Multi-terminal Networks Research Articles

Image segmentation approach of combining fuzzy clustering and graph cuts

This paper proposed an image segmentation method combining fuzzy C-means clustering and graph cuts.Based on graph cuts,considering the pixel space,establish a global energy function concerning labels,and make the FCM clustering center as terminal to found a multi-terminal network,get the global minimum of the energy function or the approximate minimum of the label function by the α expansion moving algorithm.Re-demarcate all pixels between all classes and get the right targets.Experimental results show that the method has great improvement in accuracy,performance and noise immunity.

Impact of classical forces and decoherence in multiterminal Aharonov-Bohm networks

Multi-terminal Aharonov-Bohm (AB) rings are ideal building blocks for quantum networks (QNs) thanks to their ability to map input states into controlled coherent superpositions of output states. We report on experiments performed on three-terminal GaAs/Al_(x)Ga_(1-x)As AB devices and compare our results with a scattering-matrix model including Lorentz forces and decoherence. Our devices were studied as a function of external magnetic field (B) and gate voltage at temperatures down to 350 mK. The total output current from two terminals while applying a small bias to the third lead was found to be symmetric with respect to B with AB oscillations showing abrupt phase jumps between 0 and pi at different values of gate voltage and at low magnetic fields, reminiscent of the phase-rigidity constraint due to Onsager-Casimir relations. Individual outputs show quasi-linear dependence of the oscillation phase on the external electric field. We emphasize that a simple scattering-matrix approach can not model the observed behavior and propose an improved description that can fully describe the observed phenomena. Furthermore, we shall show that our model can be successfully exploited to determine the range of experimental parameters that guarantee a minimum oscillation visibility, given the geometry and coherence length of a QN.

Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network

In this paper a new approach is presented to reduce vibrations for one- and two-dimensional mechanical structures, as beam or thin plates, by means of several piezoelectric transducers shunted with a proper electric network system. The governing equations of the whole system are coupled to each other through the direct and converse piezoelectric effect. More in detail, the mechanical equations are expressed in accordance with the modal theory considering n vibration modes and the electrical equations reduce to the one-dimensional charge equation of electrostatics for each of n considered piezoelectric transducers. In this electromechanical system, a shunting electric device forms an electric subsystem working as multi degrees of freedom (dof’s) damped vibration absorber for the mechanical subsystem. Herein, it is introduced a proper transformation of the electric coordinates in order to approximate the governing equations for the whole shunted system with n uncoupled, single mode piezoelectric shunting systems that can be readily damped by the methods reported in literature. A further numerical optimisation problem on the spatial distribution of the piezoelectric elements allows to achieve a better performance. Numerical case studies of two relevant systems, a double clamped beam and a fully clamped plate, allow to take into account issues relative to the proposed approach. Laboratory experiments carried out in real time on a beam clamped at both ends consent to validate the proposed technique.

Myopic Coding in Multiterminal Networks

This paper investigates the interplay between cooperation and achievable rates in multi-terminal networks. Cooperation refers to the process of nodes working together to relay data toward the destination. There is an inherent tradeoff between achievable information transmission rates and the level of cooperation, which is determined by how many nodes are involved and how the nodes encode/decode the data. We illustrate this trade-off by studying information-theoretic decode-forward based coding strategies for data transmission in multi-terminal networks. Decode-forward strategies are usually discussed in the context of omniscient coding, in which all nodes in the network fully cooperate with each other, both in encoding and decoding. In this paper, we investigate myopic coding, in which each node cooperates with only a few neighboring nodes. We show that achievable rates of myopic decode-forward can be as large as that of omniscient decode-forward in the low SNR regime. We also show that when each node has only a few cooperating neighbors, adding one node into the cooperation increases the transmission rate significantly. Furthermore, we show that myopic decode-forward can achieve non-zero rates as the network size grows without bound.

Geometric algebra: a multivectorial proof of Tellegen's theorem in multiterminal networks

A generalised and multivectorial proof of Tellegen's theorem in multiterminal systems is presented using a new power multivector concept defined in the frequency domain. This approach permits in nonsinusoidal/linear and nonlinear situations formulating Tellegen's theorem in a novel complex-multivector representation, similar to Steinmetz's phasor model, based on complex numbers and limited to the purely sinusoidal case. In this sense, a suitable notation of voltage and current complex-vectors, associated to the elements and nodes of the network, is defined for easy development to Kirchhoff's laws in this environment. A numerical example illustrates the clear advantages of the suggested proof.

