The Experts below are selected from a list of 2826 Experts worldwide ranked by ideXlab platform

Naohito Tomita - One of the best experts on this subject based on the ideXlab platform.

  • the Dilation property of modulation spaces and their inclusion relation with besov spaces
    Journal of Functional Analysis, 2007
    Co-Authors: Mitsuru Sugimoto, Naohito Tomita
    Abstract:

    Abstract We consider the Dilation property of the modulation spaces M p , q . Let D λ : f ( t ) ↦ f ( λ t ) be the Dilation Operator, and we consider the behavior of the Operator norm ‖ D λ ‖ M p , q → M p , q with respect to λ. Our result determines the best order for it, and as an application, we establish the optimality of the inclusion relation between the modulation spaces and Besov spaces, which was proved by Toft [J. Toft, Continuity properties for modulation spaces, with applications to pseudo-differential calculus, I, J. Funct. Anal. 207 (2004) 399–429].

  • the Dilation property of modulation spaces and their inclusion relation with besov spaces
    arXiv: Functional Analysis, 2006
    Co-Authors: Mitsuru Sugimoto, Naohito Tomita
    Abstract:

    We consider the Dilation property of the modulation spaces $M^{p,q}$. Let $D_\lambda:f(t)\mapsto f(\lambda t)$ be the Dilation Operator, and we consider the behavior of the Operator norm $\|D_\lambda\|_{M^{p,q}\to M^{p,q}}$ with respect to $\lambda$. Our result determines the best order for it, and as an application, we establish the optimality of the inclusion relation between the modulation spaces and Besov space, which was proved by Toft.

Mitsuru Sugimoto - One of the best experts on this subject based on the ideXlab platform.

  • the Dilation property of modulation spaces and their inclusion relation with besov spaces
    Journal of Functional Analysis, 2007
    Co-Authors: Mitsuru Sugimoto, Naohito Tomita
    Abstract:

    Abstract We consider the Dilation property of the modulation spaces M p , q . Let D λ : f ( t ) ↦ f ( λ t ) be the Dilation Operator, and we consider the behavior of the Operator norm ‖ D λ ‖ M p , q → M p , q with respect to λ. Our result determines the best order for it, and as an application, we establish the optimality of the inclusion relation between the modulation spaces and Besov spaces, which was proved by Toft [J. Toft, Continuity properties for modulation spaces, with applications to pseudo-differential calculus, I, J. Funct. Anal. 207 (2004) 399–429].

  • the Dilation property of modulation spaces and their inclusion relation with besov spaces
    arXiv: Functional Analysis, 2006
    Co-Authors: Mitsuru Sugimoto, Naohito Tomita
    Abstract:

    We consider the Dilation property of the modulation spaces $M^{p,q}$. Let $D_\lambda:f(t)\mapsto f(\lambda t)$ be the Dilation Operator, and we consider the behavior of the Operator norm $\|D_\lambda\|_{M^{p,q}\to M^{p,q}}$ with respect to $\lambda$. Our result determines the best order for it, and as an application, we establish the optimality of the inclusion relation between the modulation spaces and Besov space, which was proved by Toft.

Manabendra Nath Bera - One of the best experts on this subject based on the ideXlab platform.

  • quantum operations in an information theory for fermions
    Physical Review A, 2021
    Co-Authors: Nicetu Tibau Vidal, Mohit Lal Bera, Arnau Riera, Maciej Lewenstein, Manabendra Nath Bera
    Abstract:

    A reasonable quantum information theory for fermions must respect the parity superselection rule to comply with the special theory of relativity and the no-signaling principle. This rule restricts the possibility of any quantum state to have a superposition between even- and odd-parity fermionic states. thereby characterizing the set of physically allowed fermionic quantum states. Here we introduce the physically allowed quantum operations, in congruence with the parity superselection rule, that map the set of allowed fermionic states onto itself. We first introduce unitary and projective measurement operations of the fermionic states. We further extend the formalism to general quantum operations in the forms of Stinespring Dilation, Operator-sum representation, and axiomatic completely positive and trace-preserving maps. We explicitly show the equivalence between these three representations of fermionic quantum operations. We discuss the possible implications of our results in characterization of correlations in fermionic systems.

