minimum cross entropy thresholding abstract the threshold selection problem is solved by minimizing the cross entropy between the image and its segmented version the cross entropy is formulated in a pixel to pixel basis between the two images and a computationally attractive algorithm employing the histogram is developed without making a priori assumptions about the population distribution this method provides an unbiased estimate of a binarized version of the image in an information theoretic sense

broccoli curves and the tropical invariance of welschinger numbers abstract in this paper we introduce broccoli curves certain plane tropical curves of genus zero related to real algebraic curves the numbers of these broccoli curves through given points are independent of the chosen points for arbitrary choices of the directions of the ends of the curves possibly with higher weights and also if some of the ends are fixed in the toric del pezzo case we show that these broccoli invariants are equal to the welschinger invariants with real and complex conjugate point conditions thus providing a proof of the independence of welschinger invariants of the point conditions within tropical geometry the general case gives rise to a tropical caporaso harris formula for broccoli curves which suffices to compute all welschinger invariants of the plane

an intrinsic algebraic setting for poles and zeros of linear time varying systems in this paper poles and zeros are defined for linear time varying systems using suitable ground field extensions the definitions of the system poles transmission poles invariant zeros hidden modes etc are given in an intrinsic module based framework and are consistent in the sense that the poles are connected to the stability of the system and the zeros to the zeroing of the output for non zero inputs in particular it is proved that the necessary and sufficient condition for a continuous time system to be exponentially stable is similar to the well known condition in the time invariant case

tropicalization of the moduli space of stable maps let x be an algebraic variety and let s be a tropical variety associated to x we study the tropicalization map from the moduli space of stable maps into x to the moduli space of tropical curves in s we prove that it is a continuous map and that its image is compact and polyhedral loosely speaking when we deform algebraic curves in x the associated tropical curves in s deform continuously moreover the locus of realizable tropical curves inside the space of all tropical curves is compact and polyhedral our main tools are berkovich spaces formal models balancing conditions vanishing cycles and quantifier elimination for rigid subanalytic sets

kontsevich s formula and the wdvv equations in tropical geometry abstract using gromov witten theory the numbers of complex plane rational curves of degree d through 3 d 1 general given points can be computed recursively with kontsevich s formula that follows from the so called wdvv equations in this paper we establish the same results entirely in the language of tropical geometry in particular this shows how the concepts of moduli spaces of stable curves and maps evaluation and forgetful morphisms intersection multiplicities and their invariance under deformations can be carried over to the tropical world

continuous varying linear systems abstract we discuss implicit systems of ordinary linear differential equations with time variable coefficients their solutions in the signal space of hyperfunctions according to sato and their solution spaces called time varying linear systems or behaviours from the system theoretic point of view the basic result inspired by an analogous one for multidimensional constant linear systems is a duality theorem which establishes a categorical one one correspondence between time varying linear systems or behaviours and finitely generated modules over a suitable skew polynomial ring of differential operators this theorem is false for the signal spaces of infinitely often differentiable functions or of meromorphic hyper functions or of distributions on r it is used to obtain various results on key notions of linear system theory several new algorithms for modules over rings of differential operators and in particular new grobner basis algorithms due to insa and pauer make the system theoretic results effective

some basic structural properties of generalized linear systems abstract this paper shows how to give a kalman state variable realization to generalized linear systems simple characterizations of controllability observability of their duality and of a minimal realization are proposed our techniques based on elementary module theory are applicable to time varying systems as well as constant systems the note ends with a brief discussion of asymptotic observers in the constant case

notes on the definition of behavioural controllability we take another look at the behavioural definition of controllability for discrete 1d systems and its extension to multidimensional nd systems defined on z n or n n we suggest that the current definition for nd systems is inappropriate for systems defined on the domain n n and that care has to be taken even with the 1d definition we propose a new definition which applies to all standard classes of discrete nd systems

algebraic characterization of approximate controllability of behaviours of spatially invariant systems we give algebraic characterizations of the properties of autonomy and of controllability of behaviours of spatially invariant dynamical systems consisting of distributional solutions w that are periodic in the spatial variables to a system of partial differential equations corresponding to a polynomial matrix m g c 1 d mxn

