information geometry on hierarchy of probability distributions an exponential family or mixture family of probability distributions has a natural hierarchical structure this paper gives an orthogonal decomposition of such a system based on information geometry a typical example is the decomposition of stochastic dependency among a number of random variables in general they have a complex structure of dependencies pairwise dependency is easily represented by correlation but it is more difficult to measure effects of pure triplewise or higher order interactions dependencies among these variables stochastic dependency is decomposed quantitatively into an orthogonal sum of pairwise triplewise and further higher order dependencies this gives a new invariant decomposition of joint entropy this problem is important for extracting intrinsic interactions in firing patterns of an ensemble of neurons and for estimating its functional connections the orthogonal decomposition is given in a wide class of hierarchical structures including both exponential and mixture families as an example we decompose the dependency in a higher order markov chain into a sum of those in various lower order markov chains

toric degeneration of schubert varieties and gelfand tsetlin polytopes this note constructs the flat toric degeneration of the manifold fln of flags in cn due to gonciulea and lakshmibai transform groups 1 3 1996 215 as an explicit git quotient of the grobner degeneration due to knutson and miller grobner geometry of schubert polynomials ann math 2 to appear this implies that schubert varieties degenerate to reduced unions of toric varieties associated to faces indexed by rc graphs reduced pipe dreams in the gelfand tsetlin polytope our explicit description of the toric degeneration of fln provides a simple explanation of how gelfand tsetlin decompositions for irreducible polynomial representations of gln arise via geometric quantization

attractor reliability reveals deterministic structure in neuronal spike trains when periodic current is injected into an integrate and fire model neuron the voltage as a function of time converges from different initial conditions to an attractor that produces reproducible sequences of spikes the attractor reliability is a measure of the stability of spike trains against intrinsic noise and is quantified here as the inverse of the number of distinct spike trains obtained in response to repeated presentations of the same stimulus high reliability characterizes neurons that can support a spike time code unlike neurons with discharges forming a renewal process such as a poisson process these two classes of responses cannot be distinguished using measures based on the spike time histogram but they can be identified by the attractor dynamics of spike trains as shown here using a new method for calculating the attractor reliability we applied these methods to spike trains obtained from current injection into cortical neurons recorded in vitro these spike trains did not form a renewal process and had a higher reliability compared to renewal like processes with the same spike time histogram

h_ infty fuzzy control for a class of nonlinear coupled ode pde systems with input constraint this paper deals with the problem of h infty fuzzy control design with an input constraint for a class of coupled systems which consist of an n dimensional nonlinear subsystem of ordinary differential equations odes and a scalar linear parabolic subsystem of partial differential equation pde connected in feedback initially the nonlinear coupled system is represented by a takagi sugeno t s fuzzy coupled ode pde model then based on the fuzzy model and parallel distributed compensation scheme a fuzzy state feedback control design is developed via lyapunov s direct method such that the resulting closed loop fuzzy coupled system is exponentially stable and a prescribed h infty performance of disturbance attenuation is satisfied the existing condition of the proposed h infty fuzzy controllers is given in terms of linear matrix inequalities lmis moreover in order to make the attenuation level as small as possible while the input constraint is respected to avoid the high magnitude a suboptimal h infty constrained fuzzy control problem is also addressed which is formulated as an lmi optimization problem finally the proposed method is applied to the control of a hypersonic rocket car to illustrate its effectiveness

adaptive fuzzy tracking control for a class of uncertain nonaffine nonlinear systems with dead zone inputs this paper considers the problem of adaptive fuzzy tracking control for a class of uncertain nonaffine nonlinear systems with mismatched external disturbances parameter uncertainties and nonsymmetric dead zone inputs without the help of the dead zone inverse function and by incorporating the implicit function theorem both the adaptive state feedback tracking controller and the adaptive output feedback tracking controller based on high gain observer are designed by utilizing fuzzy logic systems fls to approximate the appropriate nonlinear control input functions a compounded disturbance is defined in terms of the external disturbance parameter uncertainty nonsymmetric dead zone input and approximation error of fls under the condition that the upper bound of the compounded disturbance is unknown novel adaptive laws are introduced to estimate and tune the unknown controller parameters on line furthermore on the basis of lyapunov stability analysis it is also proved that the presented control methods can guarantee that all the closed loop system error signals are uniformly ultimately bounded finally two simulation examples are provided to demonstrate efficiency of the proposed adaptive fuzzy tracking control approaches

