first passage times in renewal and nonrenewal systems fluctuations in stochastic systems are usually characterized by full counting statistics which analyzes the distribution of the number of events taking place in the fixed time interval in an alternative approach the distribution of the first passage times i e the time delays after which the counting variable reaches a certain threshold value is studied this paper presents the approach to calculate the first passage time distribution in systems in which the analyzed current is associated with an arbitrary set of transitions within the markovian network using this approach it is shown that when the subsequent first passage times are uncorrelated there exist strict relations between the cumulants of the full counting statistics and the first passage time distribution on the other hand when the correlations of the first passage times are present their distribution may provide additional information about the internal dynamics of the system in comparison to the full counting statistics for example it may reveal the switching between different dynamical states of the system additionally i show that breaking of the fluctuation theorem for first passage times may reveal the multicyclic nature of the markovian network

constructing tables of minimum aberration pn m designs fries and hunter 1980 presented a practical algorithm for selecting standard 2 n m fractional factorial designs based on a criterion they called minimum aberration in this article some simple results are presented that enable the fries hunter algorithm to be used for a wider range of n and m and for designs with factors at p levels where p 2 is prime examples of minimum aberration 2 n m designs with resolution r 4 are given for m n m 9 a matrix is given for generating 3 n m designs with m n m 6 which have or nearly have minimum aberration

nonequilibrium thermodynamics and information theory basic concepts and relaxing dynamics thermodynamics is based on the notions of energy and entropy while energy is the elementary quantity governing physical dynamics entropy is the fundamental concept in information theory in this work starting from first principles we give a detailed didactic account on the relations between energy and entropy and thus physics and information theory we show that thermodynamic process inequalities like the second law are equivalent to the requirement that an effective description for physical dynamics is strongly relaxing from the perspective of information theory strongly relaxing dynamics govern the irreversible convergence of a statistical ensemble towards the maximally non commital probability distribution that is compatible with thermodynamic equilibrium parameters in particular markov processes that converge to a thermodynamic equilibrium state are strongly relaxing our framework generalizes previous results to arbitrary open and driven systems yielding novel thermodynamic bounds for idealized and real processes

optimal control of systems possessing symmetries it is shown that a symmetry in an optimization problem induces a decomposition of the optimal feedback control law into factors one factor can be calculated algebraically and depends only on the symmetry the other factor corresponds to a lower dimensional optimization problem this gives a priori information about the structure of the optimal feedback control law and indicates a possibly more efficient method for optimizing such systems

symmetric linear systems an application of algebraic systems theory dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations to the stability augmentation of pairs of helicopters lifting a large mass linear models for such systems display certain obvious symmetries in this paper we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems such systems are inherently related to the representation theory of algebras over fields we will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra

the structure of nonlinear control systems possessing symmetries a concept of symmetry is defined for general nonlinear control systems it is shown under various technical conditions that nonlinear control systems with symmetries admit local and or global decompositions in terms of lower dimensional subsystems and feedback loops the structure of the individual subsystems is dependent on the structure of the symmetry group for example if the symmetry group is abelian one of the subsystems is a quadrature an additional feature of the decomposition is that the state space dimensions of the subsystems sum to the state space dimension of the original system

conservation of generalized momentum maps in mechanical optimal control problems with symmetry summary in this paper a structure preserving direct method for the optimal control of mechanical systems is developed the new method accommodates a large class of one step integrators for the underlying state equations the state equations under consideration govern the motion of affine hamiltonian control systems if the optimal control problem has symmetry associated generalized momentum maps are conserved along an optimal path this is in accordance with an extension of noether s theorem to the realm of optimal control problems in the present work we focus on optimal control problems with rotational symmetries the newly proposed direct approach is capable of exactly conserving generalized momentum maps associated with rotational symmetries of the optimal control problem this is true for a variety of one step integrators used for the discretization of the state equations examples are the one step theta method a partitioned variant of the theta method and energy momentum em consistent integrators numerical investigations confirm the theoretical findings copyright 2016 john wiley sons ltd

controllability and completion of partial upper triangular matrices over rings abstract for a given partial upper triangular matrix a and a matrix b over a ring we characterize the existence of a completion ac of a such that the pair ac b is controllable in terms of irreducibility

reduction of sufficient conditions for optimal control problems with subgroup symmetry in this paper we apply symmetry reduction techniques from geometric mechanics to sufficient conditions for local optimality in optimal control problems after reinterpreting some previous results for left invariant problems on lie groups we focus on optimal control problems with subgroup symmetry for these problems the necessary conditions for optimality can be simplified by exploiting symmetries so as to reduce the number of variables needed to describe trajectories of the system we show that sufficient conditions for optimality based on the non existence of conjugate points can be simplified in an analogous way to the necessary conditions we demonstrate these simplifications by analyzing an optimal control problem that models a spinning top in a gravitational field and we give particular attention to the example of an axisymmetric sleeping top the results we derive in this paper allow us to determine which trajectories of a sleeping top are locally optimal solutions of the optimal control problem which is a new result that has not appeared in previous literature

effective fluctuation and response theory the so called fluctuation theorems pushed the study of systems far beyond equilibrium whose response to thermodynamic forces affinities is characterized by the reciprocal and the fluctuation dissipation relations all these results rely on the assumption that the observer has complete information about the system no hidden leakage to the environment exact evaluation of the thermodynamic cost of processes will an observer who has marginal information be able to perform an effective thermodynamic analysis given that such observer will only be able to establish local equilibrium by perturbing the stalling currents will he she observe equilibrium like fluctuations within the formalism of markov jump processes on finite networks we provide a broad theory of the statistical behavior of some out of many currents that flow across a system in particular 1 there exist effective affinities for which an integral fluctuation relation holds 2 at stalling i e where the marginal currents vanish a symmetrized fluctuation dissipation relation holds 3 under reasonable assumptions on the parametrization of the rates effective affinities can be operationally defined by a procedure of tuning to stalling 4 there exists a notion of marginally time reversed process which restores the full fledged fluctuation relation and reciprocity 5 there exist fluctuation relations across different levels in the hierarchy of more and more complete theories the above results apply to configuration space currents and to their phenomenological linear combinations provided certain symmetries of the effective affinities are respected a condition whose range of validity we deem the most interesting question left open to future inquiry