paradigms and puzzles in the theory of dynamical systems a self contained exposition is given of an approach to mathematical models in particular to the theory of dynamical systems the basic ingredients form a triptych with the behavior of a system in the center and behavioral equations with latent variables as side panels the author discusses a variety of representation and parametrization problems in particular questions related to input output and state models the proposed concept of a dynamical system leads to a new view of the notions of controllability and observability and of the interconnection of systems in particular to what constitutes a feedback control law the final issue addressed is that of system identification it is argued that exact system identification leads to the question of computing the most powerful unfalsified model

a behavioral approach to control of distributed systems this paper develops a theory of control for distributed systems i e those defined by systems of constant coefficient partial differential operators via the behavioral approach of willems the study here is algebraic in the sense that it relates behaviors of distributed systems to submodules of free modules over the polynomial ring in several indeterminates as in the lumped case behaviors of distributed arma systems can be reduced to ar behaviors this paper first studies the notion of ar controllable distributed systems following the corresponding definition for lumped systems due to willems it shows that as in the lumped case the class of controllable ar systems is precisely the class of ma systems it then shows that controllable 2 d distributed systems are necessarily given by free submodules whereas this is not the case for n d distributed systems n ge 3 this therefore points out an important difference between these two cases this paper then defines two notions of autonomous distributed systems which mimic different properties of lumped autonomous systems control is the process of restricting a behavior to a specific desirable autonomous subbehavior a notion of stability generalizing bounded input bounded output stability of lumped systems is proposed and the pole placement problem is defined for distributed systems this paper then solves this problem for a class of distributed behaviors

the caporaso harris formula and plane relative gromov witten invariants in tropical geometry some years ago caporaso and harris have found a nice way to compute the numbers n d g of complex plane curves of degree d and genus g through 3d g 1 general points with the help of relative gromov witten invariants recently mikhalkin has found a way to reinterpret the numbers n d g in terms of tropical geometry and to compute them by counting certain lattice paths in integral polytopes we relate these two results by defining an analogue of the relative gromov witten invariants and rederiving the caporaso harris formula in terms of both tropical geometry and lattice paths

periodic polynomial interpretation for structural properties of linear periodic discrete time systems the structural properties of linear periodic discrete time systems are analyzed in the periodic polynomial representation it is shown that the classical polynomial approach for linear time invariant systems can be extended to periodic systems new definitions and properties are given in terms of skew polynomial rings and periodic difference algebra necessary and sufficient conditions for the characterization of reachability controllability observability and reconstructibility are given in this framework

rosenbrock models and their homotopy equivalence as is known the notion of homotopy equivalence is a fundamental notion of mathematics and was introduced in order to formalize a relation that is weaker than isomorphism in this note we define a homotopy equivalence of rosenbrock systems and show that it coincides with the classical equivalences of rosenbrock and fuhrmann next we show that the homotopy equivalence does preserve the important properties of a system including the properties at infinity when these are properly understood finally we define in a simple manner the states and motions of a system and claim that they are homotopy invariants

a behavioral approach to delay differential systems we will study linear time invariant delay differential systems from the behavioral point of view as it was introduced for dynamical systems by willems dynam report 2 1989 pp 171 269 a ring cal h which lies between bbb r s z z 1 and bbb r s z z 1 will be presented whose elements can be interpreted as a generalized version of delay differential operators on cal c infty bbb r bbb r in this framework a behavior is the kernel of such an operator using the ring cal h an algebraic characterization of inclusion respectively equality of the behaviors under consideration is given finally controllability of the behaviors is characterized in terms of the rank of the associated matrices in the case of time delay state space systems this criterion becomes the known hautus criterion for spectral controllability

