affine and bilinear systems on lie groups abstract in this paper we study affine and bilinear systems on lie groups we show that there is an intrinsic connection between the solutions of both systems such relation allows us to obtain some preliminary controllability results of affine systems on compact and solvable lie groups we also show that the controllability property of bilinear systems is very restricted and may only be achieved if the state space g is an euclidean space

high speed vlsi implementation of 2 d discrete wavelet transform this paper presents a systematic high speed vlsi implementation of the discrete wavelet transform dwt based on hardware efficient parallel fir filter structures high speed 2 d dwt with computation time as low as n 2 12 can be easily achieved for an ntimesn image with controlled increase of hardware cost compared with recently published 2 d dwt architectures with computation time of n 2 3 and 2n 2 3 the proposed designs can also save a large amount of multipliers and or storage elements it can also be used to implement those 2 d dwt traditionally suitable for lifting or flipping based designs such as 9 7 and 6 10 dwt the throughput rate can be improved by a factor of 4 by the proposed approach but the hardware cost increases by a factor of around 3 furthermore the proposed designs have very simple control signals regular structures and 100 hardware utilization for continuous images

self organized criticality in a nutshell in order to gain insight into the nature of self organized criticality soc we present a minimal model exhibiting this phenomenon in this analytically solvable model the state of the system is fully described by a single integer variable the system organizes in its critical state without external tuning we derive analytically the probability distribution of durations of disturbances propagating through the system as required by soc this distribution is scale invariant and follows a power law over several orders of magnitude our solution also reproduces the exponential tail of the distribution due to finite size effects moreover we show that large avalanches are suppressed when stabilizing the system in its critical state interestingly avalanches are affected in a similar way when driving the system away from the critical state with this model we have reduced soc dynamics to a leveling process as described by ehrenfest s famous flea model

the control set of a linear control system on the two dimensional lie group abstract in this paper we explicitly calculate the control sets associated with a linear control system on the two dimensional solvable lie group we show that a linear control system of such kind admits exactly one control set or infinite control sets depending on some algebraic conditions

a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

analysis of self organized criticality in ehrenfest s dog flea model the self organized criticality in ehrenfest s historical dog flea model is analyzed by simulating the underlying stochastic process the fluctuations around the thermal equilibrium in the model are treated as avalanches we show that the distributions for the fluctuation length differences at subsequent time steps are in the shape of a q gaussian the distribution which is obtained naturally in the context of nonextensive statistical mechanics if one avoids the finite size effects by increasing the system size we provide clear numerical evidence that the relation between the exponent ensuremath tau of avalanche size distribution obtained by maximum likelihood estimation and the q value of appropriate q gaussian obeys the analytical result recently introduced by caruso et al phys rev e 75 055101 r 2007 this allows us to determine the value of q parameter a priori from one of the well known exponents of such dynamical systems

flipping structure an efficient vlsi architecture for lifting based discrete wavelet transform in this paper an efficient very large scale integration vlsi architecture called flipping structure is proposed for the lifting based discrete wavelet transform it can provide a variety of hardware implementations to improve and possibly minimize the critical path as well as the memory requirement of the lifting based discrete wavelet transform by flipping conventional lifting structures the precision issues are also analyzed by case studies of the jpeg2000 default lossy 9 7 filter an integer 9 7 filter and the 6 10 filter the efficiency of the proposed flipping structure is demonstrated

