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    Gin McCollum

    Healthy human subjects can maintain adequate balance despite distorted somatosensory or visual feedback or vestibular feedback distorted by a peripheral vestibular disorder. Although it is not precisely known how this sensorimotor... more
    Healthy human subjects can maintain adequate balance despite distorted somatosensory or visual feedback or vestibular feedback distorted by a peripheral vestibular disorder. Although it is not precisely known how this sensorimotor integration task is achieved, the nervous system coordinates information from multiple sensory systems to produce motor commands differently in different sensory environments. These different ways of coordinating sensory information and motor commands can be thought of as "sensorimotor states". The way the nervous system distributes the monitoring of postural sway among states is analysed in this paper as a logical structure of transitions between states. The form of the transition structure is specified and distinguished from a finite state machine. The hypothesis that the nervous system could use a transition structure to maintain balance is tested by developing transition structures which are consistent with a set of experimental observations of postural control in healthy subjects and three groups of patients with peripheral vestibular disease.
    ... of head orientation in inertial-gravitational space, and the somatic sense of body ... Furthermore, at all three joints there is functional overlap among muscles exerting force ... and region boundary calculations is to select... more
    ... of head orientation in inertial-gravitational space, and the somatic sense of body ... Furthermore, at all three joints there is functional overlap among muscles exerting force ... and region boundary calculations is to select postural movement trajectories that reach balanced positions ...
    This paper reports a theoretical analysis of the transformation from a tactile stimulus of the face to climbing fiber responses in three regions of the cat cerebellum. The database consisted of climbing fiber receptive fields on the face... more
    This paper reports a theoretical analysis of the transformation from a tactile stimulus of the face to climbing fiber responses in three regions of the cat cerebellum. The database consisted of climbing fiber receptive fields on the face from 75 responses from the anterior lobe, 33 responses from the paramedian lobule (PML), and 52 responses from the crus IIp of the anesthetized cat. The receptive fields were similar in being composed of discrete areas on the skin, or skin compartments. The regional differences in the configurations of the receptive fields were reflected in which compartments most often combined to form receptive fields. Each region had a distinct pattern of the preponderance of skin compartments that combined to form receptive fields, and yet the preponderant compartments were all chosen from one composite set of compartments that applied to all three regions. The climbing fiber representation of the face differed over the three regions (1) in the parts of the face that were represented; (2) in the frequency with which certain areas were included in the receptive fields; and (3) in the details of the face that could be distinguished by differing ensembles of climbing fiber responses. The majority of the climbing fiber receptive fields from either the anterior lobe or the crus IIp were unique to the region, whereas the majority of the receptive fields of responses from the PML were encountered in one or both of the other regions. Overlapping all face receptive fields from each of the three regions revealed that the receptive fields were differentially focused on or around the cornea, nose, or chin. In the anterior lobe, the face receptive fields mainly included the chin (43%) and the glabrous tip of the nose (40%), but few included the cornea (1%). In the PML, the receptive fields included the cornea (24%) and the chin (58%), but none included the nose. In the crus IIp, the cornea was included in the greatest number (37%) of receptive fields, whereas the nose and the chin were included equally (24%). The different sets of climbing fiber receptive fields in each of the three regions afforded the regions differing abilities to distinguish among complex patterns of stimuli, depending on the portion of the face stimulated.
