brief paper design of highly synchronizable and robust networks in this paper the design of highly synchronizable sparse and robust dynamical networks is addressed better synchronizability means faster synchronization of the oscillators sparsity means a low ratio of links per nodes and robustness refers to the resilience of a network to the random failures or intentional removal of some of the nodes links golden spectral dynamical networks graphs are those for which the spectral spread the difference between the largest and smallest eigenvalues of the adjacency matrix is equal to the spectral gap the difference between the two largest eigenvalues of the adjacency matrix multiplied by the square of the golden ratio these networks display the property of small worldness are very homogeneous and have large isoperimetric expansion constant together with a very high synchronizability and robustness to failures of individual oscillators in particular the regular bipartite dynamical networks reported here by the first time have the best possible expansion and consequently are the most robust ones against node link failures or intentional attacks

smooth and proper noncommutative schemes and gluing of dg categories abstract in this paper we discuss different properties of noncommutative schemes over a field we define a noncommutative scheme as a differential graded category of a special type we study regularity smoothness and properness for noncommutative schemes admissible subcategories of categories of perfect complexes on smooth projective schemes provide natural examples of smooth and proper noncommutative schemes that are called geometric noncommutative schemes in this paper we show that the world of all geometric noncommutative schemes is closed under an operation of a gluing of differential graded categories via bimodules as a consequence of the main theorem we obtain that for any finite dimensional algebra with separable semisimple part the category of perfect complexes over it is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme moreover if the algebra has finite global dimension then the full subcategory is admissible we also provide a construction of a smooth projective scheme that admits a full exceptional collection and contains as a subcollection an exceptional collection given in advance as another application of the main theorem we obtain in characteristic 0 an existence of a full embedding for the category of perfect complexes on any proper scheme to the category of perfect complexes on a smooth projective scheme

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

on the ideal theory of graphs we study algebras defined by finite sets g m1 mq of monomials of a polynomial ring r there are two basic algebras i k g k m1 mq the k subalgebra of r spanned by the mi and ii the quotient ring r i g where i g m1 mq they come together in the construction of the rees algebra r i g of the ideal i g the emphasis is almost entirely on sets of squarefree monomials of degree two and their attached graphs the main results are assertions about the cohen macaulay behaviour of the koszul homology of i g and how normality or cohen macaulayness of one of the algebras can be read off the properties of the graph or in the other algebra

synchronization of harmonic oscillators under restorative coupling with applications in electrical networks the role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied necessary and sufficient conditions under which the individual systems solutions converge to a common trajectory are presented through simple physical examples the meaning and limitations of the theorems are expounded also to demonstrate their versatility the results are extended to cover lti passive electrical networks one of the extensions generalizes the well known link between the asymptotic stability of the synchronization subspace and the second smallest eigenvalue of the laplacian matrix

perverse sheaves of categories and some applications abstract we study perverse sheaves of categories their connections to classical algebraic geometry we show how perverse sheaves of categories encode naturally derived categories of coherent sheaves on p 1 bundles semiorthogonal decompositions and relate them to a recent proof of segal that all autoequivalences of triangulated categories are spherical twists furthermore we show that perverse sheaves of categories can be used to represent certain degenerate calabi yau varieties

brief paper synchronization of coupled harmonic oscillators in a dynamic proximity network in this paper we revisit the synchronization problems for coupled harmonic oscillators in a dynamic proximity network unlike many existing algorithms for distributed control of complex dynamical networks that require explicit assumptions on the network connectivity we show that the coupled harmonic oscillators can always be synchronized without imposing any network connectivity assumption moreover we also investigate the synchronization with a leader and show that all harmonic oscillators can asymptotically attain the position and velocity of the leader again without any assumption on connectivity of the followers numerical simulation illustrates the theoretical results