continuous time linear predictive control and flatness a module theoretic setting with examples a general flatness based framework for linear continuous time predictive control is presented the mathematical setting which is valid for multivariable systems is provided by the algebraic theory of modules where a controllable system corresponds to a finitely generated free module over a principal ideal ring any basis of this free module is a flat output which yields an easy calculation of the predicted trajectory this formalism permits one to handle non minimum phase systems system constraints and to deal with additive perturbations three concrete case studies namely a dc motor a flexible system and a cement mill are analysed and simulations are given these examples are written in such a way that any reader who is not familiar with module theory may nevertheless grasp the proposed control strategy

a novel image thresholding method based on parzen window estimate image segmentation is one of the most important and fundamental tasks in image processing and techniques based on image thresholding are typically simple and computationally efficient however the image segmentation results depend heavily on the chosen image thresholding methods in this paper histogram is integrated with the parzen window technique to estimate the spatial probability distribution of gray level image values and a novel criterion function is designed by optimizing the criterion function an optimal global threshold is obtained the experimental results for synthetic real world and images demonstrate the success of the proposed image thresholding method as compared with the otsu method the met method and the entropy based method

duality for differential difference systems over lie groups in modern mathematical systems theory there exist two consistent ways of defining and describing a linear system i in the behavioral approach a linear system is the kernel mathfrak b of a matrix valued operator r in a power of a signal space w ii in the module theoretic setting a linear system is the cokernel m of the above matrix r these two formulations have connections the minimal conditions under which they are equivalent are investigated in this paper the general theory is applied to differential difference systems over lie groups

multilevel minimum cross entropy threshold selection based on particle swarm optimization thresholding is one of the popular and fundamental techniques for conducting image segmentation many thresholding techniques have been proposed in the literature among them the minimum cross entropy thresholding mcet have been widely adopted although the mcet method is effective in the bilevel thresholding case it could be very time consuming in the multilevel thresholding scenario for more complex image analysis this paper first presents a recursive programming technique which reduces an order of magnitude for computing the mcet objective function then a particle swarm optimization pso algorithm is proposed for searching the near optimal mcet thresholds the experimental results manifest that the proposed pso based algorithm can derive multiple mcet thresholds which are very close to the optimal ones examined by the exhaustive search method the convergence of the proposed method is analyzed mathematically and the results validate that the proposed method is efficient and is suited for real time applications

finite poles and zeros of linear systems an intrinsic approach several kinds of finite poles and zeros are defined and their relationships are studied in an intrinsic manner some of these definitions are more precise than the usual ones all kinds of multiplicities of an input output decoupling zero are defined here in addition we believe that our approach clarifies those notions and it makes it possible to very concisely establish fundamental relationships between various poles and zeros some new relationships are derived the notions of input output stability and transfer stability are also introduced several examples illustrate the theory

multidimensional behaviours an algebraic approach to control theory for pde this paper gives an overview of the algebraic theory of multidimensional behaviours and it contains some new aspects as well some known results are restated with a new proof after a short introduction to behavioural systems theory we briefly describe the mathematical background of the algebraic approach then we study structural properties such as autonomy and over determined systems on the one hand and controllability and flat systems on the other

threshold selection based on fuzzy c partition entropy approach abstract thresholding is an important topic for image processing pattern recognition and computer vision selecting thresholds is a critical issue for many applications the fuzzy set theory has been successfully applied to many areas such as control image processing pattern recognition computer vision medicine social science etc it is generally believed that image processing bears some fuzziness in nature in this paper we use the concept of fuzzy c partition and the maximum fuzzy entropy principle to select threshold values for gray level images we have conducted experiments on many images the experimental results demonstrate that the proposed approach can select the thresholds automatically and effectively and the resulting images can preserve the main features of the components of the original images very well

