structural properties of dendrite groups let g be the homeomorphism group of a dendrite we study the normal subgroups of g for instance there are uncountably many non isomorphic such groups g that are simple groups moreover these groups can be chosen so that any isometric g action on any metric space has a bounded orbit in particular they have the fixed point property fh

brief paper anti windup and bumpless transfer schemes this paper considers the problem of windup which occurs when a controller with unstable integrator modes is subjected to input saturation or multi mode operation an optimal strategy for the so called model based approach is proposed based on an h optimisation framework this has been found to give good results on numerical examples taken from the literature

local stabilization of linear systems under amplitude and rate saturating actuators this note addresses the problem of local stabilization of linear systems subject to control amplitude and rate saturation considering the actuator represented by a first order system subject to input and state saturation a condition for the stabilization of an a priori given set of admissible initial states is formulated from certain saturation nonlinearities representation and quadratic stability results from this condition an algorithm based on the iterative solution of linear matrix inequalities based problems is proposed in order to compute the control law

average hopcount of the shortest path in tree like components with finite size abstract an exact formula for computing the average hopcount of the shortest path in finite size tree like components of undirected unweighted random networks is proposed in a tree like component with size s there exists virtually only one shortest path between two arbitrary nodes the summation of hopcounts of all shortest paths can be calculated approximately by the summation of the betweenness of all nodes and the difference between them is only a constant s s 1 therefore the average hopcount can be calculated by further dividing the summation by the number of all shortest paths in this paper we first derive the conditional probability p k s of the degree distribution of finite components with size s and the summation of all nodal betweenness respectively by means of these results we obtain the exact formula for calculating the average hopcount also we confirm the proposed formula by simulations for networks with poisson and power law degree distributions respectively

undecidability of automorphism groups we give a simple and easy to apply technique that gives the undecidability of the theory of many automorphism groups let g be a group of automorphisms of a structure suppose that g in g is not the identity and has no non singleton finite orbits if the centraliser of g is transitive on the support of g and satisfies a further technical condition then the subgroup generated by g is equal to the double centraliser of g thus if g contains such an element g that is conjugate to all its positive powers then one can interpret addition and multiplication of natural numbers in the theory of g using the parameter g consequently g has undecidable theory

cascades on a class of clustered random networks we present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution and nonzero clustering introduced previously in m e j newman phys rev lett 103 058701 2009 a condition for the existence of global cascades is derived as well as a general criterion that determines whether increasing the level of clustering will increase or decrease the expected cascade size applications examples of which are provided include site percolation bond percolation and watts threshold model in all cases analytical results give excellent agreement with numerical simulations

a scalable generative graph model with community structure network data is ubiquitous and growing yet we lack realistic generative network models that can be calibrated to match real world data the recently proposed block two level erdos renyi bter model can be tuned to capture two fundamental properties degree distribution and clustering coefficients the latter is particularly important for reproducing graphs with community structure such as social networks in this paper we compare bter to other scalable models and show that it gives a better fit to real data we provide a scalable implementation that requires only o d rm max storage where d rm max is the maximum number of neighbors for a single node the generator is trivially parallelizable and we show results for a hadoop mapreduce implementation for modeling a real world web graph with over 4 6 billion edges we propose that the bter model can be used as a graph generator for benchmarking purposes and provide idealized degree distributions and clustering coefficient profiles that can b

degree and component size distributions in the generalized uniform recursive tree we propose a generalized model for the famous uniform recursive tree urt by introducing an imperfect growth process which may generate disconnected components clusters the model undergoes an interesting phase transition from a singly connected network to a graph consisting of fully isolated nodes we investigate the distributions of degree and component sizes by both theoretical predictions and numerical simulations for the nontrivial cases we show that the network has an exponential degree distribution while its component size distribution follows a power law both of which are related to the imperfect growth process we also predict the growth dynamics of the individual components all analytical solutions are successfully contrasted with computer simulations

