stability crossing surfaces for linear time delay systems with three delays in this article the stability of linear systems with time delays is studied the cases where the characteristic equations of the system include three delays are investigated using the geometrical relations in a normalised polynomial plane a graphical method is presented to visualise the stability domains in the space of the time delays in this space the points at which the characteristic equation has a zero on the imaginary axis the border between stability and instability regions are identified these points form several surfaces called the stability crossing surfaces this work extends the results of the previous works on the stability crossing curves defined in the two dimensional space plane of delays to a higher dimension and provides new geometric interpretations for the stability crossing conditions

convex separable optimization is not much harder than linear optimization the polynomiality of nonlinear separable convex concave optimization problems on linear constraints with a matrix with small subdeterminants and the polynomiality of such integer problems provided the inteter linear version of such problems ins polynomial is proven this paper presents a general purpose algorithm for converting procedures that solves linear programming problems the conversion is polynomial for constraint matrices with polynomially bounded subdeterminants among the important corollaries of the algorithm is the extension of the polynomial solvability of integer linear programming problems with totally unimodular constraint matrix to integer separable convex programming an algorithm for finding a e accurate optimal continuous solution to the nonlinear problem that is polynomial in log 1 e and the input size and the largest subdeterminant of the constraint matrix is also presented these developments are based on proximity results between the continuous and integral optimal solutions for problems with any nonlinear separable convex objective function the practical feature of our algorithm is that is does not demand an explicit representation of the nonlinear function only a polynomial number of function evaluations on a prespecified grid

consensus of high order multi agent systems with large input and communication delays we study in this paper the consensus problem for multi agent systems with agents characterized by high order linear systems with time delays in both the communication network and inputs provided that the open loop dynamics of the agents is not exponentially unstable but may be polynomially unstable and the communication topology contains a directed spanning tree a truncated predictor feedback approach is established to solve the consensus problem it is shown that if the delays are constant and exactly known the consensus problems can be solved by both full state feedback and observer based output feedback protocols for arbitrarily large yet bounded delays if it is further assumed that the open loop dynamics of the agents only contains zero eigenvalues the delays are allowed to be time varying and unknown numerical examples are worked out to illustrate the effectiveness of the proposed approaches

combinatorial n fold integer programming and applications many fundamental mathsf np hard problems can be formulated as integer linear programs ilps a famous algorithm by lenstra solves ilps in time that is exponential only in the dimension of the program and polynomial in the size of the ilp that algorithm became a ubiquitous tool in the design of fixed parameter algorithms for mathsf np hard problems where one wishes to isolate the hardness of a problem by some parameter however in many cases using lenstra s algorithm has two drawbacks first the run time of the resulting algorithms is often double exponential in the parameter and second an ilp formulation in small dimension cannot easily express problems involving many different costs inspired by the work of hemmecke et al math program 137 1 2 ser a 325 341 2013 we develop a single exponential algorithm for so called combinatorialn fold integer programs which are remarkably similar to prior ilp formulations for various problems but unlike them also allow variable dimension we then apply our algorithm to many relevant problems problems like closest string swap bribery weighted set multicover and several others and obtain exponential speedups in the dependence on the respective parameters the input size or both unlike lenstra s algorithm which is essentially a bounded search tree algorithm our result uses the technique of augmenting steps at its heart is a deep result stating that in combinatorial n fold ips existence of an augmenting step implies existence of a local augmenting step which can be found using dynamic programming our results provide an important insight into many problems by showing that they exhibit this phenomenon and highlights the importance of augmentation techniques

a consensus protocol under directed communications with two time delays and delay scheduling this paper studies a consensus protocol over a group of agents driven by second order dynamics the communication among members of the group is assumed to be directed and affected by two rationally independent time delays one in the position and the other in the velocity information channels these delays are unknown but considered to be constant and uniform throughout the system the stability of the consensus protocol is studied using a simplifying factorisation procedure and deploying the cluster treatment of characteristic roots ctcr paradigm this effort results in a unique depiction of the exact stability boundaries in the domain of the delays the ctcr requires the knowledge of the potential stability switching loci exhaustively within this domain the creation of these loci is an important contribution of this work it is done in a new surrogate coordinate system called the spectral delay space the relative stability of the system that is the speed to reach consensus is also investigated fo

