The Experts below are selected from a list of 56484 Experts worldwide ranked by ideXlab platform
Jacek Blazewicz - One of the best experts on this subject based on the ideXlab platform.
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Structural alignment of protein descriptors – a Combinatorial Model
BMC Bioinformatics, 2016Co-Authors: Maciej Antczak, Marta Kasprzak, Piotr Lukasiak, Jacek BlazewiczAbstract:Background Structural alignment of proteins is one of the most challenging problems in molecular biology. The tertiary structure of a protein strictly correlates with its function and computationally predicted structures are nowadays a main premise for understanding the latter. However, computationally derived 3D Models often exhibit deviations from the native structure. A way to confirm a Model is a comparison with other structures. The structural alignment of a pair of proteins can be defined with the use of a concept of protein descriptors. The protein descriptors are local substructures of protein molecules, which allow us to divide the original problem into a set of subproblems and, consequently, to propose a more efficient algorithmic solution. In the literature, one can find many applications of the descriptors concept that prove its usefulness for insight into protein 3D structures, but the proposed approaches are presented rather from the biological perspective than from the computational or algorithmic point of view. Efficient algorithms for identification and structural comparison of descriptors can become crucial components of methods for structural quality assessment as well as tertiary structure prediction. Results In this paper, we propose a new Combinatorial Model and new polynomial-time algorithms for the structural alignment of descriptors. The Model is based on the maximum-size assignment problem, which we define here and prove that it can be solved in polynomial time. We demonstrate suitability of this approach by comparison with an exact backtracking algorithm. Besides a simplification coming from the Combinatorial Modeling, both on the conceptual and complexity level, we gain with this approach high quality of obtained results, in terms of 3D alignment accuracy and processing efficiency. Conclusions All the proposed algorithms were developed and integrated in a computationally efficient tool descs-standalone, which allows the user to identify and structurally compare descriptors of biological molecules, such as proteins and RNAs. Both PDB (Protein Data Bank) and mmCIF (macromolecular Crystallographic Information File) formats are supported. The proposed tool is available as an open source project stored on GitHub ( https://github.com/mantczak/descs-standalone ).
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Structural alignment of protein descriptors – a Combinatorial Model
BMC bioinformatics, 2016Co-Authors: Maciej Antczak, Marta Kasprzak, Piotr Lukasiak, Jacek BlazewiczAbstract:Structural alignment of proteins is one of the most challenging problems in molecular biology. The tertiary structure of a protein strictly correlates with its function and computationally predicted structures are nowadays a main premise for understanding the latter. However, computationally derived 3D Models often exhibit deviations from the native structure. A way to confirm a Model is a comparison with other structures. The structural alignment of a pair of proteins can be defined with the use of a concept of protein descriptors. The protein descriptors are local substructures of protein molecules, which allow us to divide the original problem into a set of subproblems and, consequently, to propose a more efficient algorithmic solution. In the literature, one can find many applications of the descriptors concept that prove its usefulness for insight into protein 3D structures, but the proposed approaches are presented rather from the biological perspective than from the computational or algorithmic point of view. Efficient algorithms for identification and structural comparison of descriptors can become crucial components of methods for structural quality assessment as well as tertiary structure prediction. In this paper, we propose a new Combinatorial Model and new polynomial-time algorithms for the structural alignment of descriptors. The Model is based on the maximum-size assignment problem, which we define here and prove that it can be solved in polynomial time. We demonstrate suitability of this approach by comparison with an exact backtracking algorithm. Besides a simplification coming from the Combinatorial Modeling, both on the conceptual and complexity level, we gain with this approach high quality of obtained results, in terms of 3D alignment accuracy and processing efficiency. All the proposed algorithms were developed and integrated in a computationally efficient tool descs-standalone, which allows the user to identify and structurally compare descriptors of biological molecules, such as proteins and RNAs. Both PDB (Protein Data Bank) and mmCIF (macromolecular Crystallographic Information File) formats are supported. The proposed tool is available as an open source project stored on GitHub ( https://github.com/mantczak/descs-standalone ).
Dmitry Korotkin - One of the best experts on this subject based on the ideXlab platform.
