The Experts below are selected from a list of 17205 Experts worldwide ranked by ideXlab platform

Herschel Rabitz - One of the best experts on this subject based on the ideXlab platform.

  • environment invariant measure of distance between evolutions of an open quantum system
    New Journal of Physics, 2010
    Co-Authors: Matthew D Grace, Jason Dominy, Robert L Kosut, Constantin Brif, Herschel Rabitz
    Abstract:

    The problem of quantifying the difference between evolutions of an open quantum system (in particular, between the actual evolution of an open system and the ideal target operation on the corresponding closed system) is important in quantum control, especially in control of quantum information processing. Motivated by this problem, we develop a measure for evaluating the distance between unitary evolution operators of a composite quantum system that consists of a sub-system of interest (e.g. a quantum information processor) and environment. The main characteristic of this measure is the invariance with respect to the effect of the evolution operator on the environment, which follows from an equivalence relation that exists between unitary operators acting on the composite system, when the effect on only the sub-system of interest is considered. The invariance to the environment's transformation makes it possible to quantitatively compare the evolution of an open quantum system and its closed counterpart. The distance measure also determines the fidelity bounds of a general quantum channel (a completely positive and trace-Preserving Map acting on the sub-system of interest) with respect to a unitary target transformation. This measure is also independent of the initial state of the system and straightforward to numerically calculate. As an example, the measure is used in numerical

  • environment invariant measure of distance between evolutions of an open quantum system
    arXiv: Quantum Physics, 2009
    Co-Authors: Matthew D Grace, Jason Dominy, Robert L Kosut, Constantin Brif, Herschel Rabitz
    Abstract:

    The problem of quantifying the difference between evolutions of an open quantum system (in particular, between the actual evolution of an open system and the ideal target operation on the corresponding closed system) is important in quantum control, especially in control of quantum information processing. Motivated by this problem, we develop a measure for evaluating the distance between unitary evolution operators of a composite quantum system that consists of a sub-system of interest (e.g., a quantum information processor) and environment. The main characteristic of this measure is the invariance with respect to the effect of the evolution operator on the environment, which follows from an equivalence relation that exists between unitary operators acting on the composite system, when the effect on only the sub-system of interest is considered. The invariance to the environment's transformation makes it possible to quantitatively compare the evolution of an open quantum system and its closed counterpart. The distance measure also determines the fidelity bounds of a general quantum channel (a completely positive and trace-Preserving Map acting on the sub-system of interest) with respect to a unitary target transformation. This measure is also independent of the initial state of the system and straightforward to numerically calculate. As an example, the measure is used in numerical simulations to evaluate fidelities of optimally controlled quantum gate operations (for one- and two-qubit systems), in the presence of a decohering environment. This example illustrates the utility of this measure for optimal control of quantum operations in the realistic case of open-system dynamics.

Fabian J Theis - One of the best experts on this subject based on the ideXlab platform.

  • paga graph abstraction reconciles clustering with trajectory inference through a topology Preserving Map of single cells
    Genome Biology, 2019
    Co-Authors: Alexander F Wolf, Fiona K Hamey, Mireya Plass, Jordi Solana, Joakim S Dahlin, Berthold Gottgens, Nikolaus Rajewsky, Lukas M Simon, Fabian J Theis
    Abstract:

    Single-cell RNA-seq quantifies biological heterogeneity across both discrete cell types and continuous cell transitions. Partition-based graph abstraction (PAGA) provides an interpretable graph-like Map of the arising data manifold, based on estimating connectivity of manifold partitions ( https://github.com/theislab/paga ). PAGA Maps preserve the global topology of data, allow analyzing data at different resolutions, and result in much higher computational efficiency of the typical exploratory data analysis workflow. We demonstrate the method by inferring structure-rich cell Maps with consistent topology across four hematopoietic datasets, adult planaria and the zebrafish embryo and benchmark computational performance on one million neurons.

  • graph abstraction reconciles clustering with trajectory inference through a topology Preserving Map of single cells
    bioRxiv, 2017
    Co-Authors: Alexander F Wolf, Fiona K Hamey, Mireya Plass, Jordi Solana, Joakim S Dahlin, Berthold Gottgens, Nikolaus Rajewsky, Lukas M Simon, Fabian J Theis
    Abstract:

