholds with different amounts of interaural correlation overall a variety of temporal effects in ild perception including binaural adaptation appear to be largely attributable to monaural peripheral auditory processing

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

variable selection for model based clustering we consider the problem of variable or feature selection for model based clustering the problem of comparing two nested subsets of variables is recast as a model comparison problem and addressed using approximate bayes factors a greedy search algorithm is proposed for finding a local optimum in model space the resulting method selects variables or features the number of clusters and the clustering model simultaneously we applied the method to several simulated and real examples and found that removing irrelevant variables often improved performance compared with methods based on all of the variables our variable selection method consistently yielded more accurate estimates of the number of groups and lower classification error rates as well as more parsimonious clustering models and easier visualization of results

localization of sound in rooms v binaural coherence and human sensitivity to interaural time differences in noise binaural recordings of noise in rooms were used to determine the relationship between binaural coherence and the effectiveness of the interaural time difference itd as a cue for human sound localization experiments showed a strong monotonic relationship between the coherence and a listener s ability to discriminate values of itd the relationship was found to be independent of other widely varying acoustical properties of the rooms however the relationship varied dramatically with noise band center frequency the ability to discriminate small itd changes was greatest for a mid frequency band to achieve sensitivity comparable to mid band the binaural coherence had to be much larger at high frequency where waveform itd cues are imperceptible and also at low frequency where the binaural coherence in a room is necessarily large rivalry experiments with opposing interaural level differences ilds found that the trading ratio between itd and ild increasingly favored the ild as coherence decreased suggesting that the perceptual weight of the itd is decreased by increased reflections in rooms

l infinity pairs and applications to singularities abstract over a field of characteristic zero every deformation problem with cohomology constraints is controlled by a pair consisting of a differential graded lie algebra together with a module unfortunately these pairs are usually infinite dimensional we show that every deformation problem with cohomology constraints is controlled by a typically finite dimensional l pair as a first application we show that for complex algebraic varieties with no weight zero 1 cohomology classes the components of the cohomology jump loci of rank one local systems containing the constant sheaf are tori this imposes restrictions on the fundamental groups the same holds for links and milnor fibers

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

rational homotopy of the space of self maps of complexes with finitely many homotopy groups for simply connected cw complexes x with finitely many finitely generated homotopy groups 1 the path components of the function space m x x of free self maps of x are all of the same rational homotopy type if and only if all the invariants of x are of finite order in case x is rationally a two stage postnikov system the space mq x x of inessential self maps of x has the structure of rational space if and only if the fc invariants of x are of finite order given spaces x and y let m x y denote the space of free continuous maps from x to y with the compact open topology given a map x y we let mf x y denote the component of in m x y in particular we denote by mq x y the space of inessential maps from x to y and by mx x x the space of self maps of x which are homotopic to the identity if x and y are spaces with base points then we have the subspace m x t of m x y consisting of all based maps between x and y given a based map x y we write mf x 7 for the component of in m x y in his 1956 paper 20 r thorn used a postnikov decomposition of y to show that the homotopy groups of m x y are determined up to a series of group extensions involving the cohomology of x with coefficients in the homo topy of y to illustrate his technique thorn computed the rational homotopy groups of certain function spaces he also showed how by analyzing the eval uation map it is possible in certain cases to determine the rational homotopy type of components of m x y while predating by many years sullivan s development of the theory of minimal models thorn s work established the techniques for studying function spaces within the framework of rational ho motopy theory in 7 haefliger completed a program initiated by sullivan 18 with the construction of a rational homotopy theoretic model for the space of sections of a nilpotent bundle the construction embodied the two aspects

a new indirect approach to the type 2 fuzzy systems modeling and design this paper proposes a new method for designing interval type 2 fuzzy logic systems it2 flss considering two issues first quality of clustering the output space and secondly approximating the output of the it2 fls based on a new output processing method based on these two issues we present a new cluster validity index capable of being used for type 1 fuzzy c means fcms interval type 2 fcm it2 fcm and possibilistic c means pcms clustering algorithms this validity index is highly efficient in determining clusters with the least similarity between them and the highest similarity between data vectors in each cluster then a new definition for uncertainty bounds is presented in order to eliminate the type reduction process in it2 flss and to increase accuracy of the existing uncertainty bounds in the literature finally effectiveness of the proposed approaches compared to several well known existing methods has been investigated computational results have verified accuracy and effectiveness of the proposed method

