Sensitivity Vector Research Articles

Two-dimensional spatiotemporal coding of linear acceleration in vestibular nuclei neurons

Response properties of vertical (VC) and horizontal (HC) canal/otolith-convergent vestibular nuclei neurons were studied in decerebrate rats during stimulation with sinusoidal linear accelerations (0.2-1.4 Hz) along different directions in the head horizontal plane. A novel characteristic of the majority of tested neurons was the nonzero response often elicited during stimulation along the "null" direction (i.e., the direction perpendicular to the maximum sensitivity vector, Smax). The tuning ratio (Smin gain/Smax gain), a measure of the two-dimensional spatial sensitivity, depended on stimulus frequency. For most vestibular nuclei neurons, the tuning ratio was small at the lowest stimulus frequencies and progressively increased with frequency. Specifically, HC neurons were characterized by a flat Smax gain and an approximately 10-fold increase of Smin gain per frequency decade. Thus, these neurons encode linear acceleration when stimulated along their maximum sensitivity direction, and the rate of change of linear acceleration (jerk) when stimulated along their minimum sensitivity direction. While the Smax vectors were distributed throughout the horizontal plane, the Smin vectors were concentrated mainly ipsilaterally with respect to head acceleration and clustered around the naso-occipital head axis. The properties of VC neurons were distinctly different from those of HC cells. The majority of VC cells showed decreasing Smax gains and small, relatively flat, Smin gains as a function of frequency. The Smax vectors were distributed ipsilaterally relative to the induced (apparent) head tilt. In type I anterior or posterior VC neurons, Smax vectors were clustered around the projection of the respective ipsilateral canal plane onto the horizontal head plane. These distinct spatial and temporal properties of HC and VC neurons during linear acceleration are compatible with the spatiotemporal organization of the horizontal and the vertical/torsional ocular responses, respectively, elicited in the rat during linear translation in the horizontal head plane. In addition, the data suggest a spatially and temporally specific and selective otolith/canal convergence. We propose that the central otolith system is organized in canal coordinates such that there is a close alignment between the plane of angular acceleration (canal) sensitivity and the plane of linear acceleration (otolith) sensitivity in otolith/canal-convergent vestibular nuclei neurons.

Intraocular pressure and retinal blood flow in the normal and glaucomatous eye

Purpose: To assess visual and circulatory responses to treatment with topical beta adrenergic antagonists. Design: Institutional prospective randomized clinical trial in normal adults. Methods: Twenty adults (36 (mean) ± 8 (S.D.) years) underwent repeated baseline perimetry (Humphrey 30-2), contrast sensitivity (Vector Vision), perimacular microcirculatory studies (Oculix blue-field entoptic simulator), intraocular pressure (IOP), heart rate (HR), and blood pressure (BP) testing. Subjects commenced either timolol 0.5% or betaxolol 0.5% twice daily on day 1, were retested on days 3 and 35, discontinued treatment for 21 days, whereupon repeated tests were performed. Treatment responses were compared by paired t-test. Results: Timolol-treated eyes showed improvement in contrast sensitivity (P=0.03) and pericentral perimetric thresholds (P=0.01), but corresponding increases among betaxolol-treated eyes were significantly higher (P=0.03 and 0.04, respectively, relative to timolol-treated eyes). Leukocyte velocity increased with both drugs, each with post-withdrawal carryover (P≤0.03). Significant IOP reduction (∼2.5 mmHg) occurred in both groups, BP fell 2.8 mmHg among betaxolol-treated subjects (P=0.02), and HR was 2 bpm slower among timolol-treated subjects (P=0.03), but all reverted to baseline values after washout. Conclusions: Both treatment groups demonstrated significant changes in visual function and perimacular hemodynamics, sustained after the terminal 3-week washout period.

Spatio-temporal convergence (STC) in otolith neurons.

