Translation Vector

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Ayan Datta - One of the best experts on this subject based on the ideXlab platform.

  • role of heavy atom tunneling in myers saito cyclization of cyclic enyne cumulene systems
    Journal of Physical Chemistry B, 2016
    Co-Authors: Sharmistha Karmakar, Ayan Datta
    Abstract:

    Direct dynamics calculation using canonical variational transtition state theory (CVT) inclusive of small curvature tunneling (SCT) reveals heavy atom tunneling in Myers–Saito cyclization of 10- and 9-membered cyclic enyne–cumulene systems like 1,6-didehydro[10]annulene and derivative of neocarzinostatin, respectively. The pure density functional theory functional, BLYP at a 6-31+G (d,p) basis set reproduce the observed reaction energies and barriers within 1.0 kcal/mol. The calculated rate constants of cyclization inclusive of heavy atom tunneling (kCVT+SCT = 3.26 × 10–4 s–1 at 222 K; t1/2 = 35 min) are in excellent agreement with experiments (t1/2 ∼ 21–31 min). Both primary and secondary kinetic isotope effect (KIE) become enhanced significantly upon inclusion of quantum mechanical tunneling. An Arrhenius plot of KIE shows measurable curvature at the experimental temperature of 222 K. The Translation Vector for the cyclization reactions in the transition-states (TS) show significant motion of primary an...

  • role of heavy atom tunneling in myers saito cyclization of cyclic enyne cumulene systems b
    The Journal of Physical Chemistry, 2016
    Co-Authors: Sharmistha Karmakar, Ayan Datta
    Abstract:

    Direct dynamics calculation using canonical variational transtition state theory (CVT) inclusive of small curvature tunneling (SCT) reveals heavy atom tunneling in Myers–Saito cyclization of 10- and 9-membered cyclic enyne–cumulene systems like 1,6-didehydro[10]annulene and derivative of neocarzinostatin, respectively. The pure density functional theory functional, BLYP at a 6-31+G (d,p) basis set reproduce the observed reaction energies and barriers within 1.0 kcal/mol. The calculated rate constants of cyclization inclusive of heavy atom tunneling (kCVT₊SCT = 3.26 × 10–⁴ s–¹ at 222 K; t₁/₂ = 35 min) are in excellent agreement with experiments (t₁/₂ ∼ 21–31 min). Both primary and secondary kinetic isotope effect (KIE) become enhanced significantly upon inclusion of quantum mechanical tunneling. An Arrhenius plot of KIE shows measurable curvature at the experimental temperature of 222 K. The Translation Vector for the cyclization reactions in the transition-states (TS) show significant motion of primary and secondary carbon atoms explaining the origin of large KIE.

  • Role of Heavy Atom Tunneling in Myers–Saito Cyclization of Cyclic Enyne-Cumulene Systems
    2016
    Co-Authors: Sharmistha Karmakar, Ayan Datta
    Abstract:

    Direct dynamics calculation using canonical variational transtition state theory (CVT) inclusive of small curvature tunneling (SCT) reveals heavy atom tunneling in Myers–Saito cyclization of 10- and 9-membered cyclic enyne–cumulene systems like 1,6-didehydro[10]­annulene and derivative of neocarzinostatin, respectively. The pure density functional theory functional, BLYP at a 6-31+G (d,p) basis set reproduce the observed reaction energies and barriers within 1.0 kcal/mol. The calculated rate constants of cyclization inclusive of heavy atom tunneling (kCVT+SCT = 3.26 × 10–4 s–1 at 222 K; t1/2 = 35 min) are in excellent agreement with experiments (t1/2 ∼ 21–31 min). Both primary and secondary kinetic isotope effect (KIE) become enhanced significantly upon inclusion of quantum mechanical tunneling. An Arrhenius plot of KIE shows measurable curvature at the experimental temperature of 222 K. The Translation Vector for the cyclization reactions in the transition-states (TS) show significant motion of primary and secondary carbon atoms explaining the origin of large KIE

David J Hawkes - One of the best experts on this subject based on the ideXlab platform.

