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This paper provides a parametrization of optimal anisotropic controllers for linear discrete time invariant systems. The controllers to be designed are limited by causal dynamic output-feedback control laws. The obtained solution depends on several adjustable parameters that determine the specific type of controller, and is of the form of a system of the Riccati equations relating to a -optimal controller for a system formed by a series connection of the original system and the worst-case generating filter corresponding to the maximum value of the mean anisotropy of the external disturbance. [ABSTRACT FROM AUTHOR]

The design problem of an adaptive state observer for linear time-varying systems is considered. Some parameters of a time-varying plant are assumed to be unknown numbers multiplied by known functions of time. The approach proposed below is based on identification methods of adaptation. In other words, the main idea is to transform a mathematical model in the form of a linear time-varying differential equation to a static linear regression model containing unknown parameters. In this case, both the unknown parameters of the plant and its initial conditions are the unknown parameters of the regression model under consideration. Further, standard gradient methods or other parametric identification approaches are used to estimate the unknown parameters of the regression model and to construct the observer. The results of computer simulations illustrate the effectiveness of the new state observer design method. [ABSTRACT FROM AUTHOR]

It is proven that the transitivity property of commutativity is always valid for second-order linear time-varying analog systems whether their initial states are zero or not. Throughout the study, it is assumed that the subsystems considered cannot be obtained from each other by any feed-forward and feedback structure. The results are well validated by MATLAB simulations. [ABSTRACT FROM AUTHOR]

We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using "rectangular vision". We prove a sharp bound on the minimum number of point guards required to cover the gallery in terms of the minimum number of vertical mobile guards and the minimum number of horizontal mobile guards required to cover the gallery. Furthermore, we show that the latter two numbers can be computed in linear time. [ABSTRACT FROM AUTHOR]

We present space-efficient algorithms for computing cut vertices in a given graph with n vertices and m edges in linear time using O(n+min{m,nloglogn}) bits. With the same time and using O(n+m) bits, we can compute the biconnected components of a graph. We use this result to show an algorithm for the recognition of (maximal) outerplanar graphs in O(nloglogn) time using O(n) bits. [ABSTRACT FROM AUTHOR]

Usually in the context of the anisotropy-based robust performance analysis stochastic systems with zero initial condition are investigated. In this paper we extend this analysis and consider a linear discrete time invariant system under random disturbances and with the nonzero initial condition. In accordance with the basic postulates of the anisotropy-based control theory the disturbance attenuation capabilities of system are quantified by the anisotropic generalized gain which is defined as the largest root mean square gain of the system with respect to a random input and the nonzero initial condition, anisotropy of which is bounded by a given nonnegative parameter a. [ABSTRACT FROM AUTHOR]

This study presents a new approach for system simplification and control. This approach is based on the behaviour of growth and reproduction of weed plants namely Invasive Weed Optimization (IWO). The micro system/simplified model of large scale single-input single-output (SISO) continuous time system is attained by optimizing a predefined objective/fitness function by weed optimization algorithm. Performance of the proposed approach is analysed in terms of transient and frequency response parameters such as rise time, peak time, maximum overshoot, gain margin and phase margin, etc. This analysis reveals that the results of this proposed approach are commensurable with other available approaches. Additionally, the application of proposed approach is explored in control of a micro system based on system simplification. The control action is obtained by achieving the unknown parameters of the proportional integral derivative (PID) controller using IWO. Further, the concept of error minimization is being utilised to obtain parameters of PID controller. The simulation results reveal that the PID controller designed by proposed approach has no affect on change of the system. The PID controller for a micro system (second order) exhibits satisfactory performance on the first order simplified system, therefore changing the system does not affect the performance of PID controller. As the proposed approach is being utilised for both micro system's simplification as well as in controller design, therefore it may be applied in various applications of Microsystems's analysis and design. [ABSTRACT FROM AUTHOR]

