limit sets zero dynamics and internal models in the problem of nonlinear output regulation in this paper we lay the foundations for a nonequilibrium theory of nonlinear output regulation giving a more general nonequilibrium definition of the problem deriving necessary conditions and using these necessary conditions we present a set of sufficient conditions and a design methodology for the solution of the problem in question our analysis leads to a nonequilibrium enhancement of the internal model principle

spreading dynamics of forget remember mechanism we study extensively the forget remember mechanism frm for message spreading originally introduced in eur phys j b 62 247 2008 epjbfy1434 602810 1140 epjb e2008 00139 4 the freedom of specifying forget remember functions governing the frm can enrich the spreading dynamics to a very large extent the master equation is derived for describing the frm dynamics by applying the mean field techniques we have shown how the steady states can be reached under certain conditions which agrees well with the monte carlo simulations the distributions of forget and remember times can be explicitly given when the forget remember functions take linear or exponential forms which might shed some light on understanding the temporal nature of diseases like flu for time dependent frm there is an epidemic threshold related to the frm parameters we have proven that the mean field critical transmissibility for the sis model and the critical transmissibility for the sir model are the lower and the the upper bounds of the critical transmissibility for the frm model respectively

low order integral action controller synthesis abstract a simple controller synthesis method is developed for certain classes of linear time invariant multi input multi output plants the number of poles in each entry of these controllers depends on the number of right half plane plant zeros and is independent of the number of poles of the plant to be stabilized furthermore these controllers have integral action so that they achieve asymptotic tracking of step input references with zero steady state error the designed controller s poles and zeros are all in the stable region with the exception of one pole at the origin for the integral action design requirement the freedom available in the design parameters may be used for additional performance objectives although the only goal here is stabilization and tracking of constant references

surface diffusion of graphs variational formulation error analysis and simulation surface diffusion is a fourth order highly nonlinear geometric driven motion of a surface with normal velocity proportional to the surface laplacian of mean curvature we present a novel variational formulation for graphs and derive a priori error estimates for a time continuous finite element discretization we also introduce a semi implicit time discretization and a schur complement approach to solve the resulting fully discrete linear systems after computational verification of the orders of convergence for polynomial degrees 1 and 2 we show several simulations in one dimension and two dimensions with and without forcing which explore the smoothing effect of surface diffusion as well as the onset of singularities in finite time such as infinite slopes and cracks

adaptive robust output regulation of uncertain linear periodic systems this paper considers the robust output regulation problem for parameterized families of periodic systems to extend the solution of the output regulation problem to the periodic or time varying setup a classification of the immersion mappings based on various non equivalent observability properties is derived the connections between different canonical realizations of internal models that fully exploit such properties for robust and adaptive output regulation design in periodic systems are investigated it is shown how non minimal realizations of suitable periodic internal models are instrumental in achieving the possibility of performing adaptive redesign to deal with parameterized families of exosystem models an important feature of the proposed solution is the fact that a persistence of excitation condition for the exogenous signals is not required for asymptotic regulation

effects of degree biased transmission rate and nonlinear infectivity on rumor spreading in complex social networks we introduce a generalized rumor spreading model and analytically investigate the spreading of rumors on scale free sf networks in the standard rumor spreading model each node has an infectivity equal to its degree and connectivity is uniform across all links to generalize this model we introduce an infectivity function that determines the number of simultaneous contacts that a given node individual may establish with its connected neighbors and a connectivity strength function csf for the direct link between two connected nodes these lead to a degree biased propagation of rumors for nonlinear functions this generalization is reflected in the infectivity s exponent ensuremath alpha and the csf s exponent ensuremath beta we show that by adjusting exponents ensuremath alpha and ensuremath beta the epidemic threshold can be controlled this feature is absent in the standard rumor spreading model in addition we obtain a critical threshold we show that the critical threshold for our generalized model is greater than that of the standard model on a finite sf network theoretically we show that ensuremath beta ensuremath 1 leads to a maximum spreading of rumors and computation results on different networks verify our theoretical prediction also we show that a smaller ensuremath alpha leads to a larger spreading of rumors our results are interesting since we obtain these results regardless of the network topology and configuration