    Sensory contribution to perception and action depends on both sensory receptors and the organization of pathways (or projections) reaching the central nervous system. Unlike the semicircular canals that are divided into three discrete... more
    Sensory contribution to perception and action depends on both sensory receptors and the organization of pathways (or projections) reaching the central nervous system. Unlike the semicircular canals that are divided into three discrete sensitivity directions, the utricle has a relatively complicated anatomical structure, including sensitivity directions over essentially [Formula: see text] of a curved, two-dimensional disk. The utricle is not flat, and we do not assume it to be. Directional sensitivity of individual utricular afferents decreases in a cosine-like fashion from peak excitation for movement in one direction to a null or near null response for a movement in an orthogonal direction. Directional sensitivity varies slowly between neighboring cells except within the striolar region that separates the medial from the lateral zone, where the directional selectivity abruptly reverses along the reversal line. Utricular primary afferent pathways reach the vestibular nuclei and cerebellum and, in many cases, converge on target cells with semicircular canal primary afferents and afference from other sources. Mathematically, some canal pathways are known to be characterized by symmetry groups related to physical space. These groups structure rotational information and movement. They divide the target neural center into distinct populations according to the innervation patterns they receive. Like canal pathways, utricular pathways combine symmetries from the utricle with those from target neural centers. This study presents a generic set of transformations drawn from the known structure of the utricle and therefore likely to be found in utricular pathways, but not exhaustive of utricular pathway symmetries. This generic set of transformations forms a 32-element group that is a semi-direct product of two simple abelian groups. Subgroups of the group include order-four elements corresponding to discrete rotations. Evaluation of subgroups allows us to functionally identify the spatial implications of otolith and canal symmetries regarding action and perception. Our results are discussed in relation to observed utricular pathways, including those convergent with canal pathways. Oculomotor and other sensorimotor systems are organized according to canal planes. However, the utricle is evolutionarily prior to the canals and may provide a more fundamental spatial framework for canal pathways as well as for movement. The fullest purely otolithic pathway is likely that which reaches the lumbar spine via Deiters' cells in the lateral vestibular nucleus. It will be of great interest to see whether symmetries predicted from the utricle are identified within this pathway.
    This review focusses attention on a ragged edge of our knowledge of self-motion perception, where understanding ends but there are experimental results to indicate that present approaches to analysis are inadequate. Although self-motion... more
    This review focusses attention on a ragged edge of our knowledge of self-motion perception, where understanding ends but there are experimental results to indicate that present approaches to analysis are inadequate. Although self-motion perception displays processes of "top-down" construction, it is typically analyzed as if it is nothing more than a deformation of the stimulus, using a "bottom-up" and input/output approach beginning with the transduction of the stimulus. Analysis often focusses on the extent to which passive transduction of the movement stimulus is accurate. Some perceptual processes that deform or transform the stimulus arise from the way known properties of sensory receptors contribute to perceptual accuracy or inaccuracy. However, further constructive processes in self-motion perception that involve discrete transformations are not well understood. We introduce constructive perception with a linguistic example which displays familiar discrete ...
    Cognitive deficits such as poor concentration and short-term memory loss are known by clinicians to occur frequently among patients with vestibular abnormalities. Although direct scientific study of such deficits has been limited, several... more
    Cognitive deficits such as poor concentration and short-term memory loss are known by clinicians to occur frequently among patients with vestibular abnormalities. Although direct scientific study of such deficits has been limited, several types of investigations do lend weight to the existence of vestibular-cognitive effects. In this article we review a wide range of studies indicating a vestibular influence on the ability to perform certain cognitive functions. In addition to tests of vestibular patient abilities, these studies include dual-task studies of cognitive and balance functions, studies of vestibular contribution to spatial perception and memory, and works demonstrating a vestibular influence on oculomotor and motor coordination abilities that are involved in the performance of everyday cognitive tasks. A growing literature on the physiology of the vestibular system has demonstrated the existence of projections from the vestibular nuclei to the cerebral cortex. The goals ...
    Although the local structure of the cerebellum is fairly uniform and its inputs are often widely shared, outputs from different regions of the cerebellar cortex reach different parts of the cerebellar and vestibular nuclei, which can... more
    Although the local structure of the cerebellum is fairly uniform and its inputs are often widely shared, outputs from different regions of the cerebellar cortex reach different parts of the cerebellar and vestibular nuclei, which can affect the rest of the nervous system in different ways. In this review, we explain how different ensembles of climbing fiber responses in the anterior lobe and paramedian lobule can be generated by a tactile stimulus to the distal hindpaw. Apart from differing in degree of activation, the cortical regions differ also in the detailed pattern of the activation transmitted. The anterior lobe can distinguish a greater diversity of stimuli to various skin surfaces than can the paramedian median lobule. This differential classification of particular stimulus arrays by the two cerebellar regions could produce distinct patterns of neuronal activity in various corticonuclear compartments.