In this paper, we study the weighted region problem (WRP) which is to compute a shortest path in a weighted partitioning of a plane. Recent results show that WRP is not solvable in any algebraic computation model over the rational numbers. Therefore, it is unlikely that WRP can be solved in polynomial time. Research has thus focused on determining approximate solutions for WRP. Approximate solutions for WRP typically show qualitatively different behaviors. We first formulate two qualitative criteria for weighted shortest paths. Then, we show how to produce a path that is quantitatively close-to-optimal and qualitatively satisfactory. More precisely, we propose an algorithm to transform any given approximate linear path into a linear path with the same (or shorter) weighted length for which we can prove that it satisfies the required qualitative criteria. This algorithm has a linear time complexity in the size of the given path. At the end, we explain our experiments on some triangular irregular networks (TINs) from Earth’s terrain. The results show that using the proposed algorithm, on average, 51% in query time and 69% in memory usage could be saved, in comparison with the existing method. [ABSTRACT FROM AUTHOR]

Given a set of n sticks of various (not necessarily different) lengths, what is the largest length so that we can cut k equally long pieces of this length from the given set of sticks? We analyze the structure of this problem and show that it essentially reduces to a single call of a selection algorithm; we thus obtain an optimal linear-time algorithm. This algorithm also solves the related envy-free stick-division problem, which Segal-Halevi et al. (ACM Trans Algorithms 13(1):1-32, 2016. ISSN: 15496325. 10.1145/2988232) recently used as their central primitive operation for the first discrete and bounded envy-free cake cutting protocol with a proportionality guarantee when pieces can be put to waste. [ABSTRACT FROM AUTHOR]

Research on space efficient graph algorithms, particularly for st-connectivity, has a long history including the celebrated polynomial time, O(lg n) bits1 algorithm in undirected graphs by Reingold J. JACM. 55(4) (2008), and polynomial time, n/2Θ(lgn) bits algorithm in directed graphs by Barnes et al. SICOMP. 27(5), 1273-1282 (1998). Recent works by Asano et al. ISAAC (2014) and Elmasry et al. STACS (2015), reconsidered classical fundamental graph algorithms focusing on improving the space complexity. Elmasry et al. gave, among others, an implementation of breadth first search (BFS) in a graph G with n vertices and m edges, taking the optimal O(m + n) time using O(n) bits improving the naïve O(n lg n) bits implementation. Similarly, Asano et al. provided space efficient implementations for performing depth first search (DFS) in a graph G. We continue this line of work focusing on improving the space requirement for implementing a few classical graph algorithms. Our first result is a simple data structure that can maintain any subset S of a universe of u elements using just u + o(u) bits and supports in constant time, apart from the standard insert, delete and membership queries, the operation findany that finds and returns any element of the set (or outputs that the set is empty). It can also enumerate all elements present currently in the set in no particular order in O(k + 1) time where k is the number of elements currently belonging to the set. While this data structure supports a weaker set of operations than that of Elmasry et al. STACS (2015), it is simple, more space efficient and is sufficient to support a BFS implementation optimally in O(m + n) time using at most 2n + o(n) bits. Later, we further improve the space requirement of BFS to at most n lg 3 + o(n) bits albeit with a slight increase in running time to O(m lg nf(n)) time where f(n) is any extremely slow growing function of n, and the o term in the space is a function of f(n). We also discuss a similar time-space tradeoff result for finding a minimum weight spanning tree of a weighted (bounded by polynomial in n) undirected graph using n + O(n/f(n)) bits and O(m lg nf(n)) time, for any function f(n) such that 1 ≤ f(n) ≤ n. For DFS in a graph G, we provide an implementation taking O(m + n) time and O(n lg m/n) bits. This partially answers at least for sparse graphs, a question asked by Asano et al. ISAAC (2014) whether DFS can be performed in O (m + n) time and using O(n) bits, and also simultaneously improves the DFS result of Elmasry et al. STACS (2015). Using our DFS algorithm and other careful implementations, we show how one can also test for biconnectivity, 2-edge connectivity, and find cut vertices and bridges of a given undirected graph within the same time and space bounds; earlier classical linear time algorithms for these problems used Ω(n lg n) bits of space. [ABSTRACT FROM AUTHOR]