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Hodge and Prym Tau Functions, Strebel Differentials and Combinatorial Model of $${\mathcal {M}}_{g,n}$$ M g , n
Communications in Mathematical Physics, 2020Co-Authors: Marco Bertola, Dmitry KorotkinAbstract:The goal of the paper is to apply the theory of integrable systems to construct explicit sections of line bundles over the Combinatorial Model of the moduli space of pointed Riemann surfaces based on Strebel differentials. These line bundles are tensor products of the determinants of the Hodge or Prym vector bundles with the standard tautological line bundles $$\mathcal {L}_j$$ L j , and the sections are constructed in terms of tau functions. The Combinatorial Model is interpreted as the real slice of a complex analytic moduli space of quadratic differentials where the phase of each tau-function provides a section of a circle bundle. The phase of the ratio of the Prym and Hodge tau functions gives a section of the $$\kappa _1$$ κ 1 -circle bundle. By evaluating the increment of the phase around co-dimension 2 sub-complexes, we identify the Poincaré dual cycles to the Chern classes of the corresponding line bundles: they are expressed explicitly as combination of Witten’s cycle $$W_{5} $$ W 5 and Kontsevich’s boundary. This provides Combinatorial analogues of Mumford’s relations on $${\mathcal {M}}_{g,n}$$ M g , n and Penner’s relations in the hyperbolic Combinatorial Model. The free homotopy classes of loops around $$W_{5} $$ W 5 are interpreted as pentagon moves while those of loops around Kontsevich’s boundary as Combinatorial Dehn twists. Throughout the paper we exploit the classical description of the Combinatorial Model in terms of Strebel differentials, parametrized in terms of period, or homological coordinates; we show that they provide Darboux coordinates for the symplectic structure introduced by Kontsevich. We also express the latter as the intersection pairing in the odd homology of the canonical double cover.
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Hodge and Prym tau functions, Jenkins-Strebel differentials and Combinatorial Model of $\mathcal M_{g,n}$
Communications in Mathematical Physics, 2020Co-Authors: Marco Bertola, Dmitry KorotkinAbstract:The goal of the paper is to apply the theory of integrable systems to construct explicit sections of line bundles over the Combinatorial Model of the moduli space of pointed Riemann surfaces based on Strebel differentials. These line bundles are tensor products of the determinants of the Hodge or Prym vector bundles with the standard tautological line bundles $$\mathcal {L}_j$$ , and the sections are constructed in terms of tau functions. The Combinatorial Model is interpreted as the real slice of a complex analytic moduli space of quadratic differentials where the phase of each tau-function provides a section of a circle bundle. The phase of the ratio of the Prym and Hodge tau functions gives a section of the $$\kappa _1$$ -circle bundle. By evaluating the increment of the phase around co-dimension 2 sub-complexes, we identify the Poincare dual cycles to the Chern classes of the corresponding line bundles: they are expressed explicitly as combination of Witten’s cycle $$W_{5} $$ and Kontsevich’s boundary. This provides Combinatorial analogues of Mumford’s relations on $${\mathcal {M}}_{g,n}$$ and Penner’s relations in the hyperbolic Combinatorial Model. The free homotopy classes of loops around $$W_{5} $$ are interpreted as pentagon moves while those of loops around Kontsevich’s boundary as Combinatorial Dehn twists. Throughout the paper we exploit the classical description of the Combinatorial Model in terms of Strebel differentials, parametrized in terms of period, or homological coordinates; we show that they provide Darboux coordinates for the symplectic structure introduced by Kontsevich. We also express the latter as the intersection pairing in the odd homology of the canonical double cover.
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Hodge and Prym tau functions, Jenkins-Strebel differentials and Combinatorial Model of $\mathcal M_{g,n}$
arXiv: Mathematical Physics, 2018Co-Authors: Marco Bertola, Dmitry KorotkinAbstract:The principal goal of the paper is to apply the approach inspired by the theory of integrable systems to construct explicit sections of line bundles over the Combinatorial Model of the moduli space of pointed Riemann surfaces based on Jenkins-Strebel differentials. The line bundles are tensor products of the determinants of the Hodge or Prym vector bundles with the standard tautological line bundles $\mathcal L_j$ and the sections are constructed in terms of tau functions. The Combinatorial Model is interpreted as the real slice of a complex analytic moduli space of quadratic differentials where the phase of each tau-function provides a section of a circle bundle. The phase of the ratio of the Prym and Hodge tau functions gives a section of the $\kappa_1$-circle bundle. By evaluating the increment of the phase around co-dimension $2$ sub-complexes, we identify the Poincare\ dual cycles to the Chern classes of the corresponding line bundles: they are expressed explicitly as combination of Witten's cycle $W_5$ and Kontsevich's boundary. This provides Combinatorial analogues of Mumford's relations on $\mathcal M_{g,n}$ and Penner's relations in the hyperbolic Combinatorial Model. The free homotopy classes of loops around $W_5$ are interpreted as pentagon moves while those of loops around Kontsevich's boundary as Combinatorial Dehn twists. Throughout the paper we exploit the classical description of the Combinatorial Model in terms of Jenkins--Strebel differentials, parametrized in terms of {\it homological coordinates}; we also show that they provide Darboux coordinates for the symplectic structure introduced by Kontsevich. We also express the latter in clear geometric terms as the intersection pairing in the odd homology of the canonical double cover.
