Tensor products of Leavitt path algebras

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Acute Damage to the Posterior Limb of the Internal Capsule on Diffusion Tensor Tractography as an Early Imaging Predictor of Motor Outcome after Stroke

Background and Purpose Early prediction of motor outcome is of interest in stroke management. We aimed to determine whether lesion location at DTT is predictive of motor outcome after acute stroke and whether this information improves the predictive accuracy of the clinical scores. Methods We evaluated 60 consecutive patients within 12 hours of MCA stroke onset. We used DTT to evaluate CST involvement in the MC and PMC, CS, CR, and PLIC and in combinations of these regions at admission, at day 3, and at day 30. Severity of limb weakness was assessed using the m-NIHSS (5a, 5b, 6a, 6b). We calculated volumes of infarct and FA values in the CST of the pons. Results Acute damage to the PLIC was the best predictor associated with poor motor outcome, axonal damage, and clinical severity at admission (P&.001). There was no significant correlation between acute infarct volume and motor outcome at day 90 (P=.176, r=0.485). The sensitivity, specificity, and positive and negative predictive values of acute CST involvement at the level of the PLIC for 4 motor outcome at day 90 were 73.7%, 100%, 100%, and 89.1%, respectively. In the acute stage, DTT predicted motor outcome at day 90 better than the clinical scores (R2=75.50, F=80.09, P&.001). Conclusions In the acute setting, DTT is promising for stroke mapping to predict motor outcome. Acute CST damage at the level of the PLIC is a significant predictor of unfavorable motor outcome.

A Monte Carlo-Based Fiber Tracking Algorithm using Diffusion Tensor MRI

Diffusion tensor magnetic resonance imaging, which measures directional information of water diffusion in the brain, has emerged as a powerful tool for human brain studies. In this paper, we introduce a new Monte Carlo-based fiber tracking approach to estimate brain connectivity. One of the main characteristics of this approach is that all parameters of the algorithm are automatically determined at each point using the entropy of the eigenvalues of the diffusion tensor. Experimental results show the good performance of the proposed approach

Distribution of single-particle strength due to short-range and tensor correlations

The distribution of single-particle strength in nuclear matter is calculated for a realistic nucleon-nucleon interaction. The influence of the short-range repulsion and the tensor component of the nuclear force on the spectral functions is to move approximately 13% of the total strength for all single-particle states beyond 100 MeV into the particle domain. This result is related to the abundantly observed quenching phenomena in nuclei which include the reduction of spectroscopic factors observed in (e,ep) reactions and the missing strength in low energy response functions.

Lagrangian and Hamiltonian BRST structures of the antysimmetric tensor gauge theory

We study the Becchi-Rouet-Stora-Tyutin (BRST) structure of a self-interacting antisymmetric tensor gauge field, which has an on-shell null-vector gauge transformation. The Batalin-Vilkovisky covariant general formalism is briefly reviewed, and the issue of on-shell nilpotency of the BRST transformation is elucidated. We establish the connection between the covariant and the canonical BRST formalisms for our particular theory. Finally, we point out the similarities and differences with Wittens string field theory.

Random mixtures with orientational order, and the anisotropic resistivity tensor of high Tc superconductors

By generalizing effective-medium theory to the case of orientationally ordered but positionally disordered two component mixtures, it is shown that the anisotropic dielectric tensor of oxide superconductors can be extracted from microwave measurements on oriented crystallites of YBa2Cu3O7¿x embedded in epoxy. Surprisingly, this technique appears to be the only one which can access the resistivity perpendicular to the copper¿oxide planes in crystallites that are too small for depositing electrodes. This possibility arises in part because the real part of the dielectric constant of oxide superconductors has a large magnitude. The validity of the effective-medium approach for orientationally ordered mixtures is corroborated by simulations on two¿dimensional anisotropic random resistor networks. Analysis of the experimental data suggests that the zero-temperature limit of the finite frequency resistivity does not vanish along the c axis, a result which would simply the existence of states at the Fermi surface, even in the superconducting state

Collineations of a symmetric 2-covariant tensor: Ricci collineations

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra, but in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra. As an application, we study the Ricci collineations of a type B warped spacetime.

