persistence exponents and scaling in two dimensional xy model and a nematic model the persistence exponents associated with the t 0 quenching dynamics of the two dimensional xy model and a two dimensional uniaxial spin nematic model have been evaluated using a numerical simulation the site persistence or the probability that the sign of a local spin component does not change starting from initial time t 0 up to a certain time t is found to decay as l t l t is the linear domain length scale with 0 305 0 020 for the two dimensional xy model and 0 199 0 009 for the two dimensional uniaxial spin nematic model we have also investigated the scaling at the late time of phase ordering associated with the correlated persistent sites in both models the persistence correlation length was found to grow in the same way as l t

persistence exponents of non gaussian processes in statistical mechanics motivated by certain problems of statistical physics we consider a stationary stochastic process in which deterministic evolution is interrupted at random times by upward jumps of a fixed size if the evolution consists of linear decay the sample functions are of the random sawtooth type and the level dependent persistence exponent can be calculated exactly we then develop an expansion method valid for small curvature of the deterministic curve the curvature parameter g plays the role of the coupling constant of an interacting particle system the leading order curvature correction to is proportional to g 2 3 the expansion applies in particular to exponential decay in the limit of large level where the curvature correction considerably improves the linear approximation the langevin equation with gaussian white noise is recovered as a singular limiting case

markov chains of nonlinear markov processes and an application to a winner takes all model for social conformity we discuss nonlinear markov processes defined on discrete time points and discrete state spaces using markov chains in this context special attention is paid to the distinction between linear and nonlinear markov processes we illustrate that the chapman kolmogorov equation holds for nonlinear markov processes by a winner takes all model for social conformity

on constructing constrained control lyapunov functions for linear systems this works considers the problem of control of linear systems with input constraints the notion of control lyapunov functions clfs is first generalized and relaxed to define a constrained control lyapunov function cclf and a constructive procedure for cclf is subsequently presented

a fuzzy syllogistic reasoning schema for generalized quantifiers in this paper a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways i a number of different types of quantifiers logical absolute proportional comparative and exception taken from theory of generalized quantifiers and similarity quantifiers taken from statistics are considered and ii any number of premises can be taken into account within the reasoning process furthermore a systematic reasoning procedure to solve the syllogism is also proposed interpreting it as an equivalent mathematical optimization problem where the premises constitute the constraints of the searching space for the quantifier in the conclusion

phase ordering and persistence in a class of stochastic processes interpolating between the ising and voter models we study the dynamics of a class of two dimensional stochastic processes depending on two parameters which may be interpreted as two different temperatures respectively associated to interfacial and to bulk noise special lines in the plane of parameters correspond to the ising model voter model and majority vote model the dynamics of this class of models may be described formally in terms of reaction diffusion processes for a set of coalescing annihilating and branching random walkers we use the freedom allowed by the space of parameters to measure by numerical simulations the persistence probability of a generic model in the low temperature phase where the system coarsens this probability is found to decay at large times as a power law with a seemingly constant exponent we also discuss the connection between persistence and the nature of the interfaces between domains

nonlinear stochastic receding horizon control stability robustness and monte carlo methods for control approximation this work considers the stability of nonlinear stochastic receding horizon control when the optimal controller is only computed approximately a number of general classes of controller approximation error are analysed including deterministic and probabilistic errors and even controller sample and hold errors in each case it is shown that the controller approximation errors do not accumulate even over an infinite time frame and the process converges exponentially fast to a small neighbourhood of the origin in addition to this analysis an approximation method for receding horizon optimal control is proposed based on monte carlo simulation this method is derived via the feynman kac formula which gives a stochastic interpretation for the solution of a hamilton jacobi bellman equation associated with the true optimal controller it is shown and it is a prime motivation for this study that this particular controller approximation method practically stabilises the underlying nonlinear process