conditions for synchronizability in arrays of coupled linear systems synchronization in arrays of coupled continuous time linear systems is studied sufficiency of certain conditions for the existence of a synchronizing feedback law are analyzed it is shown that for neutrally stable systems that are detectable from their outputs a linear feedback law exists under which any number of coupled systems synchronize provided that the directed weighted graph describing the interconnection is fixed and connected an algorithm generating one such feedback law as well as the trajectory that the solutions converge to are presented it is also shown that for critically unstable systems detectability is not sufficient whereas full state coupling is for the existence of a linear feedback law that is synchronizing for all coupling configurations described by a connected graph

on the general consensus protocol of multi agent systems with double integrator dynamics in this paper a general consensus protocol is considered for multi agent systems with double integrator dynamics the advantage of this protocol is that different consensus dynamics including linear periodic and positive exponential dynamics can be realized by choosing different gains necessary and sufficient conditions for solving the consensus problem with the considered general protocol are obtained namely all the gains realizing the consensus can be described the design method of the consensus protocol is constructively given moreover a periodic consensus protocol is obtained as a special case and it is revealed that the maximum convergence speed can be achieved by choosing suitable gains

the structure of the core of ideals the core of an r ideal i is the intersection of all reductions of i this object was introduced by d rees and j sally and later studied by c huneke and i swanson who showed in particular its connection to j lipman s notion of adjoint of an ideal being an a priori infinite intersection of ideals the core is difficult to describe explicitly we prove in a broad setting that core i is a finite intersection of minimal reductions core i is a finite intersection of general minimal reductions core i is the contraction to r of a universal ideal core i behaves well under flat extensions the proofs are based on general multiplicity estimates for certain modules

stability of a class of linear switching systems with applications to two consensus problems in this paper we first establish a stability result for a class of linear switched systems involving kronecker product the problem is interesting in that the system matrix does not have to be hurwitz at any time instant this class of linear switched systems arises in the control of multi agent systems under switching network topology as applications of this stability result we give the solvability conditions for both the leaderless consensus problem and the leader following consensus problem for general marginally stable linear multi agent systems under switching network topology in contrast with some existing results our results only assume that the dynamic graph is uniformly connected

a formula for the core of an ideal the core of an ideal is the intersection of all its reductions for large classes of ideals i we explicitly describe the core as a colon ideal of a power of a single reduction and a power of i

quantitative assessment of the toner and tu theory of polar flocks we present a quantitative assessment of the toner and tu theory describing the universal scaling of fluctuations in polar phases of dry active matter using large scale simulations of the vicsek model in two and three dimensions we find the overall phenomenology and generic algebraic scaling predicted by toner and tu but our data on density correlations reveal some qualitative discrepancies the values of the associated scaling exponents we estimate differ significantly from those conjectured in 1995 in particular we identify a large crossover scale beyond which flocks are only weakly anisotropic we discuss the meaning and consequences of these results

minimal reductions and cores of edge ideals abstract we study minimal reductions of edge ideals of graphs and determine restrictions on the coefficients of the generators of these minimal reductions we prove that when i is not basic then core i m i where i is an edge ideal in the corresponding localized polynomial ring and m is the maximal ideal of this ring we show that the inclusion is an equality for the edge ideal of an even cycle with an arbitrary number of whiskers moreover we show that the core is obtained as a finite intersection of homogeneous minimal reductions in the case of even cycles the formula for the core does not hold in general for the edge ideal of any graph and we provide a counterexample in particular we show in this example that the core is not obtained as a finite intersection of general minimal reductions

the core of zero dimensional monomial ideals the core of an ideal is the intersection of all its reductions we describe the core of a zero dimensional monomial ideal i as the largest monomial ideal contained in a general reduction of i this provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it we relate the core to adjoints and first coefficient ideals and in dimension two and three we give explicit formulas