robust adaptive output feedback tracking for a class of nonlinear time delayed plants within the model reference adaptive control mrac framework a continuous adaptive output feedback control scheme is developed for a class of nonlinear siso dynamic systems with time delays which is robust with respect to unknown time varying plant delays and to an external disturbance with unknown bounds a special form of the lyapunov krasovskii functional with a virtual adaptation gain vector is introduced to prove stability

information geometry of interspike intervals in spiking neurons an information geometrical method is developed for characterizing or classifying neurons in cortical areas whose spike rates fluctuate in time under the assumption that the interspike intervals of a spike sequence of a neuron obey a gamma process with a time variant spike rate and a fixed shape parameter we formulate the problem of characterization as a semiparametric statistical estimation where the spike rate is a nuisance parameter we derive optimal criteria from the information geometrical viewpoint when certain assumptions are added to the formulation and we show that some existing measures such as the coefficient of variation and the local variation are expressed as estimators of certain functions under the same assumptions

a novel robust adaptive fuzzy tracking control for a class of nonlinearmulti input multi output systems robust adaptive fuzzy tracking control of a class of uncertain multi input multi output nonlinear systems with coupled interconnections is considered in this paper takagi sugeno t s fuzzy systems are used to approximate the unknown system functions a novel adaptive control scheme is developed on the basis of the so called dynamic surface control and minimal learning parameters techniques the proposed scheme has following two key features first the number of parameters updated online for each subsystem is reduced to one and both problems of curse of dimension for high dimensional systems and explosion of complexity inherent in the conventional backstepping methods are circumvented second the potential controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques is overcome it is shown via lyapunov theory that all the signals in the closed loop system are semiglobally uniformly ultimately bounded finally simulation results via two examples are presented to demonstrate the effectiveness and advantages of the proposed scheme

the ornstein uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex cortical neurons of behaving animals generate irregular spike sequences recently there has been a heated discussion about the origin of this irregularity softky and koch 1993 pointed out the inability of standard single neuron models to reproduce the irregularity of the observed spike sequences when the model parameters are chosen within a certain range that they consider to be plausible shadlen and newsome 1994 on the other hand demonstrated that a standard leaky integrate and fire model can reproduce the irregularity if the inhibition is balanced with the excitation motivated by this discussion we attempted to determine whether the ornstein uhlenbeck process which is naturally derived from the leaky integration assumption can in fact reproduce higher order statistics of biological data for this purpose we consider actual neuronal spike sequences recorded from the monkey prefrontal cortex to calculate the higher order statistics of the interspike intervals consistency of the data with the model is examined on the basis of the coefficient of variation and the skewness coefficient which are respectively a measure of the spiking irregularity and a measure of the asymmetry of the interval distribution it is found that the biological data are not consistent with the model if the model time constant assumes a value within a certain range believed to cover all reasonable values this fact suggests that the leaky integrate and fire model with the assumption of uncorrelated inputs is not adequate to account for the spiking in at least some cortical neurons

robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance in this technical note we consider adaptive control of single input uncertain nonlinear systems in the presence of input saturation and unknown external disturbance by using backstepping approaches two new robust adaptive control algorithms are developed by introducing a well defined smooth function and using a nussbaum function the nussbaum function is introduced to compensate for the nonlinear term arising from the input saturation unlike some existing control schemes for systems with input saturation the developed controllers do not require assumptions on the uncertain parameters within a known compact set and a priori knowledge on the bound of the external disturbance besides showing global stability transient performance is also established and can be adjusted by tuning certain design parameters

design of a unified adaptive fuzzy observer for uncertain nonlinear systems this paper presents an adaptive fuzzy observer for a class of uncertain nonlinear systems more precisely we propose a unified approach for designing such an observer with some design flexibility so that it can be easily adaptable and employed either as a high gain or a sliding mode observer by selecting its gain appropriately additionally we derive a suitable parameter adaptation law so that the proposed observer is robust with respect to ubiquitous fuzzy approximation errors and external disturbances we also show that the observation error is ultimately bounded using a lyapunov approach without having recourse to the usual strictly positive real spr condition or a suitable observation error filtering the effectiveness of the proposed observers is illustrated through two simulation case studies taken from the adaptive fuzzy control literature