rational group decision making a random field ising model at t 0 abstract a modified version of a finite random field ising ferromagnetic model in an external magnetic field at zero temperature is presented to describe group decision making fields may have a non zero average a postulate of minimum inter individual conflicts is assumed interactions then produce a group polarization along one very choice which is however randomly selected a small external social pressure is shown to have a drastic effect on the polarization individual bias related to personal backgrounds cultural values and past experiences are introduced via quenched local competing fields they are shown to be instrumental in generating a larger spectrum of collective new choices beyond initial ones in particular compromise is found to results from the existence of individual competing bias conflict is shown to weaken group polarization the model yields new psychosociological insights about consensus and compromise in groups

robust controller design for stochastic nonlinear systems via convex optimization this paper presents a new nonlinear control design framework called convex optimization based stochastic steady state tracking error minimization cvstem for a class of ito stochastic nonlinear systems including stochastic lagrangian systems this state feedback controller design involves the use of multiple state dependent coefficient sdc models of a nonlinear system equation and computes its controller parameters by solving a convex optimization problem in order to minimize an upper bound of the steady state tracking error this problem is shown to be equivalent to the original nonlinear optimization problem of minimizing the upper bound the exponential stability and robustness properties due to the state dependent riccati inequality are proven using stochastic contraction analysis discrete time stochastic incremental contraction analysis with respect to a state and time dependent metric is also presented along with its explicit connection to continuous time contraction analysis a result of simulation is used to validate the superiority of the proposed controller compared to a known nonlinear controller a pid controller and an h infinity controller

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

constrained stochastic lqc a tractable approach despite the celebrated success of dynamic programming for optimizing quadratic cost functions over linear systems such an approach is limited by its inability to tractably deal with even simple constraints in this paper we present an alternative approach based on results from robust optimization to solve the stochastic linear quadratic control slqc problem in the unconstrained case the problem may be formulated as a semidefinite optimization problem sdp we show that we can reduce this sdp to optimization of a convex function over a scalar variable followed by matrix multiplication in the current state thus yielding an approach that is amenable to closed loop control and analogous to the riccati equation in our framework we also consider a tight second order cone socp approximation to the sdp that can be solved much more efficiently when the problem has additional constraints both the sdp and socp are tractable in the presence of control and state space constraints moreover compared to the riccati approach they provide much greater control over the stochastic behavior of the cost function when the noise in the system is distributed normally

on fuzzy type theory this paper is a generalization of classical simple type theory we have developed a formal system of fuzzy type theory which differs from the classical one essentially in extension of truth values from two to infinitely many the structure of truth values is assumed to be an imtl algebra residuated lattice with prelinearity and double negation extended by the baaz delta operation various properties of fuzzy type theory are proved including its completeness

lyapunov based model predictive control of stochastic nonlinear systems in this work we design a lyapunov based model predictive controller lmpc for nonlinear systems subject to stochastic uncertainty the lmpc design provides an explicitly characterized region from where stability can be probabilistically obtained the key idea is to use stochastic lyapunov based feedback controllers with well characterized stabilization in probability to design constraints in the lmpc that allow the inheritance of the stability properties by the lmpc the application of the proposed lmpc method is illustrated using a nonlinear chemical process system example

first order continuous models of opinion formation we study certain nonlinear continuous models of opinion formation derived from a kinetic description involving exchanges of opinion between individual agents these models imply that the only possible final opinions are the extremal ones and they are similar to models of pure drift in magnetization both analytical and numerical methods allow us to recover the final distribution of opinion between the two extremal ones

social paradoxes of majority rule voting and renormalization group real space renormalization group ideas are used to study a voting problem in political science a model to construct self directed pyramidal structures from bottom up to the top is presented using majority rules it is shown that a minority and even a majority can be systematically self eliminated from top leadership provided the hierarchy has a minimal number of levels in some cases 70 of the population is found to have zero representation after six hierarchical levels results are discussed with respect to the internal operation of political organizations

stabilization of nonlinear systems with state and control constraints using lyapunov based predictive control this work considers the problem of stabilization of nonlinear systems subject to state and control constraints for cases where the state constraints need to be enforced at all times hard constraints and where they can be relaxed for some time soft constraints we propose a lyapunov based predictive control design that guarantees stabilization and state and input constraint satisfaction for all times from an explicitly characterized set of initial conditions an auxiliary lyapunov based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation for the case when the state constraints are soft we propose a switched predictive control strategy that reduces the time during which state constraints are violated driving the states into the state and input constraints feasibility region of the lyapunov based predictive controller we demonstrate the application of the lyapunov based predictive controller designs through a chemical process example

stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set we deal with nonlinear dynamical systems consisting of a linear nominal part perturbed by model uncertainties nonlinearities and both additive and multiplicative random noise modeled as a wiener process in particular we study the problem of finding suitable measurement feedback control laws such that the resulting closed loop system is stable in some probabilistic sense to this aim we introduce a new notion of stabilization in probability which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability this notion requires that given a target set a trajectory starting from some compact region of the state space containing the target remains forever inside some larger compact set eventually enters any given neighborhood of the target in finite time and remains thereinafter all these events being guaranteed with some probability we give a lyapunov based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem finally we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems which at least include feedback linearizable systems the generality of the result is promising for applications to other classes of stochastic nonlinear systems in the deterministic case our results recover classical stabilization results for nonlinear systems

output feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance abstract we address the class of stochastic output feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori this problem is analogous to deterministic disturbance attenuation problems we first design a controller which guarantees that the solutions converge in probability to a residual set proportional to the unknown bound on the covariance then for the case of a vanishing noise vector field we design an adaptive controller which besides global stability in probability guarantees regulation of the state of the plant to zero with probability one

on a class of dynamical systems with emerging cluster structure abstract in this paper we discuss and analyze a two parameter family of systems of quadratic ordinary differential equations of interest in applied sciences whose dynamics exhibits an emerging cluster structure

multistability of impact utility and threshold concepts of binary choice models abstract the decision making problem in the context of binary choice is considered by means of impact function utility function and threshold model approaches the properties of generalized impact function and utility function are examined it is shown that these two approaches are equivalent their relation to the threshold model is studied and the correspondence between respective cumulative distribution functions is displayed the stationary state corresponding to the thermodynamic equilibrium is determined within mean field approximation multistability of the stationary state is expressed in terms of the distribution function of the random variable of impact utility function the correspondence with statistical physics predictions for ising model is discussed logistic distribution leads to the mean field result i e curie weiss approximation variations of the distribution functions and or other model parameters of social character self support nonlinearity of social interactions etc would break the direct correspondence to statistical physics of ising model leading in particular cases to richer structure of the multistability

stochastic receding horizon control of constrained linear systems with state and control multiplicative noise we develop a receding horizon control approach to stochastic linear systems with control and state multiplicative noise that also contain constraints our receding horizon formulation is based upon an on line optimization that utilizes open loop plus linear feedback and is solved as a semi definite programming problem we also provide a characterization of stability performance and constraint satisfaction properties of the receding horizon controlled system under a specific choice of terminal weight and terminal constraint a simple numerical example is used to illustrate the approach

linguistic characterization of time series the goal of this paper is to provide an overview of applications of special soft computing theories the fuzzy transform and fuzzy natural logic to analysis forecasting and mining information from time series the focus is especially placed on the ability of methods of fuzzy natural logic to provide information in sentences of natural language our approach is based on the decomposition of time series into three components the trend cycle seasonal component and noise the trend cycle is extracted using the f transform and its course is characterized by automatically generated linguistic description the latter is then used to forecast the trend cycle the trend cycle can be furthermore decomposed into trend general tendency and cycle the former is computed again using the f transform moreover the f1 transform makes it possible to estimate the direction of the trend which can then be characterized by expressions of natural language stagnating slightly increasing sharply decreasing etc finally we focus on selected problems of mining information from time series first we suggest an algorithm for finding intervals of monotonous behavior and then show how the theory of intermediate quantifiers a constituent of fuzzy natural logic and generalized aristotle s syllogisms can be applied to automatic summarization of information on time series

