How does angular resolution affect diffusion imaging measures?

A key question in diffusion imaging is how many diffusion-weighted images suffice to provide adequate signal-to-noise ratio (SNR) for studies of fiber integrity. Motion, physiological effects, and scan duration all affect the achievable SNR in real brain images, making theoretical studies and simulations only partially useful. We therefore scanned 50 healthy adults with 105-gradient high-angular resolution diffusion imaging (HARDI) at 4T. From gradient image subsets of varying size (6 ≤ N ≤ 94) that optimized a spherical angular distribution energy, we created SNR plots (versus gradient numbers) for seven common diffusion anisotropy indices: fractional and relative anisotropy (FA, RA), mean diffusivity (MD), volume ratio (VR), geodesic anisotropy (GA), its hyperbolic tangent (tGA), and generalized fractional anisotropy (GFA). SNR, defined in a region of interest in the corpus callosum, was near-maximal with 58, 66, and 62 gradients for MD, FA, and RA, respectively, and with about 55 gradients for GA and tGA. For VR and GFA, SNR increased rapidly with more gradients. SNR was optimized when the ratio of diffusion-sensitized to non-sensitized images was 9.13 for GA and tGA, 10.57 for FA, 9.17 for RA, and 26 for MD and VR. In orientation density functions modeling the HARDI signal as a continuous mixture of tensors, the diffusion profile reconstruction accuracy rose rapidly with additional gradients. These plots may help in making trade-off decisions when designing diffusion imaging protocols.

Analyzing multi-fiber reconstruction in high angular resolution diffusion imaging using the tensor distribution function

High-angular resolution diffusion imaging (HARDI) can reconstruct fiber pathways in the brain with extraordinary detail, identifying anatomical features and connections not seen with conventional MRI. HARDI overcomes several limitations of standard diffusion tensor imaging, which fails to model diffusion correctly in regions where fibers cross or mix. As HARDI can accurately resolve sharp signal peaks in angular space where fibers cross, we studied how many gradients are required in practice to compute accurate orientation density functions, to better understand the tradeoff between longer scanning times and more angular precision. We computed orientation density functions analytically from tensor distribution functions (TDFs) which model the HARDI signal at each point as a unit-mass probability density on the 6D manifold of symmetric positive definite tensors. In simulated two-fiber systems with varying Rician noise, we assessed how many diffusionsensitized gradients were sufficient to (1) accurately resolve the diffusion profile, and (2) measure the exponential isotropy (EI), a TDF-derived measure of fiber integrity that exploits the full multidirectional HARDI signal. At lower SNR, the reconstruction accuracy, measured using the Kullback-Leibler divergence, rapidly increased with additional gradients, and EI estimation accuracy plateaued at around 70 gradients.

Innovation in Road Building: Removing Obstacles for Diffusion of Novel Building Products

How can obstacles to innovation be overcome in road construction? Using a focus group methodology, and based on two prior rounds of empirical work, the analysis in this chapter generates a set of four key solutions to two main construction innovation obstacles: (1) restrictive tender assessment and (2) disagreement over who carries the risk of new product failure. The four key solutions uncovered were: 1) pre-project product certification; 2) past innovation performance assessment; 3) earlier involvement of product suppliers and road asset operators; and 4) performance-based specifications. Additional research is suggested in order to illicit deeper insights into possible solutions to construction innovation obstacles, and should emphasise furthering the theoretical interpretation of empirical phenomena.

A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

Functional localization of the human color center by decreased water displacement using diffusion-weighted fMRI

Introduction Decreased water displacement following increased neural activity has been observed using diffusion-weighted functional MRI (DfMRI) at high b-values. The physiological mechanisms underlying the diffusion signal change may be unique from the standard blood oxygenation level-dependent (BOLD) contrast and closer to the source of neural activity. Whether DfMRI reflects neural activity more directly than BOLD outside the primary cerebral regions remains unclear. Methods Colored and achromatic Mondrian visual stimuli were statistically contrasted to functionally localize the human color center Area V4 in neurologically intact adults. Spatial and temporal properties of DfMRI and BOLD activation were examined across regions of the visual cortex. Results At the individual level, DfMRI activation patterns showed greater spatial specificity to V4 than BOLD. The BOLD activation patterns were more prominent in the primary visual cortex than DfMRI, where activation was localized to the ventral temporal lobe. Temporally, the diffusion signal change in V4 and V1 both preceded the corresponding hemodynamic response, however the early diffusion signal change was more evident in V1. Conclusions DfMRI may be of use in imaging applications implementing cognitive subtraction paradigms, and where highly precise individual functional localization is required.