precision aware self quantizing hardware architectures for the discrete wavelet transform this paper presents designs for both bit parallel bp and digit serial ds precision optimized implementations of the discrete wavelet transform dwt with specific consideration given to the impact of depth the number of levels of dwt on the overall computational accuracy these methods thus allow customizing the precision of a multilevel dwt to a given error tolerance requirement and ensuring an energy minimal implementation which increases the applicability of dwt based algorithms such as jpeg 2000 to energy constrained platforms and environments additionally quantization of dwt coefficients to a specific target step size is performed as an inherent part of the dwt computation thereby eliminating the need to have a separate downstream quantization step in applications such as jpeg 2000 experimental measurements of design performance in terms of area speed and power for 90 nm complementary metal oxide semiconductor implementation are presented results indicate that while bp designs exhibit inherent speed advantages ds designs require significantly fewer hardware resources with increasing precision and dwt level a four level dwt with medium precision for example while the bp design is four times faster than the digital serial design occupies twice the area in addition to the bp and ds designs a novel flexible dwt processor is presented which supports run time configurable dwt parameters

on the number of control sets on projective spaces the purpose of this paper is to provide an upper bound for the number of control sets for linear semigroups acting on a projective space rpd 1 these semigroups and control sets were studied by colonius and kliemann 1993 who proved that there are at most d control sets here we apply the results of san martin and tonelli 1995 about control sets for semigroups in semisimple lie groups and make a case by case analysis according to the transitive groups on rpd 1 which were classified by boothby and wilson 1975 1979 in order to improve that upper bound it turns out that in some cases there are at most d 2 or d 4 control sets

aftershocks in coherent noise models the decay pattern of aftershocks in the so called coherent noise models m e j newman and k sneppen phys rev e54 6226 1996 is studied in detail analytical and numerical results show that the probability to nd a large event at timet after an initial major event decreases as t for smallt with the exponent ranging from 0 to values well above 1 this is in contrast to sneppen und newman who stated that the exponent is about 1 independent of the microscopic details of the simulation numerical simulations of an extended model c wilke t martinetz phys rev e56 7128 1997 show that the power law is only a generic feature of the original dynamics and does not necessarily appear in a more general context finally the implications of the results to the modeling of earthquakes are discussed

controllability of linear systems on lie groups with finite semisimple center this paper studies controllability for a given linear system sigma on a connected lie group g by taking into consideration the eigenvalues of an associated derivation mathcal d if we assume that the lie group g has finite center and for some tau 0 the identity element of g is an interior point of its reachable set at time tau then the system is controllable if mathcal d has only eigenvalues with zero real part

bounds for invariance pressure abstract this paper provides an upper bound for the invariance pressure of control sets with nonempty interior and a lower bound for sets with finite volume in the special case of the control set of a hyperbolic linear control system on r d this yields an explicit formula further applications to linear control systems on lie groups and to inner control sets are discussed

control sets and their boundaries under parameter variation abstract control sets i e maximal sets of approximate controllability are described for systems with parameter dependent control range if the so called inner pair condition is satisfied it is known that generically they change continuously under parameter variation while mergers of control sets produce discontinuous transitions the inner pair condition is proved for a class of control affine systems on r n furthermore continuity results for exit and entrance boundaries of control sets are given both for one control set that changes continuously and for two merging control sets the results are illustrated by means of the controlled escape equation

outer invariance entropy for linear systems on lie groups linear systems on lie groups are a natural generalization of linear systems on euclidian spaces for such systems this paper studies what happens with the outer invariance entropy introduced by colonius and kawan siam j control optim 48 2009 pp 1701 1721 it is shown that as for the linear euclidean case the outer invariance entropy is given by the sum of the positive real parts of the eigenvalues of a linear derivation mathcal d that is associated to the drift of the system

controllability properties of affine systems this paper deals with transitivity controllability of affine families of vector fields on a finite dimensional vector space v in particular we focus on affine families whose corresponding families of linear fields are transitive on v 0 and which in addition have no fixed points in v we show that such families are necessarily transitive on v and we also show that they remain transitive under small perturbations in general however affine families need not remain transitive under small perturbations for example small affine perturbations of transitive linear systems are not necessarily transitive since any affine system mathcal f naturally defines a system mathcal f r of right invariant vector fields on the semi direct product of v with gl v we also investigate transitivity properties mathcal f r our result is that if mathcal f is an affine family satisfying the preceding conditions then mathcal f r generates the full lie algebra on the semi direct product