  • quantum operations in an information theory for fermions
    arXiv: Quantum Physics, 2021
    Co-Authors: Nicetu Tibau Vidal, Mohit Lal Bera, Arnau Riera, Maciej Lewenstein, Manabendra Nath Bera
    Abstract:

    A reasonable quantum information theory for fermions must respect the parity super-selection rule to comply with the special theory of relativity and the no-signaling principle. This rule restricts the possibility of any quantum state to have a superposition between even and odd parity fermionic states. It thereby characterizes the set of physically allowed fermionic quantum states. Here we introduce the physically allowed quantum operations, in congruence with the parity super-selection rule, that map the set of allowed fermionic states onto itself. We first introduce unitary and projective measurement operations of the fermionic states. We further extend the formalism to general quantum operations in the forms of Stinespring Dilation, Operator-sum representation, and axiomatic completely-positive-trace-preserving maps. We explicitly show the equivalence between these three representations of fermionic quantum operations. We discuss the possible implications of our results in characterization of correlations in fermionic systems.

Arnau Riera - One of the best experts on this subject based on the ideXlab platform.

  • quantum operations in an information theory for fermions
    Physical Review A, 2021
    Co-Authors: Nicetu Tibau Vidal, Mohit Lal Bera, Arnau Riera, Maciej Lewenstein, Manabendra Nath Bera
    Abstract:

    A reasonable quantum information theory for fermions must respect the parity superselection rule to comply with the special theory of relativity and the no-signaling principle. This rule restricts the possibility of any quantum state to have a superposition between even- and odd-parity fermionic states. thereby characterizing the set of physically allowed fermionic quantum states. Here we introduce the physically allowed quantum operations, in congruence with the parity superselection rule, that map the set of allowed fermionic states onto itself. We first introduce unitary and projective measurement operations of the fermionic states. We further extend the formalism to general quantum operations in the forms of Stinespring Dilation, Operator-sum representation, and axiomatic completely positive and trace-preserving maps. We explicitly show the equivalence between these three representations of fermionic quantum operations. We discuss the possible implications of our results in characterization of correlations in fermionic systems.

  • quantum operations in an information theory for fermions
    arXiv: Quantum Physics, 2021
    Co-Authors: Nicetu Tibau Vidal, Mohit Lal Bera, Arnau Riera, Maciej Lewenstein, Manabendra Nath Bera
    Abstract:

    A reasonable quantum information theory for fermions must respect the parity super-selection rule to comply with the special theory of relativity and the no-signaling principle. This rule restricts the possibility of any quantum state to have a superposition between even and odd parity fermionic states. It thereby characterizes the set of physically allowed fermionic quantum states. Here we introduce the physically allowed quantum operations, in congruence with the parity super-selection rule, that map the set of allowed fermionic states onto itself. We first introduce unitary and projective measurement operations of the fermionic states. We further extend the formalism to general quantum operations in the forms of Stinespring Dilation, Operator-sum representation, and axiomatic completely-positive-trace-preserving maps. We explicitly show the equivalence between these three representations of fermionic quantum operations. We discuss the possible implications of our results in characterization of correlations in fermionic systems.

Céline Hudelot - One of the best experts on this subject based on the ideXlab platform.

  • SIMD-based Exact Parallel Fuzzy Dilation Operator for Fast Computing of Fuzzy Spatial Relations
    2020
    Co-Authors: Régis Pierrard, Laurent Cabaret, Jean-philippe Poli, Céline Hudelot
    Abstract:

    For decades, fuzzy spatial relations have demonstrated their utility and effectiveness for visual reasoning, including semantic annotation and object recognition. However, a major issue is that they often involve fuzzy morphological Operators that are compute-intensive leading to long latency in the relation evaluation. As a result, approximate methods have been proposed to compute some relations in an acceptable time, but they are not as generic as the fuzzy Dilation or do not make the most of modern computing architectures. In this paper, we introduce the Reverse and the Parallel Reverse (PR) algorithms. Reverse is an exact and efficient algorithm for the fuzzy Dilation Operator and PR combines the Reverse algorithm exactness with efficient usage of modern-processor multiple cores using OpenMP. Using SIMD extensions to enhance Parallel Reverse, PR 128 (AVX), PR 256 (AVX2), and PR 512 (AVX512) are faster than the state-of-the-art approximate methods while remaining generic and exact. To demonstrate the performance of PR and highlight the contribution of the SIMD instructions, an extensive benchmark was carried out on two datasets of natural and artificial images.