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

betweenness centrality of an edge in tree like components with finite size using the generating function formalism we propose an exact formula for estimating betweenness centrality of an edge in finite tree like components of random networks with arbitrary degree distributions as a function of the degrees of two vertices interconnected by the edge and the size of the component to which the edge belongs the formula can give an estimation of the mean value of the edge betweenness we confirm the formula by simulations for poisson and power law distributions respectively we also study the asymptotic behavior of the formula and find that there is an asymptotic power law relation with an exponent 1 5 between the edge betweenness and the size of the component to which the edge belongs

a unified framework for the study of anti windup designs we present a unified framework for the study of linear time invariant lti systems subject to control input nonlinearities the framework is based on the following two step design paradigm design the linear controller ignoring control input nonlinearities and then add anti windup bumpless transfer awbt compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance the resulting awbt compensation is applicable to multivariable controllers of arbitrary structure and order all known lti anti windup and or bumpless transfer compensation schemes are shown to be special cases of this framework it is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model the actual analysis of stability and performance and robustness issues are problems in their own right and hence not detailed here the main result is the unification of existing schemes for awbt compensation under a general framework

l hop percolation on networks with arbitrary degree distributions and its applications site percolation has been used to help understand analytically the robustness of complex networks in the presence of random node deletion or failure in this paper we move a further step beyond random node deletion by considering that a node can be deleted because it is chosen or because it is within some l hop distance of a chosen node using the generating functions approach we present analytic results on the percolation threshold as well as the mean size and size distribution of nongiant components of complex networks under such operations the introduction of parameter l is both conceptually interesting because it accommodates a sort of nonindependent node deletion which is often difficult to tackle analytically and practically interesting because it offers useful insights for cybersecurity such as botnet defense

a non square sector condition and its application in deferred action anti windup compensator design a sector condition for two connected deadzone nonlinearities is provided by introducing an additional non square operator which exploits their connectivity a more general set of sector like matrix inequalities is obtained this non square matrix inequality condition is applied to an anti windup aw problem in which the aw compensator is not activated until the unconstrained control signal reaches a well defined level beyond that of the physical actuator limits the non square sector condition allows such deferred action aw synthesis to be performed in a manner much closer to traditional immediate sector based aw with either lowered conservatism or decreased computational effort in contrast to recent work the non square condition is applicable to other aw problems

effect of edge removal on topological and functional robustness of complex networks abstract we study the robustness of several network models subject to edge removal the robustness is measured by the statistics of network breakdowns where a breakdown is defined as the destroying of the total connectedness of a network rather than the disappearance of the giant component we introduce a simple traffic dynamics as the function of a network topology and the total connectedness can be destroyed in the sense of either the topology or the function the overall effect of the topological breakdown and the functional breakdown as well as the relative importance of the topological robustness and the functional robustness are studied under two edge removal strategies

anti windup control design for exponentially unstable lti systems with actuator saturation in this paper a new saturation control technique in the framework of anti windup compensation is developed for exponentially unstable linear time invariant systems subject to input nonlinearities the proposed control algorithm guarantees regional stability in the existence of input saturation and provides less conservative performance than most existing anti windup schemes moreover an explicit form of anti windup controller with its order no more than the order of the plant is derived an inverted pendulum example is used to demonstrate the advantages of the newly proposed anti windup control technique

antiwindup for stable linear systems with input saturation an lmi based synthesis this paper considers closed loop quadratic stability and l sub 2 performance properties of linear control systems subject to input saturation more specifically these properties are examined within the context of the popular linear antiwindup augmentation paradigm linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification called the unconstrained closed loop behavior building on known results on h sub spl infin and lpv synthesis the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem which has an attractive system theoretic interpretation the lower bound on the achievable l sub 2 performance is the maximum of the open and unconstrained closed loop l sub 2 gains in the special cases of zero order static and plant order antiwindup compensation the feasibility conditions become convex linear matrix inequalities it is shown that if and only if the plant is asymptotically stable plant order linear antiwindup compensation is always feasible for large enough l sub 2 gain and that static antiwindup compensation is feasible provided a quasi common lyapunov function between the open loop and unconstrained closed loop exists using the solutions to the matrix feasibility problems the synthesis of the antiwindup augmentation achieving the desired level of l sub 2 performance is then accomplished by solving an additional lmi