Optimum synthesis of discrete capacitated networks with multi-terminal commodity flow requirements

Network design problems arise in a wide range of applied areas including telecommunications, computer networks, and transportation. In this paper, we address the following discrete capacitated multi-terminal network design problem. Given a connected digraph G = (V,A), a set of L potential facilities to be installed on each arc, and a set of K multi-terminal (non-simultaneous) commodity flow requirements, the problem is to find a set of facilities to install in order to route the K nonsimultaneous flows while minimizing the total fixed plus variable costs. We describe an exact procedure for solving this problem based on Benders decomposition. Our algorithm includes several features that significantly improve the efficiency of the basic approach. Computational results attest to the efficacy of the proposed algorithm, which can solve medium- to large-scale problems to optimality.

Revisiting parametric multi-terminal problems: Maximum flows, minimum cuts and cut-tree computations

Given an undirected network, the multi-terminal network flows analysis consists in determining the all pairs maximum flow values. In this paper, we consider an undirected network in which some edge capacities are allowed to vary and we analyze the impact of such variations on the all pairs maximum flow values. We first provide an efficient algorithm for the single parametric capacity case, and then propose a generalization to the case of multiple parametric capacities. Moreover, we provide a study on Gomory–Hu cut-tree relationships.

On code design for the Slepian-Wolf problem and lossless multiterminal networks

A Slepian-Wolf coding scheme for compressing two uniform memoryless binary sources using a single channel code that can achieve arbitrary rate allocation among encoders was outlined in the work of Pradhan and Ramchandran. Inspired by this work, we address the problem of practical code design for general multiterminal lossless networks where multiple memoryless correlated binary sources are separately compressed and sent; each decoder receives a set of compressed sources and attempts to jointly reconstruct them. First, we propose a near-lossless practical code design for the Slepian-Wolf system with multiple sources. For two uniform sources, if the code approaches the capacity of the channel that models the correlation between the sources, then the system will approach the theoretical limit. Thus, the great advantage of this design method is its possibility to approach the theoretical limits with a single channel code for any rate allocation among the encoders. Based on Slepian-Wolf code constructions, we continue with providing practical designs for the general lossless multiterminal network which consists of an arbitrary number of encoders and decoders. Using irregular repeat-accumulate and turbo codes in our designs, we obtain the best results reported so far and almost reach the theoretical bounds.

An Identification Problem for Multiterminal Networks: Solving for the Traffic Matrix from Input-Output Measurements

We consider the problem of determining the unknown characteristics of a _random routing strategy_ from _end-to-end_ measurements. More specifically, we construct aMarkov chain that models the traffic of messages in a multiterminal network consisting of _input, intermediate_, and _output_ terminals. The topology of the network is assumed to be known, but the Markovian routing strategy is not known. We solve the problem of determining the unknown one-step transition probability matrix of our random walk from input-output measurements of "travel time." We give explicit inversion formulas (up to a natural gauge) in a nontrivial example. The result holds for a large (but not arbitrary) class of multiterminal networks, many of which are indicated here. The networks that we display here are constructed in a canonical fashion from certain graphs. Some of these graphs as well as the way to go from graphs to networks are also displayed. One example of a graph for which our method works is the edge graph of a hypercube in any dimension.

Power of Balanced Poly-Phase Systems: An Application of the Multi-Terminal Network Power Theorem

The deduction methods of power formulas of balanced three-phase receivers seem to limit its reach to Y and Δ connections. Easy and general deduction procedures, with no dependence on the internal constitution of the receivers, are revealed here. Thus the complete range of these formulas is shown.