information geometric measures as robust estimators of connection strengths and external inputs information geometry has been suggested to provide a powerful tool for analyzing multineuronal spike trains among several advantages of this approach a significant property is the close link between information geometric measures and neural network architectures previous modeling studies established that the first and second order information geometric measures corresponded to the number of external inputs and the connection strengths of the network respectively this relationship was however limited to a symmetrically connected network and the number of neurons used in the parameter estimation of the log linear model needed to be known recently simulation studies of biophysical model neurons have suggested that information geometry can estimate the relative change of connection strengths and external inputs even with asymmetric connections inspired by these studies we analytically investigated the link between the information geometric measures and the neural network structure with asymmetrically connected networks of n neurons we focused on the information geometric measures of orders one and two which can be derived from the two neuron log linear model because unlike higher order measures they can be easily estimated experimentally considering the equilibrium state of a network of binary model neurons that obey stochastic dynamics we analytically showed that the corrected first and second order information geometric measures provided robust and consistent approximation of the external inputs and connection strengths respectively these results suggest that information geometric measures provide useful insights into the neural network architecture and that they will contribute to the study of system level neuroscience

a mathematical theory of energy efficient neural computation and communication a neuroscience based mathematical model of how a neuron stochastically processes data and communicates information is introduced and analyzed call the neuron in question neuron j or just j the information j transmits approximately describes the time varying intensity of the excitation j is continuously experiencing from neural spike trains delivered to its synapses by thousands of other neurons neuron j encodes this excitation history into a sequence of time instants at which it generates neural spikes of its own by propagating these spikes along its axon j acts as a multiaccess partially degraded broadcast channel with thousands of input and output terminals that employs a time continuous version of pulse position modulation the mathematical model features three parameters m and b which largely characterize j as an engine of computation and communication each set of values of these parameters corresponds to a long term maximization of the bits j conveys to its targets per joule it expends doing so which is achieved by distributing the random duration between successive spikes j generates according to a gamma pdf with parameters and b and distributing b a according to a beta probability density with parameters and m where a is the random intensity of the effectively poisson process of spikes that arrive to the union of all of j s synapses at a randomly chosen time instant

brief paper adaptive output control of uncertain nonlinear systems with non symmetric dead zone input this paper deals with the adaptive output feedback control problem of a class of uncertain nonlinear systems with an unknown non symmetric dead zone nonlinearity the nonlinear system considered here is dominated by a triangular system without zero dynamics satisfying polynomial growth in the unmeasurable states an adaptive control scheme is developed without constructing the dead zone inverse the proposed adaptive control scheme requires only the information of bounds of the slopes and the breakpoint of dead zone nonlinearity the novelty of this paper is that a universal type adaptive output feedback controller is numerically constructed by using a sum of squares sos optimization algorithm which ensures the boundedness of all the signals in the adaptive closed loop without knowing the growth rate of the uncertainties an example is presented to show the effectiveness of the proposed approach

robust adaptive sliding mode control for fuzzy systems with mismatched uncertainties this paper is devoted to design adaptive sliding mode controllers for the takagi sugeno t s fuzzy system with mismatched uncertainties and exogenous disturbances the uncertainties in state matrices are mismatched and norm bounded while the exogenous disturbances are assumed to be bounded with an unknown bound which is estimated by a simple and effective adaptive approach both state and static output feedback sliding mode control problems are considered in terms of linear matrix inequalities lmis both sliding surfaces and sliding mode controllers can be easily obtained via a convex optimization technique finally two simulation examples and a real experiment are utilized to illustrate the applicability and effectiveness of the design procedures proposed in this paper

differences in spiking patterns among cortical neurons spike sequences recorded from four cortical areas of an awake behaving monkey were examined to explore characteristics that vary among neurons we found that a measure of the local variation of interspike intervals lv is nearly the same for every spike sequence for any given neuron while it varies significantly among neurons the distributions of lv values for neuron ensembles in three of the four areas were found to be distinctly bimodal two groups of neurons classified according to the spiking irregularity exhibit different responses to the same stimulus this suggests that neurons in each area can be classified into different groups possessing unique spiking statistics and corresponding functional properties