Determination of diffusion parameters and activation energy of diffusion in V3Si phase with A15 crystal structure

Diffusion such is the integrated diffusion coefficient of the phase, the tracer diffusion coefficient of species at different temperatures and the activation energy for diffusion, are determined in V3Si phase with A15 crystal structure. The tracer diffusion coefficient of Si Was found to be negligible compared to the tracer diffusion coefficient of V. The calculated diffusion parameters will help to validate the theoretical analysis of defect structure of the phase, which plays an important role in the superconductivity.

Molecular theory for the effects of specific solute-solvent interaction on the diffusion of a solute particle in a molecular liquid

An understanding of the effect of specific solute-solvent interactions on the diffusion of a solute probe is a long standing problem of physical chemistry. In this paper a microscopic treatment of this effect is presented. The theory takes into account the modification of the solvent structure around the solute due to this specific interaction between them. It is found that for strong, attractive interaction, there is an enhanced coupling between the solute and the solvent dynamic modes (in particular, the density mode), which leads to a significant increase in the friction on the solute. The diffusion coefficient of the solute is found to depend strongly and nonlinearly on the magnitude of the attractive interaction. An interesting observation is that specific solute-solvent interaction can induce a crossover from a sliplike to a sticklike diffusion. In the limit of strong attractive interaction, we recover a dynamic version of the solvent-berg picture. On the other hand, for repulsive interaction, the diffusion coefficient of the solute increases. These results are in qualitative agreement with recent experimental observations.

Stability of a Random Diffusion with Linear Drift

We consider a Linear system with Markovian switching which is perturbed by Gaussian type noise, If the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable, We also shaw that under certain conditions the linear system with Markovian switching can be stabilized by such noisy perturbation.

Interdiffusion and Growth of the Superconductor Nb3Sn in Nb/Cu(Sn) Diffusion Couples

The confusion over the growth rate of the Nb3Sn superconductor compound following the bronze technique is addressed. Furthermore, a possible explanation for the corrugated structure of the product phase in the multifilamentary structure is discussed. Kirkendall marker experiments are conducted to study the relative mobilities of the species, which also explains the reason for finding pores in the product phase layer. The movement of the markers after interdiffusion reflects that Sn is the faster diffusing species. Furthermore, different concentrations of Sn in the bronze alloy are considered to study the effect of Sn content on the growth rate. Based on the parabolic growth constant at different temperatures, the activation energy for the growth is determined.

Preliminary investigations into the use of a functionalised polymer to reduce diffusion in Fricke gel dosimeters

Purpose A modification of the existing PVA-​FX hydrogel has been made to investigate the use of a functionalised polymer in a Fricke gel dosimetry system to decrease Fe3+ diffusion. Methods The chelating agent, xylenol orange, was chem. bonded to the gelling agent, polyvinyl alc. (PVA) to create xylenol orange functionalised PVA (XO-​PVA)​. A gel was created from the XO-​PVA (20​% w​/v) with ferrous sulfate (0.4 mM) and sulfuric acid (50 mM)​. Results This resulted in an optical d. dose sensitivity of 0.014 Gy-​1, an auto-​oxidn. rate of 0.0005 h-​1, and a diffusion rate of 0.129 mm2 h-​1; an 8​% redn. compared to the original PVA-​FX gel, which in practical terms adds approx. 1 h to the time span between irradn. and accurate read-​out. Conclusions Because this initial method of chem. bonding xylenol orange to polyvinyl alc. has inherently low conversion, the improvement on existing gel systems is minimal when compared to the drawbacks. More efficient methods of functionalising polyvinyl alc. with xylenol orange must be developed for this system to gain clin. relevance.

Structure informationnelle et constructions du kabyle : Etude de trois types de phrase dans le cadre de la grammaire constructionnelle

Information structure and Kabyle constructions Three sentence types in the Construction Grammar framework The study examines three Kabyle sentence types and their variants. These sentence types have been chosen because they code the same state of affairs but have different syntactic structures. The sentence types are Dislocated sentence, Cleft sentence, and Canonical sentence. I argue first that a proper description of these sentence types should include information structure and, second, that a description which takes into account information structure is possible in the Construction Grammar framework. The study thus constitutes a testing ground for Construction Grammar for its applicability to a less known language. It constitutes a testing ground notably because the differentiation between the three types of sentences cannot be done without information structure categories and, consequently, these categories must be integrated also in the grammatical description. The information structure analysis is based on the model outlined by Knud Lambrecht. In that model, information structure is considered as a component of sentence grammar that assures the pragmatically correct sentence forms. The work starts by an examination of the three sentence types and the analyses that have been done in André Martinet s functional grammar framework. This introduces the sentence types chosen as the object of study and discusses the difficulties related to their analysis. After a presentation of the state of the art, including earlier and more recent models, the principles and notions of Construction Grammar and of Lambrecht s model are introduced and explicated. The information structure analysis is presented in three chapters, each treating one of the three sentence types. The analyses are based on spoken language data and elicitation. Prosody is included in the study when a syntactic structure seems to code two different focus structures. In such cases, it is pertinent to investigate whether these are coded by prosody. The final chapter presents the constructions that have been established and the problems encountered in analysing them. It also discusses the impact of the study on the theories used and on the theory of syntax in general.