It has been recently demonstrated that some primary otolith afferents and most otolith-related vestibular nuclei neurons encode two spatial dimensions that can be described by two vectors in temporal and spatial quadrature. These cells are called broadly-tuned neurons. They are characterized by a non-zero tuning ratio which is defined as the ratio of the minimum over the maximum sensitivity of the neuron. Broadly-tuned neurons exhibit response gains that do not vary according to the cosine of the angle between the stimulus direction and the cell's maximum sensitivity vector and response phase values that depend on stimulus orientation. These responses were observed during stimulation with pure linear acceleration and can be explained by spatio-temporal convergence (STC) of primary otolith afferents and/or otolith hair cells. Simulations of STC of the inputs to primary otolith afferents and vestibular nuclei neurons have revealed interesting characteristics: First, in the case of two narrowly-tuned input signals, the largest tuning ratio is achieved when the input signals are of equal gain. The smaller the phase difference between the input vectors, the larger the orientation differences that are required to produce a certain tuning ratio. Orientation and temporal phase differences of 30-40 degrees create tuning ratios of approximately 0.10-0.15 in target neurons. Second, in the case of multiple input signals, the larger the number of converging inputs, the smaller the tuning ratio of the target neuron. The tuning ratio depends on the number of input units, as long as there are not more than about 10. For more than 10-20 input vectors, the tuning ratio becomes almost independent of the number of inputs. Further, if the inputs comprise two populations (with different gain and phase values at a given stimulus frequency), the largest tuning ratio is obtained when the larger population has a smaller gain. These findings are discussed in the context of known anatomical and physiological characteristics of innervation patterns of primary otolith afferents and their possible convergence onto vestibular nuclei neurons.

Strain Field Measurement in Fracture Process Zone

Center‐notched mortar plate specimens are loaded in tension. A multiple sensitivity vector holographic setup is developed to record several deformation stages during the stable crack propagation range. The three‐sensitivity vector setup enables the calculation of both crack opening displacements and strain fields around the crack trajectories. An image analysis system is used to isolate the interferometric effect from the sandwich holograms, resulting in fringe patterns with perfect contrast. Image analysis is also used as a faster, more accurate, and more consistent method for fringe count. After evaluation of the holograms, the existence of tensile forces transmitted through the crack faces is associated with the presence of tensile strain behind the crack tip. A definition of the fracture process zone (FPZ) is proposed based on the difference between experimentally observed and linear elastic fracture mechanics (LEFM) strain fields. Deviations from the linear elastic solution show a relatively small zone of nonlinearity in front of the crack tip and a wake fracture process zone (WFPZ) behind the crack tip. A cohesive crack type of model with a bilinear closing process zone is used to predict the experimental observations.

Use of sensitivity vector variations to determine absolute displacements in double exposure hologram interferometry

Two solutions are presented to the problem of unknown absolute fringe order in double exposure hologram interferometry, a problem that confronts systems that require a single view of an object. One solution determines the vectorial object displacements relative to one reference point on the object. The other employs variations of the sensitivity vectors to provide absolute displacement analysis. For absolute displacements, a minimum of four illuminations is required.

A Hierarchical Analysis Model for Multiobjective Decisionmaking

In this paper we attempt to propose a method for preference degree analysis in multiobjective decisionmaking problems(MDMPs), called the multiple factor analysis method based on a hierarchical analysis model. The concept of preference degree(PD) is first discussed. Here a PD is used as a measurement for describing preference information of decision makers (DMs) to some value of an objective. A hierarchical model for analyzing the preference information is then deduced by defining objective domain of discourse (ODD), fuzzy degree domain of discourse (FDDD), factor domain of discourse (FDD) and sensitivity vector. Furthermore, some methods are explored for analyzing DMs* PDs of objective values according to a single factor and multiple factors, respectively. At last, an example is briefly introduced.