probability distribution of persistent spins in an ising chain we study the probability distribution q n t of n t the fraction of spins unflipped up to time t in an ising chain with ferromagnetic interactions the distribution shows a peak at n nmax and in general is non gaussian and asymmetric in nature however for n nmax it shows a gaussian decay data collapse can be obtained when q n t l versus n nmax l is plotted with 0 45 and 0 6 interestingly nmax t shows different behaviour compared to n t p t the persistence probability which follows the well known behaviour p t t a quantitative estimate of the asymmetry and non gaussian nature of q n t is made by calculating its skewness and kurtosis

random sequential adsorption of lines and ellipses infinitely many lines of zero thickness may be adsorbed onto a plane without overlap and it is shown that the number of lines adsorbed should scale as 13 where is the number of adsorption trials per unit area of surface this is confirmed by numerical simulation the adsorption of ellipses with major and minor axes 2a 2b respectively is also studied the area coverage theta approaches its maximum value theta max as alpha as to infinity where alpha is typically 1 3 as b a decreases from unity theta max first increases to a maximum value 0 58 or 0 01 when b approximately 0 5 and then decreases a feature not noted in previous work

persistence in nonequilibrium surface growth persistence probabilities of the interface height in 1 1 and 2 1 dimensional atomistic solid on solid stochastic models of surface growth are studied using kinetic monte carlo simulations with emphasis on models that belong to the molecular beam epitaxy mbe universality class both the initial transient and the long time steady state regimes are investigated we show that for growth models in the mbe universality class the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady state regimes for the mbe universality class the positive and negative persistence exponents in the steady state are found to be 0 66 0 02 and 0 78 0 02 respectively in 1 1 dimensions and 0 76 0 02 and 0 85 0 02 respectively in 2 1 dimensions the noise reduction technique is applied on some of the 1 1 dimensional models in order to obtain accurate values of the persistence exponents we show analytically that a relation between the steady state persistence exponent and the dynamic growth exponent found earlier to be valid for linear models should be satisfied by the smaller of the two steady state persistence exponents in the nonlinear models our numerical results for the persistence exponents are consistent with this prediction we also find that the steady state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state the dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form

robust receding horizon control of constrained nonlinear systems we present a method for the construction of a robust dual mode receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error the controller is dual mode in a neighborhood of the origin the control action is generated by a linear feedback controller designed for the linearized system outside this neighborhood receding horizon control is employed existing receding horizon controllers for nonlinear continuous time systems which are guaranteed to stabilize the nonlinear system to which they are applied require the exact solution at every instant of an optimal control problem with terminal equality constraints these requirements are considerably relaxed in the dual mode receding horizon controller presented in this paper stability is achieved by imposing a terminal inequality rather than an equality constraint only approximate minimization is required a variable time horizon is permitted robustness is achieved by employing conservative state and stability constraint sets thereby permitting a margin of error the resultant dual mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear constrained systems

the tightness of the kesten stigum reconstruction bound of symmetric model with multiple mutations it is well known that reconstruction problems as the interdisciplinary subject have been studied in numerous contexts including statistical physics information theory and computational biology to name a few we consider a 2q state symmetric model with two categories of q states in each category and 3 transition probabilities the probability to remain in the same state the probability to change states but remain in the same category and the probability to change categories we construct a nonlinear second order dynamical system based on this model and show that the kesten stigum reconstruction bound is not tight when q ge 4

a comprehensive theory of trichotomous evaluative linguistic expressions in this paper a logical theory of the so called trichotomous evaluative linguistic expressions tev expressions is presented these are frequent expressions of natural language such as small very small roughly medium extremely big etc the theory is developed using the formal system of higher order fuzzy logic namely the fuzzy type theory generalization of classical type theory first we discuss informally what are properties of the meaning of tev expressions then we construct step by step axioms of a formal logical theory t e v of tev expressions and prove various properties of t e v all the proofs are syntactical and so our theory is very general we also outline construction of a canonical model of t e v the main elegancy of our theory consists in the fact that semantics of all kinds of evaluative expressions is modeled in a unified way we also prove theorems demonstrating that essential properties of the vagueness phenomenon can be captured within our theory

