A hierarchical anti-Hebbian network model for the formation of spatial cells in three-dimensional space.

Three-dimensional (3D) spatial cells in the mammalian hippocampal formation are believed to support the existence of 3D cognitive maps. Modeling studies are crucial to comprehend the neural principles governing the formation of these maps, yet to date very few have addressed this topic in 3D space. Here we present a hierarchical network model for the formation of 3D spatial cells using anti-Hebbian network. Built on empirical data, the model accounts for the natural emergence of 3D place, border, and grid cells, as well as a new type of previously undescribed spatial cell type which we call plane cells. It further explains the plausible reason behind the place and grid-cell anisotropic coding that has been observed in rodents and the potential discrepancy with the predicted periodic coding during 3D volumetric navigation. Lastly, it provides evidence for the importance of unsupervised learning rules in guiding the formation of higher-dimensional cognitive maps

Application of The Method of Elastic Maps In Analysis of Genetic Texts

Abstract - Method of elastic maps ( http://cogprints.ecs.soton.ac.uk/archive/00003088/ and http://cogprints.ecs.soton.ac.uk/archive/00003919/ ) allows us to construct efficiently 1D, 2D and 3D non-linear approximations to the principal manifolds with different topology (piece of plane, sphere, torus etc.) and to project data onto it. We describe the idea of the method and demonstrate its applications in analysis of genetic sequences. The animated 3D-scatters are available on our web-site: http://www.ihes.fr/~zinovyev/7clusters/ We found the universal cluster structure of genetic sequences, and demonstrated the thin structure of these clusters for coding regions. This thin structure is related to different translational efficiency

LFP beta amplitude is predictive of mesoscopic spatio-temporal phase patterns

Beta oscillations observed in motor cortical local field potentials (LFPs) recorded on separate electrodes of a multi-electrode array have been shown to exhibit non-zero phase shifts that organize into a planar wave propagation. Here, we generalize this concept by introducing additional classes of patterns that fully describe the spatial organization of beta oscillations. During a delayed reach-to-grasp task in monkey primary motor and dorsal premotor cortices we distinguish planar, synchronized, random, circular, and radial phase patterns. We observe that specific patterns correlate with the beta amplitude (envelope). In particular, wave propagation accelerates with growing amplitude, and culminates at maximum amplitude in a synchronized pattern. Furthermore, the occurrence probability of a particular pattern is modulated with behavioral epochs: Planar waves and synchronized patterns are more present during movement preparation where beta amplitudes are large, whereas random phase patterns are dominant during movement execution where beta amplitudes are small

Confocal microscopic image sequence compression using vector quantization and 3D pyramids

The 3D pyramid compressor project at the University of Glasgow has developed a compressor for images obtained from CLSM device. The proposed method using a combination of image pyramid coder and vector quantization techniques has good performance at compressing confocal volume image data. An experiment was conducted on several kinds of CLSM data using the presented compressor compared to other well-known volume data compressors, such as MPEG-1. The results showed that the 3D pyramid compressor gave higher subjective and objective image quality of reconstructed images at the same compression ratio and presented more acceptable results when applying image processing filters on reconstructed images

Shaded Tangles for the Design and Verification of Quantum Programs (Extended Abstract)

We give a scheme for interpreting shaded tangles as quantum programs, with the property that isotopic tangles yield equivalent programs. We analyze many known quantum programs in this way -- including entanglement manipulation and error correction -- and in each case present a fully-topological formal verification, yielding in several cases substantial new insight into how the program works. We also use our methods to identify several new or generalized procedures.Comment: In Proceedings QPL 2017, arXiv:1802.0973

Visualization of Data by Method of Elastic Maps and Its Applications in Genomics, Economics and Sociology

Technology of data visualization and data modeling is suggested. The basic of the technology is original idea of elastic net and methods of its construction and application. A short review of relevant methods has been made. The methods proposed are illustrated by applying them to the real economical, sociological and biological datasets and to some model data distributions. The basic of the technology is original idea of elastic net - regular point approximation of some manifold that is put into the multidimensional space and has in a certain sense minimal energy. This manifold is an analogue of principal surface and serves as non-linear screen on what multidimensional data are projected. Remarkable feature of the technology is its ability to work with and to fill gaps in data tables. Gaps are unknown or unreliable values of some features. It gives a possibility to predict plausibly values of unknown features by values of other ones. So it provides technology of constructing different prognosis systems and non-linear regressions. The technology can be used by specialists in different fields. There are several examples of applying the method presented in the end of this paper

Schnyder woods for higher genus triangulated surfaces, with applications to encoding

Schnyder woods are a well-known combinatorial structure for plane triangulations, which yields a decomposition into 3 spanning trees. We extend here definitions and algorithms for Schnyder woods to closed orientable surfaces of arbitrary genus. In particular, we describe a method to traverse a triangulation of genus $g$ and compute a so-called $g$-Schnyder wood on the way. As an application, we give a procedure to encode a triangulation of genus $g$ and $n$ vertices in $4n+O(g \log(n))$ bits. This matches the worst-case encoding rate of Edgebreaker in positive genus. All the algorithms presented here have execution time $O((n+g)g)$, hence are linear when the genus is fixed.Comment: 27 pages, to appear in a special issue of Discrete and Computational Geometr

Connectivity Compression for Irregular Quadrilateral Meshes

Applications that require Internet access to remote 3D datasets are often limited by the storage costs of 3D models. Several compression methods are available to address these limits for objects represented by triangle meshes. Many CAD and VRML models, however, are represented as quadrilateral meshes or mixed triangle/quadrilateral meshes, and these models may also require compression. We present an algorithm for encoding the connectivity of such quadrilateral meshes, and we demonstrate that by preserving and exploiting the original quad structure, our approach achieves encodings 30 - 80% smaller than an approach based on randomly splitting quads into triangles. We present both a code with a proven worst-case cost of 3 bits per vertex (or 2.75 bits per vertex for meshes without valence-two vertices) and entropy-coding results for typical meshes ranging from 0.3 to 0.9 bits per vertex, depending on the regularity of the mesh. Our method may be implemented by a rule for a particular splitting of quads into triangles and by using the compression and decompression algorithms introduced in [Rossignac99] and [Rossignac&Szymczak99]. We also present extensions to the algorithm to compress meshes with holes and handles and meshes containing triangles and other polygons as well as quads