A Control Measure for Preventing Auto-Parametric Resonance in Power Systems

Auto-parametric resonance (internal resonance) is regarded as a kind of nonlinear oscillation stemming from to the nonlinearity of synchronizing power of generators. The resonance is closely related to power system stability, especially to unstable oscillation phenomena such as "negative damping" and "sustained oscillation". The authors have already developed a quantitative analysis method and proposed stability indices to estimate power system's viability under resonance condition.This paper proposes an effective countermeasure to prevent auto-parametric resonance based on a stability index. To be specific, the sensitivity vector of the index corresponding to generator output is used to obtain an effective measure for load dispatching. The proposed control methodology can be incorporated into other control schemes such as ELD. Numerical simulations on a longitudinal 4-machine system have confirmed the effectiveness of the proposed scheme.

Holographic interferometer with mutually orthogonal arrangement of the sensitivity vectors

Holographic interferometer with mutually orthogonal arrangement of the sensitivity vectors

Numerical verification of design sensitivity analysis

Considerable progress has been made in developing analytical methods for design sensitivity analysis of structural and mechanical systems. Sensitivity expressions require numerical implementation of several steps before the final sensitivity vectors are obtained. This is particularly true for problems involving transient dynamic response and shape optimization. Therefore, it is important to verify numerical implementation and calculations based on the analytical sensitivity expressions before optimization of the problem is carried out. This paper describes three numerical procedures for verification of the sensitivity calculations. An example from optimal control literature is used to demonstrate the procedures and make recommendations for practical applications

Spatial arrangement of the vestibular and the oculomotor system in the rat

The treatment of the spatial aspects of vestibular sensation, ocular movement near primary position, and their neural processing requires numerical information about the directions of maximal sensitivity of the semicircular canals (SCC), the direction of gaze at primary position, and the directions of eye rotation generated by each individual extraocular muscle (EOM). A good approximation of this information can be gained from stereotaxic measurements of the geometrical arrangement of the canals' bony structure, from measurements of the pupil's orientation, and from measurements of the directions of muscle pull as well as of the center of eye rotation. The results of measurements in pigmented rats are given as unit sensitivity vectors and unit action in head-fixed coordinate systems and compared with data from rabbit, cat, monkey, and human. The misalignment of ‘coplanar’ SCC with 2.5–15.6° is second only to humans, while the misalignment of the vectors of ‘antagonistic’ EOM with 27.2–39° is even more oblique than in humans and thereby even more so than in the other mammals. Misalignment of SCC and ‘corresponding’ EOM with 15.5–34.2° again is largest, followed by that in humans and then the other mammals. The rat may therefore be useful in studying those mechanisms by which the central nervous system deals with the obliqueness of systems that play such an important role in humans, too.

Stroboscopic holographic interferometry: measurements of vector components of a vibration

The interpretation of time-averaged holographic fringes recorded with a vibrating object presents problems when the direction of the motion is not known or when points on the object are moving in two or three dimensions. Measurements on additional holograms with properly chosen directions of the sensitivity vector are then required to evaluate the vibration amplitude. However, reduction of the data, even along a single line, is laborious and subject to errors. This paper describes a computerized system which uses stroboscopic illumination in conjunction with digital phase-shifting techniques to evaluate the magnitude and direction of the surface displacements at a uniformly spaced array of points covering the vibrating object. These values are used along with data on the shape of the object to calculate the in-plane and out-of-plane components of the vibration at these points. The operation of the system is illustrated with some results obtained with a compressor blade from a jet engine. Measurements of the surface displacements at different epochs of the vibration cycle permit a detailed analysis of complex vibrations.

A Study of Two-Dimensional Plane Elasticity Finite Elements for Optimal Design

ABSTRACT Design of structures using a variety of two-dimensional finite elements is considered in this paper. An efficient technique of computing first-order derivatives of pointwise stress constraints for simple and higher-order two-dimensional (membrane) finite elements is presented. Computational aspects of design sensitivity vector calculation, using a semi-analytical method versus traditional methods are presented. Implementation of a fully-stressed design approach to find a suitable initial estimate leads to increased computational efficiency. These aspects of the design procedure are illustrated through analysis of numerical examples. Experience indicates that a suitable mix of low and higher-order elements yields the most efficient and accurate design model.