Determination of the components of the gyration tensor of quartz by oblique incidence transmission two-modulator generalized ellipsometry

The two independent components of the gyration tensor of quartz, g11 and g33, have been spectroscopically measured using a transmission two-modulator generalized ellipsometer. The method is used to determine the optical activity in crystals in directions other than the optic axis, where the linear birefringence is much larger than the optical activity.

Energy-momentum tensor for scalar fields coupled to the dilaton in two dimensions

We clarify some issues related to the evaluation of the mean value of the energy-momentum tensor for quantum scalar fields coupled to the dilaton field in two-dimensional gravity. Because of this coupling, the energy-momentum tensor for matter is not conserved and therefore it is not determined by the trace anomaly. We discuss different approximations for the calculation of the energy-momentum tensor and show how to obtain the correct amount of Hawking radiation. We also compute cosmological particle creation and quantum corrections to the Newtonian potential.

Combination of diffusion tensor and functional magnetic resonance imaging during recovery from the vegetative state

Background: The rate of recovery from the vegetative state (VS) is low. Currently, little is known of the mechanisms and cerebral changes that accompany those relatively rare cases of good recovery. Here, we combined functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI) to study the evolution of one VS patient at one month post-ictus and again twelve months later when he had recovered consciousness. Methods fMRI was used to investigate cortical responses to passive language stimulation as well as task-induced deactivations related to the default-mode network. DTI was used to assess the integrity of the global white matter and the arcuate fasciculus. We also performed a neuropsychological assessment at the time of the second MRI examination in order to characterize the profile of cognitive deficits. Results: fMRI analysis revealed anatomically appropriate activation to speech in both the first and the second scans but a reduced pattern of task-induced deactivations in the first scan. In the second scan, following the recovery of consciousness, this pattern became more similar to that classically described for the default-mode network. DTI analysis revealed relative preservation of the arcuate fasciculus and of the global normal-appearing white matter at both time points. The neuropsychological assessment revealed recovery of receptive linguistic functioning by 12-months post-ictus. Conclusions: These results suggest that the combination of different structural and functional imaging modalities may provide a powerful means for assessing the mechanisms involved in the recovery from the VS.

Combination of diffusion tensor and functional magnetic resonance imaging during recovery from the vegetative state

Background: The rate of recovery from the vegetative state (VS) is low. Currently, little is known of the mechanisms and cerebral changes that accompany those relatively rare cases of good recovery. Here, we combined functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI) to study the evolution of one VS patient at one month post-ictus and again twelve months later when he had recovered consciousness. Methods fMRI was used to investigate cortical responses to passive language stimulation as well as task-induced deactivations related to the default-mode network. DTI was used to assess the integrity of the global white matter and the arcuate fasciculus. We also performed a neuropsychological assessment at the time of the second MRI examination in order to characterize the profile of cognitive deficits. Results: fMRI analysis revealed anatomically appropriate activation to speech in both the first and the second scans but a reduced pattern of task-induced deactivations in the first scan. In the second scan, following the recovery of consciousness, this pattern became more similar to that classically described for the default-mode network. DTI analysis revealed relative preservation of the arcuate fasciculus and of the global normal-appearing white matter at both time points. The neuropsychological assessment revealed recovery of receptive linguistic functioning by 12-months post-ictus. Conclusions: These results suggest that the combination of different structural and functional imaging modalities may provide a powerful means for assessing the mechanisms involved in the recovery from the VS.