updated parameters and expanded simulation options for a model of the auditory periphery a phenomenological model of the auditory periphery in cats was previously developed by zilany and colleagues j acoust soc am 126 2390 2412 2009 to examine the detailed transformation of acoustic signals into the auditory nerve representation in this paper a few issues arising from the responses of the previous version have been addressed the parameters of the synapse model have been readjusted to better simulate reported physiological discharge rates at saturation for higher characteristic frequencies liberman j acoust soc am 63 442 455 1978 this modification also corrects the responses of higher characteristic frequency cf model fibers to low frequency tones that were erroneously much higher than the responses of low cf model fibers in the previous version in addition an analytical method has been implemented to compute the mean discharge rate and variance from the model s synapse output that takes into account the effects of absolute refractoriness

detection of interaural differences of intensity in trains of high frequency clicks as a function of interclick interval and number listeners were asked to detect interaural differences of time in trains of 4000 hz clicks as the interclick interval ici was varied from 10 to 1 ms and the number of clicks in a train n was varied from 1 to 32 plots of log interaural threshold versus log n produce straight lines whose absolute slopes decrease toward 0 0 with decreasing ici these results are shown to fit a saturation model which argues that as the click rate increases the evoked neural activity moves from a response that is tonic toward one which is more phasic the need to postulate neural compression is based in part on the fact that the three most commonly cited models of the limitations imposed by high frequency reduction in the depth of modulations due to narrow band filtering within the auditory system neural refractoriness and nonindependence of successive samples of internal noise do not predict a change in slope with rate

on the robustness of type 1 and interval type 2 fuzzy logic systems in modeling research on the robustness of fuzzy logic systems flss an imperative factor in the design process is very limited in the literature specifically when a system is subjected to small deviations of the sampling points operating points it is of great interest to find the maximum tolerance of the system which we refer to as the system s robustness in this paper we present a methodology for the robustness analysis of interval type 2 flss it2 flss that also holds for t1 flss hence making it more general a procedure for the design of robust it2 flss with a guaranteed performance better than or equal to their t1 counterparts is then proposed several examples are performed to demonstrate the effectiveness of the proposed methodologies it was concluded that both t1 and it2 flss can be designed to achieve robust behavior in various applications and preference one or the other in general is application dependant it2 flss having a more flexible structure than t1 flss exhibited relatively small approximation errors in the several examples investigated the methodologies presented in this paper lay the foundation for the design of flss with robust properties that will be very useful in many practical modeling and control applications

goodness of fit and variable selection in the fuzzy multiple linear regression abstract in performing a fuzzy multiple linear regression model important topics are to measure the fitting quality of the model and to find the best set of input variables that explain the variation in the observed system responses in this paper by considering an exploratory approach to express the quality of fit of a fuzzy linear regression model a coefficient of multiple determination r 2 for symmetrical fuzzy variable has been suggested furthermore for overcoming the inconveniences of r 2 an adjusted version of r 2 denoted by r 2 has been defined for measuring the fitting performances of the estimated model a fuzzy extension of another goodness of fit measure the so called mallows index c p has been considered all the proposed fitting measures have been utilized for selecting suitably the input variables of a fuzzy linear regression model to this purpose some variable selection procedures based on r 2 r 2 and c p have been suitably extended in a fuzzy framework to explain the efficacy of the goodness of fit measures and the variable selection criteria some examples are also shown

on the rational homotopy type of function spaces the main result of this paper is the construction of a minimal model for the function space f x y of continuous functions from a finite type finite dimensional space x to a finite type nilpotent space y in terms of minimal models for x and y for the component containing the constant map 7r f x y 0 q 7r y 0 h x q in positive dimensions when x is formal there is a simple formula for the differential of the minimal model in terms of the differential of the minimal model for y and the coproduct of h x q we also give a version of the main result for the space of cross sections of a fibration

