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Usha Kulshreshtha - One of the best experts on this subject based on the ideXlab platform.
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Hamiltonian Path integral and brst formulations of the vector schwinger model with a photon mass term with faddeevian regularization
International Journal of Theoretical Physics, 2016Co-Authors: Usha Kulshreshtha, Daya Shankar Kulshreshtha, J P VaryAbstract:Recently (in a series of papers) we have studied the vector Schwinger model with a photon mass term describing one-space one-time dimensional electrodynamics with mass-less fermions in the so-called standard regularization. In the present work, we study this model in the Faddeevian regularization (FR). This theory in the FR is seen to be gauge-non-invariant (GNI). We study the Hamiltonian and Path integral quantization of this GNI theory. We then construct a gauge-invariant (GI) theory corresponding to this GNI theory using the Stueckelberg mechanism and recover the physical content of the original GNI theory from the newly constructed GI theory under some special gauge-choice. Further, we study the Hamiltonian, Path integral and Becchi-Rouet-Stora and Tyutin formulations of the newly constructed GI theory under appropriate gauge-fixing conditions.
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Hamiltonian Path integral and brst formulations of large n scalar qcd _ 2 on the light front and spontaneous symmetry breaking
European Physical Journal C, 2015Co-Authors: Usha Kulshreshtha, Daya Shankar Kulshreshtha, J P VaryAbstract:Recently Grinstein, Jora, and Polosa have studied a theory of large- $$N$$ scalar quantum chromodynamics in one space and one time dimension. This theory admits a Bethe–Salpeter equation describing the discrete spectrum of quark–antiquark bound states. They consider gauge fields in the adjoint representation of $$SU(N)$$ and scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. The theory could possibly provide a good field theoretic framework for the description of a large class of diquark–antidiquark (tetra-quark) states. Recently we have studied the light-front quantization of this theory without a Higgs potential. In the present work, we study the light-front Hamiltonian, Path integral, and BRST formulations of the theory in the presence of a Higgs potential. The light-front theory is seen to be gauge invariant, possessing a set of first-class constraints. The explicit occurrence of spontaneous symmetry breaking in the theory is shown in unitary gauge as well as in the light-front ’t Hooft gauge.
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light front Hamiltonian Path integral and brst formulations of the chern simons higgs theory under appropriate gauge fixing
Physica Scripta, 2009Co-Authors: Usha Kulshreshtha, Daya Shankar Kulshreshtha, J P VaryAbstract:The light-front Hamiltonian, Path integral and BRST formulations of the Chern–Simons–Higgs theory in (2+1) dimensions are investigated under appropriate gauge fixing.
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gauge invariant reformulation of the vector schwinger model with a photon mass term and its Hamiltonian Path integral and brst formulations
International Journal of Modern Physics A, 2007Co-Authors: Usha Kulshreshtha, Daya Shankar KulshreshthaAbstract:Using the Stueckelberg formalism, we construct a gauge-invariant version of the vector Schwinger model (VSM) with a photon mass term studied by one of us recently. This model describes two-dimensional massive electrodynamics with massless fermions, where the left-handed and right-handed fermions are coupled to the electromagnetic field with equal couplings. This model describing the 2D massive electrodynamics becomes gauge-noninvariant (GNI). This is in contrast to the case of the massless VSM which is a gauge-invariant (GI) theory (as a consequence of demanding the regularization for the theory to be GI). In this work we first construct a GI theory corresponding to this model describing the 2D massive electrodynamics, using the Stueckelberg formalism and then we recover the physical contents of the original GNI theory studied earlier, under some special gauge choice. We then study the Hamiltonian, Path integral and BRST formulations of this GI theory under appropriate gauge-fixing. The theory presents a new class of models in the 2D quantum electrodynamics with massless fermions but with a photon mass term.
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Hamiltonian Path integral and brst formulations of the chern simons higgs theory in the broken symmetry phase
Physica Scripta, 2007Co-Authors: Usha KulshreshthaAbstract:The Hamiltonian, Path integral and BRST formulations of the Chern–Simons–Higgs theory in two-space one-time dimensions are investigated under appropriate gauge-fixing conditions, in the broken (or frozen) symmetry phase, where the phase (xμ) of the complex matter field Φ(xμ) carries the charge degree of freedom of the complex matter field and is, in fact, akin to the Goldstone boson.