    This paper reports a theoretical analysis of the transformation from a tactile stimulus of the face to climbing fiber responses in three regions of the cat cerebellum. The database consisted of climbing fiber receptive fields on the face... more
    This paper reports a theoretical analysis of the transformation from a tactile stimulus of the face to climbing fiber responses in three regions of the cat cerebellum. The database consisted of climbing fiber receptive fields on the face from 75 responses from the anterior lobe, 33 responses from the paramedian lobule (PML), and 52 responses from the crus IIp of the anesthetized cat. The receptive fields were similar in being composed of discrete areas on the skin, or skin compartments. The regional differences in the configurations of the receptive fields were reflected in which compartments most often combined to form receptive fields. Each region had a distinct pattern of the preponderance of skin compartments that combined to form receptive fields, and yet the preponderant compartments were all chosen from one composite set of compartments that applied to all three regions. The climbing fiber representation of the face differed over the three regions (1) in the parts of the face that were represented; (2) in the frequency with which certain areas were included in the receptive fields; and (3) in the details of the face that could be distinguished by differing ensembles of climbing fiber responses. The majority of the climbing fiber receptive fields from either the anterior lobe or the crus IIp were unique to the region, whereas the majority of the receptive fields of responses from the PML were encountered in one or both of the other regions. Overlapping all face receptive fields from each of the three regions revealed that the receptive fields were differentially focused on or around the cornea, nose, or chin. In the anterior lobe, the face receptive fields mainly included the chin (43%) and the glabrous tip of the nose (40%), but few included the cornea (1%). In the PML, the receptive fields included the cornea (24%) and the chin (58%), but none included the nose. In the crus IIp, the cornea was included in the greatest number (37%) of receptive fields, whereas the nose and the chin were included equally (24%). The different sets of climbing fiber receptive fields in each of the three regions afforded the regions differing abilities to distinguish among complex patterns of stimuli, depending on the portion of the face stimulated.
    Peripheral receptive fields of climbing fiber responses from the anterior lobe of the cat display large intersections and distinct organizations. Receptive fields of the extremities and face have boundaries that follow the lines of a... more
    Peripheral receptive fields of climbing fiber responses from the anterior lobe of the cat display large intersections and distinct organizations. Receptive fields of the extremities and face have boundaries that follow the lines of a grid. Receptive fields of the tail and ventral trunk and some of the receptive fields on the extremities form concentric sets, which can be completely ordered by inclusion. Receptive fields along the spine form a chain, which indicates rostrocaudal position. Such regularities among the intersections, especially in the grid organization, allow the receptive fields to encode combinations and alternative combinations of skin locations as a pianist might distinguish chords rather than notes.
    Healthy human subjects can maintain adequate balance despite distorted somatosensory or visual feedback or vestibular feedback distorted by a peripheral vestibular disorder. Although it is not precisely known how this sensorimotor... more
    Healthy human subjects can maintain adequate balance despite distorted somatosensory or visual feedback or vestibular feedback distorted by a peripheral vestibular disorder. Although it is not precisely known how this sensorimotor integration task is achieved, the nervous system coordinates information from multiple sensory systems to produce motor commands differently in different sensory environments. These different ways of coordinating sensory information and motor commands can be thought of as "sensorimotor states". The way the nervous system distributes the monitoring of postural sway among states is analysed in this paper as a logical structure of transitions between states. The form of the transition structure is specified and distinguished from a finite state machine. The hypothesis that the nervous system could use a transition structure to maintain balance is tested by developing transition structures which are consistent with a set of experimental observations of postural control in healthy subjects and three groups of patients with peripheral vestibular disease.
    Kinks, homotopically nontrivial lightcone fields on R, can be black holes without curvature singularities, satisfying the weak energy condition. Kinks and all other spherically symmetric stationary spacetimes on R with roots of g have... more
    Kinks, homotopically nontrivial lightcone fields on R, can be black holes without curvature singularities, satisfying the weak energy condition. Kinks and all other spherically symmetric stationary spacetimes on R with roots of g have incomplete geodesics which need ...