modeling spiking behavior of neurons with time dependent poisson processes three kinds of interval statistics as represented by the coefficient of variation the skewness coefficient and the correlation coefficient of consecutive intervals are evaluated for three kinds of time dependent poisson processes pulse regulated sinusoidally regulated and doubly stochastic among these three processes the sinusoidally regulated and doubly stochastic poisson processes in the case when the spike rate varies slowly compared with the mean interval between spikes are found to be consistent with the three statistical coefficients exhibited by data recorded from neurons in the prefrontal cortex of monkeys

capacity of a single spiking neuron channel information transfer through a single neuron is a fundamental component of information processing in the brain and computing the information channel capacity is important to understand this information processing the problem is difficult since the capacity depends on coding characteristics of the communication channel and optimization over input distributions among other issues in this letter we consider two models the temporal coding model of a neuron as a communication channel assumes the output is where is a gamma distributed random variable corresponding to the interspike interval that is the time it takes for the neuron to fire once the rate coding model is similar the output is the actual rate of firing over a fixed period of time theoretical studies prove that the distribution of inputs which achieves channel capacity is a discrete distribution with finite mass points for temporal and rate coding under a reasonable assumption this allows us to compute numerically the capacity of a neuron numerical results are in a plausible range based on biological evidence to date

decentralized adaptive tracking control of nonaffine nonlinear large scale systems with time delays this paper addresses the problem of decentralized tracking control of large scale systems with uncertain nonaffine nonlinear isolated subsystems and nonlinear interconnections with time varying delays based on lyapunov krasovskii functional approach and implicit function theorem a delay independent decentralized tracking controller is proposed due to functional approximation capability of fuzzy logic systems fls neither strict structure restrictions on the isolated subsystems nor a priori knowledge of the strong interconnections with time varying delays is required in our control design furthermore transient performance of the resulting closed loop system is also addressed under an analytical framework finally two numerical examples are provided to show the effectiveness of the proposed controller

noninteracting adaptive control of pmsm using interval type 2 fuzzy logic systems based on the type 2 fuzzy logic systems and adaptive control theory this paper develops a decentralized adaptive fuzzy controller for a permanent magnet synchronous motor pmsm the adaptive law is designed to compensate for the interconnection effects and the reconstruction errors using a sliding mode term the type 2 fuzzy logic systems are used to model the unknown functions based on lyapunov s stability theorem the stability of closed loop systems can be verified moreover the proposed overall control schemes guarantee that all the signals that are involved are bounded to demonstrate the effectiveness of the proposed methods simulation results are illustrated in this paper

stable adaptive control for nonlinear multivariable systems with a triangular control structure a stable adaptive controller is developed for a class of nonlinear multivariable systems using nonlinearly parametrized function approximators by utilizing the system triangular property integral type lyapunov functions are introduced for deriving the control structure and adaptive laws without the need of estimating the decoupling matrix of the multivariable nonlinear system it is shown that stability of the adaptive closed loop system is guaranteed and transient performance is analytically quantized by mean square and l sub spl infin tracking error bound criteria

adaptive fuzzy output feedback control of mimo nonlinear systems with unknown dead zone inputs this paper is concerned with the problem of adaptive fuzzy tracking control for a class of multi input and multi output mimo strict feedback nonlinear systems with both unknown nonsymmetric dead zone inputs and immeasurable states in this research fuzzy logic systems are utilized to evaluate the unknown nonlinear functions and a fuzzy adaptive state observer is established to estimate the unmeasured states based on the information of the bounds of the dead zone slopes as well as treating the time varying inputs coefficients as a system uncertainty a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique it is shown that the proposed control approach can assure that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded it is also shown that the observer and tracking errors converge to a small neighborhood of the origin by selecting appropriate design parameters simulation examples are also provided to illustrate the effectiveness of the proposed approach

okounkov bodies and toric degenerations let vardelta be the okounkov body of a divisor d on a projective variety x we describe a geometric criterion for vardelta to be a lattice polytope and show that in this situation x admits a flat degeneration to the corresponding toric variety this degeneration is functorial in an appropriate sense