lie brackets and local controllability a sufficient condition for scalar input systems we develop a general formalism based on exponential lie series which can be used to study control variations we apply the formalism to prove a result conjectured by h hermes that gives a sufficient condition for small time local controllability for single input systems

return distributions in dog flea model revisited abstract a recent study of coherent noise model for the system size independent case provides an exact relation between the exponent of avalanche size distribution and the q value of the appropriate q gaussian that fits the return distribution of the model this relation is applied to ehrenfest s historical dog flea model by treating the fluctuations around the thermal equilibrium as avalanches we provide a clear numerical evidence that the relation between the exponent of fluctuation length distribution and the q value of the appropriate q gaussian obeys this exact relation when the system size is large enough this allows us to determine the value of the q parameter a priori from one of the well known exponents of such dynamical systems furthermore it is shown that the return distribution in dog flea model gradually approaches q gaussian as the system size increases and this tendency can be analyzed by a well defined analytical expression

normal local controllability of order one this paper gives a sufficient condition of normal local controllability at a point x0 for a family of analytical vector fields the families considered are of the following where is a bounded subset of r the condition is of the first order that is it depends only on the values of the fields and their first derivatives at x0 it is proved that this condition is the most general condition of this type in fact if this condition is not satisfied there are families of vector fields which at the first order coincide with the given family and which are not normally locally controllable at x0

a semigroup associated to a linear control system on a lie group abstract let us consider a linear control system on a connected lie group g it is known that the accessibility set a from the identity e is in general not a semigroup in this article we associate a new algebraic object s to which turns out to be a semigroup allowing the use of the semigroup machinery to approach in particular we obtain some controllability results

a note on flipping structure an efficient vlsi architecture for lifting based discrete wavelet transform a flipping structure for the discrete wavelet transform dwt was proposed by huang et al which aimed at shortening the critical path of the lifting based one dimensional 1 d architecture and reducing the number of pipeline register used in 1 d architecture as well as the size of temporal buffer tb required in the line based two dimensional 2 d architecture in this paper we explore the intrinsic relationship between the size of tb required in the line based architecture for 2 d dwt lba2ddwt and the number of registers used in a 1 d dwt module and present a modified view on this issue that has been proposed by huang et al an improved method of mapping the registers used in 1 d dwt architecture to the tb required in lba2ddwt is presented which reduces more efficiently the size of memory required in lba2ddwt than huang s method a parallel based lifting scheme pls for dwt and its vlsi architecture are presented the proposed pls of dwt not only reduces efficiently the critical path but also results in the equality of the forward discrete wavelet transform and inverse discrete wavelet transform implementations compared with huang s method the proposed pls is more efficient in reducing critical path and or the number of registers of vlsi implementation for 1 d dwt and it can be concluded that the flipping structure of dwt is a special case of the pls based implementation

of dogs and fleas the dynamics of n uncoupled two state systems the historical ehrenfest model dating back to 1907 describes the process of equilibration together with fluctuations around the thermal equilibrium this approach represents a special case in the dynamics of n uncoupled two state systems in this article we present a generalization of the original model by introducing an additional parameter p which denotes the probability of a single state change analytical solutions for the probability distribution of the system s state as well as the fluctuation distribution are derived interestingly close inspection of the fluctuation distribution reveals an intrinsic time scale sampling the system s state at much slower rates yields the familiar macroscopic exponential distribution for equilibrium processes for faster measurements a power law extends roughly over log10 n orders of magnitude followed by an exponential tail at some point further increases of the sampling rate merely result in a shift of the fluctuation distribution towards higher values leaving plateau at small fluctuation sizes behind since the generic solution is rather unwieldy we derive and discuss simple and intuitive analytical solutions in the limit of small p and large n furthermore we relax the quantization of time by considering a complementary approach in continuous time finally we demonstrate that the fluctuation distributions resulting from the two different approaches bear identical characteristic features