synchronization of coupled discrete time harmonic oscillators with rational frequency this technical note studies the synchronization of coupled discrete time harmonic oscillators with rational frequency under switching topology the remarkable feature of this problem is that the conditions that merely involve the connectivity structure of topology does not suffice for synchronizing the oscillators we propose a frequency dependent topology condition that indicates in what way the topology switches and introduce firmly nonexpansive mapping fnm from functional analysis under the condition the synchronization of coupled oscillators is related to an infinite product of fnms which share only one zero common fixed point by a convergence result on infinite product of a finite number of fnm we present a synchronization result for the coupled oscillators finally a simulation example is given to illustrate the effectiveness of the result

distributed robust control of linear multi agent systems with parameter uncertainties this article considers the distributed robust control problems of uncertain linear multi agent systems with undirected communication topologies it is assumed that the agents have identical nominal dynamics while subject to different norm bounded parameter uncertainties leading to weakly heterogeneous multi agent systems distributed controllers are designed for both continuous and discrete time multi agent systems based on the relative states of neighbouring agents and a subset of absolute states of the agents it is shown for both the continuous and discrete time cases that the distributed robust control problems under such controllers in the sense of quadratic stability are equivalent to the h control problems of a set of decoupled linear systems having the same dimensions as a single agent a two step algorithm is presented to construct the distributed controller for the continuous time case which does not involve any conservatism and meanwhile decouples the feedback gain design from the commun

design of coupled harmonic oscillators for synchronization and coordination synchronization and coordination of coupled oscillators are fundamental behaviors in complex dynamical systems this paper considers the design of coupled harmonic oscillators to generate an orbitally stable limit cycle of prescribed oscillation profile based on the floquet theory and averaging techniques necessary and sufficient conditions are obtained for nonlinear coupling functions to achieve local exponential convergence to a desired orbit unlike globally convergent methods based on contraction analysis the result applies to oscillators without flow invariance properties insights into coordination mechanisms are gained through interpretation of the coupling structure as a directed graph the theory is illustrated by simple tutorial examples

core versus graded core and global sections of line bundles we find formulas for the graded core of certain m primary ideals in a graded ring in particular if s is the section ring of an ample line bundle on a cohen macaulay complex projective variety we show that under a suitable hypothesis the core and graded core of the ideal of s generated by all elements of degrees at least n for some equivalently every large n are equal if and only if the line bundle admits a non zero global section we also prove a formula for the graded core of the powers of the unique homogeneous maximal ideal in a standard graded cohen macaulay ring of arbitrary characteristic several open problems are posed whose solutions would lead to progress on a non vanishing conjecture of kawamata

on a non vanishing conjecture of kawamata and the core of an ideal we show under suitable hypothesis which are sharp in a certain sense that the core of an m primary ideal in a regular local ring of dimension d is equal to the adjoint or multiplier ideal of its d th power this generalizes the fundamental formula for the core of an integrally closed ideal in a two dimensional regular local ring due to huneke and swanson we also find a generalization of this result to singular non regular settings which we show to be intimately related to the problem of finding non zero sections of ample line bundles on projective varieties in particular we show that a graded analog of our formula for core would imply a remarkable conjecture of kawamata predicting that every adjoint ample line bundle on a smooth variety admits a non zero section

containment control for coupled harmonic oscillators with multiple leaders under directed topology this paper investigates the problem of containment control for coupled harmonic oscillators with multiple leaders under directed topology using tools from matrix graph and stability theories necessary and sufficient conditions are obtained for coupled harmonic oscillators under continuous time and sampled data based protocols respectively when the continuous time protocol is used it is proved that every follower will ultimately converge to the convex hull spanned by the leaders if and only if there exists at least one leader that has a directed path to that follower at any time when the sampled data based protocol is used it is shown that the containment can be achieved if and only if 1 an appropriate sampling period is chosen and 2 for every follower there exists at least one leader that has a directed path to that follower at any time and we also give the containment conditions for coupled harmonic oscillators under undirected topology as a special case finally numerical simulations are