message passing approach for recurrent state epidemic models on networks epidemic processes are common out of equilibrium phenomena of broad interdisciplinary interest recently dynamic message passing dmp has been proposed as an efficient algorithm for simulating epidemic models on networks and in particular for estimating the probability that a given node will become infectious at a particular time to date dmp has been applied exclusively to models with one way state changes as opposed to models like sis and sirs where nodes can return to previously inhabited states because many real world epidemics can exhibit such recurrent dynamics we propose a dmp algorithm for complex recurrent epidemic models on networks our approach takes correlations between neighboring nodes into account while preventing causal signals from backtracking to their immediate source and thus avoids echo chamber effects where a pair of adjacent nodes each amplify the probability that the other is infectious we demonstrate that this approach well approximates results obtained from monte carlo simulation and that its accuracy is often superior to the pair approximation which also takes second order correlations into account moreover our approach is more computationally efficient than the pair approximation especially for complex epidemic models the number of variables in our dmp approach grows as 2mk where m is the number of edges and k is the number of states as opposed to mk 2 for the pair approximation we suspect that the resulting reduction in computational effort as well as the conceptual simplicity of dmp will make it a useful tool in epidemic modeling especially for high dimensional inference tasks

robust design of nonlinear internal models without adaptation we propose a solution to the problem of semiglobal output regulation for nonlinear minimum phase systems driven by uncertain exosystems that does not rely upon conventional adaptation schemes to estimate the frequency of the exogenous signals rather the proposed approach relies upon regression like arguments used to derive a nonlinear internal model able to offset the presence of an unknown number of harmonic exogenous inputs of uncertain amplitude phase and frequency the design methodology guarantees asymptotic regulation if the dimension of the regulator exceeds a lower bound determined by the actual number of harmonic components of the exogenous input if this is not the case a bounded steady state regulation error is ensured whose amplitude though can be arbitrarily decreased by acting on a design parameter of the regulator

percolation and epidemics in a two dimensional small world percolation on two dimensional small world networks has been proposed as a model for the spread of plant diseases in this paper we give an analytic solution of this model using a combination of generating function methods and high order series expansion our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of shortcuts in the small world network our results agree with scaling hypotheses and numerical simulations for the same model

epidemics and percolation in small world networks we study some simple models of disease transmission on small world networks in which either the probability of infection by a disease or the probability of its transmission is varied or both the resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network and we give exact solutions for the position of this threshold in a variety of cases we confirm our analytic results by numerical simulation

asymptotic analysis of linearly elastic shells iii justification of koiter s shell equations we consider as in part i a family of linearly elastic shells of thickness 2 all having the same middle surfaces r3 where r2 is a bounded and connected open set with a lipschitz continuous boundary and l3 r3 the shells are clamped on a portion of their lateral face whose middle line is 0 where 0 is any portion of withlength 0 0 we make an essential geometrical assumption on the middle surfaces and on the set 0 which states that the space of inextensional displacements begin gathered v f omega eta eta i in h 1 omega times h 1 omega times h 2 omega hfill eta i partial v eta 3 0 on gamma 0 gamma alpha beta eta 0 in omega hfill end gathered where gamma alpha beta are the components of the linearized change is metric tensor ofs contains non zero functions this assumption is satisfied in particular ifs is a portion of cylinder and 0 is contained in a generatrix ofs

equivalence of several generalized percolation models on networks in recent years many variants of percolation have been used to study network structure and the behavior of processes spreading on networks these include bond percolation site percolation k core percolation bootstrap percolation the generalized epidemic process and the watts threshold model wtm we show that except for bond percolation each of these processes arises as a special case of the wtm and bond percolation arises from a small modification in fact heterogeneous k core percolation a corresponding heterogeneous bootstrap percolation model and the generalized epidemic process are completely equivalent to one another and the wtm we further show that a natural generalization of the wtm in which individuals transmit or send a message to their neighbors with some probability less than 1 can be reformulated in terms of the wtm and so this apparent generalization is in fact not more general finally we show that in bond percolation finding the set of nodes in the component containing a given node is equivalent to finding the set of nodes activated if that node is initially activated and the node thresholds are chosen from the appropriate distribution a consequence of these results is that mathematical techniques developed for the wtm apply to these other models as well and techniques that were developed for some particular case may in fact apply much more generally

finite element modeling of a linear membrane shell problem using tangential differential calculus we construct a new galerkin finite element method for the membrane elasticity problem on a meshed surface by using two dimensional elements extended into three dimensions the membrane finite element model is established using a tangential differential calculus approach that avoids the use of classical differential geometric methods the finite element method generalizes the classical flat element shell method where standard plane stress elements are used for membrane problems this makes our method applicable to a wider range of problems and of surface descriptions including surfaces defined by distance functions

minimal surface computation using a finite element method on an embedded surface we suggest a finite element method for finding minimal surfaces based on computing a discrete laplace beltrami operator operating on the coordinates of the surface the surface is a discrete repres

an adaptive finite element method for the laplace beltrami operator on implicitly defined surfaces we present an adaptive finite element method for approximating solutions to the laplace beltrami equation on surfaces in mathbb r 3 which may be implicitly represented as level sets of smooth functions residual type a posteriori error bounds which show that the error may be split into a residual part and a geometric part are established in addition implementation issues are discussed and several computational examples are given