The distinction between an overlap in species daily activity patterns and proximate co-occurrence of species for a location and time due to behavioral attraction or avoidance is critical when addressing the question of species co-occurrence. We use data from a dense grid of camera traps in a forest in central North Carolina to inform about proximate co-occurrence. Camera trigger times are recorded when animals pass in front of the camera’s field of vision. We view the data as a point pattern over time for each species and model the intensities driving these patterns. These species-specific intensities are modeled jointly in linear time to preserve the notion of co-occurrence. We show that a multivariate log-Gaussian Cox process incorporating both circular and linear time provides a preferred choice for modeling occurrence of forest mammals based on daily activity rhythms. Model inference is obtained under a hierarchical Bayesian framework with an efficient Markov chain Monte Carlo sampling algorithm. After model fitting, we account for imperfect detection of individuals by the camera traps by incorporating species-specific detection probabilities that adjust estimates of occurrence and co-occurrence. We obtain rich inference including assessment of the probability of presence of one species in a particular time interval given presence of another species in the same or adjacent interval, enabling probabilities of proximate co-occurrence. Our results describe the ecology and interactions of four common mammals within this suburban forest including their daily rhythms, responses to temperature and rainfall, and effects of the presence of predator species. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

We consider a linear time-invariant homogeneous system of first-order ordinary differential equations with a noninvertible matrix multiplying the derivative of the unknown vector function and with perturbed coefficients. We introduce a class of perturbations of the coefficient matrices of the system and determine conditions on the perturbations of this class under which they do not affect the internal structure of the system. We obtain sufficient conditions for the robust stability of the system under such perturbations. [ABSTRACT FROM AUTHOR]

In this paper modified cuckoo search (MCS) algorithm is considered to develop reduced order model (ROM) of higher-order linear time-invariant systems. Firstly, the MCS algorithm has been employed to minimize the integral square error (ISE) between original and proposed ROM to obtain its unknown coefficients. Five systems of different order are considered to obtain their reduced order model. Finally, various performance indices, such as ISE, integral of absolute and integral of time multiplied by absolute error, have been estimated to reveal the efficacy of the proposed model. Also, time and frequency response characteristics of original higher-order model are compared with the proposed MCS-based and some of other existing techniques-based ROM available in the literature. Furthermore, the results are compared in terms of time response specifications such as rise time (tr) in second, settling time (ts) in second and maximum peak overshoot (Mp) in percentage. It is revealed that the response of the proposed MCS-based ROM is much closer to the response of the original higher-order system. [ABSTRACT FROM AUTHOR]

A simultaneous embedding (with fixed edges) of two graphs G1 and G2 with common graph G=G1∩G2 is a pair of planar drawings of G1 and G2 that coincide on G. It is an open question whether there is a polynomial-time algorithm that decides whether two graphs admit a simultaneous embedding (problem Sefe). In this paper, we present two results. First, a set of three linear-time preprocessing algorithms that remove certain substructures from a given Sefe instance, producing a set of equivalent Sefe instances without such substructures. The structures we can remove are (1) cutvertices of the union graph G∪=G1∪G2, (2) most separating pairs of G∪, and (3) connected components of G that are biconnected but not a cycle. Second, we give an O(n3)-time algorithm solving Sefe for instances with the following restriction. Let u be a pole of a P-node μ in the SPQR-tree of a block of G1 or G2. Then at most three virtual edges of μ may contain common edges incident to u. All algorithms extend to the sunflower case, i.e., to the case of more than two graphs pairwise intersecting in the same common graph. [ABSTRACT FROM AUTHOR]

The dynamics of ancient civilisations according to credited historians can be explained by means of a simple linear time-invariant (LTI) feedback model whose loop only consists of a first-order process and a pure time delay. It is shown that, despite its simplicity, this model can give rise to a variety of responses, either oscillatory or aperiodic, such as those envisaged by A. Toynbee. Since modern civilisations are characterised by fast parameter variations, their description calls instead for a time-variant model. Simulations with the linear parameter-varying model obtained from the aforementioned LTI model by letting its parameter vary are carried out to show the influence of different scenarios on the system response. Even if this model is elementary, it is believed that it may serve as a stimulating “tool for thought” in the ever-popular debate on the growth and decline of civilisations. [ABSTRACT FROM AUTHOR]