equalization of nonlinear time varying channels using type 2 fuzzy adaptive filters presents a kind of adaptive filter type 2 fuzzy adaptive filter faf one that is realized using an unnormalized type 2 takagi sugeno kang tsk fuzzy logic system fls we apply this filter to equalization of a nonlinear time varying channel and demonstrate that it can implement the bayesian equalizer for such a channel has a simple structure and provides fast inference a clustering method is used to adaptively design the parameters of the faf two structures are used for the equalizer transversal equalizer te and decision feedback equalizer dfe a decision tree structure is used to implement the decision feedback equalizer in which each leaf of the tree is a type 2 faf this dfe vastly reduces computational complexity as compared to a te simulation results show that equalizers based on type 2 fafs perform much better than nearest neighbor classifiers nnc or equalizers based on type 1 fafs

uncertainty bounds and their use in the design of interval type 2 fuzzy logic systems we derive inner and outer bound sets for the type reduced set of an interval type 2 fuzzy logic system fls based on a new mathematical interpretation of the karnik mendel iterative procedure for computing the type reduced set the bound sets can not only provide estimates about the uncertainty contained in the output of an interval type 2 fls but can also be used to design an interval type 2 fls we demonstrate by means of a simulation experiment that the resulting system can operate without type reduction and can achieve similar performance to one that uses type reduction therefore our new design method based on the bound sets can relieve the computation burden of an interval type 2 fls during its operation which makes an interval type 2 fls useful for real time applications

type 2 fuzzy neural networks with fuzzy clustering and differential evolution optimization in many real world problems involving pattern recognition system identification and modeling control decision making and forecasting of time series available data are quite often of uncertain nature an interesting alternative is to employ type 2 fuzzy sets which augment fuzzy models with expressive power to develop models which efficiently capture the factor of uncertainty the three dimensional membership functions of type 2 fuzzy sets offer additional degrees of freedom that make it possible to directly and more effectively account for model s uncertainties type 2 fuzzy logic systems developed with the aid of evolutionary optimization forms a useful modeling tool subsequently resulting in a collection of efficient if then rules the type 2 fuzzy neural networks take advantage of capabilities of fuzzy clustering by generating type 2 fuzzy rule base resulting in a small number of rules and then optimizing membership functions of type 2 fuzzy sets present in the antecedent and consequent parts of the rules the clustering itself is realized with the aid of differential evolution several examples including a benchmark problem of identification of nonlinear system are considered the reported comparative analysis of experimental results is used to quantify the performance of the developed networks

hierarchical collapsing method for direct defuzzification of general type 2 fuzzy sets abstract karnik mendel km and enhanced km ekm algorithms are proved to be efficient approaches when dealing with general type 2 fuzzy sets represented by their planes on the other hand collapsing method as a type reduction algorithm for interval type 2 fuzzy sets has shown to be an effectual type reduction method for interval type 2 fuzzy sets in this paper we aim at developing mathematical formulations based on collapsing procedure and plane decomposition in order to utilize geometric properties of general type 2 fuzzy sets for preparing a direct defuzzification procedure the proposed methods are fast and robust extensive simulations have shown that the proposed algorithm outperforms most of the existing approaches in this field and its results are closer to the exact optimal defuzzified values

onset and offset specific effects in interaural level difference discrimination the relative sensitivity of human listeners to interaural level differences ilds carried by the onsets offsets and interior portions of brief sounds was examined stimuli consisted of single 4000 hz gabor clicks gaussian windowed tone bursts or trains of 16 such clicks repeating at an interclick interval ici of 2 or 5 ms in separate conditions ilds favored the right ear by a constant amount for all clicks condition rrrr or a changing amount that was maximal at sound onset condition r000 offset condition 000r both onset and offset condition r00r or at the temporal midpoint of the stimulus condition 0rr0 ild increases and decreases were implemented as linear decibel sweeps across four clicks to minimize transient distortion threshold ilds were determined adaptively for each of these conditions and for single clicks thresholds were similar for ilds presented near sound onset or offset condition r000 vs 000r but lower when ilds were carried by both onset and offset clicks condition r00r than for ilds carried by interior clicks alone condition 0rr0 the results suggest that similar sensitivity to onset and offset ild does not reflect uniform temporal weighting instead ild sensitivity favors onsets and offsets over the interior portions of sounds