Maciej Antczak - One of the best experts on this subject based on the ideXlab platform.
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Structural alignment of protein descriptors – a Combinatorial Model
BMC Bioinformatics, 2016Co-Authors: Maciej Antczak, Marta Kasprzak, Piotr Lukasiak, Jacek BlazewiczAbstract:Background Structural alignment of proteins is one of the most challenging problems in molecular biology. The tertiary structure of a protein strictly correlates with its function and computationally predicted structures are nowadays a main premise for understanding the latter. However, computationally derived 3D Models often exhibit deviations from the native structure. A way to confirm a Model is a comparison with other structures. The structural alignment of a pair of proteins can be defined with the use of a concept of protein descriptors. The protein descriptors are local substructures of protein molecules, which allow us to divide the original problem into a set of subproblems and, consequently, to propose a more efficient algorithmic solution. In the literature, one can find many applications of the descriptors concept that prove its usefulness for insight into protein 3D structures, but the proposed approaches are presented rather from the biological perspective than from the computational or algorithmic point of view. Efficient algorithms for identification and structural comparison of descriptors can become crucial components of methods for structural quality assessment as well as tertiary structure prediction. Results In this paper, we propose a new Combinatorial Model and new polynomial-time algorithms for the structural alignment of descriptors. The Model is based on the maximum-size assignment problem, which we define here and prove that it can be solved in polynomial time. We demonstrate suitability of this approach by comparison with an exact backtracking algorithm. Besides a simplification coming from the Combinatorial Modeling, both on the conceptual and complexity level, we gain with this approach high quality of obtained results, in terms of 3D alignment accuracy and processing efficiency. Conclusions All the proposed algorithms were developed and integrated in a computationally efficient tool descs-standalone, which allows the user to identify and structurally compare descriptors of biological molecules, such as proteins and RNAs. Both PDB (Protein Data Bank) and mmCIF (macromolecular Crystallographic Information File) formats are supported. The proposed tool is available as an open source project stored on GitHub ( https://github.com/mantczak/descs-standalone ).
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Structural alignment of protein descriptors – a Combinatorial Model
BMC bioinformatics, 2016Co-Authors: Maciej Antczak, Marta Kasprzak, Piotr Lukasiak, Jacek BlazewiczAbstract:Structural alignment of proteins is one of the most challenging problems in molecular biology. The tertiary structure of a protein strictly correlates with its function and computationally predicted structures are nowadays a main premise for understanding the latter. However, computationally derived 3D Models often exhibit deviations from the native structure. A way to confirm a Model is a comparison with other structures. The structural alignment of a pair of proteins can be defined with the use of a concept of protein descriptors. The protein descriptors are local substructures of protein molecules, which allow us to divide the original problem into a set of subproblems and, consequently, to propose a more efficient algorithmic solution. In the literature, one can find many applications of the descriptors concept that prove its usefulness for insight into protein 3D structures, but the proposed approaches are presented rather from the biological perspective than from the computational or algorithmic point of view. Efficient algorithms for identification and structural comparison of descriptors can become crucial components of methods for structural quality assessment as well as tertiary structure prediction. In this paper, we propose a new Combinatorial Model and new polynomial-time algorithms for the structural alignment of descriptors. The Model is based on the maximum-size assignment problem, which we define here and prove that it can be solved in polynomial time. We demonstrate suitability of this approach by comparison with an exact backtracking algorithm. Besides a simplification coming from the Combinatorial Modeling, both on the conceptual and complexity level, we gain with this approach high quality of obtained results, in terms of 3D alignment accuracy and processing efficiency. All the proposed algorithms were developed and integrated in a computationally efficient tool descs-standalone, which allows the user to identify and structurally compare descriptors of biological molecules, such as proteins and RNAs. Both PDB (Protein Data Bank) and mmCIF (macromolecular Crystallographic Information File) formats are supported. The proposed tool is available as an open source project stored on GitHub ( https://github.com/mantczak/descs-standalone ).
