a near tight lower bound on the time complexity of distributed minimum weight spanning tree construction this paper presents a lower bound of omega d sqrt n log n on the time required for the distributed construction of a minimum weight spanning tree mst in weighted n vertex networks of diameter d omega log n in the bounded message model this establishes the asymptotic near optimality of existing time efficient distributed algorithms for the problem whose complexity is o d sqrt n log n

a necessary condition for dynamic equivalence if two control systems on manifolds of the same dimension are dynamic equivalent we prove that either they are static equivalent i e equivalent via a classical diffeomorphism or they are both ruled for systems of different dimensions the one of higher dimension must be ruled a ruled system is one whose equations define at each point in the state manifold a ruled submanifold of the tangent space dynamic equivalence is also known as equivalence by endogenous dynamic feedback or by a lie backlund transformation when control systems are viewed as underdetermined systems of ordinary differential equations it is very close to absolute equivalence for pfaffian systems it was already known that a differentially flat system must be ruled this was a particular case of the present result in which one of the systems was assumed to be trivial or linear controllable

a deterministic almost tight distributed algorithm for approximating single source shortest paths we present a deterministic 1 o 1 approximation n 1 2 o 1 d 1 o 1 time algorithm for solving the single source shortest paths problem on distributed weighted networks the sf congest

the sparsest additive spanner via multiple weighted bfs trees abstract spanners are fundamental graph structures that sparsify graphs at the cost of small stretch in particular in recent years many sequential algorithms constructing additive all pairs spanners were designed providing very sparse small stretch subgraphs remarkably it was then shown that the known 6 spanner constructions are essentially the sparsest possible that is larger additive stretch cannot guarantee a sparser spanner which brought the stretch sparsity trade off to its limit distributed constructions of spanners are also abundant however for additive spanners while there were algorithms constructing 2 and 4 all pairs spanners the sparsest case of 6 spanners remained elusive we remedy this by designing a new sequential algorithm for constructing a 6 spanner with the essentially optimal sparsity of o n 4 3 edges we then show a distributed implementation of our algorithm answering an open problem in 12 a main ingredient in our distributed algorithm is an efficient construction of multiple weighted bfs trees a weighted bfs tree is a bfs tree in a weighted graph that consists of the lightest among all shortest paths from the root to each node we present a distributed algorithm in the congest model that constructs multiple weighted bfs trees in s d 1 rounds where s is the set of sources and d is the diameter of the network graph

minimum weight spanning tree construction in o log log n communication rounds we consider a simple model for overlay networks where all n processes are connected to all other processes and each message contains at most o log n bits for this model we present a distributed algorithm which constructs a minimum weight spanning tree in o log log n communication rounds where in each round any process can send a message to every other process if message size is theta n epsilon for some epsilon 0 then the number of communication rounds is o log 1 over epsilon

on some applications of transversality theory to system theory this note presents four applications of transversality theory to deriving some topological properties of linear time invariant and nonlinear affine control systems special attention is given to the following topics i stratification of linear systems ii generic one parameter families of linear systems iii genericity of affine systems having linear controllable approximations iv non genericity of affine systems equivalent to linear systems the relevance of the obtained results to the problem of classification of affine systems by state or feedback equivalence is stressed

distributed verification and hardness of distributed approximation we study the verification problem in distributed networks stated as follows let h be a subgraph of a network g where each vertex of g knows which edges incident on it are in h we would l

estimates of the bistable region in metal cutting the classical model of regenerative vibration is investigated with new kinds of nonlinear cutting force characteristics the standard nonlinear characteristics are subjected to a critical review from the nonlinear dynamics viewpoint based on the experimental results available in the literature the proposed nonlinear model includes finite derivatives at zero chip thickness and has an essential inflexion point in the case of the one degreeof freedom model of orthogonal cutting the existence of unstable self excited vibrations is proven along the stability limits which is strongly related to the force characteristic at its inflexion point an analytical estimate is given for a certain area below the stability limit where stable stationary cutting and a chaotic attractor coexist it is shown how this domain of bistability depends on the theoretical chip thickness the comparison of these results with the experimental observations and also with the subcritical hopf bifurcation results obtained for standard nonlinear cutting force characteristics provides relevant information on the nature of the cutting force nonlinearity