consensus of high order multi agent systems with switching topologies abstract in this paper a consensus problem is investigated for high order multi agent systems with switching communication networks through which only output information instead of full state information can be transmitted to neighbors based on self state feedback and neighbor output feedback a new consensus protocol is proposed which can realize arbitrary convergence rate furthermore as an application a nonlinear heading consensus protocol is designed for a multi vehicle model finally numerical simulations are given to illustrate the theoretical results

synchronization of sampled data coupled harmonic oscillators with control inputs missing abstract this paper is concerned with the synchronization problem of sampled data coupled harmonic oscillators with control inputs missing a distributed algorithm for synchronization in undirected networks of coupled harmonic oscillators is proposed based on the sampled data measurement with controller failures some generic criteria for such algorithm over respectively undirected fixed and switching network topologies are derived analytically compared with some existing works a distinctive feature of this work is to solve synchronization problem in undirected networks even if each oscillator intermittently exchanges the velocity information with its neighbors in terms of sampled data setting only at discrete moments subsequently numerical examples illustrate and visualize the effectiveness and feasibility of the theoretical results

second order leader following consensus of nonlinear multi agent systems via pinning control abstract without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree this paper studies the second order leader following consensus problem of nonlinear multi agent systems with general network topologies based on graph theory matrix theory and lasalle s invariance principle a pinning control algorithm is proposed to achieve leader following consensus in a network of agents with nonlinear second order dynamics furthermore a pinning consensus protocol is developed for coupled double integrators with a constant reference velocity in particular this paper addresses what kind of agents and how many agents should be pinned and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader numerical simulations are given to verify the theoretical analysis

consensus tracking for higher order multi agent systems with switching directed topologies and occasionally missing control inputs abstract this paper studies the distributed consensus tracking problem of linear higher order multi agent systems with switching directed topologies and occasionally missing control inputs in this framework the underlying topology of dynamic agents may switch among several directed graphs each having a directed spanning tree rooted at the leader furthermore the control inputs to the followers may be temporally missed due to actuator failures and network induced packet loss to guarantee asymptotic consensus tracking in such a multi agent system several distributed controllers are constructed based only on the relative state information of neighboring agents by appropriately constructing a switching lyapunov function and using tools from the m matrix theory some sufficient conditions for achieving distributed consensus tracking are provided finally some numerical simulations are given to illustrate the theoretical analysis

on consensus speed of multi agent systems with double integrator dynamics the performance of multi agent systems is an important issue in this paper it is focused on consensus speed for multi agent systems with double integrator dynamics and fixed undirected graphes under a kind of consensus protocols it is revealed that under some conditions the maximum consensus speed is determined by the largest and the smallest nonzero eigenvalues of the laplacian matrix of the undirected connected graph based on the mentioned results arbitrary desired consensus speed can be achieved by choosing suitable feedback gains numerical simulations are given to illustrate the main results

from discrete cucker smale model to continuous cucker smale model in a temperature field we study emergent dynamics of the discrete and continuous cucker smale c s models in a self consistent temperature field and provide refined monocluster flocking estimates more precisely we present a sufficient framework leading to the monocluster flocking toward the constant common temperature and velocity exponentially fast this improves the authors earlier work where existence of common temperature and velocity are not identified our proposed sufficient framework is formulated in terms of the initial data and system parameters using the refined flocking we also provide a uniform in time convergence from the discrete model to the continuous model under some suitable compatibility condition on the asymptotic velocities for the discrete and continuous model as the time step tends to zero we also provide several numerical examples and compare them with analytical results we study emergent dynamics of the discrete and continuous cucker smale c s models in a self consistent temperature field and provide refined monocluster flocking estimates more precisely we present a sufficient framework leading to the monocluster flocking toward the constant common temperature and velocity exponentially fast this improves the authors earlier work where existence of common temperature and velocity are not identified our proposed sufficient framework is formulated in terms of the initial data and system parameters using the refined flocking we also provide a uniform in time convergence from the discrete model to the continuous model under some suitable compatibility condition on the asymptotic velocities for the discrete and continuous model as the time step tends to zero we also provide several numerical examples and compare them with analytical results