Marco Bertola - One of the best experts on this subject based on the ideXlab platform.
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Hodge and Prym Tau Functions, Strebel Differentials and Combinatorial Model of $${\mathcal {M}}_{g,n}$$ M g , n
Communications in Mathematical Physics, 2020Co-Authors: Marco Bertola, Dmitry KorotkinAbstract:The goal of the paper is to apply the theory of integrable systems to construct explicit sections of line bundles over the Combinatorial Model of the moduli space of pointed Riemann surfaces based on Strebel differentials. These line bundles are tensor products of the determinants of the Hodge or Prym vector bundles with the standard tautological line bundles $$\mathcal {L}_j$$ L j , and the sections are constructed in terms of tau functions. The Combinatorial Model is interpreted as the real slice of a complex analytic moduli space of quadratic differentials where the phase of each tau-function provides a section of a circle bundle. The phase of the ratio of the Prym and Hodge tau functions gives a section of the $$\kappa _1$$ κ 1 -circle bundle. By evaluating the increment of the phase around co-dimension 2 sub-complexes, we identify the Poincaré dual cycles to the Chern classes of the corresponding line bundles: they are expressed explicitly as combination of Witten’s cycle $$W_{5} $$ W 5 and Kontsevich’s boundary. This provides Combinatorial analogues of Mumford’s relations on $${\mathcal {M}}_{g,n}$$ M g , n and Penner’s relations in the hyperbolic Combinatorial Model. The free homotopy classes of loops around $$W_{5} $$ W 5 are interpreted as pentagon moves while those of loops around Kontsevich’s boundary as Combinatorial Dehn twists. Throughout the paper we exploit the classical description of the Combinatorial Model in terms of Strebel differentials, parametrized in terms of period, or homological coordinates; we show that they provide Darboux coordinates for the symplectic structure introduced by Kontsevich. We also express the latter as the intersection pairing in the odd homology of the canonical double cover.
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Hodge and Prym tau functions, Jenkins-Strebel differentials and Combinatorial Model of $\mathcal M_{g,n}$
Communications in Mathematical Physics, 2020Co-Authors: Marco Bertola, Dmitry KorotkinAbstract:The goal of the paper is to apply the theory of integrable systems to construct explicit sections of line bundles over the Combinatorial Model of the moduli space of pointed Riemann surfaces based on Strebel differentials. These line bundles are tensor products of the determinants of the Hodge or Prym vector bundles with the standard tautological line bundles $$\mathcal {L}_j$$ , and the sections are constructed in terms of tau functions. The Combinatorial Model is interpreted as the real slice of a complex analytic moduli space of quadratic differentials where the phase of each tau-function provides a section of a circle bundle. The phase of the ratio of the Prym and Hodge tau functions gives a section of the $$\kappa _1$$ -circle bundle. By evaluating the increment of the phase around co-dimension 2 sub-complexes, we identify the Poincare dual cycles to the Chern classes of the corresponding line bundles: they are expressed explicitly as combination of Witten’s cycle $$W_{5} $$ and Kontsevich’s boundary. This provides Combinatorial analogues of Mumford’s relations on $${\mathcal {M}}_{g,n}$$ and Penner’s relations in the hyperbolic Combinatorial Model. The free homotopy classes of loops around $$W_{5} $$ are interpreted as pentagon moves while those of loops around Kontsevich’s boundary as Combinatorial Dehn twists. Throughout the paper we exploit the classical description of the Combinatorial Model in terms of Strebel differentials, parametrized in terms of period, or homological coordinates; we show that they provide Darboux coordinates for the symplectic structure introduced by Kontsevich. We also express the latter as the intersection pairing in the odd homology of the canonical double cover.