    A discrete formalism, d-spaces, developed for analyzing complex movements, can be used to construct modes in which a stroke patient may relearn to walk. A specific example is sketched. The analogy between movement dissonance and quantum... more
    A discrete formalism, d-spaces, developed for analyzing complex movements, can be used to construct modes in which a stroke patient may relearn to walk. A specific example is sketched. The analogy between movement dissonance and quantum incompatibility is explored, along with an observationally-based distinction between dissonant and nonfunctional movement.
    Experimental studies have shown that responses of ventral intraparietal area (VIP) neurons specialize in head movements and the environment near the head. VIP neurons respond to visual, auditory, and tactile stimuli, smooth pursuit eye... more
    Experimental studies have shown that responses of ventral intraparietal area (VIP) neurons specialize in head movements and the environment near the head. VIP neurons respond to visual, auditory, and tactile stimuli, smooth pursuit eye movements, and passive and active movements of the head. This study demonstrates mathematical structure on a higher organizational level created within VIP by the integration of a complete set of variables covering face-infringement. Rather than positing dynamics in an a priori defined coordinate system such as those of physical space, we assemble neuronal receptive fields to find out what space of variables VIP neurons together cover. Section 1 presents a view of neurons as multidimensional mathematical objects. Each VIP neuron occupies or is responsive to a region in a sensorimotor phase space, thus unifying variables relevant to the disparate sensory modalities and movements. Convergence on one neuron joins variables functionally, as space and time are joined in relativistic physics to form a unified spacetime. The space of position and motion together forms a neuronal phase space, bridging neurophysiology and the physics of face-infringement. After a brief review of the experimental literature, the neuronal phase space natural to VIP is sequentially characterized, based on experimental data. Responses of neurons indicate variables that may serve as axes of neural reference frames, and neuronal responses have been so used in this study. The space of sensory and movement variables covered by VIP receptive fields joins visual and auditory space to body-bound sensory modalities: somatosensation and the inertial senses. This joining of allocentric and egocentric modalities is in keeping with the known relationship of the parietal lobe to the sense of self in space and to hemineglect, in both humans and monkeys. Following this inductive step, variables are formalized in terms of the mathematics of graph theory to deduce which combinations are complete as a multidimensional neural structure that provides the organism with a complete set of options regarding objects impacting the face, such as acceptance, pursuit, and avoidance. We consider four basic variable types: position and motion of the face and of an external object. Formalizing the four types of variables allows us to generalize to any sensory system and to determine the necessary and sufficient conditions for a neural center (for example, a cortical region) to provide a face-infringement space. We demonstrate that VIP includes at least one such face-infringement space.
    The object of this study is to mathematically specify important characteristics of visual flow during translation of the eye for the perception of depth and self-motion. We address various strategies by which the central nervous system... more
    The object of this study is to mathematically specify important characteristics of visual flow during translation of the eye for the perception of depth and self-motion. We address various strategies by which the central nervous system may estimate self-motion and depth from motion parallax, using equations for the visual velocity field generated by translation of the eye through space. Our results focus on information provided by the movement and deformation of three-dimensional objects and on local flow behavior around a fixated point. All of these issues are addressed mathematically in terms of definite equations for the optic flow. This formal characterization of the visual information presented to the observer is then considered in parallel with other sensory cues to self-motion in order to see how these contribute to the effective use of visual motion parallax, and how parallactic flow can, conversely, contribute to the sense of self-motion. This article will focus on a central case, for understanding of motion parallax in spacious real-world environments, of monocular visual cues observable during pure horizontal translation of the eye through a stationary environment. We suggest that the global optokinetic stimulus associated with visual motion parallax must converge in significant fashion with vestibular and proprioceptive pathways that carry signals related to self-motion. Suggestions of experiments to test some of the predictions of this study are made.