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

two fast architectures for the direct 2 d discrete wavelet transform we propose two architectures for the direct two dimensional 2 d discrete wavelet transform dwt the first one is based on a modified recursive pyramid algorithm mrpa and performs a nonstandard decomposition i e mallat s 1989 tree of an n spl times n image in approximately 2n sup 2 3 clock cycles ccs this result consistently speeds up other known architectures that commonly need approximately n sup 2 ccs furthermore the proposed architecture is simpler than others in terms of hardware complexity subsequently we show how symmetric anti symmetric properties of linear phase wavelet filter bases can be exploited in order to further reduce the vlsi area this is used to design a second architecture that provides one processing unit for each level of decomposition pipelined approach and performs a decomposition in approximately n sup 2 2 ccs in many practical cases even this architecture is simpler than general mrpa based devices having only one processing unit

controllability of linear systems on solvable lie groups linear systems on lie groups are a natural generalization of linear systems on euclidian spaces for such systems this paper studies controllability by taking into consideration the eigenvalues of an associated derivation mathcal d when the state space is a solvable connected lie group controllability of the system is guaranteed if the reachable set of the neutral element is open and the derivation mathcal d has only pure imaginary eigenvalues for bounded systems on nilpotent lie groups such conditions are also necessary

invariance entropy of control sets invariance entropy for continuous time control systems measures how often open loop controls have to be updated in order to render a controlled invariant subset of the state space invariant a special type of a controlled invariant set is a control set i e a maximal set of approximate controllability in this paper we investigate the properties of the invariance entropy of such sets our main result gives an upper bound of this quantity in terms of the positive lyapunov exponents of a periodic solution in the interior of the control set moreover for one dimensional control affine systems with a single control vector field we provide an analytical formula for the invariance entropy of a control set in terms of the drift vector field the control vector field and their derivatives as an application we study a controlled bilinear oscillator

controllability of right invariant systems on real simple lie groups we deal with controllability of right invariant control systems on lie groups following the ideas of a series of papers by jurdjevic kupka gauthier bornard gauthier kupka sallet leite crouch el assoudi gauthier we obtain a generalization of these results in the general case of real semi simple lie groups

control sets of linear systems on semi simple lie groups abstract in this paper we study the main properties of control sets with nonempty interior of linear systems on semisimple lie groups we show that unlike the solvable case linear systems on semisimple lie groups may have more than one control set with nonempty interior and that they are contained in right translations of the one around the identity

on the characterization of the controllability property for linear control systems on nonnilpotent solvable three dimensional lie groups abstract in this paper we show that a complete characterization of the controllability property for linear control system on three dimensional solvable nonnilpotent lie groups is possible by the larc and the knowledge of the eigenvalues of the derivation associated with the drift of the system

invariance pressure of control sets the invariance pressure of continuous time control systems with initial states in a set k which are to be kept in a set q is introduced and a number of results are derived mainly for the case

almost riemannian geometry on lie groups a simple almost riemannian structure ars on a lie group g is defined by a linear vector field that is an infinitesimal automorphism and dim g 1 left invariant ones we state results about the singular locus the abnormal extremals and the desingularization of such arss and these results are illustrated by examples on the two dimensional affine and the heisenberg groups these arss are extended in two ways to homogeneous spaces and a necessary and sufficient condition for an ars on a manifold to be equivalent to a general ars on a homogeneous space is stated

caratheodory pesin structures associated with control systems abstract we introduce five caratheodory pesin c p structures for control systems and show that the invariance entropy studied by colonius and kawan 2009 and the topological feedback entropy in colonius et al 2013 are just quantities generated by some special c p structures that give the characteristics of dimension types for these classical control entropies we explore some basic properties of these control entropies and investigate the relationships among these quantities in addition we also obtain a sufficient condition for the existence of a generator for the invariance entropy which was posed by kawan 2013 p 87 as an open question

a review on some classes of algebraic systems in this paper we review some algebraic control system precisely linear and bilinear systems on euclidean spaces and invariant and linear systems on lie groups the fourth classes of systems have