approximate analytical solutions for primary chatter in the non linear metal cutting model this paper considers an accepted model of the metal cutting process dynamics in the context of an approximate analysis of the resulting non linear differential equations of motion the process model is based upon the established mechanics of orthogonal cutting and results in a pair of non linear ordinary differential equations which are then restated in a form suitable for approximate analytical solution the chosen solution technique is the perturbation method of multiple time scales and approximate closed form solutions are generated for the most important non resonant case numerical data are then substituted into the analytical solutions and key results are obtained and presented some comparisons between the exact numerical calculations for the forces involved and their reduced and simplified analytical counterparts are given it is shown that there is almost no discernible difference between the two thus confirming the validity of the excitation functions adopted in the analysis for the data sets used these being chosen to represent a real orthogonal cutting process in an attempt to provide guidance for the selection of technological parameters for the avoidance of primary chatter this paper determines for the first time the stability regions in terms of the depth of cut and the cutting speed co ordinates

distributed exact shortest paths in sublinear time the distributed single source shortest paths problem is one of the most fundamental and central problems in the message passing distributed computing classical bellman ford algorithm solves it in o n time where n is the number of vertices in the input graph g peleg and rubinovich 49 showed a lower bound of d s n for this problem where d is the hop diameter of g whether or not this problem can be solved in o n time when d is relatively small is a major open question despite intensive research 10 17 33 41 45 that yielded near optimal algorithms for the approximate variant of this problem no progress was reported for the original problem in this article we answer this question in the affirmative we devise an algorithm that requires o n log n 5 6 time for d e o s n log n and o d1 3 n log n 2 3 time for larger d this running time is sublinear in n in almost the entire range of parameters specifically for d e o n log2 n we also generalize our result in two directions one is when edges have bandwidth b 1 and the other is the s sources shortest paths problem for both problems our algorithm provides bounds that improve upon the previous state of the art in almost the entire range of parameters in particular we provide an all pairs shortest paths algorithm that requires o n5 3 log 2 3 n time even for b e 1 for all values of d we also devise the first algorithm with non trivial complexity guarantees for computing exact shortest paths in the multipass semi streaming model of computation from the technical viewpoint our distributed algorithm computes a hopset g of a skeleton graph g of g without first computing g itself we then conduct a bellman ford exploration in g g while computing the required edges of g on the fly as a result our distributed algorithm computes exactly those edges of g that it really needs rather than computing approximately the entire g

lessons from the congested clique applied to mapreduce the main result of this paper is a simulation algorithm which under quite general constraints transforms algorithms running in the congested clique model into algorithms running in the mapreduce model as a case study of applying this simulation algorithm we first present a distributed o coloring algorithm running on the congested clique in o 1 rounds if log 2 n and o log log log n rounds otherwise applying the simulation theorem to this congested clique o coloring algorithm yields an o 1 round o coloring algorithm in the mapreduce model we apply our simulation algorithm to other congested clique algorithms including the 2 ruling set and metric facility location algorithms of berns et al icalp 2012 our simulation algorithm illustrates a natural correspondence between per node bandwidth in the congested clique model and memory per machine in the mapreduce model in the congested clique and more generally any network in the congest model the major impediment to constructing fast algorithms is the o log n restriction on message sizes similarly in the mapreduce model the combined restrictions on memory per machine and total system memory have a dominant effect on algorithm design in showing a fairly general simulation algorithm we highlight the similarities and differences between these models

bifurcation diagrams for feedback families of linear systems abstract the purpose of this note is to give a proof of the theorem on the form of bifurcation diagrams for generic feedback families of linear systems announced in 1 the main result stated as theorem 3 1 provides explicit algebraic description of the diagrams

approximate proof labeling schemes abstract we study a new model of verification of boolean predicates over distributed networks given a network configuration the proof labeling scheme pls model defines a distributed proof in the form of a label that is given to each node and all nodes locally verify that the network configuration satisfies the desired boolean predicate by exchanging labels with their neighbors the proof size of the scheme is defined to be the maximum size of a label in this work we extend this model by defining the approximate proof labeling scheme apls model in this new model the predicates for verification are of the form where f n for a family of configurations f informally the predicates considered in this model are a comparison between two values of the configuration as in the pls model nodes exchange labels in order to locally verify the predicate and all must accept if the network satisfies the predicate the soundness condition is relaxed with an approximation ration so that only if some node must reject we focus on two verification problems upper and lower bounds on the diameter of the graph and the maximality of a given matching for these problems we present the first results that apply to all graph structures in our new apls model we show that the proof size can be much smaller than the proof size of the same predicate in the pls model moreover we prove that there is a tradeoff between the approximation ratio and the proof size finally we present the first general result for maximum cardinality matching in the pls model