convexity and convex approximations of discrete time stochastic control problems with constraints we investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time we consider minimization of an expected value cost subject to probabilistic constraints we study the convexity of a finite horizon optimization problem in the case where the control policies are affine functions of the disturbance input we propose an expectation based method for the convex approximation of probabilistic constraints with polytopic constraint function and a linear matrix inequality lmi method for the convex approximation of probabilistic constraints with ellipsoidal constraint function finally we introduce a class of convex expectation type constraints that provide tractable approximations of the so called integrated chance constraints performance of these methods and of existing convex approximation methods for probabilistic constraints is compared on a numerical example

asymptotic results for the random sequential addition of unoriented objects asymptotic kinetics for random sequential addition of unoriented nonspherical objects is characterized by an algebraic time dependence by studying 1 d systems we show that the exponents describing the random sequential addition of objects with and without proper area are not simply related whereas the asymptotic behavior for rectangles follows the expected t 1 2 law the long time kinetics for infinitely thin line segments is governed by a nontrivial irrational exponent t 2 1 which results from a competition between creation and destruction of targets in the asymptotic regime

kinetic modeling of alcohol consumption in most countries alcohol consumption distributions have been shown to possess universal features their unimodal right skewed shape is usually modeled in terms of the lognormal distribution which is easy to fit test and modify however empirical distributions often deviate considerably from the lognormal model and both gamma and weibull distributions appear to better describe the survey data in this paper we explain the appearance of these distributions by means of classical methods of kinetic theory of multi agent systems the microscopic variation of alcohol consumption of agents around a universal social accepted value of consumption is built up introducing as main criterion for consumption a suitable value function in the spirit of the prospect theory of kahneman and twersky the mathematical properties of the value function then determine the unique macroscopic equilibrium which results to be a generalized gamma distribution the modeling of the microscopic kinetic interaction allows to clarify the meaning of the various parameters characterizing the generalized gamma equilibrium

a formal theory of generalized intermediate syllogisms in this paper we continue developing the formal theory of intermediate quantifiers expressions such as most few almost all a lot of many a great deal of a large part of a small part of the theory is a fuzzy logic formalization of the concept introduced by peterson in his book we will syntactically prove that 105 generalized aristotle s syllogisms introduced in this book are valid in our theory at the same time we will also prove that syllogisms listed there as invalid are invalid also in our theory therefore we believe that our theory provides a reasonable mathematical model of the generalized syllogistics

kinetic models of opinion formation in the presence of personal conviction we consider a nonlinear kinetic equation of boltzmann type which takes into account the influence of conviction during the formation of opinion in a system of agents which interact through the binary exchanges introduced by toscani g toscani commun math sci 4 481 2006 the original exchange mechanism which is based on the human tendency to compromise and change of opinion through self thinking is here modified in the parameters of the compromise and diffusion terms which now are assumed to depend on the personal degree of conviction the numerical simulations show that the presence of conviction has the potential to break symmetry and to produce clusters of opinions the model is partially inspired by the recent work l pareschi and g toscani phil trans r soc a 372 20130396 2014 in which the role of knowledge in the formation of wealth distribution has been investigated

universality in one dimensional hierarchical coalescence processes motivated by several models introduced in the physics literature to study the nonequilibrium coarsening dynamics of one dimensional systems we consider a large class of hierarchical coalescence processes hcp an hcp consists of an infinite sequence of coalescence processes n n 1 each process occurs in a different epoch indexed by n and evolves for an infinite time while the evolution in subsequent epochs are linked in such a way that the initial distribution of n 1 coincides with the final distribution of n inside each epoch the process described by a suitable simple point process representing the boundaries between adjacent intervals domains evolves as follows only intervals whose length belongs to a certain epoch dependent finite range are active that is they can incorporate their left or right neighboring interval with quite general rates inactive intervals cannot incorporate their neighbors and can increase their length only if they are incorporated by active neighbors the activity ranges are such that after a merging step the newly produced interval always becomes inactive for that epoch but active for some future epoch without making any mean field assumption we show that i if the initial distribution describes a renewal process then such a property is preserved at all later times and all future epochs ii the distribution of certain rescaled variables for example the domain length has a well defined and universal limiting behavior as n independent of the details of the process merging rates activity ranges this last result explains the universality in the limiting behavior of several very different physical systems e g the east model of glassy dynamics or the paste all model which was observed in several simulations and analyzed in many physics papers the main idea to obtain the asymptotic result is to first write down a recursive set of nonlinear identities for the laplace transforms of the relevant quantities on different epochs and then to solve it by means of a transformation which in some sense linearizes the system