The linear-time ham-sandwich cut algorithm of Lo, Matoušek, and Steiger for bi-chromatic finite point sets in the plane works by appropriately selecting crossings of the lines in the dual line arrangement with a set of well-chosen vertical lines. We consider the setting where we are not given the coordinates of the point set, but only the orientation of each point triple (the order type) and give a deterministic linear-time algorithm for the mentioned sub-algorithm. This yields a linear-time ham-sandwich cut algorithm even in our restricted setting. We also show that our methods are applicable to abstract order types. [ABSTRACT FROM AUTHOR]

A graph with n vertices is 1-planar if it can be drawn in the plane such that each edge is crossed at most once, and is optimal if it has the maximum of $$4n-8$$ edges. We show that optimal 1-planar graphs can be recognized in linear time. Our algorithm implements a graph reduction system with two rules, which can be used to reduce every optimal 1-planar graph to an irreducible extended wheel graph. The graph reduction system is non-deterministic, constraint, and non-confluent. [ABSTRACT FROM AUTHOR]

We present a necessary and sufficient condition for existence of a contractible, non-separating and non-contractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces. We also present algorithms to construct such cycles whenever it exists where one of them is linear time and another is exponential time algorithm. [ABSTRACT FROM AUTHOR]

In this study, a new technique is suggested for simplification of linear time-invariant systems. Motivated by optimization and various system simplification techniques available in the literature, the proposed technique is formulated using Cuckoo search in combination with Lévy flight and Eigen spectrum analysis. The efficacy and powerfulness of the new technique is illustrated by three benchmark systems considered from previously published work and the results are compared in terms of performance indices. [ABSTRACT FROM AUTHOR]

We investigate cellular automata as acceptors for formal languages. In particular, we consider real-time one-way cellular automata ( $$\text{OCA}$$ ) with the additional property that during a computation any cell of the $$\text{OCA}$$ has the ability to dissolve itself, so-called shrinking one-way cellular automata ( $$\text{SOCA}$$ ). It turns out that real-time $$\text{SOCA}$$ are more powerful than real-time $$\text{OCA}$$ , since they can accept certain linear-time $$\text{OCA}$$ languages. On the other hand, linear-time $$\text{OCA}$$ are more powerful than real-time $$\text{SOCA}$$ , which is witnessed even by a unary language. Additionally, a construction is provided that enables real-time $$\text{SOCA}$$ to accept the reversal of real-time iterative array languages. Finally, restricted real-time $$\text{SOCA}$$ are investigated. We distinguish two limitations for the dissolving of cells. One restriction is to bound the total number of cells that are allowed to dissolve by some function. In this case, an infinite strict hierarchy of language classes is obtained. The second restriction is inspired by an approach to limit the amount of nondeterminism in $$\text{OCA}$$ . Compared with the first restriction, the total number of cells that may dissolve is still unbounded, but the number of time steps at which a cell may dissolve is bounded. The possibility to dissolve is allowed only in the first k time steps, where $$k\ge 0$$ is some constant. For this mode of operation an infinite, tight, and strict hierarchy of language classes is obtained as well. [ABSTRACT FROM AUTHOR]

This paper proposes a novel filtering strategy characterized by an impulsive differential system. It provides an alternative solution to the problem of $$L_2-L_\infty $$ filtering for two kinds of network-based linear time-invariant systems. The presented method highlights two features, 'plug and play' and 'always feasible,' because it is simple and does not need to solve any complex constrained optimization problems. For measurable and unmeasurable system states, two different filter frameworks are presented, respectively. The proposed filtering strategy could guarantee the asymptotic stability of the filtering error system, while ensuring an $$L_2-L_\infty $$ performance. At the same time, the relationship between the $$L_2-L_\infty $$ disturbance attenuation level bound $$\gamma $$ and the maximum time-delay upper limit $$\tau _\mathrm{m}$$ is given. Finally, three illustrative examples are given to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Despite many algorithms for embedding graphs on unbounded grids, only a few results on embedding graphs on restricted grids have been published. In this paper, we study the problem of embedding paths and cycles on solid grid graphs. We show that a cycle of length k is unit-length embeddable on a solid grid graph G if k is an even integer between four and the length of the longest cycle of G. In addition, our result shows that a path of length k is unit-length embeddable on G, between its two given vertices s and t, if $$k\le L$$ and $$k\equiv L (\mathrm{mod}\ 2)$$ , in which L is the length of the longest path between s and t. Our presented two algorithms show that such embeddings can be found in linear time for cycles and quadratic time for paths, with respect to the size of graph G. In the case of rectangular grid graphs, the running time of the algorithms can be improved to O( k) and O $$(k^2)$$ , respectively. In addition, we extend our results to $$m\times n\times o$$ 3D grids. A application of our result is in the interconnection network mapping in parallel processing. [ABSTRACT FROM AUTHOR]