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

a boundary differential equation for thin shells abstract we present a mathematical construction of boundary equations for thin shells from classical elasticity by using the differential boundary calculus and the oriented distance function this model extends to thin shells the natural theory and the theory of love kirchhoff as given by germain for plates we specify the appropriate function spaces and give existence and uniqueness theorems we conjecture that our second order model is related to the one of naghdi and that the fourth order model is related to the one of koiter

modeling and computation of two phase geometric biomembranes using surface finite elements biomembranes consisting of multiple lipids may involve phase separation phenomena leading to coexisting domains of different lipid compositions the modeling of such biomembranes involves an elastic or bending energy together with a line energy associated with the phase interfaces this leads to a free boundary problem for the phase interface on the unknown equilibrium surface which minimizes an energy functional subject to volume and area constraints in this paper we propose a new computational tool for computing equilibria based on an l 2 relaxation flow for the total energy in which the line energy is approximated by a surface ginzburg landau phase field functional the relaxation dynamics couple a nonlinear fourth order geometric evolution equation of willmore flow type for the membrane with a surface allen cahn equation describing the lateral decomposition a novel system is derived involving second order elliptic operators where the field variables are the positions of material points of the surface the mean curvature vector and the surface phase field function the resulting variational formulation uses h 1 spaces and we employ triangulated surfaces and h 1 conforming quadratic surface finite elements for approximating solutions together with a semi implicit time discretization of the evolution equations an iterative scheme is obtained essentially requiring linear solvers only numerical experiments are presented which exhibit convergence and the power of this new method for two component geometric biomembranes by computing equilibria such as dumbbells discocytes and starfishes with lateral phase separation

a nitsche method for elliptic problems on composite surfaces we develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together

cut finite element modeling of linear membranes we construct a cut finite element method for the membrane elasticity problem on an embedded mesh using tangential differential calculus i e with the equilibrium equations pointwise projected ont

dynamic message passing equations for models with unidirectional dynamics understanding and quantifying the dynamics of disordered out of equilibrium models is an important problem in many branches of science using the dynamic cavity method on time trajectories we construct a general procedure for deriving the dynamic message passing equations for a large class of models with unidirectional dynamics which includes the zero temperature random field ising model the susceptible infected recovered model and rumor spreading models we show that unidirectionality of the dynamics is the key ingredient that makes the problem solvable these equations are applicable to single instances of the corresponding problems with arbitrary initial conditions and are asymptotically exact for problems defined on locally treelike graphs when applied to real world networks they generically provide a good analytic approximation of the real dynamics

nonlinear internal models for output regulation in this note we show how nonlinear internal models can be effectively used in the design of output regulators for nonlinear systems this result provides a significant enhancement of the nonequilibrium theory for output regulation which we have presented in a recent paper

on the parametric finite element approximation of evolving hypersurfaces in r 3 we present a variational formulation of motion by minus the laplacian of curvature and mean curvature flow as well as related second and fourth order flows of a closed hypersurface in r 3 on introducing a parametric finite element approximation we prove stability bounds and compare our scheme with existing approaches the presented scheme has very good properties with respect to the distribution of mesh points and if applicable volume conservation

higher order meshing of implicit geometries part ii approximations on manifolds abstract a new concept for the higher order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher order elements is automatically generated based on level set data thereby it enables a completely automatic workflow from the geometric description to the numerical analysis without any user intervention a master level set function defines the shape of the manifold through its zero isosurface which is then restricted to a finite domain by additional level set functions it is ensured that the surface elements are sufficiently continuous and shape regular which is achieved by manipulating the background mesh the numerical results show that optimal convergence rates are obtained with a moderate increase in the condition number compared to handcrafted surface meshes

