Scalar Indices Research Articles

Mohr diagram interpretation of anisotropic diffusion indices in MRI

Descriptions of diffusion anisotropy in MR Diffusion Tensor Imaging are often based on scalar indices such as surface-to-volume ratio, volume ratio, fractional anisotropy and rotational anisotropy. Recently, Mohr diagram was introduced to visualize the anisotropic diffusion information, but in a graphical form. Even though both scalar indices and the Mohr diagram are derived from the elements of the diffusion tensor, so far, the relationships between these measures and the key aspects of the Mohr diagram have not been established. This paper demonstrates these relationships both qualitatively and quantitatively for two microscopically heterogeneous biologic tissues, kidney and spinal cord.

Evidence for a non-zero and a low matter density from a combined analysis of the 2dF Galaxy Redshift Survey and cosmic microwave background anisotropies

We perform a joint likelihood analysis of the power spectra of the 2dF Galaxy Redshift Survey (2dFGRS) and the cosmic microwave background (CMB) anisotropies under the assumptions that the initial fluctuations were adiabatic, Gaussian and well described by power laws with scalar and tensor indices of n_s and n_t. On its own, the 2dFGRS sets tight limits on the parameter combination Omega_m h, but relatively weak limits on the fraction of the cosmic matter density in baryons Omega_b/Omega_m. The CMB anisotropy data alone set poor constraints on the cosmological constant and Hubble constant because of a `geometrical degeneracy' among parameters. Furthermore, if tensor modes are allowed, the CMB data allow a wide range of values for the physical densities in baryons and cold dark matter. Combining the CMB and 2dFGRS data sets helps to break both the geometrical and tensor mode degeneracies. The values of the parameters derived here are consistent with the predictions of the simplest models of inflation, with the baryon density derived from primordial nucleosynthesis and with direct measurements of the Hubble parameter. In particular, we find strong evidence for a positive cosmological constant with a pm 2sigma range of 0.65 < Omega_Lambda < 0.85, completely independently of constraints on Omega_\Lambda derived from Type Ia supernovae.

Inflationary scenarios with scale-invariant spectral tensorial index

Next-to-leading order expressions related to Stewart-Lyth inverse problem are used to determine the inflationary models with a tensorial power spectrum described by a scale-invariant spectral index. Beyond power-law inflation, solutions are characterized by scale dependent scalar indices. These models can be used as assumption on the generation of primordial perturbations to test for scale dependence of the scalar index at large angular scales. If such a dependence is detected, a nonzero contribution of gravitational waves to the CMB spectrum must be expected.

Human acute cerebral ischemia: detection of changes in water diffusion anisotropy by using MR imaging.

To (a) determine the optimal choice of a scalar metric of anisotropy and (b) determine by means of magnetic resonance imaging if changes in diffusion anisotropy occurred in acute human ischemic stroke. The full diffusion tensor over the entire brain was measured. To optimize the choice of a scalar anisotropy metric, the performances of scalar indices in simulated models and in a healthy volunteer were analyzed. The anisotropy, trace apparent diffusion coefficient (ADC), and eigenvalues of the diffusion tensor in lesions and contralateral normal brain were compared in 50 patients with stroke. Changes in anisotropy in patients were quantified by using fractional anisotropy because it provided the best performance in terms of contrast-to-noise ratio as a function of signal-to-noise ratio in simulations. The anisotropy of ischemic white matter decreased (P = .01). Changes in anisotropy in ischemic gray matter were not significant (P = .63). The trace ADC decreased for ischemic gray matter and white matter (P < .001). The first and second eigenvalues decreased in both ischemic gray and ischemic white matter (P < .001). The third eigenvalue decreased in ischemic gray (P = .001) and white matter (P = .03). Gray matter is mildly anisotropic in normal and early ischemic states. However, early white matter ischemia is associated with not only changes in trace ADC values but also significant changes in the anisotropy, or shape, of the water self-diffusion tensor.

A Preliminary Study of Acute Responses to Clamped Alcohol Concentration and Family History of Alcoholism

The clamping method of alcohol administration was combined with a battery of dependent measures of frontal lobe brain function, and a novel index of acute adaptation, in a preliminary study in order to explore the paradigm's sensitivity to a familial history of alcoholism (FHA). Ten family history-positive (FHP) and 10 family history-negative (FHN) adult social drinkers of both genders underwent alcohol clamping. Twenty minutes after the start of an intravenous infusion of alcohol, the breath alcohol concentration was clamped at a target of 60+/-5 mg/dl for 150 min. Initial and adaptive responses to alcohol were assessed using scalar indices of change. One index assessed initial improvements or impairments in brain function after alcohol. The other index assessed acute adaptation (tolerance or sensitization) to alcohol while the brain's exposure to alcohol was held constant. The battery of dependent measures included subjective perceptions, neuropsychological tests, saccadic eye-movement tasks, and event-related potential (ERP) tasks. Effect sizes for FHA were estimated for 10 dependent variables that showed adequate baseline test-retest reliability (r>0.6). FHP subjects showed less intense initial responses to alcohol in subjective perceptions, but greater changes in the latency of volitional saccades and ERP P3 components than did the FHN controls. FHP subjects generally showed greater acute tolerance to alcohol than did controls, who showed more instances of acute sensitization at this moderate breath alcohol concentration. Effect sizes for FHA exceeded 0.4 in more than half of the indices. The BrAC clamping paradigm assesses initial and adaptive responses of a battery of behavioral and electrophysiological measures of frontal lobe function to ethanol that appear both reliable and sensitive to FHA.