persistence of non markovian gaussian stationary processes in discrete time the persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval although persistence is a simple concept to understand it is in gener

model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints abstract robust predictive control handles constrained systems that are subject to stochastic uncertainty but propagating the effects of uncertainty over a prediction horizon can be computationally expensive and conservative this paper overcomes these issues through an augmented autonomous prediction formulation and provides a method of handling probabilistic constraints and ensuring closed loop stability through the use of an extension of the concept of invariance namely invariance with probability p

constrained opinion dynamics freezing and slow evolution we study opinion formation in a population of leftists centrists and rightist in an interaction between neighbouring agents a centrist and a leftist can become both centrists or leftists and similarly for a centrist and a rightist while leftists and rightists do not affect each other the evolution is controlled by the initial density of centrists 0 for any spatial dimension the system reaches a centrist consensus with probability 0 while with probability 1 0 the final state is either an extremist consensus or a frozen population of leftists and rightists in one dimension we determine the opinion evolution by mapping the system onto a spin 1 ising model with zero temperature glauber kinetics the approach to the final state is governed by a t long time tail with 2 0 as 0 0 in the one dimensional frozen state the length distribution of single opinion domains has an algebraic small size tail x 2 1 and the average domain length is l2 where l is the length of the system

output feedback lyapunov based predictive control of stochastic nonlinear systems this paper considers the problem of output feedback control of stochastic nonlinear systems a predictive controller is designed for which stability and feasibility in a probabilistic sense are guaranteed from an explicitly characterized region of attraction the controller s performance is characterized by its risk of allowing destabilizing system behavior since the controller design relies on certain convergence properties of the state observer a compatible stochastic high gain type observer design is also presented finally simulation results illustrating the efficacy of the design are presented

the theory of intermediate quantifiers in fuzzy natural logic revisited and the model of many abstract the fuzzy natural logic fnl is a formal theory whose goal is to provide a mathematical model of natural human reasoning whose typical feature is the use of natural language one of its tasks is to develop a mathematical model of a special class of linguistic quantifiers called intermediate ones in our previous papers we introduced a general principle of how intermediate quantifiers can be formed and suggested generalized definitions of the relations of contrary contradictory subcontrary and subalterns between these quantifiers based on these relations and following peterson s book 62 we were able to suggest a formal model of the 5 square of opposition with intermediate quantifiers this paper picks up the threads of this work and has the following goals it contributes to the development of the theory of fuzzy natural logic first it gets back to some concepts of the theory of evaluative linguistic expressions introduces slight modifications and proves some not yet presented properties furthermore it improves the formal theory of intermediate quantifiers some definitions are made more precise and some new theorems are proved finally it contributes to the theory of the intermediate quantifier many and the analysis of its position in the mentioned 5 square we will show that many manifests an ambiguous relation towards the other quantifiers

persistence and dynamics in the annni chain we investigate both the local and global persistence behaviour in the annni axial next nearest neighbour ising model we find that when the ratio of the second neighbour interaction to the first neighbour interaction is less than 1 p t the probability of a spin to remain in its original state up to time t shows a stretched exponential decay for 1 p t has an algebraic decay but the exponent is different from that of the nearest neighbour ising model the global persistence behaviour shows similar features we also conduct some deeper investigations in the dynamics of the annni model and conclude that it has a different dynamical behaviour compared to the nearest neighbour ising model

min max control of constrained uncertain discrete time linear systems for discrete time uncertain linear systems with constraints on inputs and states we develop an approach to determine state feedback controllers based on a min max control formulation robustness is achieved against additive norm bounded input disturbances and or polyhedral parametric uncertainties in the state space matrices we show that the finite horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs when the optimal control law is implemented in a receding horizon scheme only a piecewise affine function needs to be evaluated on line at each time step the technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state space