robust output regulation of strongly passive linear systems with multivalued maximally monotone controls the use of multivalued controls derived from a special maximally monotone operator are studied in this paper starting with a strongly passive linear system with possible parametric uncertainty and external disturbances a multivalued control law is derived ensuring regulation of the output to a desired value the methodology used falls in a passivity based control context where we study how the multivalued control affects the dissipation equation of the closed loop system from which we derive its robustness properties finally some numerical examples together with implementation issues are presented to support the main result

a dissipativity based approach to output regulation of non minimum phase systems abstract the present paper presents a new contribution to the design of output regulators for a class of nonlinear systems characterized by a possibly unstable zero dynamics it is shown that the problem in question can be reduced to a stabilization problem with a supplementary gain constraint for a suitably defined reduced auxiliary plant

geography in a scale free network model we offer an example of a network model with a power law degree distribution p k approximately k alpha for nodes but which nevertheless has a well defined geography and a nonzero threshold percolation probability for alpha 2 the range of real world contact networks this is different from p c 0 for alpha 3 results for the original well mixed scale free networks in our lattice based scale free network individuals link to nearby neighbors on a lattice even considerable additional small world links do not change our conclusion of nonzero thresholds when applied to disease propagation these results suggest that random immunization may be more successful in controlling human epidemics than previously suggested if there is geographical clustering

nature of the epidemic threshold for the susceptible infected susceptible dynamics in networks we develop an analytical approach to the susceptible infected susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks we find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold in particular small world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit

uniform practical nonlinear output regulation in this paper we present a solution to the problem of asymptotic and practical semiglobal regulation by output feedback for nonlinear systems a key feature of the proposed approach is that practical regulation is achieved uniformly with respect to the dimension of the internal model and to the gain of the stabilizer near the zero error manifold this property renders the approach interesting for a number of real cases by bridging the gap between output regulation theory and advanced engineering applications simulation results regarding meaningful control problems are also presented

reissner mindlin shell theory based on tangential differential calculus abstract the linear reissner mindlin shell theory is reformulated in the frame of the tangential differential calculus tdc using a global cartesian coordinate system the rotation of the normal vector is modelled with a difference vector approach the resulting equations are applicable to both explicitly and implicitly defined shells because the employed surface operators do not necessarily rely on a parametrization hence shell analysis on surfaces implied by level set functions is enabled but also the classical case of parametrized surfaces is captured as a consequence the proposed tdc based formulation is more general and may also be used in recent finite element approaches such as the tracefem and cutfem where a parametrization of the middle surface is not required herein the numerical results are obtained by isogeometric analysis using nurbs as trial and test functions for classical and new benchmark tests in the residual errors optimal higher order convergence rates are confirmed when the involved physical fields are sufficiently smooth

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

epidemics disorder and percolation abstract spatial models for spread of an epidemic may be mapped onto bond percolation we point out that with disorder in the strength of contacts between individuals patchiness in the spread of the epidemic is very likely and the criterion for epidemic outbreak depends strongly on the disorder because the critical region of the corresponding percolation model is broadened in some networks the percolation threshold is zero if another kind of disorder is present namely divergent fluctuations in the number of contacts we give an example a network with a well defined geography where this is not necessarily so and discuss whether real infection networks are likely to have this property

asymptotic tracking with prescribed transient behaviour for linear systems the problem of asymptotic tracking of reference signals is considered in the context of m input m output linear systems a b c with the following structural properties i cb is sign definite but not necessarily symmetric ii the zero dynamics are exponentially stable the class yref of reference signals is the set of all possible solutions of a fixed stable linear homogeneous differential equation with associated characteristic polynomial the first control objective is asymptotic tracking by the system output y cx of any reference

output regulation for systems on matrix lie groups abstract this paper deals with the problem of output regulation for left invariant systems defined on general matrix lie groups reference trajectories to be tracked are generated by a right invariant exosystem defined on the same lie group and driven by a linear oscillator defined on the lie algebra only partial relative geometrical information of the exosystem with respect to actual system is available in the form of invariant measurements in a homogeneous space a quotient of the lie group in the spirit of the internal model principle the proposed control structure contains an embedded copy of the exosystem kinematics the dynamics associated with the mechanical systems can be handled by dynamic extension of the proposed control approach we demonstrate the approach by providing the details of this extension for the specific case of rotational dynamics on s o 3 the problem formulation considered is motivated by a wide range of real applications in robotics aerospace and computer vision where the state space of systems such as mobile robots aerial robots unmanned drones and camera homographies are naturally lie groups associated with inherent symmetry properties of the underlying physical system