a new method for computing delay margins for stability of linear delay systems this note is concerned with stability properties of linear time invariant delay systems we consider delay systems of retarded type modeled both as a high order scalar differential difference equation and as a set of first order differential difference equations expressed in state space form we provide a computational method that can be used to compute a delay interval such that the system under consideration is stable for all delay values that lie in the computed interval this method requires computing only the eigenvalues and generalized eigenvalues of certain constant matrices and it can be implemented efficiently based on this method we further state a simple necessary and sufficient condition concerning stability independent of delay for each of the two types of the models

an exact method for the stability analysis of time delayed linear time invariant lti systems a general class of linear time invariant systems with time delay is studied recently they attracted considerable interest in the systems and control community the complexity arises due to the exponential type transcendental terms in their characteristic equation the transcendentality brings infinitely many characteristic roots which are cumbersome to elaborate as evident from the literature a number of methodologies have been suggested with limited ability to assess the stability in the parametric domain of time delay this study offers an exact structured and robust methodology to bring a closure to the question at hand ultimately we present a unique explicit analytical expression in terms of the system parameters which not only reveals the stability regions pockets in the domain of time delay but it also declares the number of unstable characteristic roots at any given pocket the method starts with the determination of all possible purely imaginary resonant characteristic roots for any positive time delay to achieve this a simplifying substitution is used for the transcendental terms in the characteristic equation it is proven that the number of such resonant roots for a given dynamics is finite each one of these roots is created by infinitely many time delays which are periodically distributed an interesting property is also claimed next that the root crossing directions at these locations are invariant with respect to the delay and dependent only on the crossing frequency these two unique findings facilitate a simple and practical stability method which is the highlight of the work

consensus conditions of continuous time multi agent systems with time delays and measurement noises this work is concerned with stochastic consensus conditions of multi agent systems with both time delays and measurement noises for the case of additive noises we develop some necessary conditions and sufficient conditions for stochastic weak consensus by estimating the differential resolvent function for delay equations by the martingale convergence theorem we obtain necessary conditions and sufficient conditions for stochastic strong consensus for the case of multiplicative noises we consider two kinds of time delays appeared in the measurement term and the noise term respectively we first show that stochastic weak consensus with the exponential convergence rate implies stochastic strong consensus then by constructing degenerate lyapunov functional we find the sufficient consensus conditions and show that stochastic consensus can be achieved by carefully choosing the control gain according to the noise intensities and the time delay in the measurement term

an improved procedure in detecting the stability robustness of systems with uncertain delay a very efficient and reliable shortcut is explained here on the procedure which resolves the stability robustness of lti dynamics against an uncertain delay this procedure reduces the numerical complexity of the solution by an order of magnitude this note is in response to a number of user requests on the practicality of the mentioned methodology

polynomial methods for separable convex optimization in unimodular linear spaces with applications we consider the problem of minimizing a separable convex objective function over the linear space given by a system mx 0 with m a totally unimodular matrix in particular this generalizes the usual minimum linear cost circulation and cocirculation problems in a network and the problems of determining the euclidean distance from a point to the perfect bipartite matching polytope and the feasible flows polyhedron we first show that the idea of minimum mean cycle canceling originally worked out for linear cost circulations by goldberg and tarjan j assoc comput mach 36 1989 pp 873 886 and extended to some other problems t r ervolina and s t mccormick discrete appl math 46 1993 pp 133 165 a frank and a v karzanov technical report rr 895 m laboratoire artemis imag universite joseph fourier grenoble france 1992 t ibaraki a v karzanov and h nagamochi private communication 1993 m hadjiat technical report groupe intelligence artificielle faculte des sciences de luminy marseille france 1994 can be generalized to give a combinatorial method with geometric convergence for our problem we also generalize the computationally more efficient cancel and tighten method we then consider objective functions that are piecewise linear pure and piecewise quadratic or piecewise mixed linear and quadratic and we show how both methods can be implemented to find exact solutions in polynomial time strongly polynomial in the piecewise linear case these implementations are then further specialized for finding circulations and cocirculations in a network we finish by showing how to extend our methods to find optimal integer solutions to linear spaces of larger fractionality and to the case when the objective functions are given by approximate oracles

updating the inverse of a matrix the sherman morrison woodbury formulas relate the inverse of a matrix after a small rank perturbation to the inverse of the original matrix the history of these fomulas is presented and various applications to statistics networks structural analysis asymptotic analysis optimization and partial differential equations are discussed the sherman morrison woodbury formulas express the inverse of a matrix after a small rank perturbation in terms of the inverse of the original matrix this paper surveys the history of these formulas and we examine some applications where these formulas are helpful