IFORS' Operational Research Hall of Fame

International Transactions in Operational ResearchVolume 12, Issue 5 p. 539-543 Free Access IFORS' Operational Research Hall of Fame Ralph E. Gomory, Ralph E. GomorySearch for more papers by this author Ralph E. Gomory, Ralph E. GomorySearch for more papers by this author First published: 07 September 2005 https://doi.org/10.1111/j.1475-3995.2005.00524.xCitations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Selected original works Aráoz, J., Evans, L., Gomory, R.E., Johnson, E.L., 2003. Cyclic group and knapsack facets. Mathematical Programming Series B, 96, 377– 408. Gilmore, P.C., Gomory, R.E., 1961. A linear programming approach to the cutting-stock problem. Operations Research, 9, 849– 859. Gilmore, P.C., Gomory, R.E., 1963. A linear programming approach to the cutting-stock problem: Part II. Operations Research, 11, 863– 888. Gilmore, P.C., Gomory, R.E., 1964. Sequencing a one state-variable machine: a solvable case of the traveling salesman problem. Operations Research, 12, 665– 679. Gilmore, P.C., Gomory, R.E., 1965. Multistage cutting stock problems of two and more dimensions. Operations Research, 13, 94– 120. Gilmore, P.C., Gomory, R.E., 1966. The theory and computation of knapsack functions. Operations Research, 14, 1045– 1074. Gomory, R.E., 1958. Outline of an algorithm for integer solutions to linear programs. Bulletin of the American Mathematical Society, 64, 275– 278. Gomory, R.E., 1960. Solving linear programming problems in integers. In R. Bellman, M. Hall (eds) Combinatorial Analysis: Proceedings of Symposia in Applied Mathematics X. American Mathematical Society, Providence, Rhode Island, pp. 211– 215. Gomory, R.E., 1963. An algorithm for integer solutions to linear programs. In R.L. Graves, P. Wolfe (eds) Recent Advances in Mathematical Programming. McGraw-Hill, New York, pp. 269– 302. Gomory, R.E., 1965. On the relations between integer and noninteger solutions to linear programs. Proceedings of the National Academy of Sciences of the United States of America, 53, 260– 265. Gomory, R.E., 1967. Faces of an integer polyhedron. Proceedings of the National Academy of Sciences of the United States of America, 57, 16– 18. Gomory, R.E., 1969. Some polyhedra related to combinatorial problems. Linear Algebra and its Applications, 2, 451– 558. Gomory, R.E., Baumol, W.J., 1960. Integer programming and pricing. Econometrica, 28, 521– 550. Gomory, R.E., Baumol, W.J., 2000. Global Trade and Conflicting National Interests. MIT Press, Cambridge, MA. Gomory, R.E., Hu, T.C., 1961. Multi-terminal network flows. Journal of SIAM, 9, 551– 570. Gomory, R.E., Johnson, E.L., 1972a. Some continuous functions related to corner polyhedra. Mathematical Programming, 3, 23– 85. Gomory, R.E., Johnson, E.L., 1972b. Some continuous functions related to corner polyhedra II. Mathematical Programming, 3, 359– 389. Gomory, R.E., Johnson, E.L., 1973. The group problem and subadditive functions. In T.C. Hu, S.M. Robinson (eds) Mathematical Programming. Academic Press, New York, pp. 157– 184. Gomory, R.E., Johnson, E.L., 2003. T-space and cutting planes. Mathematical Programming Series B, 96, 341– 375. Gomory, R.E., Johnson, E.L., Evans, L., 2003. Corner polyhedra and their connection with cutting planes. Mathematical Programming Series B, 96, 321– 339. Gomory, R.E., Richmond, D.E., 1951. Boundaries for the limit cycle of van der Pol's equation. Quarterly of Applied Mathematics, 9, 205– 209. Biographical material Gomory, R.E., 2002. Early integer programming. Operations Research, 50, 78– 81. Wilson, D.M., 2004. At the frontiers of science and technology. Williams Alumni Review, Fall, 12– 15. Citing Literature Volume12, Issue5September 2005Pages 539-543 ReferencesRelatedInformation

Optimum Synthesis of Multi-Terminal Networks

Optimum Synthesis of Multi-Terminal Networks

Weak localization in multiterminal networks of diffusive wires.

We study the quantum transport through networks of diffusive wires connected to reservoirs in the Landauer-Büttiker formalism. The elements of the conductance matrix are computed by the diagrammatic method. We recover the combination of classical resistances and obtain the weak localization corrections. For arbitrary networks, we show how the Cooperon must be properly weighted over the different wires. Its nonlocality is clearly analyzed. We predict a new geometrical effect that may change the sign of the weak localization correction in multiterminal geometries.