Unsupervised time series classification

In this paper a scheme for unsupervised probabilistic time series classification is detailed. The technique utilizes autocorrelation terms as discriminatory features and employs the Volterra Connectionist Model (VCM) to transform the multi-dimensional feature information of each training vector to a one-dimensional classification space. This allows the probability density functions (PDFs) of the scalar classification indices to be represened as a function of the classifier weights. The weight values are chosen so as to maximize the separability of the class conditional PDFs. Statistical similarity tests based on the overlap area of the PDFs are then performed to determine the class membership of each training vector. Results are presented that illustrate the performance of the scheme applied to synthetic and real world data.

Vector efficiency in multiparameter estimation

Relative efficiencies are studied through invariance in multiparameter estimation. Scalar efficiency indices, together with lower and upper bounds, are generated via invariant monotone functions, and are augmented to include tripartite efficiency numbers. Bounds on directed Fisher efficiencies emerge through generalized Rayleigh quotients. Applications are noted in improving estimators through conditioning, in comparing regular estimators with efficient estimators achieving their minimal dispersion bounds, and in comparing two second-order experimental designs.

Fuzzy cardinality and the modeling of imprecise quantification

The concept of cardinality of a fuzzy set has received attention from several researchers and has been defined in several apparently independent manners. A systematic investigation of this notion is performed which unifies and improves previous attempts. The cardinality of a fuzzy set, viewed as a fuzzy integer, is related to scalar cardinality indices. The closely related question of the probability of a fuzzy event is dealt with. Lastly, the usefulness of fuzzy cardinality for meaning representation of statements or queries involving fuzzy linguistic quantifiers is emphasized.

High‐latitude indices of electric and magnetic variability during the CDAW 6 intervals

For the two Coordinated Data Analysis Workshop 6 intervals, we derived the global distribution above the north polar region of ionospheric currents, field‐aligned currents, electric fields and Joule heat from geomagnetic variations recorded at 107 stations and modeled values of ionospheric conductance (Kamide et al., 1983). In addition, we computed several scalar indices which summarize changes in the magnetic and electric fields at high latitudes. Since these indices were derived from the same data, namely ground magnetic variations, a high degree of similarity is expected to exist among their temporal variations, as the correlation coefficients lie between 0.41 and 0.98. From the cross correlation between the total auroral electrojet currents and the AU and AL indices of electrojet current density, we find that the latitudinal width of the westward electrojet expands (contracts) simultaneously with an increase (decrease) in current density. However, the lower correlation between AU and the total eastward current demonstrates the importance of changes of latitudinal width to the total eastward current. The relatively poor correlation between AU and AL highlights the differences between the two indices and raises doubts about the meaning of the AE index, which is a linear combination of the two. We notice that both electric potential and conductivity changes influence the electrojets. When the electric potential difference across the polar cap is large in relation to a given intensity of the total current, the “true” ionospheric current shows a maximum westward electrojet near dawn and a maximum eastward electrojet near dusk. When the two indices are relatively equal, the westward electrojet maximum moves toward midnight while the eastward electrojet stays near dusk.

Control of a Distributed Parameter System Using Vector Performance Index

The design of a feedback controller for a 1aree countercurrent heat exchanger employed as once-through steam generator for a nuclear power plant is presented in this paper. The specific design procedure is based on the minimization (noninferiority) of a vector performance index in which the components of the vector performance index are scalar performance indices. For this study, a three-dimensional performance index is used and the components represent: error in outlet steam pressure regulation; error in outlet steam temperature regulation; and error in load following. The objective of the study is that of finding the set of noninferior control parameters which give the corresponding noninferior performance vectors and describe the range of obtainable system performance.The mathematical model of the exchanger consists of a set of nonlinear partial differential equations with boundary conditions specified at three space points. The system structure does not allow the control signals to be distributed in space. They are applied only at the system boundaries. A simplified system model is used for the control optimization. This model is obtained by applying the method of weighted residuals to the linearized partial differential equations. The results of the control study show pressure regulation to be insensitive to changes in load regulation for a wide range of controller parameters. On the other hand, considerable trade off between the temperature and load regulation is observed.

Motion discomfort and transportation guideway form

A three-dimensional theory of motion discomfort is developed by defining scalar indices measuring discomfort due to acceleration and jerk. These indices are functions of effective acceleration and jerk vectors and their orientation to the preferred configuration of a subject. The optimal bank angle of a guideway is defined and shown to minimize acceleration discomfort. Isotropic approximations to the discomfort indices are proposed. Expressions for the indices are obtained in terms of the vehicle motion and guideway geometry. Deatiled analyses of motion along optimally banked circular helical and three-dimensional spiral curves are presented. Motion with zero fore-aft thrust on a curve in a vertical plane is also detailed. The approach assumes a smooth guideway and so vibrational inputs are not included. The analysis should be followed up by an experimental program before it is taken too seriously in design.

Automated Network Design-The Frequency-Domain Case

Application of Tellegen's theorem to an originally specified network leads to a simple computation of the unnormalized sensitivity of any associated network function with respect to all pertinent network parameters in terms of analysis of it and its topologically equivalent adjoint network. The reinterpretation of this sensitivity to scalar indices of network performance provides an automated frequency-domain network design principle of far-reaching consquences. A computer program has been written to implement the design algorithm. Preliminary results show this program to be highly effective.