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

a continuous time ehrenfest model with catastrophes and its jump diffusion approximation we consider a continuous time ehrenfest model defined over the integers from n to n and subject to catastrophes occurring at constant rate the effect of each catastrophe istantaneously resets the process to state 0 we investigate both the transient and steady state probabilities of the above model further the first passage time through state 0 is discussed we perform a jump diffusion approximation of the above model which leads to the ornstein uhlenbeck process with catastrophes the underlying jump diffusion process is finally studied with special attention to the symmetric case arising when the ehrenfest model has equal upward and downward transition rates

control systems which generate decomposable lie algebras let x y be real analytic vector fields on an n manifold m ad x y x y denote the lie product inductively ad k 1 x y x ad k x y and 1 ad v x y v 0 the attainable set at time t denoted download full size image t for the control system 1 x x x u t y x x 0 p u t 1 is contained in the integral manifold through p of the lie algebra l 1 generated by 1 l 1 is said to be decomposable at p if essentially when dim l 1 p n the solution of 1 can be written as exp tx exp f 1 t u v 1 exp f n t u v n p with v 1 v n l 1 this is true for example at any p if l 1 is nilpotent the f i t u are shown to satisfy a system on n of the form 2 x i u t g i t x 1 x i 1 x i 0 0 i 1 n where if l 1 is nilpotent each g i is a polynomial in x 1 x i 1 in this case reachability properties of 2 for controls being countably additive measures impluses reduce to the study of algebraic equations homogeneity allows these to be considered on projective space n giving local results by bezout s theorem similar results hold for controls in the unit ball of krener s results on approximating systems of the form 1 by systems which generate nilpotent lie algebras can then be used to remove the condition that l 1 be nilpotent the method applies to show that if m denotes the set of all products of k elements of 1 with k m and dim span m 1 p dim span m for all odd m then exp tx p int download full size image t for all t 0

analysis of return distributions in the coherent noise model return distributions of the coherent noise model are studied for the system size independent case it is shown that in this case these distributions are in the shape of q gaussians which are the standard distributions obtained in nonextensive statistical mechanics moreover an exact relation connecting the exponent of avalanche size distribution and the q value of appropriate q gaussian has been obtained as q 2 making use of this relation one can easily determine q parameter values of the appropriate q gaussians a priori from one of the well known exponents of the system since the coherent noise model has the advantage of producing different t values by varying a model parameter clear numerical evidences on the validity of the proposed relation have been achieved for various cases finally the effect of the system size has also been analyzed and an analytical expression has been proposed which is corroborated by the numerical results

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators

efficient architectures for 1 d and 2 d lifting based wavelet transforms the lifting scheme reduces the computational complexity of the discrete wavelet transform dwt by factoring the wavelet filters into cascades of simple lifting steps that process the input samples in pairs we propose four compact and efficient hardware architectures for implementing lifting based dwts namely one dimensional 1 d and two dimensional 2 d versions of what we call recursive and dual scan architectures the 1 d recursive architecture exploits interdependencies among the wavelet coefficients by interleaving on alternate clock cycles using the same datapath hardware the calculation of higher order coefficients along with that of the first stage coefficients the resulting hardware utilization exceeds 90 in the typical case of a five stage 1 d dwt operating on 1024 samples the 1 d dual scan architecture achieves 100 datapath hardware utilization by processing two independent data streams together using shared functional blocks the recursive and dual scan architectures can be readily extended to the 2 d case the 2 d recursive architecture is roughly 25 faster than conventional implementations and it requires a buffer that stores only a few rows of the data array instead of a fixed fraction typically 25 or more of the entire array the 2 d dual scan architecture processes the column and row transforms simultaneously and the memory buffer size is comparable to existing architectures