Swaroop Darbha - One of the best experts on this subject based on the ideXlab platform.
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approximation algorithms for a heterogeneous multiple depot Hamiltonian Path problem
American Control Conference, 2011Co-Authors: S Yadlapalli, Jungyun Bae, Sivakumar Rathinam, Swaroop DarbhaAbstract:In this article, we present the first approximation algorithm for a routing problem that is frequently encountered in the motion planning of Unmanned Vehicles (UVs). The considered problem is a variant of a Multiple Depot-Terminal Hamiltonian Path Problem and is stated as follows: There is a collection of m UVs equipped with different sensors on-board and there are n targets to be visited by them collectively. There are restrictions on the targets of the following type: (1) A target may be visited by any UV, (2) a target must be visited only by a subset of UVs (with appropriate on-board sensor) and (3) a target may not be visited by a subset of UVs (as the set of on-board sensors on the UV may not be suitable for viewing the targets). The UVs are otherwise identical from the viewpoint of dynamic constraints on their motion and hence, the cost of traveling from a target A to a target B is the same for all vehicles. We will assume that triangle inequality is satisfied by the cost associated with travel, i.e., it is cheaper to travel from a target A to a target B directly than to go via an intermediate target C. The UVs may possibly start from different locations (referred to as depots) and are not required to return to the depot. While there are different objectives that can be considered for this problem, we consider the total cost of travel of all the UVs as an objective to be minimized. The problem considered in this article is a generalized version of single depot-terminal Hamiltonian Path Problem and is NP-hard.
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approximation algorithms and heuristics for a 2 depot heterogeneous Hamiltonian Path problem
International Journal of Robust and Nonlinear Control, 2011Co-Authors: Riddhi Doshi, Sivakumar Rathinam, S Yadlapalli, Swaroop DarbhaAbstract:This article addresses an important routing problem that arises in surveillance applications involving two heterogeneous vehicles. As the addressed routing problem is NP-Hard, we develop an approximation algorithm and heuristics to solve the problem. Our approach involves solving the routing problem in two main steps: Partitioning and Sequencing. Partitioning involves finding a distinct set of targets to be visited by each vehicle. Sequencing provides the order in which each vehicle must visit the subset of targets assigned to it. The problem of partitioning is tackled by solving a linear program (LP) obtained by relaxing some of the constraints of an integer programming model for the problem. We consider two LP models for partitioning. The first LP model is obtained by mainly relaxing both the integrality and degree constraints, whereas the second model relaxes mainly the integrality constraints. Once the targets are partitioned, the sequencing problem can be solved either by Hoogeveen's algorithm or by the Lin–Kernighan heuristic to yield an approximately optimal solution. Computational results show that the algorithms based on the second LP model, on an average, provided better (closer to the optimum) solutions as compared with those based on the first LP model. We also observed that for both the LP models, the average quality of solutions given by the heuristics were found to be within 4% of the optimum, whereas the average quality of solutions obtained from the approximation algorithms were within 8–20% of the optimum depending on the problem size. Copyright © 2011 John Wiley & Sons, Ltd.
Sivakumar Rathinam - One of the best experts on this subject based on the ideXlab platform.
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approximation algorithms for multiple terminal Hamiltonian Path problems
Optimization Letters, 2012Co-Authors: Jungyun Bae, Sivakumar RathinamAbstract:This article presents a new 2-approximation algorithm for a multiple depot, multiple terminal, Hamiltonian Path problem when the costs satisfy the triangle inequality. For the case where all the salesmen start from the same depot, we present another algorithm with an approximation ratio of $${\frac{5}{3}}$$ . These results generalize the approximation algorithms currently available for the single depot, single terminal Hamiltonian Path problem.