  • automated three dimensional registration of magnetic resonance and positron emission tomography brain images by multiresolution optimization of voxel similarity measures
    Medical Physics, 1997
    Co-Authors: Colin Studholme, Derek L G Hill, David J Hawkes
    Abstract:

    Approaches using measures of voxel intensity similarity are showing promise in fully automating magnetic resonance (MR) and positron emission tomography (PET) image registration in the head, without requiring extraction and identification of corresponding structures. In this paper a method of multiresolution optimization of these measures is described and five alternative measures are compared: cross correlation, minimization of corresponding PET intensity variation, moments of the distribution of values in the intensity feature space, entropy of the intensity feature space and mutual information. Their ability to recover registration is examined for ten clinically acquired image pairs with respect to the size of initial misregistration, the precision of the final result, and the accuracy assessed by visual inspection. The mutual information measure proved the most robust to initial starting estimate, successfully registering 98.8% of 900 trial misregistrations. Success is defined as providing a visually acceptable solution to a trained observer. A high resolution search (1/16 mm step size) of 30 trial misregistrations showed that optimization using the mutual information measure provided solutions with 0.13 mm, 0.11 mm and 0.17 mm standard deviations in the three Cartesian axes of the Translation Vector and 0.2 degree, 0.3 degree and 0.2 degree standard deviations for rotations about the three axes. The algorithm takes between 4 and 8 minutes to run on a typical workstation, including visual inspection of the result.

  • automated three dimensional registration of magnetic resonance and positron emission tomography brain images by multiresolution optimization of voxel similarity measures
    Medical Physics, 1997
    Co-Authors: Colin Studholme, D Hill, David J Hawkes
    Abstract:

    Approaches using measures of voxel intensity similarity are showing promise in fully automating magnetic resonance(MR) and positron emission tomography(PET)image registration in the head, without requiring extraction and identification of corresponding structures. In this paper a method of multiresolution optimization of these measures is described and five alternative measures are compared: cross correlation, minimization of corresponding PET intensity variation, moments of the distribution of values in the intensity feature space, entropy of the intensity feature space and mutual information. Their ability to recover registration is examined for ten clinically acquired image pairs with respect to the size of initial misregistration, the precision of the final result, and the accuracy assessed by visual inspection. The mutual information measure proved the most robust to initial starting estimate, successfully registering 98.8% of 900 trial misregistrations. Success is defined as providing a visually acceptable solution to a trained observer. A high resolution search ( 1 16 mm step size) of 30 trial misregistrations showed that optimization using the mutual information measure provided solutions with 0.13 mm, 0.11 mm and 0.17 mm standard deviations in the three Cartesian axes of the Translation Vector and 0.2°, 0.3° and 0.2° standard deviations for rotations about the three axes. The algorithm takes between 4 and 8 minutes to run on a typical workstation, including visual inspection of the result.

Theodore E. Matikas - One of the best experts on this subject based on the ideXlab platform.

  • cyclic loading of a sic fiber reinforced ceramic matrix composite reveals damage mechanisms and thermal residual stress state
    Composites Part A-applied Science and Manufacturing, 2013
    Co-Authors: Konstantinos G Dassios, Evangelos Z. Kordatos, Dimitrios G Aggelis, Theodore E. Matikas
    Abstract:

    Abstract This study reports on the effects of axial thermal residual stresses, cyclic loading and presence of notches on the tensile performance of a SiC-fiber-reinforced barium–magnesium–alumina–silicate (BMAS) ceramic matrix composite. The residual stress state of the composite was experimentally measured by interrogation of the tensile curves at a uniquely well-defined common intersection point of unloading–reloading cycles in the tensile domain. Notch presence was critical on the material’s mechanical response and promoted catastrophic failure shortly after the achievement of a saturated matrix crack state. The result of cyclic loading was an increase by 20% in sustainable stress throughout loading, as compared to pure tension. Scatter in elastic properties within specimens of different notch-to-width ratios was reconciled with theoretical expectations by application of a Translation Vector approach in the stress–strain plane, based on the material’s residual stress state. Acoustic emission and infrared thermography provided valuable insight into damage identification, location and sequence.