fuzzy approximation based adaptive control of nonlinear delayed systems with unknown dead zone this paper focuses on the problem of adaptive fuzzy control for a class of nonlinear systems without a strict feedback form a new adaptive fuzzy control scheme is proposed for nonlinear delayed systems with unknown dead zone nonlinearity control design is achieved by introducing a variable separation approach and employing the unique structural property of fuzzy logic systems the proposed adaptive fuzzy controller guarantees that all the closed loop signals are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin two simulation examples illustrate the effectiveness of the proposed approach

adaptive fuzzy output feedback tracking backstepping control of strict feedback nonlinear systems with unknown dead zones in this paper an adaptive fuzzy backstepping control approach is considered for a class of nonlinear strict feedback systems with unknown functions unknown dead zones and immeasurable states fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy filters state observer is designed to estimate the immeasurable states by using the adaptive backstepping recursive design technique and constructing the dead zone inverse a new adaptive fuzzy backstepping output feedback control approach is developed it is mathematically proved that all the signals of the resulting closed loop adaptive control system are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin by appropriate choice of design parameters the proposed approach cannot only solve the problem of the dead zones but also cancel the restrictive assumption in the previous literature that the states are all available for measurement two simulation examples are provided to show the effectiveness of the proposed approach

state observer based adaptive fuzzy output feedback control for a class of uncertain nonlinear systems this paper aims to develop state observer based adaptive fuzzy control techniques for controlling a class of uncertain nonlinear systems with bounded external disturbances an adaptive fuzzy observer is proposed to estimate the system state variables it is shown that the observation errors obtained from the observer are uniformly ultimately bounded applying the estimated system state for design of an output feedback controller the uniformly ultimate boundedness of the tracking errors for the resulting closed loop system can be guaranteed a typical robot arm system is employed in our simulation studies and the results demonstrate the usefulness and effectiveness of the proposed techniques for controlling nonlinear systems with bounded external disturbances

on the toric ideal of a matroid abstract describing minimal generating set of a toric ideal is a well studied and difficult problem in 1980 white conjectured that the toric ideal associated to a matroid is equal to the ideal generated by quadratic binomials corresponding to symmetric exchanges we prove white s conjecture up to saturation that is that the saturations of both ideals are equal in the language of algebraic geometry this means that both ideals define the same projective scheme additionally we prove the full conjecture for strongly base orderable matroids

universal fuzzy models and universal fuzzy controllers for stochastic nonaffine nonlinear systems this paper investigates the universal fuzzy model and universal fuzzy controller problems for stochastic nonaffine nonlinear systems the underlying mechanism of stochastic fuzzy logic is first discussed and a stochastic generalized fuzzy model with new stochastic fuzzy rule base is then given based on their function approximation capability these kinds of stochastic generalized fuzzy models are shown to be universal fuzzy models for stochastic nonaffine nonlinear systems under some sufficient conditions an approach to stabilization controller design for stochastic nonaffine nonlinear systems is then developed through their stochastic generalized takagi sugeno t s fuzzy approximation models then the results of universal fuzzy controllers for two classes of stochastic nonlinear systems along with constructive procedures to obtain the universal fuzzy controllers are also provided respectively finally a numerical example is presented to illustrate the effectiveness of the proposed approach

adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays the problem of robust tracking and model following is considered for a class of linear systems with multiple delayed state perturbations time varying uncertain parameters and disturbance in this note it is assumed that the upper bounds of the delayed state perturbations uncertainties and external disturbances are unknown an improved adaptation law with spl sigma modification is proposed to estimate such unknown bounds and on the basis of the updated values of these unknown bounds a class of continuous memoryless state feedback controllers is constructed for robust tracking of dynamical signals the proposed adaptive robust tracking controller can guarantee that the tracking error decreases asymptotically to zero in the presence of multiple delayed state perturbations time varying uncertain parameters and disturbance in addition it is also shown that this improved adaptation law with spl sigma modification can be applied to the general adaptive control problems to obtain some more exact control results finally a numerical example is given to demonstrate the validity of the results