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approximation algorithms for a heterogeneous multiple depot Hamiltonian Path problem
American Control Conference, 2011Co-Authors: S Yadlapalli, Jungyun Bae, Sivakumar Rathinam, Swaroop DarbhaAbstract:In this article, we present the first approximation algorithm for a routing problem that is frequently encountered in the motion planning of Unmanned Vehicles (UVs). The considered problem is a variant of a Multiple Depot-Terminal Hamiltonian Path Problem and is stated as follows: There is a collection of m UVs equipped with different sensors on-board and there are n targets to be visited by them collectively. There are restrictions on the targets of the following type: (1) A target may be visited by any UV, (2) a target must be visited only by a subset of UVs (with appropriate on-board sensor) and (3) a target may not be visited by a subset of UVs (as the set of on-board sensors on the UV may not be suitable for viewing the targets). The UVs are otherwise identical from the viewpoint of dynamic constraints on their motion and hence, the cost of traveling from a target A to a target B is the same for all vehicles. We will assume that triangle inequality is satisfied by the cost associated with travel, i.e., it is cheaper to travel from a target A to a target B directly than to go via an intermediate target C. The UVs may possibly start from different locations (referred to as depots) and are not required to return to the depot. While there are different objectives that can be considered for this problem, we consider the total cost of travel of all the UVs as an objective to be minimized. The problem considered in this article is a generalized version of single depot-terminal Hamiltonian Path Problem and is NP-hard.
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approximation algorithms and heuristics for a 2 depot heterogeneous Hamiltonian Path problem
International Journal of Robust and Nonlinear Control, 2011Co-Authors: Riddhi Doshi, Sivakumar Rathinam, S Yadlapalli, Swaroop DarbhaAbstract:This article addresses an important routing problem that arises in surveillance applications involving two heterogeneous vehicles. As the addressed routing problem is NP-Hard, we develop an approximation algorithm and heuristics to solve the problem. Our approach involves solving the routing problem in two main steps: Partitioning and Sequencing. Partitioning involves finding a distinct set of targets to be visited by each vehicle. Sequencing provides the order in which each vehicle must visit the subset of targets assigned to it. The problem of partitioning is tackled by solving a linear program (LP) obtained by relaxing some of the constraints of an integer programming model for the problem. We consider two LP models for partitioning. The first LP model is obtained by mainly relaxing both the integrality and degree constraints, whereas the second model relaxes mainly the integrality constraints. Once the targets are partitioned, the sequencing problem can be solved either by Hoogeveen's algorithm or by the Lin–Kernighan heuristic to yield an approximately optimal solution. Computational results show that the algorithms based on the second LP model, on an average, provided better (closer to the optimum) solutions as compared with those based on the first LP model. We also observed that for both the LP models, the average quality of solutions given by the heuristics were found to be within 4% of the optimum, whereas the average quality of solutions obtained from the approximation algorithms were within 8–20% of the optimum depending on the problem size. Copyright © 2011 John Wiley & Sons, Ltd.
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32 approximation algorithm for two variants of a 2 depot Hamiltonian Path problem
Operations Research Letters, 2010Co-Authors: Sivakumar Rathinam, Raja SenguptaAbstract:We consider two variants of a 2-depot Hamiltonian Path problem and show that they have an algorithm with an approximation ratio of 32 if the costs are symmetric and satisfy the triangle inequality. This improves the 2-approximation algorithm already available for the problem.
Tzung-shi Chen - One of the best experts on this subject based on the ideXlab platform.
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a dual Hamiltonian Path based multicasting strategy for wormhole routed star graph interconnection networks
Journal of Parallel and Distributed Computing, 2002Co-Authors: Nenchung Wang, Chihping Chu, Tzung-shi ChenAbstract:Multicast is an important collective communication operation on multicomputer systems, in which the same message is delivered from a source node to an arbitrary number of destination nodes. The star graph interconnection network has been recognized as an attractive alternative to the popular hypercube network. In this paper, we first address a dual-Hamiltonian-Path-based routing model with two virtual channels based on two Hamiltonian Paths (HPs) and a network partitioning strategy for wormhole-routed star graph networks. Then, we propose three efficient multicast routing schemes on basis of such a model. All of the three proposed schemes are proved deadlock-free. The first scheme, network-selection-based dual-Path routing, selects subnetworks that are constructed either by the first HP or by the second HP for dual-Path routing. The second one, optimum dual-Path routing, selects subnetworks with optimum routing Path for dual-Path routing. The third scheme, two-phase optimum dual-Path routing, includes two phases, source-to-relay and relay-to-destination. Finally, experimental results are given to show that our proposed three routing schemes outperform the unicast-based, the HP, and the single-HP-based dual-Path routing schemes significantly.