asymptotic behavior of densities for two particle annihilating random walks consider the system of particles on d where particles are of two types a andb and execute simple random walks in continuous time particles do not interact with their own type but when ana particle meets ab particle both disappear i e are annihilated this system serves as a model for the chemical reactiona b inert we analyze the limiting behavior of the densities a t and b t when the initial state is given by homogeneous poisson random fields we prove that for equal initial densities a 0 b 0 there is a change in behavior fromd 4 where a t b t c t d 4 tod 4 where a t b t c tast for unequal initial densities a 0 b 0 a t e c l ind 1 a t e ct logt ind 2 and a t e ct ind 3 the termc depends on the initial densities and changes withd techniques are from interacting particle systems the behavior for this two particle annihilation process has similarities to those for coalescing random walks a a a and annihilating random walks a a inert the analysis of the present process is made considerably more difficult by the lack of comparison with an attractive particle system

on the linear discrepancy model and risky shifts in group behavior a nonlinear fokker planck perspective using a nonlinear fokker planck perspective we re formulate the linear discrepancy model proposed by boster and colleagues that describes the emergence of risky shifts during group decision making analytical expressions for the stationary case are derived and risky shifts are obtained by monte carlo simulations striking similarities with the kuramoto model for group synchronization are pointed out

stochastic aggregation scaling properties we study the scaling properties of stochastic aggregation processes in one dimension numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent non trivial exponents corresponding to the survival probability of particles and monomers the overall behaviour agrees qualitatively with the mean field theory this theory also provides a useful approximation for the decay exponents as well as the limiting mass distribution

stochastic model predictive control of lpv systems via scenario optimization a stochastic receding horizon control approach for constrained linear parameter varying discrete time systems is proposed in this paper it is assumed that the time varying parameters have stochastic nature and that the system s matrices are bounded but otherwise arbitrary nonlinear functions of these parameters no specific assumption on the statistics of the parameters is required by using a randomization approach a scenario based finite horizon optimal control problem is formulated where only a finite number m of sampled predicted parameter trajectories scenarios are considered this problem is convex and its solution is a priori guaranteed to be probabilistically robust up to a user defined probability level p the p level is linked to m by an analytic relationship which establishes a tradeoff between computational complexity and robustness of the solution then a receding horizon strategy is presented involving the iterated solution of a scenario based finite horizon control problem at each time step our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time either deterministically or with probability no smaller than p the features of the approach are illustrated by a numerical example

a new method of identifying influential nodes in complex networks based on topsis abstract in complex networks identifying influential nodes is the very important part of reliability analysis which has been a key issue in analyzing the structural organization of a network in this paper a new evaluation method of node importance in complex networks based on technique for order performance by similarity to ideal solution topsis approach is proposed topsis as a multiple attribute decision making madm technique has been an important branch of decision making since then in addition topsis is first applied to identify influential nodes in a complex network in this open issue in different types of networks in which the information goes by different ways we consider several different centrality measures as the multi attribute of complex network in topsis application topsis is utilized to aggregate the multi attribute to obtain the evaluation of node importance of each node it is not limited to only one centrality measure but considers different centrality measures because every centrality measure has its own disadvantage and limitation then we use the susceptible infected si model to evaluate the performance numerical examples are given to show the efficiency and practicability of the proposed method