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Hodge and Prym tau functions, Jenkins-Strebel differentials and Combinatorial Model of $\mathcal M_{g,n}$
arXiv: Mathematical Physics, 2018Co-Authors: Marco Bertola, Dmitry KorotkinAbstract:The principal goal of the paper is to apply the approach inspired by the theory of integrable systems to construct explicit sections of line bundles over the Combinatorial Model of the moduli space of pointed Riemann surfaces based on Jenkins-Strebel differentials. The line bundles are tensor products of the determinants of the Hodge or Prym vector bundles with the standard tautological line bundles $\mathcal L_j$ and the sections are constructed in terms of tau functions. The Combinatorial Model is interpreted as the real slice of a complex analytic moduli space of quadratic differentials where the phase of each tau-function provides a section of a circle bundle. The phase of the ratio of the Prym and Hodge tau functions gives a section of the $\kappa_1$-circle bundle. By evaluating the increment of the phase around co-dimension $2$ sub-complexes, we identify the Poincare\ dual cycles to the Chern classes of the corresponding line bundles: they are expressed explicitly as combination of Witten's cycle $W_5$ and Kontsevich's boundary. This provides Combinatorial analogues of Mumford's relations on $\mathcal M_{g,n}$ and Penner's relations in the hyperbolic Combinatorial Model. The free homotopy classes of loops around $W_5$ are interpreted as pentagon moves while those of loops around Kontsevich's boundary as Combinatorial Dehn twists. Throughout the paper we exploit the classical description of the Combinatorial Model in terms of Jenkins--Strebel differentials, parametrized in terms of {\it homological coordinates}; we also show that they provide Darboux coordinates for the symplectic structure introduced by Kontsevich. We also express the latter in clear geometric terms as the intersection pairing in the odd homology of the canonical double cover.
Alberto Rodriguez - One of the best experts on this subject based on the ideXlab platform.
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a convex Combinatorial Model for planar caging
Intelligent Robots and Systems, 2019Co-Authors: Bernardo Aceitunocabezas, Hongkai Dai, Alberto RodriguezAbstract:Caging is a promising tool which allows a robot to manipulate an object without directly reasoning about the contact dynamics involved. Furthermore, caging also provides useful guarantees in terms of robustness to uncertainty, and often serves as a way-point to a grasp. However, caging is traditionally difficult to integrate as part of larger manipulation frameworks, where caging is not the goal but an intermediate condition. In this paper, we develop a convex-Combinatorial Model to characterize caging from an optimization perspective. More specifically, we derive a set of sufficient constraints to enclose the configuration of the object in a compact-connected component of its free-space. The convex-Combinatorial nature of this approach provides guarantees on optimality and convergence, and its optimization nature makes it versatile for further applications on robot manipulation tasks. To the best of our knowledge, this is the first optimization-based approach to formulate the caging condition.
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IROS - A Convex-Combinatorial Model for Planar Caging
2019 IEEE RSJ International Conference on Intelligent Robots and Systems (IROS), 2019Co-Authors: Bernardo Aceituno-cabezas, Hongkai Dai, Alberto RodriguezAbstract:Caging is a promising tool which allows a robot to manipulate an object without directly reasoning about the contact dynamics involved. Furthermore, caging also provides useful guarantees in terms of robustness to uncertainty, and often serves as a way-point to a grasp. However, caging is traditionally difficult to integrate as part of larger manipulation frameworks, where caging is not the goal but an intermediate condition. In this paper, we develop a convex-Combinatorial Model to characterize caging from an optimization perspective. More specifically, we derive a set of sufficient constraints to enclose the configuration of the object in a compact-connected component of its free-space. The convex-Combinatorial nature of this approach provides guarantees on optimality and convergence, and its optimization nature makes it versatile for further applications on robot manipulation tasks. To the best of our knowledge, this is the first optimization-based approach to formulate the caging condition.
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a convex Combinatorial Model for planar caging
arXiv: Robotics, 2018Co-Authors: Bernardo Aceitunocabezas, Hongkai Dai, Alberto RodriguezAbstract:Caging is a promising tool which allows a robot to manipulate an object without directly reasoning about the contact dynamics involved. Furthermore, caging also provides useful guarantees in terms of robustness to uncertainty, and often serves as a way-point to a grasp. Unfortunately, previous work on caging is often based on computational geometry or discrete topology tools, causing restriction on gripper geometry, and difficulty on integration into larger manipulation frameworks. In this paper, we develop a convex-Combinatorial Model to characterize caging from an optimization perspective. More specifically, we study the configuration space of the object, where the fingers act as obstacles that enclose the configuration of the object. The convex-Combinatorial nature of this approach provides guarantees on optimality, convergence and scalability, and its optimization nature makes it adaptable for further applications on robot manipulation tasks.