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multicast communication in wormhole routed star graph interconnection networks
Parallel Computing, 2000Co-Authors: Tzung-shi Chen, Nenchung WangAbstract:Multicast, an important communication mechanism, is frequently applied in parallel computing. The star graph interconnection network, when compared with the hypercube network, being with low degree and small diameter, has been recognized to be an attractive alternative to the popular hypercube network. In this paper, we derive a node labeling formula based on a Hamiltonian Path and propose four efficient multicast routing schemes in wormhole-routed star networks with multidestination routing capability. All of the four proposed schemes are Path-based and deadlock-free. The first scheme, dual-Path routing, sends the message in parallel through two independent Paths (toward high label nodes and low label nodes). The second one, shortcut-node-based dual-Path routing, is similar to dual-Path routing except that the routing tries to find a shortcut node to route the message as soon as possible to reduce the length of transmission Path. The third one, multiPath routing, is a multiple dual-Path routing strategy that includes source-to-relay and relay-to-destination phases. The last scheme, proximity grouping routing, is similar to multiPath routing except that in the partitioning step of source and destination nodes the relation of spatial locality of nodes is also taken into account to reduce the length of transmission Paths. Finally, the experimental results are given to show that the performance based on unicast-based and traditional Hamiltonian-Path routing schemes can be improved significantly by the four proposed routing schemes respectively.
Nenchung Wang - One of the best experts on this subject based on the ideXlab platform.
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a dual Hamiltonian Path based multicasting strategy for wormhole routed star graph interconnection networks
Journal of Parallel and Distributed Computing, 2002Co-Authors: Nenchung Wang, Chihping Chu, Tzung-shi ChenAbstract:Multicast is an important collective communication operation on multicomputer systems, in which the same message is delivered from a source node to an arbitrary number of destination nodes. The star graph interconnection network has been recognized as an attractive alternative to the popular hypercube network. In this paper, we first address a dual-Hamiltonian-Path-based routing model with two virtual channels based on two Hamiltonian Paths (HPs) and a network partitioning strategy for wormhole-routed star graph networks. Then, we propose three efficient multicast routing schemes on basis of such a model. All of the three proposed schemes are proved deadlock-free. The first scheme, network-selection-based dual-Path routing, selects subnetworks that are constructed either by the first HP or by the second HP for dual-Path routing. The second one, optimum dual-Path routing, selects subnetworks with optimum routing Path for dual-Path routing. The third scheme, two-phase optimum dual-Path routing, includes two phases, source-to-relay and relay-to-destination. Finally, experimental results are given to show that our proposed three routing schemes outperform the unicast-based, the HP, and the single-HP-based dual-Path routing schemes significantly.
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multicast communication in wormhole routed star graph interconnection networks
Parallel Computing, 2000Co-Authors: Tzung-shi Chen, Nenchung WangAbstract:Multicast, an important communication mechanism, is frequently applied in parallel computing. The star graph interconnection network, when compared with the hypercube network, being with low degree and small diameter, has been recognized to be an attractive alternative to the popular hypercube network. In this paper, we derive a node labeling formula based on a Hamiltonian Path and propose four efficient multicast routing schemes in wormhole-routed star networks with multidestination routing capability. All of the four proposed schemes are Path-based and deadlock-free. The first scheme, dual-Path routing, sends the message in parallel through two independent Paths (toward high label nodes and low label nodes). The second one, shortcut-node-based dual-Path routing, is similar to dual-Path routing except that the routing tries to find a shortcut node to route the message as soon as possible to reduce the length of transmission Path. The third one, multiPath routing, is a multiple dual-Path routing strategy that includes source-to-relay and relay-to-destination phases. The last scheme, proximity grouping routing, is similar to multiPath routing except that in the partitioning step of source and destination nodes the relation of spatial locality of nodes is also taken into account to reduce the length of transmission Paths. Finally, the experimental results are given to show that the performance based on unicast-based and traditional Hamiltonian-Path routing schemes can be improved significantly by the four proposed routing schemes respectively.