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

universal scaling function for domain growth in the glauber ising chain the equal time correlation function is calculated at t 0 for the one dimensional ising model with glauber dynamics random initial conditions appropriate to a sudden quench from non zero temperature are imposed averaging over initial conditions yields the scaling form c r t f r2 t the scaling function is given by f x integral 01 dy pi y 1 y 1 2 exp x 4y and is universal i e independent of the probability distribution for the initial conditions

nearest neighbor distances in diffusion controlled reactions modelled by a single mobile trap we consider a system consisting of an infinite number of identical particles on a latttce initially uniformly distributed which diffuse in the presence of a single mobile trap and ask for the time dependent behavior of the distance of the trap from the nearest particle this quantity is a measure of the tendency of the system to self segregate we show by a simulation incorporating the exact enumeration method that in one dtmension the expected distance l t scales as l t t as t 0 where the exponent a depends only on the ratio of the diffusion constants a heuristic expression for a ts suggested analogous to a rigorous exponent found by ben avraham for a similar but not identical problem the flux into the trap is found to vary as t t independent of the dtffusion constants

size distribution of cities a kinetic explanation abstract we present a kinetic approach to the formation of urban agglomerations which is based on simple rules of immigration and emigration in most cases the boltzmann type kinetic description allows to obtain within an asymptotic procedure a fokker planck equation with variable coefficients of diffusion and drift which describes the evolution in time of some probability density of the city size it is shown that in dependence of the microscopic rules of migration the equilibrium density can follow both a power law for large values of the size variable which contains as particular case a zipf s law behavior and a lognormal law for middle and low values of the size variable in particular connections between the value of pareto index of the power law at equilibrium and the disposal of the population to emigration are outlined the theoretical findings are tested with recent data of the populations of italy and switzerland

from individual choice to group decision making some universal features are independent of both the social nature of the individuals making the decision and the nature of the decision itself on this basis a simple magnet like model is built pair interactions are introduced to measure the degree of exchange among individuals while discussing an external uniform field is included to account for a possible pressure from outside individual biases with respect to the issue at stake are also included using local random fields a unique postulate of minimum conflict is assumed the model is then solved with emphasis on its psycho sociological implications counter intuitive results are obtained at this stage no new physical technicality is involved instead the full psycho sociological implications of the model are drawn few cases are then detailed to enlight them in addition several numerical experiments based on our model are shown to give both an insight on the dynamics of the model and suggest further research directions

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

on the analysis of set based fuzzy quantified reasoning using classical syllogistics syllogism is a type of deductive reasoning involving quantified statements the syllogistic reasoning scheme in the classical aristotelian framework involves three crisp term sets and four linguistic quantifiers for which the main support is the linguistic properties of the quantifiers a number of fuzzy approaches for defining an approximate syllogism have been proposed for which the main support is cardinality calculus in this paper we analyze fuzzy syllogistic models previously described by zadeh and dubois et al and compare their behavior with that of the classical aristotelian framework to check which of the 24 classical valid syllogistic reasoning patterns or moods are particular crisp cases of these fuzzy approaches this allows us to assess to what extent these approaches can be considered as either plausible extensions of the classical crisp syllogism or a basis for a general approach to the problem of approximate syllogism

kinetics of random sequential parking on a line we study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line for the simplest fixed length parking distribution the model reduces to the known car parking problem and we present an alternate solution to this problem we also consider the general homogeneous case when the parking distribution varies asx 1 atx 1 with the lengthx of the filling interval we develop a scaling theory describing such mixture deposition processes and show that the scaled hole size distribution with xtz a scaling variable decays with the scaled mass as exp const 1 as we determine scaling exponentsz and and find that at large times the coverage t has a power law form 1 t t v with nonuniversal exponent 2 1 depending on the homogeneity index

the structure of generalized intermediate syllogisms abstract in this paper we continue development of the formal theory of intermediate quantifiers which are expressions of the natural language most many few etc in the previous paper we demonstrated that 105 generalized syllogisms are valid in our theory we introduce the generalization of all the figures and we show that for the proof of validity of all the generalized syllogisms we need to prove the validity of only few of them so that the validity of the other ones immediately follows

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

non trivial exponents in the zero temperature dynamics of the 1d ising and potts models we consider the glauber dynamics of the q state potts model in one dimension at zero temperature starting with a random initial configuration we measure the density r t of spins which have never flipped from the beginning of the simulation until time t we find that for large t the density r t has a power law decay left r t sim t theta right where the exponent theta varies with q our simulations lead to theta simeq 37 for q 2 theta simeq 53 for q 3 and theta longrightarrow 1 as q longrightarrow infty