Algorithm for positive realization of transfer functions

The aim of this brief is to present a finite-step algorithm for the positive realization of a rational transfer function H(z). In comparision with previously described algorithms we emphasize that we do not make an a priori assumption on (but, instead, include a finite step procedure for checking) the non- negativity of the impulse response sequence of H(z). For primitive transfer functions a new method for reducing the pole order of the dominant pole is also proposed

An Accelerated Chow and Liu Algorithm: Fitting Tree Distributions to High Dimensional Sparse Data

Chow and Liu introduced an algorithm for fitting a multivariate distribution with a tree (i.e. a density model that assumes that there are only pairwise dependencies between variables) and that the graph of these dependencies is a spanning tree. The original algorithm is quadratic in the dimesion of the domain, and linear in the number of data points that define the target distribution $P$. This paper shows that for sparse, discrete data, fitting a tree distribution can be done in time and memory that is jointly subquadratic in the number of variables and the size of the data set. The new algorithm, called the acCL algorithm, takes advantage of the sparsity of the data to accelerate the computation of pairwise marginals and the sorting of the resulting mutual informations, achieving speed ups of up to 2-3 orders of magnitude in the experiments

Sheet-metal press line parameter tuning using a combined DIRECT and Nelder-Mead algorithm

It is a great challenge to obtain an efficient algorithm for global optimisation of nonlinear, nonconvex and high dimensional objective functions. This paper shows how the combination of DIRECT and Nelder-Mead algorithms can improve the efficiency in the parameter tuning of a sheet-metal press line. A combined optimisation algorithm is proposed that determines and utilises all local optimal points from DIRECT algorithm as Nelder-Mead starting points. To reduce the total optimisation time, all Nelder-Mead optimisations can be executed in parallel. Additionally, a Collision Inspection Method is implemented in the simulation model to reduce the evaluation time. Altogether, this results in an industrially useful parameter tuning method. Improvements of an increased production rate of 7% and 40% smoother robot motions have been achieved

Extended Dijkstra algorithm and Moore-Bellman-Ford algorithm

Study the general single-source shortest path problem. Firstly, define a path function on a set of some path with same source on a graph, and develop a kind of general single-source shortest path problem (GSSSP) on the defined path function. Secondly, following respectively the approaches of the well known Dijkstra's algorithm and Moore-Bellman-Ford algorithm, design an extended Dijkstra's algorithm (EDA) and an extended Moore-Bellman-Ford algorithm (EMBFA) to solve the problem GSSSP under certain given conditions. Thirdly, introduce a few concepts, such as order-preserving in last road (OPLR) of path function, and so on. And under the assumption that the value of related path function for any path can be obtained in $M(n)$ time, prove respectively the algorithm EDA solving the problem GSSSP in $O(n^2)M(n)$ time and the algorithm EMBFA solving the problem GSSSP in $O(mn)M(n)$ time. Finally, some applications of the designed algorithms are shown with a few examples. What we done can improve both the researchers and the applications of the shortest path theory.Comment: 25 page

Algorithm for efficient symbolic analysis of large analogue circuits

An algorithm is presented that generates simplified symbolic expressions for the small-signal characteristics of large analogue circuits. The expressions are approximated while they are computed, so that only the most significant terms are generated which remain in the final expression. This principle leads to dramatic savings in CPU time and memory compared to existing techniques, significantly increasing the maximum size of circuits that can be analysed. By taking into account a range for the value of a circuit parameter rather than one single number the generated symbolic expressions are also generally valid

Algorithm for Mesoscopic Advection-Diffusion

In this paper, an algorithm is presented to calculate the transition rates between adjacent mesoscopic subvolumes in the presence of flow and diffusion. These rates can be integrated in stochastic simulations of reaction-diffusion systems that follow a mesoscopic approach, i.e., that partition the environment into homogeneous subvolumes and apply the spatial stochastic simulation algorithm (spatial SSA). The rates are derived by integrating Fick's second law over a single subvolume in one dimension (1D), and are also shown to apply in three dimensions (3D). The proposed algorithm corrects the derived rates to ensure that they are physically meaningful and it is implemented in the AcCoRD simulator (Actor-based Communication via Reaction-Diffusion). Simulations using the proposed method are compared with a naive mesoscopic approach, microscopic simulations that track every molecule, and analytical results that are exact in 1D and an approximation in 3D. By choosing subvolumes that are sufficiently small, such that the Peclet number associated with a subvolume is sufficiently less than 2, the accuracy of the proposed method is comparable with the microscopic method, thus enabling the simulation of advection-reaction-diffusion systems with the spatial SSA.Comment: 12 pages, 9 figures. Submitted to IEEE Transactions on NanoBioscienc

Human vs. Algorithm

We consider the roles of algorithm and human and their inter-relationships. As a vehicle for some of our ideas we describe an empirical investigation of software professionals using analogy-based tools and unaided search in order to solve various prediction problems. We conclude that there exist a class of software engineering problems which might be characterised as high value and low frequency where the human-algorithm interaction must be considered carefully if they are to be successfully deployed in industry

The CONEstrip algorithm

Uncertainty models such as sets of desirable gambles and (conditional) lower previsions can be represented as convex cones. Checking the consistency of and drawing inferences from such models requires solving feasibility and optimization problems. We consider finitely generated such models. For closed cones, we can use linear programming; for conditional lower prevision-based cones, there is an efficient algorithm using an iteration of linear programs. We present an efficient algorithm for general cones that also uses an iteration of linear programs