finite complex reflection arrangements are k pi 1 let v be a finite dimensional complex vector space and w gl v be a finite complex reflection group let v reg be the complement in v of the reflecting hyperplanes we prove that v reg is a k 1 space this was predicted by a classical conjecture originally stated by brieskorn for complexified real reflection groups the complexified real case follows from a theorem of deligne and after contributions by nakamura and orliksolomon only six exceptional cases remained open in addition to solving these six cases our approach is applicable to most previously known cases including complexified real groups for which we obtain a new proof based on new geometric objects we also address a number of questions about 1 w v the braid group of w this includes a description of periodic elements in terms of a braid analog of springer s theory of regular elements

andre quillen cohomology and rational homotopy of function spaces we develop a simple theory of andre quillen cohomology for commutative differential graded algebras over a field of characteristic zero we then relate it to the homotopy groups of function spaces and spaces of homotopy self equivalences of rational nilpotent cw complexes this puts certain results of sullivan in a more conceptual framework

minimax e stable cluster validity index for type 2 fuzziness in this paper we concentrate on the usage of uncertainty associated with the level of fuzziness in determination of the number of clusters in fcm for any data set we propose a minimax e stable cluster validity index based on the uncertainty associated with the level of fuzziness within the framework of interval valued type 2 fuzziness if the data have a clustered structure the optimum number of clusters may be assumed to have minimum uncertainty under upper and lower levels of fuzziness upper and lower values of the level of fuzziness for fuzzy c mean fcm clustering methodology have been found as m 2 6 and 1 4 respectively in our previous studies our investigation shows that the stability of cluster centers with respect to the level of fuzziness is sufficient for the determination of the number of clusters

a cluster validation index for gk cluster analysis based on relative degree of sharing in this paper the problem of traditional validity indices when applied to the gustafson kessel gk clustering are reviewed a new cluster validity index for the gk algorithm is proposed this validity index is defined as the average value of the relative degrees of sharing of all possible pairs of fuzzy clusters in the system it computes the overlap of each pair of fuzzy clusters by considering the degree of sharing of each data point in the overlap the optimal number of clusters is obtained by minimizing the validity index experiments in which the proposed validity index and several traditional validity indices were applied to 6 data sets highlight the superior qualities of the proposed index the results indicate that the proposed validity index is very reliable

algebraic models of non connected spaces and homotopy theory of l algebras we develop a homotopy theory of l algebras based on the lawrence sullivan construction a complete differential graded lie algebra which as we show satisfies the necessary properties to become the right cylinder in this category as a result we obtain a general procedure to algebraically model the rational homotopy type of non connected spaces 2012 elsevier ltd

maurer cartan moduli and models for function spaces we set up a formalism of maurer cartan moduli sets for l algebras and associated twistings based on the closed model category structure on formal differential graded algebras a k a differential graded coalgebras among other things this formalism allows us to give a compact and manifestly homotopy invariant treatment of chevalley eilenberg and harrison cohomology we apply the developed technology to construct rational homotopy models for function spaces

lie models for the components of sections of a nilpotent fibration we give an explicit lie model for any component of the space of free and pointed sections of a nilpotent fibration and in particular of the free and pointed mapping spaces among the applications presented we obtain a lie model of the exponential law and prove that in many cases the rank of the homotopy groups of the mapping space grows at the same rate as the rank of the homotopy groups of the target space

some topological properties of kahler manifolds and homogeneous spaces on donne des calculs explicites des groupes d homotopie rationnels du monoide topologique de toutes les auto equivalences d homotopie d une variete de kahler homogene

temporal weighting of binaural cues revealed by detection of dynamic interaural differences in high rate gabor click trains listeners detected interaural differences of time itds or level ilds carried by single 4000 hz gabor clicks gaussian windowed tone bursts and trains of 16 such clicks repeating at an interclick interval ici of 2 5 or 10 ms in separate conditions target interaural differences favored the right ear by a constant amount for all clicks condition rr attained their peak value at onset and diminished linearly to 0 at offset condition r0 or grew linearly from 0 at onset to a peak value at offset condition 0r threshold itds and ilds were determined adaptively in separate experiments for each of these conditions and for single clicks itd thresholds were found to be lower for 16 click trains than for single clicks at 10 ms ici regardless of stimulus condition at 2 ms ici thresholds in rr and r0 conditions were similar to single click thresholds at 2 ms ici thresholds in the 0r condition were significantly worse than for single clicks at 2 ms ici consistent with strong rate dependent onset dominance in listeners temporal weighting of itd ild thresholds in contrast were predominantly unaffected by ici suggesting little or no onset dominance for ild of high rate stimuli