output regulation with nonlinear internal models this paper addresses the problem of semi global nonlinear output regulation for a class of nonlinear systems possessing a nonlinear internal model it is shown that under appropriate and verifiable hypotheses the standard assumption that the feed forward inputs needed to keep the zero error manifold invariant satisfy a linear differential equation can be weakened

solutions of integral and integro differential equation systems by using differential transform method in this study differential transform method dtm is applied to both integro differential and integral equation systems the method is further expanded with a formulation to treat fredholm integrals if the system considered has a solution in terms of the series expansion of known functions this powerful method catches the exact solution so as to show this capability and robustness some systems of integral and integro differential equations are solved as numerical examples

semi global robust output regulation of minimum phase nonlinear systems based on high gain nonlinear internal model we consider the assumption of existence of the general nonlinear internal model that is introduced in the design of robust output regulators for a class of minimum phase nonlinear systems with rth degree r 2 the robust output regulation problem can be converted into a robust stabilisation problem of an augmented system consisting of the given plant and a high gain nonlinear internal model perfectly reproducing the bounded including not only periodic but also nonperiodic exogenous signal from a nonlinear system which satisfies some general immersion assumption the state feedback controller is designed to guarantee the asymptotic convergence of system errors to zero manifold furthermore the proposed scheme makes use of output feedback dynamic controller that only processes information from the regulated output error by using high gain observer to robustly estimate the derivatives of the regulated output error the stabilisation analysis of the resulting closed loop systems leads to regional as wel

critical probabilities for site and bond percolation models cc weak inequality p site p bond is strengthened to strict inequality for a cc broad category of graphs g including all the usual finite dimensional lattices in two and more dimensions the complementary inequality p site c bond 1 1 1 p is proved also where denotes the supremum of c the vertex degrees of g 0 introduction and results let g v e be an infinite connected graph our target in this paper is to study the relationship between site and bond percolation on g and particularly to prove inequalities between the two critical probabilities p site p bond of these models to date the only general cc inequality of this type appears to be the weak inequality p site p bond valid cc for all connected graphs g our principal purpose here is to extend the coupling arguments used in proving this weak inequality and to exploit recently developed methods for proving strict inequalities in order to obtain the inequality p site p bond for a certain broad category of graphs cc several difficulties arise in this program under two general headings first a method is required for utilizing the strict inequality methods of aizenman and grimmett 1991 in the nonstatic setting which occurs when studying stochastic couplings of site and bond percolation second there are graph theoretic complications in applying such techniques to general graphs we shall give two theorems about strict inequalities rather than one only our first such result is theorem 1 which applies specifically to hypercubic lattices in d 2 dimensions this will be proved using a relatively straightforward construction although this construction may in principle be ex tended with some combinatorial complications to certain other graphs on an ad hoc basis it does not seem to be easy to adapt it to a broad general class of graphs therefore we have separated out in theorem 2 our more general result the proof of which requires substantially deeper ideas than that of

output stabilization via nonlinear luenberger observers the present paper addresses the problem of the existence of an output feedback law that asymptotically steers to zero prescribed outputs while keeping all state variables bounded for any initial conditions in a given compact set the problem can be viewed as an extension of the classical problem of semiglobally stabilizing the trajectories of a controlled system to a compact set the problem also encompasses a version of the classical problem of output regulation under only a weak minimum phase assumption it is shown that there exists a controller solving the problem at hand the paper is deliberately focused on theoretical results regarding the existence of such a controller practical aspects involving the design and the implementation of the controller are left to a forthcoming work

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

tangential differential equations for dynamical thin shallow shells abstract we present the mathematical construction of a dynamical second order operational differential equation for thin shallow shells from elasticity by using the tangential differential calculus and the oriented boundary distance function this model extends to thin shallow shells the natural theory and the theory of love kirchhoff of plates we specify the appropriate function spaces and give existence and uniqueness theorems

observation and output adaptive tracking for a class of nonlinear non minimum phase systems abstractin this paper the output tracking problem for a class of systems with unstable zero dynamics is addressed the state is assumed not measurable the output of the dynamical system to be controlled has to track a signal which is the sum of a known number of sinusoids with unknown frequencies amplitudes and phases the non minimum phase nature of the considered systems prevents the direct tracking by standard sliding mode methods which are known to generate unstable behaviours of the internal dynamics the proposed method relies on the availability of a flat output and its time derivatives which are functions of the unavailable state therefore a nonlinear observer is needed due to the uncertainty in the frequencies and in the parameters defining the relationship between the output of the system and the flat states adaptive indirect methods are applied