an integral invariance principle for differential inclusions with applications in adaptive control the byrnes martin integral invariance principle for ordinary differential equations is extended to differential inclusions on bbb r n the extended result is applied in demonstrating the existence of adaptive stabilizers and servomechanisms for a variety of nonlinear system classes

on the consensus protocol of conspecific agents abstract we present a class of consensus protocols over groups of agents with stochastically switching directed and weighted communication topologies in this protocol an agent s traits that is the cardinality of its neighbor set and the weight assigned to its neighbors in the updating process are given by two jointly distributed random variables and the neighbors of an agent are selected with equal probability we provide closed form results for the asymptotic convergence rate and for the steady state mean square deviation in the presence of additive noise these results are specialized to consensus protocols based on erd s renyi and numerosity constrained networks

degeneration of surfaces with trivial canonical bundle the object of this note is to prove the theorem stated below the main idea of the proof and much of the detail are already to be found in v i kulikov s important paper k our contribution to the proof and the differences with kulikov s paper are discussed later in this introduction theorem let wl x d be a semistable degeneration of surfaces such that

consensus for multi agent systems with inherent nonlinear dynamics under directed topologies abstract this paper considers the consensus problem for multi agent systems with inherent nonlinear dynamics under directed topologies a variable transformation method is used to convert the consensus problem to a partial stability problem both first order and second order systems are investigated under fixed and switching topologies respectively it is assumed that the inherent nonlinear terms satisfy the lipshitz condition sufficient conditions on the feedback gains are given based on a lyapunov function method for first order systems under a fixed topology the consensus is achieved if the feedback gain related to the agents positions is large enough for first order systems under switching topologies the effect of the minimum dwell time for the switching signal on the consensus achievement is considered for second order systems under a fixed topology the consensus is achieved if the feedback gains related to the agents positions and velocities respectively are both large enough for second order systems under switching topologies a switching variable transformation is given then the consensus problem is investigated when all the digraphs are strongly connected and weighted balanced with a common weighted vector finally numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results

the synchronization of instantaneously coupled harmonic oscillators using sampled data with measurement noise in this brief we propose an effective algorithm for synchronization of instantaneously coupled harmonic oscillators by using sampled data which may contain measurement noise we discuss the convergence of this algorithm for both fixed and switching directed network topologies in the presence or absence of leaders we also establish sufficient conditions under which the coupled harmonic oscillators could attain synchronized oscillatory motions in the presence of noise and moreover it is shown that synchronization can be attained even when the velocity information is exchanged only at discrete time instants finally we give some numerical examples to illustrate the effectiveness of the theoretical results

sparsity promoting optimal control of systems with symmetries consensus and synchronization networks abstract optimal control problems in systems with symmetries and consensus synchronization networks are characterized by structural constraints that arise either from the underlying group structure or the lack of absolute measurements for part of the state vector our objective is to design controller structures and resulting control strategies that utilize limited information exchange between subsystems in large scale networks to obtain controllers with low communication requirements we seek solutions to regularized versions of the h 2 optimal control problem non smooth regularization terms are introduced to tradeoff network performance with sparsity of the feedback gain matrix in contrast to earlier results our framework allows the state space representations that are used to quantify the system s performance and sparsity of the static output feedback controller to be expressed in different sets of coordinates we show how alternating direction method of multipliers can be leveraged to exploit the underlying structure and compute sparsity promoting controllers in particular for spatially invariant systems the computational complexity of our algorithm scales linearly with the number of subsystems we also identify a class of optimal control problems that can be cast as semidefinite programs and provide an example to illustrate our developments