Consideration was given to a model of recursive conveyor process which is an extension of the classical conveyor. A method for efficient calculation of the process time characteristics in a linear time was described. On the basis of the calculated characteristics, the scheduling of recursive conveyor processes comes to calculation of analytical expressions. The proposed model can be used in the APS-systems and MES-systems of control of production, as well as for scheduling in some traditional fields of application of the scheduling theory. [ABSTRACT FROM AUTHOR]

An inversion problem for a linear time-invariant MIMO system with possibly unstable zero dynamics is considered. Sufficient conditions for the invertibility of such systems are given, and an algorithm for invertor synthesis is proposed. The results are extended to time-delay systems with commensurable delays. [ABSTRACT FROM AUTHOR]

We propose a linear time and linear space algorithm which constructs a minimal sequence of operations rearranging one structure (directed graph of cycles and paths) into another. Structures in such a sequence may have a varying number of edges; a list of operations is fixed and includes deletion and insertion of a fragment of a structure. We give a complete proof that the algorithm is correct, i.e., finds the corresponding minimum. [ABSTRACT FROM AUTHOR]

Let P be a closed simple polygon with n vertices. For any two points in P, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in P. The geodesic center of P is the unique point in P that minimizes the largest geodesic distance to all other points of P. In 1989, Pollack et al. (Discrete Comput Geom 4(1): 611-626, 1989) showed an $$O(n\log n)$$ -time algorithm that computes the geodesic center of P. Since then, a longstanding question has been whether this running time can be improved. In this paper we affirmatively answer this question and present a deterministic linear-time algorithm to solve this problem. [ABSTRACT FROM AUTHOR]

This paper proposes a new similarity measure that is invariant to global and local affine illumination changes. Unlike existing methods, its computational complexity is very low. When used for stereo correspondence estimation, its computational complexity is linear in the number of image pixels and disparity searching range. It also outperforms the current state of the art similarity measures in terms of accuracy on the Middlebury benchmark (with radiometric differences). [ABSTRACT FROM AUTHOR]

Handling delays and uncertain parameters in control systems is an interesting and challenging class of problems. In this paper, we consider the problem of 'bounded-input bounded-output stabilizing' a class of single-input single-output, linear time-varying plant models with a time-delay margin as large as desired and a considerable amount of uncertainty in the input matrix of the state-space model. The proposed controller, while periodic and mildly nonlinear, is of low complexity; it tolerates slow variations in the delay and the elements of the input matrix as well as occasional jumps in these parameters, and guarantees that the effect of the initial condition decays exponentially to zero, even in the presence of noise. [ABSTRACT FROM AUTHOR]

Domino tileability is a classical problem in Discrete Geometry, famously solved by Thurston for simply connected regions in nearly linear time in the area. In this paper, we improve upon Thurston's height function approach to a nearly linear time in the perimeter. [ABSTRACT FROM AUTHOR]

Coefficient diagram method is a controller design technique for linear time-invariant systems. This design procedure occurs into two different domains: an algebraic and a graphical. The former is closely paired to a conventional pole placement method and the latter consists on a diagram whose reading from the plotted curves leads to insights regarding closed-loop control system time response, stability and robustness. The controller structure has two degrees of freedom and the design process leads to both low overshoot closed-loop time response and good robustness performance regarding mismatches between the real system and the design model. This article presents an overview on this design method. In order to make more transparent the presented theoretical concepts, examples in M atlabcode are provided. The included code illustrates both the algebraic and the graphical nature of the coefficient diagram design method. [ABSTRACT FROM AUTHOR]