distributed random walks performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science including distributed computing in this article we focus on the problem of sampling random walks efficiently in a distributed network and its applications given bandwidth constraints the goal is to minimize the number of rounds required to obtain random walk samples all previous algorithms that compute a random walk sample of length e as a subroutine always do so naively that is in o e rounds the main contribution of this article is a fast distributed algorithm for performing random walks we present a sublinear time distributed algorithm for performing random walks whose time complexity is sublinear in the length of the walk our algorithm performs a random walk of length e in o ed rounds o hides polylog n factors where n is the number of nodes in the network with high probability on an undirected network where d is the diameter of the network for small diameter graphs this is a significant improvement over the naive o e bound furthermore our algorithm is optimal within a poly logarithmic factor as there exists a matching lower bound nanongkai et al 2011 we further extend our algorithms to efficiently perform k independent random walks in o ked k rounds we also show that our algorithm can be applied to speedup the more general metropolis hastings sampling our random walk algorithms can be used to speed up distributed algorithms in applications that use random walks as a subroutine we present two main applications first we give a fast distributed algorithm for computing a random spanning tree rst in an arbitrary undirected unweighted network which runs in o md rounds with high probability m is the number of edges our second application is a fast decentralized algorithm for estimating mixing time and related parameters of the underlying network our algorithm is fully decentralized and can serve as a building block in the design of topologically aware networks

a distributed enumeration algorithm and applications to all pairs shortest paths diameter we consider the standard message passing model we assume the system is fully synchronous all processes start at the same time and time proceeds in synchronised rounds in each round each vertex can transmit a different message of size o 1 to each of its neighbours this paper proposes and analyses a distributed enumeration algorithm of vertices of a graph having a distinguished vertex which satisfies that two vertices with consecutive numbers are at distance at most 3 we prove that its time complexity is o n where n is the number of vertices of the graph furthermore the size of each message is o 1 thus its bit complexity is also o n we provide some links between this enumeration and hamiltonian graphs from which we deduce that this enumeration is optimal in the sense that there does not exist an enumeration which satisfies that two vertices with consecutive numbers are at distance at most 2 we deduce from this enumeration algorithms which compute all pairs shortest paths and the diameter with a time complexity and a bit complexity equal to o n

dynamic input output decoupling of nonlinear control systems the problem of dynamic input output decoupling of nonlinear control systems is studied based on an analytic algorithm the authors obtain necessary and sufficient conditions for the solvability of this problem the solution of the problem is constructed by applying a series of simple precompensations and linking maps some interesting connections with other approaches in nonlinear control theory are discussed the authors also give a few simple examples to illustrate the methods used

the only stable normal forms of affine systems under feedback are linear abstract we consider the problem of existence of structurally stable normal forms of affine control systems with m inputs and n dimensional state space equipped with c whitney topology and acted on by the static state feedback group it is proved that structurally stable normal forms exist only if m n or m 1 and n 2 and are linear there are no stable normal forms in any other range of dimensions m n

on structural instability of normal forms of affine control systems subject to static state feedback smooth affine control systems acted on by the feedback group are dealt with from the viewpoint of the existence of structurally stable normal forms detailed analysis of the action of the approximate feedback group of order 1 has revealed that in most cases an obstacle to structural stability appears just in the action of this group

a simple deterministic distributed mst algorithm with near optimal time and message complexities the distributed minimum spanning tree mst problem is one of the most central and fundamental problems in distributed graph algorithms kutten and peleg devised an algorithm with running time o d n log n where d is the hop diameter of the input n vertex m edge graph and with message complexity o m n3 2 peleg and rubinovich showed that the running time of the algorithm of kutten and peleg is essentially tight and asked if one can achieve near optimal running time together with near optimal message complexity in a recent breakthrough pandurangan et al answered this question in the affirmative and devised a randomized algorithm with time o d n and message complexity o m they asked if such a simultaneous time and message optimality can be achieved by a deterministic algorithm in this article building on the work of pandurangan et al we answer this question in the affirmative and devise a deterministic algorithm that computes mst in time o d n log n using o m log n n log n cdot log n messages the polylogarithmic factors in the time and message complexities of our algorithm are significantly smaller than the respective factors in the result of pandurangan et al in addition our algorithm and its analysis are very simple and self contained as opposed to rather complicated previous sublinear time algorithms finally we use our new algorithm to devise a randomized mst algorithm with running time o g n and message complexity o e where radius g d is a graph parameter which is typically much smaller than d this improves a previous bound from elkin