minimal models of quantum homotopy lie algebras via the bv formalism using the batalin vilkovisky formalism of mathematical physics an explicit construction for the minimal model of a quantum l algebra is given as a formal super integral the approach taken herein to these formal integrals is axiomatic and they can be approached using perturbation theory to obtain combinatorial formulae as shown in the appendix additionally there exists a canonical differential graded lie algebra morphism mapping formal functions on homology to formal functions on the whole space an inverse l algebra morphism to this differential graded lie algebra morphism is constructed as a formal super integral using the batalin vilkovisky formalism of mathematical physics an explicit construction for the minimal model of a quantum l algebra is given as a formal super integral the approach taken herein to these formal integrals is axiomatic and they can be approached using perturbation theory to obtain combinatorial formulae as shown in the appendix additionally there exists a canonical differential graded lie algebra morphism mapping formal functions on homology to formal functions on the whole space an inverse l algebra morphism to this differential graded lie algebra morphism is constructed as a formal super integral

discrimination of interaural differences of level as a function of frequency discrimination of interaural differences of level idls was measured for pure tones as a function of frequency and as a function of the interaural difference of phase or level of a standard varying the interaural difference of the standard was assumed to change the lateral position of its intracranial image threshold idls were approximately constant over a frequency range from 200 5000 hz except in a region near 1000 hz where they were slightly elevated thresholds increased as the value of the standard interaural differences of phase or level increased implying that interaural resolution declines as the lateral image moves away from midline the results are generally consistent with the predictions of current models of lateralization but additions to these models are required in order for them to account for the slight frequency dependence of threshold idls

experimental study of intelligent controllers under uncertainty using type 1 and type 2 fuzzy logic uncertainty is an inherent part in control systems used in real world applications the use of new methods for handling incomplete information is of fundamental importance type 1 fuzzy sets used in conventional fuzzy systems cannot fully handle the uncertainties present in control systems type 2 fuzzy sets that are used in type 2 fuzzy systems can handle such uncertainties in a better way because they provide us with more parameters and more design degrees of freedom this paper deals with the design of control systems using type 2 fuzzy logic for minimizing the effects of uncertainty produced by the instrumentation elements environmental noise etc the experimental results are divided in two classes in the first class simulations of a feedback control system for a non linear plant using type 1 and type 2 fuzzy logic controllers are presented a comparative analysis of the systems response in both cases was performed with and without the presence of uncertainty for the second class a non linear identification problem for time series prediction is presented based on the experimental results the conclusion is that the best results are obtained using type 2 fuzzy systems

generalized type 2 fuzzy weight adjustment for backpropagation neural networks in time series prediction in this paper the comparison of a proposed neural network with generalized type 2 fuzzy weights nngt2fw with respect to the monolithic neural network nn and the neural network with interval type 2 fuzzy weights nnit2fw is presented generalized type 2 fuzzy inference systems are used to obtain the generalized type 2 fuzzy weights and are designed by a strategy of increasing and decreasing an epsilon variable for obtaining the different sizes of the footprint of uncertainty fou for the generalized membership functions the proposed method is based on recent approaches that handle weight adaptation using type 1 and type 2 fuzzy logic the approach is applied to the prediction of the mackey glass time series and results are shown to outperform the results produced by other neural models gaussian noise was applied to the test data of the mackey glass time series for finding out which of the presented methods in this paper shows better performance and tolerance to noise