    Abstract Single-cell RNA-seq allows quantification of biological heterogeneity across both discrete cell types and continuous cell differentiation transitions. We present approximate graph abstraction (AGA), an algorithm that reconciles the computational analysis strategies of clustering and trajectory inference by explaining cell-to-cell variation both in terms of discrete and continuous latent variables (https://github.com/theislab/graph_abstraction). This enables to generate cellular Maps of differentiation manifolds with complex topologies — efficiently and robustly across different datasets. Extended Abstract Approximate graph abstraction quantifies the connectivity of partitions of a neighborhood graph of single cells, thereby generating a much simpler abstracted graph whose nodes label the partitions. Together with a random walk-based distance measure, this generates a topology Preserving Map of single cells — a partial coordinatization of data useful for exploring and explaining its variation. We use the abstracted graph to assess which subsets of data are better explained by discrete clusters than by a continuous variable, to trace gene expression changes along aggregated single-cell paths through data and to infer abstracted trees that best explain the global topology of data. We demonstrate the power of the method by reconstructing differentiation processes with high numbers of branchings from single-cell gene expression datasets and by identifying biological trajectories from single-cell imaging data using a deep-learning based distance metric. Along with the method, we introduce measures for the connectivity of graph partitions, generalize random-walk based distance measures to disconnected graphs and introduce a path-based measure for topological similarity between graphs. Graph abstraction is computationally efficient and provides speedups of at least 30 times when compared to algorithms for the inference of lineage trees.

Joakim S Dahlin - One of the best experts on this subject based on the ideXlab platform.

  • paga graph abstraction reconciles clustering with trajectory inference through a topology Preserving Map of single cells
    Genome Biology, 2019
    Co-Authors: Alexander F Wolf, Fiona K Hamey, Mireya Plass, Jordi Solana, Joakim S Dahlin, Berthold Gottgens, Nikolaus Rajewsky, Lukas M Simon, Fabian J Theis
    Abstract:

    Single-cell RNA-seq quantifies biological heterogeneity across both discrete cell types and continuous cell transitions. Partition-based graph abstraction (PAGA) provides an interpretable graph-like Map of the arising data manifold, based on estimating connectivity of manifold partitions ( https://github.com/theislab/paga ). PAGA Maps preserve the global topology of data, allow analyzing data at different resolutions, and result in much higher computational efficiency of the typical exploratory data analysis workflow. We demonstrate the method by inferring structure-rich cell Maps with consistent topology across four hematopoietic datasets, adult planaria and the zebrafish embryo and benchmark computational performance on one million neurons.

  • graph abstraction reconciles clustering with trajectory inference through a topology Preserving Map of single cells
    bioRxiv, 2017
    Co-Authors: Alexander F Wolf, Fiona K Hamey, Mireya Plass, Jordi Solana, Joakim S Dahlin, Berthold Gottgens, Nikolaus Rajewsky, Lukas M Simon, Fabian J Theis
    Abstract:

    Abstract Single-cell RNA-seq allows quantification of biological heterogeneity across both discrete cell types and continuous cell differentiation transitions. We present approximate graph abstraction (AGA), an algorithm that reconciles the computational analysis strategies of clustering and trajectory inference by explaining cell-to-cell variation both in terms of discrete and continuous latent variables (https://github.com/theislab/graph_abstraction). This enables to generate cellular Maps of differentiation manifolds with complex topologies — efficiently and robustly across different datasets. Extended Abstract Approximate graph abstraction quantifies the connectivity of partitions of a neighborhood graph of single cells, thereby generating a much simpler abstracted graph whose nodes label the partitions. Together with a random walk-based distance measure, this generates a topology Preserving Map of single cells — a partial coordinatization of data useful for exploring and explaining its variation. We use the abstracted graph to assess which subsets of data are better explained by discrete clusters than by a continuous variable, to trace gene expression changes along aggregated single-cell paths through data and to infer abstracted trees that best explain the global topology of data. We demonstrate the power of the method by reconstructing differentiation processes with high numbers of branchings from single-cell gene expression datasets and by identifying biological trajectories from single-cell imaging data using a deep-learning based distance metric. Along with the method, we introduce measures for the connectivity of graph partitions, generalize random-walk based distance measures to disconnected graphs and introduce a path-based measure for topological similarity between graphs. Graph abstraction is computationally efficient and provides speedups of at least 30 times when compared to algorithms for the inference of lineage trees.

Anura P. Jayasumana - One of the best experts on this subject based on the ideXlab platform.

  • Topology Preserving Map to Physical Map - A Thin-Plate Spline Based Transform
    2016 IEEE 41st Conference on Local Computer Networks (LCN), 2016
    Co-Authors: Ali F. Buoud, Anura P. Jayasumana
    Abstract:

    A Topology Preserving Map (TPM) is an easily obtainable localization free connectivity based Map that preserves physical layout features of 2D/3D sensor networks. This paper considers how to obtain physical Maps and physical coordinates from a TPM when the physical locations of a subset of nodes are known. First, we present a General Procrustes Alignment (GPA) based solution, which is the optimal linear transformation solution to the problem. Second approach is based on thin-plate spline (TPS), which transforms the set of topology coordinates to physical coordinates using radial basis functions. Five representative 2D network topologies are used to evaluate and compare the TPS approach with GPA approach, and also with the existing distance vector-hop (DV-Hop) technique. Results are presented for the cases where the reference nodes are selected randomly from the entire network, or randomly from the inner and outer boundaries of the network. The results show that with less than 10% of nodes as reference nodes, a Map with an average error less than 0.6 of radio range can be achieved with the TPS approach, which significantly outperforms both the GPA and the DV-Hop. TPS approach generalizes directly to 3-D networks as well.