An improved method is proposed to determine the reduced order model of large scale linear time invariant system. The dominant poles of the low order system are calculated by clustering method. The selection of pole to the cluster point is based on the contributions of each pole in redefining time moment and redefining Markov parameters. The coefficients of the numerator polynomial for reduced model are obtained using a factor division algorithm. This method is computationally efficient and keeps up the stability and input output characteristic of the original arrangement. [ABSTRACT FROM AUTHOR]

Based on an improved $$H_\infty $$ performance index, the method of designing a reliable adaptive $$H_\infty $$ controller with quantized state is addressed for the time-varying delayed system in this paper. On the basis of online estimates of actuator faults, the controller parameters are updated automatically to compensate the influence of actuator faults on the system while the desired improved $$H_\infty $$ performance is preserved. A Lyapunov function candidate is constructed to prove that the closed-loop system is asymptotically stable. And the existing sufficient conditions of the controller are proved to be less conservative. The gains of the controller and the parameters of the adaptive law are co-designed and obtained in terms of solutions to a set of linear matrix inequalities. Finally, two numerical examples are given to illustrate that the proposed method is more effective than the previous methods for time-varying delayed systems. [ABSTRACT FROM AUTHOR]

We extend and unify most known results about guarding orthogonal polygons by introducing the same-sign diagonal graphs of a convex quadrangulation and applying results about vertex covers for graphs. Our approach also yields new theorems and often guarantees two disjoint vertex guard sets of relatively small cardinality. For instance, an orthogonal polygon on n vertices has two disjoint vertex guard sets of cardinality at most $$\lfloor n/4\rfloor $$ . We give new proofs of Aggarwal's one-hole theorem and the orthogonal fortress theorem. We prove that an orthogonal polygon with n vertices and any number of holes can be protected by at most $$\lfloor (17n-8)/52\rfloor $$ vertex guards, improving the best known bound of $$\lfloor n/3\rfloor $$ . Also, an orthogonal polygon with n vertices and h holes can be protected by $$\lfloor (n+2h)/3\rfloor $$ guarded guards, which is best possible when $$n\ge 16h$$ . Moreover, for orthogonal fortresses with n vertices, $$\lfloor (n+6)/3\rfloor $$ guarded guards are always sufficient and sometimes necessary. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new self-stabilizing algorithm for minimal weakly connected dominating sets (called algorithm $$\mathtt{MWCDS}$$ ). For an arbitrary connected graph with $$n$$ nodes, algorithm $$\mathtt{MWCDS}$$ terminates in $$O(n)$$ steps using a synchronous daemon. The space requirement at each node is $$O(\log n)$$ bits. In the literature, the best reported stabilization time for a minimal weakly connected dominating set algorithm is $$O(nmA)$$ under a distributed daemon, where $$m$$ is the number of edges and $$A$$ is the number of moves to construct a breadth-first tree. [ABSTRACT FROM AUTHOR]

We obtain the linear time-dependent constants of motion of the parametric amplifier and use them to determine the evolution of a general two-mode Gaussian state in the tomographic-probability representation. By means of the discretization of the continuous variable density matrix, we calculate the von Neumann and linear entropies to measure the entanglement properties between the modes of the amplifier. We compare the obtained results for the nonlocal correlations with those associated to a linear map of discretized symplectic Gaussian-state tomogram onto a qubit tomogram. We use this qubit portrait procedure to establish Bell-type inequalities, which provide a necessary condition to determine the separability of quantum states, which can be evaluated through homodyne detection. We define the other no-signaling nonlocal correlations through the portrait procedure for noncomposite systems. [ABSTRACT FROM AUTHOR]