complete stability robustness of third order lti multiple time delay systems a unique procedure is presented in this paper for a complete stability robustness of the third order lti multiple time delay systems lti mtds the uniqueness of the treatment is simply due to the fact that there is no comparable methodology presently in the literature the end result of this procedure is an exhaustive and precise determination of the stable regions in the domain of time delays the backbone of the method is a novel framework called the cluster treatment of characteristic roots ctcr ctcr is constructed over two fundamental propositions the first proposition claims the existence of a bounded number of so called kernel curves where the only imaginary characteristic roots occur the second proposition is on an interesting directional invariance property of the crossing tendencies of these imaginary roots for simplicity of conveyance and without loss of generality the number of time delays is taken as two in this document the new methodology is expandable to higher order dynamics with more time delays than two as the authors intend to demonstrate in future publications publications

negative cycle detection algorithms we study the problem of finding a negative length cycle in a network an algorithm for the negative cycle problem combines a shortest path algorithm and a cycle detection strategy we survey cycle detection strategies study various combinations of shortest path algorithms and cycle detection strategies and find the best combinations one of out discoveries is that a cycle detection strategy of tarjan greatly improves computational performance of a classical shortest path algorithm making it competitive with the fastest known algorithms on a wide range of problems as a part of out study we develop problem families for testing negative cycle algorithms

a polynomial time descent method for separable convex optimization problems with linear constraints we propose a polynomial algorithm for a separable convex optimization problem with linear constraints we do not make any additional assumptions about the structure of the objective function except for polynomial computability that is the objective function can be non differentiable the running time of our algorithm is polynomial in the size of the input consisting of an instance of the problem and the accuracy with which the problem is to be solved our algorithm uses an oracle for solving auxiliary systems of linear inequalities this oracle can be any polynomial algorithm for linear programming

leader following consensus problem with a varying velocity leader and time varying delays abstract in this paper we study a leader following consensus problem for a multi agent system with a varying velocity leader and time varying delays here the interaction graph among the followers is switching and balanced at first we propose a neighbor based rule for every agent to track a leader whose states may not be measured in addition we consider the convergence analysis of this multi agent system under two different conditions the connection between the followers and the leader is time invariant and time varying for the first case a novel decomposition method is introduced to facilitate the convergence analysis by utilizing a lyapunov krasovskii functional we obtain sufficient conditions for uniformly ultimately boundedness of the tracking errors finally two simulations are also presented to illustrate our theoretical results

consensus analysis with large and multiple communication delays using spectral delay space concept in this study we consider the consensus problem for a group of second order agents interacting under a fixed undirected communication topology communication lines are affected by two rationally independent delays the first delay is assumed to be in the position information channels whereas the second delay is in the velocity information exchange the delays are assumed to be large and uniform throughout the entire network the stability analysis of such systems becomes quickly intractable as the number of agents increases and the delays enlarge to resolve this dilemma we first reduce the complexity of the problem dramatically by decomposing the characteristic equation of the system into a set of second order factors then we assess the stability of the resulting subsystems exactly and exhaustively in the domain of the time delays using the cluster treatment of characteristic roots ctcr paradigm ctcr requires the determination of all the potential stability switching loci in the domain of the d

the composition factors of the functor of permutation modules the grothendieck group of permutation modules for a finite group g becomes a biset functor when g is allowed to vary all the composition factors of this biset functor are determined

solving the convex cost integer dual network flow problem in this paper 1 we consider an integer convex optimization problem where the objective function is the sum of separable convex functions that is of the form i j eq f ij w ij iep b i i the constraints are similar to those arising in the dual of a minimum cost flow problem that is of the form i j w ij i j q with lower and upper bounds on variables letn p m q andu be the largest magnitude in the lower and upper bounds of variables we call this problemthe convex cost integer dual network flow problem in this paper we describe several applications of the convex cost integer dual network flow problem arising in a dial a ride transit problem inverse spanning tree problem project management and regression analysis we develop network flow based algorithms to solve the convex cost integer dual network flow problem we show that using the lagrangian relaxation technique the convex cost integer dual network flow problem can be transformed into a convex cost primal network flow problem where each cost function is a piecewise linear convex function with integer slopes its special structure allows the convex cost primal network flow problem to be solved ino nmlog n2 m log nu time this time bound is the same time needed to solve the minimum cost flow problem using the cost scaling algorithm and is also is best available time bound to solve the convex cost integer dual network flow problem

atlas of finite groups maximal subgroups and ordinary characters for simple groups this atlas covers groups from the families of the classification of finite simple groups recently updated incorporating corrections