fixed charge transportation problem with type 2 fuzzy variables this paper considers two fixed charge transportation problems with type 2 fuzzy parameters unit transportation costs fixed costs in the first problem and unit transportation costs fixed costs supplies and demands in the second problem are type 2 fuzzy variables for the first problem to get corresponding defuzzified values of the type 2 fuzzy cost parameters first critical value cv based reduction methods are applied to reduce type 2 fuzzy variables into type 1 fuzzy variables and then centroid method is used for complete defuzzification besides this we also apply geometric defuzzification method to the type 2 fuzzy cost parameters in the first problem to provide a comparison of the results coming to the second problem a chance constrained programming model is formulated using generalized credibility measure for the objective function as well as the constraints with the cv based reductions of corresponding type 2 fuzzy parameters next the reduced model is turned into equivalent parametric programming problem the deterministic problems so obtained are then solved by using the standard optimization solver lingo we have provided numerical examples illustrating the proposed models and techniques some sensitivity analyzes for the second model are also presented

simulation of the bird age structured population growth based on an interval type 2 fuzzy cellular structure in this paper an age structured population growth model based on a fuzzy cellular structure is proposed an age structured population growth model enables a better description of population dynamics in this paper the dynamics of a particular bird species is considered the dynamics is governed by the variation of natality mortality and emigration rates which in this work are evaluated using an interval type 2 fuzzy logic system the use of type 2 fuzzy logic enables handling the effects caused by environment heterogeneity on the population a set of fuzzy rules about population growth are derived from the interpretation of the ecological laws and the bird life cycle the proposed model is formulated using discrete mathematics within the framework of a fuzzy cellular structure the fuzzy cellular structure allows us to visualize the evolution of the population s spatial dynamics the spatial distribution of the population has a deep effect on its dynamics moreover the model enables not only to estimate the percentage of occupation on the cellular space when the species reaches its stable equilibrium level but also to observe the occupation patterns

the evaluation map in field theory sigma models and strings ii in this paper we examine specifically the role of the evaluation map in sigma models and strings we discuss the difference between sigma models and field theory as far as anomaly cancellation is concerned the introduction of the wess zumino terms in different sigma models is considered anomalies in string theory are discussed with special attention to the conformal anomalies and to the sigma model anomalies for the imbedded or immersed world sheet of the string conformal anomalies in two dimensions are connected to holomorphic and gravitational anomalies in order to have the cancellation of the sigma model anomalies of the string certain topological conditions must be satisfied by the ambient manifold the role of the evaluation map in the calculations of global anomalies is also discussed both for field theories and for sigma models in particular global anomalies are connected with the differential characters of cheeger and simons we show that the absence of global anomalies in sigma models is guaranteed by the absence of torsion in suitable homology groups of the target space

rational homotopy of the space of sections of a nilpotent bundle we show that an algebraic construction proposed by sullivan is indeed a model for the rational homotopy type of the space of sections of a nilpotent bundle in his paper uhomologie des espaces fonctionnels r thom studied the homotopy type of the space f of continuous maps of x into f homotopic to a given map starting from a postnikov decomposition of f he built the functional space f step by step he also indicated how one could construct a differential graded algebra describing the rational homotopy type of f later on sullivan gave an algebraic model which mirrors this construction in terms of a dg algebra representing x and the minimal model of f the aim of this paper is to show following the method of thom that the model of sullivan is indeed a model for the functional space under suitable restrictions as in 3 we consider the slightly more general problem of the determination of the rational homotopy type of the space of sections ts of a nilpotent fiber space p y x homotopic to a given section s in 1 we explain thorn s geometric construction in 2 we describe an algebraic model for an abelian galois covering of a nilpotent space in 3 we show how the model of sullivan fits with the geometry i thank the referee for many improvements of this paper 1 a postnikov factorization of the space of sections 1 1 let g be a finitely generated abehan group and let x be a path connected space whose cohomology groups hk x g are finitely generated for each k to avoid difficulties with the topologies cf 4 we can work in the category of simplicial sets proposition thom 4 the space k g m x of continuous maps of x in the eilenberg mac lane complex k g m is homotopically equivalent to the product nr ra fthe eilenberg mac lane spaces ki k hm x g i more precisely let x g hm k g m g be the fundamental class of k g m if e k g m x xx k g m