Multilevel substructuring sensitivity analysis

Solution techniques for handling large scale engineering optimization problems are reviewed. Potentials for practical applications as well as their limited capabilities are discussed. A new solution algorithm for design sensitivity is proposed. The algorithm is based upon the multilevel substructuring concept to be coupled with the adjoint method of sensitivity analysis. There are no approximations involved in the present algorithm except the usual approximations introduced due to the discretization of the finite element model. It is a well-known fact that substructuring concept can be exploited in order to reduce computer core memory requirement and the total solution time executed. These advantages have been realized not only for statics analysis, but also for design sensitivity analysis. For truly large scale structures, however, it is necessary to use multilevel substructuring. The present paper has formulated a multilevel algorithm for design sensitivity analysis. A two-level substructuring example is used to verify the proposed algorithm. The sensitivity vector obtained by the multilevel algorithm is exactly identical to the one obtained by a more conventional approach.

Network Sensitivity Analysis

Incremental as well as large change sensitivity computation is frequently required for design optimization and computer aided design. For probabilistic analysis need also exists for multi variable sensitivity computation. In general incremental sensitivity computation can be handled using sensitivity network, adjoint network and algebraic matrix techniques. With sensitivity and adjoint network approaches, the algebraic differential operator notation presents an integrated approach for derivation of results in frequency and time domain. The main difference in the two approaches consists in solution of all or one network variable with respect to one or all m parameters undergoing change. Further difference exists when considering higher order sensitivity co-efficients since use of sensitivity network approach for nth order co-efficients necessitates solution of all (n—1) order sensitivity networks but adjoint network technique entails solution of (m+2) networks of which one is original and (m+1) are adjoint networks with unit drivers. The adjoint networks results also facilitate extension to a variety of applications. The algebraic matrix approach as applicable to linear time invariant networks in frequency domain is based on sensitivity network concept but results in ex plicit sensitivity vectors corresponding to hybrid formulation. The latter formulation is also used to derive explicit expression for large change sensitivity in terms of a modified system matrix of order typically equal to number of varying parameters. Since the number of parameters undergoing change is generally small as compared to total number of components in a large system, the method results in computational saving.

A quantitative analysis of the spatial organization of the vestibulo-ocular reflexes in lateral- and frontal-eyed animals—I. Orientation of semicircular canals and extraocular muscles

The spatial relationship between extraocular muscles and semicircular canals was evaluated in cat (frontal-eyed animal) and rabbit (lateral-eyed animal). Semicircular canal orientations in the rabbit were determined by a principal components analysis of data points obtained from the exposed osseous canals using a three-axis micromanipulator. Canal orientations were presented in terms of unit sensitivity vectors. Orientation of cxtraocular muscles in rabbits and cats was derived from measurements of the insertion and origin of each muscle with respect to a reference point on the skull and a calculated estimate of the center of the eye. Muscle orientations were presented in terms of unit action vectors. Semicircular canal planes of the rabbit labyrinth were not orthogonal, having deviations up to 14. Pairs of antagonistically acting vertical semicircular canals, left (right) anterior right (left) posterior deviated from coplanarity by 16, while the deviation for the horizontal canals was 9. In both animals, muscles of an antagonistic pair were coplanar to within 8, with the exception of the oblique muscles in the rabbit for which the deviation was 19. The three pairs of antagonistic muscles were almost orthogonal to each other, the maximum deviation between any of the pairs being 8 in the cat and 18 in the rabbit. Comparing extraocular muscle planes and semicircular canal planes reveals that they are roughly aligned. However, there were slight but consistent differences between a given semicircular canal plane and the planes of the muscles to which this canal is connected by the classical three-neuron-arc (principal vestibulo-ocular reflex circuits). This incongruence should be reflected in the connectivity of vestibuloocular reflex pathways, other than the principal connections.