Most of the physical systems can be represented by mathematical models. The mathematical procedure of system modeling often leads to a comprehensive description of a process in the form of higher-order differential equations which are difficult to use either for analysis or for controller synthesis. It is, therefore, useful and sometimes necessary to find the possibility of some equations of the same type but of lower order that may be considered to adequately reflect almost all essential characteristics of the system under consideration. This paper proposes a new method for order reduction of higher-order linear time invariant systems based on stability equation method and particle swarm optimization algorithm. Reduced-order model will definitely be stable if the original model is stable. The superiority of the proposed method is illustrated by numerical examples of single-input, single-output systems and multiple-input and multiple-output systems. The results are compared with well-known methods available in the literature. [ABSTRACT FROM AUTHOR]

Discussed are different types of high resolving mass spectrographs and spectrometers. In detail outlined are (1) magnetic and electric sector field mass spectrographs, which are the oldest systems, (2) Penning Trap mass spectrographs and spectrometers, which have achieved very high mass-resolving powers, but are technically demanding (3) time-of-flight mass spectrographs using high energy ions passing through accelerator rings, which have also achieved very high mass-resolving powers and are equally technically demanding, (4) linear time-of-flight mass spectrographs, which have become the most versatile mass analyzers for low energy ions, while the even higher performing multi-pass systems have only started to be used, (5) orbitraps, which also have achieved remarkably high mass-resolving powers for low energy ions. [ABSTRACT FROM AUTHOR]

We consider the output stabilization problem for a linear time-independent system. We show that if the system output is zero, y( t) ≡ 0, then, for the stabilization of the entire state vector, the sufficient condition of stability of the zero dynamics can be replaced by the boundedness of the system input (provided that the characteristic polynomial of the zero dynamics has no eigenvalues on the imaginary axis). [ABSTRACT FROM AUTHOR]

Infill walls are commonly used in RC frame structures but are neglected in the structural analysis. It is well known that infill walls could have a significant effect on the structural performance of RC frames under seismic actions, as recently occurred in Italy during the L'Aquila event; furthermore, in many cases, the damage to infill walls is due to out-of-plane actions that can pose a risk to human life (falling of heavy parts). The current paper addresses the behavior of out-of-plane infill walls by conducting parametric linear dynamic time-history analyses. The scope of the parametric study is to evaluate the seismic demand of out-of-plane infill walls by considering the variation of the walls' properties and the position in the building. Finally, the code provisions for evaluating the seismic action on the infill walls by equivalent static forces are examined and compared with the analytical results from the detailed dynamic analysis. [ABSTRACT FROM AUTHOR]

A class of linear time-delay systems with periodic coefficients and a large parameter is studied. We establish conditions under which the zero solution is asymptotically stable. This result allows us to study the asymptotic stability of the zero solution to the time-delay systems without spectral methods and Lyapunov-Krasovskii functionals. [ABSTRACT FROM AUTHOR]

We consider the problem of asymptotic analysis of the zeros of a sampled system of a linear time-invariant continuous system as the sampling period decreases. We show that for a continuous prototype system with delay the limits of a part of the model's zeros are roots of certain polynomials whose coefficients are determined by the relative order of the prototype system and delay. In the special case of zero delay these polynomials coincide with Euler polynomials. Zeros of these generalized Euler polynomials are localized: we show that they are all simple and negative, and that they move monotonically between the zeros of classical Euler polynomials as the fractional part of the delay divided by the sampling period grows. Our results lead to sufficient and 'almost necessary' conditions for the stable invertible of the discrete model for all sufficiently small values of the sampling period. [ABSTRACT FROM AUTHOR]

We consider the problem of mapping digital data encoded on a quantum register to analog amplitudes in parallel. It is shown to be unlikely that a fully unitary polynomial-time quantum algorithm exists for this problem; NP becomes a subset of BQP if it exists. In the practical point of view, we propose a nonunitary linear-time algorithm using quantum decoherence. It tacitly uses an exponentially large physical resource, which is typically a huge number of identical molecules. Quantumness of correlation appearing in the process of the algorithm is also discussed. [ABSTRACT FROM AUTHOR]

A graph is 1-planar if it can be embedded in the plane with at most one crossing per edge. It is known that the problem of testing 1-planarity of a graph is NP-complete. In this paper, we study outer-1-planar graphs. A graph is outer-1-planar if it has an embedding in which every vertex is on the outer face and each edge has at most one crossing. We present a linear time algorithm to test whether a given graph is outer-1-planar. The algorithm can be used to produce an outer-1-planar embedding in linear time if it exists. [ABSTRACT FROM AUTHOR]