conservation laws in hamiitonian control systems under unmodelled dynamics utilisation pour la definition des lois de conservation de commande d un concept plus general qui comprend la consideration des quantites a la fois conservees et non conservees etude de l influence des dynamiques lineaires non modelisees sur les lois de conservation

better foldover fractions for resolution iii 2k p designs this article describes a family of resolution iiidesigns for which the usual advice regarding foldover reversing all factors is ill advised the smallest such designs have 16 runs for designs in this family alternative foldover fractions not only increase the resolution to iv but also separate some of the aliased two factor interactions although resolution iv designs obtained by reversing all factors provide fewer than half the degrees of freedom for estimating two factor interactions the recommended foldovers for designs in this class permit estimation of many more two factor interactions this result implies that designs in this class make attractive initial designs even if they are not minimum aberration

small composite designs small second order composite designs were suggested by hartley 1959 westlake 1965 provided even smaller designs for k 5 7 and 9 factors for which intricate construction methods were needed here simple designs formed using plackett and burman 1946 designs are offered for k 5 7 and 9 designs with one run fewer than westlake s for k 5 and 7 and three fewer for k 9 are feasible by deleting repeat points that occur in some of the designs

the analysis of zero dynamics of nonlinear control systems with symmetries zero dynamics of nonlinear control systems with symmetries are studied in this paper it is shown that the zero dynamics of a symmetric system is also symmetric and admits a special form of cascade decomposition a local zero dynamics is always possible to be extended to the semiglobal case the relation between the zero dynamics and the quotient system is also discussed

symmetry reduction of optimal control systems and principal connections this paper explores the role of symmetries and reduction in nonlinear control and optimal control systems the focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to obtain explicit expressions of the reduced system by exploiting the geometry in particular we show how to obtain a principal connection to be used in the reduction for various choices of symmetry groups as opposed to assuming such a principal connection is given or choosing a particular symmetry group to simplify the setting our result synthesizes some previous works on symmetry reduction of nonlinear control and optimal control systems affine and kinematic optimal control systems are of particular interest we explicitly work out the details for such systems and also show a few examples of symmetry reduction of kinematic optimal control problems

symmetries and conservation laws for hamiltonian systems with inputs and outputs a generalization of noether s theorem the definition of symmetries and conservation laws for autonomous i e without external cases hamiltonian systems are generalized to hamiltonian systems with inputs and outputs it is shown that a symmetry implies the existence of a conservation law and vice versa thereby generalizing noether s theorem for autonomous hamiltonian systems

symmetric systems structure of the state space it is shown that every module of every finite dimensional associative algebra is associated with the state space of some class of symmetric systems the general structure of symmetric systems is investigated

fluctuating currents in stochastic thermodynamics i gauge invariance of asymptotic statistics stochastic thermodynamics uses markovian jump processes to model random transitions between observable mesoscopic states physical currents are obtained from antisymmetric jump observables defined on the edges of the graph representing the network of states the asymptotic statistics of such currents are characterized by scaled cumulants in the present work we use the algebraic and topological structure of markovian models to prove a gauge invariance of the scaled cumulant generating function exploiting this invariance yields an efficient algorithm for practical calculations of asymptotic averages and correlation integrals we discuss how our approach generalizes the schnakenberg decomposition of the average entropy production rate and how it unifies previous work the application of our results to concrete models is presented in an accompanying publication

connections between two level designs of resolutions iii and v resolution iii designs are resolution iii designs in which no two factor interactions are confounded with one another they arise naturally in the search for small composite designs and were first suggested by hartley 1959 new results given here link resolution iii designs to resolution v designs enabling passage between the two types of designs to be made this means that previously untabulated resolution iii designs can be derived directly from known resolution v designs for example a hartley type composite design can be based on a 27 1 iii design derived from a 26 1 v design the usual composite design is based on a 27 1 v design double the number of factorial runs the resolution iii designs can also be usefully modified for specific industrial applications box and jones 1989 moreover the maximum number of factors it is possible to accommodate in a resolution iii design of a given size can be obtained directly from the known maximum for resolution v designs of the same size

optimal planar turns under acceleration constraints this technical note considers the problem of finding optimal trajectories for a particle moving in a 2 d plane from a given initial position and velocity to a specified terminal heading under a magnitude constraint on the acceleration the cost functional to be minimized is the integral over time of a non negative power of the particle s speed special cases of such a cost functional include travel time and path length unlike previous work on related problems variations in the magnitude of the velocity vector are allowed pontryagin s maximum principle is used to show that the optimal paths possess a special property whereby the vector that divides the velocity and acceleration vectors in a specific ratio which depends on the cost functional is a constant this property is used to characterize the optimal acceleration vector and obtain the parametric equations of the corresponding optimal paths sufficiency conditions for optimality are used to show that trajectories satisfying the necessary conditions are actually optimal if the heading change required is sufficiently small solutions of the time optimal and the length optimal problems are obtained as special cases of the general problem

pole shifting for matrices over real algebras abstract pole shifting of multivariable control system dot x ax bu over finite dimensional real algebras is studied the main results are expressed in terms of the minimal polynomial of a bf where f is a feedback