Combination of diffusion tensor and functional magnetic resonance imaging during recovery from the vegetative state

Background: The rate of recovery from the vegetative state (VS) is low. Currently, little is known of the mechanisms and cerebral changes that accompany those relatively rare cases of good recovery. Here, we combined functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI) to study the evolution of one VS patient at one month post-ictus and again twelve months later when he had recovered consciousness. Methods fMRI was used to investigate cortical responses to passive language stimulation as well as task-induced deactivations related to the default-mode network. DTI was used to assess the integrity of the global white matter and the arcuate fasciculus. We also performed a neuropsychological assessment at the time of the second MRI examination in order to characterize the profile of cognitive deficits. Results: fMRI analysis revealed anatomically appropriate activation to speech in both the first and the second scans but a reduced pattern of task-induced deactivations in the first scan. In the second scan, following the recovery of consciousness, this pattern became more similar to that classically described for the default-mode network. DTI analysis revealed relative preservation of the arcuate fasciculus and of the global normal-appearing white matter at both time points. The neuropsychological assessment revealed recovery of receptive linguistic functioning by 12-months post-ictus. Conclusions: These results suggest that the combination of different structural and functional imaging modalities may provide a powerful means for assessing the mechanisms involved in the recovery from the VS.

onductivitat tèrmica i índex de refracció no lineal dels compostos KRE(WO4)2 (RE=Gd,Y, Yb and Lu)

Projecte de recerca elaborat a partir d’una estada al Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy entre setembre i desembre 2007. Els materials monocristal•lins tungstats dobles de potassi i terra rara, KRE(WO4)2, a partir d'ara KREW, són en l'actualitat un material competitiu com a material actiu per sistemes de làser d'estat sòlid. Aquests materials monoclínics són fàcils de dopar amb altres densitats de ions lantànid, Ln3+, i a més presenten unes seccions eficaces d'absorció i d'emissió, molt elevades. Dins d’aquesta família, destaca el KLuW; degut als seus millors resultats com a material làser. Durant aquesta estada d’un mes al laboratori Max Born de Berlin, s’han realitzat les mesures de conductivitat tèrmica d’aquest material, per tal de obtenir el seu tensor de segon ordre de conductivitat tèrmica. El bombeig òptic dels materials làser d’estat sòlid genera calor com a resultat de la termalització en els multiplets, de les relaxacions no-radiatives i de les absorcions residuals (defectes, impureses). Per tant, el coneixement de les propietats tèrmiques de qualsevol material actiu és essencial pel disseny de la cavitat làser i l’avaluació de la funció làser, especialment en règims d’altes potències(...)

Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

Estrategies per la inversió tridimensional de dades magnetotel.lúriques:

Projecte de recerca elaborat a partir d’una estada a la Dublin Institute for Advanced Studies, Irlanda, entre setembre i desembre del 2009.En els últims anys s’ha realitzat un important avanç en la modelització tridimensional en magnetotel•lúrica (MT) gracies a l'augment d’algorismes d’inversió tridimensional disponibles. Aquests codis utilitzen diferents formulacions del problema (diferències finites, elements finits o equacions integrals), diverses orientacions del sistema de coordenades i, o bé en el conveni de signe, més o menys, en la dependència temporal. Tanmateix, les impedàncies resultants per a tots els valors d'aquests codis han de ser les mateixes una vegada que es converteixen a un conveni de signe comú i al mateix sistema de coordenades. Per comparar els resultats dels diferents codis hem dissenyat models diferents de resistivitats amb estructures tridimensional incrustades en un subsòl homogeni. Un requisit fonamental d’aquests models és que generin impedàncies amb valors importants en els elements de la diagonal, que no són menyspreables. A diferència dels casos del modelització de dades magnetotel.lúriques unidimensionals i bidimensionals, pel al cas tridimensional aquests elements de les diagonals del tensor d'impedància porten informació sobre l'estructura de la resistivitat. Un dels models de terreny s'utilitza per comparar els diferents algoritmes que és la base per posterior inversió dels diferents codis. Aquesta comparació va ser seguida de la inversió per recuperar el conjunt de dades d'una estructura coneguda.