a strongly polynomial algorithm for linear systems having a binary solution this paper proposes a strongly polynomial algorithm which either finds a solution of a linear system ax b 0 x 1 or correctly decides that the system has no 0 1 solutions the algorithm can be used as the basis for the construction of a polynomial algorithm for linear programming

on bouc s and thevenaz s conjectures on b groups abstract bouc proposed the following conjecture a finite group g is nilpotent if and only if its largest quotient b group g is nilpotent and thevenaz proposed another conjecture a finite group g is solvable if and only if its largest quotient b group g is solvable bouc has proven that his conjecture holds when g is solvable in this paper we consider some cases when g is not solvable let s be a nonabelian simple group except the chevalley groups a n q d n q e 6 q and a n 2 q if the group g has exactly one composition factor isomorphic to s then g is not solvable of course is not nilpotent that means we prove the conjectures in these cases

exact stability analysis of second order leaderless and leader follower consensus protocols with rationally independent multiple time delays abstract an investigation of double integrator agents with directed asymmetric consensus protocols and multiple rationally independent time delays is presented in this paper from two novel perspectives first we complement the group consensus literature on crucial stability analysis using a recent technique called the cluster treatment of characteristic roots ctcr for the first time on this class of time delayed systems the ctcr paradigm is pursued after a block diagonalization mode decoupling transformation on the system this treatment produces some unique stability tables for the dynamics in the space of the delays which are non conservative and exhaustive second a novel concept of spectral delay space is presented as an overture to the ctcr for the determination of the complete set of stability crossing switching hypersurfaces in the delay space examples are provided to display the strengths and efficiency of this new stability analysis mechanism

computational aspects of two segment separable programming recursive separable programming algorithms based on local two segment approximations are described for the solution of separable convex programs details are also given for the computation of lower bounds on the optimal value by both a primal and a dual approach and these approaches are compared computational comparisons of the methods are provided for a variety of test problems including a water supply application with more than 600 constraints and more than 900 variables and an econometric modelling problem with more than 200 variables

a conjecture on b groups in this note i propose the following conjecture a finite group g is nilpotent if and only if its largest quotient b group beta g is nilpotent i give a proof of this conjecture under the additional assumption that g be solvable i also show that this conjecture is equivalent to the following the kernel of restrictions to nilpotent subgroups is a biset subfunctor of the burnside functor

a polynomial projection algorithm for linear feasibility problems we propose a polynomial algorithm for linear feasibility problems the algorithm represents a linear problem in the form of a system of linear equations and non negativity constraints then it uses a procedure which either finds a solution for the respective homogeneous system or provides the information based on which the algorithm rescales the homogeneous system so that its feasible solutions in the unit cube get closer to the vector of all ones in a polynomial number of calls to the procedure the algorithm either proves that the original system is infeasible or finds a solution in the relative interior of the feasible set

technical communique on delay robustness analysis of a simple control algorithm in high speed networks this paper focuses on the robustness analysis of a simple second order control algorithm for data transfer in high speed networks the model under consideration derived using a fluid approximation technique can be found in izmailov siam j contr optimiz 34 1996 1767 the novelty of the approach lies in characterizing the stability of the scheme in the delay parameter space where the delays correspond to the control time interval and to the round trip time respectively thus we shall compute some delay insensitive measures for the algorithm which give upper and lower bounds for the uncertainty in the knowledge of the round trip times

an e relaxation method for separable convex cost generalized network flow problems cover title the extended abstract of this article appeared in the proceedings of the 5th international ipco conference vancouver june 1996 p 1

optimal objective function approximation for separable convex quadratic programming we present an optimal piecewise linear approximation method for the objective function of separable convex quadratic programs the method provides guidelines on how many grid points to use and how to position them for a piecewise linear approximation if the error induced by the approximation is to be bounded a priori

an exact method for the stability analysis of linear consensus protocols with time delay this technical note presents a methodology for the stability analysis of linear consensus protocols with time delayed communications second order agent dynamics with a fixed and undirected communication topology and uniform delays are considered this class of group dynamics is very complex and is not fully explored to date the proposed technique takes advantage of the general structure of the control protocols in performing a state transformation that allows a decomposition of the characteristic equation into a set of factors these factors distribute the imprint of the delay in the characteristic equation in a much simpler form to achieve the stability analysis in parts the procedure also prepares the characteristic equation for the deployment of the cluster treatment of characteristic roots paradigm a recent method which declares the stability features of the system for various compositions of the time delay and other control parameters in order to show the effectiveness of this approach it is applied to different consensus protocols under the assumptions of fixed and undirected communication topologies and uniform communication time delays