    In this article results of several published studies are synthesized in order to address the neural system for the determination of eye and head movement amplitudes of horizontal eye/head gaze shifts with arbitrary initial head and eye... more
    In this article results of several published studies are synthesized in order to address the neural system for the determination of eye and head movement amplitudes of horizontal eye/head gaze shifts with arbitrary initial head and eye positions. Target position, initial head position, and initial eye position span the space of physical parameters for a planned eye/head gaze saccade. The principal result is that a functional mechanism for determining the amplitudes of the component eye and head movements must use the entire space of variables. Moreover, it is shown that amplitudes cannot be determined additively by summing contributions from single variables. Many earlier models calculate amplitudes as a function of one or two variables and/or restrict consideration to best-fit linear formulae. Our analysis systematically eliminates such models as candidates for a system that can generate appropriate movements for all possible initial conditions. The results of this study are stated in terms of properties of the response system. Certain axiom sets for the intrinsic organization of the response system obey these properties. We briefly provide one example of such an axiomatic model. The results presented in this article help to characterize the actual neural system for the control of rapid eye/head gaze shifts by showing that, in order to account for behavioral data, certain physical quantities must be represented in and used by the neural system. Our theoretical analysis generates predictions and identifies gaps in the data. We suggest needed experiments.
    Organizational structures intrinsic to nervous systems can be more precisely analyzed and compared with other logical structures once they are expressed in mathematical languages. A standard mathematical language for expressing... more
    Organizational structures intrinsic to nervous systems can be more precisely analyzed and compared with other logical structures once they are expressed in mathematical languages. A standard mathematical language for expressing organizational structure is that of groups. Groups are especially well suited to organizational structures involving multiple symmetries such as spatial structures. The vestibular system is widely believed to mediate many neural functions involving spatial structure. The vestibular nuclei receive direct projections from the vestibular endorgans, the semicircular canals and the otolith organs. The near-orthogonal directions of the semicircular canals are embedded in the bone. However, those canal directions are external to the nervous system. This study addresses the way the three-dimensional space of rotations is also embedded in the group structure of neural connectivity. Although we know a great deal about physical rotation, it is not clear that nervous systems organize rotations in the same way as physicists do. It would make sense for nervous systems to organize rotations in such a way as to provide physiologically relevant information about performing or compensating for rotations. The vestibular nuclei, which might be expected to display an organization that binds rotations into a rotation space, do not give a clear organization. This may be because of the multiplicity of spatial functions performed by the vestibular nuclei; rather than one spatial organization, the vestibular nuclei are likely to accommodate multiple, related spatial organizations. This study evaluates one particular data set from the literature that specifies the organization of the disynaptic canal-neck projection; other projections and neuronal populations may have other intrinsic organizations. The data are evaluated directly for their symmetry group. In the symmetry group, the vertebrate requirement that physiology have a right and left is found to be satisfied in two ways: (i) by a hexagonal symmetry arising from the right-left doubling of front and back, (ii) along with separate organizations on the two sides that may be required to operate independently to some extent. The eight observed muscle innervation patterns from the data are the complete set of possible combinations of inhibitory/excitatory polarities from three canal pairs. These eight innervation patterns are organized as the vertices of a cube. The two types of side muscles provide the vertical direction. As the head rotates in physical space, the cube rotates in sensorimotor space. Like the canal-neck projection, otolith projections and proprioceptive afferents contact both the vestibular nuclei and neck motoneurons. They may have a similar organization, perhaps with extensions of the same pattern. Otherwise, like a checkerboard superimposed over a paisley, they will form an overlapping organization with the disynaptic canal-neck projection. Further research is required to determine whether the sensorimotor spatial structure of the canal-neck projection is widespread in nervous systems or whether there are several complete structures that are fragmented and reintegrated.
    ABSTRACT The authors' review of alternative models for reading is of great value in identifying issues and progress in the field. More emphasis should be given to distinguishing between models that offer an explanation for... more
    ABSTRACT The authors' review of alternative models for reading is of great value in identifying issues and progress in the field. More emphasis should be given to distinguishing between models that offer an explanation for behavior and those that merely simulate experimental data. An analysis of a model's discrete structure can allow for comparisons of models based upon their inherent dimensionality and explanatory power.
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