robust tracking observer based adaptive fuzzy control design for uncertain nonlinear mimo systems with time delayed states this paper addresses the problem of designing robust observer based adaptive fuzzy tracking control scheme for a class of mimo nonlinear systems with plant uncertainties time delayed uncertainties and external disturbances a fuzzy logic system fls is utilized to approximate the unknown nonlinear functions and an adaptive fuzzy observer is introduced for state estimations the proposed control law is based on indirect adaptive fuzzy control and uses two on line estimations this allows for the simultaneous inclusion of identifying gains of the delayed state uncertainties and training of the weights of the fuzzy system by introducing estimated error vectors the advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with online update laws the adaptive fuzzy tracking control using variable structure vs control technique is derived based on lyapunov criterion and the riccati inequality to resolve system uncertainties time delayed uncertainties and external disturbances this is done in such a way that all states of the system are bounded and the h tracking performance is achieved finally a two connected inverted pendulums on carts system liu et al 2011 29 is used for simulation purposes and some comparisons are given to illustrate the validity and effectiveness of the proposed method

cooperative adaptive fuzzy tracking control for networked unknown nonlinear multiagent systems with time varying actuator faults in this paper the cooperative adaptive fault tolerant fuzzy tracking control caftftc problem of networked high order multiagent with time varying actuator faults is studied and a novel caftftc scheme is proposed to guarantee that all follower nodes asymptotically synchronize a leader node with tracking errors converging to a small adjustable neighborhood of the origin in spite of actuator faults the leader node is modeled as a higher order nonautonomous nonlinear system it acts as a command generator giving commands only to a small portion of the networked group each follower is assumed to have nonidentical unknown nonlinear dynamics and the communication network is also assumed to be a weighted directed graph with a fixed topology a distributed robust adaptive fuzzy controller is designed for each follower node such that the tracking errors are cooperative uniform ultimate boundedness cuub moreover these controllers are distributed in the sense that the controller designed for each follower node only requires relative state information between itself and its neighbors the adaptive compensation term of the optimal approximation errors and external disturbances is adopted to reduce the effects of the errors and disturbances which removes the assumption that the upper bounds of unknown function approximation errors and disturbances should be known analysis of stability and parameter convergence of the proposed algorithm are conducted that are based on algebraic graph theory and lyapunov theory comparing with results in the literature the caftftc scheme can minimize the time delay between fault occurrence and accommodation and reduce its adverse effect on system performance in addition the ftc scheme requires no additional fault isolation model which is necessary in the traditional active ftc scheme finally an example is provided to validate the theoretical results

estimating instantaneous irregularity of neuronal firing cortical neurons in vivo had been regarded as poisson spike generators that convey no information other than the rate of random firing recently using a metric for analyzing local variation of interspike intervals researchers have found that individual neurons express specific patterns in generating spikes which may symbolically be termed regular random or bursty rather invariantly in time in order to study the dynamics of firing patterns in greater detail we propose here a bayesian method for estimating firing irregularity and the firing rate simultaneously for a given spike sequence and we implement an algorithm that may render the empirical bayesian estimation practicable for data comprising a large number of spikes application of this method to electrophysiological data revealed a subtle correlation between the degree of firing irregularity and the firing rate for individual neurons irregularity of firing did not deviate greatly around the low degree of dependence on the firing rate and remained practically unchanged for individual neurons in the cortical areas v1 and mt whereas it fluctuated greatly in the lateral geniculate nucleus of the thalamus this indicates the presence and absence of autocontrolling mechanisms for maintaining patterns of firing in the cortex and thalamus respectively

adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non symmetric dead zone nonlinearities this paper is concerned with the problem of robust adaptive fuzzy tracking controller design for a class of uncertain nonaffine nonlinear systems with external disturbances and non symmetric dead zone nonlinearities with the help of fuzzy logic systems flss to approximate the desired nonlinear functions a novel direct adaptive tracking control scheme is established first the implicit function theorem and the mean value theorem are used to deal with the nonaffine term with unknown dead zone input then based on the estimation information for the unknown upper bound of the compounded disturbance an adaptive fuzzy tracking controller with the corresponding parameter updating laws is designed to eliminate the effect of the compounded disturbance furthermore it is proved that all the resulting closed loop system signals are uniformly bounded and the tracking error can asymptotically converge to zero via the lyapunov stability analysis finally a numerical example is provided to verify the effectiveness of the proposed adaptive fuzzy asymptotic tracking design method