  • large scale interfacial damage and residual stresses in a glass ceramic matrix composite
    Composite Interfaces, 2012
    Co-Authors: Konstantinos G Dassios, Theodore E. Matikas
    Abstract:

    The current work is concerned with the micro-mechanics of fracture of a SiC-fiber-reinforced barium osumilite (BMAS) ceramic matrix composite tested under both monotonic and cyclic tension. The double-edge notch (DEN) specimen configuration was employed in order to confine material damage within a predefined gage length. The imposition of successive loops of unloading to complete load relaxation and subsequent reloading were found to result in an increase by 20% in material strength as compared to pure tension; the finding is attributed to energy dissipation from large-scale interfacial debonding phenomena that dominated the post-elastic mechanical behavior of the composite. Cyclic loading also helped establish the axial residual stress state of the fibers in the composite, of tensile nature, via a well-defined common intersection point of unloading–reloading cycles. An approach consisting of the application of a Translation Vector in the stress–strain plane was successfully used to derive the residual st...

Kawin Ethayarajh - One of the best experts on this subject based on the ideXlab platform.

  • rotate king to get queen word relationships as orthogonal transformations in embedding space
    Empirical Methods in Natural Language Processing, 2019
    Co-Authors: Kawin Ethayarajh
    Abstract:

    A notable property of word embeddings is that word relationships can exist as linear substructures in the embedding space. For example, ‘gender’ corresponds to v_woman - v_man and v_queen - v_king. This, in turn, allows word analogies to be solved arithmetically: v_king - v_man + v_woman = v_queen. This property is notable because it suggests that models trained on word embeddings can easily learn such relationships as geometric Translations. However, there is no evidence that models exclusively represent relationships in this manner. We document an alternative way in which downstream models might learn these relationships: orthogonal and linear transformations. For example, given a Translation Vector for ‘gender’, we can find an orthogonal matrix R, representing a rotation and reflection, such that R(v_king) = v_queen and R(v_man) = v_woman. Analogical reasoning using orthogonal transformations is almost as accurate as using Vector arithmetic; using linear transformations is more accurate than both. Our findings suggest that these transformations can be as good a representation of word relationships as Translation Vectors.

  • rotate king to get queen word relationships as orthogonal transformations in embedding space
    arXiv: Computation and Language, 2019
    Co-Authors: Kawin Ethayarajh
    Abstract:

    A notable property of word embeddings is that word relationships can exist as linear substructures in the embedding space. For example, $\textit{gender}$ corresponds to $\vec{\textit{woman}} - \vec{\textit{man}}$ and $\vec{\textit{queen}} - \vec{\textit{king}}$. This, in turn, allows word analogies to be solved arithmetically: $\vec{\textit{king}} - \vec{\textit{man}} + \vec{\textit{woman}} \approx \vec{\textit{queen}}$. This property is notable because it suggests that models trained on word embeddings can easily learn such relationships as geometric Translations. However, there is no evidence that models $\textit{exclusively}$ represent relationships in this manner. We document an alternative way in which downstream models might learn these relationships: orthogonal and linear transformations. For example, given a Translation Vector for $\textit{gender}$, we can find an orthogonal matrix $R$, representing a rotation and reflection, such that $R(\vec{\textit{king}}) \approx \vec{\textit{queen}}$ and $R(\vec{\textit{man}}) \approx \vec{\textit{woman}}$. Analogical reasoning using orthogonal transformations is almost as accurate as using Vector arithmetic; using linear transformations is more accurate than both. Our findings suggest that these transformations can be as good a representation of word relationships as Translation Vectors.