The response of a linear time-invariant (LTI) system to harmonic input generates a harmonic output with constant frequency but varying magnitude and phase. Many structural dynamic systems have been modeled as linear time-varying periodic (LTP) systems. Previous studies have reported that the response of an LTP system to an exponential input establishes an infinite number of frequencies. These studies have presented a new, exponentially modulated periodic signal space and a corresponding harmonic transfer function as useful tools in the operational modal analysis of LTP systems. In consideration of this new approach, this study mainly identifies the frequencies of a typical LTP system, such as a beam that is subject to the intermittent passage of moving masses. Upon obtaining the harmonic transfer function for the beam-moving mass system, conventional frequency domain methods for LTI systems are used to derive the frequency characteristics of the LTP system from the system response. These methods include the peak-picking method. As expected in an LTP system, an infinite number of pseudo-natural frequencies resonate in the beam-moving mass system. [ABSTRACT FROM AUTHOR]

In this paper we analyze approximation of stable linear time-invariant systems, like the Hilbert transform, by sampling series for bandlimited functions in the Paley-Wiener space PW. It is known that there exist systems and functions such that the approximation process is weakly divergent, i.e., divergent for certain subsequences. Here we strengthen this result by proving strong divergence, i.e., divergence for all subsequences. Further, in case of divergence, we give the divergence speed. We consider sampling at Nyquist rate as well as oversampling with adaptive choice of the kernel. Finally, connections between strong divergence and the Banach-Steinhaus theorem, which is not powerful enough to prove strong divergence, are discussed. [ABSTRACT FROM AUTHOR]

This paper considers some synthesis issues for SISO LTI systems. It is shown that direct application of universal methods (such as the two-Riccati approach or the LMI technique) appears impossible in degenerate situations without noisy measurements. [ABSTRACT FROM AUTHOR]

We derive a linear system of equations governing the interaction of water waves with partially or totally submerged freely floating structures in a two-layer fluid. We establish conditions for the stability of equilibrium and, by considering time-harmonic motions, rewrite the problem as a spectral boundary-value problem consisting of a differential equation and an algebraic system, coupled through boundary conditions. We give also a suitable variational formulation for the problem and provide examples of configurations where the problem admits only the trivial solution. [ABSTRACT FROM AUTHOR]

In this note, we obtain some necessary and sufficient conditions for the controllability and observability in a linear time-varying control system with piecewise constant state variables. The controllability results can be understood in terms of classical control systems on intervals [ k, k+1] with $k\in\mathbb{Z}$. We have preferred to use a global treatment instead of the reduction to a discrete equation. We also derive some results for the linear time-invariant case. Illustrative examples are presented. [ABSTRACT FROM AUTHOR]

Evaluation of text chunking is revisited. The proposed method tries to analyze the errors made by a chunker and formulates an evaluation strategy that brings out the strength and weakness of a chunker in a better way than the existing precision, recall and F score based methods or their variants do. A tree-matching based algorithm of linear time complexity is designed, analyzed, and illustrated by giving examples. Correctness of the algorithm is checked by using a chunker and a set of test sentences. [ABSTRACT FROM AUTHOR]

A drawing of a graph is a monotone drawing if for every pair of vertices u and v there is a path drawn from u to v that is monotone in some direction. In this paper we investigate planar monotone drawings in the fixed embedding setting, i.e., a planar embedding of the graph is given as part of the input that must be preserved by the drawing algorithm. In this setting we prove that every planar graph on n vertices admits a planar monotone drawing with at most two bends per edge and with at most 4 n−10 bends in total; such a drawing can be computed in linear time and requires polynomial area. We also show that two bends per edge are sometimes necessary on a linear number of edges of the graph. Furthermore, we investigate subclasses of planar graphs that can be realized as embedding-preserving monotone drawings with straight-line edges. In fact, we prove that biconnected embedded planar graphs and outerplane graphs always admit such drawings, and describe linear-time drawing algorithms for these two graph classes. [ABSTRACT FROM AUTHOR]