synchronization of coupled harmonic oscillators with local instantaneous interaction in this brief we propose a distributed algorithm for synchronization of coupled harmonic oscillators with local instantaneous interaction we provide convergence analysis for such algorithm without and with a leader over fixed and switching undirected network topologies respectively we also establish the conditions by which the coupled harmonic oscillators achieve synchronized oscillatory motions under instantaneous network connectivity it is shown that the coupled harmonic oscillators can be synchronized even each oscillator instantaneously exchanges the velocity information with its neighbors only at discrete moments subsequently numerical examples illustrate and visualize the effectiveness and feasibility of the theoretical results

consensus of second order multi agent systems with delayed nonlinear dynamics and intermittent communications this article investigates the second order consensus problem of multi agent systems with inherent delayed nonlinear dynamics and intermittent communications each agent is assumed to obtain the measurements of relative states between its own and the neighbours only at a sequence of disconnected time intervals a new kind of protocol based only on the intermittent measurements of neighbouring agents is proposed to guarantee the states of agents to reach second order consensus under a fixed strongly connected and balanced topology by constructing a common lyapunov function it is shown that consensus can be reached if the general algebraic connectivity and communication time duration are larger than their corresponding threshold values respectively finally simulation examples are provided to verify the effectiveness of the theoretical analysis

decentralized event triggered consensus with general linear dynamics the consensus problem with general linear dynamics and undirected graphs is studied in this paper by means of event triggered control strategies a novel consensus protocol is proposed where each agent implements a model of the decoupled dynamics of its neighbors under this control strategy transmission of information does not occur continuously but only at discrete points in time the approach presented in this paper provides both a decentralized control law and a decentralized communication policy we are able to design thresholds that only depend on local information and guarantee asymptotic consensus positive inter event times are guaranteed for particular cases of the linear dynamics in an extension a positive constant is added to the thresholds in order to exclude zeno behavior for general linear dynamics the difference between agents trajectories can be bounded in this case and bounds on the state disagreement are derived

flocks herds and schools a quantitative theory of flocking we present a quantitative continuum theory of flocking the collective coherent motion of large numbers of self propelled organisms in agreement with everyday experience our model predicts the existence of an ordered phase of flocks in which all members of even an arbitrarily large flock move together with the same mean velocity stackrel ensuremath rightarrow v ensuremath ne 0 this coherent motion of the flock is an example of spontaneously broken symmetry no preferred direction for the motion is picked out a priori in the model rather each flock is allowed to and does spontaneously pick out some completely arbitrary direction to move in by analyzing our model we can make detailed quantitative predictions for the long distance long time behavior of this broken symmetry state the goldstone modes associated with this spontaneously broken rotational symmetry are fluctuations in the direction of motion of a large part of the flock away from the mean direction of motion of the flock as a whole these goldstone modes mix with modes associated with conservation of bird number to produce propagating sound modes these sound modes lead to enormous fluctuations of the density of the flock far larger at long wavelengths than those in e g an equilibrium gas our model is similar in many ways to the navier stokes equations for a simple compressible fluid in other ways it resembles a relaxational time dependent ginsburg landau theory for an n d component isotropic ferromagnet in spatial dimensions dg4 the long distance behavior is correctly described by a linearized theory and is equivalent to that of an unusual but nonetheless equilibrium model for spin systems for dl4 nonlinear fluctuation effects radically alter the long distance behavior making it different from that of any known equilibrium model in particular we find that in d 2 where we can calculate the scaling exponents exactly flocks exhibit a true long range ordered spontaneously broken symmetry state in contrast to equilibrium systems which cannot spontaneously break a continuous symmetry in d 2 the mermin wagner theorem we make detailed predictions for various correlation functions that could be measured either in simulations or by quantitative imaging of real flocks we also consider an anisotropic model in which the birds move preferentially in an easy e g horizontal plane and make analogous but quantitatively different predictions for that model as well for this anisotropic model we obtain exact scaling exponents for all spatial dimensions including the physically relevant case d 3