component sizes in networks with arbitrary degree distributions we give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions the solution tells us the probability that a randomly chosen node belongs to a component of size s for any s we apply our results to networks with the three most commonly studied degree distributions poisson exponential and power law as well as to the calculation of cluster sizes for bond percolation on networks which correspond to the sizes of outbreaks of epidemic processes on the same networks for the particular case of the power law degree distribution we show that the component size distribution itself follows a power law everywhere below the phase transition at which a giant component forms but takes an exponential form when a giant component is present

antiwindup design with guaranteed regions of stability an lmi based approach this note addresses the design of antiwindup gains for obtaining larger regions of stability for linear systems with saturating inputs considering that a linear dynamic output feedback has been designed to stabilize the linear system without saturation a method is proposed for designing an antiwindup gain that maximizes an estimate of the basin of attraction of the closed loop system it is shown that the closed loop system obtained from the controller plus the antiwindup gain can be modeled by a linear system with a deadzone nonlinearity a modified sector condition is then used to obtain stability conditions based on quadratic lyapunov functions differently from previous works these conditions are directly in linear matrix inequality form some numerical examples illustrate the effectiveness of the proposed design technique when compared with the previous ones

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

brief multivariable anti windup controller synthesis using linear matrix inequalities we present a general formulation of the problem of multi variable anti windup bumpless transfer awbt controller synthesis which provides sufficient conditions for stability covering a large class of typical input nonlinearities such as saturation deadzone and switching override nonlinearities the resulting synthesis method demonstrates graceful performance degradation whenever input nonlinearities are active through minimization of a weighted l 2 gain the main contribution of the paper is that the awbt controller synthesis using static compensation is cast as a convex optimization over linear matrix inequalities

betweenness centrality in finite components of complex networks abstract we use generating function formalism to obtain an exact formula of the betweenness centrality in finite components of random networks with arbitrary degree distributions the formula is obtained as a function of the degree and the component size and is confirmed by simulations for poisson exponential and power law degree distributions we find that the betweenness centralities for the three distributions are asymptotically power laws with an exponent 1 5 and are invariant to the particular distribution parameters

subgroups of the group of homeomorphisms of the cantor space and a duality between a class of inverse monoids and a class of hausdorff etale groupoids abstract under non commutative stone duality there is a correspondence between second countable hausdorff etale groupoids which have a cantor space of identities and what we call tarski inverse monoids that is countable boolean inverse monoids with semilattices of idempotents which are countable and atomless tarski inverse monoids are therefore the algebraic counterparts of the etale groupoids studied by matui and provide a natural setting for many of his calculations under this duality we prove that natural properties of the etale groupoid correspond to natural algebraic properties of the tarski inverse monoid effective groupoids correspond to fundamental tarski inverse monoids and minimal groupoids correspond to 0 simplifying tarski inverse monoids particularly interesting are the principal groupoids which correspond to tarski inverse monoids where every element is a finite join of infinitesimals and idempotents here an infinitesimal is simply a non zero element with square zero the groups of units of fundamental tarski inverse monoids generalize the finite symmetric groups and include amongst their number the thompson groups g n 1 as well as the groups of units of af inverse monoids krieger s ample groups being examples

nonlinear scheduled anti windup design for linear systems the nonlinear l sub 2 anti windup framework introduced in teel and kapor 1997 reduces the anti windup synthesis problem to a state feedback synthesis problem for linear systems with input saturation and input matched l sub 2 disturbances in this note based on the structure proposed in that previous paper we provide a linear matrix ineqaulity lmi formulation of high performance anti windup design for control systems with linear asymptotically stable plants in particular we first give a linear quadratic based formulation of linear anti windup compensation in terms of the solution of a set of always feasible lmi constraints then we propose a nonlinear scheduling technique where hysteresis switching among a family of linear gains is employed for performance improvement both design techniques are demonstrated on an academic example