Geometry and dimensionality reduction of feature spaces in primary visual cortex

Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data. In particular, several relationships between the cortical morphologies and the parametric dependencies of extracted features are formalized and considered from a harmonic analysis point of view

Minimal Surfaces in Sub-Riemannian Structures and Functional Geometry of the Visual Cortex

We develop geometrical models of vision consistent with the characteristics of the visual cortex and study geometric flows in the relevant model geometries. We provide a novel sub-Riemannian model of the primary visual cortex, which models orientation-frequency selective phase shifted cortex cell behavior and the associated horizontal connectivity. We develop an image enhancement algorithm using sub-Riemannian diffusion and Laplace-Beltrami flow in the model framework. We provide two geometric models for multi-scale orientation map and orientation-frequency preference map construction which employ Bargmann transform in high dimensional cortical spaces. We prove the uniqueness of the solution to sub-Riemannian mean curvature flow equation in the Heisenberg group geometry. An iterative diffusion process followed by a maximum selection mechanism was proposed by Citti and Sarti in the sub-Riemannian setting of the roto-translation group. They conjectured that this two-fold procedure is equivalent to a mean curvature flow. However a complete proof was missing, even in the Euclidean setting. We prove in the Euclidean setting that this two fold procedure is equivalent to mean curvature flow

Beyond Rehabilitation of Acuity, Ocular Alignment, and Binocularity in Infantile Strabismus

Infantile strabismus impairs the perception of all attributes of the visual scene. High spatial frequency components are no longer visible, leading to amblyopia. Binocularity is altered, leading to the loss of stereopsis. Spatial perception is impaired as well as detection of vertical orientation, the fastest movements, directions of movement, the highest contrasts and colors. Infantile strabismus also affects other vision-dependent processes such as control of postural stability. But presently, rehabilitative therapies for infantile strabismus by ophthalmologists, orthoptists and optometrists are restricted to preventing or curing amblyopia of the deviated eye, aligning the eyes and, whenever possible, preserving or restoring binocular vision during the critical period of development, i.e., before ~10 years of age. All the other impairments are thus ignored; whether they may recover after strabismus treatment even remains unknown. We argue here that medical and paramedical professionals may extend their present treatments of the perceptual losses associated with infantile strabismus. This hypothesis is based on findings from fundamental research on visual system organization of higher mammals in particular at the cortical level. In strabismic subjects (as in normal-seeing ones), information about all of the visual attributes converge, interact and are thus inter-dependent at multiple levels of encoding ranging from the single neuron to neuronal assemblies in visual cortex. Thus if the perception of one attribute is restored this may help to rehabilitate the perception of other attributes. Concomitantly, vision-dependent processes may also improve. This could occur spontaneously, but still should be assessed and validated. If not, medical and paramedical staff, in collaboration with neuroscientists, will have to break new ground in the field of therapies to help reorganize brain circuitry and promote more comprehensive functional recovery. Findings from fundamental research studies in both young and adult patients already support our hypothesis and are reviewed here. For example, presenting different contrasts to each eye of a strabismic patient during training sessions facilitates recovery of acuity in the amblyopic eye as well as of 3D perception. Recent data also demonstrate that visual recoveries in strabismic subjects improve postural stability. These findings form the basis for a roadmap for future research and clinical development to extend presently applied rehabilitative therapies for infantile strabismus

Parsimony, exhaustivity and balanced detection in neocortex

International audienceThe layout of sensory brain areas is thought to subtend perception. The principles shapingthese architectures and their role in information processing are still poorly understood.Weinvestigate mathematically and computationally the representation of orientation and spatialfrequency in cat primary visual cortex. We prove that two natural principles, local exhaustivityand parsimony of representation, would constrain the orientation and spatial frequencymaps to display a very specific pinwheel-dipole singularity. This is particularly interestingsince recent experimental evidences show a dipolar structures of the spatial frequency mapco-localized with pinwheels in cat. These structures have important properties on informationprocessing capabilities. In particular, we show using a computational model of visualinformation processing that this architecture allows a trade-off in the local detection of orientationand spatial frequency, but this property occurs for spatial frequency selectivitysharper than reported in the literature. We validated this sharpening on high-resolution opticalimaging experimental data. These results shed new light on the principles at play in theemergence of functional architecture of cortical maps, as well as their potential role in processinginformation

Contemporary Natural Philosophy and Philosophies - Part 2

Modern technology has eliminated barriers posed by geographic distances between people around the globe, making the world more interdependent. However, in spite of global collaboration within research domains, fragmentation among research fields persists and even escalates. Disintegrated knowledge has become subservient to the competition in the technological and economic race, leading in the direction chosen not by reason and intellect but rather by the preferences of politics and markets. To restore the authority of knowledge in guiding humanity, we have to reconnect its scattered isolated parts and offer an evolving and diverse but shared vision of objective reality connecting the sciences and other knowledge domains and informed by and in communication with ethical and esthetic thinking and being. This collection of articles responds to the second call from the journal Philosophies to build a new, networked world of knowledge with domain specialists from different disciplines interacting and connecting with the rest of the knowledge-producing and knowledge-consuming communities in an inclusive, extended natural-philosophic, human-centric manner. In this process of reconnection, scientific and philosophical investigations enrich each other, with sciences informing philosophies about the best current knowledge of the world, both natural and human-made, while philosophies scrutinize the ontological, epistemological, and methodological foundations of sciences

Theories of Informetrics and Scholarly Communication

Scientometrics have become an essential element in the practice and evaluation of science and research, including both the evaluation of individuals and national assessment exercises. Yet, researchers and practitioners in this field have lacked clear theories to guide their work. As early as 1981, then doctoral student Blaise Cronin published "The need for a theory of citing" —a call to arms for the fledgling scientometric community to produce foundational theories upon which the work of the field could be based. More than three decades later, the time has come to reach out the field again and ask how they have responded to this call. This book compiles the foundational theories that guide informetrics and scholarly communication research. It is a much needed compilation by leading scholars in the field that gathers together the theories that guide our understanding of authorship, citing, and impact

Theories of Informetrics and Scholarly Communication

Scientometrics have become an essential element in the practice and evaluation of science and research, including both the evaluation of individuals and national assessment exercises. Yet, researchers and practitioners in this field have lacked clear theories to guide their work. As early as 1981, then doctoral student Blaise Cronin published The need for a theory of citing - a call to arms for the fledgling scientometric community to produce foundational theories upon which the work of the field could be based. More than three decades later, the time has come to reach out the field again and ask how they have responded to this call. This book compiles the foundational theories that guide informetrics and scholarly communication research. It is a much needed compilation by leading scholars in the field that gathers together the theories that guide our understanding of authorship, citing, and impact

Contemporary Natural Philosophy and Philosophies—Part 2

This is a short presentation by the Guest Editors of the series of Special Issues of the journal Philosophies under the common title "Contemporary Natural Philosophy and Philosophies" in which we present Part 2. The series will continue, and the call for contributions to the next Special Issue will appear shortly