braid group actions on derived categories of coherent sheaves this paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety x the motivation for this is m kontsevich s homological mirror conjecture together with the occurrence of certain braid group actions in symplectic geometry one of the main results is that when dim x geq 2 our braid group actions are always faithful we describe conjectural mirror symmetries between smoothings and resolutions of singularities which lead us to find examples of braid group actions arising from crepant resolutions of various singularities relations with the mckay correspondence and with exceptional sheaves on fano manifolds are given moreover the case of an elliptic curve is worked out in some detail

ideals having the expected reduction number 1 introduction let r be a noetherian local ring with infinite residue field k and let be an r ideal when studying algebraic properties of the blow up of spec along v l it is often important to have good upper bounds for the reduction number of the ideal recall that an ideal c is a reduction of if the extension of rees algebras r jt c r it is module finite or equivalently if ir l j r for some r 0 32 the least such r is denoted by rj i a reduction is minimal if it is minimal with respect to inclusion and the reduction number r l of is defined as min o j a minimal reduction of finally the analytic spread i of is the krull dimension of the fiber ring r lt r k or equivalently the minimal number of generators jbi j of any minimal reduction j of 1 32 philosophically speaking j is a simplification of with the reduction number r l measuring how closely the two ideals are related of the numerous recent results about rees algebras and associated graded rings of ideals having small reduction number 18 19 38 35 12 13 14 4 3

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

core and residual intersections of ideals d rees and j sally defined the core of an r ideal i as the in tersection of all minimal reductions of i however it is not easy to give an explicit characterization of it in terms of data attached to the ideal until recently the only case in which a closed formula was known is the one of inte grally closed ideals in a two dimensional regular local ring due to c huneke and i swanson the main result of this paper explicitly describes the core of a broad class of ideals with good residual properties in an arbitrary local cohen macaulay ring we also find sharp bounds on the number of minimal reductions that one needs to intersect to get the core

synchronization of coupled harmonic oscillators with local interaction this paper studies synchronization of coupled second order linear harmonic oscillators with local interaction we analyze convergence conditions over respectively directed fixed and switching network topologies by using tools from algebraic graph theory matrix theory and nonsmooth analysis it is shown that the coupled harmonic oscillators can be synchronized under mild network connectivity conditions examples are given to validate the convergence conditions the theoretical result is also applied to synchronized motion coordination of multi agent systems as a proof of concept

optimal iterative learning control design for multi agent systems consensus tracking abstract under a repeatable operation environment this paper proposes an iterative learning control scheme that can be applied to multi agent systems to perform consensus tracking under the fixed communication topology the agent dynamics are modeled by time varying nonlinear equations which satisfy the global lipschitz continuous condition in addition the desired consensus trajectory is only accessible to a subset of the followers by using the concept of the graph dependent matrix norm the convergence conditions can be specified at the agent level which depend on a set of eigenvalues that are associated with the communication topology the results are first derived for homogeneous agent systems and then extended to heterogeneous systems next optimal controller gain design methods are proposed in the sense that the norm of tracking error converges at the fastest rate which imposes a tightest bounding function for the actual tracking error in the norm analysis framework in the end an illustrative example of a group of heterogeneous agents is provided to demonstrate the effectiveness of the proposed design methods

uniqueness of enhancement for triangulated categories the paper contains general results on the uniqueness of a dg enhancement for trian gulated categories as a consequence we obtain such uniqueness for the unbounded categories of quasi coherent sheaves for the triangulated categories of perfect complexes and for the bounded de rived categories of coherent sheaves on quasi projective schemes if a scheme is projective then we also prove a strong uniqueness for the triangulated category of perfect complexes and for the bounded de rived categories of coherent sheaves these results directly imply that fully faithful functors from the bounded derived categories of coherent sheaves and the triangulated categories of perfect complexes on projective schemes can be represented by objects on the product