numerical bifurcation analysis of delay differential equations numerical methods for the bifurcation analysis of delay differential equations ddes have only recently received much attention partially because the theory of ddes smoothness boundedness stability of solutions is more complicated and less established than the corresponding theory of ordinary differential equations as a consequence no established software packages exist at present for the bifurcation analysis of ddes we outline existing numerical methods for the computation and stability analysis of steady state solutions and periodic solutions of systems of ddes with several constant delays

remarks on nonlinear planar control systems which are linearizable by feedback abstract the possibility that certain nonlinear systems can be linearized by the nonlinear feedback group has recently attracted a great deal of attention in the literature at least for mechanical systems the apparent ubiquity of linearizable systems is often accounted for by the claim that scalar control systems defined on r 2 are generically linearizable since there are several possible interpretations of the term generic and since until now no rigorous proof of genericity for any use of the term has been offered i thought it worthwhile to investigate in what sense if any this folklore theorem is valid contrary to the prevailing intuition linearizable systems fail to be dense in any topology for which evaluation of vector fields at points is a continous operation this includes for example both the weak and strong c topologies what then are the global properties of the class of linearizable systems in this note it is also shown that this class has no interior points in any reasonable complete topology making feedback operations continuous in particular linearizable systems in r 2 are far from being structurally stable in the weak c topology in the other hand one of the main results presented here is that globally linearizable systems are open in the strong or whitney topology thus globally linearizable planar systems are structurally stable if the well known local conditions actually implied global linearizability this result would be trivial recent work of boothby shows however that global linearization is far more subtle for this reason in the course of the proof it is necessary to modify the existing global linearization criteria in particular a nonvanishing criterion for irjectivity of smooth maps on r sharpening the so called ratio condition is presented this result appears to be of independent interest and leads to improvements of the global linearization condition in r due to hunt su and meyer and of the global non linear observability conditions in r due to kou elliott and tarn

parallel metric tree embedding based on an algebraic view on moore bellman ford a metric tree embedding of expected stretch 1 maps a weighted n node graph g e v e to a weighted tree t e vt et t with v s vt such that for all v w v dist v w g dist v w t and e dist v w t dist v w g such embeddings are highly useful for designing fast approximation algorithms as many hard problems are easy to solve on tree instances however to date the best parallel polylog n depth algorithm that achieves an asymptotically optimal expected stretch of i o log n requires n2 work and a metric as input in this article we show how to achieve the same guarantees using polylog n depth and o m1 v work where m e e and v 0 is an arbitrarily small constant moreover one may further reduce the work to o m n1 e at the expense of increasing the expected stretch to o e 1 log n our main tool in deriving these parallel algorithms is an algebraic characterization of a generalization of the classic moore bellman ford algorithm we consider this framework which subsumes a variety of previous moore bellman ford like algorithms to be of independent interest and discuss it in depth in our tree embedding algorithm we leverage it to provide efficient query access to an approximate metric that allows sampling the tree using polylog n depth and o m work we illustrate the generality and versatility of our techniques by various examples and a number of additional results specifically we 1 improve the state of the art for determining metric tree embeddings in the congest model 2 determine a 1 e approximate metric regarding the distances in a graph g in polylogarithmic depth and o n m n1 e work and 3 improve upon the state of the art regarding the k median and the buy at bulk network design problems

a sublinear time distributed algorithm for minimum weight spanning trees this paper considers the question of identifying the parameters governing the behavior of fundamental global network problems many papers on distributed network algorithms consider the task of optimizing the running time successful when an o n bound is achieved on an n vertex network we propose that a more sensitive parameter is the network s diameter diam this is demonstrated in the paper by providing a distributed minimum weight spanning tree algorithm whose time complexity is sublinear in n but linear in diam specifically o diam n varepsilon cdot log n for varepsilon frac ln 3 ln 6 0 6131 our result is achieved through the application of graph decomposition and edge elimination by pipelining techniques that may be of independent interest