  • anchor selection and topology Preserving Maps in wsns a directional virtual coordinate based approach
    Local Computer Networks, 2011
    Co-Authors: Dulanjalie C Dhanapala, Anura P. Jayasumana
    Abstract:

    Virtual Coordinate Systems (VCS) characterize each node in a network by its hop distances to a subset of nodes called anchors. Performance of VCS based algorithms is highly sensitive to number of anchors and their placement. Extreme Node Search (ENS), a novel and efficient anchor placement scheme, is proposed that demonstrates significantly improved performance over state-of-the-art. ENS starts with two randomly placed anchors and then uses a Directional Virtual Coordinate (DVC) transformation, which restores the lost directionality in traditional VCS, to identify anchor candidates in a completely distributed manner. A vector-based representation is proposed for the DVC domain, which is then used to introduce the concept of angles between virtual directions in the transformed domain. Ability to specify cardinal directions and use angles is a radical change from the traditional VC system approaches. By selecting two anchor pairs with near orthogonal directional coordinates under the DVC transformation, a novel Topology Preserving Map (TPM) generation scheme is developed. This new TPM generation scheme requires significantly less computations than the existing PCA based method. Use of ENS significantly enhances the PCA based TPM generation as well. Simulation results for representative WSNs indicate that the ENS based anchor sets significantly improve performance of all prominent VC based routing schemes. For instance, Directional Virtual Coordinate Routing, when combined with ENS anchor placement strategy, outperforms even the geographic Greedy Perimeter Stateless Routing scheme that relies on exact physical node coordinates.

Matthew D Grace - One of the best experts on this subject based on the ideXlab platform.

  • environment invariant measure of distance between evolutions of an open quantum system
    New Journal of Physics, 2010
    Co-Authors: Matthew D Grace, Jason Dominy, Robert L Kosut, Constantin Brif, Herschel Rabitz
    Abstract:

    The problem of quantifying the difference between evolutions of an open quantum system (in particular, between the actual evolution of an open system and the ideal target operation on the corresponding closed system) is important in quantum control, especially in control of quantum information processing. Motivated by this problem, we develop a measure for evaluating the distance between unitary evolution operators of a composite quantum system that consists of a sub-system of interest (e.g. a quantum information processor) and environment. The main characteristic of this measure is the invariance with respect to the effect of the evolution operator on the environment, which follows from an equivalence relation that exists between unitary operators acting on the composite system, when the effect on only the sub-system of interest is considered. The invariance to the environment's transformation makes it possible to quantitatively compare the evolution of an open quantum system and its closed counterpart. The distance measure also determines the fidelity bounds of a general quantum channel (a completely positive and trace-Preserving Map acting on the sub-system of interest) with respect to a unitary target transformation. This measure is also independent of the initial state of the system and straightforward to numerically calculate. As an example, the measure is used in numerical

  • environment invariant measure of distance between evolutions of an open quantum system
    arXiv: Quantum Physics, 2009
    Co-Authors: Matthew D Grace, Jason Dominy, Robert L Kosut, Constantin Brif, Herschel Rabitz
    Abstract:

    The problem of quantifying the difference between evolutions of an open quantum system (in particular, between the actual evolution of an open system and the ideal target operation on the corresponding closed system) is important in quantum control, especially in control of quantum information processing. Motivated by this problem, we develop a measure for evaluating the distance between unitary evolution operators of a composite quantum system that consists of a sub-system of interest (e.g., a quantum information processor) and environment. The main characteristic of this measure is the invariance with respect to the effect of the evolution operator on the environment, which follows from an equivalence relation that exists between unitary operators acting on the composite system, when the effect on only the sub-system of interest is considered. The invariance to the environment's transformation makes it possible to quantitatively compare the evolution of an open quantum system and its closed counterpart. The distance measure also determines the fidelity bounds of a general quantum channel (a completely positive and trace-Preserving Map acting on the sub-system of interest) with respect to a unitary target transformation. This measure is also independent of the initial state of the system and straightforward to numerically calculate. As an example, the measure is used in numerical simulations to evaluate fidelities of optimally controlled quantum gate operations (for one- and two-qubit systems), in the presence of a decohering environment. This example illustrates the utility of this measure for optimal control of quantum operations in the realistic case of open-system dynamics.