Sensitivity study of an untransposed overhead transmission line

A theory for the sensitivity analysis of the receiving-end voltage and power in an untransposed transmission line for perturbations in line parameters and line lenght is described. It is shown how the sensitivity vectors of a particular quantity can be evaluated once the sensitivity vectors of the eigenvalues and eigenvectors of the product matrix ZY are known Z and Y being the series impedance and shunt-admittance matrices of the multiconductor transmission line, respectively.

Perspective corrections for measurement of deformations by holographic interferometry

In all quantitative analyses of holographic interferograms used for displacement or strain measurements it is the sensitivity vector that defines the geometry of the optical setup used for recording. Although the determination of this sensitivity vector is no easy task, one must know its variation in order to take into account changes in the conditions of illumination or observation along the different perspectives under which the object is seen. We describe here a gauging technique for making perspective corrections directly from the holographic image. The use of this technique has the advantage of freeing the object from the optical environment necessary to perform the recording.

Optimal design of superconducting turbogenerators via polyparametric sensitivity analysis

In this paper the dynamic behaviour of a superconducting turbogenerator is simulated by means of the Park's non-linear mathematical model in the state-space form so as to analyze the influence of the machine parameters simultaneous variations upon its dynamic behaviour via polyparametric sensitivity analysis approach. The computer program worked out by the authors is used to simulate a 2,000 MVA, three-phase, two-pole superconducting turbogenerator as well as to generate its parametric sensitivity functions. The machine model is subjected to a step input simulating a sudden three-phase short circuit occurring at the unit terminals. Its response is observed in the time domain simultaneously with the sensitivity functions, so as to determine the influence of each parameter variations on the dynamic behaviour of the simulated system. Investigation is here confined to the machine resistive parameters and only the ones which largely affect the machine dynamic response will be considered. The values of these ones are selected which achieve the most suitable machine dynamic response. Moreover a polyparametric sensitivity vector is derived from the parametric sensitivity functions in order to investigate the mutual influence of the parameter variations in their chosen ranges.

EFFICIENT TREATMENT OF CONSTRAINTS IN LARGE-SCALE STRUCTURAL OPTIMIZATION

The paper presents a new concept for the treatment of large numbers of stress and displacement constraints in finite dimensional optimal structural design. The idea is to replace a large number of stress and displacement constraints by a small number of equivalent functional constraints. The genesis of this concept is the distributed parameter and transient response structural design formulations where it has been used quite effectively. The major advantage of this constraint formulation is that design sensitivity vectors need to be calculated for only the reduced number of equivalent stress and displacement constraints. Thus, there is substantial computational advantage with the new formulation. Implications of the formulation are studied and several example problems are presented to show its potential in practical design applications.

Analysis of optimality criteria and gradient projection methods for optimal structural design

Abstract A general mathematical model for optimal design of structural and mechanical systems is defined. The finite element techniques for analysis of these systems are incorporated into the model. Optimality conditions for the model are derived. It is shown that an analytical solution of the optimality conditions is impossible except for trivial design problems. Numerical methods for solving these optimality conditions are presented. A direct method based on the gradient projection concept is derived. Numerical aspects for the method are discussed. These include step size selection, calculation of Langrange multipliers, identification of dependent design sensitivity vectors of constraint functions, and convergence criterion. Both direct and indirect approaches require total derivatives of cost and various constraint functions with respect to design variables. This is accomplished by integrating into both the approaches the state space design sensitivity analysis that has proven to be very general and efficient. It is shown that other major calculations of the two approaches are essentially the same. Thus there is potential for continuous transition between various algorithms for structural optimization. Optimal solutions for two design examples are obtained by hybrid methods to show the potential for further development of these methods.