real time dynamic substructuring in a coupled oscillator pendulum system real time dynamic substructuring is a powerful testing method which brings together analytical numerical and experimental tools for the study of complex structures it consists of replacing one part of the structure with a numerical model which is connected to the remainder of the physical structure the substructure by a transfer system in order to provide reliable results this hybrid system must remain stable during the whole test a primary mechanism for destabilization of these type of systems is the delays which are naturally present in the transfer system in this paper we apply the dynamic substructuring technique to a nonlinear system consisting of a pendulum attached to a mechanical oscillator the oscillator is modelled numerically and the transfer system is an actuator the system dynamics is governed by two coupled second order neutral delay differential equations we carry out local and global stability analyses of the system and identify the delay dependent stability boundaries for this type of system we then perform a series of hybrid experimental tests for a pendulum oscillator system the results give excellent qualitative and quantitative agreement when compared to the analytical stability results

on the analysis of the double hopf bifurcation in machining processes via centre manifold reduction the single degree of freedom model of orthogonal cutting is investigated to study machine tool vibrations in the vicinity of a double hopf bifurcation point centre manifold reduction and normal form calculations are performed to investigate the long term dynamics of the cutting process the normal form of the four dimensional centre subsystem is derived analytically and the possible topologies in the infinite dimensional phase space of the system are revealed it is shown that bistable parameter regions exist where unstable periodic and in certain cases unstable quasi periodic motions coexist with the equilibrium taking into account the non smoothness caused by loss of contact between the tool and the workpiece the boundary of the bistable region is also derived analytically the results are verified by numerical continuation the possibility of transient chaotic motions in the global non smooth dynamics is shown

periodic solutions in a model of recurrent neural feedback an equation which plant used to model recurrent neural feedback with delay is analyzed to determine its periodic solution structure as a two parameter hopf bifurcation problem the model exhibits

numerical hopf bifurcation for a class of delay differential equations abstract in this paper we consider discretization of parameter dependent delay differential equations of the form x t f x t x t r we show that if the delay differential equation undergoes a hopf bifurcation then the discrete scheme undergoes a hopf bifurcation of the same type the results of this paper extend the results of our previous analysis relating to the discretization of the delay logistic equation to a wider class of problems

local computation lower and upper bounds the question of what can be computed and how efficiently is at the core of computer science not surprisingly in distributed systems and networking research an equally fundamental question is what can be computed in a distributed fashion more precisely if nodes of a network must base their decision on information in their local neighborhood only how well can they compute or approximate a global optimization problem in this paper we give the first polylogarithmic lower bound on such local computation for optimization problems including minimum vertex cover minimum connected dominating set maximum matching maximal independent set and maximal matching in addition we present a new distributed algorithm for solving general covering and packing linear programs for some problems this algorithm is tight with the lower bounds whereas for others it is a distributed approximation scheme together our lower and upper bounds establish the local computability and approximability of a large class of problems characterizing how much local information is required to solve these tasks

on approximate feedback equivalence of affine control systems as a generalization of some ideas of krener 1984 a b we introduce problems of k l and k r feedback equivalence of affine systems and relate them to the action of so called k l and k r feedback groups then using some elementary properties of jets of smooth maps we establish necessary conditions under which the groups act on a manifold of systems with open orbits this result allows us to determine a range of dimensions n m k r where n is the dimension of the state space and m the number of input within which the problems are ill posed in particular the result applies to problems of k r reduction of affine systems i e of finding a feedback transforming the kth order taylor polynomial of an affine system into the rth order one r k

a randomized linear time algorithm to find minimum spanning trees we present a randomized linear time algorithm to find a minimum spanning tree in a connected graph with edge weights the algorithm uses random sampling in combination with a recently discovered linear time algorithm for verifying a minimum spanning tree our computational model is a unit cost random access machine with the restriction that the only operations allowed on edge weights are binary comparisons

retarded differential equations retarded differential equations rdes are differential equations having retarded arguments they arise in many realistic models of problems in science engineering and medicine where there is a time lag or after effect numerical techniques for such problems may be regarded as extensions of dense output methods for ordinary differential equations odes but scalar rdes are inherently infinite dimensional with a richer structure than their ode counterparts we give background material develop a theoretical foundation for the basic numerics and give some results not previously published