what do homotopy algebras form abstract in paper 4 we constructed a symmetric monoidal category s lie mc whose objects are shifted and filtered l algebras here we fix a cooperad c and show that algebras over the operad cobar c naturally form a category enriched over s lie mc following 4 we integrate this s lie mc enriched category to a simplicial category hoalg c whose mapping spaces are kan complexes the simplicial category hoalg c gives us a particularly nice model of an 1 category of cobar c algebras we show that the homotopy category of hoalg c is the localization of the category of cobar c algebras and morphisms with respect to quasi isomorphisms finally we show that the homotopy transfer theorem is a simple consequence of the goldman millson theorem

discrete interval type 2 fuzzy system models using uncertainty in learning parameters fuzzy system modeling fsm is one of the most prominent tools that can be used to identify the behavior of highly nonlinear systems with uncertainty conventional fsm techniques utilize type 1 fuzzy sets in order to capture the uncertainty in the system however since type 1 fuzzy sets express the belongingness of a crisp value x of a base variable x in a fuzzy set a by a crisp membership value mua x they cannot fully capture the uncertainties due to imprecision in identifying membership functions higher types of fuzzy sets can be a remedy to address this issue since the computational complexity of operations on fuzzy sets are increasing with the increasing type of the fuzzy set the use of type 2 fuzzy sets and linguistic logical connectives drew a considerable amount of attention in the realm of fuzzy system modeling in the last two decades in this paper we propose a black box methodology that can identify robust type 2 takagi sugeno mizumoto and linguistic fuzzy system models with high predictive power one of the essential problems of type 2 fuzzy system models is computational complexity in order to remedy this problem discrete interval valued type 2 fuzzy system models are proposed with type reduction in the proposed fuzzy system modeling methods fuzzy c means fcm clustering algorithm is used in order to identify the system structure the proposed discrete interval valued type 2 fuzzy system models are generated by a learning parameter of fcm known as the level of membership and its variation over a specific set of values which generate the uncertainty associated with the system structure

rational homotopy of the homotopy fixed point sets of circle actions in this paper when g is the circle s 1 and m is a g space we study the rational homotopy type of the fixed point set m g the homotopy fixed point set m hg and the natural injection m g m hg c 2009 elsevier inc all rights reserved

topological andre quillen cohomology and e andre quillen cohomology abstract we show that the andre quillen cohomology of an e simplicial algebra with arbitrary coefficients and the topological andre quillen cohomology of an e ring spectrum with eilenberg mac lane coefficients may be calculated as the andre quillen cohomology of an associated e differential graded algebra

hybrid learning mechanism for interval a2 c1 type 2 non singleton type 2 takagi sugeno kang fuzzy logic systems a proposed learning methodology based on a hybrid mechanism for training interval a2 c1 type 2 non singleton type 2 takagi sugeno kang fuzzy logic systems uses a recursive square root filter to tune the type 1 consequent parameters and the steepest descent method to tune the interval type 2 antecedent parameters the proposed hybrid learning algorithm changes the interval type 2 model parameters adaptively to minimize some criterion function as new information becomes available and to match desired input output data pairs its antecedent sets are type 2 fuzzy sets its consequent sets are type 1 fuzzy sets and its inputs are interval type 2 non singleton fuzzy numbers with uncertain standard deviations as reported in the literature the performance indices of hybrid models have proved to be better than those of the individual training mechanisms used alone comparison with non hybrid interval a2 c1 type 2 takagi sugeno kang fuzzy logic systems and with non hybrid a1 c0 type 1 takagi sugeno kang fuzzy logic systems shows that the proposed hybrid mechanism is a well performing non linear adaptive method that enables the interval type 2 fuzzy model to match an unknown non linear mapping and to converge very fast experiments were carried out involving the application of the hybrid interval a2 c1 type 2 non singleton type 2 takagi sugeno kang fuzzy logic systems for modeling and prediction of the scale breaker entry temperature in a hot strip mill for three different types of coils the results demonstrate how the interval type 2 fuzzy system learns from selected input output data pairs and improves its performance as hybrid training progresses

on some formality criteria for dg lie algebras abstract we give some formality criteria for a differential graded lie algebra to be formal for instance we show that a dg lie algebra l is formal if and only if the natural spectral sequence computing the chevalley eilenberg cohomology h ce l l degenerates at e 2

continuous cohomology and real homotopy type various aspects of homotopy theory in the category of simplicial spaces are developed topics covered include continuous cohomology continuous de rham cohomology the kan extension condition the homotopy relation fibrations the serre spectral sequence real homotopy type and its relation to graded commutative differential algebras over the reals