La contextualisation du discours radiophonique par des moyens prosodiques. L’exemple de cinq grands philosophes français du XXe siècle

"Radiodiskurssin kontekstualisointi prosodisin keinoin. Esimerkkinä viisi suurta ranskalaista 1900-luvun filosofia" Väitöskirja käsittelee puheen kontekstualisointia prosodisin keinoin. Toisin sanottuna työssä käsitellään sitä, miten puheen prosodiset piirteet (kuten sävelkulku, intensiteetti, tauot, kesto ja rytmi) ohjaavat puheen tulkintaa vanhastaan enemmän tutkittujen sana- ja lausemerkitysten ohella. Työssä keskitytään seitsemään prosodisesti merkittyyn kuvioon, jotka koostuvat yhden tai usean parametrin silmiinpistävistä muutoksista. Ilmiöitä käsitellään sekä niiden akustisten muotojen että tyypillisten esiintymisyhteyksien ja diskursiivisten tehtävien näkökulmasta. Aineisto koostuu radio-ohjelmista, joissa puhuu viisi suurta ranskalaista 1900-luvun filosofia: Gaston Bachelard, Albert Camus, Michel Foucault, Maurice Merleau-Ponty ja Jean-Paul Sartre. Ohjelmat on lähetetty eri radiokanavilla Ranskassa vuosina 1948–1973. Väitöskirjan tulokset osoittavat, että prosodisesti merkityt kuviot ovat moniulotteisia puheen ilmiöitä, joilla on keskeinen rooli sanotun kontekstualisoinnissa: ne voivat esimerkiksi nostaa tai laskea sanotun informaatioarvoa, ilmaista puhujan voimakasta tai heikkoa sitoutumista sanomaansa, ilmaista rakenteellisen kokonaisuuden jatkumista tai päättymistä, jne. Väitöskirja sisältää myös kontrastiivisia osia, joissa ilmiöitä verrataan erääseen klassisessa pianomusiikissa esiintyvään melodiseen kuvioon sekä erääseen suomen kielen prosodiseen ilmiöön. Tulokset viittaavat siihen, että tietynlaista melodista kuviota käytetään samankaltaisena jäsentämiskeinona sekä puheessa että klassisessa musiikissa. Lisäksi tulokset antavat viitteitä siitä, että tiettyjä melodisia muotoja käytetään samankaltaisten implikaatioiden luomiseen kahdessa niinkin erilaisessa kielessä kuin suomessa ja ranskassa. Yksi väitöskirjan osa käsittelee pisteen ja pilkun prosodista merkitsemistä puheessa. Tulosten mukaan pisteellä ja pilkulla on kummallakin oma suullinen prototyyppinsä: piste merkitään tyypillisesti sävelkulun laskulla ja tauolla, ja pilkku puolestaan sävelkulun nousulla ja tauolla. Merkittävimmät tulokset koskevat kuitenkin tapauksia, joissa välimerkki tulkitaan prosodisesti epätyypillisellä tavalla: sekä pisteellä että pilkulla vaikuttaisi olevan useita eri suullisia vastaavuuksia, ja välimerkkien tehtävät voivat muotoutua hyvin erilaisiksi niiden prosodisesta tulkinnasta riippuen.

Pour une éthique du traducteur poéticien

This doctoral thesis starts with a comprehensive introduction seeking to anchor the problematics of the ethics of the poetician translator (a translator of literary and similar texts) in a theoretical framework drawing on moral philosophy. This introductory section is followed by six published papers (four journal articles and two papers from conference proceedings), forming the main body of the thesis, which progressively develop a possible application of this theoretical framework. Starting from the acknowledgement that one of the ethical stakes in translation is constructed around the relation to the foreign and to the other , the translation process is scrutinized through the prism of the philosophies of Dialogue , focusing on how the translating actors relate to their task. The central notions around which philosophies of Dialogue are built are introduced and applied to translation. The question of intersubjective relations, addressed from a philosophical perspective, is developed with the help of the works of Martin Buber, Gabriel Marcel, Emmanuel Levinas and Paul Ric ur. The introductory section presents and explicates the thought of each of these philosophers and extracts the concepts that are then developed in the articles and conference papers collected here. Each paper concentrates on the notions of one of the philosophers referred to above and places these notions in perspective with other philosophies of Dialogue. All the papers contribute to explicating the relationship between the multiple philosophical notions that address the problematics of alterity and the condition of the translator. The work as a whole leads to the idea that the task of the poetician translator is not only to translate a text properly but above all to rouse and increase the desire of linguistic communities to live together.