Sharmistha Karmakar - One of the best experts on this subject based on the ideXlab platform.

  • role of heavy atom tunneling in myers saito cyclization of cyclic enyne cumulene systems
    Journal of Physical Chemistry B, 2016
    Co-Authors: Sharmistha Karmakar, Ayan Datta
    Abstract:

    Direct dynamics calculation using canonical variational transtition state theory (CVT) inclusive of small curvature tunneling (SCT) reveals heavy atom tunneling in Myers–Saito cyclization of 10- and 9-membered cyclic enyne–cumulene systems like 1,6-didehydro[10]annulene and derivative of neocarzinostatin, respectively. The pure density functional theory functional, BLYP at a 6-31+G (d,p) basis set reproduce the observed reaction energies and barriers within 1.0 kcal/mol. The calculated rate constants of cyclization inclusive of heavy atom tunneling (kCVT+SCT = 3.26 × 10–4 s–1 at 222 K; t1/2 = 35 min) are in excellent agreement with experiments (t1/2 ∼ 21–31 min). Both primary and secondary kinetic isotope effect (KIE) become enhanced significantly upon inclusion of quantum mechanical tunneling. An Arrhenius plot of KIE shows measurable curvature at the experimental temperature of 222 K. The Translation Vector for the cyclization reactions in the transition-states (TS) show significant motion of primary an...

  • role of heavy atom tunneling in myers saito cyclization of cyclic enyne cumulene systems b
    The Journal of Physical Chemistry, 2016
    Co-Authors: Sharmistha Karmakar, Ayan Datta
    Abstract:

    Direct dynamics calculation using canonical variational transtition state theory (CVT) inclusive of small curvature tunneling (SCT) reveals heavy atom tunneling in Myers–Saito cyclization of 10- and 9-membered cyclic enyne–cumulene systems like 1,6-didehydro[10]annulene and derivative of neocarzinostatin, respectively. The pure density functional theory functional, BLYP at a 6-31+G (d,p) basis set reproduce the observed reaction energies and barriers within 1.0 kcal/mol. The calculated rate constants of cyclization inclusive of heavy atom tunneling (kCVT₊SCT = 3.26 × 10–⁴ s–¹ at 222 K; t₁/₂ = 35 min) are in excellent agreement with experiments (t₁/₂ ∼ 21–31 min). Both primary and secondary kinetic isotope effect (KIE) become enhanced significantly upon inclusion of quantum mechanical tunneling. An Arrhenius plot of KIE shows measurable curvature at the experimental temperature of 222 K. The Translation Vector for the cyclization reactions in the transition-states (TS) show significant motion of primary and secondary carbon atoms explaining the origin of large KIE.

  • Role of Heavy Atom Tunneling in Myers–Saito Cyclization of Cyclic Enyne-Cumulene Systems
    2016
    Co-Authors: Sharmistha Karmakar, Ayan Datta
    Abstract:

    Direct dynamics calculation using canonical variational transtition state theory (CVT) inclusive of small curvature tunneling (SCT) reveals heavy atom tunneling in Myers–Saito cyclization of 10- and 9-membered cyclic enyne–cumulene systems like 1,6-didehydro[10]­annulene and derivative of neocarzinostatin, respectively. The pure density functional theory functional, BLYP at a 6-31+G (d,p) basis set reproduce the observed reaction energies and barriers within 1.0 kcal/mol. The calculated rate constants of cyclization inclusive of heavy atom tunneling (kCVT+SCT = 3.26 × 10–4 s–1 at 222 K; t1/2 = 35 min) are in excellent agreement with experiments (t1/2 ∼ 21–31 min). Both primary and secondary kinetic isotope effect (KIE) become enhanced significantly upon inclusion of quantum mechanical tunneling. An Arrhenius plot of KIE shows measurable curvature at the experimental temperature of 222 K. The Translation Vector for the cyclization reactions in the transition-states (TS) show significant motion of primary and secondary carbon atoms explaining the origin of large KIE