rational homotopy of spaces of maps into spheres and complex projective spaces we investigate the rational homotopy classification problem for the components of some function spaces with sn or cpn as target space

derived koszul duality and tq homology completion of structured ring spectra abstract working in the context of symmetric spectra we consider algebraic structures that can be described as algebras over an operad o topological quillen homology or tq homology is the spectral algebra analog of quillen homology and stabilization working in a framework for homotopical descent the associated tq homology completion map appears as the unit map of an adjunction comparing the homotopy categories of o algebra spectra with coalgebra spectra over the associated comonad via tq homology we prove that this adjunction between homotopy categories can be turned into an equivalence by replacing o algebras with the full subcategory of 0 connected o algebras we also construct the spectral algebra analog of the unstable adams spectral sequence that starts from the tq homology groups tq x of an o algebra x and prove that it converges strongly to x when x is 0 connected

the de rham homotopy theory and differential graded category this paper is a generalization of moriya in j pure appl algebra 214 4 422 439 2010 we develop the de rham homotopy theory of not necessarily nilpotent spaces we use two algebraic objects closed dg categories and equivariant dg algebras we see these two objects correspond in a certain way proposition 3 3 4 theorem 3 4 5 we prove an equivalence between the homotopy category of schematic homotopy types toen in selecta math n s 12 1 39 135 2006 and a homotopy category of closed dg categories theorem 1 0 1 we give a description of homotopy invariants of spaces in terms of minimal models theorem 1 0 2 the minimal model in this context behaves much like the sullivan s minimal model we also provide some examples we prove an equivalence between fiberwise rationalizations bousfield and kan in lecture notes in mathematics vol 304 springer berlin 1972 and closed dg categories with subsidiary data theorem 1 0 4

models for classifying spaces and derived deformation theory using the theory of extensions of l l l algebras we construct rational homotopy models for classifying spaces of fibrations giving answers in terms of classical homological functors namely the chevalley eilenberg and harrison cohomology we also investigate the algebraic structure of the chevalley eilenberg complexes of l l l algebras and show that they possess along with the gerstenhaber bracket an l l l structure that is homotopy abelian

disconnected rational homotopy theory we construct two algebraic versions of homotopy theory of rational disconnected topological spaces one based on differential graded commutative associative algebras and the other one on complete differential graded lie algebras as an application of the developed technology we obtain results on the structure of maurer cartan spaces of complete differential graded lie algebras

a version of the goldman millson theorem for filtered l algebras abstract in this paper we consider l algebras equipped with complete descending filtrations we prove that under some mild conditions an l quasi isomorphism u l l induces a weak equivalence between the deligne getzler hinich dgh groupoids corresponding to l and l respectively this paper may be considered as a modest addition to foundational paper 10 by ezra getzler

uncertain fuzzy clustering interval type 2 fuzzy approach to c means in many pattern recognition applications it may be impossible in most cases to obtain perfect knowledge or information for a given pattern set uncertain information can create imperfect expressions for pattern sets in various pattern recognition algorithms therefore various types of uncertainty may be taken into account when performing several pattern recognition methods when one performs clustering with fuzzy sets fuzzy membership values express assignment availability of patterns for clusters however when one assigns fuzzy memberships to a pattern set imperfect information for a pattern set involves uncertainty which exist in the various parameters that are used in fuzzy membership assignment when one encounters fuzzy clustering fuzzy membership design includes various uncertainties e g distance measure fuzzifier prototypes etc in this paper we focus on the uncertainty associated with the fuzzifier parameter m that controls the amount of fuzziness of the final c partition in the fuzzy c means fcm algorithm to design and manage uncertainty for fuzzifier m we extend a pattern set to interval type 2 fuzzy sets using two fuzzifiers m1 and m2 which creates a footprint of uncertainty fou for the fuzzifier m then we incorporate this interval type 2 fuzzy set into fcm to observe the effect of managing uncertainty from the two fuzzifiers we also provide some solutions to type reduction and defuzzification i e cluster center updating and hard partitioning in fcm several experimental results are given to show the validity of our method