study of interacting particle systems the transition to the oscillatory behavior of a prey predator model abstract a prey predator system with intelligent pursuit and evasion is studied by means of computer simulations it is found that the model exhibits a coexistence state between prey and predators in this state and depending on the parameters the system may evolve toward two different regimes characterized by the behavior of the prey predator population whitin the oscillatory fixed point regime the specie s density changes periodically remains constant respectively the transition between such regimes is rationalized in terms of a dynamic percolation process

multi agent second order average consensus with prescribed transient behavior the problem of consensus reaching with prescribed transient behavior for a group of double integrator agents is addressed the information exchange of the multi agent system is described by a static communication network we initially set time dependent constraints on the transient response of the relative positions between neighboring agents and we propose a distributed control law consisting of a proportional term of the transformed error and an additional damping term based on absolute velocities measurements we also design an agreement protocol that can additionally achieve prescribed performance for a combined error of positions and velocities under a sufficient condition for the damping gains the proposed nonlinear time dependent distributed controllers guarantee that the predefined constraints are not violated and that consensus is achieved with a convergence rate independent of the underlying communication graph furthermore connectivity maintenance can be ensured by appropriately designing the performance bounds theoretical results are supported by simulations

closed form solution for optimal convergence speed of multi agent systems with discrete time double integrator dynamics for fixed weight ratios abstract this paper considers the convergence speed of multi agent systems with discrete time double integrator dynamics the communication topology is assumed to be fixed and undirected the speed of convergence of the associated average consensus protocol is analyzed and the problem of maximizing the convergence speed over the free parameters in the consensus protocol is considered a closed form solution to this problem is proposed assuming that the ratios of weights of communication links are fixed furthermore it is shown that when the weight ratios are considered as decision variables a global optimum of the convergence speed can be obtained by solving an lmi problem simulation results are provided that demonstrate the effectiveness of the proposed approach

optimal convergence speed of consensus under constrained damping for multi agent systems with discrete time double integrator dynamics abstract this paper considers the optimization of the convergence speed of consensus under given damping constraints for multi agent systems with discrete time double integrator dynamics with fixed interconnection topology this work summarizes and details existing results in the case of undirected topologies and extends them to directed ones the interconnection topology is assumed to be connected or to contain a rooted out branching respectively depending on the minimum required damping for undirected interconnection topologies in most cases analytic solutions are provided the structure of these solutions is independent of the size of the network and only depends on the largest and second smallest eigenvalue of the corresponding laplacian for the remaining cases without analytic solutions provided a combined bisection grid search is presented that solves the constrained optimization problem efficiently this algorithm can also be applied to directed interconnection topologies and as for the undirected case converges to the single optimum simulation results are provided that demonstrate the effectiveness of the proposed approach

robust consensus control with guaranteed rate of convergence using second order hurwitz polynomials abstractthis paper considers homogeneous networks of general linear time invariant second order systems we consider linear feedback controllers and require that the directed graph associated with the network contains a spanning tree and systems are stabilisable we show that consensus with a guaranteed rate of convergence can always be achieved using linear state feedback to achieve this we provide a new and simple derivation of the conditions for a second order polynomial with complex coefficients to be hurwitz we apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph laplacian matrix may have complex eigenvalues based on the conditions found methods to compute feedback gains are proposed we show that gains can be chosen such that consensus is achieved robustly over a variety of communication structures and system dynamics we also consider the use of static output feedback

consensus analysis of switching multi agent systems with fixed topology and time delay abstract this paper investigates the average consensus problems of the discrete time markov switching linear multi agent systems lmas with fixed topology and time delay firstly we introduce a concept of the average consensus to adapt the stochastic systems secondly a time delay switching consensus protocol is proposed by developing a new signal mode the switching signal of the systems and the time delay signal of the controller can be merged into one signal thirdly by lyapunov technique two lmis criteria of average consensus are provided and they reveal that the consensus of the multi agent systems relates to the spectral radius of the laplacian matrix furthermore by our results and ccl type algorithms we can get the gain matrices finally a numerical example is given to illustrate the efficiency of our results