the time dependent generalized membrane shell model and its numerical computation abstract in this paper we discuss the time dependent generalized membrane shell model which has not been addressed numerically in literature we show that the solution of this model exists and is unique we first provide a numerical method for the time dependent generalized membrane shell concretely we semi discretize the space variable and fully discretize the problem using time discretization by the newmark scheme the corresponding numerical analyses of existence uniqueness stability and convergence with a priori error estimates are given finally we present numerical experiments with a portion of the conical shell and a portion of the hyperbolic shell to verify theoretical convergence results and demonstrate the effectiveness of the numerical scheme

epidemic threshold for the susceptible infectious susceptible model on random networks we derive an analytical expression for the critical infection rate r c of the susceptible infectious susceptible sis disease spreading model on random networks to obtain r c we first calculate the probability of reinfection defined as the probability of a node to reinfect the node that had earlier infected it we then derive r c from using percolation theory we show that is governed by two effects i the requirement from an infecting node to recover prior to its reinfection which depends on the sis disease spreading parameters and ii the competition between nodes that simultaneously try to reinfect the same ancestor which depends on the network topology

a finite element boundary element method for three dimensional large displacement fluid structure interaction abstract this paper presents a hybrid finite element boundary element method for fluid structure interaction simulations of inflatable structures the flow model consists of the steady stokes equation which admits a boundary integral formulation the structure is represented by a kirchhoff love shell the boundary element approximation of the stokes equation reduces the flow problem to an integral equation on the actual structure configuration thus obviating the need for volumetric meshing of the strongly deforming fluid domain the stokes model moreover exhibits a lubrication effect that acts as an intrinsic mechanism to treat the ubiquitous self contact that occurs in inflation problems the aggregated fluid structure interaction problem composed of the boundary integral equation and the kirchhoff love shell connected by dynamic and kinematic interface conditions is approximated by means of isogeometric discretizations to accommodate the smoothness requirements on the approximation spaces imposed by the flexural rigidity in the kirchhoff love shell and to provide an accurate and smooth representation of the boundary for the boundary element method auxiliary results presented in this paper are 1 a parametrization free kirchhoff love formulation 2 establishment of a cubic relationship between distance and tractions due to the lubrication effect and 3 the interpretation of the lagrange multiplier pertaining to fluid incompressibility as the total excess pressure

a finite element method for elliptic equations on surfaces in this paper a new finite element approach for the discretization of elliptic partial differential equations on surfaces is treated the main idea is to use finite element spaces that are induced by triangulations of an outer domain to discretize the partial differential equation on the surface the method is particularly suitable for problems in which there is a coupling with a flow problem in an outer domain that contains the surface we give an analysis that shows that the method has optimal order of convergence both in the h 1 and in the l 2 norm results of numerical experiments are included that confirm this optimality

a unifying framework for global regulation via nonlinear output feedback from iss to iiss this paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input to state stable inverse dynamics subject to possibly unknown control direction the contribution of the paper is two fold firstly we consider the problem of global regulation instead of global asymptotic stabilization gas for systems with generalized dynamic uncertainties it is shown by an elementary example that gas is not solvable using conventional smooth output feedback secondly we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system using our framework most of the known classes of output feedback form systems are broadened in several directions unmeasured states and unknown parameters can appear nonlinearly restrictive matching and growth assumptions are removed the dynamic uncertainty satisfies the weaker condition of sontag s integral input to state stability and the sign of high frequency gain may be unknown a constructive strategy is proposed to design a dynamic output feedback control law that drives the state to the origin while keeping all other closed loop signals bounded

second look at the spread of epidemics on networks in an important paper newman phys rev e66 016128 2002 claimed that a general network based stochastic susceptible infectious removed sir epidemic model is isomorphic to a bond percolation model where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor in this paper we show that this isomorphism is incorrect and define a semidirected random network we call the epidemic percolation network that is exactly isomorphic to the sir epidemic model in any finite population in the limit of a large population i the distribution of self limited outbreak sizes is identical to the size distribution of small out components ii the epidemic threshold corresponds to the phase transition where a giant strongly connected component appears iii the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in component and iv the relative final size of an epidemic is equal to the proportion of the network contained in the giant out component for the sir model considered by newman we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold the same epidemic threshold and the same final size of an epidemic as the bond percolation model however the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution we confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations in the appendix we show that an isomorphism to an epidemic percolation network can be defined for any time homogeneous stochastic sir model