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

a behavioral approach to the pole structure of one dimensional and multidimensional linear systems we use the tools of behavioral theory and commutative algebra to produce a new definition of a finite pole of a linear system this definition agrees with the classical one and allows a direct dynamical interpretation it also generalizes immediately to the case of a multidimensional nd system we make a natural division of the poles into controllable and uncontrollable poles when the behavior in question has latent variables we make a further division into observable and unobservable poles in the case of a one dimensional 1d state space model the uncontrollable and unobservable poles correspond respectively to the input and output decoupling zeros whereas the observable controllable poles are the transmission poles most of these definitions can be interpreted dynamically in both the 1d and nd cases and some can be connected to properties of kernel representations we also examine the connections between poles transfer matrices and their left and right matrix fraction descriptions mfds we find behavioral results which correspond to the concepts that a controllable system is precisely one with no input decoupling zeros and an observable system is precisely one with no output decoupling zeros we produce a decomposition of a behavior as the sum of subbehaviors associated with various poles this is related to the integral representation theorem which describes every system trajectory as a sum of integrals of polynomial exponential trajectories

brief paper output feedback pole placement for linear time varying systems with application to the control of nonlinear systems the output feedback pole placement problem is solved in an input output algebraic formalism for linear time varying ltv systems the recent extensions of the notions of transfer matrices and poles of the system to the case of ltv systems are exploited here to provide constructive solutions based as in the linear time invariant lti case on the solutions of diophantine equations also differences with the results known in the lti case are pointed out especially concerning the possibilities to assign specific dynamics to the closed loop system and the conditions for tracking and disturbance rejection this approach is applied to the control of nonlinear systems by linearization around a given trajectory several examples are treated in detail to show the computation and implementation issues

key problems in the extension of module behaviour duality the duality for linear constant coefficient partial differential equations between behaviours and finitely generated modules over the operator ring is a very powerful tool linking equation structure to dynamic behaviour this duality is critically dependent on the choice of signal space in this paper we discuss two key algebraic problems which form an obstacle to the extension of this theory to general signal spaces the first of these is the so called willems closure problem which limits the ability of system equations to directly describe the system the second is the elimination problem the general solution of which depends upon an algebraic property injectivity of the signal space we demonstrate the importance of these problems in the module behaviour framework and some of the useful consequences of a full or partial solution the issues here are of particular relevance to the extension of the current duality theory for behaviours defined by linear partial differential equations from the case of constant to non constant coefficients

an adaptive neuro fuzzy system for automatic image segmentation and edge detection an autoadaptive neuro fuzzy segmentation and edge detection architecture is presented the system consists of a multilayer perceptron mlp like network that performs image segmentation by adaptive thresholding of the input image using labels automatically pre selected by a fuzzy clustering technique the proposed architecture is feedforward but unlike the conventional mlp the learning is unsupervised the output status of the network is described as a fuzzy set fuzzy entropy is used as a measure of the error of the segmentation system as well as a criterion for determining potential edge pixels the proposed system is capable to perform automatic multilevel segmentation of images based solely on information contained by the image itself no a priori assumptions whatsoever are made about the image type features contents stochastic model etc such an universal algorithm is most useful for applications that are supposed to work with different and possibly initially unknown types of images the proposed system can be readily employed as is or as a basic building block by a more sophisticated and or application specific image segmentation algorithm by monitoring the fuzzy entropy relaxation process the system is able to detect edge pixels

on interconnections control and feedback the purpose of this paper is to study interconnections and control of dynamical systems in a behavioral context we start with an extensive physical example which serves to illustrate that the familiar input output feedback loop structure is not as universal as we have been taught to believe this leads to a formulation of control problems in terms of interconnections subsequently we study interconnections of linear time invariant systems from this vantage point let us mention two of the results obtained the first one states that any polynomial can be achieved as the characteristic polynomial of the interconnection with a given plant provided the plant is not autonomous the second result states that any subsystem of a controllable system can be implemented by means of a singular feedback control law these results yield pole placement and stabilization of controllable plants as a special case these ideas are finally applied to the stabilization of a nonlinear system around an operating point

direct methods for primary decomposition leti be an ideal in a polynomial ring over a perfect field we given new methods for computing the equidimensional parts and radical ofi for localizingi with respect to another ideal and thus for finding the primary decomposition ofi our methods rest on modern ideas from commutative algebra and are direct in the sense that they avoid the generic projections used by hermann 1926 and all others until now