estimating spiking irregularities under changing environments we considered a gammadistribution of interspike intervals as a statistical model for neuronal spike generation a gamma distribution is a natural extension of the poisson process taking the effect of a refractory period into account the model is specified by two parameters a time dependent firing rate and a shape parameter that characterizes spiking irregularities of individual neurons because the environment changes over time observed data are generated from a model with a time dependent firing rate which is an unknown function a statistical model with an unknown function is called a semiparametric model and is generally very difficult to solve we used a novel method of estimating functions in information geometry to estimate the shape parameter without estimating the unknown function we obtained an optimal estimating function analytically for the shape parameter independent of the functional form of the firing rate this estimation is efficient without fisher information loss and better than maximum likelihood estimation we suggest a measure of spiking irregularity based on the estimating function which may be useful for characterizing individual neurons in changing environments

adaptive output feedback fuzzy tracking control for a class of nonlinear systems this paper is concerned with the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems the dynamic feedback strategy begins with an input driven filter by utilizing fuzzy logic systems to approximate unknown and desired control input signals directly instead of the unknown nonlinear functions an output feedback fuzzy tracking controller is designed via a backstepping approach it is shown that the proposed fuzzy adaptive output controller can guarantee that all the signals remain bounded and that the tracking error converges to a small neighborhood of the origin simulations results are presented to demonstrate the effectiveness of the proposed methods

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

toric ideals generated by quadratic binomials abstract a combinatorial criterion for the toric ideal arising from a finite graph to be generated by quadratic binomials is studied such a criterion guarantees that every koszul algebra generated by squarefree quadratic monomials is normal we present an example of a normal non koszul squarefree semigroup ring whose toric ideal is generated by quadratic binomials as well as an example of a non normal koszul squarefree semigroup ring whose toric ideal possesses no quadratic grobner basis in addition all the affine semigroup rings which are generated by squarefree quadratic monomials and which have 2 linear resolutions will be classified moreover it is shown that the toric ideal of a normal affine semigroup ring generated by quadratic monomials is generated by quadratic binomials if its underlying polytope is simple

adaptive neural control of high order uncertain nonaffine systems a transformation to affine systems approach abstract this brief investigates the adaptive neural network nn control of a class of high order nonaffine nonlinear systems with completely unknown dynamics since the control terms appear within the unknown nonlinearity traditional control schemes and stability analysis are usually rendered extremely complicated our main contribution includes a novel system transformation that converts the nonaffine system into an affine system through a combination of a low pass filter and state transformation as a result the state feedback control of the nonaffine system can be viewed as the output feedback control of an affine system in normal form the transformed system becomes linear with respect to the new input while the traditional backstepping approach is not needed thus allowing the synthesis to be extremely simplified it is theoretically proven that all the signals in the closed loop system are uniformly ultimately bounded uub simulation results are provided to demonstrate the performance of the developed controller

information geometric measures for estimation of connection weight under correlated inputs the brain processes information in a highly parallel manner determination of the relationship between neural spikes and synaptic connections plays a key role in the analysis of electrophysiological data information geometry ig has been proposed as a powerful analysis tool for multiple spike data providing useful insights into the statistical interactions within a population of neurons previous work has demonstrated that ig measures can be used to infer the connection weight between two neurons in a neural network this property is useful in neuroscience because it provides a way to estimate learning induced changes in synaptic strengths from extracellular neuronal recordings a previous study has shown however that this property would hold only when inputs to neurons are not correlated since neurons in the brain often receive common inputs this would hinder the application of the ig method to real data we investigated the two neuron ig measures in higher order log linear models to overcome this limitation first we mathematically showed that the estimation of uniformly connected synaptic weight can be improved by taking into account higher order log linear models second we numerically showed that the estimation can be improved for more general asymmetrically connected networks considering the estimated number of the synaptic connections in the brain we showed that the two neuron ig measure calculated by the fourth or fifth order log linear model would provide an accurate estimation of connection strength within approximately a 10 error these studies suggest that the two neuron ig measure with higher order log linear expansion is a robust estimator of connection weight even under correlated inputs providing a useful analytical tool for real multineuronal spike data