Multi-Terminal Network Power Measurement

This paper presents a simple and general theory on power absorbed by multi-terminal networks and the way to measure it, which has direct application to unification of active and reactive power measurement procedures of polyphase loads. This approach to the subject is highly efficient, not only for its simplicity, but also because it eliminates all particular demonstrations or proofs of different measurement methods, with consequent time and effort savings for students. It also offers absolute certainty about the scope of every power measurement procedure and their possible variations.

Superposition and Constructions of Graphs Without Nowhere-zero k-flows

Using multi-terminal networks we build methods on constructing graphs without nowhere-zero group- and integer-valued flows. In this way we unify known constructions of snarks (nontrivial cubic graphs without edge- 3-colorings, or equivalently, without nowhere-zero 4-flows) and provide new ones in the same process. Our methods also imply new complexity results about nowhere-zero flows in graphs and state equivalences of Tutte’s 3- and 5-flow conjectures with formally weaker statements.

A nonlinear inverse problem inspired by three‐dimensional diffuse tomography: Explicit formulas

AbstractWe use time of flight information to obtain explicit inversion formulas for a simple model of optical tomography. This can be considered as an instance of a more general nonlinear inversion problem for multi‐terminal networks. In this case the network is nonplanar with lots of cycles but the underlying physical model yields a highly structured situation. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 198–203, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10031

A cut-tree-based approach for clustering machine cells in the bidirectional linear flow layout

This paper considers the joint cell clustering-layout problem where machine cells are to be located along the popular bidirectional linear material flow layout. The joint problem seeks to minimize the actual intercell flow cost instead of the typical measure that minimizes the number of intercell movements when the layout problem is excluded from the clustering process. Owing to the computational difficulty, a three-phase approach is proposed using the cut-tree-network model to solve this joint problem. The cell clustering and layout problem is transformed into a multi-terminal network flow model. A cut tree is constructed and partitioned into a number of subgraphs via the selected primary path. Each subgraph is a clustered cell and their locations are assigned to the layout sequence by comparing the cut capacities. Thus, the proposed approach concurrently determines the machine cells and their relative sequences in the bidirectional linear flow layout. Computational procedures are illustrated and additional experiments, with data adapted from the literature, are performed to demonstrate the viability of the approach.

A unified domination approach for reliability analysis of networks with arbitrary logic in vertices

The concept of a probabilistic graph G has been used as a universal model for network reliability. Most of the literature on this subject concentrates on computing various reliability measures (such as k-terminal reliability or all-terminal reliability) which are the probability that vertices of G can communicate with other specified vertices. Primarily, this paper provides a common theoretical framework for addressing k-terminal reliability problems. To this end, it extends the model admitting vertex functions of G to be arbitrary monotone Boolean functions: in this case G is called a monotone (S,t)-graph. In such graphs the signal passability across a node is carried out in accordance with collections of signals delivered on the node inputs from other ones, the collections are subjected to some logic principle realized by a Boolean function. Monotone (S,t)-graphs include all known classes of directed multi-terminal network reliability models. The main result of this paper is the reliability expression for computing the probability of an acyclic monotone (S,t)-graph G being operational. The expression uses the local domination parameters introduced here. That reduces the system level of consideration to the element level, providing a unifying understanding of the combinatorial nature of some results based on the domination theory and developed earlier for ordinary networks.

On Monte Carlo Estimates in Network Reliability

The paper considers representations of network reliability measures as the mean value of a random variable defined on the trajectories of a certain Markov process and investigates utility of such formulae for Monte Carlo (MC) estimating. Such an MC estimator is called (ε,δ)-polynomial if its relative error is less than ε with probability >1 – δ, for any sample size equal to or greater than a polynomial of ε-1, δ-1, and the size of the network. One of the main results: The suggested MC estimator for the disconnectedness probability of a multiterminal network is (ε,δ)-polynomial, under a certain natural condition on the edge failure probabilities. The method applies also to estimating the percolation critical point and certain equilibrium characteristics of renewal networks.

Towards equitable distribution via proportional equity constraints

We propose a new approach to the formulation of models for solving problems of equitable distribution. Equity is achieved by the use of “proportional equity constraints” which require that each recipient must receive ashare of the total distribution which falls within a prespecified range. The algorithmic implications of this new approach are illustrated using two mathematical models. We consider the problem of maximizing total flow in a multiterminal network with proportional equity constraints. An efficient algorithm for solving this problem is provided. As a further application, we show that the introduction of such constraints still permits easy solutions for the linear knapsack problem.