the contact problem for linear continuous time dynamical systems a geometric approach in this paper linear time invariant dynamical systems described by a combination of differential equalities and static inequalities in state space formulation are investigated of special interest is the contact problem the effect of the boundary of the constraint set on the behavior of the system this effect is studied by dividing the state space in a number of disjunct subsets it is shown that these subsets are invariant under linear state feedback in our framework a specific place is reserved for modeling the laws of collision i e physical modeling which are regarded as external factors our main results are a system theoretical framework in which we describe what happens upon contact and a definition of the constrained state space system in terms of its restricted behavior the results presented here can be considered as an extension for restricted linear systems of the classic positive invariance theory for linear systems

a remark on willems trajectory characterization of linear controllability abstract willems trajectory characterization of linear controllability is related to some module theoretic property

the tropical vertex elements of the tropical vertex group are formal families of symplectomorphisms of the 2 dimensional algebraic torus we prove that ordered product factorizations in the tropical vertex group are equivalent to calculations of certain genus zero relative gromov witten invariants of toric surfaces the relative invariants which arise have full tangency to a toric divisor at a single unspecified point the method uses scattering diagrams tropical curve counts degeneration formulas and exact multiple cover calculations in orbifold gromov witten theory

a multilevel image thresholding using the honey bee mating optimization image thresholding is an important technique for image processing and pattern recognition many thresholding techniques have been proposed in the literature among them the maximum entropy thresholding met has been widely applied in this paper a new multilevel met algorithm based on the technology of the honey bee mating optimization hbmo is proposed this proposed method is called the maximum entropy based honey bee mating optimization thresholding mehbmot method three different methods such as the particle swarm optimization pso the hybrid cooperative comprehensive learning based pso algorithm hcoclpso and the fast otsu s method are also implemented for comparison with the results of the proposed method the experimental results manifest that the proposed mehbmot algorithm can search for multiple thresholds which are very close to the optimal ones examined by the exhaustive search method in comparison with the other three thresholding methods the segmentation results using the mehbmot algorithm is the best and its computation time is relatively low furthermore the convergence of the mehbmot algorithm can rapidly achieve and the results validate that the proposed mehbmot algorithm is efficient

the numbers of tropical plane curves through points in general position we show that the number of tropical curves of given genus and degree through some given general points in the plane does not depend on the position of the points in the case when the degree of the curves contains only primitive integral vectors this statement has been known for a while now but the only known proof was indirect with the help of mikhalkin s correspondence theorem that translates this question into the well known fact that the numbers of complex curves in a toric surface through some given points do not depend on the position of the points this paper presents a direct proof entirely within tropical geometry that is in addition applicable to arbitrary degree of the curves

application of honey bee mating optimization algorithm on clustering cluster analysis is one of attractive data mining technique that use in many fields one popular class of data clustering algorithms is the center based clustering algorithm k means used as a popular clustering method due to its simplicity and high speed in clustering large datasets however k means has two shortcomings dependency on the initial state and convergence to local optima and global solutions of large problems cannot found with reasonable amount of computation effort in order to overcome local optima problem lots of studies done in clustering over the last decade modeling the behavior of social insects such as ants and bees for the purpose of search and problem solving has been the context of the emerging area of swarm intelligence honey bees are among the most closely studied social insects honey bee mating may also be considered as a typical swarm based approach to optimization in which the search algorithm is inspired by the process of marriage in real honey bee honey bee has been used to model agent based systems in this paper we proposed application of honeybee mating optimization in clustering hbmk means we compared hbmk means with other heuristics algorithm in clustering such as ga sa ts and aco by implementing them on several well known datasets our finding shows that the proposed algorithm works than the best one

primeness of multivariate polynomial matrices abstract different characterizations of primeness of polynomial matrices that are mutually equivalent in the one dimensional case of univiriate polynomials lead to various primeness concepts in the multivariate situation applied to systems theory this fact gives rise to a more refined view to observability and controllability of multidimensional systems algorithms for testing primeness properties are given based on computer algebraic techniques