robust adaptive control of a class of nonlinear systems with unknown dead zone this paper deals with the adaptive control of a class of continuous time nonlinear dynamic systems preceded by an unknown dead zone by using a new description of a dead zone and by exploring the properties of this dead zone model intuitively and mathematically a robust adaptive control scheme is developed without constructing the dead zone inverse the new control scheme ensures global stability of the adaptive system and achieves desired tracking precision simulations performed on a typical nonlinear system illustrate and clarify the validity of this approach

non affine nonlinear adaptive control of decentralized large scale systems using neural networks this paper introduces a new decentralized adaptive neural network controller for a class of large scale nonlinear systems with unknown non affine subsystems and unknown interconnections represented by nonlinear functions a radial basis function neural network is used to represent the controller s structure the stability of the closed loop system is guaranteed through lyapunov stability analysis the effectiveness of the proposed decentralized adaptive controller is illustrated by considering two nonlinear systems a two inverted pendulum and a turbo generator the simulation results verify the merits of the proposed controller

influence of external inputs and asymmetry of connections on information geometric measures involving up to ten neuronal interactions the investigation of neural interactions is crucial for understanding information processing in the brain recently an analysis method based on information geometry ig has gained increased attention and the property of the pairwise ig measure has been studied extensively in relation to the two neuron interaction however little is known about the property of ig measures involving more neuronal interactions in this study we systematically investigated the influence of external inputs and the asymmetry of connections on the ig measures in cases ranging from 1 neuron to 10 neuron interactions first the analytical relationship between the ig measures and external inputs was derived for a network of 10 neurons with uniform connections our results confirmed that the single and pairwise ig measures were good estimators of the mean background input and of the sum of the connection weights respectively for the ig measures involving 3 to 10 neuronal interactions we found that the influence of external inputs was highly nonlinear second by computer simulation we extended our analytical results to asymmetric connections for a network of 10 neurons the simulation showed that the behavior of the ig measures in relation to external inputs was similar to the analytical solution obtained for a uniformly connected network when the network size was increased to 1000 neurons the influence of external inputs almost disappeared this result suggests that all ig measures from 1 neuron to 10 neuron interactions are robust against the influence of external inputs in addition we investigated how the strength of asymmetry influenced the ig measures computer simulation of a 1000 neuron network showed that all the ig measures were robust against the modulation of the asymmetry of connections our results provide further support for an information geometric approach and will provide useful insights when these ig measures are applied to real experimental spike data

adaptive fuzzy hierarchical sliding mode control for the trajectory tracking of uncertain underactuated nonlinear dynamic systems the trajectory tracking of uncertain underactuated nonlinear dynamic systems is tackled by an adaptive fuzzy hierarchical sliding mode control afhsmc first one of the subsystems is assigned as the first layer sliding surface next a second layer sliding surface from the first layer sliding surface and the sliding surface of another subsystem is constructed in this paper the nth layer is supposed to be the top layer or hierarchical layer for including the sliding surfaces of all subsystems because two nonlinear system functions and the time varying external disturbance of each subsystem are supposed to be unknown different online fuzzy models are employed to approximate these nonlinear system functions and the upper bounded functions of external disturbances moreover the upper bound of uncertainties caused by these fuzzy modeling errors is estimated online based on these learning fuzzy models and the estimated upper bound of these modeling errors an afhsmc is developed the stability analysis and tracking performance of the closed loop system are verified by lyapunov stability theory finally two simulation examples including different amplitudes of external disturbance and comparison with hierarchical sliding mode control confirm the effectiveness and robustness of the proposed control

toric degenerations of grassmannians and schubert varieties from matching field tableaux abstract we study grobner degenerations of grassmannians and the schubert varieties inside them we provide a family of binomial ideals whose combinatorics is governed by matching field tableaux in the sense of sturmfels and zelevinsky in 31 we prove that these ideals are all quadratically generated and they yield a sagbi basis of the plucker algebra this leads to a new family of toric degenerations of grassmannians moreover we apply our results to construct a family of grobner degenerations of schubert varieties inside grassmannians we provide a complete characterization of toric ideals among these degenerations in terms of the combinatorics of matching fields permutations and semi standard tableaux